FINAL Exam Jameel Communication Systems FALL 2013 Updated
FINAL Exam Jameel Communication Systems FALL 2013 Updated
FINAL Exam Jameel Communication Systems FALL 2013 Updated
______________________________ Section
______________________________ Semester
______________________________ EXAM:
EE410
Academic Year
Communication Systems
Time Allowed
Jan 22, 2014
Total Marks
M Ilyas Khan, Dr M. Tahir Mushtaq, Jameel Ahmad
_____________
Fall 2013
Final
2013
120 min.
100
Question
Q1
Q2
Q3
Q4
Total
Total Marks
25
25
25
25
100
Marks Obtained
Student ID:________________
Question No.1
PART-A
Section:_______
Student ID:________________
Section:_______
b) Determine the bandwidth if the amplitude of the message signal is doubled. (3 points)
c) Determine the bandwidth if the frequency of the message signal is doubled. (3 points)
Student ID:________________
Section:_______
Question No.2
a) The sinusoidal signal, ( ) = 8 sin(2 ) volts, is transmitted using a 4 bit binary
PCM system. The quantizer is of midrise type, with step size of 1 volt. Sketch the
resulting PCM wave for one complete cycle of the input. Assume a sample rate of
four samples per second, with samples taken at = , , , . . ,
(15 points)
b) Calculate the signal to quantization noise ratio (SQNR) for the above PCM signal. (5 points)
Student ID:________________
Section:_______
c) In the following an NRZ waveform is shown. Draw Manchester and bipolar RZ signals for the
same. (2.5+2.5 points)
Manchester
___________________________________________________________
Bipolar RZ
________________________________________________________________________
Student ID:________________
Section:_______
Question-No-3 (3+2+15+5)
a) Write the general expression for the impulse response of a matched filter ( 3points)
. Show all important steps and any assumptions. The received signal is
is
Your final expression should look like the following using either Q( ) function or complementary error
function erfc ( ).
2. Calculate
for Eb=2x10
-19
-20
Watts/Hz ( 2points)
Student ID:________________
Section:_______
Student ID:________________
Section:_______
Student ID:________________
Section:_______
d) Describe the Nyquist criterion for zero ISI (Inter symbol interference) (5points)
Solution
Question-No-4
Part-A
a) Block diagram of FSK generation is shown below. Write the corresponding output equation
( ) for this scheme.
Student ID:________________
Section:_______
Solution: (2.5points)
(2.5 points) Describe the following FSK receiver as coherent receiver or non-coherent receiver and Why?
Solution:
b) An FSK system transmits binary data at the rate of 2.5x106 bits per second. During the course of
transmission, white Gaussian Noise of zero mean and power spectral density No=10-20 Watt/Hz is
added to the signal. In the absence of noise, the amplitude, A, of the received sinusoidal wave for
digit 1 or 0 is 1 milli Volt. Determine the average probability of error for FSK.
Solution (5points)
= (
Student ID:________________
Section:_______
c) What are the 3 similarities and 3 differences in MSK and GMSK? (3points)
Similarities
Differences
MSK
GMSK
d) Draw the block diagram of MSK OR GMSK transmitter and receiver. Write a general time-domain
mathematical expression for a Gaussian filter impulse response used in GMSK. (1.5+1.5 points)
Student ID:________________
Section:_______
f)
MSK and GMSK are continuous phase modulation schemes while PSK has phase discontinuity.
What is the effect of phase discontinuity on spectrum? Why continuous phase is preferred?
(4points)
Student ID:________________
Section:_______
g) Explain which modulation scheme has better BER performance by observing the following BER
curves for GMSK, BPSK or MSK.(2 points)
GMSK
MSK
BPSK
Part-B
a)
Student ID:________________
b)
Section:_______
(5points)
In a random experiment, a trial of four successive tosses of a coin. If we define an RV X as the number
of heads appearing in a trial, determine Px(x)
c)
(5points)
and FX(x)
Student ID:________________
Sx( )=
Section:_______
d)
e)
(5points)
Student ID:________________
Section:_______
Student ID:________________
Appendix-A
Section:_______
Q Function:
An alternate form of error function. It basically defines the area under the
Standardized Gaussian tail. For a standardized Gaussian random variable X of zero
mean and unit variance, the Q-function is defined by
Q (v )
1
2
x2
v exp 2 dx
-------- ( A6.6)
(i)
(ii)
Q (v )
1
v
erfc
2
2
erfcu 2Q( 2u )
------- ( A6.7a)
------ ( A6.7b)
x
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
Q(x)
0.5
0.48006
0.46017
0.44038
0.42074
0.40129
0.38209
0.36317
0.34458
0.32636
0.30854
0.29116
0.27425
0.25785
0.24196
0.22663
0.21186
0.19766
0.18406
0.17106
0.15866
0.14686
0.13567
0.12507
0.11507
0.10565
0.0968
0.088508
0.080757
0.073529
0.066807
0.060571
0.054799
0.049471
0.044565
0.040059
0.03593
0.032157
0.028717
0.025588
0.02275
0.020182
0.017864
0.015778
0.013903
0.012224
x
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
3.75
3.80
3.85
3.90
3.95
4.00
4.05
4.10
4.15
4.20
4.25
4.30
4.35
4.40
4.45
4.50
Table 1: Values
Q(x)
0.010724
0.0093867
0.0081975
0.0071428
0.0062097
0.0053861
0.0046612
0.0040246
0.003467
0.0029798
0.0025551
0.002186
0.0018658
0.0015889
0.0013499
0.0011442
0.0009676
0.00081635
0.00068714
0.00057703
0.00048342
0.00040406
0.00033693
0.00028029
0.00023263
0.00019262
0.00015911
0.00013112
0.0001078
8.8417105
7.2348105
5.9059105
4.8096105
3.9076105
3.1671105
2.5609105
2.0658105
1.6624105
1.3346105
1.0689105
8.5399106
6.8069106
5.4125106
4.2935106
3.3977106
1
of Q(x) for 0 x 9
x
Q(x)
4.55 2.6823106
4.60 2.1125106
4.65 1.6597106
4.70 1.3008106
4.75 1.0171106
4.80 7.9333107
4.85 6.1731107
4.90 4.7918107
4.95 3.7107107
5.00 2.8665107
5.05 2.2091107
5.10 1.6983107
5.15 1.3024107
5.20 9.9644108
5.25
7.605108
5.30 5.7901108
5.35 4.3977108
5.40
3.332108
5.45 2.5185108
5.50
1.899108
5.55 1.4283108
5.60 1.0718108
5.65 8.0224109
5.70 5.9904109
5.75 4.4622109
5.80 3.3157109
5.85 2.4579109
5.90 1.8175109
5.95 1.3407109
6.00 9.86591010
6.05 7.24231010
6.10 5.30341010
6.15 3.87411010
6.20 2.82321010
6.25 2.05231010
6.30 1.48821010
6.35 1.07661010
6.40 7.76881011
6.45 5.59251011
6.50 4.0161011
6.55 2.87691011
6.60 2.05581011
6.65 1.46551011
6.70 1.04211011
6.75 7.39231012
x
6.80
6.85
6.90
6.95
7.00
7.05
7.10
7.15
7.20
7.25
7.30
7.35
7.40
7.45
7.50
7.55
7.60
7.65
7.70
7.75
7.80
7.85
7.90
7.95
8.00
8.05
8.10
8.15
8.20
8.25
8.30
8.35
8.40
8.45
8.50
8.55
8.60
8.65
8.70
8.75
8.80
8.85
8.90
8.95
9.00
Q(x)
5.2311012
3.69251012
2.60011012
1.82641012
1.27981012
8.94591013
6.23781013
4.33891013
3.01061013
2.08391013
1.43881013
9.91031014
6.80921014
4.6671014
3.19091014
2.17631014
1.48071014
1.00491014
6.80331015
4.59461015
3.09541015
2.08021015
1.39451015
9.32561016
6.2211016
4.13971016
2.7481016
1.81961016
1.20191016
7.91971017
5.20561017
3.41311017
2.23241017
1.45651017
9.47951018
6.15441018
3.98581018
2.5751018
1.65941018
1.06681018
6.84081019
4.3761019
2.79231019
1.77741019
1.12861019
erfc(x)
erfc(x)
1.000000
0.5
0.479500
x
1
erfc(x)
erfc(x)
0.157299
1.5
0.033895
x
2
erfc(x)
erfc(x)
0.004678
2.5
0.000407
erfc(x)
3
0.00002209
0.01
0.988717
0.51
0.470756
1.01
0.153190
1.51
0.032723 2.01
0.004475 2.51
0.000386
3.01
0.00002074
0.02
0.977435
0.52
0.462101
1.02
0.149162
1.52
0.031587 2.02
0.004281 2.52
0.000365
3.02
0.00001947
0.03
0.966159
0.53
0.453536
1.03
0.145216
1.53
0.030484 2.03
0.004094 2.53
0.000346
3.03
0.00001827
0.04
0.954889
0.54
0.445061
1.04
0.141350
1.54
0.029414 2.04
0.003914 2.54
0.000328
3.04
0.00001714
0.05
0.943628
0.55
0.436677
1.05
0.137564
1.55
0.028377 2.05
0.003742 2.55
0.000311
3.05
0.00001608
0.06
0.932378
0.56
0.428384
1.06
0.133856
1.56
0.027372 2.06
0.003577 2.56
0.000294
3.06
0.00001508
0.07
0.921142
0.57
0.420184
1.07
0.130227
1.57
0.026397 2.07
0.003418 2.57
0.000278
3.07
0.00001414
0.08
0.909922
0.58
0.412077
1.08
0.126674
1.58
0.025453 2.08
0.003266 2.58
0.000264
3.08
0.00001326
0.09
0.898719
0.59
0.404064
1.09
0.123197
1.59
0.024538 2.09
0.003120 2.59
0.000249
3.09
0.00001243
0.1
0.887537
0.6
0.396144
1.1
0.119795
1.6
2.6
0.000236
3.1
0.00001165
0.11
0.876377
0.61
0.388319
1.11
0.116467
1.61
0.022793 2.11
0.023652
2.1
0.002845 2.61
0.002979
0.000223
3.11
0.00001092
0.12
0.865242
0.62
0.380589
1.12
0.113212
1.62
0.021962 2.12
0.002716 2.62
0.000211
3.12
0.00001023
0.13
0.854133
0.63
0.372954
1.13
0.110029
1.63
0.021157 2.13
0.002593 2.63
0.000200
3.13
0.00000958
0.14
0.843053
0.64
0.365414
1.14
0.106918
1.64
0.020378 2.14
0.002475 2.64
0.000189
3.14
0.00000897
0.15
0.832004
0.65
0.357971
1.15
0.103876
1.65
0.019624 2.15
0.002361 2.65
0.000178
3.15
0.00000840
0.16
0.820988
0.66
0.350623
1.16
0.100904
1.66
0.018895 2.16
0.002253 2.66
0.000169
3.16
0.00000786
0.17
0.810008
0.67
0.343372
1.17
0.098000
1.67
0.018190 2.17
0.002149 2.67
0.000159
3.17
0.00000736
0.18
0.799064
0.68
0.336218
1.18
0.095163
1.68
0.017507 2.18
0.002049 2.68
0.000151
3.18
0.00000689
0.19
0.788160
0.69
0.329160
1.19
0.092392
1.69
0.016847 2.19
0.001954 2.69
0.000142
3.19
0.00000644
0.2
0.777297
0.7
0.322199
1.2
0.089686
1.7
0.016210
0.001863
0.000134
3.2
0.00000603
2.2
2.7
0.21
0.766478
0.71
0.315335
1.21
0.087045
1.71
0.015593 2.21
0.001776 2.71
0.000127
3.21
0.00000564
0.22
0.755704
0.72
0.308567
1.22
0.084466
1.72
0.014997 2.22
0.001692 2.72
0.000120
3.22
0.00000527
0.23
0.744977
0.73
0.301896
1.23
0.081950
1.73
0.014422 2.23
0.001612 2.73
0.000113
3.23
0.00000493
0.24
0.734300
0.74
0.295322
1.24
0.079495
1.74
0.013865 2.24
0.001536 2.74
0.000107
3.24
0.00000460
0.25
0.723674
0.75
0.288845
1.25
0.077100
1.75
0.013328 2.25
0.001463 2.75
0.000101
3.25
0.00000430
0.26
0.713100
0.76
0.282463
1.26
0.074764
1.76
0.012810 2.26
0.001393 2.76
0.000095
3.26
0.00000402
0.27
0.702582
0.77
0.276179
1.27
0.072486
1.77
0.012309 2.27
0.001326 2.77
0.000090
3.27
0.00000376
0.28
0.692120
0.78
0.269990
1.28
0.070266
1.78
0.011826 2.28
0.001262 2.78
0.000084
3.28
0.00000351
0.29
0.681717
0.79
0.263897
1.29
0.068101
1.79
0.011359 2.29
0.001201 2.79
0.000080
3.29
0.00000328
0.3
0.671373
0.8
0.257899
1.3
0.065992
1.8
0.010909
0.001143
0.000075
3.3
0.00000306
2.3
2.8
0.31
0.661092
0.81
0.251997
1.31
0.063937
1.81
0.010475 2.31
0.001088 2.81
0.000071
3.31
0.00000285
0.32
0.650874
0.82
0.246189
1.32
0.061935
1.82
0.010057 2.32
0.001034 2.82
0.000067
3.32
0.00000266
0.33
0.640721
0.83
0.240476
1.33
0.059985
1.83
0.009653 2.33
0.000984 2.83
0.000063
3.33
0.00000249
0.34
0.630635
0.84
0.234857
1.34
0.058086
1.84
0.009264 2.34
0.000935 2.84
0.000059
3.34
0.00000232
0.35
0.620618
0.85
0.229332
1.35
0.056238
1.85
0.008889 2.35
0.000889 2.85
0.000056
3.35
0.00000216
0.36
0.610670
0.86
0.223900
1.36
0.054439
1.86
0.008528 2.36
0.000845 2.86
0.000052
3.36
0.00000202
0.37
0.600794
0.87
0.218560
1.37
0.052688
1.87
0.008179 2.37
0.000803 2.87
0.000049
3.37
0.00000188
0.38
0.590991
0.88
0.213313
1.38
0.050984
1.88
0.007844 2.38
0.000763 2.88
0.000046
3.38
0.00000175
0.39
0.581261
0.89
0.208157
1.39
0.049327
1.89
0.007521 2.39
0.000725 2.89
0.000044
3.39
0.00000163
0.4
0.571608
0.9
0.203092
1.4
0.047715
1.9
0.41
0.562031
0.91
0.198117
1.41
0.046148
1.91
0.007210
2.4
0.006910 2.41
2.9
0.000041
3.4
0.00000152
0.000654 2.91
0.000689
0.000039
3.41
0.00000142
0.42
0.552532
0.92
0.193232
1.42
0.044624
1.92
0.006622 2.42
0.000621 2.92
0.000036
3.42
0.00000132
0.43
0.543113
0.93
0.188437
1.43
0.043143
1.93
0.006344 2.43
0.000589 2.93
0.000034
3.43
0.00000123
0.44
0.533775
0.94
0.183729
1.44
0.041703
1.94
0.006077 2.44
0.000559 2.94
0.000032
3.44
0.00000115
0.45
0.524518
0.95
0.179109
1.45
0.040305
1.95
0.005821 2.45
0.000531 2.95
0.000030
3.45
0.00000107
0.46
0.515345
0.96
0.174576
1.46
0.038946
1.96
0.005574 2.46
0.000503 2.96
0.000028
3.46
0.00000099
0.47
0.506255
0.97
0.170130
1.47
0.037627
1.97
0.005336 2.47
0.000477 2.97
0.000027
3.47
0.00000092
0.48
0.497250
0.98
0.165769
1.48
0.036346
1.98
0.005108 2.48
0.000453 2.98
0.000025
3.48
0.00000086
0.49
0.488332
0.99
0.161492
1.49
0.035102
1.99
0.004889 2.49
0.000429 2.99
0.000024
3.49
0.00000080