Channel in Digital communication

8/11/2019 Channel in Digital communication

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Mobile Radio Propagation:

Fading and Multipath



Large scale propagation effectsPath loss (function of distance)Shadowing (obstacle between Tx and Rx)

Small scale propagation effectsMultipath (short distance ~ signal

wavelength)





Simplified path loss model:



Log-normal shadowing: isassumed random with log-normal distribution (basedon LLN applied to many attenuating objects) :



Combined Path Loss and Shadowing

),(~,log10log10)( 2

01010 N d

d

K dB P

P dBdB

t

r

=0 when average shadowing incorporated into K and , else <0



Model Parameters fromEmpirical Measurements

Fit model to data

Path loss (K, ), d 0 known:“Best fit” line through dB data K obtained from measurements at d 0.Exponent is MMSE estimate based on data

Captures mean due to shadowingShadowing variance

Variance of data relative to path loss model

(straight line) with MMSE estimate for

P r (dB)

log(d)10

K (dB)

log(d 0)

2



Small-Scale Multipath Propagation

The three most important effectsRapid changes in signal strength over a small travel distance or timeintervalRandom frequency modulation due to varying Doppler shifts on

different multipath signals Time dispersion caused by multipath propagation delays

Factors influencing small-scale fadingMultipath propagation: reflection objects and scattersSpeed of the mobile: Doppler shiftsSpeed of surrounding objects

Transmission bandwidth of the signal The received signal will be distorted if the transmission bandwidth isgreater than the bandwidth of the multipath channel.Coherent bandwidth: bandwidth of the multipath channel.



Statistical Multipath Model

Random # of multipath components, each withRandom amplitudeRandom phaseRandom Doppler shiftRandom delay

Random components change with time

Leads to time-varying channel impulse response



Time Varying Impulse Response

Response of channel at t to impulse at t- t :

t is time when impulse response is observed

t-t is time when impulse put into the channelt is how long ago impulse was put into the

channel for the current observation path delay for MP component currently observed

))(()(),(1

)( t e t t c n

N

n

t j n

n t t t



Received Signal Characteristics

Received signal consists of many multipathcomponents

Amplitudes change slowlyPhases change rapidly

Constructive and destructive addition of signal

components Amplitude fading of received signal (both wideband and narrowband signals)



Narrowband Model

Assume delay spread max m,n | t n (t)- t m (t) | <<1/B

Then u(t) u(t- t ).

Received signal given by

No signal distortion (spreading in time)Multipath affects complex scale factor in brackets.

Characterize scale factor by setting u(t)=e j 0

)(

0

)(2 )()()(t N

n

t jn

t f j nc et et ut r f



In-Phase and Quadratureunder CLT Approximation

In phase and quadrature signal components:

For N(t) large, r I(t) and r Q(t) jointly Gaussian byCLT (sum of large # of random vars).

Received signal characterized by its mean,autocorrelation, and cross correlation.

If n (t) uniform, the in-phase/quad components are

mean zero, indep., and stationary.

),2cos()()()(

0

)( t f et t r c

t N

n

t jn I

n f

)2sin()()()(

0

)( t f et t r c

t N

n

t jnQ

n f



Auto and Cross Correlation(Section 3.2.1)

Assume n~U[0,2 ]Recall that qn is the multipath arrival angle

Autocorrelation of inphase/quad signal is

Cross Correlation of inphase/quad signal is

Autocorrelation of received signal is

q t t t q /cos],2[cos)()( n D Dr r v f f PE A AnnnQ I

)(]2[sin)( ,, t t t q Q I nnQ I r r Dr r A f PE A

)2sin()()2cos()()(,

t t t t t cr r cr r

f A f A AQ I I



Envelope and Power Distributions



Main PointsPath loss and shadowing parameters are obtainedfrom empirical measurements

Statistical multipath model leads to a time-varyingchannel impulse response

Narrowband model has in-phase and quad. compsthat are zero-mean stationary Gaussian processes Auto and cross correlation depends on AOAs of multipath

Channel in Digital communication

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