Lecture 7,8: Diversity

Aliazam Abbasfar

Outline

Diversity types

Diversity combining

DiversityRelying on a single channel

Deep fade disrupts communicationAll modulations perform very badly in fadingPe Decays linearly with SNR

Solution : diversityMultiple independent channels for communication

Micro-diversity : multipath fadingTime, frequency, spatial, polarization, …

Macro-diversity : shadowingNetwork management

Time diversity Sending bits again in different times

Same bits experience different fades Repetition code + Interleaving Interleaver spread > Coherence time (Tc)

L = # of repetition Diversity branches

Less likely to be in deep fade all the time

Rate reduction penalty

Coded systems Diversity, and Coding gain

Frequency diversitySending data over different frequency bands at the

same time Bandwidth separation > Coherence bandwidth (Wc)

The same baseband signal, different carrier frequencies Multiple up-converter/down-converter circuits

Less likely to be in deep fade in all bands

Bandwidth penalty Spectrum is very expensive

Case study : GSM

Spatial (antenna) diversitySending/receiving bits to/from multiple

antennasAntennas are separated enough to ensure un-

correlated channelsTransmit/Receive diversity

10 / /2 antenna separation

No rate reduction or bandwidth penalty

Polarization diversityMultipath channel have uncorrelated

polarizationsNo spatial separation

Diversity combiningSelection(switch) diversity

Simplest typePick one branch to detect data

Maximal Ratio Combining (MRC)Optimum combining of the received

signals in all branches

Equal Gain Combining (EGC)Combining of the received signals in all

branches with equal gain

Switch diversityBest branch selection

Need L receivers to monitor SNRs

Switch to another branch when SNR is less than a threshold (SNR0) Needs only one receiver Switch and examine Switch and stay

Deep fade is less likely when all branches are

in deep fade

Switching criterion Narrowband : total received signals power Wideband : Signal power + ISI measure

Best branch selection

Outage probability

Fading margin for 1% outage L= 1 : 20 dB L=2 : 10 dB L=3 : 6 dB

Probability of error

L])SNR/SNRexp[1()SNRP(SNR P avg00out

L

1kavg

L21

k

1SNR E[SNR]

)SNR...,,SNR,max(SNRSNR

SNR 2Q [Pe E

Switch and staySwitch to another

branch when SNR falls bellow a thresholdLess sensitive to noise

Outage probability can be as good as best branch selection

Maximal Ratio Combining (MRC) Combine branches linearly

Find linear coefficients to maximize SNROptimum coefficients : hi*

Co-phase the branches Branches with high SNR have higher weights

SNR = SNRi =‖h‖2 SNRavg

E[ SNR] = L SNRavg

‖h‖2 Chi-square distribution

BER

Maximal Ratio Combining (MRC)Pe Upperbound

At high SNR

Achieves full diversity order

L

L

i

L

i

E

)SNR 5.01

1( P

SNR 5.01

1 ] e E[ P

] e E[ ])SNR Q( [P

avge

1 avgi,1

/2SNR -e

SNR/2 -e

i

L)SNR 5.0( P

avge

Equal Gain Combining (EGC)Co-phase the branches and add them

Simpler receiver (No variable gain)

Small performance degradation1 dB of power penalty

Diversity gain – Array/Coding gain

Ch. 7 GoldsmithCh. 3 Tse

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