CM GL PNMP V03 160725
CM GL PNMP V03 160725
CM GL PNMP V03 160725
CM-GL-PNMP-V03-160725
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Contents
1 SCOPE ................................................................................................................................................................... 15
1.1 Introduction and Purpose ................................................................................................................................ 15
1.2 PNM Background and History ....................................................................................................................... 16
2 REFERENCES ..................................................................................................................................................... 19
2.1 Informative References ................................................................................................................................... 19
2.2 Reference Acquisition..................................................................................................................................... 19
3 TERMS AND DEFINITIONS ............................................................................................................................. 20
4 ABBREVIATIONS AND ACRONYMS ............................................................................................................. 26
5 PNM USING UPSTREAM EQUALIZATION .................................................................................................. 29
5.1 Reactive versus Proactive Network Maintenance ........................................................................................... 29
5.2 Linear Impairments ......................................................................................................................................... 29
5.2.1 Micro-reflection Types ............................................................................................................................ 30
5.3 Pre-equalization Mechanism Enabled through DOCSIS Ranging .................................................................. 34
5.3.1 Pre-equalization Enabling Messages ..................................................................................................... 36
5.3.2 CM and CMTS Equalization Information ............................................................................................... 37
5.4 Upstream Pre-equalization in DOCSIS 1.0, DOCSIS 1.1 and DOCSIS 2.0 ................................................... 39
5.4.1 DOCSIS 1.1 Pre-equalization Considerations........................................................................................ 39
5.5 Limitations on Pre-equalization Compensation .............................................................................................. 40
5.6 DOCSIS Pre-equalization MIBs ..................................................................................................................... 41
5.6.1 DOCSIS 2.0 and 3.0 Pre-equalization MIBs .......................................................................................... 42
6 METHODOLOGY FOR PNM USING UPSTREAM EQUALIZATION ....................................................... 44
6.1 General Approach and Processes .................................................................................................................... 44
6.2 Format Verification, Normalization and Guidelines ....................................................................................... 45
6.2.1 Four Nibble 2s Complement Pre-equalization Coefficient Representation ........................................... 46
6.2.2 Three Nibble 2s Complement Pre-equalization Coefficient Representation ......................................... 46
6.2.3 Universal Decoding ................................................................................................................................ 46
6.3 Key Metrics .................................................................................................................................................... 47
6.3.1 Adaptive Equalizer Main Tap Energy..................................................................................................... 47
6.3.2 Main Tap Nominal Energy and Main Tap Nominal Amplitude .............................................................. 47
6.3.3 Pre-Main Tap Energy ............................................................................................................................. 47
6.3.4 Post-Main Tap Energy ............................................................................................................................ 47
6.3.5 Total Tap Energy .................................................................................................................................... 47
6.3.6 Main Tap Compression ........................................................................................................................... 48
6.3.7 Main Tap Ratio ....................................................................................................................................... 48
6.3.8 Non-Main Tap to Total Energy Ratio (Distortion Metric) ...................................................................... 48
6.3.9 Pre-Main Tap to Total Energy Ratio ...................................................................................................... 49
6.3.10 Post-Main Tap to Total Energy Ratio ..................................................................................................... 49
6.3.11 Pre-Post Energy Symmetry Ratio ........................................................................................................... 49
6.3.12 Group Delay Distortion .......................................................................................................................... 49
6.4 DOCSIS Pre-equalization Coefficient Data Collection .................................................................................. 54
6.4.1 SNMP Implementation and Performance Considerations ...................................................................... 55
6.4.2 Data Collection Strategy ........................................................................................................................ 56
6.5 Calibration Mechanisms ................................................................................................................................. 57
6.5.1 CMTS-CM Short Reference Plant ........................................................................................................... 57
6.5.2 Pre-equalization Calibration Approach ................................................................................................. 59
6.6 Fault Localization ........................................................................................................................................... 63
6.6.1 Fault Localization Examples .................................................................................................................. 64
6.6.2 Determining Micro-reflection Signatures ............................................................................................... 65
6.6.3 Determining Micro-reflection Boundaries Edges ................................................................................... 67
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Figures
Figure 1 - Micro-reflection with Multiple-Transit Echoes ............................................................................................. 31
Figure 2 - Micro-reflection with Single Impedance Mismatch Interface........................................................................ 33
Figure 3 - Composite Micro-reflection Resulting from Type 1 and Type 2 Micro-reflections ...................................... 34
Figure 4 - A Single Micro-reflection that Goes Back to the Source ............................................................................... 34
Figure 5 - Upstream Equalizer Structure ........................................................................................................................ 35
Figure 6 - CM-CMTS Ranging Interaction Enabling Pre-equalization Process ............................................................. 36
Figure 7 - Range Response Message Format .................................................................................................................. 37
Figure 8 - Range Request Message Format .................................................................................................................... 37
Figure 9 - CM Pre-eq Coefficients Values and Frequency Response Scenarios ............................................................ 38
Figure 10 - CMTS CM Pre-equalization Coefficients Values and Frequency Response Scenarios ............................... 39
Figure 11 - Pre-equalization Compensation Capabilities under Short and Long Delay Micro-reflection Scenarios...... 41
Figure 12 - MIB Format for docsIfCmStatusEqualizationData ...................................................................................... 42
Figure 13 - Proactive Network Maintenance Processes based on Pre-equalization........................................................ 44
Figure 14 - Equalizer Structure HEXDECIMAL-to-DECIMAL Conversion ................................................................ 45
Figure 15 - Group Delay Increase with Increasing Cascade Depth ................................................................................ 50
Figure 16 - Pre Main Tap Energy Increase with Cascade Depth (Fc=40.4 MHz, Ch. W=3.2 MHz, No Micro-
reflections, First 12 Taps Shown ) .......................................................................................................................... 51
Figure 17 - Pre Main Tap Energy Increase with Cascade Depth (Fc=40.4 MHz, Ch. W=3.2 MHz, with 0.5 s Micro-
reflection, First 12 Taps Shown ) ........................................................................................................................... 52
Figure 18 - Tap Energy for Different Cascade Depth Scenarios (Fc=14 MHz, Ch. W=3.2 MHz, with 0.5 s Micro-
reflection, First 12 Taps Shown) ............................................................................................................................ 54
Figure 19 - Short Reference Plant Block Diagram ......................................................................................................... 59
Figure 20 - CM & CMTS Elements Contributing To US Distortion (In Orange) .......................................................... 60
Figure 21 - Pre-equalizer Frequency Response with (0.5s, -10 Dbc) and without Micro-reflection ............................ 62
Figure 22 - Calibrated Pre-equalizer Frequency Response Obtained from Micro-reflection on (0.5s, -10 dBc) and Off
Scenarios................................................................................................................................................................. 63
Figure 23 - Correlation of Topology with Distortion to Provide Fault Localization ...................................................... 64
Figure 24 - Observation of Multiple CMs Frequency Response .................................................................................... 65
Figure 25 - Identified Micro-reflection Patterns ............................................................................................................. 66
Figure 26 - Clustering of Common Micro-reflection Signatures .................................................................................... 66
Figure 27 - Common Micro-reflection Signature - Case A ............................................................................................ 67
Figure 28 - Common Micro-reflection Signature - Case B ............................................................................................ 68
Figure 29 - Example Test Case Parabolic Interpolator ................................................................................................... 69
Figure 30 - Severity Metrics ........................................................................................................................................... 71
Figure 31 - Micro-reflection Amplitude Data of Same Two CMs to Highlight Trending Over Time ........................... 75
Figure 32 - CM Micro-reflection Amplitude Over Time Highlighting Intermittent Issues ............................................ 76
Figure 33 - Example of Five Groups of Modems Affected by Five Different Plant Problems....................................... 77
Figure 34 - A Coefficient Set in the Time Domain for Modem A .................................................................................. 81
Figure 35 - A Coefficient Set in the Frequency Domain for Modem A ......................................................................... 81
Figure 36 - A Coefficient Set in the Time Domain for Modem B .................................................................................. 82
Figure 37 - A Coefficient Set in the Frequency Domain for Modem B.......................................................................... 82
Figure 38 - A Quotient Set in the Frequency Domain for Modem B Divided by Modem A.......................................... 83
Figure 39 - An IFFT of the Quotient Set of Figure 38 .................................................................................................... 83
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Figure 40 - Amplitude vs. Frequency Peak/Valley of 10.55 Db with Echo Present in Impulse Response ..................... 87
Figure 41 - Entire Upstream Scan Shows No Similar Signatures Shared by Other Modems ......................................... 87
Figure 42 - Distance Calculation Applied With Customer Address and Mapping ......................................................... 88
Figure 43 - Single Customer Modem Demonstrates the Effects of Ingress .................................................................... 90
Figure 44 - Multiple Modems on the Same Upstream Demonstrate the Effects of Ingress ............................................ 90
Figure 45 - Effects of Ingress When Mapped ................................................................................................................. 91
Figure 46 - Spectrum Analyzer Display of a Portion of a Cable Networks Downstream Spectrum. ............................ 97
Figure 47 - FBC Display Showing FM and LTE Ingress (circled) in the Downstream Spectrum of a Cable Network . 98
Figure 48 - Examples of Problems That Can Be Identified Using FBC ......................................................................... 98
Figure 49 - Digital Spectrum Analyzer Block Diagram ................................................................................................. 99
Figure 50 - FBC Showing FM and LTE Ingress........................................................................................................... 100
Figure 51 - Multiple Problems Are Apparent in this FBC Screen Shot........................................................................ 100
Figure 52 - FBC from Several Modems ....................................................................................................................... 100
Figure 53 - Examples of Standing Waves .................................................................................................................... 101
Figure 54 - FBC Traces Showing the Presence of Filters ............................................................................................. 101
Figure 55 - Rolloff at the Upper End of the Downstream Spectrum ............................................................................ 102
Figure 56 - Negative Tilt (Top) and Positive Tilt (Bottom ........................................................................................... 102
Figure 57 - Examples of Resonant Peaking in the Downstream Spectrum .................................................................. 103
Figure 58 - Ripples indicate an echo tunnel, but no phase data is available. ................................................................ 105
Figure 59 - Impulse associated with frequency domain ripple is in among the teeth of the comb, which come every
166.67 nS. ............................................................................................................................................................. 105
Figure 60 - CPD in a Mostly Analog Network ............................................................................................................. 107
Figure 61 - Detailed Structure of CPD Captures Showing Difference Frequencies Around Beats at 24 MHz ............ 107
Figure 62 - Detailed Structure of CPD Captures Showing Difference Frequencies Due to 12.5 And 25 KHz FAA
Offsets for Aeronautical Band Operation ............................................................................................................. 108
Figure 63 - CPD In A Network With Both Analog And Digital Downstream Signals. Yellow Marks Show The Gaps
Between Each QAM Signal-Like Beat. Image Courtesy Of Viavi Solutions (Formerly JDSU) .......................... 109
Figure 64 - Second Order Modeled CPD Behavior From All-Digital Downstreams (Not Scaled. .............................. 109
Figure 65 - Full Band RF Capture From Example Node With Suspected Nonlinearity, Entire Spectrum ................... 110
Figure 66 - RF Capture From Example Node, Upstream Band Only ........................................................................... 110
Figure 67 - Simulated 3rd Order CPD Nonlinearity From Example Node (Not Scaled) ............................................. 111
Figure 68 - Active CPD Measurement Technique Whereby an Injected Carrier Is Used To Produce a 2nd Order
Difference Frequency of 40.5 MHz ...................................................................................................................... 112
Figure 69 - Radar-Correlation Based CPD Detection (Courtesy Of Arcom Digital) ................................................... 113
Figure I-1 - A Filter's Time Delay-Versus-Frequency Curve Often Has A Bathtub Shape .......................................... 118
Figure I-2 - Phase-Versus-Frequency For 100 Feet Of Coax ....................................................................................... 120
Figure I-3 - Time Delay-Versus-Frequency For 100 Feet Of Coax.............................................................................. 120
Figure I-4 - Complex Frequency Response In The Return Path ................................................................................... 121
Figure I-5 - Ideal Transmission Line Model ................................................................................................................. 122
Figure I-6 - Real-World Transmission Line Model ...................................................................................................... 123
Figure I-7 - Creation of Reflections in a Cable Network's Feeder Plant ...................................................................... 124
Figure I-8 - Graphic Representation of Incident Signal and Second Reflection ........................................................... 124
Figure I-9 - Reflection Example that will be Used to Illustrate the Formation of Amplitude Ripple ........................... 126
Figure I-10 - Phasor View of Incident Signal Vector (Long Arrow) and Reflection Vector (Short Arrow) ................ 126
Figure I-11 - Reflection Vector Rotated 45 Degrees From Original Position .............................................................. 126
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Figure I-12 - Reflection Vector Rotated 90 Degrees From Original Position .............................................................. 127
Figure I-13 - Reflection Vector Rotated 135 Degrees From Original Position ............................................................ 127
Figure I-14 - Reflection Vector Rotated 180 Degrees From Original Position ............................................................ 127
Figure I-15 - Reflection Vector Rotated 225 Degrees From Original Position ............................................................ 128
Figure I-16 - Reflection Vector Rotated 270 Degrees From Original Position ............................................................ 128
Figure I-17 - Reflection vector rotated 315 degrees from original position ................................................................. 128
Figure I-18 - Reflection Vector Back At Original Position After Rotating 360 Degrees ............................................. 128
Figure I-19 - Amplitude-Versus-Phase Plot Of Phasor View Vector Sum Vectors ..................................................... 129
Figure I-20 - Example Of Flat Amplitude-Versus-Frequency Response ...................................................................... 130
Figure I-21 - Example of tilted or sloped amplitude-versus-frequency response ......................................................... 130
Figure I-22 - Example Of Upstream 64-QAM Signal With Substantial In-Channel Tilt ............................................. 130
Figure I-23 - Example Of 64-QAM Signal After Adaptive Pre-Equalization Eliminated Most of the In-channel Tilt 131
Figure I-24 - A Signal Carried in the Sloped Portion of the Widely Spaced Amplitude Ripple Will Exhibit In-channel
Tilt ........................................................................................................................................................................ 131
Figure I-25 - 64-QAM Signal With Good (36.3 dB) MER .......................................................................................... 132
Figure I-26 - 64-QAM Signal With Poor (23.2 dB) MER ............................................................................................ 132
Figure I-27 - 16-QAM Constellation Showing Target Symbol, Transmitted (or Received ) Symbol, and Modulation
Error Vectors ........................................................................................................................................................ 133
Figure I-28 - MER is the Ratio of Average Symbol Power to Average Error Power ................................................... 134
Figure I-29 - QAM Receiver Block Diagram ............................................................................................................... 135
Figure I-30 - Each Vector Has a Real (In-Phase or I) and Imaginary (Quadrature or Q) Component ......................... 137
Figure I-31 - Unequalized 64-QAM Constellation ....................................................................................................... 139
Figure I-32 - Equalized 64-QAM Constellation ........................................................................................................... 139
Figure I-33 - Generic 4-tap Adaptive Equalizer ........................................................................................................... 142
Figure I-34 - Amplitude-versus-time Plot of an Incident Signal and Micro-reflection ................................................ 143
Figure I-35 - Amplitude-versus-Frequency Response .................................................................................................. 143
Figure I-36 - Phase-versus-Frequency Response .......................................................................................................... 144
Figure I-37 - Required Magnitude-and Phase-versus-frequency Response to Cancel Echo......................................... 144
Figure I-38 - Adaptive Equalizer that will be Used in the Example in the Text ........................................................... 145
Figure I-39 - Operation of the Adaptive Equalizer's First Tap ..................................................................................... 146
Figure I-40 - Operation of the Adaptive Equalizer's Second Tap ................................................................................. 146
Figure I-41 - Summing the Outputs of the Adaptive Equalizer's First and Second Taps ............................................. 147
Figure I-42 - Operation of the Adaptive Equalizer's Third Tap .................................................................................... 147
Figure I-43 - Summing the Output of the Adaptive Equalizer's Third Tap With the Previously Summed First and
Second Taps.......................................................................................................................................................... 148
Figure I-44 - Operation of the Adaptive Equalizer's Fourth Tap .................................................................................. 148
Figure I-45 - Final Summing Process Provides an Equalized Output .......................................................................... 149
Figure I-46 - Final Amplitude and Phase-versus-frequency Response After Adaptive Equalization ........................... 150
Figure I-47 - Upstream Pre-equalization is Able to Compensate for In-channel Tilt ................................................... 151
Figure I-48 - DFT Matrix (Only Half is Shown) Contains Rows of Sine (Red) and Cosine (Blue) Waves ................. 154
Figure I-49 - Full DFT Matrix for N = 16 .................................................................................................................... 155
Figure I-50 - This DFT Matrix with N = 64 is about the Largest We can Clearly Show in a Small Diagram ............. 156
Figure I-51 - This DFT Matrix with N = 256 is Still Nowhere Near N = 4096 or 8192 for DOCSIS 3.1 .................... 156
Figure I-52 - OFDM Transmitter: a Single IDFT is Equivalent to 4096- or 8192-QAM Modulators plus their Summing
Network ................................................................................................................................................................ 157
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Figure I-53 - OFDM Receiver: a Single DFT is Equivalent to 4096- or 8192-QAM Demodulators ........................... 158
Figure I-54 - Block Diagram of a Digital Spectrum Analyzer...................................................................................... 160
Figure I-55 - Full-band Spectrum as seen at the CM .................................................................................................... 161
Figure I-56 Typical Data-tapering Window Functions .............................................................................................. 162
Figure IV-1 - Equivalent Reflection Coefficient E..................................................................................................... 165
Figure V-1 - A Multiple Recursion Echo ..................................................................................................................... 167
Figure V-2 - Wiring Diagrams to Make Echoes in a Lab ............................................................................................. 168
Figure V-3 - A Single Recursion Echo Example .......................................................................................................... 168
Figure V-4 - How A Multiple Recursion Echo can be Canceled with Predistortion .................................................... 169
Figure V-5 - Comparison of Signal Path Impulse Responses and Programming for Adaptive Equalizers .................. 171
Figure VI-1 - Software Sequence Diagram SD-PNM200 ............................................................................................ 172
Figure VI-2 - Software Sequence Diagram SD-PNM201 ............................................................................................ 172
Figure VII-1 - An Upstream Feeder Leg With a Pair of Damage Points Separated by a LENGTH. The Reflection
Points Form an Echo Tunnel ................................................................................................................................ 174
Figure VII-2 - A Screen Shot of the Software Showing Graphs 1-5 and Controls on the Right .................................. 175
Figure VIII-1 - Diagram Showing Detection of a Single Reflection ............................................................................ 176
Figure VIII-2 - A Digital Cable Signal that was Captured by Rapidly Retuning an SDR. The Standing Wave Indicates
a Reflected Signal is Present................................................................................................................................. 177
Figure VIII-3 - A Processed Signal Showing the Single Reflection, Plus Harmonics Caused by Roll-Off of the 6 MHz
Haystacks at Band Edges ...................................................................................................................................... 177
Figure VIII-4 - A Cablelabs Engineer Making a TDR Measurement in the Field. The SDR is in his Backpack ......... 178
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Tables
Figure 1 - Micro-reflection with Multiple-Transit Echoes ............................................................................................. 31
Figure 2 - Micro-reflection with Single Impedance Mismatch Interface........................................................................ 33
Figure 3 - Composite Micro-reflection Resulting from Type 1 and Type 2 Micro-reflections ...................................... 34
Figure 4 - A Single Micro-reflection that Goes Back to the Source ............................................................................... 34
Figure 5 - Upstream Equalizer Structure ........................................................................................................................ 35
Figure 6 - CM-CMTS Ranging Interaction Enabling Pre-equalization Process ............................................................. 36
Figure 7 - Range Response Message Format .................................................................................................................. 37
Figure 8 - Range Request Message Format .................................................................................................................... 37
Figure 9 - CM Pre-eq Coefficients Values and Frequency Response Scenarios ............................................................ 38
Figure 10 - CMTS CM Pre-equalization Coefficients Values and Frequency Response Scenarios ............................... 39
Figure 11 - Pre-equalization Compensation Capabilities under Short and Long Delay Micro-reflection Scenarios...... 41
Figure 12 - MIB Format for docsIfCmStatusEqualizationData ...................................................................................... 42
Figure 13 - Proactive Network Maintenance Processes based on Pre-equalization........................................................ 44
Figure 14 - Equalizer Structure HEXDECIMAL-to-DECIMAL Conversion ................................................................ 45
Figure 15 - Group Delay Increase with Increasing Cascade Depth ................................................................................ 50
Figure 16 - Pre Main Tap Energy Increase with Cascade Depth (Fc=40.4 MHz, Ch. W=3.2 MHz, No Micro-
reflections, First 12 Taps Shown ) .......................................................................................................................... 51
Figure 17 - Pre Main Tap Energy Increase with Cascade Depth (Fc=40.4 MHz, Ch. W=3.2 MHz, with 0.5 s Micro-
reflection, First 12 Taps Shown ) ........................................................................................................................... 52
Figure 18 - Tap Energy for Different Cascade Depth Scenarios (Fc=14 MHz, Ch. W=3.2 MHz, with 0.5 s Micro-
reflection, First 12 Taps Shown) ............................................................................................................................ 54
Figure 19 - Short Reference Plant Block Diagram ......................................................................................................... 59
Figure 20 - CM & CMTS Elements Contributing To US Distortion (In Orange) .......................................................... 60
Figure 21 - Pre-equalizer Frequency Response with (0.5s, -10 Dbc) and without Micro-reflection ............................ 62
Figure 22 - Calibrated Pre-equalizer Frequency Response Obtained from Micro-reflection on (0.5s, -10 dBc) and Off
Scenarios................................................................................................................................................................. 63
Figure 23 - Correlation of Topology with Distortion to Provide Fault Localization ...................................................... 64
Figure 24 - Observation of Multiple CMs Frequency Response .................................................................................... 65
Figure 25 - Identified Micro-reflection Patterns ............................................................................................................. 66
Figure 26 - Clustering of Common Micro-reflection Signatures .................................................................................... 66
Figure 27 - Common Micro-reflection Signature - Case A ............................................................................................ 67
Figure 28 - Common Micro-reflection Signature - Case B ............................................................................................ 68
Figure 29 - Example Test Case Parabolic Interpolator ................................................................................................... 69
Figure 30 - Severity Metrics ........................................................................................................................................... 71
Figure 31 - Micro-reflection Amplitude Data of Same Two CMs to Highlight Trending Over Time ........................... 75
Figure 32 - CM Micro-reflection Amplitude Over Time Highlighting Intermittent Issues ............................................ 76
Figure 33 - Example of Five Groups of Modems Affected by Five Different Plant Problems....................................... 77
Figure 34 - A Coefficient Set in the Time Domain for Modem A .................................................................................. 81
Figure 35 - A Coefficient Set in the Frequency Domain for Modem A ......................................................................... 81
Figure 36 - A Coefficient Set in the Time Domain for Modem B .................................................................................. 82
Figure 37 - A Coefficient Set in the Frequency Domain for Modem B.......................................................................... 82
Figure 38 - A Quotient Set in the Frequency Domain for Modem B Divided by Modem A.......................................... 83
Figure 39 - An IFFT of the Quotient Set of Figure 38 .................................................................................................... 83
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Figure 40 - Amplitude vs. Frequency Peak/Valley of 10.55 Db with Echo Present in Impulse Response ..................... 87
Figure 41 - Entire Upstream Scan Shows No Similar Signatures Shared by Other Modems ......................................... 87
Figure 42 - Distance Calculation Applied With Customer Address and Mapping ......................................................... 88
Figure 43 - Single Customer Modem Demonstrates the Effects of Ingress .................................................................... 90
Figure 44 - Multiple Modems on the Same Upstream Demonstrate the Effects of Ingress ............................................ 90
Figure 45 - Effects of Ingress When Mapped ................................................................................................................. 91
Figure 46 - Spectrum Analyzer Display of a Portion of a Cable Networks Downstream Spectrum. ............................ 97
Figure 47 - FBC Display Showing FM and LTE Ingress (circled) in the Downstream Spectrum of a Cable Network . 98
Figure 48 - Examples of Problems That Can Be Identified Using FBC ......................................................................... 98
Figure 49 - Digital Spectrum Analyzer Block Diagram ................................................................................................. 99
Figure 50 - FBC Showing FM and LTE Ingress........................................................................................................... 100
Figure 51 - Multiple Problems Are Apparent in this FBC Screen Shot........................................................................ 100
Figure 52 - FBC from Several Modems ....................................................................................................................... 100
Figure 53 - Examples of Standing Waves .................................................................................................................... 101
Figure 54 - FBC Traces Showing the Presence of Filters ............................................................................................. 101
Figure 55 - Rolloff at the Upper End of the Downstream Spectrum ............................................................................ 102
Figure 56 - Negative Tilt (Top) and Positive Tilt (Bottom ........................................................................................... 102
Figure 57 - Examples of Resonant Peaking in the Downstream Spectrum .................................................................. 103
Figure 58 - Ripples indicate an echo tunnel, but no phase data is available. ................................................................ 105
Figure 59 - Impulse associated with frequency domain ripple is in among the teeth of the comb, which come every
166.67 nS. ............................................................................................................................................................. 105
Figure 60 - CPD in a Mostly Analog Network ............................................................................................................. 107
Figure 61 - Detailed Structure of CPD Captures Showing Difference Frequencies Around Beats at 24 MHz ............ 107
Figure 62 - Detailed Structure of CPD Captures Showing Difference Frequencies Due to 12.5 And 25 KHz FAA
Offsets for Aeronautical Band Operation ............................................................................................................. 108
Figure 63 - CPD In A Network With Both Analog And Digital Downstream Signals. Yellow Marks Show The Gaps
Between Each QAM Signal-Like Beat. Image Courtesy Of Viavi Solutions (Formerly JDSU) .......................... 109
Figure 64 - Second Order Modeled CPD Behavior From All-Digital Downstreams (Not Scaled. .............................. 109
Figure 65 - Full Band RF Capture From Example Node With Suspected Nonlinearity, Entire Spectrum ................... 110
Figure 66 - RF Capture From Example Node, Upstream Band Only ........................................................................... 110
Figure 67 - Simulated 3rd Order CPD Nonlinearity From Example Node (Not Scaled) ............................................. 111
Figure 68 - Active CPD Measurement Technique Whereby an Injected Carrier Is Used To Produce a 2nd Order
Difference Frequency of 40.5 MHz ...................................................................................................................... 112
Figure 69 - Radar-Correlation Based CPD Detection (Courtesy Of Arcom Digital) ................................................... 113
Figure I-1 - A Filter's Time Delay-Versus-Frequency Curve Often Has A Bathtub Shape .......................................... 118
Figure I-2 - Phase-Versus-Frequency For 100 Feet Of Coax ....................................................................................... 120
Figure I-3 - Time Delay-Versus-Frequency For 100 Feet Of Coax.............................................................................. 120
Figure I-4 - Complex Frequency Response In The Return Path ................................................................................... 121
Figure I-5 - Ideal Transmission Line Model ................................................................................................................. 122
Figure I-6 - Real-World Transmission Line Model ...................................................................................................... 123
Figure I-7 - Creation of Reflections in a Cable Network's Feeder Plant ...................................................................... 124
Figure I-8 - Graphic Representation of Incident Signal and Second Reflection ........................................................... 124
Figure I-9 - Reflection Example that will be Used to Illustrate the Formation of Amplitude Ripple ........................... 126
Figure I-10 - Phasor View of Incident Signal Vector (Long Arrow) and Reflection Vector (Short Arrow) ................ 126
Figure I-11 - Reflection Vector Rotated 45 Degrees From Original Position .............................................................. 126
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Figure I-12 - Reflection Vector Rotated 90 Degrees From Original Position .............................................................. 127
Figure I-13 - Reflection Vector Rotated 135 Degrees From Original Position ............................................................ 127
Figure I-14 - Reflection Vector Rotated 180 Degrees From Original Position ............................................................ 127
Figure I-15 - Reflection Vector Rotated 225 Degrees From Original Position ............................................................ 128
Figure I-16 - Reflection Vector Rotated 270 Degrees From Original Position ............................................................ 128
Figure I-17 - Reflection vector rotated 315 degrees from original position ................................................................. 128
Figure I-18 - Reflection Vector Back At Original Position After Rotating 360 Degrees ............................................. 128
Figure I-19 - Amplitude-Versus-Phase Plot Of Phasor View Vector Sum Vectors ..................................................... 129
Figure I-20 - Example Of Flat Amplitude-Versus-Frequency Response ...................................................................... 130
Figure I-21 - Example of tilted or sloped amplitude-versus-frequency response ......................................................... 130
Figure I-22 - Example Of Upstream 64-QAM Signal With Substantial In-Channel Tilt ............................................. 130
Figure I-23 - Example Of 64-QAM Signal After Adaptive Pre-Equalization Eliminated Most of the In-channel Tilt 131
Figure I-24 - A Signal Carried in the Sloped Portion of the Widely Spaced Amplitude Ripple Will Exhibit In-channel
Tilt ........................................................................................................................................................................ 131
Figure I-25 - 64-QAM Signal With Good (36.3 dB) MER .......................................................................................... 132
Figure I-26 - 64-QAM Signal With Poor (23.2 dB) MER ............................................................................................ 132
Figure I-27 - 16-QAM Constellation Showing Target Symbol, Transmitted (or Received ) Symbol, and Modulation
Error Vectors ........................................................................................................................................................ 133
Figure I-28 - MER is the Ratio of Average Symbol Power to Average Error Power ................................................... 134
Figure I-29 - QAM Receiver Block Diagram ............................................................................................................... 135
Figure I-30 - Each Vector Has a Real (In-Phase or I) and Imaginary (Quadrature or Q) Component ......................... 137
Figure I-31 - Unequalized 64-QAM Constellation ....................................................................................................... 139
Figure I-32 - Equalized 64-QAM Constellation ........................................................................................................... 139
Figure I-33 - Generic 4-tap Adaptive Equalizer ........................................................................................................... 142
Figure I-34 - Amplitude-versus-time Plot of an Incident Signal and Micro-reflection ................................................ 143
Figure I-35 - Amplitude-versus-Frequency Response .................................................................................................. 143
Figure I-36 - Phase-versus-Frequency Response .......................................................................................................... 144
Figure I-37 - Required Magnitude-and Phase-versus-frequency Response to Cancel Echo......................................... 144
Figure I-38 - Adaptive Equalizer that will be Used in the Example in the Text ........................................................... 145
Figure I-39 - Operation of the Adaptive Equalizer's First Tap ..................................................................................... 146
Figure I-40 - Operation of the Adaptive Equalizer's Second Tap ................................................................................. 146
Figure I-41 - Summing the Outputs of the Adaptive Equalizer's First and Second Taps ............................................. 147
Figure I-42 - Operation of the Adaptive Equalizer's Third Tap .................................................................................... 147
Figure I-43 - Summing the Output of the Adaptive Equalizer's Third Tap With the Previously Summed First and
Second Taps.......................................................................................................................................................... 148
Figure I-44 - Operation of the Adaptive Equalizer's Fourth Tap .................................................................................. 148
Figure I-45 - Final Summing Process Provides an Equalized Output .......................................................................... 149
Figure I-46 - Final Amplitude and Phase-versus-frequency Response After Adaptive Equalization ........................... 150
Figure I-47 - Upstream Pre-equalization is Able to Compensate for In-channel Tilt ................................................... 151
Figure I-48 - DFT Matrix (Only Half is Shown) Contains Rows of Sine (Red) and Cosine (Blue) Waves ................. 154
Figure I-49 - Full DFT Matrix for N = 16 .................................................................................................................... 155
Figure I-50 - This DFT Matrix with N = 64 is about the Largest We can Clearly Show in a Small Diagram ............. 156
Figure I-51 - This DFT Matrix with N = 256 is Still Nowhere Near N = 4096 or 8192 for DOCSIS 3.1 .................... 156
Figure I-52 - OFDM Transmitter: a Single IDFT is Equivalent to 4096- or 8192-QAM Modulators plus their Summing
Network ................................................................................................................................................................ 157
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Figure I-53 - OFDM Receiver: a Single DFT is Equivalent to 4096- or 8192-QAM Demodulators ........................... 158
Figure I-54 - Block Diagram of a Digital Spectrum Analyzer...................................................................................... 160
Figure I-55 - Full-band Spectrum as seen at the CM .................................................................................................... 161
Figure I-56 Typical Data-tapering Window Functions .............................................................................................. 162
Figure IV-1 - Equivalent Reflection Coefficient E..................................................................................................... 165
Figure V-1 - A Multiple Recursion Echo ..................................................................................................................... 167
Figure V-2 - Wiring Diagrams to Make Echoes in a Lab ............................................................................................. 168
Figure V-3 - A Single Recursion Echo Example .......................................................................................................... 168
Figure V-4 - How A Multiple Recursion Echo can be Canceled with Predistortion .................................................... 169
Figure V-5 - Comparison of Signal Path Impulse Responses and Programming for Adaptive Equalizers .................. 171
Figure VI-1 - Software Sequence Diagram SD-PNM200 ............................................................................................ 172
Figure VI-2 - Software Sequence Diagram SD-PNM201 ............................................................................................ 172
Figure VII-1 - An Upstream Feeder Leg With a Pair of Damage Points Separated by a LENGTH. The Reflection
Points Form an Echo Tunnel ................................................................................................................................ 174
Figure VII-2 - A Screen Shot of the Software Showing Graphs 1-5 and Controls on the Right .................................. 175
Figure VIII-1 - Diagram Showing Detection of a Single Reflection ............................................................................ 176
Figure VIII-2 - A Digital Cable Signal that was Captured by Rapidly Retuning an SDR. The Standing Wave Indicates
a Reflected Signal is Present................................................................................................................................. 177
Figure VIII-3 - A Processed Signal Showing the Single Reflection, Plus Harmonics Caused by Roll-Off of the 6 MHz
Haystacks at Band Edges ...................................................................................................................................... 177
Figure VIII-4 - A Cablelabs Engineer Making a TDR Measurement in the Field. The SDR is in his Backpack ......... 178
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1 SCOPE
1.1 Introduction and Purpose
As cable networks evolve, and many diverse services such as telephony, data, video, business and
advanced services (e.g., tele-medicine, remote education, home monitoring) are carried over those
networks, the demand for maintaining a high level of reliability for services increases. To achieve such high
reliability, operators should fix problems before they have any impact on service.
Some commonly tracked cable modem (CM) and cable modem termination system (CMTS) metrics include
CM status; upstream transmit level; CMTS upstream receive level; upstream modulation error ratio (MER,
also called upstream signal-to-noise ratio or SNR); upstream codeword error ratio (CER); downstream
receive level; downstream MER/SNR; and downstream CER or bit error ratio (BER). While these metrics
are good indicators of the existence of problems, they dont always reveal the cause of those problems.
Increasingly, intelligent end devices are deployed in cable networks, and termination devices and
monitoring instruments are installed in headends (HEs) and hubs. The new devices being deployed by
operators, such as digital set-top boxes (STBs), multimedia terminal adapters (MTAs) and embedded
MTAs, hybrid monitoring systems and even high end television sets are DOCSIS capable, resulting in
DOCSIS ubiquity. A conservative scenario in a serving area assuming 60% penetration of STBs, 35% of CMs
and 15% of eMTAs, all enabled with DOCSIS, clearly highlights the trend towards DOCSIS ubiquity.
As DOCSIS devices evolve and are equipped with elaborate monitoring tools, it becomes practical to use
them for plant monitoring purposes. By using these devices as network probes, cable operators can collect
device and network parameters. Combining the analysis of the data along with network topology and
device location, it is possible to isolate the source of a problem. A proactive maintenance plan can be
developed using this information.
This document describes guidelines and best practices for proactive network maintenance mechanisms
that rely on DOCSIS upstream pre-equalization coefficients and spectrum capture. The processes
described here will help cable operators and industry vendors implement smart monitoring tools, improve
maintenance practices, gain better insight in network problems, and enhance network reliability, among
other things.
Even though the focus for the development of a proactive network maintenance strategy is through the
use of pre-equalization coefficients, the intent is for this effort to expand in the future to include other
plant metrics that could help identify and resolve plant issues.
The key outcome of this effort is the reduction of troubleshooting and problem resolution time thereby
reducing operational costs. In addition, improvements in network reliability enable the introduction of
business and advanced services that require SLAs (service level agreements) thereby generating new
revenue. This mechanism adds the capability to detect and resolve problems before they impact customer
service, which helps with churn reduction.
This V03 revision of the PNMP guidelines document was updated to include DOCSIS 3.0 using Full Band
Capture.
Even though the focus for the development of a proactive network maintenance strategy is through the
use of pre-equalization coefficients, the intent is for this effort to expand in the future to include other
plant metrics that could help identify and resolve plant issues.
Valuable metrics that have been traditionally been used to assess performance include, downstream and
upstream SNR and MER, codeword error statistics as well as transmit and receive levels. These metrics by
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themselves wont facilitate the location of the source of a plant problem. Nevertheless, when these
metrics are associated with equalizer responses and spectrum captures, the value of these metrics
increases as they provide additional evidence to the existence of a problem.
The key outcome of this effort is the reduction of troubleshooting and problem resolution time, thereby
reducing operational costs. In addition, improvements in network reliability enable the introduction of
business and advanced services that require SLAs (service level agreements) thereby generating new
revenue. This mechanism adds the capability to detect and resolve problems before they impact customer
service, which helps with churn reduction.
The eight or so traditional DOCSIS service indicators that operators have relied upon for years are CM
status, upstream transmit level, upstream receive level, upstream SNR (MER), upstream codeword error
rate, downstream receive level, downstream SNR (MER), and DS codeword error rate. One question that
arises is why additional information is needed? The answer is that these indicators, while valuable, are
poor at answering the question exactly whats wrong or what is the root cause of poor service. On the
other hand, upstream equalization and full band capture data speak much more clearly as to root causes,
although some interpretation skill is still needed. That is one of the reasons for this document.
Most RF communication systems, including DOCSIS systems, use a variety of techniques to adjust and
compensate for variations in time, frequency, transmit power level, and for linear distortion. It has been
recognized for quite some time that useful plant health information can be derived from the parameters
that describe the compensation and adjustments that take place. This network monitoring advantage is
enhanced by the ubiquity of DOCSIS devices operating as network probes across the entire HFC footprint.
Some device parameters that provide significant insight into the characteristics of the DOCSIS upstream
transmission channel are the pre-equalization coefficients. Pre-equalization techniques are used to
compensate for linear distortion in the upstream channel. Examples of linear distortions include micro-
reflections, amplitude ripple, tilt, and group delay distortion. In most cases pre-equalization is able to
completely compensate for linear distortion problems without having the customer perceive an impact on
performance. This provides the operator time to fix the problem before any service degradation has taken
place thereby facilitating a proactive network maintenance strategy.
In the cable domain, pre-standard data-over-cable system vendor, LANcity had equalization functionality
in some of its products. Nevertheless, this proprietary protocol feature was not leveraged as the cable
industry transitioned to the standard DOCSIS technology.
Even though in DOCSIS systems, pre-equalization has been mandatory since the DOCSIS 1.1 specification
version, pre-equalization data was only used starting half-way through the deployment of DOCSIS 2.0
compliant devices around 2005. DOCSIS systems have a variety of channel width and modulation order
configuration options. Operators earlier use of narrower bandwidth channels (predominantly 1.6 MHz)
and lower order modulations (e.g., QPSK) did not require the use of pre-equalization. Moreover, some
operators were reluctant to turn on pre-equalization due to a history of certain DOCSIS 1.0 CMs
misbehaving when pre-equalization was turned on. The need to turn pre-equalization on became
apparent in scenarios when increased upstream peak rates and transport robustness were needed.
Demand for higher peak rates and higher capacity lead to the migration to 3.2 MHz and 6.4 MHz
bandwidth channels and the use of higher order modulations such as 64-QAM.
Pre-equalization in DOCSIS 1.0 was optional and was left unspecified. Pre-equalization in DOCSIS 1.1 was
not only defined accurately but was also mandatory for channels up to 3.2 MHz. The mandatory nature of
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pre-equalization in DOCSIS 1.1 and proper identification and isolation of misbehaving CMs enabled cable
operators to turn on pre-equalization.
A couple of years later, after the DOCSIS 2.0 specification was released, pre-equalization MIBs became
also available. This event made possible the use of pre-equalization information for network management
purposes.
Earlier work by Holtzman, Inc., Motorola, and CableLabs highlighted the value for understanding linear
distortions, additive impairments, and their impact on service performance.
In 2005, CableLabs and Charter Communications collected pre-equalization data from multiple nodes in
Estes Park, Colorado. Only a portion of the data collected was easily readable but subsets of that data
exhibited an apparent correlation. This was the start of the equalization coefficient decoding and
normalization effort. Cable operators could now begin to make sense of distortion signatures and how
they relate to problems in the field.
The use of DOCSIS pre-equalization coefficients along with plant topology information to pinpoint
problems in the network were described in a series of CableLabs internal reports in 2006 and at the SCTE
Cable-Tec Expo 2008 in Philadelphia [1]. This proposed approach relied on the following steps:
1) Derivation of frequency response signatures from pre-equalization coefficients
2) Identification and grouping of linear distortions from the frequency response data 3) Correlation of
impacted CMs with topology information to locate the cause of the problem.
A CableLabs-sponsored Proactive Network Maintenance (PNM) working group was formed in 2009 to
leverage information obtained from DOCSIS devices and to troubleshoot the plant. This group comprised
cable operators, CableLabs, and silicon, CM, CMTS, and instrumentation vendors. Tasks of the PNM
working group included the development of techniques to relate pre-equalization signatures to problems
in the field. PNM working group participation by the North American cable operator Comcast not only
facilitated the use of large amounts of field data to understand pre-equalization coefficient information,
but also provided valuable field information of what impairment was associated with what distortion
signature. One key output of the PNM working group was the Best Practices and Guidelines Document of
Proactive Network Maintenance Using Pre-Equalization [2] published in 2010.
The original PNM working group output also lead to operator implementations of PNM based tools. The
first implementation of an operator-developed pre-equalization analysis tool was the Scout Flux tool from
Comcast. This tool was implemented and released in 2009. Comcasts technical workforce played an
integral role in determining a variety of plant impairment scenarios and their signatures. Charters Node
Slayer PNM tool followed as well as tools from other cable operators.
Although the PNM working group initially focused on upstream pre-equalization, other topics were also
discussed. These topics included downstream equalization, which still suffers from lack of compliance and
discrepancies in MIB interpretation. Upstream spectrum analysis, required in DOCSIS 3.0 for a single
channel but supported in a proprietary fashion by numerous CMTS vendors across the full upstream
spectrum was also discussed. Cisco Systems lead efforts assessing the impact that LTE ingress has on
performance. The introduction in DOCSIS 3.0 of multiple bonded channels resulted in high sampling rate
receiver implementations. Industry leaders such as Broadcom leverage CPE spectrum capture or full band
capture (FBC) 1 from this feature and Comcast introduced it into their network management systems
shortly after its availability.
1
Generically speaking, the industry calls CPE spectrum capture full-band capture (FBC). MaxLinear calls it Full Spectrum
Capture (FSC).
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FBC enabled operators to have spectrum analysis capabilities wherever modern DOCSIS 3.0 CMs have
been deployed. This enables operators to take remote spectrum captures at the customer premises
without having to carry an expensive spectrum analyzer and without requiring access into a subscribers
home. FBC resulted in significant operational advantages not to mention operational cost savings. With an
increasing number of DOCSIS 3.0 CMs being deployed, these spectrum analysis probes have gathered
critical mass and are able to correlate spectrum signatures from neighboring CMs to troubleshoot and
locate problems. The width of the spectrum (full band) has allowed operators to detect very short micro-
reflections not visible when a single channel is analyzed through equalization. FBC also has enabled
verification of channel level alignment and the detection of ingress. Correlation of CM signatures before
and after actives enables the detection of nonlinear problems at amplifiers. Automated spectrum
signature analysis and impairment detection are being implemented to scale the analysis to the millions of
CMs deployed with this functionality.
An extended capability of FBC is upstream spectrum capture at the CM. Although the lower frequency
upstream signals are attenuated at the downstream receiver port by the diplex filter, in many cases
enough energy passes through to allow for the detection of impulse noise at the customer premises. This
is a very promising technique that can be enhanced through CM design, including, for example, diplex
filter bypass.
More recently, leveraging field data collected at Comcast, Armstrong Cable, and Suddenlink
Communications, CableLabs has demonstrated the correlation between equalization coefficient variability
and MER variation with impulse noise. This has opened the door to solving ingress localization problems
for certain types of noise. Ingress localization is one of the remaining challenges to conquer in HFC plant
troubleshooting.
The work of the PNM working group has been crucial in the incorporation of PNM tools into the DOCSIS
3.1 specification. Under the leadership of Broadcom, DOCSIS 3.1 incorporated hooks in the specification
that allow systems to emulate spectrum analyzers, vector network analyzers, vector signal analyzers, and
other tools.
After five years since the initial PNM documents publication, an updated version is intended through this
document. Different innovations in the area of proactive network maintenance have been discussed but
not recorded. It is the goal of this document to incorporate all the relevant topics in the area of PNM since
that last publication.
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2 REFERENCES
2.1 Informative References
Cable Television Laboratories, Inc., 858 Coal Creek Circle, Louisville, CO 80027;
Phone +1-303-661-9100; Fax +1-303-661-9199; http://www.cablelabs.com
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Composite Triple Beat (CTB) Clusters of third order distortion beats generated in cable network active
devices that carry multiple RF signals. When the primary RF signals are
digitally modulated signals instead of analog TV channels, the distortions
are noise-like rather than clusters of discrete beats.
Convolution A process of combining two signals in which one of the signals is time-
reversed and correlated with the second signal. The output of a filter is the
convolution of its impulse response with the input signal.
Correlation A process of combining two signals in which the signals are multiplied
sample-by-sample and summed; the process is repeated at each sample as
one signal is slid in time past the other.
Cross Modulation (XMOD) A form of television signal distortion where modulation from one or more
television channels is imposed on another channel or channels.
Decibel (dB) Ratio of two power levels expressed mathematically as dB = 10log10(P1/P2).
decibel millivolt (dBmV) Unit of RF power expressed in terms of voltage, defined as decibels relative
to 1 millivolt, where 1 millivolt equals 13.33 nanowatts in a 75 ohm
impedance. Mathematically, dBmV = 20log10(value in mV/1 mV).
Decision Feedback Equalizer An adaptive equalizer, usually comprising a combination of feedforward and
(DFE) feedback filters, that uses previously detected symbols to suppress inter-
symbol interference in the current symbol being detected.
Discrete Fourier Transform Part of the family of mathematical methods known as Fourier analysis,
(DFT) which defines the decomposition of signals into sinusoids. Forward DFT
transforms from the time to the frequency domain, and inverse DFT
transforms from the frequency to the time domain.
Downstream The direction of RF signal transmission from headend to subscriber. In
North American cable networks, the downstream or forward spectrum
occupies frequencies from 54 MHz to as high as 1002 MHz.
Drop Coaxial cable and related hardware that connects a residence or service
location to a tap in the nearest coaxial feeder cable. Also called drop cable or
subscriber drop.
Embedded Multimedia Terminal A multimedia terminal adapter that has been combined with a cable modem
Adapter (eMTA) (see multimedia terminal adapter).
Equalizer Tap See tap.
Fast Fourier Transform (FFT) An algorithm to compute the discrete Fourier transform (DFT), typically far
more efficiently than methods such as correlation or solving simultaneous
linear equations.
Feeder Outside plant hardline coaxial cables that are part of the coaxial
distribution network. These coaxial cables are installed on utility poles or
buried underground, are routed near the homes in the service area, and have
taps installed that are used to provide connections to the subscribers
premises.
Feeder Tap See tap.
Feedforward Equalizer (FFE) An adaptive equalizer that corrects the received waveform using samples of
the waveform itself at successive time delays, not using information about
the logical decisions made on the waveform.
Fiber Node See node.
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Finite Impulse Response (FIR) A type of filter or system in which the impulse response is finite in duration
that is, the impulse response settles to zero in a finite number of sample
intervals. A FIR filter is usually implemented as a tapped delay line, with the
tap outputs weighted and summed to produce each output sample.
Forward See downstream.
Forward Error Correction A method of error detection and correction in which redundant information
(FEC) is sent with a data payload in order to allow the receiver to reconstruct the
original data if an error occurs during transmission.
Frequency Response A complex quantity describing the flatness of a channel or specified
frequency range, and that has two components: amplitude (magnitude)-
versus-frequency, and phase-versus-frequency.
Full Band Capture (FBC) CPE-based spectrum analyzer-like functionality, in which time domain
samples are captured and Fourier transformed to produce a spectral display.
Group Delay The negative derivative of phase with respect to frequency, expressed
mathematically as GD = -(d/d) and expressed in units of time such as
nanoseconds.
Group Delay Variation (GDV) The difference in propagation time between one frequency and another. That
Or Group Delay Distortion is, some frequency components of the signal may arrive at the output before
others, causing distortion of the received signal.
Group Delay Ripple Group delay variation which has a sinusoidal or scalloped sinusoidal shape
across a specified frequency range.
Headend A central facility that is used for receiving, processing, and combining
broadcast, narrowcast and other signals to be carried on a cable network.
Somewhat analogous to a telephone companys central office. Location from
which the DOCSIS cable plant fans out to subscribers.
Hybrid Fiber/Coax (HFC) A broadband bidirectional shared-media transmission system or network
architecture using optical fibers between the headend and fiber nodes, and
coaxial cable distribution from the fiber nodes to the subscriber locations.
Impedance The combined opposition to current in a circuit that contains both resistance
and reactance, represented by the symbol Z and expressed in ohms. See also
characteristic impedance.
Impedance Mismatch Any variation in the uniformity of the nominal impedance of a transmission
line or device connected to a transmission line, and which generates a
reflected wave.
Impulse Noise Noise that is bursty in nature, characterized by non-overlapping transient
disturbances. May be repetitive. Generally of short durationfrom about 1
microsecond to a few tens of microsecondswith a fast risetime and
moderately fast falltime.
Impulse Response The output of a filter when its input is excited by an impulse function.
Impulse Function A sequence of samples consisting of a single 1, surrounded by all 0s. Also
called Kronecker delta function.
Incident Wave A traveling wave in a transmission line that is propagating from the source
toward the load.
Index of Refraction The ratio of the velocity of an electromagnetic wavespecifically what is
known as a transverse electromagnetic (TEM) mode wavein a vacuum to
its velocity in a dielectric material, TEM(vacuum)/TEM(dielectric).
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Infinite Impulse Response (IIR) A type of filter or system in which the impulse response is infinite in
durationthat is, the impulse response keeps going on forever. A IIR filter is
usually implemented as a feedback mechanism, where both the input and the
previous output are used to produce the next output.
Least Mean Squares (LMS) Search or adaptive algorithm used in adaptive transversal (tapped delay line)
filters. The algorithm attempts to minimize the error energy that occurs
between the output and the detected or desired signal.
Linear Distortion Distortion that occurs when the overall response of the system (including
transmitter, cable plant, and receiver) differs from the ideal or desired
response. This class of distortions maintains a linear, or 1:1, signal-to-
distortion relationship (increasing signal by 1 dB causes distortion to
increase by 1 dB), and often occurs when amplitude-versus-frequency and/or
phase-versus-frequency depart from ideal. Linear distortions include
impairments such as micro-reflections, amplitude ripple/tilt, and group delay
variation, and can be corrected by an adaptive equalizer.
Media Access Control (MAC) A sublayer of the OSI Models data link layer (Layer 2), which manages
access to shared media such as the OSI Models physical layer (Layer 1).
Media Access Control (MAC) The built-in hardware address of a device connected to a shared medium.
Address
Micro-Reflection A short time delay echo or reflection caused by an impedance mismatch. A
micro-reflections time delay is typically in the range from less than a
symbol period to several symbol periods.
Modulation Error Ratio (MER) The ratio of average symbol power to average error power. The higher the
MER, the cleaner the received signal.
Multimedia Terminal Adapter A device that provides an interface between analog telephones and an IP
(MTA) network.
MTR The ratio of energy in the main tap to the energy in all other taps combined.
Node An optical-to-electrical (RF) interface between a fiber optic cable and the
coaxial cable distribution network. Also called fiber node.
Noise See thermal noise.
Nonlinear Distortion A class of distortions caused by a combination of small signal nonlinearities
in active devices and by signal compression that occurs as RF output levels
reach the active devices saturation point. Nonlinear distortions generally
have a nonlinear signal-to-distortion amplitude relationshipfor instance,
1:2, 1:3 or worse (increasing signal level by 1 dB causes distortion to
increase by 2 dB, 3 dB, or more). The most common nonlinear distortions
are even order distortions such as composite second order (CSO), and odd
order distortions such as composite triple beat (CTB). Passive components
can generate nonlinear distortions under certain circumstances.
Pre-Equalizer See adaptive pre-equalizer.
QAM Receiver A circuit that receives, processes, and demodulates a QAM signal.
QAM Signal Analog RF signal that uses quadrature amplitude modulation to convey
information.
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Quadrature Amplitude A modulation technique in which an analog signals amplitude and phase
Modulation (QAM) vary to convey information, such as digital data. The name quadrature
indicates that amplitude and phase can be represented in rectangular
coordinates as in-phase (I) and quadrature (Q) components of a signal.
Quadrature Two sine waves are in quadrature if their phases differ by 90 degrees, such
as sine and cosine.
Radio Frequency (RF) That portion of the electromagnetic spectrum from a few kilohertz to just
below the frequency of infrared light.
Reflected Wave A traveling wave in a transmission line, caused by an impedance mismatch
that is propagating from the point where the impedance mismatch exists
back toward the incident waves source.
Reflection Coefficient Ratio of reflected voltage E- to incident voltage E+, expressed
mathematically as = E-/E+ where (uppercase Greek letter gamma) is the
reflection coefficient.
Return See upstream.
Return Loss (R) The ratio of incident power PI to reflected power PR, expressed
mathematically as R = 10log10(PI/PR), where R is return loss in decibels.
Reverse See upstream.
Root Mean Square (RMS) A statistical measure of the magnitude of a varying quantity such as current
or voltage, where the RMS value of a set of instantaneous values over, say,
one cycle of alternating current is equal to the square root of the mean value
of the squares of the original values.
Receive MER (RxMER) The modulation error ratio at the receiver, at the point at which symbol
decisions are made. A high RxMER results in a clean constellation plot,
where each symbol point exhibits a tight cluster separated from the
neighboring symbols. (See Appendix I.)
Standing Wave A distribution of fields along a transmission line caused by the interaction of
an incident and reflected wave, such that the peaks and troughs of the wave
are stationary in location.
Subscriber Drop See drop.
Tap (1) In the feeder portion of a coaxial cable distribution network, a passive
device that comprises a combination of a directional coupler and splitter to
tap off some of the feeder cable RF signal for connection to the subscriber
drop. So-called self-terminating taps used at feeder ends-of-line are splitters
only and do not usually contain a directional coupler. Also called a multitap.
(2) The part of an adaptive equalizer where some of the main signal is
tapped off, and which includes a delay element and multiplier. The gain of
the multipliers are set by the equalizers coefficients. (3) One term of the
difference equation in a finite impulse response or a infinite impulse
response filter. The difference equation of a FIR follows: y(n) = b0x(n) +
b1x(n-1) + b2x(n-2) + + bNx(n-N).
Thermal Noise The fluctuating voltage across a resistance due to the random motion of free
charge caused by thermal agitation. When the probability distribution of the
voltage is Gaussian, the noise is called additive white Gaussian noise
(AWGN).
Upstream The direction of RF signal transmission from subscriber to headend. Also
called return or reverse. In most North American cable networks, the
upstream spectrum occupies frequencies from 5 MHz to as high as 42 MHz.
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Vector A quantity that expresses magnitude and direction (or phase), and is
represented graphically using an arrow.
Velocity Factor (V) The reciprocal of index of refraction, expressed in decimal format.
Velocity Of Propagation (VP or The speed at which an electromagnetic wave travels through a medium such
VoP) as coaxial cable, expressed as a percentage of the free space value of the
speed of light. For example, VP in a typical coaxial cable is about 85% to
87% of the speed of light. VP in a typical single mode optical fiber is about
67% to 69%.
Voltage Standing Wave Ratio Ratio of a standing waves maximum voltage Emax to its minimum voltage
(VSWR) Emin along a transmission line, expressed mathematically as VSWR =
Emax/Emin, or VSWR = (1+||)/(1-||).
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IP Internet protocol
kHz Kilohertz
km Kilometer
LMS Least mean squares
MAC Media Access Control
MTC Main tap compression
MTNE Main tap nominal energy
MER Modulation error ratio
MHz Megahertz
MIB Management information base
ML Maximum likelihood
MPEG Moving Picture Experts Group
ms Millisecond
MSE Mean square error
Msym/sec Mega symbols per second
MTC Main tap compression
MTE Main tap energy
MTNA Main tap nominal amplitude
MTNE Main tap nominal energy
MTR Main tap ratio
mV Millivolt
NMTER Mon-main tap to total energy ratio
ns Nanosecond
NTSC National Television System Committee
OID Object identifier
PNM Proactive Network Maintenance
PostMTE Post-main tap energy
PostMTTER Post-main tap to total energy ratio
PPESR Pre-post energy symmetry ratio
PPTSR Pre-post tap symmetry ratio
PreMTE Pre-main tap energy
PreMTTER Pre-main tap to total energy ratio
QAM Quadrature amplitude modulation
R Return loss
RF Radio frequency
RNG-REQ Ranging request
RNG-RSP Ranging response
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In this document, the definition of reactive network maintenance is a stringent one and, in the era of
multimedia, business and advanced services, is perhaps one that the cable industry should follow.
Reactive network maintenance consists of network maintenance practices that are initiated by metrics
which show service performance has been impacted. Under this definition, it is not assumed the need of
customer feedback/calls for network maintenance to be reactive. As long as conditions such as FEC
statistics, power starvation, CPD, narrowband interferers, laser clipping, impulse noise and other service
impacting symptoms are detected, the response to such is reactive. In the case of distortion that is
completely corrected by pre-equalization there is no performance impact, therefore maintenance actions
that arise from these impairment discoveries are considered to be proactive. If there are symptoms that
combine performance impacting conditions with distortion detected through equalization, the
maintenance that arises from it is still considered reactive.
Impairments that result in network maintenance classified as reactive would likely be given higher priority
for resolution because they are already impacting performance.
In most scenarios, upstream pre-equalization mechanisms can completely compensate for certain
problems in the network and no symptoms are detected in FEC statistics or through other metrics. The
fact that equalization can fully compensate for network linear distortion can buy the operator time in
resolving the issue before there is service impact, thus enabling a proactive network maintenance
strategy.
In the upstream portion of the CATV network there are different types of impairments. These can be
classified based on the impact these impairments have on the signal as linear as well as nonlinear
impairments. In the case of a linear impairment, the impact on the signal will be given by a change in
amplitude and phase of the original signal. In the case of a nonlinear impairment, the signal generates
distortion components, including harmonics of the original signal or multiplies the original signal with
other energy present in the return band. For example, in the linear distortion case, transmitting
information across the upstream channel will result in an amplitude and phase deviation for a given
frequency point. A micro-reflection, which is analogous to a wireless multipath signal, could result from
the bouncing back and forth of a signal between two interfaces that have impedance mismatches,
generating an amplitude and phase distortion of the signal as summation of a time-delayed signal copy
the reflection or echocombined with the desired signal. A second example of a linear distortion occurs at
the diplex filter rolloff that marks the upper edge of the upstream frequency spectrum around 42 MHz. At
this rolloff frequency, the amplitude and the phase suffer considerable distortion. In particular, the phase
distortion is noticeable prior to reaching the band-edge. This phase distortion is more easily shown when
expressed as group delay which is defined as:
d
GroupDelay =
d
where is the phase in radians, is the frequency in radians per second, and group delay is in seconds.
Group delay is ideally constant across the band of interest. Group delay variation across the band is known
as group delay distortion. Additional discussion about linear impairments can be found in the tutorial
material in Appendix I.
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One thing to keep in mind is that even impairments that are considered nonlinear such as common path
distortion (CPD) may have associated linear distortion elements. For instance, the corrosion of a center
conductor that generates a mixer effect also results in an impedance mismatch that can generate a
noticeable micro-reflection.
Examples of impairments that are nonlinear include the previously mentioned CPD, as well as composite
second order (CSO) and composite triple beat (CTB) distortions, cross-modulation, and laser clipping.
Ingress and impulse noise are considered additive impairments, although if an impairment such as impulse
noise is high enough to cause laser clipping, it can be considered nonlinear in nature too.
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the same ratio 1 2 or, dB difference 10 log 1 + 10 log 2). The decaying micro-reflections may quickly be
lost in the noise floor after two or three trips through the micro-reflection source.
Conversely, the adaptive equalizer response, which is approximately the inverse of the channel response,
will have only a single tap after the main tap for this case.
Though the reflector examples in Figure 1 are feeder taps, it should be noted that many devices can
produce similar results, including damaged cables or corroded splices, which are often causes of micro-
reflections as well.
Note that the delay between echoes equals twice the propagation delay between the two reflection
points 1 and 2, so the distance between the two reflectors is known. However it does not relate how far
along the plant these two reflectors are, that is, the location of the impairment in the plant. To determine
the location of the fault, additional information is necessary as described in Section 6.6, Fault Localization.
Channel Impulse Response Representation
0 Main Tap
Magnitude (dB)
Roundtrip Attenuation
Reflected Signal Attenuation Factor & Delay A*e-jT
E = A 12 e-jt
Upstream Signal #2
Figure 1 - Micro-reflection with Multiple-Transit Echoes
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signal will be reflected back in the direction of the upstream signal and will be combined with the main
signal at the 23 dB feeder tap where it originated. This micro-reflection is easily observed in cases where
there is long un-tapped span of cable between the first feeder tap, the 23 dB feeder tap in this case, and
low-value feeder taps with open terminations. All of these unterminated feeder tap ports create their own
micro-reflections. This condition usually creates multiple micro-reflections, and since there was an open
port at the 11 dB feeder tap and another at the 8 dB feeder tap, there would be two different cable
lengths resulting in two different micro-reflection delay characteristics.
This case is important to mention since the reflector, 1, is not in the tree of the devices between the CM
and the CMTS, but includes devices that are downstream from the CM feeder tap location. This
phenomenon, as mentioned earlier, is more noticeable at the high value feeder tap, because as the feeder
tap value decreases, the amplitude difference between the desired signal and the micro-reflection
increases. If both the 23 dB feeder tap and the 11 dB feeder tap had 35 dB tap-port-to-output-port
isolation, there would be 12 dB greater separation between desired and the micro-reflection signal.
Additionally, the 23 dB feeder tap location is near the amplifier followed by a long length of cable, where
the 11 dB feeder tap is found near the end of the cable so the cable length for the 11 dB feeder tap is
shorter and the micro-reflection delay characteristic is correspondingly less.
This type of micro-reflection does not exhibit an unending IIR response, since the reflected energy from
Tap 8 passes through Tap 23 relatively unimpeded and continues upstream. This type of response, which
stops after a single echo, is called finite impulse response (FIR). The signature will show a single main echo
without trailing echoes.
Conversely, the adaptive equalizer response, which is approximately the inverse of the channel response,
will have a sequence of smaller and smaller taps for this case. This is because the equalizer internally
generates additional echoes as it cancels the original echo in the signal. As it generates an echo, it must
use another tap to cancel the new echo. This process goes on until the end of the equalizer tapped delay
line is reached. Any remaining echo energy is uncompensated after this point, and results in reduced
RxMER.
To summarize, a multiple-transit echo scenario (Example 1) has an unending sequence of decaying echoes
in the channel response, and the corresponding adaptive equalizer response has a single echo. A single-
reflection scenario (Example 2) has a single echo in its channel response, and the corresponding adaptive
equalizer response has a decaying sequence of echoes continuing to the end of the equalizer tapped delay
line.
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response. Unfortunately, some energy is lost so receive signal levels will be low. (Note: lost RF energy
sometimes indicates signal leakage.) As anticipated, this type of impairment is difficult to detect. One
method of detecting this problem is via a standing wave measurement in the field, which requires probing
the line with a high impedance probe, such as a Trilithic I-Stop, as illustrated in Figure 4. Note that if a
system has an echo tunnel caused by two plant defects, repairing one of the defects will cause the echo
tunnel to disappear, but the other defect remains. See Appendix VIII for a discussion of this type of
detection.
Reflection 2 Reflection 1
TAP23 TAP11
AMP Delay 2*T2
Reflected Signal #1
Reflected Signal #2
Main Signal
Coupling Delay 2*T1
Isolation
Loss
Upstream Signal
Figure 3 - Composite Micro-reflection Resulting from Type 1 and Type 2 Micro-reflections
The upstream pre-equalization mechanism relies on the interactions of the DOCSIS ranging process in
order to determine and adjust the CM pre-equalization coefficients. The intent is for the CM to use its
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coefficients to predistort the upstream signal such that the predistortion equals the approximate inverse
of the upstream path distortion, so that as the predistorted upstream signal travels through the network it
is corrected and arrives free of distortion at the upstream receiver at the CMTS.
The pre-equalization coefficients of the CM are the complex coefficients (F1 through F24) of the 24-tap
linear transversal filter structure shown in Figure 5.
Input
+ + + ... + + + +
Equalizer
Output
In this structure the blocks with z-1 label represents delay elements, each of which in the DOCSIS 2.0 pre-
equalizer is the symbol period T (in DOCSIS 1.1 it can also represent delays equal to T/2 and T/4).
In the ranging process the CM sends a ranging request message (RNG-REQ) to the CMTS. The CMTS may
use a known portion of this message, such as the preamble, as well as other known messages to
determine the quality of the received signal, as well as to determine the adjustment the CM should make
to its pre-equalization coefficients to better compensate the upstream distortion. In response to the RNG-
REQ message, the CMTS sends a ranging response (RNG-RSP) message with a set of 24 coefficients and a
parameter that indicates whether these coefficients are intended to result in a set or adjust operation by
the CM. In the case of a set command, the CM will replace its existing coefficients with the ones sent by
the CMTS. In the case of an adjust command, the CM convolves its coefficients with the ones sent by the
CMTS to achieve the adjusted coefficients (Figure 6).
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Amp.
CMTS CM
RNG-REQ
Calculates
PreEq.
Coefficients for
CM RNG-RSP
Generates new
Timing Adjust coefficients
Power Adjust based on the
Freq. Adjust ones sent by
CMTS
Transmit Eq. Adjust
Ranging Status
Transmit Eq. Set
Figure 6 - CM-CMTS Ranging Interaction Enabling Pre-equalization Process
The CMTS may not be completely satisfied with the quality of the signal the CM is sending after the initial
try. This is an iterative process which may take a few interactions before the coefficients are stable.
CMTS implementations use for the most part the transmit-equalization-adjust option to convey
information. Only after the initial ranging request, one may see a CMTS send a transmit-equalization-set
message to make sure that the CM initializes properly. In principle the CMTS could use this message when
it needs to reset the coefficients.
A CMTS that is completely satisfied with the values of the pre-equalization coefficients sends an adjust
message where all coefficients are zero except for the pre-equalizers main tap coefficients, which has
maximum or nominal value. This represents a Kronecker delta or impulse function, and any data set
convolved with an impulse results in the original data set, which in this case is the CM pre-equalization
coefficients, unchanged.
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The RNG-REQ message is generated by the CM and sent to the CMTS. The RNG-REQ is used as the
reference to determine whether the CM signal needs any adjustment. These adjustments could be in
frequency, power level, timing offset, and distortion. Once the CMTS receives the RNG-REQ message it
uses a known portion of this message as the reference of what the signal should look like. Typically that
known portion of the message is the preamble. If the CM is not finished implementing the changes the
CMTS is asking for, the CM includes in the RNG-REQ message a ranging status indicating whether or not
the ranging changes are still pending. This is the pending till complete field in the RNG-REQ message
payload. The RNG-REQ message also carries a downstream channel ID that associates the upstream being
used with a downstream channel. Figure 8 shows the structure of the RNG-REQ message.
Mini-Slot
Integer Number of
Boundary of
Minislots
previous Burst
Preamble FEC Info/Parity Next
Zero-Fill if Overhead
0-1024 bits 18-255 bytes
Burst
necessary
Ramp-Up (0-128 Bytes) (10-25% of user data) Ramp-Down Preamble
Guard Time
5-255 symbols
1.25-63.75 bytes QPSK
2.5-127.5 bytes 16QAM
MAC Header MAC mgmt msg
6 bytes +EHDR 24-1522 bytes
Pending Till
SID DS Ch. ID
Ranging Request (RNG-REQ) Complete
2 bytes 1 byte
1 byte
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or opposite response of the plant. The pre-equalization coefficients provide detailed characteristics of the
channel distortion, although the coefficients do not directly indicate the level of micro-reflections.
Assuming negligible group delay distortion and a single micro-reflection, a quick estimate of micro-
reflection level can sometimes be obtained using the energy in the adaptive equalizers non-main taps. In
general, an elaborate analysis is required to uniquely resolve micro-reflection level/delay signature
characteristics. An upstream channel that exhibits no distortion has all the energy concentrated in the
adaptive equalizer main tap while one that exhibits distortion also has energy in taps other than the main
tap (Figure 9).
No Channel Distortion
Gain
fC
fC - fSymb/2 fC + fSymb/2
Gain
fC
fC - fSymb/2 fC + fSymb/2
The pre-equalization data which the CMTS continues to send to the CM indicates how successful a CM has
been in compensating for the distortion by showing what is left to compensate to achieve ideal reception.
Ideally and typically, the CM starts with no compensation and after a few ranging intervals, achieves a
steady state where the CM compensates for all the distortion. At that point the CMTS pre-equalization
data exhibits a flat response indicating that further compensation is not required (Figure 10).
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Magnitude
Gain
fC
fC - fSymb/2 fC + fSymb/2
Gain fC
fC - fSymb/2 fC + fSymb/2
Figure 10 - CMTS CM Pre-equalization Coefficients Values and Frequency Response Scenarios
The upstream CM equalization data collected by the CMTS is analyzed to verify that any plant distortion
has been compensated. There is the possibility of a distortion being so severe (e.g., a micro-reflection
having a very long delay) that the pre-equalization process would not be able to fully compensate for it.
These scenarios are rare in current HFC architectures, but if this does occur, one must be aware that an
impairment identification process using only CM pre-equalization data will not yield accurate results.
5.4 Upstream Pre-equalization in DOCSIS 1.0, DOCSIS 1.1 and DOCSIS 2.0
Upstream pre-equalization in DOCSIS 1.0 was left as optional and the equalization process between CMTS
and CM was not defined in sufficient detail. An unexpected result occurred when DOCSIS 1.1 and 2.0 were
introduced with a well-defined process. A few 1.0 CMs that implemented pre-equalization exhibited
erratic behavior in the presence of downstream RNG-RSP messages that were generated by 1.1 or 2.0
CMTSs. For quite some time operators have not been motivated to turn pre-equalization on, in part
because the demand for capacity and spectrum availability have not been significant enough to warrant
the use of wider channels, higher order modulations, or frequencies near the edges of the upstream
spectrum where linear distortion occurs.
Some 1.0 CMs exhibiting the problem have been successfully upgraded with firmware that corrects this
issue. Unfortunately it has not been possible to correct this issue on all affected CMs. To support reliable
use of upstream pre-equalization, operators have been replacing 1.0 CMs having known issues.
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which 1.1 CM versions are decreasing with time, it is important to determine at what point the procedures
described in this documentation will be worthwhile to implement.
In a scenario of an upstream path that exhibits a micro-reflection, the maximum delay compensation that
can be achieved using pre-equalization is limited by the amount of delay that can be generated within the
pre-equalization filter structure shown in Figure 5. The maximum delay that can be generated is given by
the delay between the adaptive equalizers main tap and the last adaptive equalizer tap.
In DOCSIS 2.0 and 3.0, the delay or spacing between each adaptive equalizer tap location is equal to the
symbol period, because it always has a parameter of adaptive equalizer taps/symbol equal to 1. Typical
implementations in DOCSIS 2.0 and 3.0 have the main equalizer tap in the eighth position out of a 24-tap
delay line. Therefore the maximum delay that can be generated in that filter structure is 16T (last tap
position main tap position) where T equals the symbol period.
In DOCSIS 1.1 the delay between different adaptive equalizer tap locations can be a fraction of a symbol
period. That is, the number of equalizer taps/symbol parameter is allowed to be 1, 2 or 4, resulting
respectively in delay differences between adaptive equalizer tap locations of T, T/2 and T/4. This option
has not been implemented in a CMTS. Therefore, in DOCSIS 1.1 CMTS scenarios, the maximum delay that
can be generated is equal to 4T (last tap position main tap position). Table 1 shows the maximum delays
that are generated in DOCSIS 1.1 and 2.0 or 3.0 filter structures at different symbol rates using the typical
equalizer main tap configurations (position 4 for DOCSIS 1.1 and position 8 for DOCSIS 2.0 and 3.0).
Table 1 - Maximum Delays Generated by Pre-equalization Filter Structures in DOCSIS 1.1 and 2.0
It cannot be assumed that a DOCSIS 2.0 filter structure can fully compensate for a micro-reflection with a
delay of 3.125 microseconds. Typically energy in the neighboring equalizer taps help in the fine tuning of
that compensation and a micro-reflection that pushes the delay to the limit of the equalizer wont have
longer delay equalizer taps available to help in the representation of the exact value. This is especially true
if the echo delay is not a multiple of the symbol period, since the equalizer taps are then not spaced at the
exact intervals to efficiently cancel the echo, and more equalizer taps are needed to provide effective
cancellation. This will impact more severely higher order modulation scenarios such as 64-QAM where the
adjustment is more critical.
In addition, in the case of strong micro-reflections, the equalizer may have a decaying sequence of taps as
described in Example 2. For proper cancellation of the echo, taps at 2 or 3 times the echo delay may be
needed. This implies that the echo must be 2 or 3 times shorter than the equalizer length.
Here are some examples of a few micro-reflection scenarios in potential HFC plant configurations. The first
scenario is a micro-reflection that occurs between an amplifier and a feeder tap that are separated by 75
feet (150 feet round trip distance) and that have a return loss of 6 dB on each reflection interface
(interface where impedance mismatch occurred). The feeder cable between these interfaces has a
diameter of 0.625 and an attenuation of 1.2 dB/300 feet. This is considered a strong and short micro-
reflection. Figure 11 shows the level and delay of the third transit and its subsequent multiple transit
echoes.
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The second scenario is a micro-reflection that occurs between two amplifiers and there are no feeder taps
in between. They are separated by 1200 feet (2400 feet round trip distance) and that have a return loss of
8 dB on each reflection interface (interface where impedance mismatch occurred). The feeder cable
between these interfaces has a diameter of 1.000 and an attenuation of 0.8 dB/300 feet. This is
considered a strong and long-delay micro-reflection. Figure 11 shows the level and delay of the third
transit echo (top large blue square). The fifth transit echo of this micro-reflection is too low in amplitude
to be noticeable.
The third scenario is a micro-reflection that occurs between two amplifiers and with feeder taps in
between. The amplifiers are separated by 1200 feet (2400 feet round trip distance) and each has a return
loss of 8 dB on each reflection interface (interface where impedance mismatch occurred). The aggregate
insertion loss (also called through loss) in the feeder taps is equal to 6 dB (12 dB round trip). The feeder
cable between the interfaces has a diameter of 1.000 and an attenuation of 0.8 dB/300 feet. This is
considered a mild and long-delay micro-reflection. Figure 11 shows the level and delay of the third transit
echo. The fifth transit echo of this micro-reflection is too low in amplitude to be noticeable.
Figure 11 also indicates which scenarios can be compensated in the different DOCSIS configurations. The
scenarios that lie to the left of the vertical line that corresponds to a given channel width /DOCSIS mode
combination can be compensated, while the ones that lie to the right of the line cannot be properly
compensated. It is also worth noting that in cases close to the vertical line, higher order modulation may
not be possible.
4*T@2.56 MHz
16*T@5.12 MHz
Level Relative to Main Signal
0
-4
-8
-12 Third Transit Echo - Short
-16
(dB)
Figure 11 - Pre-equalization Compensation Capabilities under Short and Long Delay Micro-reflection Scenarios
The examples just discussed assumed 0.625 cable for the short time delay reflection and 1 cable for the
long time delay reflection. The short time delay reflection scenario includes data points at 150, 300, and
600 round trip distances and the long time delay reflection includes data points at 2400, 2700, and
3000.
DOCSIS pre-equalization coefficients indicate different things depending whether the CMTS or the CM is
being queried. The information that is available through MIBs relate to what the CMTS and CM keep track
of at the time the respective devices are being queried. Through the ranging interaction discussed in
Section 5.3.1, the CMTS MIB (docsIfCmtsCmStatusEqualizationData) provides the adjustment necessary to
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update the CM coefficients and achieve upstream path distortion compensation. The CM MIB
(docsIfCmStatusEqualizationData) indicates the current predistortion that is applied to the upstream
signals.
The MIB format is as follows:
Bits 0 15 31
F1real F1imag
F2real F2imag
...
F24real F24imag
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over time, can be used to detect ingress and interference in the downstream spectrum. The downstream
equalization structure is not specified. The implementer has the flexibility to differentiate in the type of
equalizer structure and design used. Traditional feed-forward structures or decision feedback structures
are implementation examples, although decision feedback structures have likely been used. The current
MIBs may not properly described the state of the downstream equalizers implemented. A number of
downstream equalization MIB implementations are not reliable. In order to effectively leverage
information from the downstream equalizers, it is important to introduce a specification update through
the EC process.
For the CMTS this object was intended to report some type of aggregated equalization value for the entire
upstream channel. RFI MIB [RFC4546] clarifies the CMTS does not need to report a value other than an
empty string.
Note that this equalization data is not relevant to the scope of this document.
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The proactive network maintenance methodology that is based on pre-equalization coefficients can be
described in terms of a few key general components.
The first general component is the data collection process. It comprises polling all CMs and CMTSs to
obtain pre-equalization data from all configured upstream channels. The gathered data is verified for
format integrity and is normalized to be useful for comparison. For scalability purposes, the data collection
process is conducted using a more frequent polling cycle for the CMs that exhibited apparent distortion
above a pre-determined level and a less frequent cycle for all CMs.
The second general process incorporates the initial distortion assessment that is conducted on all CMs
that are monitored more frequently. This process uses the non-main tap to total energy (NMTER) ratio to
discriminate which CMs should be examined in more detail and which should be left for evaluation in the
next coarse monitoring cycle.
The third component in this approach conducts the detail analysis that includes the calibration process
and the determination of the distortion signatures from frequency domain and time domain analysis.
These signatures include group delay and micro-reflections. In case of multiple different micro-reflections,
the signatures are obtained after a discrimination process.
The fourth component takes the distortion signatures and evaluates whether from a static perspective
they should be classified as red which implies the need for immediate action, or as yellow which indicates
the CM should be monitored more frequently and its distortion data be stored for observation over time.
The information describing which CMs have to be examined more frequently is communicated to the data
collection process. Green classification indicates that no action is necessary.
The fifth process takes the CM signatures and identifies within a fiber nodes service area which micro-
reflections are common to several CMs. The next process identifies by comparing historical data collected
in the yellow classified CMs whether intermittent issues or trending issues are of concern and may require
action.
The last process is the one that correlates the affected CM or CMs with the outside plant topology and
uses that information to determine fault location. Figure 13 shows a diagram of the process just described.
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The structure of the pre-equalization information has been described in Section 5.6. How the values within
this structure are interpreted depends on implementation. The first four byte-long elements in the header
are to be interpreted in HEX mode. For example, the number of adaptive equalizer taps value of 18 in HEX
is 24 in decimal (Figure 14). The rest of the equalizer structure defined in two byte increments containing
the real and imaginary coefficients should be interpreted according to 2s complement over the entire two
bytes or 4 nibbles describing the real or the imaginary coefficients. For example, the 2s complement of a
2 byte such as the fourth real coefficient is FFFC which in 2s complement is -4 (red circle).
MainT T/Symb #Taps Rsvd F1r F1i F2r F2i F3r F3i F4r F4i
08 01 18 00 FF FF 00 02 FF FF 00 01 00 03 FF FF FF FC 00 00
-1 2 -1 1 3 -1 -4 0
F5r F5i F6r F6i F7r F7i F8r F8i F9r F9i
00 0B FF FF FF EE 00 04 00 21 FF FB 07 FE 00 31 FF F3 FF E8
11 -1 -18 4 33 -5 2046 49 -13 -24
F10r F10i F11r F11i F12r F12i F13r F13i F14r F14i
00 18 FF F0 FF F4 00 05 00 09 FF FB FF FA 00 01 00 06 FF FD
24 -16 -12 5 9 -5 -6 1 6 -3
F15r F15i F16r F16i F17r F17i F18r F18i F19r F19i
FF FD 00 00 00 05 FF FD FF FD 00 01 00 01 00 01 FF FE 00 00
-3 0 5 -3 -3 1 1 1 -2 0
F20r F20i F21r F21i F22r F22i F23r F23i F24r F24i
FF FF 00 00 FF FF FF FF 00 00 FF FF 00 00 FF FF FF FE FF FD
-1 0 -1 -1 0 -1 0 -1 -2 -3
The representation of coefficients often differs among CM vendors. There are variations in maximum
amplitude as well as variations in the way the coefficients are interpreted. Table 3 highlights the different
interpretations that exist for the most popular CMs deployed.
Table 3 - Maximum Amplitude and Encoding Formats for the 16 Most Popular 2.0 CMs In US
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The CM vendors had two interpretations of how to decode the coefficients. One is the four nibble 2s
complement interpretation and the other is the three nibble 2s complement interpretation. The four
nibble 2s complement interpretation is the one assumed by the spec but there is a significant number of
CMs deployed with the three nibble 2s complement interpretation. Regarding maximum amplitude, CMs
have maximum amplitude equal to 2047, 1023 or 511. If the coefficients are normalized, the difference in
CMs maximum coefficient amplitude turns into a difference in granularity. The difference then becomes
one of decoding interpretation of coefficients.
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The real and imaginary complex coefficients of a DOCSIS 2.0 upstream pre-equalizer defined as:
F1R, F1I, F2R, F2I, F3R, F3I, F4R, F4I,. . . F23R, F23I, F24R, F24I,
and will be used to define several key metrics that follow.
MTE = F8 R + F8 I
2 2
6.3.2 Main Tap Nominal Energy and Main Tap Nominal Amplitude
The DOCSIS pre-equalization taps exhibit different nominal or maximum amplitudes depending on CM
implementations. The maximum of amplitude implementations from CMs are 2047, 1023 or 511. This
parameter is defined here as the main tap nominal amplitude (MTNA). The square of the nominal
amplitude yields the nominal tap energy.
The main tap nominal energy (MTNE), assuming main tap is in the eighth position, is defined as:
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TTE
MTC = 10 Log
MTE
Main tap compression at the CM translates to a less RF power level delivered to the CMTS. An MTC of 2 dB
results in the CMTS receiving 2 dB less input power.
Main tap compression at the CMTS is not expected under normal operating conditions. Any level of main
tap compression at the CMTS should raise an alarm.
Pr eMTE + PostMTE
NMTER = 10 Log
TTE
Notice that the main tap energy in the numerator is missing. The non-main tap energy ratio is also a good
estimation of the MER assuming that the signal is not impacted by impairments that are not considered
linear distortions, such as burst noise and nonlinear impairments.
Non-main tap to total energy ratio at the CMTS is a good indicator of the type of upstream performance
the CM signals have based on the amount of linear distortion present. If a 27 dB CNR is assumed for
negligible errors with a 64-QAM signal, a NMTER target value of -27 dB can be assumed for comparable
performance. If a 30 dB CNR is the threshold where correctable errors are beginning to appear, that would
also correspond to a threshold of -30 dB NMTER when correctable errors begin to appear. This CNR to
NMTER relationships are useful in determining thresholds from the NMTER values. An operator could
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assume an immediate action (red) NMTER threshold of -27 dB for 64-QAM operation and a monitor more
frequently (yellow) NMTER threshold of -30 dB.
Pr eMTE
Pr eMTTER = 10 Log
TTE
PostMTE
PostMTTER = 10 Log
TTE
Pr eMTE
PPESR = 10 Log
PostMTE
For practical purposes, the pre-post energy symmetry may be approximated using only the two taps
adjacent to the main tap, giving the pre-post tap symmetry ratio (PPTSR):
F7 2 + F7 I 2
PPTSR = 10Log R 2
2
F9R + F9I
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2: 79.202 ns
CH1 S21 delay 100 ns/ REF 0 s 42. 008 MHz
1000 ns
1: 69.659 ns
40.872 MHz
900 ns
800 ns
700 ns
600 ns
500 ns
400 ns
As observed in Figure 15, there is a variation in group delay of up to 300 ns in a channel that is located at
the band-edge. The pre-tap equalization coefficient energy increases in the presence of group delay
distortion. Additional group delay details are discussed in the tutorial section (Appendix I).
N+4 -51.2 -44.1 -40.7 -38.2 -32.6 -27.1 -18.2 -0.08 -31 -47.2 -40.9 -49.1 -47.9 -60.2 -54.2 -53.2 -57.2 -100 -53.2 -49.1 -57.2 -53.2 -50.2 -57.2
N+3 -60.2 -47.2 -44.9 -37.7 -34.2 -28.5 -19.8 -0.06 -38.1 -34.9 -44.2 -60.2 -46.2 -57.2 -60.2 -54.2 -53.2 -60.2 -50.2 -53.2 -53.2 -47.2 -50.2 -100
N+2 -57.2 -47.9 -44.9 -38.6 -36.4 -30.7 -22.3 -0.03 -34.2 -40.3 -46.2 -54.2 -50.7 -60.2 -60.2 -60.2 -60.2 -45.6 -53.2 -51.2 -47.2 -46.1 -57.2 -57.2
N+1 -60.2 -54.2 -50.2 -44.6 -40.7 -34.2 -26 -0.01 -41.9 -49.1 -54.2 -60.2 -50.7 -51.2 -57.2 -60.2 -49.1 -50.7 -49.1 -57.2 -57.2 -51.2 -100 -49.1
N+0 -60.2 -57.2 -60.2 -46.2 -44.6 -39.6 -30.2 -0.01 -47.2 -46.2 -46.2 -57.2 -54.2 -60.2 -53.2 -49.1 -57.2 -50.2 -60.2 -60.2 -57.2 -53.2 -53.2 -100
Table Note: No micro-reflections, 40.4 MHz center frequency, and 3.2 MHz channel width
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Figure 16 shows how when operating at the band-edge, the pre-main tap energy increases proportionally
with increasing cascade depth. This is characteristic of the group delay distortion impact on tap energy.
The effect of group delay distortion could be hidden just by looking at cascade depth in a plant topology
map. In-line equalizers which may not be obvious in a plant topology diagram may contribute to distortion
just as diplexers within amplifiers do. In severe distortion cases, assessment of pre-main tap energy could
be used to determine whether certain CMs should be moved to lower distortion channels in the middle of
the upstream band.
0
-5
Normalized Magnitude (dB)
-10
-15 N+5
N+4
-20
N+3
-25
N+2
-30 N+1
-35 N+0
-40
-45
-50
1 2 3 4 5 6 7 8 9 10 11 12
Taps
Figure 16 - Pre Main Tap Energy Increase with Cascade Depth (Fc=40.4 MHz, Ch. W=3.2 MHz,
No Micro-reflections, First 12 Taps Shown )
Key metrics worth highlighting in Table 5 are the PreMTTER that increases with cascade depth while the
PostMTTER shows low values as no micro-reflections are present. The PPESR show high positive values
since in this scenario the dominant impairment is group delay distortion. The low values of MTC are
indicative that the pre-equalization compensation is effective.
Table 5 - Pre-equalization Metrics at Band-Edge (No Micro-reflections)
MTC NMTER PreMTTER PostMTTER PPESR
N+5 0.11 dB -15.9 dB -16.3 dB -25.9 dB 9.53 dB
Cascade
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N+4 -53.2 -57.2 -43.8 -38.5 -31.6 -25.8 -17.1 -0.46 -14.4 -14.3 -33.3 -25.1 -32.6 -33.2 -37.2 -38.7 -43.8 -46.4 -49 -46.9 -51.2 -53.2 -54.2 -60.2
N+3 -60.2 -50.7 -43.3 -37.9 -31.9 -26.7 -17.6 -0.46 -15.1 -13.6 -34.8 -24.6 -32.6 -32.2 -38.2 -37.1 -53.2 -47.2 -47.6 -50.2 -53.2 -47.2 -54.2 -54.2
N+2 -100 -50.9 -44.6 -41.3 -33.7 -28.2 -19.6 -0.38 -14.6 -14.9 -36.4 -25.7 -37.5 -34.7 -38.4 -42.5 -48.1 -52.1 -50.9 -59.2 -59.2 -50.1 -49.2 -66.2
N+1 -54.2 -50.2 -44.6 -39.3 -33.2 -27.5 -19.1 -0.43 -14.5 -14 -34.6 -24.7 -33.4 -32.7 -37.2 -37.2 -44.1 -47.9 -43 -53.2 -50.7 -44.2 -44.9 -53.2
N+0 -59.2 -52.2 -47.1 -40.8 -35.1 -29.7 -21.7 -0.4 -14 -14.5 -35.3 -25.5 -37.9 -34.9 -40.5 -40.6 -47.2 -52.1 -48.6 -63.2 -56.7 -46.2 -57.2 -47.1
Table Note: 0.5 microsecond delay micro-reflection, 40.4 MHz center frequency, and 3.2 MHz channel width
Figure 17 shows how when operating at the band-edge, the pre-main tap energy increases with increasing
cascade depth but not as noticeably as the scenario without micro-reflections depicted in Figure 16. This is
due to some pre-main tap energy needed to compensate for the micro-reflection which adds to the pre-
main tap energy that is caused by group delay distortion. This leaking of energy into the pre-main tap
region is more prevalent with shorter micro-reflections that use the taps closer to the main tap for
compensation than the longer micro-reflections that use the higher value taps.
0
-5
Normalized Magnitude (dB)
-10
N+5
-15
N+4
-20
N+3
-25
N+2
-30
N+1
-35 N+0
-40
-45
-50
1 2 3 4 5 6 7 8 9 10 11 12
Taps
Figure 17 - Pre Main Tap Energy Increase with Cascade Depth (Fc=40.4 MHz, Ch. W=3.2 MHz, with 0.5 s Micro-
reflection, First 12 Taps Shown )
Key metrics worth highlighting from Table 7 are the PreMTTER that increases with cascade depth. The
PostMTTER shows a high value indicative of the micro-reflection present. The PPESR show negative values
since in this scenario the dominant impairment is micro-reflection. The combined group delay distortion
and micro-reflection by themselves is properly compensated through the pre-equalization process,
although some increase in MTC begins to show.
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N+4 -59.2 -60.2 -46.2 -41.1 -34.8 -29.2 -20.7 -0.8 -11.2 -11.8 -21.2 -21.9 -28.2 -31.8 -33.4 -39.4 -40.5 -45.5 -45.1 -56.2 -50.9 -51.2 -53.9 -47.2
N+3 -59.2 -53.2 -47.6 -41.6 -35.1 -30.3 -22.3 -0.81 -10.9 -11.8 -21.1 -22.5 -29 -33.1 -35.3 -41.4 -42.1 -50.9 -48.4 -50.2 -63.2 -53.9 -57.2 -59.2
N+2 -59.2 -55.1 -46.2 -41.7 -34.2 -28.5 -20.4 -0.8 -11.3 -11.8 -21 -22.1 -28.2 -32.2 -33.7 -39.2 -39.8 -44.6 -49 -46.7 -50.9 -48.6 -47.1 -47.6
N+1 -100 -56.2 -45.4 -42 -34 -29.1 -20.6 -0.83 -11 -11.7 -21.6 -21.8 -28.6 -31.5 -33.4 -39.1 -40.2 -42.8 -57.2 -53.2 -56.2 -49 -63.2 -46.4
N+0 -57.2 -60.2 -47.2 -41.6 -32.9 -27.8 -18.7 -0.79 -11.8 -11.6 -22.2 -21.7 -28.7 -31.2 -33.1 -39.6 -37.6 -47.9 -42.6 -50.2 -49.1 -60.2 -57.2 -57.2
Table Note: 0.5 microsecond delay micro-reflection, 14 MHz center frequency, and 3.2 MHz channel width
Figure 18 shows how when operating in the middle of the band, there is no increase in pre-main tap
energy with increasing cascade depth as the group delay is fairly flat. (See also Figure 15.) Figure 18 shows
how post-main tap energy is used in compensating for the micro-reflection. Figure 18 also illustrates how
a small amount of pre-main tap energy is used in compensating for the fractional delay 0.5 s micro-
reflection. When the micro-reflection delay doesnt coincide with a tap delay, neighboring taps are used
for compensation. This explains why in Figure 17 the increase of pre-main tap energy with increasing
cascade depth is not as noticeable as in the group delay only case depicted in Figure 16. The combined
effect of group delay distortion and a 0.5 s micro-reflection of Figure 17 can be approximated to a rough
superposition of Figure 16 representing the group delay only case and Figure 18 representing the
micro-reflection only case.
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-5
-10
Normalized Magnitude (dB)
-15 N+5
-20 N+4
N+3
-25
N+2
-30 N+1
-35 N+0
-40
-45
-50
1 2 3 4 5 6 7 8 9 10 11 12
Taps
Figure 18 - Tap Energy for Different Cascade Depth Scenarios (Fc=14 MHz, Ch. W=3.2 MHz, with 0.5 s Micro-
reflection, First 12 Taps Shown)
Some key metrics from Table 9 are worth highlighting. The low PreMTTER value is indicative of negligible
group delay distortion. The PostMTTER high value is indicative of the strong micro-reflection present. The
PPESR show negative values since in this scenario the dominant impairment is the micro-reflection. The
MTC value is higher than the previous two scenarios which indicates that the pre-equalizer may be
beginning to lose its equalization compensation effectiveness.
Table 9 - Pre-equalization Metrics at Middle of Upstream Band (with 0.5 s Micro-reflection)
MTC NMTER PreMTTER PostMTTER PPESR
N+5 0.8 dB -7.73 dB -17.4 dB -8.23 dB -9.18 dB
Cascade
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response prior to equalization. The CMTS offers a post-equalization view of the inverted channel response
as it is received from the cable modem. This can be helpful when evaluating the performance of the
modems upstream pre-equalizers. It can also help identify issues where the impairment is changing
frequently.
In addition to the three required data elements, there are other metrics which can be used to help identify
and localize areas of impairment. These other elements may already be available as a result of pre-existing
monitoring systems. One should extend or reuse existing data as opposed to over-polling the modems or
CMTS.
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If the network topology is well known at the time of polling, a geographically sensitive polling approach
might be considered. Also, market specific maintenance windows may be among the factors to consider in
polling cycle timing.
6.4.2.1 Low Rate (once daily, rotating across eight-hour time-shifts, adjustable)
Modem based pre-equalization coefficient data should be collected once per day. Its possible that certain
plant problems might be specific to the time of day. These scenarios might include weather patterns,
watering systems and other time-based anomalies. Assuming an eight-hour window to complete polling
(including accommodation for maintenance), a three shift pattern should work well. This could be
achieved by a single daily poll with a time offset of 32 hours. Likewise, the modem population could be
divided by three and the load distributed throughout the day. In the latter approach, it would be
important to rotate the three modem populations to correctly achieve the desired result (Table 10 and
Table 11).
CMTS based equalization coefficient data should be collected as close in time to the modems as possible.
Understanding that the SNMP process for gathering data from the CMTS will be decoupled from the
modems is important. The most efficient way to obtain this data from the CMTS would be a bulk walk
(SNMP) of the docsIfCmtsCmStatusEqualizationData table. This will return a large swath of data, while the
modem collection threads are completely independent and non-synchronized with the CMTS process.
Using the main tap compression and non-main tap to total energy ratio formulas (see Key Metrics, Section
6.3), modems of interest are identified and promoted to the medium-rate polling cycle. These will remain
under medium-rate scrutiny until the correct threshold is met for some predetermined time. Initially, 48
hours is recommended.
Table 10 - Low Rate Once Daily Rotating Eight Hour Time Shifts - Three Day Cycle
Groups Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9
1 6 AM 2 PM 10 PM 6 AM 2PM 10 PM 6 AM 2 PM 10 PM
2 2 PM 10 PM 6 AM 2PM 10 PM 6 AM 2 PM 10 PM 6 AM
3 10 PM 6 AM 2PM 10 PM 6 AM 2 PM 10 PM 6 AM 2 PM
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Table 13 - Medium Rate Once Every Four Hours - One day cycle - Four Groups (All Times in EST)
Groups Day 1 Day 1 Day 1 Day 1 Day 1 Day 2 Day 2 Day 2 Day 2
EST 6 AM 10 AM 2 PM 6 PM 10PM 2 AM 6 AM 10 AM 2 PM
CST 7 AM 11 AM 3 PM 7 PM 11PM 3 AM 7 AM 11 AM 3 PM
MT 8 AM 12 PM 4 PM 8 PM 12AM 4 AM 8 AM 12 PM 4 PM
PST 9 AM 1 PM 5 PM 9 PM 1 AM 5 AM 9 AM 1 PM 5 PM
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Bill of Materials
22 ea. precision male pin F connectors to match coax
2 ea. adapters, female F-to-connector type used on CMTS
(if needed)
3 ea. male-male F splice
1 ea. 30 dB fixed attenuator
1 ea. 20 dB fixed attenuators
1 ea. 10 dB fixed attenuator
11 ea. 6 dB fixed attenuators
2 ea. precision 75-ohm male F terminators
50~300 feet quad-shield coax
1 ea. diplex filter
1 ea. 8-way splitter
1 ea. 20 dB directional coupler
1 ea. 2-way splitter
8 ea. DOCSIS 2.0 or later cable modems
Note: DOCSIS specifies that a CMTS must
support +50 to +61 dBmV downstream RF output
(single channel). Typical CMTS downstream
level is +55 to +58 dBmV as shown here.
30 dB
6-series coax, <20 feet 20 dB downstream
Downstream
H test point (terminate
+55 to +58 dBmV when not in use)
RF output
Diplex filter
Belden 1855A, <10 feet
CMTS
6 dB C DC-20
Upstream 10 dB
0 dBmV F-type male-male splice
6 dB 6 dB
8-way splitter
With the configuration shown, each cable
modems downstream input will be
approx. 0 to +3 dBmV, and upstream
output (single channel) will be approx.
+45 dBmV
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Cable Modem
DOCSIS Downstream
MAC Rx Elements Diplex
Filter
DOCSIS Transmit Nyquist
US Data Equalizer Modulator Filter Amp
Filter
HFC Plant
CMTS
HE US RF De- Adaptive
Front End Filter US Data
Combining Modulator Equalizer
MAC & DS
Elements
Headend
If there was a-priori knowledge of the distortion contributed by the CM and CMTS, it could be calibrated
out in order to have a more accurate representation of the distortion in the field.
Generating a database with all the possible CM and CMTS model pairs is feasible given that there are a
limited number of CM and CMTS implementations. A known short plant setup consisting of a CMTS-CM
pair and a few fully characterized components enables determining almost exclusively the contribution of
the CM and CMTS internal distortion. Section 6.5.1 describes an example of a known short plant where
the internal characteristics of the CMTS and CM can be measured. The CMTS-CM internal distortion is
obtained by gathering the pre-equalization coefficients of the CM after allowing a few maintenance
intervals to elapse to achieve convergence of the coefficients.
Assuming that the real and imaginary values of the 24 CM pre-equalization coefficients for a particular
CMTS-CM model pair measured on a short calibrated plant are given by:
F1CR, F1CI, F2CR, F2CI, F3CR, F3CI, F4CR, F4CI,. . . F23CR, F23CI, F24CR, F24CI
For every ith real and imaginary coefficient, the resulting complex number is obtained,
FiCR + j FiCI = FiC
Resulting in the following complex coefficients
F1C, F2C, F3C, F4C, F5C, F6C, F7C, F8C,. . . F21C, F22C, F23C, F24C
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Similarly, assuming that the real and imaginary values of the 24 CM pre-equalization coefficients obtained
in the field, matching the CMTS-CM model pair being analyzed, are given by:
F1R, F1I, F2R, F2I, F3R, F3I, F4R, F4I,. . . F23R, F23I, F24R, F24I
The resulting complex coefficients are
F1, F2, F3, F4, F5, F6, F7, F8,. . . F21, F22, F23, F24
Given 24 complex coefficients and assuming that the equalizers main tap is located at tap position
number 8, a 32 element fast Fourier transform can be used to translate from the time domain into the
frequency domain. Tap 8 would coincide with FFT input element 16 to preserve the relative position of the
response in frequency.
The mapping of coefficients to FFT input parameters follows:
Fin1 through Fin8 = 0
Fin9 = F1, Fin10 = F2, Fin11 = F3, , Fin16= F8, ,Fin31 = F23, Fin32= F24
The mapping for the coefficients obtained using the short plant measurement results in the following:
FCin1 through FCin8 = 0
FCin9 = F1C, FCin10 = F2C, , FCin16= F8C, ,FCin31 = F23C, FCin32= F24C
After calculating the 32 point FFT the following frequency response values are obtained:
Fouti for i =1 to 32 and FCouti for i =1 to 32
For calibration, the magnitude of the field coefficients are divided by the magnitude of the short plant
coefficients and the phase of the short plant coefficients are subtracted from the phase of the field
coefficients.
|Fouti| = |Fouti|/|FCouti| for i =1 to 32
(Fouti) = (Fouti) (|FCouti) for i =1 to 32
From the calculated magnitude and phase values, the corrected Fout frequency response values are
obtained
Fouti for i =1 to 32
Additional granularity in the frequency response representation can be obtained by inserting zeroes to a
larger size FFT such as a 64, 128 or 256 FFT.
An example of the calibration process is illustrated next.
Figure 21 shows the distortion of a CMTS/CM pair in a short calibrated plant versus the same CMTS/CM
pair measured in the field. The pre-equalization coefficients obtained from the CM MIBs are shown in
Table 15.
Table 15 - Pre-equalization Coefficients of Upstream Path with and without Micro-reflection
Field CM Eq Data MIB 08 01 18 00 FF FF 00 00 00 00 00 01 FF FE FF FD 00 03 00 04 FF FA FF FB 00 08 00 09 FF F0 FF
EA 01 EE 00 00 FF EF FF EC 00 38 FF D8 00 55 FF D7 FF E2 00 03 00 1F FF E5 FF FC FF FA 00
01 FF FE 00 01 FF F7 FF FE 00 02 FF FF FF FD FF FF 00 00 00 00 00 00 FF FF 00 00 00 00 00 00
00 00 00 00 00 00 00 00
Short Plant CM Eq Data 08 01 18 00 00 00 FF FF FF FF 00 01 00 00 FF FE FF FF 00 02 00 01 FF FA FF FE 00 0A FF FE FF
MIB E5 01 FE 00 00 FF FF FF E3 00 05 FF F5 FF FE 00 04 FF FF FF FD 00 00 00 02 FF FF FF FE FF
FF 00 02 FF FF FF FF 00 00 00 01 00 00 FF FE 00 00 00 00 FF FD FF FF FF FF FF FF FF FF 00 00
00 00 00 01 FF FF 00 00
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The first four bytes 08 01 18 00 provide the main tap position 08, the number of taps per symbol 01,
the number of taps 18 (hex number for 24) and a reserved byte. The rest of the information are the real
and imaginary coefficient data (2 bytes each) for the 24 taps.
3.5
3
2.5
2
1.5
Magnitude (dB)
1
0.5 Field
Short Plant
0
-0.5
-1
-1.5
-2
-2.5
-3
-3.5
-3.2
-2.8
-2.4
-1.6
-1.2
-0.8
-0.4
0.4
0.8
1.2
1.6
2.4
2.8
3.2
-2
2
Relative Frequency (MHz)
Figure 21 - Pre-equalizer Frequency Response with (0.5s, -10 Dbc) and without Micro-reflection
The distortion in the short plant scenario is predominantly impacted by the CMTS receiver and CM
transmitter. Therefore, to calibrate out the impact of the CMTS and CM, the frequency response of the
short plant (micro-reflection off) is subtracted from the frequency response of the micro-reflection on
scenario. This calibrated response is shown in blue in Figure 22.
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3.5
3
2.5
2
1.5
Magnitude (dB)
1
0.5
Corrected
0 Field
Short Plant
-0.5
-1
-1.5
-2
-2.5
-3
-3.5 F
-3.20
-2.88
-2.56
-2.24
-1.92
-1.60
-1.28
-0.96
-0.64
-0.32
0.00
0.32
0.64
0.96
1.28
1.60
1.92
2.24
2.56
2.88
3.20
Relative Frequency (MHz)
Figure 22 - Calibrated Pre-equalizer Frequency Response Obtained from Micro-reflection
on (0.5s, -10 dBc) and Off Scenarios
Averaging F and A values is no longer necessary since the calibrated response is fairly even across the
frequency range under observation.
The process of fault detection and localization relies on monitoring the network for general plant-wide or
neighborhood-localized problems as well as for specific end devices. In this process it is assumed that
there is detailed knowledge of the node service areas topology. It is also assumed that distortion data
(pre-equalizer coefficients and other applicable information) has been collected from the CMs and
analyzed to determine the distortion signatures of the affected CM(s). Next, a process is described by
which, through correlation of topology with distortion signatures, the location of faults can be
determined.
In the example highlighted in Figure 23 is a group of CMs, identified in red, that exhibit the same unique
distortion. The CMs in green are CMs that dont share that specific distortion.
It is assumed that to obtain the distortion signatures, an analysis and classification process of the
impairments has already taken place.
If only information from one CM were available, the problem area could only be isolated to somewhere
along the path between the CM and the fiber node (dashed line). The more interesting process is when
the relationships of CMs that share specific impairments (as well as those that do not) to upstream paths
are examined.
In order to estimate the impairment location, the common path shared by the end devices showing the
specific impairment is found. This path containing the impairment is further constrained by excluding the
path that is shared with the end devices that operate properly.
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Knowledge of the micro-reflection signature also helps localize the problem. For example, in Figure 23 a
triple transit reflection signature with delay matching the distance between known devices on the plant,
such as distance between taps, length of drops, or distance between amplifiers, can point to the likely
cause or narrow down the possible set of causes of the problem.
After analysis and path manipulation of the end devices showing impairments such as micro-reflections, a
potential location of the problem is determined. These areas are shown in purple on Figure 23. This
mechanism maps the devices that have the same unique micro-reflection attribute and pinpoints the
portion of the network that exhibits the impairment.
Headend CMTS
Taps
Rigid
Coax CM CM
Cable modems
Cable modems NOT
affected by detected
affected by detected
micro-reflection
Cable modems NOT CM micro-reflection
affected by detected CM
micro-reflection
CM CM
CM
Taps CM
Drop
Potential area of Impedance Cable CM
problem based on mismatches
CM pre-eq causing
coefficients micro-reflections Home Wiring
readings
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2.5
1.5
0.5
0
-35 -30 -25 -20 -15 -10 -5 0
As seen in Figure 25, the amplitude ripple of the frequency response is sufficient to determine group the
CMs with same micro-reflection. Some amplitude variability margin must be allowed. Note that in a few
cases, the same ripple magnitude range could correspond to different micro-reflections. In such cases the
estimation of echo delay can provide an unambiguous answer. For typical fiber node sizes the probability
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of uniqueness of a micro-reflection is very high. In rare exceptions, the micro-reflection signature pair will
not be sufficient to determine the CM clusters (e.g., a sub-T echo delay). In such cases, only the topology
resolution will provide final resolution of such conditions. Figure 26 shows the way that common
signatures of CMs are correlated. The delay is an approximation of the estimated maximum delay and it is
expressed as 2T where T is the inverse of the symbol period. That means the distance between the two
reflectors is calculated based on half the delay. Delay below the "no action required" threshold is not
relevant.
Figure 28 shows the case of a single sub-T echo. The two signatures come from the same household, H1,
and note the neighbor CMs: CM4, 5, 6, and 7 do not register the same micro-reflection signature as the
CMs in observation.
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Note that limited data could lead to non-optimal location of the micro-reflection. For example, fewer CMs
reporting pre-equalization data or few customers in the fiber node branch will reduce the possibility to
accurately estimating the location of the micro-reflection.
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35
30
Magnitude of y
25
20
15
10
0
-4 -3 -2 -1 0 1 2 3 4
Time (samples, 0=center sample #10 used by interpolator)
The algorithm inputs are the 3 taps around the (local) peak: (x0,y0), (x1,y1), (x2,y2), where the middle
sample (x1,y1) is the local peak of interest. The x value is the pre-equalizer tap number (typically in the
range from 1-24) and the y value is the tap magnitude in dB. It has been found empirically that using the
dB values gives good results; it is not necessary to convert from dB values to power ratios. Hence for our
example we have the following inputs to the algorithm:
x0 = 9
y0 = 35
x1 = 10
y1 = 40
x2 = 11
y2 = 29
The algorithm fits a parabola, shown in the figure as a dotted blue line, to the 3 taps. We assume the
equation for the parabola is y = a*x^2 + b*x + c.
The following code solves for the location of the peak of this parabola:
a = (y0 - 2*y1 + y2)/2; % Coefficient a in y = a*x^2 + b*x + c; note: a should be negative, otherwise no
peak exists
b = (y2 - y0)/2; % Coefficient b in y = a*x^2 + b*x + c
c = y1; % Coefficient c in y = a*x^2 + b*x + c
xm = (y0 - y2)/(4*a); % x-axis offset from max sample (samples)
ym = -(y0 - y2)^2/(16*a); % Magnitude (y-axis) offset from max sample
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The goal of any operators service department is to be invisible to its customers experience. Too often
leaders have reviewed post mortem reports only to discover the failure was a slow degradation caused by
water migration and corrosion. In other words, there was an opportunity to resolve the impairment
before the customer had to alert the cable company to the failure with a trouble call. This issue points
squarely at the operators preventive maintenance program or lack thereof. A plant inspection program
such as system sweep is a great idea but operators rarely have enough resources available to inspect,
locate and make repairs before a customer notices the failure. Tracking the length of time it has been
since an area has been inspected is fine but it doesnt solve the resource problem. Operators are left with
sweeping areas/nodes that are showing an increase in the number of trouble calls or outages. This
method is reactive, not proactive.
Planning an effective preventive maintenance program is based on historical practices. When an operator
uses statistics such as MER (SNR), FEC, T1-T4 timeouts, receive level and transmit power, which are all
important variables to track over time, data is being used that would be better served in an active
maintenance program. That being said, if the MER and FEC are bad then the customer has already been
influenced in a negative way. If the modem is timing out on a range request or response, then the
customer is being affected. If the levels are fluctuating outside the expected range of the design, then
customers usually feel the pain. It turns out that adaptive pre-equalization resolves a lot of plant
impairments. Of course, there is a limit to what can be compensated for using adaptive equalizers and for
how long. This is especially true when consideration is given to the fact that whatever is already broken
will continue to derade. The power of PNM lies in the ability to be alerted to failure before MER and FEC
and other statistics begin to ring the alarm bells. If an operator is able to solve the problem within the
window that pre-equalization is saving the day, then trouble calls and outages are being prevented and
the customers experience is being preserved.
One of the first things an operator will need to determine is the MTR threshold for what is good and bad.
A good starting point would be to review the original recommendations from CableLabs first document
on PNM. The following recommendations were included in that document: Thresholds will determine
which modems are green (no action required), yellow (high monitoring frequency) and red (immediate
action required). That information can then be used for CMTS health. If the thresholds show most of the
modems in red, then that means that everything must be inspected. On the other hand, if the thresholds
are not reviewed regularly and updated, the operator could be missing opportunities to improve. A few of
the variables which the operator should consider when selecting threshold include amplifier cascade,
node size and bandwidth utilization.
MTR severity should still be graded into three categories: immediate action required (Red), high
monitoring frequency (Yellow), and no action required (Green).
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From the original PNM document, the three severity assessment metrics that are used for a single CM are
defined as follows:
The first severity metric is a static classification conducted solely based on the relative level of the MTR.
A second severity metric results from a trending analysis that is conducted so that a network operator can
identify an impairment degrading at a rate that will result in immediate action in the near future (e.g., one
week). This method requires time stamping of the measurements gathered so that a history of the
impairment is obtained. Typically 3 dB of level change is worth attention.
A third severity metric is generated from a historical comparison of the MTR levels of the high frequency
monitored CMs. This third metric measures intermittent fluctuations that would be considered significant,
but which did not rise to the immediate action level. The measurements should be conducted over
multiple days. The comparison of the measurements is done at the same time of the day. Again, 3 dB of
level change should ring alarm bells.
It is noteworthy to point out that this same approach can be applied to other levels like micro-reflection or
group delay. Micro-reflection levels can be calculated by using the same formula for MTR while utilizing
the equalizer tap values that compensate for micro-reflections Post-MTR (usually taps 9 through 24).
Group delay level is typically calculated using taps 1 through 7.
Operators that are new to the PNM process may want to use the following metrics as a starting point for
the first year or two. Explaining to a team of technicians that 50% or better of their network is suddenly
bad will not inspire them to fully grasp a new idea. The metric in Table 16 will also ensure that the most
vulnerable parts of the network will receive attention first.
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Systems that have short amplifier cascades may want to stick with the original recommendation from
CableLabs which is represented in Table 17. Amplifier cascades that are fewer than four and have a well-
established PNM team for support would fall into this category. Plant Health index, which will be
explained later, that falls in the neighborhood of five would be well served by this metric because there is
room to improve.
Table 17 - PNM Metric (Established Networks)
MTR GOOD Greater Than or Equal to25 dB
MTR MARGINAL Between 18 and 25 dB
MTR - BAD Less Than 18 dB
Another point that operators should consider is when a modem starts using a more robust modulation
type such as 16-QAM because of high noise, it is a clear sign that something is broken and needs attention.
However, if the metric doesnt change in pace with the less demanding modulation type, a problem could
be concealed.
Table 18 - PNM Metric (Lower Modulation Type than Expected)
MTR GOOD Greater Than or Equal to32 dB
MTR MARGINAL Between 25 and 32 dB
MTR - BAD Less Than 25 dB
It is valuable to know that a modem is compensating for impairments, but if that was the limit of what
could be ascertained, then it is unlikely PNM would be a successful tool. The power of PNM is the
comparison to and correlation with other modems to identify clusters or groups that may be affected by
the same impairment. It is like turning all of the modems into mini-sweep meters then comparing the
response of those meters to identify problems. An operator should keep track of the total number of
groups and focus on reducing the number over time.
CMTS or Plant Health is calculated by using the formulas on the next page. This is an excellent way to take
large numbers of modems MTR values and place them on a scale from 1 to 10, with 10 being perfect.
Since the desire is to identify which node or upstream interface needs attention, a Health Index by node
doesnt work well because it lacks clarity with so few modems. It is better to flush out upstreams using an
average level of MTR, micro-reflection or group delay. The formulas are fairly simple in that they compare
the number of troubled modems or the total number of registered modems on the CMTS. Only 50% of the
marginal/yellow modems are used in the formula since they are not as damning as the critical/red
modems. There are two basic spins on the Health Formula which varies by the denominator. If a modem is
unable to produce an accurate MTR value, such as a legacy modem that doesnt utilize pre-equalization,
then that modem should be excluded as shown in Formula 1. On the other hand, if a significant number of
green modems stop communicating because of something outside the control of the operator, like
commercial power, than an operator could use Formula 2. Keep in mind the larger the total number of
modems that are being used in the formula, the better the index will be. A well-operating system typically
lives around the index of 7, but what is more important is for an operator to have room to improve.
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Customers care little about a cable operators measuring tools when it comes to their ability to enjoy the
service being provided.
CMTS/Plant Health Formula 1:
The use of the trending or intermittent approach could be difficult since it requires time stamping pre-
equalization records and deploys an effective filtering process that produces usable data without getting
drowned by information over- load. A good example would be the CableLabs-authored SCTE/ISBE Cable-
Tec Expo 2015 operational practice2. The authors were able to show the ability to flush out noisy drops,
which is traditionally a painstaking activity, through the use of monitoring intermittent MTR activity.
Considering intermittent activity could be a tough sell if the plate is already more than full with just trying
to diminish the static opportunities. However, every operator would benefit by building, early in their
PNM tool development, a methodology to time stamp and store data points. That data would provide
huge dividends as the outside plant performance improves. It is also worth pointing out that tracking
other metrics, which are easily recorded and available, such as modems transmit or received power, could
aid in the initial identification of trouble-prone areas which could benefit from some PNM support.
Using the pre-equalization mechanism defined in DOCSIS is efficient, resulting in no performance
degradation even in the presence of strong micro-reflections. Pre-equalization may help decrease the
urgency for plant repair, but it should not be used to circumvent required plant maintenance. The purpose
of proactive network maintenance is to listen to important network health metrics and take action before
service is impacted.
Micro-reflection severity can be graded into three categories: immediate action required (Red), high
monitoring frequency (Yellow), and no action required (Green).
The three severity assessment metrics that are considered for a single CM are defined as follows:
The first severity metric is a static classification conducted solely based on the relative level of the micro-
reflection amplitude.
A second severity metric results from a trending analysis that is conducted so that network operators can
identify an impairment degrading at a rate that will result in immediate action in the near future (e.g., one
week). This method requires time stamping of the measurements gathered so that a history of the
impairment is obtained.
A third severity metric is generated from historical comparison of the micro-reflection levels of the high-
frequency monitored CMs. This third metric measures intermittent fluctuations that would be considered
significant, but which did not rise to the immediate action level. The measurements should be conducted
over multiple days. The comparison of the measurements is done at the same time of the day.
2
Hunter, D. and Williams, T., 2015. Improved Customer Service Through Intermittent Detection, found at
http://www.scte.org/SCTE/Resources/SCTE_Knowledge_Resource_Collection.aspx
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6.7.2 Severity Analysis Strategy for Static or Single Data Point Scenario
In a static environment where no change of pre-equalization data is assumed, or when there is only one
data point and not able to determine change, a simple set of fixed thresholds can be used to determine
severity categories.
For example, a total distortion energy amplitude of -25 dBc or lower may fall into the category of No
Action Required, while -18 dBc or greater may be considered in the category of Immediate Action
Required. Two thresholds determine the three categories. In Figure 29, the values below -25 dBc belong
to the No Action Required category or green severity. The values above -18 dBc belong to Immediate
Action Required category or red severity. The values between -18 dBc and -25 dBc belong to the category
High Monitoring Frequency Category or yellow severity.
As additional data points are collected, time dependent analysis can be conducted which is described in
the next section. Since time dependent analysis is conducted for CMs that are already in the yellow
category from a static perspective, the time dependent severity classifications only have to define a red
classification criteria.
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The time measurement reference parameter Tn_m is coded as follows; the first number (n) indicates the
number of days after the initial measurement date, while the second number (m) corresponds to the
approximate time of day when measurement was taken. This means that measurement T0_16 was taken
at 4:00 p.m. on the same day as the initial stored measurement, and measurement T2_12 was taken two
days after the first measurement and at 12:00 p.m.
Figure 31 plots Table 19s micro-reflection amplitude versus time, indicating that in less than three days,
CM#1 will be going from yellow to red according to the static criteria while CM#2 stays in the yellow
region. These trends should be conducted using data points measured at the same time of the day so that
approximately equal temperature data points are obtained.
-18
-19
Reflection Amplitude (dB)
-20
CM#1
-21
CM#2
-22
-23
-24
T0_0 T0_4 T0_8 T0_12 T0_16 T0_20 T1_0 T1_4 T1_8 T1_12 T1_16 T1_20
Figure 31 - Micro-reflection Amplitude Data of Same Two CMs to Highlight Trending Over Time
If CM#1 shows a delta of 1.8 dB between T0_0 (-22.2 dBc) and T1_0 (-20.4 dBc), at that rate of change it
will reach -18 dBc in less than three days with respect to T1_0. The estimated level at T2_0 is -18.6 dBc
and T3_0 would be -16.8 dBc, crossing into the red region.
If delta amplitude per day is D, the last amplitude measured was MRLast and if MRLast + 3*D > Trending
Red Threshold then it is classified as red for the trending criteria.
3D is a variable subject to operator adjustment and is intended as a recommendation.
In addition, another indicator of urgency is determined by the number of days that the operator has until
the micro-reflection amplitude reaches the red region.
Target#ofDaysToRepair = (-18 - MRLast)/D
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Figure 32 plots Table 20s micro-reflection amplitude versus time showing CM#1 with significant micro-
reflection amplitude swings. Both CMs remained in the yellow region under the static severity criteria but
CM#1 shows drastic changes in micro-reflection amplitude which could be a loose connector or something
likely to break in the very near future.
-18
-19
Reflection Amplitude (dB)
-20
CM#1
-21 CM#2
-22
-23
-24
T0_0 T0_4 T0_8 T0_12 T0_16 T0_20 T1_0 T1_4 T1_8 T1_12 T1_16 T1_20
CM#2 shows gradual amplitude swings that could be attributed to daily temperature variations. CM#1
shows significant variations in micro-reflection amplitudes. A metric that could define the red classification
criteria for intermittent behavior is proposed as follows.
Intermittent Red Threshold = Avg 4 hour Ref. Amp / (Static Red Threshold Avg. Refl. Amp.) > 0.25
where the average four hour delta of the reflection amplitude represents the average swing in dB over the
four hour interval which corresponds the monitoring granularity in time of the devices that were deemed
to need high-frequency monitoring and historical data tracking. The average reflection amplitude is
measured up to a fixed number of days (for instance, four days). If this metric approaches 1 it indicates
that the reflection amplitude is varying with swings that approach the static threshold level. If this metric
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is smaller than 0.1, for example, one can say that the reflection amplitude swings occur at a safe margin
below the static threshold.
The scenarios just discussed dealt with the quantification of the degree of impairment of a single CM. It is
assumed that a cable operator may add weighting factors to indicate urgency in addressing these issues
after the previous information is correlated with the number of CMs affected by a particular impairment.
The analysis used to determine fault location can also be used to determine how many users will be
impacted.
Figure 33 - Example of Five Groups of Modems Affected by Five Different Plant Problems
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However it is possible for two modems both to share a common impairment, but one or the other can also
have unique impairments. For example, an impedance mismatch inside a home could create a non-shared
impairment. Fortunately, most unique echo tunnels are less than 50 meters, which affect only taps 9 and
10.
When working on a trouble call, a technician wants to know if an upstream linear distortion impairment
problem one customer is experiencing is shared by multiple subscribers. Localizing the impairment will
determine where the repair truck should go and whether an installer or line technician is required to fix
the plant fault.
The equalization coefficient data may be extracted from a database, or alternatively the data may be
obtained real-time by polling.
Digital signal processing is performed by processing one CMs equalizer data with another CMs equalizer
data. Two methods are discussed. A first method uses complex frequency domain division of coefficients,
where a resulting flat frequency response means a perfect match. A second method is simpler complex
time-domain coefficient subtraction, followed by a restoration of the main tap.
6.7.6.1 Process:
1. Determine all the MAC addresses connected to a node. This can be done by connectivity records, or by
examining the MAC addresses that are connected to an upstream interface.
2. For each MAC address, obtain CM coefficient data and eliminate invalid responses. This results in a
reduced node list, with all CMs having valid coefficient data. It is now desirable to reduce the number
of match computations, because the number of match computations is proportional to the number of
CMs squared. (The number match calculation for a typical nodes population, while not negligible, can
be done in several seconds with modern computers.)
3. CMs must also belong to the same logical channel, including the same center frequency and same
bandwidth. Optionally, eliminate CMs that have unimpaired responses. That is, if the main tap to all
other tap energy (MTR) is below some threshold, such as 25dB, there is no serious echo. This results in
a node list with all CMs having echoes needing to be matched, if possible. (Note that if a very low
match threshold is used, CMs coming out of the same factory or of the same design will match.)
4. Going round-robin fashion, process each CMs coefficients with each of the other CMs coefficients
and compute a single match value for each match pair. If a match value is above some threshold (such
as 18dB), indicating the two unit match, a match result of 1 is set. Otherwise a match result of 0 is set.
Match results may be stored in a square matrix. If a nodes list of CMs needing to be processed is 100
CMs, 10,000 comparisons will need to be computed, resulting in 10,000 match values. See Table 21 for
an example 20 x 20 matrix created with a match threshold of 18 dB. Because every unit matches
perfectly with itself, a diagonal line of 1s is obtained. Note in Table 21 for an example 20 x 20 matrix
created with a match threshold of 18 dB. Because every unit that units 0 and 1 match, units 3 and 9
match, and units 11 and 17 match. More on matching processes later.
5. Convert the matrix into a symmetrical triangular matrix by forcing all matching pairs to agree. For
example, if unit 11 matches with unit 17, unit 17 is forced to match with unit 11.
6. From the matrix form groups of CMs with matching coefficients, and plot them on a GIS map. One
group-forming strategy is to remove CMs from the pool once they are in a group. Another strategy is
to incorporate GIS data to prevent a mismatch. That is, a distant CM probably found its way into a
group accidentally.
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7. Create work tickets for line technicians for each matching group.
8. Create work tickets for service technicians (or installers) with single homes having unmatched bad
responses.
6.7.6.2 Frequency Domain Division Method to Determine If Two CMs Responses Match
One method that can be employed to see if two units have matching responses is to just look at or
eyeball a plot of the complex coefficients in either in the time domain or in the frequency domain. This
is complicated by the coefficients being complex with both real and imaginary components, so a two-
dimensional plot can be hard to interpret. So despite the human eye being a versatile instrument, it is
difficult for the human eye to establish a single number that quantifies a difference between two similar-
looking responses. Other less-effective methods that could be used are to numerically measure the ripple
of the responses, or use the frequencies of peaks and troughs in the responses.
A simpler method is to perform a de-convolution with a frequency domain (FD) division of one units FD
coefficients with the other units FD coefficients. If two responses are exactly the same, a resulting
quotient frequency response will be unity at all frequencies, with a flat phase response at zero degrees.
This method is essentially a calibration process, with the denominator unit being used as a reference
value. De-convolution is a standard Matlab function, and is most efficiently performed in the FD.
Example:
Assume the 24 coefficients from the MIB (time values) are zero-padded out to 32 and converted with a
FFT, giving 32 frequency domain points.
Figure 34 is a plot of a set of coefficients for cable modem A with about a 14 dB T-spaced echo. The main
tap on the plot has been barrel-rotated (circular) from index 8 to 0. The main tap has a value of
approximately 1.0, but the vertical scale has been compressed to 0.2 to enhance the values of the taps on
a linear scale. The ratio of the energy in the main tap to all other taps combined is 14.09 dB for modem A.
The corresponding correction frequency response is shown is Figure 35. Note that the frequency
response of the physical channel will be approximately a frequency domain inverse of the response shown
in Figure 35.
Figure 36 and Figure 37 are the corresponding frequency responses of Figure 34 and Figure 36 look alike in
the time domain, and responses of Figure 35 and Figure 37 look alike in the frequency domain. The ratio
of the energy in the main tap to all other taps combined is 15.3 dB for modem B.
Figure 38 is a quotient frequency set obtained by dividing each coefficient in Figure 35 by a same-
frequency coefficient in Figure 37. Thus, if a frequency domain coefficient in Figure 35 is .55 at an angle of
130 degrees, and the corresponding same-frequency coefficient in Figure 37 is 0.57 at 120 degrees, a
resulting coefficient in Figure 38 is 0.9065 (.55/.57) at an angle of 10 (130-120) degrees. If the coefficients
in CM A and CM B were identical, Figure 38 would have a response of 1.0 at zero degrees at all
frequencies.
At this point, a 32-point IFFT is employed to find an impulse response (time domain) associated with the
frequency-domain quotient response associated with Figure 38, and a resulting time plot is shown in
Figure 39 If the two responses are absolutely identical, the impulse response would be 1.0 real and 0.0
imag at index 0 and 0.0 real and 0.0 imag (MTR) at every other time index. The units are matched if the
ratio of energy in the main tap to the energy in all other taps is below some threshold, such as 25 dB. (In
general, it is good to make the threshold level adjustable.)
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Experience has shown that some CMs that are experiencing a common hard-line echo may also be
experiencing a unique in-home echo. The presence of an in-home echo may cause the matching process to
fail for this house. This problem can be mathematically remedied by zeroing-out the close-in taps on
either side of the main tap, thereby eliminating the energy of the house echo. This method only works
well when the hard-line echo is of a relatively long duration.
In digital signal processing, equivalent processing can be done in either the time domain or frequency
domain. Time domain convolution is functionally equivalent to frequency domain multiplication.
Matching code is available in the CableLabs member-accessible code repository.
Table 21 - A Match Result Matrix for 20 CMs
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
7 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
8 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
9 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
10 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
13 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
17 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Table 21 indicates a good match (18 dB or greater); a 0 indicates less than a good match.
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0.2
T.D. Numerator
0.15
0.1
0.05 REAL
IMAG
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
-0.05
-0.1
-0.15
Main tap is 1.0, but vertical axis is clipped at 0.2 to enhance other taps on linear vertical scale. MTR = 15.3
dB
1.6
F.D. Numerator
1.4
1.2
0.8 REAL
0.6 IMAG
0.4
0.2
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
-0.2
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0.2
T.D. Denominator
0.15
0.1
0.05 REAL
IMAG
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
-0.05
-0.1
-0.15
Main tap is 1.0, but vertical axis is clipped at 0.2 to enhance other taps on linear vertical scale. MTR =
14.09 dB
1.6
F.D. Denominator
1.4
1.2
0.8 REAL
0.6 IMAG
0.4
0.2
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
-0.2
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1.2
F.D. Quotient
1
0.8
0.6 REAL
IMAG
0.4
0.2
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
-0.2
Figure 38 - A Quotient Set in the Frequency Domain for Modem B Divided by Modem A
NOTE: Because CM A and CM B are experiencing the same echo, the quotient set is relatively flat.
0.2
T.D. Quotient
0.15
0.1
REAL
IMAG
0.05
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31
-0.05
Main tap is 1.0, but vertical axis is clipped at 0.2 to enhance other taps on linear vertical scale. MTR = 27.3
dB, so the match is excellent and both modems are seeing the same echo.
6.7.6.3 Method 2: Time Domain Subtraction Method to Determine If Two CMs Responses Match
This method is conceptually simpler than the frequency domain division method, but produces similar
results.
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1. Take the 24 time domain coefficients from two CMs and normalizing the responses by scaling. For
example, if the main tap target is 2048, divide all complex coefficients by 2048 to make a unity
(approximately) main tap.
2. Then perform a complex subtraction of each time domain coefficient. Make one response the
subtrahend and the other response the minuend. This will normally cancel the main tap, which
must be restored.
3. Restore the main tap. There are a number of approaches to restore the main tap. A first method is
simply to make it 1.0 real and 0.0 imaginary. Another is to use the main tap of the subtrahend or
the main tap of the minuend. Another method is to use a conservation of energy approach, and
subtract a sum of all other taps energy from unity. This yields a residual energy, and the main tap
is the square root of the residual energy, which should be a value just under 1.0.
The following four listed states describe the condition of the plant and the performance of the
measurement devices for different scenarios operators may encounter in the field.
State 1. Adaptive equalizer tool is working properly and plant is within acceptable limits.
State 2. Adaptive equalizer tool is working properly, and plant exhibits severe linear distortion.
Plant is stable
Plant is unstable (intermittent or trending)
State 3. Adaptive equalizer tool is working properly, but CMTS/CM is reacting badly
Transmission characteristics in channel have resulted in no solution for CM coefficients (e.g., a
deep suck-out or echo is too long or too severe)
Upstream impulsive noise is causing wrong or unstable adaption.
CM needs to be replaced
State 4. Adaptive equalizer tool is not working correctly because of equipment design or configuration.
CMs are giving wrong MIB data, but working properly.
CMs are giving wrong/no MIB data and not working properly.
Wrong configuration of CMs or CMTS.
The CMTS is not configured for adaptive pre-equalization in the upstream
CM includes DOCSIS capable devices STBs and MTAs
Distortion red = static or trending or intermittent
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Extensions
4a. in Step 4, the customer information is not located.
Trouble is escalated to billing department for account reconciliation.
4b. in Step 4, the modem or CMTS do not support equalization analysis.
Trouble resolution reverts to conventional process.
5a. in Step 5, analysis data shows no trouble present.
Customer account is noted for future reference
2. Proactive monitoring is escalated to a higher rate
5b. in Step 5, customer has multiple devices at premises.
1. All devices are analyzed for similar distortion characteristics
1a. multiple devices share distortion - common fault is noted in analysis
1b. Single device demonstrates distortion - scope of analysis is narrowed to in home
5c. in Step 5, adjacent homes may also be analyzed
1. All devices within a specified radius are analyzed for similar distortion characteristics
1a. multiple customer devices share distortion - common fault is likely to be at or above the tap.
1b. single customer devices demonstrate distortion - fault is more likely to between the tap and
something in the customers home.
Variations
1a. in Step 1, proactive monitoring may provide use case trigger.
1b. in Step 1, automations such as an interactive telephone system may provide use case trigger.
2a. in Step 2, the Support User role may be implemented as an automated telephone system.
3a. in Step 3, the customer identification may be any one of MAC, telephone number or account
number.
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Frequency
Use case is executed per each trouble call, day of install or subject to the frequency of proactive
monitoring.
Assumptions
Users of the system must have basic knowledge of troubleshooting cable service problems.
Users must have required access and training of the analysis tools.
Special Requirements
All systems must support authentication and encryption pursuant to corporate security standards.
Issues
1. Distance calculations are preliminary, subject to market specific conditions and trial findings.
2. Distance estimates actually describe the distance between two impedance mismatches
(reflectors). In the case of in or near home, the assumption is made that one of the reflections is
within the subscribers home. This may not always be the case however the majority of the time,
this holds correct. There will be some cases where an outside plant issue may be incorrectly
characterized as in or near home problem.
To do
1. Validate use case in arid climates with less water ingress and corrosion.
2. Track distance estimates with actual problems found to identify opportunities of improvement in
the distance calculations.
Visualizations
Figure 40 - Amplitude vs. Frequency Peak/Valley of 10.55 Db with Echo Present in Impulse Response
Figure 41 - Entire Upstream Scan Shows No Similar Signatures Shared by Other Modems
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Post Conditions
Success end condition
Reactively, the problem was identified and repaired to the satisfaction of the customer. Proactively,
the problem was identified and repaired before the customer perceived a problem. Customers
modem and entire node show improved performance.
Failure end condition
Intermittent ingress such as impulse may no longer be present. Modem fails to demonstrate any
actionable performance metrics. No remediation of problem, customer may experience recurrence or
deterioration of service.
Trigger
Proactive alert identifies possible service affecting problem OR reactive alert, customer calls with
trouble.
Main Success Scenario
1. Customer calls with service trouble.
2. Support User initiates analysis tool, providing customer identification.
3. Customer identification is used to obtain the modem MAC address and CMTS for the customer.
4. MAC address is used to query both the modem and CMTS for performance information.
Reference SD-PNM200 for software sequence. (Appendix VI)
5. Performance data is analyzed to obtain the distortion present at the CMTS after equalization.
6. Support User evaluates performance of all modems on the same node.
7. Support User determines that only the single customer demonstrates a noisy response.
8. Customer is asked to tighten connectors and remove extra cable or splitters.
9. Support User rescans device for performance information and perceives that the problem has
been resolved.
Extensions
4a. in Step 4, the customer information is not located.
2. Trouble is escalated to billing department for account reconciliation.
4b. in Step 4, the modem or CMTS do not support equalization analysis.
2. Trouble resolution reverts to conventional process.
5a. in Step 5, analysis data shows no trouble present.
3. Customer account is noted for future reference
4. Proactive monitoring is escalated to a higher rate
6a. in Step 6, modems on same node may also be analyzed
2. All devices sharing the common upstream interface are analyzed
1a. multiple customer devices share ingress one or more points of ingress need to be resolved.
a. Trouble is escalated to Dispatch for maintenance scheduling
1b. single customer device demonstrates noisy response likely impedance problem caused by
loose, damaged or corroded connectors or cable.
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Variations
1a. in Step 1, proactive monitoring may provide use case trigger.
1b. in Step 1, automations such as an interactive telephone system may provide use case trigger.
2a. in Step 2, the Support User role may be implemented as an automated telephone system.
3a. in Step 3, the customer identification may be any one of MAC, telephone number or account number.
Frequency
Use case is executed per each trouble call, day of install or subject to the frequency of proactive
monitoring.
Assumptions
Users of the system must have basic knowledge of troubleshooting cable service problems.
Users must have required access and training of the analysis tools.
Special Requirements
All systems must support authentication and encryption pursuant to corporate security standards.
Issues
3. Magnitude of equalized response ripples from the CMTS need to be correlated to concrete BER /
MER values. Pending lab work.
To do
3. Better correlate the perception of noise with unstable equalizer operation. This is reproducible
with corrosion.
Visualizations
Figure 44 - Multiple Modems on the Same Upstream Demonstrate the Effects of Ingress
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Group of CMs
Expected Outcome: Resolved Issue (non-main adaptive equalizer tap or coefficient energy
reduced)
5. CMTS having issues due to equalization. Unable to compensate for channel. Micro-reflection too
long or no inverse solution, e.g., notch in channel. Upstream burst noise interfering with the
correct ranging of CMs coefficients. State 3.
Actors: Technician, NOC, CSR, HE Tech
External Event: Distortion red, other indicators yellow or red
Reactive/High distortion detected
Group of CMs
Expected Outcome: Fix cause of impairment
6. QA for accessing a node health score. Goes along with upstream MER (on a per CMTS port or per
CM basis). States 1 and 2.
Actors: Technician, NOC (QA)
External Event: Periodic scan and alarms - Distortion red, other indicators red/yellow/green
Reactive and Proactive/High distortion detected
Group of CMs
Expected Outcome: Distortion removed
7. Identification or location of faults. Combine location technique with GPS data or plant connectivity
data. Accurate micro-reflection time delay is important. Condition 2. (Subset)
8. Qualifying an upstream for a wider channel RF bandwidth or higher order modulation.
Qualification can also be done to verify a service level agreement (SLA). States 1 and 2.
Actors: Initially NOC, then technicians
External Event: Distortion red, other indicators yellow/green
Use higher order modulation and wide bandwidth channel as reference
Generally Proactive/High distortion detected
Group of CMs
Expected Outcome: Node qualified
9 CSR quick check. See if something abnormal is going on, and if the neighbors have the same
problem. All Conditions
Actors: CSR, Technician
External Event: Customer complaint
Reactive/High distortion detected
1 device possible others
Expected Outcome: Trouble ticket or no distortion problem, service call avoided
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6.9 Post-equalization
As its name indicates, post-equalization is the process of distortion compensation after the signal has been
received. In the cable environment, post-equalization has been used mostly in the downstream direction
where a CPE device always receives a continuous signal coming from one location, usually the headend.
That fixed location signal source simplified downstream distortion compensation implementation using
adaptive equalization at the receiver. In the upstream direction the upstream signals come from multiple
sources. Transmission is bursty and one burst may have suffered a different distortion from the next
because the upstream paths traversed may be different. A post-equalization approach would require the
receiver to compensate for distortion on a per burst basis. Early in DOCSIS, it was deemed that a post-
equalization approach would be a significant processing burden on the CMTS, which led to the
implementation of the upstream pre-equalization approach covered in this document. Processing
capabilities improvements have enabled the implementation of per burst equalization which is now
common in CMTSs. The advantages and disadvantages of pre- versus post-equalization are discussed next.
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Superior equalized MER capability compared to that provided by post-equalization when the
channel is at the upper edge of the return path spectrum. The superiority is also a function of the
depth of the return path amplifier cascade
Another advantage of pre-equalization over post-equalization is that throughput is somewhat
higher when pre-equalization is used because there is no need to equalize the data transmission
burst. This is related to the difference in the length of the data burst preamble.
Pre-equalization is beneficial to virtually all DOCSIS 2.0 and DOCSIS 3.0 services. In some cases there would
appear to be some instability or inconsistency in the metrics being reported when using pre-equalization.
Some causes for such behavior are discussed next.
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If there is sufficient headroom for the cable modem to increase its upstream transmit level, then there is
no penalty for the significantly improved performance. If the cable modem does not have sufficient
margin to increase its transmit level to the correct amount then the CMTS will only allow as much low
input signal level to exist as was defined in the CMTSs operating configuration.
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equalizer noise enhancement penalty becomes more significant to the point that the post-equalization
mode of operation total available or usable bandwidth on a given return path becomes much less than
when using pre-equalization.
Generally speaking, much poorer estimate for both amplitude roll-off and group delay distortion when
attempting to extract the information from a single equalized data burst for any given cable modem.
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Spectrum analyzers have been used by cable operators for decades for routine maintenance and
troubleshooting. However, spectrum analyzers are expensive instruments, so they have not typically been
widely available to field personnel. Technicians could only imagine having a spectrum analyzer in every
home.
FBC is a relatively new concept that takes advantage of low-cost discrete Fourier transform (DFT) and fast
Fourier transform (FFT) technology to support spectrum analyzer-like functionality in customer premises
equipment such as cable modems.
Integrated spectrum analyzer-like functionality is supported by the latest Broadcom and MaxLinear CPE
silicon. The CPEs spectrum data can be accessed remotely using simple network management protocol
(SNMP) or similar, allowing a cable operator to see where ingress or other impairments might be
problematic. Figure 47 shows an example of FBC, in which FM and LTE ingress are visible.
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Figure 47 - FBC Display Showing FM and LTE Ingress (circled) in the Downstream Spectrum of a Cable
Network
Problems can be identified by evaluating the RF spectrum without rolling a truck. If a sufficient number of
FBC-equipped devices are available in subscribers homes, it may be possible to determine the
approximate location of the source of a given impairment. A technician can be dispatched directly to the
suspected problem area, simplifying troubleshooting and saving time.
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Frequency
Capture Square Domain
Trigger Root Samples
Digital Tuner (Magnitude)
Figure 49 shows a block diagram of a digital spectrum analyzer which may reside in a cable modem or
CMTS. The input signal enters at the left of the diagram; this signal is the full upstream or downstream
band of the cable plant. An analog front end amplifies the signal and provides RF gain control. A high-
speed analog-to-digital converter (ADC), typically 2.5 giga-samples per second (Gsps) or higher, provides
digital samples of the signal. A digital tuner, consisting of a digital oscillator and lowpass filter, selects the
desired analysis band around a specified center frequency. The signal from the selected band is applied to
the FFT, which multiplies the signal by the DFT matrix. Each bin of the FFT output comprises a complex
value consisting of two numbers, real (I) and imaginary (Q), giving the correlation of the input signal with
the particular frequency corresponding to a single row of the DFT matrix. Typically a spectrum analyzer is
only concerned with the magnitude, not the phase, of the FFT output. So, the power (magnitude-squared)
of each bin is computed, that is, I2 + Q2 for each bin. If spectrum smoothing is to be applied, the
previously-described process is repeated with a fresh set of data from the same band, and the power
values from several captures are averaged at each bin location. The smoothed bins are converted to
decibels by taking 10*log10 of each bin power value. These decibel values, one for each frequency bin, are
displayed as the spectrum of the input signal.
Note that if the entire band is able to be processed as a single analysis band, the tuner shown in Figure 49
is not necessary. However, if the band is being analyzed in segments, then the tuner is used to step
through a sequence of analysis segments of the band, and the individual spectrum segments are spliced
together to produce the overall wideband spectrum.
This section includes several examples of FBC screen shots as seen at the cable modem. The horizontal
axis in each figure is frequency in MHz, and the vertical axis is in dB. Images are courtesy of Comcast.
7.2.1 Ingress
Technicians can look at a captured spectrum display for indications of the presence of downstream ingress
(and in some cases, direct pickup). If a sufficient number of FBC capable devices are available, it may be
possible to roughly isolate the area of plant where the ingress is entering the network. Figure 50 shows an
example of visible ingress in the FM band (left edge of figure) as well as in the LTE band (near the right end
of the figure).
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The most serious problem is the suckout (notch) visible between 697 MHz and 731 MHz. The suckout,
which is about 18 dB deep, affects a half dozen QAM channels. Another problem evident in the display is
called adjacency, where a group of eight channels in the roughly 600 MHz to 650 MHz range are several
dB higher than other channels in that part of the spectrum, likely caused by incorrect narrowcast injection
levels. A third problem is a QAM channel near 563 MHz that is a few dB lower than the adjacent channels.
A fourth problem also is level-related, in the vicinity of 250 MHz.
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Standing waves, also known as amplitude ripple, are caused by impedance mismatches in the RF signal
path. Standing waves are usually easy to see in a FBC display. Figure 53 shows several examples of
standing waves. Of particular interest is the combination of two standing waves in the lower right screen
shot.
7.2.5 Rolloff
Rolloff is a non-flat loss of signal level-versus-frequency at or near the lower or upper end of the RF
spectrum. When rolloff occurs at the upper end of the downstream spectrum, the cause can be active
device misalignment, active or passive device damage, presence of older cable or equipment in the
network designed for a lower upper frequency limit than the networks existing operating frequency
range, and so on. Figure 55 shows examples of rolloff at the upper end of the downstream spectrum.
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7.2.6 Tilt
Tilt describes the condition where signal levels vary from low to high in a more or less linear manner as
frequency increases (positive tilt), or from high to low in a linear manner as frequency increases (negative
tilt). Depending on the location in the plant, tilt may be desirable for example, at the output of an
amplifier. Ideally the frequency response at the input to CPE should be flat, but in some cases the
response may be tilted excessively for a variety of reasons. Figure 56 shows examples of negative and
positive tilt.
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defective components, cold solder joints, loose modules (or module covers), loose or missing screws, and
so forth. Figure 57 highlights examples of resonant peaking.
7.2.8.1 How to Capture Data from Devices Equipped with FBC Functionality
7.2.8.1.1 Design Considerations
Capturing spectrum information requires SNMP read/write access to the cable modems, which generally
are on RFC 1918 address space. This means that direct access from a workstation is unlikely. In general,
implementations will consist of a server (or servers) that has access to the non-routable IP addresses used
by the modems, and has an external IP address or a static network address translation (NAT) that allows
external clients access to it so that the server can make the SNMP requests on behalf of the clients. The
clients could be web based, mobile, or desktop software. An operator likely will already have one or more
OSS servers that fits these requirements, but the existing servers may or may not have sufficient capacity
for the additional load. Additionally, the implementation of FBC will be done for a somewhat different
operational group and in many cases a different department - than the primary OSS users, since field
technicians are going to be much more likely to use this data than some of the other normal OSS tools. A
good exercise is taking a look at how field technicians currently use their hand held meters, as well as
thinking about other uses for a remote spectrum display that aren't practical today.
There are several considerations that development teams need to understand before getting started.
Security is a large issue for this kind of system, because it is necessary to perform SNMP SET operations to
enable the capture, and have access to parts of the network that aren't normally reachable. Some sort of
server side authentication system should be used to ensure that only authorized users can access and use
the server. In some cases the FBC requests will be coming from devices over untrusted networks, such as
field technicians using tablets or smart phones. This could be resolved by requiring virtual private network
(VPN) connections before allowing usage, or with strong authentication coupled with transport layer
security (TLS) or other encryption. Locking and session management are also needed, because having
multiple users trying to perform a capture on the same device can cause issues for that device. Other
multiple user issues could occur if the device changes frequency or some other variable in response to one
user while another is trying to interpret results for a different setting. An important consideration is how
to deal with the data. In general, a maximum granularity capture across the widest window will generate a
10-20 kbps stream of data. By itself this isn't a large data stream, but it does mean that it's not practical
for most organizations to collect this data for all modems and then store the information in a database for
analysis the way that is typically done for OSS functions. If a user is only going to work on a real time
display then this consideration isn't particularly problematic, but if the data is for proactive analytics then
it's a large challenge.
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7.3 Method to Find a Time Response from an IFFT when Phase Data is Not
Available
The FBC is used by cable modems and set-top boxes to provide magnitude-only spectral data about RF
path conditions in a remote location, such as a home. In some cases, the downstream channels being
monitored are digital channels, such as 64- or 256-QAM. In other cases the signals are analog signals or
noise and ingress.
This method applies to blocks of QAM signals to identify the existence of an echo tunnel that causes ripple
in the frequency response. See `
7.3.1 Method:
1. Pick a block of averaged (smoothed) contiguous digital signals, as many as possible. For example,
each 7.5 MHz block of frequency domain data may have 256 spectral components, and multiple
blocks are pasted together to make a wide spectral response.
2. Extract samples from the lower band edge of the lowest QAM signal to the upper band edge of
the highest QAM signal, and convert the values into linear values. Use these values as I (in-phase)
components.
3. Use zeroes for all Q (quadrature) values.
4. If necessary zero-pad the values to fill out a 2^n IFFT transform, such as 16,384 or 4096.
5. Optionally, a window should be applied to the data.
6. A frequency region with another signal, such as an analog RF carrier, or vacant band can be filled
in with a straight line connecting the channel just above the vacant band to the channel just below
the vacant band.
7. Perform an IFFT to put the data into the time domain.
8. Transformed data will be symmetrical due to not providing quadrature values. You can discard the
image.
9. A DC term will be present. Comb teeth will be present every 166.67 ns due to the notch between 6
MHz channels.
10. If there is an echo in the frequency response, there will be a ripple in the frequency domain. The
ripple will linearly transform to an impulse located among the comb teeth. If the echo is an exact
multiple of 166.67 ns, it cannot as easily be observed. The delay between the main impulse and
echo is the round trip time of an echo tunnel, corrected for velocity of prorogation velocity of
cable. Since you know the shape of the teeth on the comb, they can be removed by subtraction.
This method is valuable because the wide bandwidth of the multiple QAM signals makes for exceedingly
accurate time resolution, so the cable operator makes a hole to repair a buried cable, not a trench.
Another anticipated method to remove effect of the notches between carriers is to interpolate over the
notches. Yet another method to reduce the effect of the notches is to equalize the magnitude response,
but equalization cannot go all the way to zero due to negligible energy in the notch.
This method could also work with analog spectrum analyzers, for example, using GPIB or other interface
technology supported by the analyzer to extract the magnitude data.
Note that it should not work to detect group delay problems, since there is no phase information
available.
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The code to do this is in the CableLabs Spectrum Impairment Detector (SID) which is in the PNM
repository.
Figure 59 - Impulse associated with frequency domain ripple is in among the teeth of the comb, which come
every 166.67 nS.
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8 CPD DETECTION
8.1.1 Common Path Distortion Detection
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MHz and so on. In Europe and other regions using 8 MHz channel spacing, the mixing products appear
every 8 MHz: 8, 16, 24 MHz, and so on. Third order distortions result in other frequencies that are formed
by the difference between one carrier frequency and two times another carrier frequency and thus
produce beats at 9, 15, 21, 27, 33 and 39 MHz, for a North American or other system with 6 MHz
downstream channel spacing [Howard NCTA]. Because of the mixing of aural and visual carriers, additional
beats can appear at 1.25 MHz on either side of the 6 MHz-spaced second order distortion beats.
Figure 60 shows a low resolution spectrum analyzer display of CPD with both second- and third-order
beats every 6 MHz. Each group of beats has three components: The second-order beats are the middle
(and typically taller) beat cluster in each group, and the third-order beats are the shorter beats on either
side of the second-order beats. The actual appearance of CPD beats in a cable networks upstream
spectrum depends on the nature of the diode-like junction that is generating the beats. In some cases only
second-order beats appear, sometimes only third-order beats appear, and sometimes both types are
visible, as shown in Figure 60.
A higher resolution view can be produced using a spectrum analyzer or other monitoring technology with
a suitably narrow resolution bandwidth, or by capturing the upstream with a digital sampling oscilloscope
or real time FFT analyzer. These captures reveal much more structure in the CPD that is due to not just the
difference frequencies between visual carriers, aural carriers, or combinations thereof, but also the beat
clusters caused by frequency offsets for aeronautical band operation and even the variations in
downstream carrier frequencies. Figure 61 and Figure 62 show this detailed CPD structure.
Figure 61 - Detailed Structure of CPD Captures Showing Difference Frequencies Around Beats at 24 MHz
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-20
-30
-40
-50
Figure 62 - Detailed Structure of CPD Captures Showing Difference Frequencies Due to 12.5 And 25 KHz FAA
3
Offsets for Aeronautical Band Operation
Note that there may be a raised noise floor due to the QAM nonlinear products, as will be seen next.
In cable networks with all-digital downstreams, it can be more difficult to detect CPD because it lacks the
narrowband structure of CPD from analog signals. With digital downstream signals, the mixing products
are lower in power spectral density and spread out and form a raised noise-like floor that may nonetheless
have some structure that can be seen in upstream RF spectrum captures. There is a CPD from analog
downstream signals is therefore narrowband and of a known structure, and can be easily detected using
upstream RF spectrum captures and observing specific beat frequencies known to result from CPD. When
the downstream spectrum has both analog and digital signals, it is still possible to detect CPD using this
approach, since the analog carriers will continue to produce the same misconception that in a mostly- or
all-digital network, CPD disappears; however it doesnt go away, it just takes on a different appearance. An
example of CPD caused by digital downstream signals is shown in Figure 63.
To understand how the structure arises for CPD from digital signals, it is easiest to develop the CPD
structure in the frequency domain using the convolution theorem from Fourier analysis, whereby
multiplication in the time domain can be represented as convolution in the frequency domain, and vice
versa. So a second order CPD nonlinearity means the signal is multiplied by itself or squared in the time
domain, which is like convolving its spectrum with itself in the frequency domain. Convolving a QAM
haystack with itself produces a triangular shaped resulting spectrum that is twice the bandwidth of the
original QAM haystack.
Figure 3. CPD in a network with both analog and digital downstream signals. Yellow
marks show the gaps between each QAM signal-like beat. Image courtesy of Viavi
Solutions (formerly JDSU).
3
Detection and classification of RF impairments for higher capacity upstreams using advanced TDMA, D. Howard, NCTA
Technical Papers 2001, found on http://www.nctatechnicalpapers.com
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Figure 63 - CPD In A Network With Both Analog And Digital Downstream Signals. Yellow Marks Show The Gaps
Between Each QAM Signal-Like Beat. Image Courtesy Of Viavi Solutions (Formerly JDSU)
The actual QAM downstream spectrum is a sequence of QAM haystacks with small gaps in between them.
In this case, the convolution of two QAM trains of spectra produces a periodic CPD spectrum of peaks
that correspond to difference frequencies where the QAM haystacks are in alignment. Figure 64 shows
this expected CPD behavior for all-digital downstreams. Note the peaks at 6, 12, 18, 24, 30, 36 and 42
MHz.
Figure 64 - Second Order Modeled CPD Behavior From All-Digital Downstreams (Not Scaled.
When there are both analog and digital downstream signals, the analog carriers effectively sample the
QAM haystacks during the convolution process, thereby reproducing them in the second order CPD
spectrum. This results in reproducing the QAM haystacks themselves, and the gaps between them every 6
MHz in the CPD spectrum, as seen in Figure 63.
As an example of the combination of full band RF capture capabilities with a CPD model based on
convolution of spectra, Figure 65 shows an example RF spectrum capture using PNM technology in a node
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that was suspected of having nonlinear behavior. Figure 65 shows just the upstream RF frequency band of
this capture, which highlights the structure of the upstream RF band.
Figure 65 - Full Band RF Capture From Example Node With Suspected Nonlinearity, Entire Spectrum
Figure 67 was produced by taking the RF capture and convolving it with itself and then convolving it with
the first convolution to produce a 3rd order CPD spectrum in the manner described in Howard [NCTA 2001
paper]. The overall structure in Figure 67 is well reproduced by the convolution model of CPD using full
band RF capture data with PNM technology.
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Figure 67 - Simulated 3rd Order CPD Nonlinearity From Example Node (Not Scaled)
4
http://www.scte.org/documents/pdf/standards/ANSI_SCTE%20109%202010.pdf
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nd
Figure 68 - Active CPD Measurement Technique Whereby an Injected Carrier Is Used To Produce a 2 Order
Difference Frequency of 40.5 MHz
Finally, to determine the actual location of the CPD in the plant, two methods are possible. First, a third-
party CPD detection and troubleshooting tool is available from at least one vendor. 5 The troubleshooting
tool produces a highly accurate time delay associated with a round-trip distance to the source of the
impairment, thereby enabling the determination of the actual location of the CPD impairment. It does so
by using a passive radar-type approach and an associated correlation process to detect CPD and
determine the distance to the impairment source.
Here is how it works: Test equipment is connected to a network test point, and as QAM channels
propagate through the network and pass the connection point, the radar captures samples of the QAM
channels, and presents the samples to a built-in CPD simulator such that a CPD reference signature is
created at the connection point of time = 0. The QAM signals continue to propagate through the network,
and when they pass through a source of CPD, intermodulation products will be created at many
frequencies. Some of the intermodulation products will travel back via the return path, and importantly,
the spectral characteristics of the intermodulation signal will be the same as the reference signal
generated at the connection point. The passive radar then looks at the return signals as they pass by the
connection point and performs a correlation process whereby the reference signal is time shifted a few
thousand times, and compared to the return signal. At some time delay the two signals will be statistically
the same (correlated), and with certainty the source of the CPD will be located at half of that time delay
distance. The time distance is then easily converted to the linear distance and the distance to the source is
identified.
5
Arcom Digital has a product called Hunter for detecting and locating common path distortion
(http://www.arcomlabs.com/4HunterPlatform.html).
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Since the correlation process essentially integrates the signal in time (analogous to video averaging on a
spectrum analyzer), the noise floor of the measurement is significantly below the cable network noise
floor. As such, impairments that may not yet be visible on a return spectrum analyzer in the form of an
elevated noise floor (digital CPD) or recurring 6 MHz or 8 MHz spikes (analog CPD), are identifiable and can
be located and mitigated. The first screen capture in Figure 69 shows an example of CPD which is not yet
affecting the network performance, and the second screen shot shows the same source only two hours
later, where the CPD level increased by 26 dB such that it now affects network performance and is
deteriorating the return channel MER.
Since the source of CPD most often also creates an impedance mismatch, it is possible to use PNM
technology to locate the impairment in some cases where this is an echo cavity created by the CPD source
and another impedance mismatch.
CPD continues to be of interest to cable technical personnel for two reasons: First, it continues to occur
and when severe enough, it can affect the entire upstream and degrade performance. Second, as even
higher orders of modulation for the upstream are considered, especially as DOCSIS 3.1 is deployed, what
was an acceptable amount of CPD in the past may not be acceptable in the future. This is even more
important in all-digital plants since the broadband noise-like behavior of CPD cannot be easily mitigated,
even by DOCSIS 3.1s OFDMA technology. The good news is that cable operators who have deployed PNM
technology at scale, and aggressively fix the plant issues detected by PNM technology, report that CPD is
less of a concern now; by finding micro-reflections in the network and fixing them proactively, the
incidence of serious CPD appears to be on the decline.
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For more information on CPD causes and a description of it in analog-only plants, see Characterisation of
Common Path Distortions by Barry Patel, 6 and for the detailed structure of CPD and modeling of it, see
Detection and classification of RF impairments for higher capacity upstreams using advanced TDMA, by
Daniel Howard. 7
6
The Patel CPD paper can be found at http://cable.doit.wisc.edu/cable_resources.html. Scroll to near the bottom of the web page to
Report on Dynamic CPD.
7
The Howard CPD paper can be found at http://www.nctatechnicalpapers.com, use search or select the year 2001.
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9 CONCLUSION
This best practices and guidelines document covers different aspects of network maintenance that rely on
upstream pre-equalization and FBC to proactively maintain the CATV network. Even though the initial
purpose of this effort was to implement a network maintenance strategy that is able to take corrective
action before service is impacted, the outcome of this effort has also proven to be very powerful in
implementing and optimizing numerous reactive maintenance tasks present in day to day operations.
Reactive maintenance is defined here as maintenance triggered by any perceivable deterioration in service
performance.
Linear distortion including two types of micro-reflections and group delay distortion have been discussed
in detail, as well as the ranging process that CMTS and CM go through to sound the upstream channel and
compute the equalization coefficients. From these parameters the CM information indicates the estimated
distortion in the upstream path while the CMTS indicates the extent to which the distortion compensation
of the upstream path of a CM has been completed.
Interpretation of the CM/CMTS MIB data has been provided including the implementation details of a
universal decoder that translates all known CM MIB interpretations.
This document describes how to take advantage of pre-equalization analysis both in the time and
frequency domains. Other topics covered here include scalable data collection approaches; distortion
compensation capabilities of DOCSIS pre-equalization; pre-equalization calibration techniques, which
included the details of a short reference plant; severity assessment for static, trending and intermittent
distortion environments; definitions of key equalization metrics; extrapolation of coefficients for
neighboring channels; and use of FBC for troubleshooting plant problems.
Additional supporting information can be found in the Appendices.
A key outcome of this effort is the fault localization processes to pinpoint the problem location which
leads to reduced mean time to repair and improved reliability. This is obtained through the correlation of
the CATV network topology with the impairment-unique characteristics derived from the CM pre-
equalization data.
This gathered knowledge has been leveraged to implement use cases describing guidelines to resolve
proactive as well as reactive operational, engineering and maintenance issues.
Even though the emphasis here has been on leveraging pre-equalization, incorporation of additional
metrics and the correlation among metrics will increase the efficacy in troubleshooting network problems.
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Appendix I Tutorial
I.1 Nonlinear Distortions
Active devices such as amplifiers and optoelectronics are devices that do not operate perfectly linearly.
For example, the RF signals at the output of a perfect amplifier would be identical to the input signals, but
at a higher power level. The RF signals at the output of a real-world amplifier are increased to a higher
power level and are almost identical to the input signals, but are distorted somewhat by nonlinearities in
the amplifier. Nonlinear operation in an amplifier is caused by small-signal nonlinearities in the active
devices semiconductors, and by signal compression that takes place as higher RF output levels reach the
amplifiers saturation point. All of this means that a real-world amplifiers output includes both the
amplified signals and distortions. As the amplifiers RF output level is increased to even higher amplitudes,
the distortions get worse (think of a stereo that distorts the sound as the volume is turned up too high).
Nonlinear distortions of most interest to equipment manufacturers and cable operators include even
order distortions such as composite second order (CSO), odd order distortions such as composite triple
beat (CTB), and cross modulation (XMOD). One might think that as an amplifiers RF output level changes
by, say, 1 decibel (dB), the amplitude of the distortions also would change by 1 dB. But they do not.
CSO distortion amplitudes change by 2 dB for every 1 dB change in the amplifiers output level, while CTB
distortion amplitudes change 3 dB for every 1 dB change in the amplifiers output level. 8 Nonlinear
distortions get their name in part because of the nonlinear 1:2 and 1:3 signal-to-distortion relationship,
as well as from the fact that the distortions are a function of the active devices inherent nonlinear
operation. As RF output levels approach or reach the active devices saturation threshold, the distortion
amplitudes may begin to change at ratios other than the expected 1:2 or 1:3.
The tendency is to think of nonlinear distortions coming primarily from active devices whose output levels
are too high, as just discussed. Common path distortion (CPD) is an interesting class of nonlinear distortion
in that its often generated in a diode-like junction somewhere in the transmission path that is common to
both the forward and return, hence the name common path distortion. The culprit is typically corrosion of
some sort, where the corrosions oxide layer itselfwhich may be only a few molecules thickbehaves
somewhat like a diode. As you know, diodes are used to make electronic mixer circuits. The presence of
downstream signals at the diode-like corrosion-based mixer results in the generation of various second-
and third-order distortions. Many of those distortions appear in the return spectrum. For instance, in an
NTSC network, CPDs second order beat clusters may appear every 6 MHz: 6, 12, 18, 24, 30, 36 MHz and so
on. Third order distortions may appear 1.25 MHz either side of the 6 MHz-spaced second order
distortions. Sometimes only the second order distortions are present, sometimes only the third order
distortions are present, sometimes both are present, and sometimes CPD manifests itself as an elevated
noise floor.
In some circumstances the mechanism that generates CPD may also be a noticeable impedance mismatch
that creates a micro-reflection.
Nonlinear distortions can be generated in a cable networks passive devices, separate from the
mechanism that creates CPD. One example is passive device intermodulation, which occurs when
excessive RF levels saturate the ferrite material in, say, drop splitter toroidal transformers (the ferrite
material generally must have some residual magnetism present). Newer passive designs minimize passive
8
The ratios of desired signal amplitudes to CSO and CTB distortion amplitudes change by 1 dB and 2 dB respectively for each 1
dB change in amplifier output level.
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Time delay
4
3
2
1
0
Frequency
Figure I-1 - A Filter's Time Delay-Versus-Frequency Curve Often Has A Bathtub Shape
If propagation or transit time through a device is the same at all frequencies, phase is said to change
proportionally with respect to frequency. If phase changes proportionally with frequency, an output signal
will be identical to the input signalexcept that it will have a time shift because of the uniform delay
through the device. If propagation or transit time through a device is different at different frequencies, the
result is delay shift or nonlinear phase shift. If phase does not change proportionally with frequency, the
output signal will be distorted.
Delay distortionalso known as phase distortionis usually expressed in units of time: milliseconds (ms),
microseconds (s) or nanoseconds (ns) relative to a reference frequency.
Phase distortion is related to phase delay, and is measured using a parameter called envelope delay
distortion, or group delay distortion.
According to the IEEE Standard Dictionary of Electrical and Electronics Terms, group delay is the
[negative] derivative of radian phase with respect to radian frequency. It is equal to the phase delay for an
ideal non-dispersive delay device, but may differ greatly in actual devices where there is a ripple in the
phase versus frequency characteristic. 9
Group delay is expressed mathematically as
d
GD =
d
where GD is group delay in seconds, is phase in radians, and is frequency in radians per second.
Translation? If phase-versus-frequency response does not change in proportion to frequency, group delay
exists. In a system, network, device or component with no group delay variation or group delay distortion,
all frequencies are transmitted through the system, network, device or component in the same amount of
timethat is, with equal time delay. If group delay distortion exists, signals at some frequencies travel
faster than signals at other frequencies.
Group delay distortion exists if phase-versus-frequency deviates from ideal. But just what does that mean?
As an example, using a 100 ft. piece of .500 feeder cable, hardline coax installed in cable networks for
feeder applications has a velocity of propagation of around 87% (refer to the tutorial section on Velocity of
Propagation for more information). The speed of light in free space or a vacuum is 299,792,458 meters per
second, or 983,571,056.43 feet per second1 foot in about 1.02 ns.
In coaxial cable with a velocity of propagation of 87%, electromagnetic signals travel at a velocity equal to
87% of the free space value of the speed of light. That works out to 260,819,438.46 meters per second, or
855,706,819.09 feet per second1 foot in about 1.17 ns.
9
The IEEEs dictionary definition does not include the word negative.
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So, electromagnetic signals will travel 100 feet in a vacuum in 101.67 ns, and through a 100 ft. piece of
coax in 116.86 ns.
Wavelength () is the speed of propagation of an electromagnetic signal divided by its frequency (f) in
hertz (Hz). It is further defined as the distance a wave travels through some medium in one period of an
electromagnetic signal, or the distance over which a waves shape repeats. The period (T) of an
electromagnetic signal (in seconds) = 1/f, that is, the reciprocal of the electromagnetic signals frequency
in Hz. In a vacuum, wavelength in feet (ft) = 983,571,056.43/fHz, which is the same as ft = 983.57/fMHz. In
coaxial cable with 87% velocity of propagation, ft = 855,706,819.09 /fHz or ft = 855.71/fMHz.
For instance, the period of a 10 MHz sine wave is 1/10,000,000 Hz = 1x10-7 second, or 0.1 s. That means a
10 MHz signal takes 0.1 s to complete one cycle, or 1 second to complete 10,000,000 cycles. In a vacuum
an electromagnetic signal travels 98.36 ft. in 0.1 s. This distance is one wavelength in a vacuum for a 10
MHz signal. In 87% velocity of propagation coax, the 10 MHz signal travels 85.57 ft. in 0.1 s. This distance
is one wavelength in coax for a 10 MHz signal.
By calculating a given frequencys wavelength in feet, it can be said that a 100 ft. piece of .500 coax is
equivalent to a certain number wavelengths at that frequency! From the previous example, it stands to
reason that a 100 ft. piece of coax is equivalent to just over one wavelength at 10MHz. That is, the 10 MHz
signals 85.57 ft. wavelength in coax is just shy of the 100 ft. overall length of the piece of coax.
Consider the wavelength in feet for several frequencies in a vacuum and in our 100 ft. piece of coax, using
the previous formulas. Because of the cables velocity of propagation, each frequencys wavelength in the
cable will be a little less than it is in a vacuum. The number of wavelengths can also be figured out for each
frequency in the 100 ft. piece of coax. Finally, knowing that one wavelength (cycle) of a sine wave equals
360 degrees of phase, the total number of degrees of phase the 100 ft. piece of cable represents at each
frequency can be calculated. All of this is summarized in the following table.
Table I-1 - Frequency, Wavelength, and Phase Relationships In 100 Feet Of Coax
Next, plot the 100 ft. piece of cables phase-versus-frequency on a graph. In the example in Figure I-2, the
line is a sloped straight linethat is, phase varies proportionally with frequency.
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3000
x
2000 x
x
1000
x
x
0
0 10 2 3 4 5 6 7 8 9 100 11
Frequency (MHz)
Figure I-2 - Phase-Versus-Frequency For 100 Feet Of Coax
Finally, plot the time delay for each frequency through the 100 ft. piece of cable. The line in Figure I-3 is
the negative derivative of radian phase with respect to radian frequency. Its a flat straight line; because
the delay is the same at all frequencies, there is no group delay variation!
400
300
200
Time delay
100
0
0 1 20 3 4 5 6 7 8 9 100 11
Frequency (MHz)
Another way of looking at this is to say that the cables velocity of propagation is the same at all
frequencies! In other words, every frequency takes 116.86 ns to travel from one end of the 100 ft. piece of
cable to the other end. But what happens if something in the signal path causes some frequencies to
travel a little slower than other frequencies?
Look at the phase-versus-frequency trace (the sawtooth-shaped waveform) in Figure I-4. Where phase
does not vary proportionally with frequencythat is, where the sloped line is not straightgroup delay
variation exists. The bottom bathtub-shaped trace in the figure is group delay, plotted as frequency in the
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horizontal axis versus time (100 ns/div) in the vertical axis. The group delay trace reveals that a signal at 40
MHz takes about 300 ns longer to travel through the network than a signal at 20 MHz.
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where:
Z0 = coaxial cable characteristic impedance
D = inside diameter of shield
d = outside diameter of center conductor
r = dielectric constant
Consider 6-series coaxial cable, commonly used in cable subscriber drop applications. A typical nominal
impedance specification for 6-series subscriber drop cable is 75 ohms 3 ohms, with a nominal 85 percent
velocity of propagation. Assume the center conductor is 18 AWG (0.040 inch diameter), and the inside
diameter of the shield is 0.180 inch. The cables 85 percent velocity of propagation translates to a
dielectric constant of 1.3841 (see the tutorial section on Velocity of Propagation). Using the previous
formula, the calculated impedance Z0 of the 6-series cable in this example is 76.6 ohms, well within the
specified 75 ohms 3 ohms range.
Transmission line fundamentals typically are based upon a simplified model that includesas shown in
ZS = ZT =
Figure I-5a signal source S, a lossless transmission line T, and a terminating impedance comprising some
sort of load or termination L. The assumption is that all three components have the same characteristic
impedance Z, such that all power in the incident wave transmitted from the source is absorbed by the
load.
ZS = ZT =
Figure I-5 - Ideal Transmission Line Model
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In the real world the signal source, transmission line, and load rarely have the same impedance at all
frequencies. As well, the transmission line has attenuation which reduces the RF power of the signal(s)
passing through it. When the impedance of, say, the load L is different from that of the transmission
medium T (see Figure I-6), it is said that an impedance mismatch exists. An impedance mismatch causes
some or all the incident wave to be reflected back toward the source 10. The ratio of reflected to incident
voltages is known as the reflection coefficient , described mathematically as = E-/E+, where E- is the
reflected waves voltage, and E+ is the incident waves voltage 11.
The reflected wave interacts with the incident wave to produce standing waves, also known as amplitude
ripple. Impedance mismatches exist everywhere in our cable networks. Indeed, while the nominal
impedance of a coaxial cable network and its components is said to be 75 ohms, every connector,
amplifier, node, splitter, coupler, power inserter, feeder tap, terminator, and even the cable itself
represent an impedance mismatch of some sort. The question is just how severe are those impedance
mismatches? There are several ways to characterize the severity of an impedance mismatch. One is
known as voltage standing wave ratio (VSWR), defined as the ratio of the standing waves maximum
voltage Emax to its minimum voltage Emin along the transmission line:
VSWR = Emax/Emin
VSWR also is related to reflection coefficient :
VSWR = (1+||)/(1-||)
Another way to characterize the severity of an impedance mismatch is return loss (R), which is the ratio in
decibels of incident power PI to reflected power PR:
R = 10log10(PI/PR)
Consider a scenario in which the incident power is 20 watts, and an impedance mismatch causes the
reflected power to be 5 watts. The return loss is 10log10(20 watts/5 watts) = 6.02 dB. The relationship
between VSWR and R is given by VSWR = (10R/20 + 1)/(10R/20 1) and R(dB) = 20log10[(VSWR+1)/(VSWR-1)].
In this example, 6.02 dB return loss equals a VSWR of 3.0:1. Note that return loss is always a positive
number, since it is the number of decibels between the amount of power in the incident and reflected
10
For an overview of the mechanics of how an impedance mismatchspecifically an open or short circuitcreates a reflection, see
Impedance Mismatches and Reflections in the December 2005 issue of Communications Technology magazine.
http://www.cable360.net/ct/operations/testing/15296.html
11
Reflection coefficients are ratios of phasors and as such are complex quantities. Mathematically, = ||, where is the angle
of , and is the angle by which the reflected voltage leads the incident voltage. The magnitude of can vary from 0 to 1, where 0
indicates all power is absorbed by the load (no reflection), and 1 indicates 100% reflection from an open circuit, short circuit, or
pure reactance.
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signals. Some references (and test equipment!) show return loss as a negative number, but this is
incorrect.
The worst case impedance mismatch is a short circuit, open circuit, or pure reactance, all of which reflect
100% of the incident wave back toward the source. In these three cases R = 0 dB. When a perfect
impedance match existsthat is, when ZT = ZLall of the incident wave is absorbed by the load and R is
infinite (). While there are exceptions, most real-world impedance mismatches cause return loss to be
somewhere between 0 dB and , since impedance mismatches are rarely pure short or open circuits, and
a truly perfect impedance match with infinite return loss is more of a mathematical construct. From a
practical perspective, typical return loss values of components in cable networks vary from a few dB to 30
dB or more.
When multiple impedance mismatches exist in a transmission mediumone example might be two water-
damaged feeder taps in the outside plant separated by a span of feeder cablemultiple reflections occur!
Figure I-7 shows an example in which a +31 dBmV incident signal travels right to left from the upstream
output of the first water-damaged feeder tap (right side of figure) through a 100 ft. span of cable with 1
dB of loss. The first reflection occurs when the now +30 dBmV incident signal reaches an impedance
mismatchthe upstream input of a second water-damaged feeder tap (left side of figure)that has 7 dB
return loss. A +23 dBmV reflection is created (+30 dBmV incident signal 7 dB return loss = +23 dBmV
reflection), which travels back toward the first feeder tap that also has 7 dB return loss. The now +22
dBmV reflection is re-reflected at a level of +15 dBmV at the first feeder tap (+22 dBmV reflection 7 dB
return loss = +15 dBmV second reflection), which travels back toward the second feeder tap and arrives
there at +14 dBmV. And so on.
The scenario in Figure I-7 can be represented graphically as shown in Figure I-8.
The tall vertical line marked +30 dBmV represents the incident signal at the upstream input to the feeder
tap on the left side of Figure I-7. The second, somewhat shorter vertical line marked +14 dBmV represents
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the second reflection, also at the input to the first feeder tap on the left side of Figure I-7. The horizontal
separation between the two vertical lines represents the time delay between the +30 dBmV incident
signal and the +14 dBmV reflection. Assuming the 100 ft. span of cable has a velocity of propagation of
87%, RF travels through each foot of coax in about 1.17 nanosecond. Since the roundtrip distance for the
reflection is 100 ft. + 100 ft. = 200 ft., the second reflections time delay is 200 ft. x 1.17 nanosecond = 234
nanoseconds.
I.5.1 Reflection or Micro-reflection?
When an impedance mismatch causes some or all of the incident wave to be reflected back toward the
source, the reflected wave is called simply a reflection or an echo. In the world of high-speed data
communications over cable networks, the term micro-reflection is frequently used. A micro-reflection is
still a reflection or echo. Micro-reflection generally denotes a reflection with a short time delaythat is,
a close-in reflection whose time delay relative to the incident signal ranges from less than a symbol period
to perhaps several symbol periods.
As noted earlier in this tutorial, reflections (and micro-reflections) are caused by impedance mismatches.
Some of the more typical causes of impedance mismatches and the resulting micro-reflections in cable
networks include:
Damaged or missing end-of-line terminators
Damaged or missing chassis terminators on directional coupler, splitter, or multiple-output
amplifier unused ports
Loose center conductor seizure screws
Unused feeder tap ports not terminated; this is especially critical on low value feeder taps, but all
unused feeder tap ports should be terminated with 75-ohm terminations (locking terminators
without resistors or stingers do not terminate the feeder tap port)
Poor isolation in splitters, feeder taps, and directional couplers
Unused customer premises splitter and directional coupler ports not terminated
Use of so-called self-terminating feeder taps at ends-of-line; these are the equivalent of splitters,
and do not properly terminate the feeder cable unless all feeder tap ports are terminated
Kinked or damaged cable (includes cracked cable, which causes a reflection and ingress)
Defective or damaged actives or passives (water-damaged, water-filled, cold solder joint,
corrosion, loose circuit board screws, etc.)
Cable-ready TVs and VCRs connected directly to the drop (return loss on most cable-ready devices
is poor)
Some traps and filters have been found to have poor return loss in the upstream, especially those
used for data-only service
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Figure I-9 - Reflection Example that will be Used to Illustrate the Formation of Amplitude Ripple
First, convert the incident and reflected signals from dBmV to millivolts (mV) using the formula mV = 10
(dBmV/20)
. This results in +30 dBmV = 31.62 mV and +14 dBmV = 5.01 mV. Next look at phasor views of the
incident and reflected signals, with each represented as a vector 12. The length of each vector corresponds
to the signal magnitude in millivolts, and the direction vectors point is phase. In this example make the
incident signals vector (long arrow) stationary while the reflections vector (short arrow) rotates
counterclockwise around the end of the incident signals vector. The vector sum of the two vectors will be
plotted on a graph from which the amplitude ripple is derived. In Figure I-10 the incident and reflected
signals are in phase, represented by the two arrows placed end-to-end in series. The vector sum in this
case is simply 31.62 mV + 5.01 mV = 36.63 mV.
Vi = 31.62 mV Vr = 5.01 mV
Figure I-10 - Phasor View of Incident Signal Vector (Long Arrow) and Reflection Vector (Short Arrow)
Figure I-11 shows the reflections vector rotated counterclockwise 45 degrees from its original position. In
reality the reflection vector rotates continuously around the end of the incident signal vector; it does not
move in increments of 45 degrees. The latter is for illustrative purposes. The vector sum of the incident
and reflection vectors is 35.34 mV (fine dashed arrow), which is calculated using basic geometry.
Vs = 35.34 mV
V
m
01
5.
=
Vi = 31.62 mV
r
V
12
A vector is a quantity that has magnitude and direction, and is represented graphically with an arrow. One example of the use of
vectors is the weather forecast on local TV news. Wind vectors (arrows) are overlaid on a map, and those vectors represent wind
the length of the arrows correspond to the winds velocity, and the direction the arrows point show the direction the wind is
blowing. In the case of an RF signal, a vectors length represents the magnitude or amplitude of the RF signal, and the direction the
vector points represents the phase of the RF signal compared to an agreed reference signal.
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The Figure I-12 shows the reflection vector has rotated counterclockwise 90 degrees from its original
position. The vector sum of the incident and reflection vectors is 32.01 mV (fine dashed arrow).
Vr = 5.01 mV
Vs = 32.01 mV
Vi = 31.62 mV
Figure I-13 shows the reflection vector rotated counterclockwise 135 degrees from its original position.
The vector sum of the incident and reflection vectors is 28.3 mV (fine dashed arrow).
Vr
Vs = 28.30 mV
=
5.
01
m
V
Vi = 31.62 mV
Figure I-13 - Reflection Vector Rotated 135 Degrees From Original Position
Figure I-14 shows the reflection vector rotated counter clockwise 180 degrees from its original position.
Since the incident and reflection vectors are out of phase, the vector sum is 31.62 mV 5.01 mV = 26.61
mV.
Vs = 26.61 mV
Vi = 31.62 mV Vr = 5.01 mV
Figure I-14 - Reflection Vector Rotated 180 Degrees From Original Position
The following figures show the reflection vectors phase in 45 degree increments, until it reaches 360
degrees (0 degrees), from which the counterclockwise rotation continues.
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Vi = 31.62 mV
V
m
01
5.
Vs = 28.30 mV
=
r
V
Figure I-15 - Reflection Vector Rotated 225 Degrees From Original Position
Vi = 31.62 mV
Vr = 5.01 mV
Vs = 32.01 mV
Figure I-16 - Reflection Vector Rotated 270 Degrees From Original Position
Vi = 31.62 mV
Vr
=
5.
01
m
Vs = 35.34 mV
Figure I-17 - Reflection vector rotated 315 degrees from original position
Vi = 31.62 mV Vr = 5.01 mV
Vs = 36.63 mV
Figure I-18 - Reflection Vector Back At Original Position After Rotating 360 Degrees
The next step is to plot the vector sum vectorsthe fine-dashed arrowson a graph of amplitude-versus-
phase (time), as shown in Figure I-19. Note that connecting the dots along the tops of the plotted vector
sum vectors traces out the amplitude ripple caused by the reflection!
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millivolts
0 45 90 135 180 225 270 315 360 45 90 135 180 225 270 315 360 45 90 135 180
Now that the magnitude of the amplitude ripple has been plotted, other details of interest can be derived
from the response. The peak-to-valley amplitude ripple in decibels is 20log10(EP/EN)where EP is the
ripples peak voltage and EN is the ripples null voltageor, for the example in Figure I-19, 20log10(36.63
mV/26.61 mV) = 2.78 dB. By already knowing the incident signal amplitude is +30 dBmV and the
reflections amplitude is +14 dBmV (16 dB difference), the relative amplitude difference between the
incident and reflection signals from the amplitude ripple plot can be validated. That is done using the
formula 20log10[(EP-EN)/(EP+EN)], or 20log10[(36.63-26.61)/(36.63+26.61)] = -16 dBc.
The frequency of the amplitude ripple example being discussed here is the reciprocal of the reflections
234 ns time delay: 1/0.000000234 second = 4,273,504 Hz or 4.27 MHz. This is equal to the frequency
spacing between adjacent ripple peaks or nulls. The distance between the two impedance mismatches in
feet is 492*(V/FMHz), where V is the coaxial cables velocity factor (velocity of propagation expressed in
decimal form rather than percentage), and FMHz is the frequency spacing in MHz between adjacent peaks
or nulls. Assuming 0.87 velocity factor (87% velocity of propagation) and approximately 4.27 MHz
frequency spacing between adjacent peaks or nulls, the distance is 492*(0.87/4.27) 100 feet.
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Amplitude
Frequency
Figure I-21 shows amplitude tilt, indicated by the sloping dashed line.
Amplitude
Frequency
Figure I-22 and Figure I-23 show two upstream 6.4 MHz 64-QAM signals, one with significant in-channel
tilt and one that is mostly flat.
Figure I-22 - Example Of Upstream 64-QAM Signal With Substantial In-Channel Tilt
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Figure I-23 - Example Of 64-QAM Signal After Adaptive Pre-Equalization Eliminated Most of the In-channel Tilt
Among the causes of amplitude tilt are defective active or passive devices, as well as active device
misalignment. Note that many cable network distribution actives are often set up with an intentionally
sloped output in part to compensate for the attenuation-versus-frequency characteristic of coaxial cable
following the active device.
Other causes of amplitude tilt include operation near band edges or rolloff areas of the spectrum (or a
filter), where amplitude-versus-frequency may not be flat. As well, short time delay reflections will result
in widely spaced amplitude ripple, which may tilt the amplitude-versus-frequency response of signals in
the sloped portion of the ripple. Figure I-24 shows an example of the latter scenario, where amplitude tilt
is present between the two vertical dashed lines.
Figure I-24 - A Signal Carried in the Sloped Portion of the Widely Spaced Amplitude Ripple Will Exhibit In-
channel Tilt
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One analogy that might help to clarify the concept of MER is target shooting. A typical target used at the
range comprises a set of concentric circles printed on a piece of paper. The center of the target is called
the bulls-eye, which carries the highest point value. The further away from the bulls-eye, the lower the
assigned points. Ideally, one would always hit the bulls-eye and get the maximum possible score. In the
real world, this seldom happens. Instead, one or two shots might hit at or near the bulls-eye, and most of
the rest hit somewhere in the circles surrounding the center of the target. For a person who is a decent
shot, a round of target shooting usually results in a fairly uniform fuzzy cloud of holes in and around the
bulls-eye. The smaller the diameter of this cloud and the closer it is to the bulls-eye, the higher the score.
A variety of factors affects how close to the bulls-eye the shots land. Some of those factors include the
quality and accuracy of the firearm, type of ammunition used, weather conditions if outdoors, ambient
lighting, distance to the target, steadiness of aim, breathing control, and so on.
Now visualize the constellation display on a QAM analyzer (refer to Figure I-25 and Figure I-26). Each
symbol landing on the constellation can be thought of as a target of sorts. For instance, a 64-QAM
constellation has 64 targets arranged in an eight-by-eight square-shaped grid. Ideally, when the 64
symbols are transmitted, they should land exactly on their respective targets bulls-eyes in the
constellation display. In reality, the symbols form a fuzzy cloud at and around the constellations target
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centers. Measuring MER is, in effect, measuring the fuzziness of those clouds. The smaller the fuzzy
clouds, the higher the MER. Like a high score in target shooting, the higher the MER, the better.
Modulation error ratio is digital complex baseband SNRin fact, in the data world, the terms SNR and
MER are often used interchangeably, adding to the confusion that sometimes exists about SNR,
especially considering that in the telecommunications world, the terms carrier-to-noise ratio (CNR) and
SNR are often used interchangeably.
Why use MER to characterize a data signal? Modulation error ratio is a direct measure of modulation
quality and has linkage to bit error rate. Modulation error ratio is normally expressed in decibels, so it is a
measurement that is familiar to cable engineers and technicians. Its a useful metric with which to gauge
the end-to-end health of a network, although by itself, MER provides little or no insight about the type of
impairments that exist.
Figure 27 illustrates a 16-QAM constellation. A perfect, unimpaired 16-QAM digitally modulated signal
would have all of its symbols land at exactly the same 16 points on the constellation over time. Real-world
impairments cause most of the symbol landing points to be spread out somewhat from the ideal symbol
landing points. If a constellation diagram is used to plot the landing points of a given symbol over time, as
previously mentioned the resulting display forms a small cloud of symbol landing points rather than a
single point.
Figure 27 shows the vector for a target symbol the ideal symbol to be transmitted. Because of one or
more impairments, the transmitted symbol vector (or received symbol vector) is a little different than
ideal. Modulation error is the vector difference between the ideal target symbol vector and the
transmitted symbol vector. That is,
Figure I-27 - 16-QAM Constellation Showing Target Symbol, Transmitted (or Received ) Symbol, and
Modulation Error Vectors
Modulation error ratio is the ratio, in decibels, of average symbol power to average error power: MER(dB) =
10log(average symbol power/average error power). From this, you can see that the fuzzier the symbol
cloudin other words, the greater the average error powerthe lower the MER. See Figure I-28.
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Figure I-28 - MER is the Ratio of Average Symbol Power to Average Error Power
MER = 10 log10 N
j =1
2 2
I j + Q j
j =1
where I and Q are the real (in-phase) and imaginary (quadrature) parts of each sampled ideal target
symbol vector, and I and Q are the real (in-phase) and imaginary (quadrature) parts of each modulation
error vector. This definition assumes that a long enough sample is taken so that all the constellation
symbols are equally likely to occur. Refer to the RxMER Measurement in Appendix I.9 tutorial section for
more information on how MER is computed.
MER is affected by pretty much everything in a digitally modulated signals transmission path: transmitted
phase noise; carrier-to-noise ratio; nonlinear distortions (composite triple beat, composite second order,
cross modulation, common path distortion); linear distortions (micro-reflections, amplitude tilt/ripple,
group delay); in-channel ingress; laser clipping; data collisions; and even suboptimal modulation profiles.
Some of these can be controlled fairly well, but no matter what is done, a digitally modulated signal is
going to be impaired as it makes its way through a cable network. The worse the impairments, the fuzzier
the constellation landings. The fuzzier the constellation landings, the lower the MER.
As such, the constellations symbol landings will never be perfectly small points. They will always be
spread out at least a little, the extent of which is described by MER. By itself, a low measured MER value
doesnt determine what caused it to be low in the first place, only that it is low. Poor carrier-to-noise
ratio? In-channel ingress? Group delay? Micro-reflection? Hard to say, until additional diagnostics are
done with test equipment such as a QAM analyzer.
13
I.9 RxMER Measurement in a Digital Receiver
This tutorial discusses how a digital receiver is implemented, and how RxMER is measured. Figure I-29 is a
generalized block diagram of a digital QAM receiver. The receiver may reside in the CMTS, in which case it
receives time-division multiple access (TDMA) or synchronous code division multiple access (S-CDMA)
upstream bursts; or it may reside in a cable modem or set-top box (STB), in which case it receives a
13
Excerpted from the paper Digital Transmission: Carrier-to-Noise, Signal-to-Noise, and Modulation Error Ratio, by Bruce
Currivan (Broadcom) and Ron Hranac (Cisco).
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continuous stream of downstream digital data. The RF signal from the cable plant enters at the left of the
diagram, and is processed by analog and digital front-end components that perform tuning, automatic
gain control, channel selection, analog-to-digital conversion, and related functions. The square-root
Nyquist filter has a response matched to the symbol or S-CDMA chip (a chip is a bit in the
pseudorandom spreading code used in S-CDMA). An adaptive equalizer compensates for channel response
effects, including group delay variation, amplitude tilt or ripple, and micro-reflections. An ingress canceller
is normally included in a CMTS burst receiver to remove in-channel narrowband interference. Acquisition
and tracking loops provide estimates of frequency, phase, and symbol timing, allowing the receiver to lock
to the incoming signal. In the CMTS burst receiver, preamble symbols are used as a reference to aid in the
acquisition and tracking of each upstream burst. In the case of S-CDMA, the chips are despread. The
received QAM symbol, or soft decision, is passed to the slicer, which selects the nearest ideal symbol or
hard decision, from the QAM constellation. The decisions are passed to the Trellis decoder, descrambler,
deinterleaver, Reed-Solomon (RS) FEC decoder and MPEG deframer, and on to the MAC layer, which
assembles and outputs received packets to the user.
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property. This property, expressed in the time domain, results in ideally zero ISI, even when symbols are
transmitted so close together in time that their responses significantly overlap.
Adaptive equalizer: This element compensates for channel effects, including group delay variation,
amplitude slope or tilt, and micro-reflections. It adapts its filter coefficients to dynamically varying channel
responses so as to maximize the receive MER. In effect, an adaptive equalizer creates a digital filter with
the opposite response of the impaired channel.
Ingress canceller: An ingress canceller is normally included in a CMTS burst receiver to remove
narrowband interference (including CB, ham and shortwave radio signals, etc.). It operates by dynamically
detecting and measuring the interference, and adapting its coefficients to cancel it.
Acquisition and tracking loops: Tracking loops provide estimates of frequency, phase, and symbol timing,
allowing the receiver to lock to the incoming signal. Acquisition refers to the initialization and pull-in
process that occurs when the receiver is first powered on or changes channels.
Despreader: (S-CDMA upstream only) Despreading consists of multiplying the composite received signal by
a given code sequence, and summing over all 128 chips in the code. There are 128 despreaders, one for
each code. The output of the despreader is a soft symbol decision.
Slicer: The slicer selects the nearest ideal symbol, known as a hard decision, from the QAM constellation.
Trellis decoder: (Downstream and some S-CDMA upstream modes) The trellis decoder uses the Viterbi
algorithm to choose the most likely sequence of symbols and thereby reject noise.
Descrambler: The descrambler adds a pseudorandom bit sequence to the received data bits, reversing the
scrambling operation performed at the transmitter. The purpose of scrambling is to randomize the
transmitted data in order to provide an even distribution of QAM symbols across the constellation.
Deinterleaver: The deinterleaver pseudo-randomly reorders groups of received bits, reversing the
interleaving operation performed at the transmitter. The purpose of deinterleaving is to break up long
bursts of noise so that the errored bits can be corrected by the Reed-Solomon decoder.
Reed-Solomon (RS) FEC decoder: This device processes groups of bits (7- or 8-bit symbols) arranged in
codeword blocks, in terms of an algebraic code using Galois field arithmetic. By processing the received
code words, which include redundant parity symbols, receive symbol errors can be found and corrected,
up to one corrected RS symbol for each two redundant RS parity symbols.
MPEG deframer: The downstream DOCSIS signal is grouped into 188-byte MPEG transport packets,
permitting the multiplexing of video and data over the common physical layer. The MPEG deframer
removes the MPEG transport overhead to recover the bytes that are delivered to the MAC layer.
MAC: The media access control (MAC) layer controls the physical (PHY) layer and is the source and sink of
PHY data. The MAC layer processes data frames delineated by DOCSIS headers. In the upstream, the MAC
layer governs how cable modems share the channel through a request or grant mechanism.
The input and output of the slicer are complex numbers or vectors, each represented by two components:
magnitude and phase, or equivalently, real (in-phase or I) and imaginary (quadrature or Q) parts, as
shown in Figure I-30. In an ideal zero-noise, zero-ISI condition, the soft decision would lie exactly on one of
the constellation points, and the magnitude of the error between them would be zero. In a real-world
receiver, subtracting the hard-decision vector from the soft-decision vector gives the error or noise vector
at each symbol time. The implicit assumption is that a low symbol error rate exists that is, very few
decisions are incorrect, ensuring that the decision-directed error vector from the nearest symbol nearly
always equals the true error vector from the correct reference symbol.
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Figure I-30 - Each Vector Has a Real (In-Phase or I) and Imaginary (Quadrature or Q) Component
For RxMER, the concern is with the average power of the error vector, which is computed by taking the
complex magnitude-squared of the error vector and accumulating or averaging it over a given number of
symbols N. This process gives the error vector power (or noise power) at the slicer. To obtain the ratio of
signal to noise, the average signal power (a known constant for each constellation, such as 64-QAM or
256-QAM) is divided by the average error vector power. Then take the logarithm to convert to decibels,
giving RxMER in dB. To summarize: RxMER is simply the ratio of average symbol power to average slicer
error power, expressed in dB.
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techno-speak. Included is a step-by-step example of how a simple four-tap adaptive equalizer can be used
to reduce in-channel impairments caused by a severe micro-reflection.
Consider first the concept of equalization from the perspective of a cable TV distribution network. It is
understood that in a given length of coaxial cable higher frequencies are attenuated more than lower
frequencies. For instance, if all downstream signals in the 54-870 MHz spectrum have the same amplitude
at the output of an amplifier, the overall frequency responsetechnically speaking, amplitude (or
magnitude)-versus-frequency responseis flat. For the following example, assume there is no slope at an
amplifiers output (and the amplifier has no internal slope or tilt), and our equal-amplitude signals leave
the output of the first amplifier and travel through 1,000 feet of 0.500 inch diameter coax to the second
amplifier.
Since 0.500 inch diameter distribution cables attenuation is about 0.5 dB/100 ft. at 54 MHz and 2.3
dB/100 ft. at 870 MHz, our hypothetical 1,000 ft. span of coax has a total of 5 dB of attenuation at 54 MHz
and 23 dB of attenuation at 870 MHz. The 54-870 MHz spectrum will be tilted a bunch at the second
amplifiers input! The goal is to see a flat amplitude-versus-frequency response across the spectrum, so it
is necessary to install a fixed-value plug-in equalizer at the second amplifier. The equalizer is a small
passive circuit that has the opposite amplitude-versus-frequency response of the 1,000 feet of coaxial
cable preceding the amplifier. The equalizer is in effect a broadband filter that cancels the tilted
response from 54 to 870 MHz, resulting in a flat amplitude-versus-frequency spectrum at the second
amplifiers internal gain stages.
Adaptive equalization performs a function similar to that of a cable amplifiers fixed-value plug-in
equalizer. Rather than equalizing the entire 54-870 MHz downstream or 5-42 MHz upstream RF spectrum,
it deals with just a single channel. Adaptive means the equalizer can change its characteristics as channel
conditions change.
An adaptive equalizer is a digital circuit that compensates for a digitally modulated signals in-channel
complex frequency response impairments. The cable industry has long used the term frequency response
to describe amplitude (or magnitude)-versus-frequencythat is, what is seen on the display of test
equipment used to sweep outside plant. True frequency response is a complex entity that has two
components: amplitude-versus-frequency, and phase-versus-frequency. An adaptive equalizer can
compensate for in-channel amplitude- and phase-versus-frequency impairments.
The adaptive equalizer uses sophisticated algorithms to derive coefficients for an equalizer solution on
the flyin effect, creating a digital filter with essentially the opposite complex frequency response of the
impaired channel. Because the adaptive equalizers complex frequency response is in theory a mirror
image of the impaired channels complex frequency response, the adaptive equalizer cancels out most or
all of the degraded in-channel frequency response that is affecting the digital signalwithin the limits of
the adaptive equalizers capabilities, of course.
Its important to note that at high signal-to-noise ratio (ES/N0), the adaptive equalizer will synthesize the
opposite response of the channel. At lower SNR doing so would cause noise enhancement, so a
compromise solution is derived.
Ideal adaptive equalizer coefficients yield maximum modulation error ratio (MER) by minimizing total
impairments including inter-symbol interference (ISI), within the limits of the equalizers capabilities
(number of adaptive equalizer taps, etc.).
If the in-channel impairment suddenly changes or goes away, the adaptive equalizer will distort the signal,
at least until new equalizer coefficients for the current channel conditions are derived and the equalizers
operation updated. This adaptation process is very fast, typically completed in milliseconds.
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The test equipment screen shot in Figure I-31 shows an unequalized 64-QAM constellation. Note that the
constellations 64 symbol landings are fuzzy, caused by degraded modulation error ratio. Indeed, the
unequalized MER is about 25 dB, only a few dB above the lower ES/N0 threshold for 64-QAM. 14
The screen shot in Figure I-32 shows the same 64-QAM signal after adaptive equalization. The 64 symbol
landings are small and almost dot-like. The equalized MER is >40 dB. The adaptive equalizer has effectively
compensated for in-channel response impairments, but the equalized MER and constellation do not
provide a way to determine how close to the failure threshold the signal really is.
By evaluating both unequalized and equalized MER, one can determine available MER headroom, and also
see how well adaptive equalization is able to improve the signal.
In order for an adaptive equalizers algorithms to begin the process of deriving coefficients that will be
used to create a filter whose complex frequency response is opposite of the channels complex
frequency response, the equalizer starts with an adaptation source. The adaptation source can be a
transmitted training sequence, or the signal itself.
14
The lower ES/N0 threshold is in effect the unequalized MER failure threshold for the modulation format in use.
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Transmitted training sequence: In conventional zero-forcing or minimum mean square error (MSE)
equalizers, a known training sequence is transmitted to the receiver for the purpose of initially adjusting
adaptive equalizer coefficients. In the DOCSIS upstream pre-equalization process (discussed in the
Adaptive Pre-equalization tutorial section), data transmissions from all cable modems include a preamble
at the beginning of each burst. The preamble is used as a training signal for the cable modem termination
systems (CMTSs) adaptive equalizer.
The signal itself: Adaptive equalizers that do not rely upon transmitted training sequences for the initial
adjustment of the coefficients are called self-recovering or blind adaptive equalizers. The adaptive
equalizer in the downstream receiver of a DOCSIS cable modem (or a digital set-top) is a blind adaptive
equalizer. In the case of cable modems, DOCSIS does not specify a training sequence in the downstream
signal.
Several types of adaptive equalization methods are used in data transmission. For example, one method is
based on maximum-likelihood (ML) sequence detection; another uses a linear filter with adjustable
coefficients. Decision-feedback equalizationcomprising a combination of feedforward and feedback
filtersuses previously detected symbols to suppress inter-symbol interference in the current symbol
being detected. A commonly used adaptive equalization type is a combination of decision-feedback and
feedforward equalizers.
Powerful algorithms are used to automatically adjust adaptive equalizer coefficients to achieve optimum
performance, and to rapidly adapt to changing channel characteristics. General criteria for defining
optimum performance include minimizing peak distortion at the equalizer output, or minimizing the MSE
at the equalizer output. In other words, the algorithm adjusts equalizer coefficients on the fly to
converge on a solution that best reduces, say, MSE.
Zero-forcing and least-mean-square (LMS) are among the algorithms used in adaptive equalizers.
Fractionally spaced equalizers (FSE) may use a LMS algorithm or a tap-leakage algorithm.
If faster convergence is desired in an equalizer, more complex algorithms generally have to be used.
Examples include a recursive least-squares (Kalman) algorithm. Blind equalizers may use stochastic
gradient algorithms such as Godard, Sato, Benveniste-Goursat, or stop-and-go.
Digital Communications, 4th Edition, by John G. Proakis (McGraw-Hill, 2001, ISBN 0-07-232111-3),
includes in-depth explanations of the adaptive equalizer and algorithm types mentioned here.
An important parameter in an adaptive equalizer is its span, defined mathematically as (number of
equalizer taps 1) x equalizer tap spacing. This particular definition assumes that the equalizers first tap
is the main tap. Adaptive equalizer tap spacing is the amount of time delay per equalizer tap. An adaptive
equalizers span is directly related to the maximum amount of time delay in a micro-reflection that can be
compensated for.
The adaptive equalizer tap spacing of a DOCSIS 2.0 cable modems upstream pre-equalizer taps is called T-
spaced, or symbol-spaced. Symbol-spaced means the time delay per adaptive equalizer tap is equal to the
symbol period, which is the reciprocal of the symbol ratethat is, 1/T. For example, if the upstream
digitally modulated signals symbol rate is 5.12 megasymbols per second (Msym/sec), the adaptive
equalizer tap spacing is 0.1953125 microsecond (s) per tap: 1/5,120,000 = 1.953125 x 10-7 second, or
0.1953125 s.
Since DOCSIS 2.0 specifies 24-tap T-spaced pre-equalization in the upstream, the maximum span of an
adaptive equalizer for a 5.12 Msym/sec signal is (24 1) x 0.1953125 s = 4.49 s. Another way to
calculate this value is (24 1)/5.12 = 4.49 s.
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Currently available CMTS burst receivers, which incorporate DOCSIS 2.0 and later 24-tap adaptive
equalization, support main tap positions of 2 through 10. Adaptive equalizer tap position 8 generally is the
default setting. How does that affect the maximum usable equalizer span when it comes to dealing with
micro-reflections? Assuming that adaptive equalizer tap #8 is the main tap, that results in a usable span of
(24 8) x 0.1953125 s = 3.13 s. If the adaptive equalizer main tap is changed to #10, the usable span
becomes (24-10) x 0.1953125 = 2.73 s, and if the adaptive equalizer main tap is changed to #2 the usable
span becomes (24-2) x 0.1953125 = 4.3 s.
T-spaced equalizers are the most commonly used. As discussed previously, T-spaced means the equalizer
taps are spaced at the reciprocal of the symbol rate.
A fractionally spaced equalizer is based on sampling the incoming signal at least as fast as the Nyquist rate.
(From Wikipedia: The Nyquist rate is the minimum sampling rate required to avoid aliasing when
sampling a continuous signal. In other words, the Nyquist rate is the minimum sampling rate required to
allow unambiguous reconstruction of a band limited continuous signal from its samples. If the input signal
is real and band limited, the Nyquist rate is simply twice the highest frequency contained within the
signal.)
A T-spaced (also written as T/2-spaced) equalizer is used in many applications requiring a FSE. Other
applications may use T-spaced (T/4-spaced) equalizers, and so forth.
Why use a FSE? They often perform better than T-spaced equalizers in the presence of symbol clock timing
errors, because FSEs are less sensitive to timing phase. Despite their better performance, FSEs are not as
common as T-spaced equalizers because of computational complexity and convergence performance.
DOCSIS supports T-spaced and fractionally spaced equalizers under the following conditions for upstream
pre-equalization, defined in the DOCSIS 2.0 Radio Frequency Interface Specification: There are two modes
of operation for the pre-equalizer of a CM: DOCISIS 1.1 mode, and DOCSIS 2.0 mode. In DOCSIS 1.1 mode,
the CM MUST support a (T)-spaced equalizer structure with 8 taps; the pre-equalizer MAY have 1, 2 or 4
samples per symbol, with a tap length longer than 8 symbols. In DOCSIS 1.1 mode, for backwards
compatibility, the CMTS MAY support fractionally spaced equalizer format (T/2 and T/4). In DOCSIS 2.0
mode, the pre-equalizer MUST support a symbol (T)-spaced equalizer structure with 24 taps.
If the channel response contains a reflection (caused by an impedance mismatch) that is further out in
delay than the span of the adaptive equalizer, the adaptive equalizer cannot compensate for that
reflection.
For example, if there is a significant amount of ISI from a SAW filters triple transit, and this ISI is
equivalent to a reflection at a large delay that is beyond the span of the equalizers taps, then the
equalizer will still do its best on the other impairments. But it wont be able to cancel the triple transit
reflections since they are beyond the limits of the adaptive equalizers capabilitiesin this case, the
equalizer span.
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Delay element
Main tap
UNEQUALIZED
INPUT
-1 -1 -1 -1
Z Z Z Z
Multipliers with
equalization
coefficients
b-2 b-1 b0 b+1 b+
EQUALIZED
OUTPUT
Algorithm for
tap gain
Figure I-33 illustrates a generic adaptive equalizer. The top row with boxes labeled Z-1 can be thought of as
a tapped delay line. Each box marked Z-1 is a delay element, with the amount of time delay per box equal
to the reciprocal of the symbol rate in a T-spaced equalizer. A delay element is often called a tap, but an
adaptive equalizer tap also can be considered the combination of a delay element, the point where some
of the signal is tapped off, and a multiplier. The boxes labeled b-2, b-1, b0, etc., are multipliers with
coefficients that set the gain for each adaptive equalizer tap. The algorithm adjusts the equalization
coefficients that set the gain for each multiplier. The circles marked are summing or combining circuits.
One adaptive equalizer tap is called the main tap (the second Z-1 delay element to multiplier b0 and
highlighted in red in the figure). The main tap has a gain of 1, and passes the input signal at its original
amplitude. Other adaptive equalizer taps represent either the past or future relative to the main tap,
and vary the amplitudes of the respective signals passing through them as required.
While an adaptive equalizer is a digital circuit, one can think of its operation as functionally similar to an
analog circuit that combines different amplitudes and phases of an input waveform to achieve a desired
output waveform.
To better understand how a simple adaptive equalizer works, consider a scenario in which an impedance
mismatch results in a severe micro-reflection. Assume that the incident signal has an amplitude of 1, and
the echo (micro-reflection) caused by the impedance mismatch has an amplitude of -0.5 and is offset in
time by 1 s. The minus sign indicates that the echo has the opposite phase of the incident signal. Figure I-
34 illustrates the incident signal and echo graphically in terms of amplitude-versus-time.
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Incident signal
+1.0 1.0
Echo
+0.5
Amplitude
Time
1 s
- 0.5
- 0.5
- 1.0
Figure I-35 shows amplitude (or magnitude)-versus-frequency response caused by the 1 s micro-
reflection from Figure I-34. When the incident and micro-reflection vectors are in phase, they add to
create a vector whose sum is 1.5; when the two vectors are out of phase, the resulting vector sum is 0.5.
This makes the scalloped sine waves peak-to-peak amplitude vary from 0.5 to 1.5, which, in decibels, is
20log(1.5/0.5) = 9.54 dB. The frequency spacing between successive peaks is 1/1 s, or 1 MHz.
Figure I-36 shows the resulting phase-versus-frequency response caused by the micro-reflection in Figure
I-34. The maximum phase excursion occurs when the vector sum vector is tangent to the circle on a
phasor diagram representation of the incident and reflection vectors. That forms a right-triangle with side
cthe hypotenuseequal to 1.0 (incident signal vector length); side bthe opposite sideequal to 0.5
(reflection vector length), and side athe adjacent sideequal to 0.886 (vector sum length). Trigonometry
can be used to calculate the peak phase excursion, which equals the right-triangles angle B: sinB =
opp/hyp, or angle B = arcsine(opp/hyp): arcsine(0.5/1) = 30.
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In order to cancel the echo and get a flat response, an adaptive equalizer with the opposite amplitude
(magnitude)-versus-frequency and phase-versus-frequency response is needed. Figure I-34
Figure I-37 shows the required amplitude and phase response to cancel the -0.5 amplitude 1 s echo.
Why is the peak-to-peak linear magnitude of the needed opposite amplitude-versus-frequency response
0.667 to 2.0 rather than the original 0.5 to 1.5?
A time-invariant system such as a filter can be characterized by its impulse response h(t) or by its
frequency response H(f), which comprise what is known as a Fourier transform pair. Flat response occurs
when H(f) multiplied by 1/H(f) equals 1.00. If H(f) is 0.5, then 1/H(f) is 2.0; likewise, if H(f) is 1.5, then
1/H(f) is 0.667. In the example in the figure, 0.5 x 2 = 1.00 and 1.5 x 0.667 = 1.00.
For this example, use a simple 4-tap adaptive equalizer to compensate for the impaired frequency
response caused by the -0.5 amplitude 1 s echo. The first adaptive equalizer tap will be the main tap, so
b0 will have a gain of 1. Note that there is no delay element feeding the first equalizer tap.
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Figure I-38 - Adaptive Equalizer that will be Used in the Example in the Text
Assume the algorithm has converged on a solution that derived the following coefficients: b0 = 1.0, b1 =
+0.5, b2 = +0.25, and b3 = +0.125, and each delay element Z-1 equals 1 s. 15
An analog equivalent of whats going on here is something like the following: Each of the Z-1 delay
elements is equivalent to about 1,000 feet of lossless coaxial cable (1 foot of cable has about 1
nanosecond of delay, so 1,000 feet of coax delays the signal by approximately 1,000 nanoseconds or 1 s).
Each multiplier is equivalent to a variable attenuator. Attenuator b0 is adjusted for no attenuation (unity
gain), b1 is adjusted to attenuate the signal by a factor of half, b2 by a factor of one-fourth, and so on. Each
of the summing circuits can be thought of as backwards two-way splitters functioning as combiners,
except that these, too, are assumed to be lossless for this example. Keep in mind that this analog
equivalent is just thatan equivalent. A real-world adaptive equalizer is actually a digital circuit.
Figure I-39 shows the operation of the adaptive equalizers first tap, which in this example also is the main
tap. The unequalized input signal (1.0 amplitude incident signal and -0.5 amplitude 1 s echo) does not
pass through a delay element, but does pass through multiplier b0. Since the b0s coefficient is 1, the
output of b0 is identical to the input. The unaltered incident signal and its echo are routed to one input of
the first summing circuit.
15
These equalizer coefficients have been simplified to illustrate this example. In practice, equalizer coefficients are complex
coefficients, comprising real and imaginary components.
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Figure I-40 shows the second taps operation. The unequalized input signal passes through the first delay
element Z-1, which delays the incident signal and echo by 1 s. The delayed incident signal and echo next
pass through multiplier b1, which has a coefficient of +0.5. The delayed incident signal and echo are
multiplied by +0.5, which decreases the amplitude of the incident signal from 1.0 to 0.5, and the echo
from -0.5 to -0.25. The delayed and attenuated incident signal and echo are routed to the second input of
the first summing circuit.
The first summing circuit combines the original undelayed, unattenuated incident signal and its echo with
the delayed and attenuated incident signal and echo from the second tap. The output of the first summing
circuit, which is connected to an input of the second summing circuit, has the original incident signal at
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amplitude 1.0, and a residual -0.25 amplitude 2 s echo. The original -0.5 amplitude 1 s echo was
cancelled (-0.5 + 0.5 = 0). This is illustrated in Figure I-41.
Figure I-41 - Summing the Outputs of the Adaptive Equalizer's First and Second Taps
Figure I-42 shows the operation of the adaptive equalizers third tap. The unequalized input signal passes
through the first and second delay elements, which together delay the incident signal and echo by a total
of 2 s. The delayed incident signal and echo next pass through multiplier b2, which has a coefficient of
+0.25. The twice-delayed incident signal and echo are multiplied by +0.25, which decreases the amplitude
of the incident signal from 1.0 to 0.25, and the echo from -0.5 to -0.125. The delayed and attenuated
incident signal and echo are routed to the second input of the second summing circuit.
Referring to Figure I-43, the combined signal from the first summing circuit (1.0 amplitude incident signal
and -0.25 amplitude 2 s echo) and the delayed and attenuated signal from the adaptive equalizers third
tap (0.25 amplitude incident signal and -0.125 amplitude echo) are combined in the second summing
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circuit. The output of the second summing circuit, which is connected to an input of the third summing
circuit, has the original incident signal at amplitude 1.0, and a residual -0.125 amplitude 3 s echo. The -
0.25 amplitude 2 s echo was cancelled (-0.25 + 0.25 = 0).
Figure I-43 - Summing the Output of the Adaptive Equalizer's Third Tap With the Previously Summed First and
Second Taps
Figure I-44 shows the operation of the fourth tap. The unequalized input signal passes through the first,
second and third delay elements, which together delay the incident signal and echo by a total of 3 s. The
delayed incident signal and echo next pass through multiplier b3, which has a coefficient of +0.125. The
delayed incident signal and echo are multiplied by +0.125, which decreases the amplitude of the incident
signal from 1.0 to 0.125, and the echo from -0.5 to -0.0625. The delayed and attenuated incident signal
and echo are routed to the second input of the third summing circuit.
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The combined signal from the second summing circuit (1.0 amplitude incident signal and -0.125 amplitude
3 s echo) and the delayed and attenuated signal from the fourth tap (0.125 amplitude incident signal and
-0.0625 amplitude echo) are combined in the third summing circuit. The output of the third summing
circuit is the equalized output signal, which has the original incident signal at amplitude 1.0, and a residual
-0.0625 amplitude 4 s echo. The -0.125 amplitude 3 s echo was cancelled (-0.125 + 0.125 = 0). See
Figure I-45.
The original -0.5 amplitude echo was reduced to an amplitude of -0.0625, or an 18 dB improvement:
20log(-0.5/-0.0625) = 18.06 dB. The echo also was shifted in time (delayed) to 4 s from the original 1 s.
Figure I-46 shows the resulting amplitude-versus-frequency and phase-versus-frequency response after
the 4-tap equalizer has compensated for the original -0.5 amplitude 1 s echo. The residual echo is -
0.0625 amplitude at 4 s, which results in the response shown in the figure. The amplitude (or
magnitude)-versus-frequency response is now 1.87 dB, compared to the original 9.54 dB. The phase-
versus-frequency response now is 3.58 degrees, compared to the original 30 degrees. Note that the
amplitude and phase ripple, which was 1 MHz before, is now 250 kHz.
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Figure I-46 - Final Amplitude and Phase-versus-frequency Response After Adaptive Equalization
16
8-tap and 24-tap refer to the number of adaptive equalizer taps used for upstream pre-equalization in DOCSIS
implementations.
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Heres an example. The upstream QAM signal from a given modem has several dB of in-channel tilt
because of some problem in the outside plant. The CMTS sees that tilt and gives that modem the
appropriate coefficients so that the modem can pre-equalize or tilt its transmitted QAM signal
approximately the same amount in the OPPOSITE direction. When that pre-equalized QAM signal is
received by the CMTS, it should now be flat. Refer to Figure I-47, which shows an upstream 6.4 MHz
bandwidth 64-QAM signal as received at the CMTS. Note the substantial in-channel tilt before pre-
equalization, and the same signalnow nearly flatafter pre-equalization.
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TEM(vacuum)/TEM(dielectric), equals what is called index of refraction. 17 Velocity factor is the reciprocal of
index of refraction.
The dielectrics magnetic permeability (represented by the symbol and expressed in henrys/meter) and
electric permittivity (represented by the symbol and expressed in farads/meter) are two key properties
that determine the velocity of electromagnetic waves in coaxial cable. The ratio of (dielectric)/(vacuum)
is the dielectric constant r. The velocity of an electromagnetic wave in a dielectric is equal to the ratio of
its velocity in a vacuum to the square root of the dielectric constant: TEM(dielectric) = TEM(vacuum)/r. A
little number crunching with the latter equation and the ratio that defines index of refraction is 1/r =
velocity factor.
The dielectric constant r of the coaxial cable in the example in the first paragraph is approximately 1.32,
so the velocity factor is 1/1.32 = 0.87. Velocity of propagation is velocity factor expressed as a
percentage. So, a velocity factor of 0.87 is 87% velocity of propagation, which means that radios waves
travel through the coaxial cable at 87% the free-space value of the speed of light.
One application for understanding velocity of propagation is calculating propagation or transit delay in a
cable networkthat is, the time it takes for electromagnetic waves to travel from one point to another.
The Data-Over-Cable Service Interface Specification (DOCSIS) Radio Frequency Interface Specification
includes assumed downstream and upstream RF channel transmission characteristics for cable networks.
Among those assumed characteristics is the previously mentioned transit delay. For instance, the transit
delay from the headend to the most distant customer is assumed to be less than or equal to 0.800
millisecond (ms). Note that 0.800 ms (800 microseconds) is a one-way specification. The same assumed
transit delay also applies in the upstream direction.
The approximate downstream or upstream transit delay can be calculated if one knows the length of the
optical fiber link between the headend or hub and node, as well as the length of distribution network
coaxial cable from the node to the most distant customer. The calculation is done using the reciprocal of
the fibers index of refractionits velocity factor, which is then converted to velocity of propagationand
the velocity of propagation of the coaxial cable. The approximate index of refraction for single mode
optical fiber at 1310 nm is 1.46, making its velocity factor 0.68 and its velocity of propagation 68%. In
other words, light propagates through the optical fiber at a velocity that is 68% of the speed of light in a
vacuum. A typical velocity of propagation for commonly used hardline distribution-type coaxial cables is
the previously discussed 87%.
Since the speed of light in a vacuum is 299,792,458 meters per second, 68% of that value is 203,858,871
meters per second. Thus, light will propagate through 203,858,871 meters of optical fiber in one second.
For coaxial cable with a velocity of propagation of 87%, RF will propagate through 260,819,438 meters of
coax in one second.
Example: Assume a cable system with an optical fiber link from headend to node that is 30 kilometers (km)
long. The coaxial cable distribution network connected to the node has a coax run that extends an
additional 2 km beyond the node. What is the approximate transit delay from the headend to the most
distant customer, excluding delay through active and passive devices?
Solution: Light propagates through 30 km (30,000 meters) of optical fiber in 1.47 x 10-4 second (30,000
meters/203,858,871.44 meters per second = 0.00014716 second). RF propagates through 2 km (2,000
meters) of coax in 7.6681 x 10-6 second (2,000 meters/260,819,438.46 meters per second =
The ratio TEM(vacuum)/TEM(dielectric) is called the index of refraction because the difference in the velocity of electromagnetic
17
waves in a vacuum and some other medium results in refraction at the interface between the two media.
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0.00000076681 second). Combining these two numbers yields 1.55 x 10-4 second, or 0.155 ms. This is well
within the DOCSIS one-way transit delay specification of 0.800 ms.
Table I-2 summarizes transit delay in ns-per-foot and ns-per-meter for several values of velocity of
propagation. The velocity factor of a vacuum is 1.0 and its velocity of propagation is 100%, because
electromagnetic signals travel at the free-space value of the speed of light.
The dielectric constant of dry air at a pressure of one atmosphere and a temperature of 23 C is 1.00068,
so the velocity factor is 1/1.00068 = 0.999660173 and the velocity of propagation is 99.966%. The values
for a vacuum and air are usually considered to be the same in all but the most critical applications because
of the negligible difference between them.
Table I-2 - Velocity of Propagation versus Transit Delay
Typical published velocities of propagation for modern foam dielectric coaxial cables used by the cable
industry are 84-85% for drop-type cables and 87-88% for hardline trunk and feeder cables. Published
values for disc-and-air dielectric designs are as high as 93%. As previously noted, the typical velocity of
propagation for single mode optical fiber at 1310 nm is about 68%.
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What is the DFT? The DFT is a way of expressing any waveform in terms of sine waves. The DFT breaks
down a signal into many sine waves. It is used in a DOCSIS 3.1 OFDM receiver, in which a single DFT
implements 4096 or 8192 demodulators. It is also used for spectrum analysis at the CM or CMTS, in which
the DFT calculates the frequency content of the cable plant signal. The inverse DFT (IDFT) does the
reverse: it sums many sine waves to construct a signal. It is used in a DOCSIS 3.1 OFDM transmitter, in
which a single DFT implements 4096 or 8192 modulators and their combining network.
How does the DFT computation work? To apply the DFT just multiply by a matrix. Multiplying by this
matrix converts between the time and frequency domains, and performs modulation, demodulation and
spectrum analysis.
What does the DFT matrix look like? The DFT matrix simply contains rows of sine and cosine waves as
shown in Figure I-48 for N = 16 rows. Just half of the matrix is shown in the figure. Each row has a slightly
higher frequency (contains one more full cycle) than the previous row. The first row in the figure
represents DC, that is, zero cycles; the next row one full cycle, the next two full cycles, etc., up to seven full
cycles.
Figure I-48 - DFT Matrix (Only Half is Shown) Contains Rows of Sine (Red) and Cosine (Blue) Waves
To be more complete, Figure I-49 shows the full DFT matrix for N = 16. The DC signal (corresponding to the
center frequency at RF) shows up in the 9th row. The rows below DC have sine leading cosine and the rows
above DC have sine lagging cosine. This allows the DFT to distinguish between positive and negative
frequencies, that is frequencies greater or less than the RF center frequency.
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What does the IDFT matrix look like? The IDFT matrix is identical to the DFT matrix with its sines negated,
and it typically has a different scale factor.
How big is the DFT matrix for DOCSIS 3.1 OFDM? The simple example in Figure I-49 shows the DFT matrix
with N = 16 rows. In DOCSIS 3.1 the DFT matrix is much larger, containing N = 4096 or 8192 rows of sine
and cosine waves. To give some idea of the size of the DOCSIS 3.1 DFT, Figure I-50 shows a DFT matrix with
N = 64. This is getting close to the limit of what can be shown clearly in a diagram. Figure I-51 shows a DFT
matrix with N = 256, and is way too dense to see clearly, yet is still much smaller than N = 4096 or 8192 for
DOCSIS 3.1.
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Figure I-50 - This DFT Matrix with N = 64 is about the Largest We can Clearly Show in a Small Diagram
Figure I-51 - This DFT Matrix with N = 256 is Still Nowhere Near N = 4096 or 8192 for DOCSIS 3.1
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How does a DOCSIS 3.1 OFDM transmitter use the IFFT? We start with 4096 or 8192-QAM symbols.
Multiply by the IDFT matrix; actually use the IFFT which is 600 to 1200 times faster to give the same
answer as the IDFT. This gives the equivalent of 4096 or 8192-QAM modulators summed together, as
shown in Figure I-52 very powerful! We send this summed signal over the cable channel. A guard
interval, also called a cyclic prefix, is typically added to the signal to improve echo tolerance. A guard
interval is nothing more than a number of time samples copied from the front of the waveform and
appended to the end of the waveform. Ideally, the longest echo in a channel is shorter than the length of
the guard interval.
Figure I-52 - OFDM Transmitter: a Single IDFT is Equivalent to 4096- or 8192-QAM Modulators plus their
Summing Network
How does a DOCSIS 3.1 OFDM receiver use the FFT? We start with 4096 or 8192 samples received from
the cable channel. Multiply by the DFT matrix using the FFT which is 600 to 1200 times faster. This gives
the equivalent of 4096 or 8192-QAM demodulators, as shown in Figure I-53. The resulting 4096 or 8192-
QAM soft decisions are sent to the de-interleaver and FEC for error correction, then to the MAC.
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Figure I-53 - OFDM Receiver: a Single DFT is Equivalent to 4096- or 8192-QAM Demodulators
How does the FFT save so much computation compared to the DFT? The FFT uses a divide-and-conquer
strategy. Say we want to multiply by a DFT matrix with N = 4096. This takes 4096*4096 = 16 million
complex multiplications, since the input vector has to be multiplied by each row of the matrix, there are N
rows, and each row has N elements. The trick is to break the DFT down into two DFTs each of half size, or
2048 rows each, and combine the two to get the original DFT. This takes 2048*2048 operations for the
first half and 2048*2048 for the second half, for a total of 8 million operations, plus the combining which
is actually small enough to be neglected. So, we gained almost a factor of 2x by breaking the DFT in half. If
that worked so well, why not do it again and get another factor of 2 improvement? In fact, we keep
dividing 4096 by 2 over and over (12 times which is log2(4096)) until we end up with 4096 trivial DFTs of
length 1, and the 1-point DFT of a number is just the number itself. The above description is a little
simplified; the actual number of operations required for the FFT is usually counted as (N/2) log2(N),
compared to N^2 for direct computation of the DFT. Table I-3 shows the actual numbers for the two
DOCSIS 3.1 transform lengths.
Table I-3 - The FFT is 600 to 1200 Times Faster than the DFT for DOCSIS 3.1 OFDM Transforms
4K FFT 8K FFT
DFT length N 4096 8192
DFT computations N^2 16777216 67108864
FFT computations (N/2) log2(N) 24576 53248
FFT speed improvement factor over DFT 683 1260
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What are two fundamental ways to interpret a matrix multiplication? Recall that the DFT or IDFT
multiplies the input vector by the DFT or IDFT matrix. This matrix multiplication can be looked at in one of
two ways:
(1) a series of dot products
(2) a weighted sum of the rows of the matrix
The dot-product interpretation lends itself to demodulation or spectral analysis using the DFT. The
weighted-sum interpretation is a natural for modulation using the IDFT. Recall that the DFT and IDFT are
basically the same matrix (except the IDFT has its sines negated and a constant scale factor), so there is no
fundamental difference between the computations of the DFT and IDFT.
How can we interpret a matrix multiplication as a series of dot products? The multiplication of the input
vector by the DFT matrix can be thought of as a dot product of the input vector with each row of the
matrix. A dot product of two vectors is the sum of the individual pairwise products of the elements of the
vectors. As a simple example with N = 4, the dot product of the two vectors [1,2,3,4] and [5,6,7,8] is
1*5 + 2*6 + 3*7 + 4*8 = 70
The two input vectors to a dot product have N elements each and the dot product gives a single number
as its output. For the DFT matrix with N = 4096, the 1st element of the DFT output vector is the dot
product of the input vector with the 1st row of the DFT matrix. The 2nd element of the DFT output vector is
the dot product of the input vector with the 2nd row of the DFT matrix. And so on; the 4096th element of
the DFT output vector is the dot product of the input vector with the 4096th row of the DFT matrix. In the
above Figure I-53 showing an OFDM receiver, each individual QAM receiver block is a dot product of the
input with a single row of the matrix corresponding to one subcarrier.
How does the DFT perform demodulation? Demodulation utilizes the fact that the dot product acts as a
correlator. Correlation is the comparison of two signals to see how similar they are. If the input signal
closely matches a particular DFT sine/cosine row, its dot product with that row will have a large
magnitude. Conversely, if the input signal does not match up with the sine/cosine wave, the dot product
will be small. So, by taking the dot product of the input vector with each sine/cosine row of the DFT
matrix, we are asking the question, How does the input vector correlate with each row, that is, with each
frequency? Each individual dot product or correlation can be positive or negative. We get a separate
correlation of the input with the DFT cosine wave (I) and sine wave (Q). When we plot the I and Q
components of the dot product on x and y axes, we get a soft decision, that is, a point on the received
QAM constellation diagram, not necessarily landing exactly on one of the constellation symbols. Correctly
determining which constellation point was sent by the transmitter gives us the data bits for output to the
FEC.
How can we interpret a matrix multiplication as a weighted sum of rows? Instead of interpreting the DFT
matrix multiplication as a series of dot products with the input vector, we can take the exact same
computation and interpret it as the weighted sum of the rows of the IDFT matrix, where the weights are
QAM symbols. To do this, we interpret each element of the input vector as a QAM symbol. We interpret
each row of the IDFT matrix as a carrier wave at a particular frequency; this is easy to visualize looking at
Figure I-53 above, which show the sine and cosine waves in the rows of the matrix.
How does the DFT perform modulation? The goal is to modulate the input QAM symbols onto the
respective carriers. We take the 1st row of the IDFT matrix and multiply every element of this row by the
1st QAM symbol. This modulates the 1st QAM symbol to the carrier frequency of the 1st row. Take the 2nd
row of the IDFT matrix and multiply every element of this row by the 2nd QAM symbol. This modulates the
2nd QAM symbol to the carrier frequency of the 2nd row. And so forth for all the carriers. This gives us 4096
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or 8192-QAM modulators. We then sum all these modulator outputs to get a single composite signal. This
summation, analogous to a large RF combining network, comes for free as part of the matrix
multiplication. So, multiplication by the IDFT matrix is equivalent to 4096 or 8192-QAM modulators plus
their combining network. In the above figure showing an OFDM transmitter, each individual QAM
modulator block is the product of an input QAM symbol with a single row of the matrix corresponding to
one subcarrier.
What about complex arithmetic? The DFT uses complex multiplication, in which each complex number
consists of a pair of real numbers: the real or I (in-phase) component, and the imaginary or Q (quadrature)
component. Equivalently, in polar form each complex number consists of an amplitude and a phase
relative to the RF center frequency. The multiplication of two complex numbers requires 4 real
multiplications and two real additions. In this tutorial we have not placed emphasis on this mathematical
detail, but a web search will provide further information on complex arithmetic for the interested reader.
How is the DFT/FFT used for spectrum analysis? A spectrum analyzer is a device which measures the
frequency content of an input signal. Fortunately, this is precisely what the DFT does. Multiplying by the
DFT matrix measures the correlation (dot product) of the input signal with each row in the DFT matrix, and
each row is a sine/cosine of a particular frequency. Thus, each output bin gives the frequency content at
that frequency.
Figure I-54 shows a block diagram of a digital spectrum analyzer which may reside in the CM or CMTS. The
input signal enters at the left of the diagram; this signal is the full upstream or downstream band of the
cable plant. An analog front end amplifies the signal and provides RF gain control. A high-speed analog-to-
digital converter (ADC), typically 2.5 Gsps or higher, provides digital samples of the signal. A digital tuner,
consisting of digital oscillator and lowpass filter, selects the desired analysis band around a specified
center frequency, and outputs complex (I and Q) sample values. The signal from the selected band is
applied to the FFT, which multiplies the signal by the DFT matrix as described in earlier sections. Each bin
of the FFT output consists of a complex value consisting of two numbers, real (I) and imaginary (Q), giving
the correlation of the input signal with the particular frequency corresponding to a single row of the DFT
matrix. Typically a spectrum analyzer is only concerned with the magnitude, not the phase, of the FFT
output. So, the power (magnitude-squared) of each bin is computed, that is, I^2 + Q^2 for each bin. If
spectrum smoothing (time averaging) is to be applied, the above process is repeated with a fresh set of
data from the same band, and the power values from several captures are averaged at each bin location.
The smoothed bins are converted to dB by taking 10*log10 of each bin power value. These dB values, one
for each frequency bin, are displayed as the spectrum of the input signal.
Note that if the spectrum analyzer is able to process the entire signal in one shot as a single analysis band,
the tuner is not necessary. The tuner is useful to provide a selectable spectrum analysis center frequency
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and span, that is, the ability to zoom into a particular portion of the band for detailed analysis. If a narrow
span is selected, the output sample rate may be reduced in accordance with the sampling theorem. The
sampling theorem states that a sample rate of real samples greater than twice the signal bandwidth, or a
sample rate of complex (I and Q) samples greater than the signal bandwidth, is adequate to represent the
signal without loss of information. If the band is being analyzed in pieces, then the tuner is used to step
through a sequence of center frequencies corresponding to multiple analysis segments of the band, and
the individual spectrum segments are spliced together to produce the overall wideband spectrum.
Figure I-55 shows a full-band spectrum as seen at the CM. The horizontal axis is in MHz, and the vertical
axis is in dB. This spectrum was spliced together from approximately 100 analysis segments, each of width
7.5 MHz. Time averaging of approximately 16 captures was used to smooth the spectrum plot.
What is windowing? Recall that the DFT matrix of Figure I-48 consists of rows of sines and cosines, with
each row containing a whole number of cycles. If the input signal happens to be a sine wave (CW) with a
frequency exactly equal to one of the rows of the DFT matrix, it will correlate perfectly with that row and
have zero correlation with the other rows. However, what happens if the frequency of the input signal
falls somewhere between two DFT rows, or off bin? (This is actually the most likely case.) In this case the
signal will correlate slightly with all the DFT rows. This will cause what is called spectral leakage wherein
an off-bin CW signal, instead of producing a single spike in the spectrum, produces a large number of
spikes.
To solve the spectral leakage problem, a data-tapering window is often used. A window is a sequence with
gradual reduction at the edges that is multiplied by the input signal before the signal is multiplied by the
DFT matrix. Its purpose is to taper the ends of the input signal vector, providing a smooth transition to
zero at the two ends. Tapering reduces spectral leakage and causes a CW signal to produce a compact
spectral spike, as we are used to when using an analog spectrum analyzer. There is a catch; the spectral
spike for a CW signal with windowing is slightly wider than it would be without windowing, implying that
windowing slightly degrades the resolution of the spectrum measurement. Figure I-56 shows some typical
window functions. An example of a popular window is the Hanning window, which has a raised-cosine
shape that is zero at both ends and rises smoothly to one in the center. The resolution bandwidth of a
Hanning window is 1.5 times the FFT bin spacing, an example of the reduction in resolution due to
windowing.
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Where Z0 is the characteristic impedance of the transmission line, in this case 75 ohms, and ZE is the
equivalent impedance of the reflected wave that adds to and interferes with the incident signal.
It is considered an equivalent impedance because it contains the impact of the reflection against two
mismatched interfaces as well as the round trip attenuation and delay between these two interfaces (See
Figure IV-1).
TAP20 TAP17
TAP23
AMP First Reflection 1
Main Signal
Second Reflection 2
Reflected Signal
Roundtrip Attenuation
& Delay A*e-jT
Equivalent Reflection Coefficient E = A 12 e-jt
The VSWR, which is the ratio between Emax and Emin, reveals the ripple magnitude. The VSWR in terms of
the reflection coefficient is given by:
1 + E
VSWR =
1 E
Since VSWR is a ratio of voltages, to obtain the equivalent peak-to-valley power ratio or ripple in dB,
Ripple (dB) = 10log10(VSWR2)
Alternatively the process can be reversed by solving for E in the previous equation to obtain:
VSWR 1
E =
VSWR + 1
The equivalent reflection coefficient E provides the micro-reflection level in dB in the following expression
Micro-reflection Level (dB) = 10log10(E 2)
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V.1 Background
CableLabs has established a DOCSIS Proactive Network Maintenance working group with a goal of
utilizing the data in DOCSIS-based communications systems to improve plant operations. The groups first
task is to produce a recommended practices document that enables cable operators to mine the
predistortion coefficients from the cable modems (CM) upstream adaptive equalizer.
Cable lines typically have many small echoes, so-called micro-reflections, which will disrupt digital
transmissions if not canceled. This is particularly true for high-speed upstream signals having a higher
order modulation, such as 64-QAM, or having wider bandwidth, such as 6.4 MHz. The system chosen by
DOCSIS uses predistortion (or pre-equalization), where a burst transmission is distorted prior to
transmission, and arrives at a cable modem termination system (CMTS) receiver with the plants distortion
canceled. The idea is that by reading the CMs predistortion coefficients using a network management
system, technicians can tell what plant impairments a CM is compensating for, and then compute what
may be wrong with the cable plant. By reading the data from many CMs you can localize the problems
using maps or connectivity data.
The process of programming the predistortion coefficients in the CM is handled during a periodic ranging
process, which is controlled by the CMTS.
The groups name, DOCSIS Proactive Network Maintenance, is somewhat limiting since the techniques
being developed show a reactive ability to speed time-to-repair. The utility of the technique is that it can
reduce expensive truck-rolls, either reactively or proactively.
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In this echo situation, an upstream transmission gets bounced back and forth between two impedance
discontinuities. The multiple recursion echo may be created in a situation such as is shown in the top of
Figure V-1. An upstream signal travels from right to left through an amplifier, a span of cable with taps,
and another amplifier. There are two impedance mismatches, labeled reflection points, which cause a
portion of the upstream signal to reflect back and forth until the reflections eventually die out. The
bottom of Figure V-1 shows the impulse response of the upstream channel. Note that there is a main
signal, followed by multiple recursions, each caused by a re-reflection. In this example, the echo is very
strong, so there are many significant recursions.
The multiple recursion scenario also has been observed in a drop cable, where a filter on one end has bad
upstream return loss, and a house on the other end also has bad return loss due to un-terminated
splitters. A CMs transmission from the house picks up multiple recursions.
REFLECTION
MAIN SIGNAL
REFLECTION REFLECTION
POINT POINT
MAIN
SIGNAL
1ST
RECURSION
AMPLITUDE
2ND
RECURSION
3RD
RECURSION
4TH
RECURSION
TIME
DELTA
T
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LONG CABLE
IN OUT
OPEN
OPEN
WIRING DIAGRAM TO MAKE A
MULTIPLE RECURSION ECHO
LONG CABLE
IN OUT
SHORT CABLE
-35 dB SIGNAL
CAUSED BY REFLECTION
MAIN SIGNAL
POOR TAP- POINT
TO-OUTPUT
ISOLATION
MAIN
SIGNAL
AMPLITUDE
1ST
RECURSION
TIME
DELTA
T
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POINT D
POINT C 1ST
RECURSION
FROM CM
MAIN SIGNAL
REFLECTION REFLECTION
POINT A POINT B
Figure V-4 - How A Multiple Recursion Echo can be Canceled with Predistortion
1 + a + a 2 + a 3 + a 4 + .....
where 1.0 is the main signal amplitude and a is the first echos amplitude in linear terms. That is, for a -3
dBc echo a = 0.707. The a2, a3, a4 components and so on represent respectively the amplitude of the
recurring second, third, fourth and higher order echoes. In a baseband channel a is real, but in an RF
channel a may be complex. To be more precise,
a = Ae j 2fT
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where A is the amplitude of the echo, f is carrier frequency (MHz) and T is the delay of the echo (sec).
However, the equations are easier to present by simply using a.
So its solution, meaning the inverse distortion that has to be applied for upstream path distortion
compensation, can be computed as:
1
=1 a
1 + a + a + a 3 + a 4 ....
2
which shows that an infinitely recursive echo can be canceled by a single recursion. So you should be able
to cancel a multiple recursion echo with an adaptive equalizer with only two taps one for the main signal
and one for the echo. To be precise, this example applies to an ideal case where the echo delay T equals a
multiple of the symbol period, which for a 5.12 Msym/sec DOCSIS upstream symbol rate is Ts = 195 ns. So,
the pre-equalizer can exactly cancel the echo with a single tap if the single echo has delay T = 195 ns, 390
ns, or 585 ns, etc. If the echo lies between these multiples, the equalizer will activate additional taps to
provide interpolation. In that case it will be more difficult to see the pattern of a single main recursion.
A single recursion echo can be modeled by 1 + a where 1.0 is the main signal amplitude and a is the
echos amplitude in linear terms.
The equalizer solution is for a single recursion echo is:
1
= 1 a + a2 a3 + a4
1+ a
So the result is what was expected.infinitely recursive. The first term 1 represents the main tap of the
equalizer. The second term -a acts to cancel the echo by subtracting it. However, in doing so, it causes
another, smaller echo in the response. This smaller echo requires the third term to cancel it. This produces
another, yet smaller echo, which requires the fourth term to cancel it, and so on until reaching the end of
the equalizer delay line. After that, any remaining echo energy (hopefully very small) is not canceled, and
shows up as reduced RxMER (received modulation error ratio), essentially a noise floor, in the receiver.
If a is a relatively big number such as 0.707 (-3 dBc), and the delay T of the echo is several symbol
periods, the taps might run out in the pre-equalizer before getting an accurate solution. DOCSIS 2.0 and
later pre-equalizers have 24 taps, with 7 taps normally assigned ahead of the main tap, leaving 16 taps to
cancel the echo. For a small value of a such as 0.1 (-20 dBc), with a short echo delay, 16 taps are normally
sufficient to cancel the echo with minimal residual energy.
Note that the recursions in the previous equation have alternating signs. To check for this effect, examine
the real and imaginary parts of the equalizer taps. If the response is alternating in sign, it is a hint that this
type of solution may be present.
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MAIN MAIN
SIGNAL SIGNAL
1ST 1ST
RECURSION RECURSION
AMPLITUDE
AMPLITUDE
2ND
RECURSION
3RD
RECURSION
4TH
RECURSION
MAIN MAIN
SIGNAL SIGNAL
1ST 1ST
RECURSION RECURSION
AMPLITUDE
AMPLITUDE
2ND
RECURSION
3RD
RECURSION
4TH
RECURSION
Figure V-5 - Comparison of Signal Path Impulse Responses and Programming for Adaptive Equalizers
Figure V-5 summarizes both types of echoes and the resulting programming that could be found in the
adaptive equalizer to cancel the echoes.
V.5.4 Conclusion
The upstream cable plant can have two distinctly different types of echoes, but if the echoes are relatively
weak, the differences may not be significant. If the echoes are strong, the differences can be exploited to
help a cable technician diagnose and fix the cause of the strong echo.
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Analysis Tool SNMP Coefficient Parser FFT Transform CMTS Modem Analysis Module
snmp collection()
snmp results()
parsed eq data()
fft data()
evaluate boundaries()
boundary results()
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from the origin (0,0) to any point on the plot. The phase is the angle (in radians) of a line drawn from the
origin (0,0) to any point on the plot. Observe that the echo makes a circle on the plot, and the bigger the
reflections, the bigger the diameter of the circle. Likewise, the greater the LENGTH, the faster the circle
rotates as the frequency is changed. (An alternate way of conveying phase information would be a phase
vs. frequency plot, which could be also be placed on graph 3, using a different color and vertical scale.)
The softwares invert button inverts the frequency response. So if the magnitude went up at some
frequency, when inverted it will go down. This illustrates how the CM would be programmed vs.
frequency.
Suggested experiments:
One of the interesting conditions that happen in the field is the case of a single reflection that sends a
signal backwards. But the back reflection is never seen at the end (CM for downstream or CMTS for
upstream). This could happen if there were only one impedance mismatch, but the launch amplifier had
good output return loss and absorbed the reflected energy.
Make 1 =0.8 and 2 = 0, and watch the ripples go away. This effectively opens up one end of the echo
tunnel and makes the ripple go away. However, note on graph 2 that the peak amplitude is not 1.0
anymore, it has dropped due to a large percentage of the signal being reflected. This really happens in
cable plant can be a cause for low signal levels.
Change cable type to a lossy type and watch the effect on graph 1. Cable loss dampens the reflections.
Decrease the LENGTH until there a just a few ripples on graph 1. Now note on graph 2 one cant really
observe ripples, but maybe just a tilt or a flat attenuation, depending on center frequency. This short
length could indicate that an echo tunnel is inside a home.
Figure VII-1 - An Upstream Feeder Leg With a Pair of Damage Points Separated by a LENGTH. The Reflection
Points Form an Echo Tunnel
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Figure VII-2 - A Screen Shot of the Software Showing Graphs 1-5 and Controls on the Right
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18
Patents pending.
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Amplitude in dB
50
40
30
20
10
0
261
521
781
1041
1301
1561
1821
2081
2341
2601
2861
3121
3381
3641
3901
4161
4421
4681
4941
5201
1
Frequency Samples
Figure VIII-2 - A Digital Cable Signal that was Captured by Rapidly Retuning an SDR. The Standing Wave
Indicates a Reflected Signal is Present
Figure VIII-3 - A Processed Signal Showing the Single Reflection, Plus Harmonics Caused by Roll-Off of the 6
MHz Haystacks at Band Edges
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Figure VIII-4 - A Cablelabs Engineer Making a TDR Measurement in the Field. The SDR is in his Backpack
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Appendix IX MIBS
The CableLabs DOCS-IF3-MIB defines the SNMP calls and responses that will be used to set the variables of
the capture, turn it on, receive and interpret the data, and then finally turn the capture off. The current
version of the MIB is here: http://mibs.cablelabs.com/MIBs/
To set the parameters of the capture:
EXAMPLE CODE
iii. Creating a spectrum display
iv. Exporting spectrum display
i. MIBs, etc.
ii. Creating a spectrum display
iii. Exporting spectrum display
a. What else?
1 and 2 are functionally equivalent but I would use 1 since it is also supported by Intel modems.
1 and 2 may coexist on the same modem.
2 and 3 will not coexist since 2 is a superset of 3.
1 and 3 do not typically coexist on the same modem
IX.2 DocsIF3
This is all described in great detail in the DOCS-IF3-MIB, but here is an overview.
IX.2.1 docsIf3CmSpectrumAnalysisCtrlCmd
These mibs control the start/stop frequencies, segment width and bin counts
1.3.6.1.4.1.4491.2.1.20.1.34.1 = mib enable
1.3.6.1.4.1.4491.2.1.20.1.34.2 = mib inactivity timeout
1.3.6.1.4.1.4491.2.1.20.1.34.3 = first segment center frequency
1.3.6.1.4.1.4491.2.1.20.1.34.4 = last segment center frequency
1.3.6.1.4.1.4491.2.1.20.1.34.5 = segment frequency span
1.3.6.1.4.1.4491.2.1.20.1.34.6 = number of bins per segment
1.3.6.1.4.1.4491.2.1.20.1.34.7 = equivalent noise bandwidth
1.3.6.1.4.1.4491.2.1.20.1.34.8 = window function (see options below in tree)
1.3.6.1.4.1.4491.2.1.20.1.34.9 = number of averages NOTE: Often only 1 is supported
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IX.2.2 docsIf3CmSpectrumAnalysisMeasTable
This is the table where the actual spectrum data is found.
1.3.6.1.4.1.4491.2.1.20.1.35 = Table
1.3.6.1.4.1.4491.2.1.20.1.35.1 = TableEntry
1.3.6.1.4.1.4491.2.1.20.1.35.1.1 = center frequency
1.3.6.1.4.1.4491.2.1.20.1.35.1.2 = amplitude data (in a hex string)
1.3.6.1.4.1.4491.2.1.20.1.35.1.3 = segment power
+--docsIf3CmSpectrumAnalysisMeasTable(35)
|
+--docsIf3CmSpectrumAnalysisMeasEntry(1)
| Index: docsIf3CmSpectrumAnalysisMeasFrequency
|
+-- ---- Integer32 docsIf3CmSpectrumAnalysisMeasFrequency(1)
+-- -R-- String docsIf3CmSpectrumAnalysisMeasAmplitudeData(2)
| Textual Convention: AmplitudeData
| Size: 0 | 2..4116
+-- -R-- Integer32 docsIf3CmSpectrumAnalysisMeasTotalSegmentPower(3)
Textual Convention: TenthdB
IX.3.2 cmSpectrumAnalysisEnabledCtrlCmd
These are the rest of the objects mentioned earlier that may require the mib to be enabled. If the modem
has an older version of the Broadcom mib, these may not exist and default settings must be used.
1.3.6.1.4.1.4413.2.2.2.1.2.5.5 = first segment center frequency
[cmSpectrumAnalysisFirstSegmentCenterFrequency]
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IX.3.3 cmSpectrumAnalysisMeasurementTable
This is the equivalent of the docsIf3CmSpectrumAnalysisMeasTable
1.3.6.1.4.1.4413.2.2.2.1.2.5.1 = BCSpectrumAnalysisMeasTable
[cmSpectrumAnalysisMeasurementTable]
1.3.6.1.4.1.4413.2.2.2.1.2.5.1.1 = BCSpectrumAnalysisMeasEntry
[cmSpectrumAnalysisMeasurementEntry]
1.3.6.1.4.1.4413.2.2.2.1.2.5.1.1.1 = Index: Center Frequency
[cmSpectrumAnalysisFrequency]
1.3.6.1.4.1.4413.2.2.2.1.2.5.1.1.2 = Spectrum Amplitude Data
[cmSpectrumAnalysisAmplitudeData]
IX.4 Broadcom
Broadcom names are unofficial.
Convention is to relate them to the docsIf3 version for which we have a mib.
IX.4.1 BCSpectrumCtrlCmd
This is the equivalent of the docsIf3CmSpectrumAnalysisCtrlCmd objects. However, (unlike the docsIf3
mib) certain versions requires the mib to be enabled before the rest of these objects become settable.
IX.4.2 BCSpectrumEnabledCtrlCmd
These are the rest of the objects mentioned earlier that may require the mib to be enabled. If the modem
has an older version of the Broadcom mib, these may not be exist and default settings must be used.
1.3.6.1.4.1.4413.2.2.2.1.2.5.5 = first segment center frequency
1.3.6.1.4.1.4413.2.2.2.1.2.5.6 = last segment center frequency
1.3.6.1.4.1.4413.2.2.2.1.2.5.7 = segment width
1.3.6.1.4.1.4413.2.2.2.1.2.5.8 = number of bins per segment
1.3.6.1.4.1.4413.2.2.2.1.2.5.9 = window function (same values as docsIf3 mib)
1.3.6.1.4.1.4413.2.2.2.1.2.5.10 = equivalent noise bandwidth
IX.4.3 BCSpectrumAnalysisMeasTable
This is the equivalent of the docsIf3CmSpectrumAnalysisMeasTable
1.3.6.1.4.1.4413.2.2.2.1.2.5.1 = BCSpectrumAnalysisMeasTable
1.3.6.1.4.1.4413.2.2.2.1.2.5.1.1 = BCSpectrumAnalysisMeasEntry
1.3.6.1.4.1.4413.2.2.2.1.2.5.1.1.1 = Index: Center Frequency
1.3.6.1.4.1.4413.2.2.2.1.2.5.1.1.2 = Spectrum Amplitude Data Software Example Programs
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Common Project
Git Repository Name Description
Name
Applications:
FBC graphing utility. Can graph data from files or by connecting
SAGraph SAGraph directly to cable modems or CMTS devices.
SID (sometimes called Spectra) is a library designed to identify
Spectrum Impairment
Detector Spectra impairments in a downstream spectrum. It provides a Swing program
to view spectrum data and visualize SIDs results.
LeakageDetector LeakageDetector Software Defined Radio- based signal leakage detection.
Tool that connects to a CMTS and gather various mib values
PreEqGather PreEqGather (including preeq data)
Application that correlates MTR to SNR data to detect intermittent
IntermittentCorr IntermittentCorr cable modems.
PNM Pre-Equalization. Decodes, Groups and plots modem pre-eq
PreEqualizationAnalysis PreEqualizationAnalysis data.
TunnelEchoSimulator TunnelEchoSimulator Learning/teaching tool, to help explain how echo tunnels work.
Cable Modem grouping based on Pre-Equalization data. (C++)
cm-matcher cm-matcher (Newer work in Utilities/Cable Modem Utils)
SDR SDR Software Defined Radio
Utility for mapping known RF sources (Radio, Broadcast TV,...)
qammap qammap alongside modem/set-top box information about error rates.
Post analysis tool for power data captured by the JouleTool.
PowerBrowser PowerBrowser Generates histograms of the various frequency bands power
information.
Post analysis tool for data captured by the JouleTool or many VSAs.
JouleToolBrowser JouleToolBrowser Supports amplitude only or IQ value pairs (one per line).
Tool that uses an NI digitizer to gather upstream data and save
JouleTool JouleTool samples from it and information about the power levels encountered.
eq2fr scans cable modems' equalizer data at various upstream
eq2fr eq2fr channel frequencies and converts them into frequency response plots
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Appendix XI Acknowledgements
On behalf of the cable industry and our member and vendor companies, CableLabs would like to thank the
numerous individuals who contributed to the development of this document. In particular, we want to
extend our sincere appreciation and gratitude to the following Proactive Network Maintenance Working
Group members.
Contributor Company Affiliation
Alexander Adams Adams Consulting
Ayham Al-Banna, Rohini Telukutla Arris International
Thomas Clack, Bruce Currivan, Roger Fish Broadcom Corporation
Ken Martin Buckeye CableSystem
Robert Cruickshank Cablevision
Alberto Campos, Eduardo Cardona, Kevin Kershaw, Bill Kostka, Dustin Tracy, Ryan Vail, Cable Television Laboratories, Inc.
Tom Williams
Todd J. Gingrass CCI Systems
Ron Hranac Cisco Systems
Pradeep Anand, Will Berger, Kirk Erichsen Charter Communications
Phillip Chang, Robert Gonsalves, Spondon Hazarika, Larry Wolcott Comcast Cable.
Jeff Finkelstein, Mark Geiger, Christopher Reyes, Jason Sailor, Huy Tran Cox Communications
John Moran Huawei
Patricio Latini Intraway
Walter Miller JDSU
Charles Moore, Jack Moran, Robert Thompson Motorola, Inc.
James Medlock Ponderosa Systems
Jim Liu, Michael Truong Rogers
David Hunter Scrub Jay Communications
Niem Dang, Daniel Howard, Dean Stoneback SCTE
Steve Saunders Sentosa Technologies
Jerry Green Sunrise Telecom
Rob Richards VeEX, Inc.
Antonio Bonici, Alex Garcia Videotron
Brady Volpe The Volpe Firm
Scott Helms Zcorum
We would particularly like to thank Robert Thompson of Motorola and Ron Hranac of Cisco for their
commitment and leadership as the Proactive Network Maintenance Working Group editors; Alberto
Campos of CableLabs for all his efforts as Working Group Lead; Eduardo Cardona of CableLabs for leading
the reference implementation development effort; and all other participants who provided input to the
working group.
Our sincere appreciation goes to operator members who supported this effort providing feedback and
facilitating field data; in particular Nick Segura from Charter, Chris Nelson from Time Warner Cable, Wil
Colon from Comcast, Joe Jensen from Buckeye, Mike Giobbi from Armstrong, Bob Cruickshank from
Cablevision and George Hart from Rogers. Special thanks to Todd Szuter and Scott Johnston from Comcast
for field verification of impairment scenarios and to Anupama Purohit from CableLabs for laboratory
verification of micro-reflection and group delay scenarios.
07/25/16 CableLabs 183