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فيدينگ بخشکانال مقدمه

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References• Wireless Communications: Principles and Practice, Chapters 3 and

4, T. Rappaport, Prentice Hall, 1996.• Principles of Mobile Communication, Chapter 2, G. Stüber, Kluwer

Academic Publishers, 1996.• Slides for EE535, K. Chugg, 1999.• Spread Spectrum Systems, Chapter 7, R. Dixon, Wiley, 1985 (there

is a newer edition).• Wideband CDMA for Third Generation Mobile Communications,

Chapter 4, T. Ojanpera, R. Prasad, Artech, House 1998.• Propagation Measurements and Models for Wireless

Communications Channels, Andersen, Rappaport, Yoshida, IEEE Communications, January 1995.

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Radio Propagation Effects

Transmitterd

Receiver

hb

hm

Diffracted Signal

Reflected Signal

Direct Signal

Building

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Propagation Mechanisms• Reflection

– Propagation wave impinges on an object which is large as compared to wavelength

- e.g., the surface of the Earth, buildings, walls, etc.– Surface large relative to wavelength of signal– May have phase shift from original– May cancel out original or increase it

• Diffraction– Radio path between transmitter and receiver obstructed

by surface with sharp irregular edges– Waves bend around the obstacle, even when LOS (line of sight)

does not exist– Edge of impenetrable body that is large relative to wavelength– May receive signal even if no line of sight (LOS) to transmitter

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… Propagation Mechanisms

• Scattering - Objects smaller than the wavelength of the

propagation wave e.g. foliage, street signs, lamp posts

– Obstacle size on order of wavelengthLamp posts etc.

• If LOS, diffracted and scattered signals not significant– Reflected signals may be

• If no LOS, diffraction and scattering are primary means of reception

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Essential Definitions• Reflection: A change in the direction of a signal without

penetrating the object. Occurs when the path of a signal

is obstructed. The dimensions of the obstructing object

is larger than the wavelength of the signal

• Diffraction: An object with large dimension blocks the path of a wave.

• Scattering: An object in the path of a wave causes it to spread or scatter in different directions. Occurs when the dimensions of the object are comparable to the wavelength of the signal.

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Reflection, Diffraction, Scattering

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Types of Waves

Transmitter ReceiverEarth

Sky wave

Space wave

Ground waveTroposphere

(0 - 12 km)

Stratosphere (12 - 50 km)

Mesosphere (50 - 80 km)

Ionosphere (80 - 720 km)

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Propagation mechanisms

CA

D

BReceiverTransmitter

A: free spaceB: reflectionC: diffractionD: scattering

A: free spaceB: reflectionC: diffractionD: scattering

reflection: object is large compared to wavelengthscattering: object is small or its surface irregular

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Refraction• Perfect conductors reflect

with no attenuation• Dielectrics reflect a fraction

of incident energy– “Grazing angles” reflect

max*– Steep angles transmit max*

r

t

• Reflection induces 180 phase shift

*The exact fraction depends on the materials and frequencies involved

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Diffraction

• Diffraction occurs when waves hit the edge of an obstacle– “Secondary” waves propagated into

the shadowed region– Excess path length results in a phase

shift– Fresnel zones relate phase shifts to

the positions of obstacles

TR

1st Fresnel zone

Obstruction

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Scattering

• Rough surfaces– critical height for bumps is f(,incident angle) – scattering loss factor modeled with Gaussian

distribution.• Nearby metal objects (street signs, etc.)

– Usually modelled statistically• Large distant objects

– Analytical model: Radar Cross Section (RCS)

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Free Space 2a

• Free space power flux density (W/m2)– power radiated over surface area of sphere

– where Gt is transmitter antenna gain

• By covering some of this area, receiver’s antenna “catches” some of this flux

2π4 dGPP tt

d

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Free Space 2b

• Fraunhofer distance: d > 2D2/ • Antenna gain and antenna aperture

– Ae is the antenna aperture, intuitively the area of the antenna perpendicular to the flux

– Gr is the antenna gain for a receiver. It is related to Ae.

– Received power (Pr) = Power flux density (Pd) * Ae

2λπ4 eAG

π4λ 2GAe

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Free Space 2c

– where L is a system loss factor– Pt is the transmitter power

– Gt and Gr are antenna gains is the carrier wavelength

Watts)π(4

λ 1)( 2

2

2 LGGP

ddP rtt

r

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Free Space

• Assumes far-field (Fraunhofer region) – d >> D and d >> , where

• D is the largest linear dimension of antenna is the carrier wavelength

• No interference, no obstructions

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Free Space Propagation Model

• Received power at distance d is

– where Pt is the transmitter power in Watts

– a constant factor K depends on antenna gain, a system loss factor, and the carrier wavelength

Watts)( 2dPKdP t

r

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2-Ray Ground Reflection

• For d >> hrht, – low angle of incidence allows the earth to act

as a reflector– the reflected signal is 180 out of phase– Pr 1/d4 (=4)

RT

ht hr

Phase shift!

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Ground Reflection 1.5

• The power at the receiver in this model is– derivation calculates E field; – Pr = |E|2Ae; Ae is ant. aperture

• The “breakpoint” at which the model changes from 1/d2 to 1/d4 is 2hthr/– where hr and ht are the receiver and

transmitter antenna heights

4

22

dhhGGPP rt

rttr

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Ground Reflection 2• Intuition: ground blocks 1st Fresnel zone

– Reflection causes an instantaneous 180 phase shift– Additional phase offset due to excess path length– If the resulting phase is still close to 180, the gound

ray will destructively interfere with the LOS ray.

RT

ht hrp1

p0

180

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Hilly Terrain

• Propagation can be LOS or result of diffraction over one or more ridges

• LOS propagation modelled with ground reflection: diffraction loss

• But if there is no LOS, diffraction can actually help!

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Hilly Terrain

• Propagation can be LOS or result of diffraction over one or more ridges

• But if there is no LOS, diffraction can actually help!

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Fresnel Zones

• Bounded by elliptical loci of constant delay• Alternate zones differ in phase by 180

– Line of sight (LOS) corresponds to 1st zone– If LOS is partially blocked, 2nd zone can

destructively interfere (diffraction loss)

Fresnel zones are ellipses with the T&R at the foci; L1 = L2+

Path 1

Path 2

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Fresnel Zones– The Fresnel zones are propagation break points

– At the first Fresnel zone (n=1) no reflections of waves can take place and

– The distance to this point is:– Until this point, the propagation is assumed to be free space

and rays travel is direct (point to point) with no reflections– Free space and terrestrial propagation models are used for

design of microcells and also for in building coverage or solutions

– when the distance is less than the first Fresnel zone, none of the models is adequate and empirical design is used

tro hhd 4

4/dhh tr

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What is Radio?

• Radio Xmitter induces E&M fields– Electrostatic field components 1/d3

– Induction field components 1/d2

– Radiation field components 1/d• Radiation field has E and B component

– Field strength at distance d = EB 1/d2

– Surface area of sphere centered at transmitter

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General Intuition

• Two main factors affecting signal at receiver– Distance (or delay) Path attenuation – Multipath Phase differences

Green signal travels 1/2 farther than Yellow to reach receiver, who sees Red. For 2.4 GHz, (wavelength) =12.5cm.

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Objective

• Invent models to predict what the field looks like at the receiver. – Attenuation, absorption, reflection,

diffraction...– Motion of receiver and environment…– Natural and man-made radio interference...– What does the field look like at the receiver?

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Models are Specialized

• Different scales– Large scale (averaged over meters)– Small scale (order of wavelength)

• Different environmental characteristics– Outdoor, indoor, land, sea, space, etc.

• Different application areas– macrocell (2km), microcell(500m), picocell

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Radio Propagation Mechanisms

• Free Space propagation• Refraction

– Conductors & Dielectric materials (refraction)• Diffraction

– Fresnel zones• Scattering

– “Clutter” is small relative to wavelength

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Fading - Multipath Propagation

• Multipath– Signals on transmission take many paths to arrive at a

receiver (multipath)– The strongest component arrives from the direct path

• Multipath Effects cause

– time variations due to multiple delays– random frequency modulations due to Doppler shifts– random changes in signal strengths over short periods– Multipath delay causes the signal to appear noise-like

in amplitude

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Effects of Multipath Propagation

• Signals may cancel out due to phase differences• Intersymbol Interference (ISI)

– Sending narrow pulse at given frequency between fixed antenna and mobile unit

– Channel may deliver multiple copies at different times– Delayed pulses act as noise making recovery of bit

information difficult– Timing changes as mobile unit moves

• Harder to design signal processing to filter out multipath effects

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• Fading is rapid fluctuations 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 transmitted signal, which arrives at the receiver at slightly different times.

• These multipath waves combine at the receiver antenna to give a resultant signal, which can vary in delay, in amplitude and phase.

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Multipath effects– Rapid changes in signal strength over a small

distance or time interval.– Random frequency modulation due to varying

Doppler shift on different multipath signals.– Time dispersion (echoes) caused by multipath

propagation delay.

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Causes of fading• In urban areas, fading occurs because the height of

mobile is << height of surrounding structures, such as buildings and trees.

• Existence of several propagation paths between transmitter and receiver.

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Analysis methods of multipath channel

Receiver

dd

Spatial Spatial positionposition

Transmitter

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Convolution model for multipath propagation

Received signal: y(t) = x(t) + A1 x(t - 1) + A2 x(t - 2) + ...

TT RR

AA22 x(t- x(t- 22))

AA11 x(t- x(t- 11))

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Convolution Integral

• Convolution is defined by this integral:

τ)τ()τ()(

)()()(

dthxty

thtxty

Indexes relevant portion of impulse response

Scales past input signal

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Time varying system model for channel

• For a fixed position d, the channel between transmitter & receiver can be modulated as a linear time varying system (LTV system).

• Impulse response of the LTI system can be given as h(d,t).• If x(t) is the transmitted signal, the received signal can be

represented as:y(d,t) = x(t) * h(d,t)

– * denotes convolution – h(d,t) is impulse response of the system

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y(d,t) = x(t) * h(d,t)

ty(d,t) = x() h1(d,t - ) d

-

Distance d = v.t where v is constant velocity of the receiver.

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ty(vt,t) = x() h1(vt,t - ) d -

This is a time varying system with impulse response of h(t, )

d)(x)t,t(h)t(r

d)t(x),t(h)t(r

),t(h)t(x)t(r

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System definition

Linear Time Varying (LTV) System

h(t, h(t, ))x(t)x(t) y(t)y(t)

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Signal definitions

j 2 fct

x(t) = Re { c(t) e }

Transmitted signalTransmitted signal

C(t)C(t)

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...Signal definitions

j2 fct

y(t) = Re {r(t) e }

j2fct

h(t, ) = Re {hb(t, ) e }

Received signalReceived signal

Impulse responseImpulse response

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Base band equivalent channel impulse response model

hhbb(t, (t, ))c(t)c(t) r(t)r(t)

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r(t) = c(t) * hb(t, )

Modeling of the base band impulse response model

hhbb(t,(t,)) tt33

tt22

tt11

tt00N-2 N-2 N-1N-1 oo 11 22

MathematicalMathematical modelmodel

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Factors Influencing Fading

• Motion of the receiver: Doppler shift• Transmission bandwidth of signal

– Compare to BW of channel• Multipath propagation

– Receiver sees multiple instances of signal when waves follow different paths

– Very sensitive to configuration of environment

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Effects of Multipath Signals

• Rapid change in signal strength due to phase cancellation

• Frequency modulation due to Doppler shifts from movement of receiver/environment

• Echoes caused by multipath propagation delay

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The Multipath Channel• One approach to small-scale models is to

model the “Multipath Channel” – Linear time-varying function h(t,)

• Basic idea: define a filter that encapsulates the effects of multipath interference– Measure or calculate the channel impulse response

(response to a short pulse at fc):

h(t,) t

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Channel Sounding

• “Channel sounding” is a way to measure the channel response– transmit impulse, and measure the response to find

h(). – h() can then be used to model the channel response

to an arbitrary signal: y(t) = x(t)h().– Problem: models the channel at single point in time;

can’t account for mobility or environmental changes

h(t,)

SKIP

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Characterizing Fading*

• From the impulse response we can characterize the channel:

• Characterizing distortion– Delay spread (d): how long does the channel

ring from an impulse?– Coherence bandwidth (Bc): over what

frequency range is the channel gain flat? d1/Bc

In time domain, roughly corresponds to the “fidelity” of the response; sharper pulse requires wider band

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WSSUS*

• Wide Sense Stationary (WSS)– Statistics are independent of small perturbations in

time and position– I.e. fixed statistical parameters for stationary nodes

• Uncorrelated Scatter (US)– Separate paths are not correlated in phase or

attenuation– I.e. multipath components can be independent RVs

• Statistics modeled as Gaussian RVs