lecture 7,8: diversity aliazam abbasfar. outline diversity types diversity combining
TRANSCRIPT
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
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