Mobile Radio Propagation

Module2
Wireless communication by Rappaport

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Answer the quiz on Radio Propagation,it is part of Formative assessment
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https://h5p.org/node/968158
Mobile Radio Propagation

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 Introduction
 The transmission path between the transmitter and the receiver can vary
from simple line-of-sight to one that is severely obstructed by buildings,
mountains, and foliage.
 The speed of motion impacts how rapidly the signal level fades as a
mobile terminal moves in space.
 The mechanisms behind electromagnetic wave propagation can generally
be attributed to reflection, diffraction and scattering.
 Due to multiple reflections from various objects, the electromagnetic
waves travel along different paths of varying lengths. 4
Multipath Signals
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 Introduction
 The interaction between these waves causes multipath fading at a specific
location and the strengths of the waves decrease as the distance between
the transmitter and receiver increases.

 Propagation models focused on predicting the average received signal

strength at a given distance from the transmitter, as well as the
variability of the signal strength in close spatial proximity to a
particular location.
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 Mobile Radio Propagation

Large Scale Small Scale Propagation

Propagation Model Model (Fading)

 T-R Distance: several hundreds or  T-R Distance: Few wavelength or orders of

thousands of meters seconds
 Behavior is slowly time varying  Behavior varies much faster in time
 Due to terrain and the density & dimensions  Due to environment local to the receiver
of objects and mobility
 Important for predicting coverage areas and  Important in design of modulation format
service availability & general transceiver design
 Characterized statistically by Log distance  Often characterized statistically as
& log normal shadowing path loss Rayleigh fading 7
Free Space Propagation Model

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 Free Space Propagation Model
 Used to predict signal strength for LOS path
 Friis free space equation: receive power at antenna separated by distance d from
transmitter  Gt Gr 2  Pt
Pr(d) =   2
 ( 4 ) L  d
2

Pr & Pt = received & transmitted power

Gt & Gr = gain of transmit & receive antenna
 = wavelength
d = T-R separation
L = system losses (line attenuation, filters, antenna)
- not from propagation
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- practically, L  1, if L = 1  ideal system with no losses

 Free Space Propagation Model
4
Antenna Gain G= Ae
 2

Ae = effective area of absorption– related to antenna size

Isotropic Radiator: ideal antenna (used as a reference antenna) radiates power with
unit gain uniformly in all directions; surface area of a sphere = 4πd 2
2
Effective Area of isotropic antenna given by Aiso =
4
Isotropic Received Power PR =  2
  1  2

 4  4d 2  PT  4d 2 PT

  

d = transmitter-receiver separation 10
 maximum antenna gain in either direction is given by
Ae 4
G=  Ae
Aiso  2

EIRP: effective isotropic radiated power

• represents maximum radiated power available from a transmitter
• measured in the direction of maximum antenna gain as compared to isotropic radiator
EIRP = PtGiso
ERP: effective radiated power - often used in practice
• denotes maximum radiated power compared to ½ wave dipole antenna
• dipole antenna gain = 1.64 (2.15dB) > isotropic antenna
• thus EIRP will be 2.15dB smaller than ERP for same system
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ERP = PtGdipole
 Path Loss (PL)

PL = Pt  (4 ) 2 d 2 
=  2 

Pr  Gt Gr  
 Gt Gr 2  1

PL (dB) = 10 log 10 (Pt /Pr) =  10 log 10 

2  2
 ( 4 ) d
if G is assumed unit gain:

  1 2
 10 log10 
PL (dB) =
 (4 ) 2  d 2
 
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 Far-field region of an antenna
Eqs. only valid for d in the far-field of transmitting antenna
• d  df (far-field distance)
• far-field distance or Fraunhofer region  G G 2
P
Pr(d) =  t r2  t2
 (4 ) L  d
 
2D 2
df =

• D = largest physical linear dimension of transmitters antenna aperture
df >> D and df >>  must hold
2
 d0 
Pr(d) (watts) = Pr(d0)   d  d0  df
d 
d0 must be selected to lie in far-field region d0  df
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d0 selected to be smaller than any practical d in mobile system

Example 1

2
2D


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Measuring in dB (dbm & dBW relative power measurements)

Pr in mobile systems can change by many dB in a coverage area ≈ 1km2

• dBm or dBW units are used to express power levels
• conversion from watts – take log of both sides & multiply by 10

 Pr (d 0 )   d0  d  d0  df
Pr(d) dBm = 10 log   20 log 
 0.001W  d 
e.g. Pr = 20 mW  Pr (dBm) = 10 log(20 mW/1mW) = 13 dBm

dBi – antenna gain with respect to isotropic source

dBd – antenna gain with respect to dipole antenna 15

Measuring in dB (dbm & dBW relative power measurements)

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Receiver Input Voltage And Receive Power Level
•model receive antenna as matched resistive load, Rant
• receiver antenna will induce rms voltage, V, into receiver
• induced voltage = ½ open circuit voltage at antenna: V = ½ Vant
• Rant = antenna resistance
open circuit Rant
Pr(d) =
V / 2 2  V2 Vant V
to matched
receiver
Rant 4 Rant

Induced Electric Field, E vs Receiver Input Voltage, V

2 2
Pr(d) = E V
Ae 
120 4 Rant 17
Example 2

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  Pr (d 0 )   d0  d  d0  df
Solution Pr(d) dBm = 10 log   20 log 
 0.001W  d 

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Solution continued
 Pr (d 0 )   d0  d  d0  df
Pr(d) dBm = 10 log   20 log 
 0.001W  d 

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Example 3

d) The power flux density

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Solution
a)

b)

c)

d) Pd = (Pt Gt)/ (4 ∏)2 d2 = 50*1 / (4*3.14)2 *10000 = 0.0316mW

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 Three Basic Propagation Mechanisms

Reflection Diffraction Scattering

 Refection from Dielectric  Fresnel Zone Geometry

 Brewster Angle  Surface Roughness
 Reflection from Conductors Models
Model
Knife edge Diffraction Model Radar Cross Section Model
Model
Ground Refection  Multiple Knife edge
Model (2- ray Model) Diffraction Model

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 Basic Propagation Mechanisms
(1) Reflection: propagating wave impinges on object with size >> 
• examples include ground, buildings, walls

(2) Diffraction: transmission path obstructed by objects with edges

• 2ndry waves are present throughout space (even behind object)
• gives rise to bending around obstacle (NLOS transmission path)

(3) Scattering propagating wave impinges on object with size < 

• number of obstacles per unit volume is large (dense)
• examples include rough surfaces, foliage, street signs, lamp posts
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 Reflection from Dielectrics
Vertical Polarization: E-field in Horizontal Polarization: E-field
the plane of incidence normal to plane of incidence
Ei Er

Ei Er Hr
Hi
Hi Hr 1,1, 1
i r 1,1, 1 i r
2,2, 2
t 2,2, 2 t
Et Et

1, 2 = Permittivity,1, 2 =Permeability,1, 2 = Conductance

r = Relative permittivity 30
 Reflection from Dielectrics
 Fresnel reflection coefficients for E-field polarization at
reflecting surface boundary
 || represents coefficient for || E-field polarization

|| =
Er 2 sin t  1 sin i

Ei 2 sin t  1 sin i

  represents coefficient for  E-field polarization

Er 2 sin i  1 sin t
 = 
Ei 2 sin i  1 sin t

i = intrinsic impedance of the ith medium

• ratio of electric field to magnetic field for uniform plane wave in ith medium
i  i
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i =
 Reflection from Dielectrics

Assuming radio wave propagating in free space (1st medium is free space) 1 = 2

|| =   r sin i   r  cos i 2

 r sin i   r  cos i
2

 = sin i   r  cos i 2

sin i   r  cos i 2

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   r sin i  r  cos2 i
|| =
 r sin i   r  cos2 i
sin i   r  cos2 i
 =
sin i 33  r  cos2 i
 Brewster Angle (B )
• Brewster angle only occurs for vertical (parallel) polarization.
•Angle at which no reflection occurs in medium of origin occurs when incident
angle i is such that || = 0  i = B

B satisfies sin(B) = 1
1   2
• if 1st medium = free space & 2nd medium has relative permittivity r
then above equation can be expressed as

r 1
sin(B) =
 r 1
2

1.34
 Brewster Angle
 The Brewster angle occurs only for vertical (i.e. parallel) polarization.

Brewster's angle (also known as the polarization angle) is an angle of incidence at

which light with a particular polarization is perfectly transmitted through a
1.35
transparent dielectric surface, with no reflection.
 Brewster Angle
Applications:

Polarized sunglasses

Photography

Photographers use the same principle to remove reflections from water so

that they can photograph objects beneath the surface. In this case, the
polarizing filter camera attachment can be rotated to be at the correct angle

1.36
 Brewster Angle

Photographs taken of a window with a camera polarizer filter rotated to two different angles.
In the picture at left, the polarizer is aligned with the polarization angle of the window reflection.
In the picture at right, the polarizer has been rotated 90° eliminating the heavily polarized reflected sunlight.

1.37
sin(B) =  r  1
 r 1
2

1.38
Ground Reflection (Two- Ray Model )

• ELOS = E-field of LOS component

• Eg = E-field of ground reflected component
Radio propagation

ETOT = ELOS + Eg
 Ground Reflection (Two- Ray Model )
(1) Determine Total Received E-field (in V/m) ETOT

Let E0 = free space E-field (V/m) at distance d0

For d > d0 , Propagating Free Space E-field, is given by:

E-field’s envelope at distance d from transmitter given by:

|E(d,t)| = E0 d0/d
Radio propagation
 Ground Reflection (Two- Ray Model )
E-field for LOS and reflected wave relative to E0 given by:
ELOS d’
E0 d 0   d' 
ELOS(d’,t) = cos wc  t   
d'   c  ht Ei

E0 d 0   d"  hr
Eg(d”,t) = Γ cos wc  t    i 0
d"   c  d”

and ETOT = ELOS + Eg d

Assumes LOS & reflected waves arrive at the receiver with

d’ = distance of LOS wave
d” = distance of reflected wave
Radio propagation
 Ground Reflection (Two- Ray Model )
According to laws of reflection in dielectrics
i = 0
Eg =  Ei
Et = (1+) Ei

 = reflection coefficient for ground

Assume
i. perfect horizontal E-field Polarization
ii. perfect ground reflection
iii. small i   ≈ -1 & Et ≈ 0
Radio propagation
 Ground Reflection (Two- Ray Model )
Reflected wave & incident wave have equal magnitude.
Reflected wave is 180o out of phase with incident wave

Resultant E-field is vector sum of ELOS and Eg

• Total E-field Envelope is given by |ETOT| = |ELOS + Eg|
• Total electric field given by

E0 d 0   d '   E0 d 0   d "  
ETOT(d,t) = cos wc  t     (1) cos wc  t   
d'   c  d"   c 
Radio propagation
 Ground Reflection (Two- Ray Model )
(2) Calculate Path difference,
phase delay and time delay

• Path difference  = d” – d’
(determined from method of images)

 = ht  hr   d  ht  hr   d
2 2 2 2

2ht hr
 
if d >> hr + ht  Taylor series approximations yields:
Radio propagation d
 Ground Reflection (Two- Ray Model )
 Phase difference
2   wc
  =  Eq (e)
Δ  c
0 π 2π

 
 Time delay d = 
c 2f c

As d becomes large   = d”- d’ becomes small

• amplitudes of ELOS & Eg are nearly identical & differ only in phase
E0d0 E0d0 E0d0
Radio propagation
 
d d' d"
 Ground Reflection (Two- Ray Model )
(4) Determine exact E-field for 2-ray ground model at distance d

Use phasor diagram to find

resultant E-field from combined
direct & ground reflected rays:

|ETOT(d)|=  E0 d 0 
=   2  2 cos 
 d 
 E0 d 0    
= 2  sin  
 d   2 
Radio propagation
For Your reference:
For Your reference:
For phase difference, sin(0.5 )   This occurs when  /2 is less than 0.3 radians

|ETOT(d)|  2 E0 d0    

 d  2 
 1 2 2ht hr
   0.3rad
2 2  d
20ht hr 20ht hr
this implies whenever d >  Eq (p)
3 
if d satisfies Eq (p)  total E-field can be approximated as:

ETOT(d)  2 E0 d 0  2ht hr  k V/m

  2
d  d  d
k is a constant related to E0 ht,hr, and 
Radio propagation

e.g. at 900MHz  if  < 0.03m  total E-field decays with d2

 Received Power at d is related to square of E-field:
2 2
Pr(d) =
ht hr
Pt Gt Gr 4
d
E0 (d ) 2 ER (d ) 2  Gr 2 
Pr(d) = Ae    Eq (q)
120 120  4 

• Eq (q) must hold if d >> ht hr

• received power falls off at 40dB/decade

Radio propagation
 Path Loss for 2-ray model with antenna gains is expressed as:

1
Pt  ht2hr2 
PL = 
 Gt Gr 4


Pr  d 

PL(dB) = 40log d - (10logGt + 10logGr + 20log ht + 20 log hr )

• Eq(p) must hold

•Receive power & path loss become independent of frequency

Radio propagation
Radio propagation
 E0 (d ) 2 ER (d ) 2  Gr 2 
Ae   
120 120  4 

Radio propagation
Diffraction

 Diffraction allows radio signals to propagate behind

obstacles between a transmitter and a receiver
Huygen’s Principle & Diffraction
 All points on a wavefront can be
considered as point sources for the
production of secondary wavelets.
These wavelets combine to produce
a new wavefront in the direction of
propagation.

 Diffraction is caused by the

propagation of secondary wavelet
into a shadowed region.
Fresnel Zone Geometry
Fresnel Zone Geometry
 Fresnel Zone Geometry

1) Δ: Excess Path Length (Difference between Diffracted Path and Direct Path)
2)The phase difference is given by

Equation for the phase difference is generally normalized using the dimensionless
Fresnel-Kirchoff Diffraction parameter v which is given by

V 2 = 2,6,10… Corresponds to destructive interference between direct and diffracted paths

V 2 = 4,8,12… Corresponds to constructive interference between direct and diffracted paths
 Fresnel Zones
Successive regions where secondary waves have a path length from the

transmitter to receiver which is nλ/2 greater than the total path length of
a line-of-sight path
 Fresnel Zones

n rn2  d1  d 2  n d 1 d 2
   rn 
2 2 d1d 2  d1  d 2 
rn: Radius of the nth Fresnel Zone
 Fresnel Zones

A rule of thumb used for design of line-of-sight microwave links is that as

long as 55% of the first Fresnel zone is kept clear, then further Fresnel zone
clearance does not significantly alter the diffraction loss.
Knife-Edge Diffraction Scenarios

h & ν are +ve, Relatively High Diffraction Loss

h =0, Diffraction Loss = 0.5

h & ν are –ve, Relative Low Diffraction Loss

Knife-Edge Diffraction Model
The field strength at point Rx located in the
shadowed region is a vector sum of the fields
due to all of the secondary Huygen’s sources in
the plane above the knife-edge

Electric Field Strength, Ed, of a Knife-Edge

Diffracted Wave is given By:

E0: Free-Space Field Strength in absence of Ground Reflection and Knife-Edge Diffraction
F(ν) is called the complex Fresnel Integral 67
Diffraction Gain

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Diffraction Gain Approximation
 Multiple Knife-Edge Diffraction

Optimistic solution by Bullington

 Scattering
 The actual received signal in a mobile radio environment is often stronger than
what is predicted by reflection and diffraction models alone. This is because,
the reflected energy is spread out (diffused) in all directions due to scattering

 Surface roughness is often tested using the Rayleigh criterion which defines
a critical height (hc) of surface protuberances for a given angle of incidence
θi , given by

 A surface is considered smooth if h < hc

rough if h > hc
 Scattering
 For rough surfaces, the flat surface reflection coefficient needs to be

multiplied by a scattering loss factor, ρs .

 Ament assumed that the surface height h is a Gaussian distributed

random variable with a local mean and found ρs to be given by

where σh is the standard deviation of the surface height about the

mean surface height.
 Scattering
 The scattering loss factor derived by Ament was modified by Boithias to
give better agreement with measured results, and is given by

where Io is the Bessel function of the first kind and zero order.

 The reflected E-fields for h > hc can be solved for rough surfaces
using a modified reflection coefficient given as
 Radar Cross Section Model
 In radio channels where large distant objects induce scattering,
knowledge of the physical location of such objects can be used to
accurately predict scattered signal strengths.

 The radar cross section (RCS) of a scattering object is defined as the

ratio of the power density of the signal scattered in the
direction of the receiver to the power density of the radio wave
incident upon the scattering object, and has units of square meters.

power density of the signal scattered in the direction of the receiver

power density of the radio wave incident upon the scattering object
 Radar Cross Section Model
For urban mobile radio systems, models based on the bistatic radar equation.
 It may be used to compute the received power due to scattering in the far field.
 It describes the propagation of a wave traveling in free space, and is then
reradiated in the direction of the receiver, given by

where dT = distance from the scattering object to the transmitter

dR = distance from the scattering object to the receiver.

 For medium and large size buildings located 5 - 10 km away, RCS values were
found to be in the range of 14.1dB•m2 to 55.7 dB.m2.
Practical Link Budget Design using Path Loss Models

 Most radio propagation models are derived using a combination of

analytical and empirical methods.

 The empirical approach is based on fitting curves or analytical

expressions that recreate a set of measured data.

 This has the advantage of implicitly taking into account all

propagation factors, both known and unknown, through actual
field measurements.
Practical Link Budget Design using Path Loss Models
Path loss models are used
 To estimate the received signal level as a function of distance,
 To predict the SNR for a mobile communication system

Path Loss Models

 Log-distance Path Loss Model

 Log-normal Shadowing Model
 Log-distance Path Loss Model
 Both theoretical and measurement based propagation models indicate that
average received signal power decreases logarithmically with distance, whether
in outdoor or indoor radio channels.
 The average large-scale path loss for an arbitrary T-R separation is expressed as a
function of distance by using a path loss exponent, n.

where n is the path loss exponent (rate at which the path loss increases )
do is the close-in reference distance
d is the T-R separation distance.
 Log-distance Path Loss Model
 In large coverage cellular systems, 1 km reference distances
 In microcellular systems, 100 m or 1 m as reference distance.

Environment Path-Loss Exponent n

Free-Space 2
Urban area cellular radio 2.7 to 3.5
Shadowed urban cellular radio 3 to 5
In building line-of-sight 1.6 to 1.8
Obstructed in building 4 to 6
Obstructed in factories 2 to 3
 Log-normal Shadowing
 The Log distance path loss model does not consider the fact that the
surrounding environmental clutter may be vastly different at two
different locations having the same T-R separation.
 Distance between two nodes alone cannot fully explain the signal strength
level at the receiver
 This leads to measured signals which are vastly different than the
average value predicted by log distance equation .
 Measurements have shown that at any value of d, the path loss PL(d)
at a particular location is random and distributed log-normally (normal
in dB) about the mean distance- dependent value .
 Log-normal Shadowing
Log-distance Path Loss Model
That is

where Xσ is a zero-mean Gaussian distributed random variable

(in dB) with standard deviation σ (also in dB).

 The log-normal distribution describes the random shadowing effects which

occur over a large number of measurement locations which have the same
T-R separation, but have different levels of clutter on the propagation
path. This phenomenon is referred to as log-normal shadowing.
 Log-normal Shadowing

PR  d 

d d X1
X 4
PT - PL  d  X3
4 3 X2

d
d

Position
Index

1 2 1 2 3 4
γ: Desired received power threshold
 Propagation Models

Outdoor Models Indoor Models

1. Longley-Rice Model 1. Partition Losses (Same Floor)
2. Durkin’s Model 2. Partition Losses between Floors
3. Okumura’s Model
3. Log-distance path loss model
4. Hata Model
4. Ericsson Multiple Breakpoint Model
5. PCS extension to Hata Model
5. Attenuation Factor Model
6. Walfisch and Bertoni
7. Wideband PCS Microcell Model
 Longely Rice Model (ITS irregular terrain model)

 Used for point-point systems under different types of terrain

 Frequency ranges from 40MHz-100GHz
(i) Median Transmission Loss predicted using path geometry of terrain profile & refractivity of
troposphere.
(ii) Signal Strengths within radio horizon predicted using Geometric Optics Techniques
(primarily 2-ray ground reflection)
(ii) Diffraction Loss over isolated obstacles predicted using Fresnel- Kirchoff knife edge models
(iv) Troposcatter over long distances predicted using Forward Scatter Theory
(v) Far-Field Diffraction losses in double horizon paths predicted using Modified Van der Pol-
Bremner Method
89
 Longely Rice Model
 It is available as a computer program
 It calculates large scale median transmission loss over irregular terrain for frequencies between
20MHz-10GHz
Input parameters include:
• transmission frequency,
• path length & antenna heights,
• polarization,
• surface refractivity
• earth radius & climate
• ground conductivity & ground dielectric constant
• path specific parameters: antennas’ horizon distance, horizon elevation angle, terrain irregularity
90
 Longely Rice Model
Modes for Longely Rice for prediction:
 1. point-point : when detailed terrain profile or path specific parameters are known.

 2. area mode : If terrain profile is not known then it estimated path specific parameters
Modifications and corrections:
 It introduces an excess term called the urban factor (UF) as an allowance for the
additional attenuation due to urban clutter near the receiving antenna.
 This extra term, has been derived by comparing the predictions by the original
Longley-Rice model with those obtained by Okumura.
 Longely Rice Model
Disadvantage:

 It does not provide a way of determining corrections due to environmental

factors in the immediate vicinity of the mobile receiver, or consider
correction factors to account for the effects of buildings and foliage.

 Multipath is not considered.

 Indoor Propagation Model
The indoor radio channel differs from the traditional mobile radio channel
 The distances covered are much smaller,
 The variability of the environment is much greater for a smaller range of T-R separation
 strongly influenced by building features, layout, materials
 conditions vary from: doors open/closed, antenna position

•Dominated by same mechanisms as outdoor propagation (reflection, refraction, scattering)

• Classified as either LOS or OBS

1. Partition Losses (Same Floor)

2. Partition Losses between Floors
3. Log-distance path loss model
4. Ericsson Multiple Breakpoint Model
5. Attenuation Factor Model
93
 Indoor Propagation Model
1.Partition Losses – Same Floor
• Hard partitions: immovable, part of building
• Soft partitions: movable, lower than the ceiling

Material Type Loss(db) Frequency

All metal 26 815 MHz
Aluminium siding 20.4 815 MHz
Concrete block wall 13 1300MHz
Loss from one floor 20-30 1300MHz
Loss from one floor and one wall 40-50 1300MHz

Concrete floor 10 1300MHz

Dry plywood (3/4 in) - 1 sheet 1 9.6GHz
 Indoor Propagation Model
2.Partition Losses between Floor:
Dependent on external building dimensions, structural characteristics & materials

Floor Attenuation Factor

(FAF) increases as we
increase the no of floors
 Indoor Propagation Model
3. Log-distance path loss model: accurate for many indoor paths
 d 
PL(dB) = PL(d 0 )  10n log     •n depends on surroundings and building type
 d0 
 Small-Scale Fading and Multipath
 Small-scale fading, or simply fading, is used to describe the rapid fluctuation
of the amplitude of a radio signal over a short period of time or travel distance.
 Fading is caused by interference between two or more versions of the
transmitted signal which arrive at the receiver at slightly different times. These
waves, called multipath waves, combine at the receiver antenna.
 It vary widely in amplitude and phase, depending on the distribution of the
intensity and relative propagation time of the waves and the bandwidth of the
transmitted signal

98
 Small-Scale Fading
Multi path in radio channel creates small scale fading effects Three most important effects:
 Rapid changes in signal strength over a small travel distance or time interval
 Random frequency modulation due to varying Doppler shifts on different multi path
signals
 Time dispersion (echoes) caused by multi path propagation delays.

Fading signals occur due to

 Reflections from ground & surrounding buildings (clutter)
 Scattered signals from trees, people, towers, etc.
 Motion of objects (cars, people, trees, etc.) in surrounding environment off of
which come the reflections
 Multi-Path Propagation

100
 Multi-Path Propagation Modeling

Power

Multi-Path
Components

τ0 τ1 τ2 Time

Multi-path results from reflection, diffraction, and scattering off environment surroundings
 Factors Influencing Small Scale Fading
1) Multipath Propagation :

 The presence of reflecting objects and scatters in the channe1 creates a constantly
changing environment. It dissipates the signal energy in amplitude, phase, and time.

 These effects result in multiple versions of the transmitted signal that arrive at the
receiving antenna, displaced with respect to one another in time and spatial orientation.

 The random phase and amplitudes of the different multipath components cause fluctuations
in signal strength, thereby inducing small-scale fading, signal distortion, or both.

 Multipath propagation often lengthens the time required for the baseband portion
of the signal to reach the receiver.

 It can cause signal smearing due to intersymbol interference.

 Factors Influencing Small Scale Fading
2) Speed of Mobile
 Relative motion between base station & mobile causes random frequency
modulation due to Doppler shift (fd)
 Different multipath components may have different frequency shifts.
3) Speed of Surrounding Objects
 Influence Doppler shifts on multipath signals
 Dominates small-scale fading if speed of objects > mobile speed, otherwise ignored
4) Tx signal bandwidth (Bs)

 If the transmitted radio signal bandwidth is greater than the "bandwidth" of

the multipath channel, the received signal will be distorted

 but the received signal strength will not fade much over a local area (i.e., the
small-scale signal fading will not be significant).
 Doppler Shift
 Motion causes frequency modulation due to Doppler shift (fd)
 path difference is Δl = dcosθ = vΔtcosθ

 v : velocity (m/s)
 λ : wavelength (m)
 θ : angle between mobile
direction and arrival direction of RF energy
 + shift → mobile moving toward S
 − shift → mobile moving away from S
Following parameters are used for mobile multipath
channels:
1.Time dispersion parameter
2.Coherence Bandwidth
3.Doppler spread and coherence Time
 Time Dispersion Parameters
 The mean excess delay, rms delay spread, and excess delay spread (X dB) are multipath
channel parameters that can be determined from a power delay profile.

 The time dispersive properties of wide band multipath channels are most commonly
quantified by their mean excess delay (τ) and rms delay spread (στ )

 The mean excess delay is the first moment of the power delay profile and is defined to be

 The rms delay spread is the square root of the second central moment of the power
delay profile and is defined to be
 Time Dispersion Parameters
Where

 These delays are measured relative to the first detectable signal arriving
at the receiver at to = 0
 The maximum excess delay (X dB) of the power delay profile is defined to be
the time delay during which multi path energy falls to X dB below the
maximum.
Time Dispersion Parameters
 outdoor channel ~ on the order of microseconds
 indoor channel ~ on the order of nanoseconds
 Coherence BW (Bc)
 Coherence Bandwidth Bc ,is a defined relation derived from the rms delay spread.
 It is a statistical measure of the range of frequencies over which the channel
can be considered "flat" (i.e., a channel which passes all spectral components with
approximately equal gain and linear phase).

OR
 It is the range of frequencies over which two frequency components have a
strong potential for amplitude correlation.
 If frequency correlation function is above 0.9

 If frequency correlation function is above 0.5

 Coherence BW (Bc)
 Coherence Bandwidth Bc ,is a defined relation derived from the rms delay spread.
 It is a statistical measure of the range of frequencies over which the channel
can be considered "flat" (i.e., a channel which passes all spectral components with
approximately equal gain and linear phase).

OR
 It is the range of frequencies over which two frequency components have a
strong potential for amplitude correlation.
 If frequency correlation function is above 0.9

 If frequency correlation function is above 0.5

Coherence BW (Bc)
114
 The mean excess delay is the first moment of the power delay profile and is
defined as

w
 Doppler Spread
 Doppler spread BD is a measure of the spectral broadening caused by the time
rate of change of the mobile radio channel.

 BD is defined as the range of frequencies over which the received Doppler

spectrum is essentially non-zero.

 When a pure sinusoidal tone of frequency fc is transmitted, the received

signal spectrum, called the Doppler spectrum, will have components in the range
fc-fd to fc+fd, where fd is the Doppler shift.

 If the baseband signal bandwidth is much greater than BD, the effects of Doppler
spread are negligible at the receiver. This is a slow fading channel.
 Coherence Time
 The Doppler spread and coherence time are inversely proportional to one another.

where fm =maximum Doppler shift given by fm = v/λ.

 Coherence time is actually a statistical measure of the time duration over which the
channel impulse response is essentially invariant, and quantifies the similarity of
the channel response at different times.
 Coherence time is the time duration over which two received signals have a strong
potential for amplitude correlation.
 If the reciprocal bandwidth of the baseband signal is greater than the coherence
time of the channel, then the channel will change during the transmission of the
baseband message, thus causing distortion at the receiver.
 Coherence Time
 If the coherence time is defined as the time over which the time correlation function
is above 0.5,then the coherence time is approximately

 where fm =maximum Doppler shift given by fm = v/λ.

 A popular rule of thumb for modern digital communications is to define the

coherence time as the geometric mean

 The definition of coherence time implies that two signals arriving with a time
separation greater than Tc are affected differently by the channel.
 Types of Small-Scale Fading
 Fading can be caused by two independent MRC propagation mechanisms:

1) Time dispersion → multipath delay (Coherence Bandwidth Bc , rms delay spread   )

2) Frequency dispersion → Doppler spread (Doppler spread BD , Coherence time Tc)

 Important digital Tx signal parameters → symbol period & signal BW

Types of small-scale fading
 Fading due to Multipath Delay Spread
1. Flat fading
 If the mobile radio channel has a constant gain and linear phase
response over a bandwidth which is greater than the bandwidth of the
transmitted signal, then the received signal will undergo flat fading.

 The strength of the received signal changes with time, due to

fluctuations in the gain of the channel caused by multipath.
 1. Flat Fading
The spectral characteristics of the transmitted signal are preserved at the receiver.
 1. Flat Fading
 Flat fading channels are also known as Amplitude varying channels or referred to as
narrowband channels, since the bandwidth of the applied signal is narrow as
compared to the channel flat fading bandwidth.

 Typical flat fading channels cause deep fades, and thus may require 20 or 30 dB
more transmitter power to achieve low bit error rates.

 The distribution of the instantaneous gain of flat fading channels is important for
designing radio links, and the most common amplitude distribution is the Rayleigh
distribution.

 A signal undergoes flat fading if Bs << Bc

or Ts >>  
 2. Frequency Selective Fading

 If the channel possesses a constant-gain and linear phase response over a bandwidth
that is smaller than the bandwidth of transmitted signal, then the channel creates
frequency selective fading on the received signal.

 The channel impulse response has a multi path delay spread which is greater
than the reciprocal bandwidth of the transmitted message waveform.

 When this occurs, the received signal includes multiple versions of the
transmitted waveform which are attenuated(faded) and delayed in time and hence
the received signal is distorted.
 2. Frequency Selective Fading

 Frequency selective fading is due to time dispersion of the transmitted symbols

within the channel. Thus the channel induces intersymbol interference (ISI).
 For analysing frequency selective small-scale fading :
statistical impulse response models such as the 2-ray Rayleigh fading model
 2. Frequency Selective Fading
 Frequency selective fading is caused by multipath delays which approach or exceed
the symbol period of the transmitted symbol.

 frequency selective fading channels are also known as wideband channels since
the bandwidth of the signal s(t) is wider than the bandwidth of the channel
impulse response. As time varies, the channel varies in gain and phase across the
spectrum of s(t), resulting in time varying distortion in the received signal r(t).

 Frequency Selective Fading → Bs > Bc

Ts <  

If Ts  10  Frequency selective fading

Flat Fading Vs Frequency Selective Fading

P(τ)
Flat Fading Power Delay Profile

BS  BC TS  σ τ
A Common Rule of Thumb:
τ0 τ1 τN τ
TS>10σt  Flat fading Symbol Time (Digital Communication) TS

1 0 1 + Minimal
Wireless
Channel ISI
+

τ0 τN
τa
128
 Flat Fading Vs Frequency Selective Fading

P(τ)
Frequency Selective Fading Power Delay Profile

BS  BC TS  σ τ
A Common Rule of Thumb: τ0 τ1 τ2 τ3 τN τ
TS<10σt  Frequency Selective Fading
Symbol Time (Digital Communication) TS

1 0 1 + Significant
Wireless
Channel ISI
+

τ0 τa τN

129
Slow Fading vs Fast Fading

P(τ0,t)
Power Delay Profile
P(τ)
P(τ0,TC) P(τ ,2T )
0 C

P(τ0,3TC)
P(τ0,KTC)

τ0 τ
0 TC 2TC 3TC KTC t

 Consider a wireless channel comprised of a single path component.

 The power delay profile reflects average measurements
 P(τ0) shall vary as the mobile moves

Fast Fading Slow Fading

TS  TC BS  BD BS  BD
TS  TC
Frequency dispersion
(time selective fading)
 Fading Effects due to Doppler spread
1. Fast Fading:
 Depending on how rapidly the transmitted baseband signal changes
as compared to the rate of change of the channel, a channel may be
classified either as a fast fading or slow fading channel.

 In a fast fading channel, the channel impulse response changes rapidly

within the symbol duration. Coherence time of the channel is smaller than
the symbol period of the transmitted signal. This causes frequency dispersion
(also called time selective fading) due to Doppler spreading, which leads
to signal distortion.
 Therefore, a signal undergoes fast fading if Bs < BD or Ts > Tc
 1. Fast Fading

 A flat fading, fast fading channel is a channel in which the amplitude of the delta
function varies faster than the rate of change of the transmitted baseband signal.

 In frequency selective, fast fading channel, the amplitudes, phases, and time
delays of anyone of the multi path components vary faster than the rate of change of
the transmitted signal.

 In practice, fast fading only occurs for very low data rates.
 2. Slow Fading
 In a slow fading channel, the channel impulse response changes at a rate
much slower than the transmitted baseband signal s(t).

 In the frequency domain, this implies that the Doppler spread of the channel
is much less than the bandwidth of the baseband signal.

 A signal under goes slow fading if Ts << Tc or Bs >> BD

  rms delay spread

Flat Fading
TS  σ τ BS  BC
Frequency Selective Fading

BS  BC TS  σ τ

Type of the fading experienced

by a signal as a function of
(a) Symbol Period
(b) Baseband signal bandwidth

Fast fading
Bs < BD or Ts > Tc
Slow fading

Ts << Tc or Bs >> BD
134