41st IEEE CDC Las Vegas, Nevada December 9th 2002 Workshop M-5:Wireless Communication Channels: Modeling, Analysis, Simulations and Applications Organizers:Charalambos.

41st IEEE CDC

Las Vegas, Nevada

December 9th 2002

Workshop M-5: Wireless Communication Channels: Modeling, Analysis, Simulations and Applications

Organizers: Charalambos D. CharalambousNickie Menemenlis

Wireless Communication Channels

Schedule08:00-08:45 Introduction to Wireless Communication Channels (C.D. Charalambous) 8:45-9:15 Statistical Analysis of Wireless Fading Channels (C.D. Charalambous)

9:15-9:25 Break

9:25 -10:10 Stochastic Differential Equations in Modeling Log-Normal Shadowing (N. Menemenlis) 10:10-10:55 Stochastic Differential Equations in Modeling Short-Term Fading (N. Menemenlis)

10:55-11:00 Break

11:00-12:00 Applications (C.D. Charalambous)

Additional information can be found at: http://www.site.uottawa.ca/~chadcha/CDC2002

Introduction to Wireless Communication Channels

Shannon’s communication channel

Impulse response of wireless fading channels

Large-scale and small scale propagation models Log-Normal shadowing channel Short-term fading channel

Autocorrelation functions and power spectral densities Assumption: WSSUS Time spreading Time variations

Channel classification

Channel simulations

Chapter 1: Shannon’s Wireless Communication System

SourceSource

EncoderChannelEncoder

Mod-ulator

UserSource

DecoderChannelDecoder

Demod-ulator

MessageSignal

Channel code word

Estimate ofMessage

signalEstimate of

channel code word

ReceivedSignal

ModulatedTransmitted

Signal

Wireless

Channel

Chapter 1: Large and Small Scale Propagation Models

Area 2Area 1

Transmitter

Log-normalshadowing

Short-term fading

Chapter 1: Impulse Response Characterization

(t0)t0

t2

(t2)

t1(t1)

Time spreading property

Time va

riatio

ns property

Impulse response: Time-spreading : multipath

and time-variations: time-varying environment

Complex low-pass representation of impulse response

Chapter 1: Multipath Fading Components

( )( ; )

1

Response at of the channel at time due an impulse

applied at time - .

( ; ) ( ; ) ( ( ))

( ; ): Signal attenuation (R.P.)

( ; ) ( ) : Phase angle (R.P.)

(

i

i i

N tj t

l i ii

i

i i c d d

i

t

t

C t r t e t t

r t

t t

t

) : Propagation delay (R.P.)

( ): Number of waves impinging on the receiver

antenna at time (a counting R.P.)

N t

t

Band-pass representation of impulse response:

Chapter 1: Band-pass Representation of Impulse Response

( )( ; )

1

( )

1

( ; ) Re ( ; ) ( ( ))

( ; ) cos ( ; )sin ( ( ))

( ; ) ( ; ) cos( ( ; )) In-phase component

( ; ) ( ; )sin( ( ; )) Quadra

i c

N tj t j t

i ii

N t

i c i c ii

i i i

i i i

C t r t e e t t

I t t Q t t t t

I t r t t

Q t r t t

2 2

1

ture component

( ; ) ( ; ) ( ; ) Attenuation

( ; )( ; ) tan Phase( ; )

ii i

ii

i

r t I t Q t

Q tt I t

Low-pass and band-pass representation of received signal:

Chapter 1: Representation of Additive Noise Channel

( )( ; ( ))

1

( )

1

0

( ) ( ; ( )) ( ( )) ( )

( ) Re{ ( ) }

( ; ( )) cos ( ; ( ))sin ( ( )) ( )

( ) : arbitrary low-pass transmitted signal

{ ( )} : co

i i

c

N tj t t

l i i l i li

j tl

N t

i i c i i c l ii

l

l t

y t r t t e s t t n t

y t y t e

I t t t Q t t t s t t n t

s t

n t

mplex valued noise process

Large scale propagation models:

T-R separation distances are largeMain propagation mechanism: reflectionsAttenuation of signal strength due to power loss along distance traveled: shadowingDistribution of power loss in dBs: Log-NormalLog-Normal shadowing modelFluctuations around a slowly varying mean



Small scale propagation: T-R separation distances are smallHeavily populated, urban areasMain propagation mechanism: scatteringMultiple copies of transmitted signal arriving at the transmitted via different paths and at different time-delays, add vectotrially at the receiver: fading

Distribution of signal attenuation coefficient: Rayleigh, Ricean.Short-term fading modelRapid and severe signal fluctuations around a slowly varying mean

Chapter 1: Log-Normal Shadowing Model

00 0

0 0

Average power of received signal at

( ) ( ) ,

: Reference distance, i.e. 1 m. for indoors

: Characterizes the environment

d

dP d P d d d

d

d d


00 0

2

( )[

Average power path-loss in dBs at distance

( )[ ] ( )[ ] 10 log ,

Power path-loss in dB's

( )[ ] ( )[ ] , (0, )

Signal Attenuation Coefficient

( )( )

d d

d

kPL d d

t

d

dPL d dB PL d dB d d

d

PL d dB PL d dB X X N

P dr d e

P

] ln10, log-normal, 20

( ) : received power at

: power of transmitted signal

B

t

k

P d d

P


Power path-loss in dB’s, x, and Distributions: x : normal and attenuation coefficient, r, vs d r=ekx : log-normal

2 2( ) / 2 2

22 2

1( ) , [ ], ( )

2

1( ) exp (ln ) / 2 , [ ] exp , 0

22

xx xx

x

xx

x

f x e x E x Var x

f r r x E r x rr

Chapter 1: Short-Term Fading Model

n

n

x

z

y

nth inco

ming wave

E n=:{r n

, n, n

, n}; n

=1,…, N

O

O’(x0 ,y0 ,z0)

direction of motion of mobile on x-y plane

v

x0

z0

y0

O’’

3-Dimensional Model [Clarke 68, Aulin 79]


3-D Model [Clarke 68, Aulin 79]

Transmitted signal: Re{ejct}Total field at mobile, or receiving location, O’(x0, y0, z0)

1

( )

0 0 0

1

( ) ( )

( ) Re cos( ( ) ), 1,

2cos cos sin cos sin

, : carrier frequency, : speed of light

, , , : random variables, stati

n c n

N

nn

j j tn n n c n n

c n n n n n n

c c

N

n n n n n

E t E t

E t r e e r t n N

x y z

c f f c

r

2 0

stically independent,

: signal attenuation coefficient; 0, 2 , [ ]n n n

Er U E r

N


3-D Model [Clarke 68, Aulin 79]Total field at receiving location when mobile moves

O’(x0, y0, z0) => (x0+vtcos, y0 +vtsin, z0), v: velocity of mobile

( )

1 1

( ) Re

cos( ) cos sin( )sin

( ) cos ( )sin

2cos cos ,

( ) ( ) cos ( )sin

( ) cos( ), ( ) sin( )

c n nn j tjn n

n n n c n n n c

n c n c

n n n n n c n

c c

N N

n n n n n nn n

E t r e e

r t t r t t

I t t Q t t

v

E t I t t Q t t

I t r t Q t r t

I

( ) : In-phase component, ( ) : Quadrature component

: Doppler shiftn

t Q t


3-D Model [Clarke 68, Aulin 79]Statistical characterization of {I(t), Q(t)}

2

2

for N large ( 6) ( ), ( ) ( , ), i.e. Gaussian

{ ( ), ( )}, [ ( )] [ ( )], ( ) ( )

Usually assume ( ), ( ) uncorrelated and therefore independent

No specular componen

x

x

I t Q t N x

x I t Q t x E I t E Q t Var I t Var Q t

I t Q t

2

2

t: 0 : ( ), ( ) (0, )

With specular component

or a direct path between transmitter and receiver: 0

( ) ( ) ( ) cos ( ) ( ) sin

( ) ( ) , ( ) ( ) ( , )

x

d c d c

d d x

x I t Q t N

x

E t I t I t t I t I t t

I t I t I t I t N x


Statistical characterization of rn

2 2

2 22

2 2 2 202

2 22 2 2

From above ( ) ( ) ( ),

No specular component: ( ) Rayleigh

( ) exp / 2 ,

[ ] , 2

With specular component: r Ricean

( ) exp / 2 / ,

( ) ( ) , 2

xx

x

s x s xx

s x

r t I t Q t

r t

rf r r

E r

rf r r r I rr

r E I t E Q t E r

2

0 : modified Bessel function of the first kind of order 0

sr

I

Autocorrelation functions


0

0

00

0

Autocorrelation of ( ) : ( )

( ) ( ) ( ) ( ) cos ( )sin

( ) ( ) ( ) cos , 2

( ) ( ) ( ) sin2

For : uniform in (0,2 ]

2( ) cos ( ) , ( ) 0

2

: Bes

E

E c c

n

n

n

E t R

R E E t E t c

EE I t I t E

Ec E Q t Q t E

E vJ p d c

J

sel function of the first kind of order 0.


0

210

Power Spectral Density of ( ) : ( ) ( )

cosFor : uniform in (0,2 ] and ( ) , ,

2sin 2

0,

( ) , cos4 sin

2cos 1 ( / ) csin ,4 sin 2 1 ( / )

D E

n mm

m

D m m mm m

m mm

m m m

E t S f F R

p

f fE

S f f f ff

E f f f ff f f

os

: Maximum

m

mf

Doppler frequency

Chapter 1: Time Delays of Paths

Complex low-pass representation of impulse response:

Typically the time delays are modeled using exponential distribution, implying that the number of paths is a Poisson counting process

In reality this representation is not very accurate.

( )( ; )

1

( ; ) ( ; ) ( ( ))

( ) : Propagation delay (R.P)

( ): Number of waves impinging on the receiver

antenna at time (a counting R.P.)

i

N tj t

l i ii

i

C t r t e t t

t

N t

t

General expressions for the Autocorrelation function are introduced by Bello ’63 for a widely accepted Wide-Sense Stationary Uncorrelated Scattering (WSSUS) channel

WSS in the time-domainUS attenuation and phase shift of paths i and j are uncorrelated

Chapter 1: Channel Autocorrelation Functions

( )( ; )

1

c 1 2 1 2 1 1 2 2

Linear time-varying filter

( ; ) ( ; ) ( ( ))

General autocorrelation function is defined by:

, ; , =E ( ; ) ( ; )

i

l

N tj t

l i ii

l

C t r t e t t

t t C t C t

Time-spreading: Multipath characteristics of channel


1 2 c 1 2 1

c

1. Autocorrelation in the Time-Domain

Average power output of the channel as a

function of time-delay, , and the difference in the

observation time t

E ( ; ) ( ; ) ;

; :

.

2

llC t C t t t

t

c c c 0

c

. Power-delay profile

Average power output of the channel as a

function of the time-delay, or excess

0; ;

:

delay, .

tt



c

2c c

c c 0

c

3. Space-frequency, space-time

Note: US condition WSS in the frequency domain

observation time t.

4. Power-delay s

;

pectrum

5. Frequency

;

ar

;

;

v

j f

t

F et f t t d

Ff t f

2

iations of the channel

( ; ) ( ; ) ( ; ) j fl l lC t f F C t C t e d


Multi-path delay spread, Tm Characterizes time dispersiveness of the channel,

Obtained from power delay-profile, c()Indicates delay during which the power of the received signal is above a certain value.

Coherence bandwidth, Bc approx. 1/ Tm

Indicates frequencies over which the channel can be considered flat

Two sinusoids separated by more than Bc: affected differently by the channelIndicates frequency selectivity during transmission.


Time variations of channel: Frequency-spreading


c c c

c

c2

c c0

2

1a. Double Fourier transform of

1b. Doppler Power Spectum of channel

Power output of the channel

( ; )

; ; ;

;

; ;

as a

0

j

t t

f

j t

l

t

C t

S f F t FF

e d t

e

t f

t f

S S f d tt

c

function of the

Doppler frequency shift , , (w.r.t. carrier frequency ).

No time variat a deltion a functions:

cf

S



c c c

1c

2

2c

2. Scattering function

Represents average power of the channel as a function

of different time-delays, , and the Doppler freque

; ; ;

; ;

n

f

j t

f

t

j

S e d t

e d f

F t t

F S f S f

c

c

;

cy, .

Power delay profile :

Doppler power spectrum: ;

c

c

S d

S dS


Doppler Spread, Bd

Characterizes frequency dispersiveness of the channel, or the spreading of transmitted frequency due to different Doppler shifts

Obtained from Doppler spectrum, Sc()Indicates range of frequencies over which the received Doppler spectrum is above a certain value

Coherence time, Tc approx. 1/ Bd

Time over which the channel is time-invariant A large coherence time: Channel changes slowly



c( t;)

Sc( ;)

Sc(; f)

ScatteringFunction

F

FtF

Ft

WSSUS Channel

Power DelayProfile

Power DelaySpectrum

c()

Tm

fBc

|c(f)|

F

t=0

tTc

|c(t)|

f=0

t=0

Bd

Sc( )

f=0

Ft

Doppler Power Spectrum

dS );(

dS );(

t

|c(t;f)|

f

Sc()

Chapter 1: Channel Classification

Based on Time-Spreading

Flat Fading1. BS < BC Tm < Ts

2. Rayleigh, Ricean distrib.3. Spectral chara. of transmitted

signal preserved

Frequency Selective1. BS > BC Tm > Ts

2. Intersymbol Interference3. Spectral chara. of transmitted

signal not preserved4. Multipath components resolved

Signal

Channel

freq.BSBC freq.BC

BS

Channel

Signal


Based on Time-Variations

Fast Fading1. High Doppler Spread2. 1/Bd TC < Ts

Slow Fading1. Low Doppler Spread2. 1/Bd TC> Ts

Signal

freq.BDBSfreq.BS

BD

Doppler

Signal

Doppler

Underspread channel: TmBd << 1

Channel characteristics vary slowly (Bd small) or paths obtained within a short interval of time (Tm small).Easy to extract channel parameters.

Overspread channel: TmBd >> 1Hard to extract parameters as channel characteristics vary fast and channel changes before all paths can be obtained.


Flat Fading

(t): Rayleigh or Ricean

Chapter 1: Flat Fading Channel Simulations

2

2

( )

( ) ; ( ) ; ( )

;0 ( ) ;0 ( )

( ) ( );

( ) ( )

; ;

j ftl l l l l

j ftl l l

j tl

l l

l l

y t C t s t d C t f S f e df

C t S f e df C t s t

t e s t

S f F s t

C t f F C t

Input Signalxl (t)

90o phaseshift

Gaussiannoise

source

Shapingfilter

Balancedmodulator

Gaussiannoise

source

Shapingfilter

Balancedmodulator

Rayleighfadingsignal

Frequency Selective

Chapter 1: Frequency Selective Channel Simulations

( )2 /

1

2

( )

1

1; ; ;

( ) ; ( ) ; ( )

1;

W: bandwidth of real band-pass signal

s

s

N Tj fn W

l li

j ftl l l l l

N T

l li

nC t f C t e

W W

y t C t s t d C t f S f e df

n nC t s t

W W W

Receiver

Delay-line

rL(t)ejL(t)r0(t)ej0(t)

Fading Signal Output

Input SignalxL(t)

Tapped-delay line

r1(t)ej1(t)

directpath

...

G.L. Turin. Communication through noisy, random-multipath channels. IRE Convention Record, pp. 154-166, 1956.P. Bello. Characterization of random time-variant linear channels. IEEE Transactions in Communications, pp 360-393, 1963.J.F. Ossanna. A model for mobile radio fading due to building reflections: Theoretical and experimental waveform power spectra. Bell Systems Technical Journal, 43:2935-2971, 1964. R.H. Clarke. A statistical theory of mobile radio reception. Bell Systems Technical Journal, 47:957-1000, 1968.M.J Gans. A power-spectral theory of propagation in the mobile-radio environment. IEEE Transactions on Vehicular Technology, VT-21(1):27-38, 1972.H. Suzuki. A statistical model for urban radio propagation. IEEE Transactions in Communications, 25:673-680, 1977.T. Aulin. A modified model for the fading signal at a mobile radio channel. IEEE Transactions on Vehicular Technology, VT-28(3):182-203, 1979.A.D.Saleh, R.A.Valenzuela. A statistical model for indoor multi-path propagation. IEEE Journal on Selected Areas in Communications, 5(2):128-137, 1987.

Chapter 1: References

M. Gudamson. Correlation model for shadow fading in mobile radio systems. Electronics Letters, 27(23):2145-2146, 1991.D. Giancristofaro. Correlation model for shadow fading in mobile radio channels. Electronics Letters, 32(11):956-958, 1996.A.J. Coulson, G. Williamson, R.G. Vaughan. A statistical basis for log-normal shadowing effects in multipath fading channels. IEEE Transactions in Communications, 46(4):494-502, 1998.E. Biglieri, J. Proakis, S. Shamai. Fading channels: Information-theoretic and communication aspects. IEEE Transactions on Information Theory, 44(6):2619-2692, October 1998.W.C.Jakes. Microwave mobile communications, New York, Wiley-Interscience, 1974.K. Pahlavan, A.H. Levesque. Wireless Information Networks, New York, Wiley-Interscience, 1995.J.G. Proakis. Digital Communications, Mc-Graw-Hill, New-York, 1995.T.S. Rappaport. Wireless Communications, Prentice Hall, 1996.

Chapter 1: References

41st IEEE CDC Las Vegas, Nevada December 9th 2002 Workshop M-5:Wireless Communication Channels: Modeling, Analysis, Simulations and Applications Organizers:Charalambos.

Documents

timevarying environment

varying mean slide

modeling lognormal shadowing

large scale propagation

modeling shortterm fading

varying mean chapter

wssus time

severe signal fluctuations