Chapter 1: Free space path loss model

Wireless Propagation Characteristics

• Most wireless radio systems operate in urban area

– No direct line-of
of-sight
sight (los) between transmitter and receiver

• Radio wave propagation attributed to

– Reflection

– Diffraction and

– Scattering

• Waves travel along different paths of varying lengths

– Multipath propagation

– Interaction of these waves can be constructive or destructive

 Strengths of the waves decrease as the distance between Tx and Rx

increase
 We need Propagation models thathatt predict the signal strength at Rx from a
Tx
 One of the challenging tasks due to randomness and unpredictability in the
surrounding environment

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 What is the general principle?

o The received power decays as a function of Tx-Rx separation distance

raised to some power
o i.e., power-law function
 Path loss for unobstructed LOS path
 Power falls off : Proportional to d2 P c
Pr (d )  t2 and ,  
d f
Pt Gt Gr 2 4 Ae
Pr (d )  where, G 
(4 ) 2 d 2 L 2

 What is the path loss?

Tx power P
 t
– Represents signal attenuation Rx power Pr

– What will be the order of path loss for a FM radio system that
transmits with 100 kW with 50 km range?

Also calculate: what will be the order of path loss for a Wi-Fi radio system that
transmits with 0.1 W with 100 m range?

Path Loss in dB

 It is difficult to express Path loss using transmit/receive power

– Can be very large or

– Very small

 Expressed as a positive quantity measured in dB

– dB is a unit expressed using logarithmic scale

– Widely used in wireless

Pt  Gt Gr 2 
PL(dB )  10 log   10 log  2 2
Pr  (4 ) d 

Expressed as a positive quantity measured in d

Pt  2  2
PL(dB )  10 log   10 log  2 2
Pr  (4 ) d 
dBm and dBW

 dBm and dBW are other two variations of dB

– dB references two powers (Tx and Rx)

– dBm expresses measured power referenced to one mW

– Particularly applicable for very low received signal strength

– dBW expresses measured power referenced to one watt

– dBm Widely used in wireless

– P in mW  P 
x dBm  10 log 
 1mW 
 In a wireless card specification, it is written that typical range for IEEE
802.11 received signal strength is -60 to -80 dBm. What is the received
signal strength range in terms of watt or mW?
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 The received power at a distance d is then d 
Pr (d )  Pr (d 0 )  0 
d 
In dBm,   d0  
2

 Pr (d 0 )   
Pr (d ) (dBm)  10 log  d  
 1mW 
 
 
 P (d )  d 
Pr (d ) (dBm)  10 log  r 0   20 log  0 
 1mW  d 

d 
Pr (d ) (dBm)  Pr (d 0 )(dBm)  20 log  0 
d 

Propagation Mechanism

propagation in mobile radio communication system are:

 Reflection

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  Diffraction

 Scattering

Snell’s Law

Reflection (smooth surface)

• Occurs when wave impinges upon another medium having different

electrical properties

• If radio wave is incident on a perfect dielectric

 Part of energy is reflected back

 Part of energy is transmit

Reflection - Brewster Angle

• No reflection occurs.

• Occurs only for parallel polarization

Diffraction (rough surfaces)

• Diffraction is the bending of wave fronts around obstacles.

• Diffraction allows radio signals to propagate behind obstructions and is

thus one of the factors why we receive

• signals at locations where there is no line-of-sight from base stations

• Although the received field strength decreases rapidly in shadow zones.

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Scattering (many directions)

• Scattering occurs when the medium through which the wave travels
consists of objects with dimensions that are small compared to the
wavelength, and where the number of obstacles per unit volume is large.

Scattered waves are produced by

 rough surfaces,

 small objects,

 or by other irregularities in the channel.

Two Ray Model:

• Free space propagation model is inaccurate in many if the cases when

used alone.

• This model is designed for both LOS and Reflected rays.

• This model is accurate for predicting the large scale signal strength over
distance of several Kilometers.

• In most of the cases the T-R Separation is only few tens of kilometers hence
the earth is assumed to be FLAT.

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General Expression for E field w.r.t “d” and “t”

E Field in Free space Prop is Given by:

Eo - Free Space E Field Envelope of E Field

do - Reference Distance

Two waves arrives at the receiver:

– Direct wave at distance d’

– Reflected wave at distance d”

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The Resulting E Field is given by:

Path difference calculation:

• The line of sight rays and reflected rays have different paths.

• This difference is calculated by the method of imaging .

• The method of images (or method of mirror images) is a mathematical tool

for solving differential equations, in which the domain of the sought
function is extended by the addition of its mirror image.

• Generally they are used for analysing the charges and the magnetic substances.

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When T-R Separation is very large compared to ht + hr the equation can be
simplified by using Taylor’s series approximation

Once the path difference is known, then the Phase Difference between the two E
Field Components and Time Delay between the arrival of the two components
can be easily computed by the following relations:

• When “d” becomes larger and larger the differences between the d’ and d”
becomes very small.

• In this case the amplitude levels of both LOS and Reflected Rays are
virtually identical.

Final Receive Power

• Finally, the Received power at the distance d from the transmitter for the 2
ray model is given by:

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Out door models

Outdoor radio transmission - irregular terrain

The terrain profile to be considered for estimating path loss (trees, buildings,
hills)

• Some common models used are

 Longley Rice Model

 Okumura Model

 Hata model

Longley Rice model

 Point to point communication

 Frequency range 40MHz to 100MHz
 Two ray model is used
 Computer model (20MHz to 10 GHz)
 (input frequency, path length, Polarization, Antenna type, Surface
condition, climatically conditions)

Modes

1. Terrain path profile (Path specific)

2. Area mode (estimate the prediction)

Okumura Model:

 In 1968 Okumura produced a new model by lot of measurements

 Used for signal prediction in urban areas
 It is a graphical method to predict the median attenuation relative to free-
space for a quasi smooth terrain

 The model consists of set of curves developed from measurements

 valid for a particular set of system parameters

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  carrier frequency, antenna height, etc.

 valid only for 400 > fc > 1500 MHz - large city
30 > hte > 200 m; 1 > hre > 10 m;

Other forms depends on the scenario L50(d)(dB) = LF(d)+ Amu (f,d) – G(hte )
– G(hre) – GArea

• L50: 50th percentile (i.e., median) of path loss

• LF(d): free space propagation path loss.

• Amu(f,d): median attenuation relative to free space

• G(hte ) : base station antenna high gain factor

• G(hre) : mobile antenna height gain factor

• GArea: gain due to type of environment

Antenna gain varies at rate of 20dB or 10dB per decade

 G(hte ) = 20log(hte/200) :1000m > hte > 30m

 G(hre) = 10log(hre /3) : hre <= 3m

 G(hre) = 20log(hre /3) : 10m > hre > 3m

Hata Model

 Most widely used model in Radio frequency

 Predicts the behavior of cellular communication in built up areas
 Applicable to transmission in cities
 Suited for point to point and broadcast transmission
 150 MHz to 1.5 GHz, Transmission height up to 200m and link distance < 20
Km
 Valid from 150MHz to 1500MHz,
extension of Okumura model
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  For urban areas the formula is:
 L50(urban,d)(dB)=69.55+26.16logfc- 13.82loghte– a(hre)+(44.9 –
6.55loghte)logd
where
 fc is the frequency in MHz
 hte is effective transmitter antenna height in meters (30-200m)
 hre is effective receiver antenna height in meters (1-10m) d is T-R
separation in km
 a(hre) = correction factor for effective mobile antenna height = (1.1logfc –
0.7)hre – (1.56logfc – 0.8) dB for a small to medium sized city

Indoor model:

Indoor Channels are different from traditional channels in two ways

 The distances covered are much smaller

 The variability of environment is much greater for a much small range of

Tx and Rx separation

Propagation inside a building is influenced by:

 Layout of the building

 Construction materials

 Building type: office , home or factory

Indoor models are dominated by the same mechanism as out door models:

- Reflection, Diffraction and Scattering

Conditions are much more variable

 Doors/Windows open or not

 Antenna mounting : desk ceiling etc

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  The levels of floor

Indoor models are classified as

 Line of sight (LOS)

 Obstructed (OBS) with varying degree of clutter

Partition losses (same floor)

Two types of partitions

 Hard partitions: Walls of room

 Soft partitions : Moveable partitions that do not span to ceiling

Partitions vary widely in their Physical and electrical properties.

Path loss depend upon the types of partitions

Partitions losses (between floors)

These losses depends on

• External dimension and material used for buildings

• Types of construction used to create floors

External surroundings

• Number of windows used

• Tinting on the windows

• Floor Attenuation Factor (FAF) increases with the number of floors

Log distance path loss model

Path loss can be given as

where n is path loss exponent, σ is standard deviation

n and σ depend on the building type.

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Smaller value of σ indicates better accuracy of path loss model

Attenuation factor model

Obtained by measurement in multiple floors building

FAF: Floor attenuation factor

nsf : Path loss exponent same floor

Signal penetration into building

 Frequency sharing with neighboring buildings.

 Model for signal penetration with external transmitter at lower floor
 Clutter introduce attenuation in buildings
 At higher floor a LoS may exist
 RF penetration is function of frequency and height within the building
 The antenna pattern matters
 Penetration loss decreases with increasing frequency
 Windows show less penetration loss

Small Scale Fading

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Fading :

 The term fading is used to describe rapid fluctuation of the amplitude of a

radio signal over a short period of time or travel distance
 Fading is caused by destructive interference between two or more versions
of the transmitted signal being slightly out of phase due to the different
propagation time
 This is also called multipath propagation
 The different components are due to reflection and scattering form trees
buildings and hills etc.
 At a receiver the radio waves generated by same transmitted signal may
come
 From Different direction
 With Different propagation delays
 With Different amplitudes
 With Different phases
 Each of the factor given above is random
 The multipath components combine vectorially at the receiver and produce
a fade or distortion.

Effects of Fading
 Multipath propagation creates small-scale fading effects.
 The three most important effects are:

 Rapid changes in signal strength over a small travel distance or time

interval;

 Random frequency modulation due to varying Doppler shifts on different

multipath signals; and

 Time dispersion (echoes) caused by multipath propagation delays.

 Even when a mobile receiver is stationary, the received signal may fade due
to a non-stationary nature of the channel (reflecting objects can be moving)

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Factors influencing small-scale fading

 Multipath propagation
 Speed of mobile receiver
 Speed of surrounding objects
 The transmission bandwidth

Parameters of Mobile Multipath Channels

Time Dispersion Parameters

 Grossly quantifies the multipath channel

 Determined from Power Delay Profile

 Parameters include

 Mean Access Delay

 RMS Delay Spread

 Excess Delay Spread (X dB)

 Coherence Bandwidth

 Doppler Spread

 Coherence Time

Timer Dispersion Parameters

Determined from a power delay profile

Mean excess delay =

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 Rms delay spread=

Maximum Excess Delay (X dB):

 Defined as the time delay value after which the multipath energy falls to
X dB below the maximum multipath energy (not necessarily belonging to
the first arriving component).
 It is also called excess delay spread.

Delay Spread, Coherence BW

 Describes the time dispersive nature of a channel in a local area

 A received signal suffers spreading in time compared to the transmitted
signal
 Delay spread can range from a few hundred nanoseconds for indoor
scenario up to some microseconds in urban areas
 The coherence bandwidth Bc translates time dispersion into the
language of the frequency domain.
 It specifies the frequency range over which a channel affects the signal
spectrum nearly in the same way, causing an approximately constant
attenuation and linear change in phase
 The rms delay spread and coherence bandwidth are inversely
proportional to each other.

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Coherence Bandwidth (Bc)

 Range of frequencies over which the channel can be considered flat (i.e.
channel passes all spectral components with equal gain and linear phase).
 It is a definition that depends on RMS Delay Spread.
 Two sinusoids with frequency separation greater than Bc are affected quite
differently by the channel.
 Frequency correlation between two sinusoids: 0 <= Cr1, r2 <= 1.
 If we define Coherence Bandwidth (BC) as the range of frequencies over
which the frequency correlation is above 0.9, then

 where is rms delay

 If we define Coherence Bandwidth as the range of frequencies over which

the frequency correlation is above 0.5, then

 This is called 50% coherence bandwidth.

Doppler Spread and Coherence time

 Doppler Spread and Coherence time are parameters which describe the
time varying nature of the channel in a small-scale region.
 Time varying nature of channel caused either by relative motion between
BS and mobile or by motions of objects in channel are categorized by BD
and Tc.

Doppler Spread

 Measure of spectral broadening caused by motion

 We know how to compute Doppler shift: fd
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  Doppler spread, BD, is defined as the maximum Doppler shift: fm = v/λ
 if Tx signal bandwidth (Bs) is large such that Bs>> BD then effects of Doppler
spread are not important so Doppler spread is only important for low bps
(data rate) applications (e.g. paging),slow fading channel

Coherence Time

 Coherence time is the time duration over which the channel impulse
response is essentially invariant.
 If the symbol period of the baseband signal (reciprocal of the baseband
signal bandwidth) is greater the coherence time, than the signal will distort,
since channel will change during the transmission of the signal.

 Coherence time is also defined as:

 Coherence time definition implies that two signals arriving with a time
separation greater than TC are affected differently by the channel.

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Chapter 2 : Diversity Techniques

Small-Scale Multipath Measurements

• Multipath structure is very important for small scale fading.

Several Methods
 Direct RF Pulse System
 Spread Spectrum Sliding Correlator Channel Sounding
 Frequency Domain Channel Sounding
• These techniques are also called channel sounding techniques

Direct RF Pulse System

• This method help us to determine the power delay profile directly

• Objective is to find impulse response
• A narrow pulse is used for channel sounding.
• At the receiver the signal is amplified and detected using an envelop
detector.
• It is then stored on a high speed digital oscilloscope.
• If the receiver is set on averaging mode, the local average power delay
profile is obtained

Spread Spectrum Sliding Correlator Channel Sounding:

• The probing signal is wide band but the receiver is narrow band

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• The carrier signal is spread over large bandwidth by mixing it with
Pseudorandom noise(PN) sequence having chip rate Tc.

• At receiver signal is despread using same PN

• The transmitter chip clock rate is a little faster then the receiver chip clock
rate

• The result is sliding correlator.

• If the sequences are not maximally correlated then the mixer will further
despread the signal

• The chip rate Rc=1/Tc.

• RF bandwidth = 2Rc

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 • Processing gain:

• Time resolution Δτ=2Tc = 2/Rc

• Sliding factor (gamma)γ=α/α-β

• Alpha= transmitter chip rate

• Beta=receiver chip rate

Frequency Domain Channel Sounding

• Because of the dual relationship between time and frequency it is possible

to measure channel impulse response in frequency domain

• A vector network analyzer is used.

• The S-parameter test set is used to monitor the frequency response of the
channel.

• The frequency sweeper scans a particular frequency band by stepping

through the discrete frequencies.

Disadvantages:
• System requires careful calibration

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 • System required hardwired synchronization between transmitter and receiver.

• Practical only for indoor channel measurements

• Non real time nature of measurements

• For time varying channels the channel impulse response may change giving erroneous
measurements

Diversity combining methods

1. Selection combing:

2. Maximal Ratio Combining (MRC)

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 3. Equal Gain Combining

RAKE Receiver
 The RAKE receiver uses principle of multipath diversity
 A Rake Receiver is a radio receiver designed to counter the effects of multipath fading
 Several sub-receivers called ‘fingers’ are used
 RAKE receiver attempts to collect the time-shifted versions of the original signal by providing a
separate correlation receiver for each of the multipath signals

The overall signal Z' is given by :

The weighting coefficients:

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Advantages and Drawbacks
Advantage:

 Improved SNR
 Improved performance

Disadvantage:

 Cost
 Size
 Complexity

Macro Diversity

 Provides a method to mitigate the effects of shadowing, as in case of Large

scale fading
 Long term fading can be mitigated by macroscopic diversity like the
diversity using two base stations
 Large scale fading
 Shadow zone
 Log normally distributed
 Improves SNR in forward link
 Useful at base station
 Antenna selection with strong signal input
Micro Diversity

 provides a method to mitigate the effects of multi-path fading

 These fades are caused by multiple reflections from surroundings
 Short term fading can be mitigated by the diversity using multiple
antennas on the base station or mobile unit
 Small scale fading
 Prevents deep fades
 Narrow band signals
 Rapid fluctuations of the signal amplitude

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