2 Outline Introduction to Diversity Receiver Diversity Combining TechniquesPerformance of Diversity in FadingSelection CombiningMaximal Ratio CombiningMGF Approach to MRC PerformanceEGCTransmit Diversity
3 Introduction to Diversity Basic IdeaSend same bits over independent fading pathsIndependent fading paths obtained by time, space, frequency, or polarization diversityCombine paths to mitigate fading effectsTb瑞利衰落和对数正态衰落都会使调制性能产生很大的功率损失。减轻衰落影响的有效技术之一就是对独立的衰落信号进行分集合并。分集是在独立的衰落路径上发送相同的数据。由于独立路径在同一时刻经历深衰落的概率很小，因此经过适当的合并后，接收信号的衰落程度会被减小。Multiple paths unlikely to fade simultaneouslyt
4 Realization of independent fading paths Space diversityPolarization diversityAngle (pattern) diversityFrequency diversityTime diversity
5 Receiver Diversity System Model Coherently combine the independent fading pathsS(t) multiplied by a random complex amplitude termSuppose no fadingso that , noise PSD N0/2 on each branch and pulse shaping such that BTs=1.Then each branch has the same SNR:SetThen the received SNR after combination:Array gain: SNR increase in the absence of fading
6 Receiver Diversity System Model With fadingMore favorable distribution of , increase and PoutAverage probability of errorOutage probabilityDiversity gain: change in BER slopeThe average probability of errorDiversity order: Mhow the slope of average probability of error as a function of average SNR changes with diversity.
7 Array/Diversity gainArray gain is from noise averaging (AWGN and fading)Diversity gain is change in BER slope (fading)
8 Receiver Diversity ——Combining Techniques Selection CombiningFading path with highest gain usedMaximal Ratio CombiningAll paths cophased and summed with optimal weighting to maximize combiner output SNREqual Gain CombiningAll paths cophased and summed with equal weighting
9 Selection Combining Analysis and Performance CDF ofPDF ofDifferentiating relative toFor Rayleigh fading, the average SNR on the ith branch asThe SNR distribution:Outage probability for a target on ith branch in Rayleigh fading:Outage probability of SC:If the average SNR for all branches are the same ( , for all i)
10 Selection Combining Analysis and Performance CDF ofDifferentiating relative toAverage SNR of combiner output in independent and identically distributed Rayleigh fading:The average SNR gain and corresponding array gain increase with M, but not linearly.Average probability of symbol error , we can have diversity gain.
11 Selection Combining Analysis and Performance Selection Combining (SC)Combiner SNR is the maximum of the branch SNRs.CDF easy to obtain, pdf found by differentiating.Diminishing returns with number of antennas.Can get up to about 20 dB of gain.OutageProbability
12 MRC and its Performance With MRC, gS=gi for branch SNRs giOptimal technique to maximize output SNRYields dB performance gainsDistribution of gS hard to obtainStandard average BER calculationHard to obtain in closed formIntegral often divergesMGF Approach
13 EGC EGQ simpler than MRC Harder to analyze Performance about 1 dB worse than MRC
14 Transmit DiversityWith channel knowledge, similar to receiver diversity, same array/diversity gainWithout channel knowledge, can obtain diversity gain through Alamouti scheme: works over 2 consecutive symbols
16 Single and double symbol detection Y1=[y1,k y1,k+1];Y2=[y2,k y2,k+1]Maximal-ratio receiver combining (MRRC)
17 two-branch transmit diversity scheme with one receiver
18 two-branch transmit diversity scheme with two receivers
19 Attached Matlab Program FunctionGUI interfaceOriginal referenceS. M. Alamouti, A Simple Transmit Diversity Technique for Wireless Communications, IEEE Journal on Select Areas in Communications, vol. 16, no. 8, Oct
21 Total data sub-carrier Frequency domainFrequencyFrequencyF 1,1F 2,1-F 2,1*F 1,1*F 1,96F 2,96-F 2,96*F 1,96*TimeTimeTotal data sub-carrier192Total pilots8DC1FFT size256
22 Main PointsDiversity overcomes the effects of fading by combining fading pathsDiversity typically entails some penalty in terms of rate, bandwidth, complexity, or size.Techniques trade complexity for performance.MRC yields dB gain, SC around 20 dB.Analysis of MRC simplified using MGF approachEGC easier to implement than MRC: hard to analyze.Performance about 1 dB worse than MRCTransmit diversity can obtain diversity gain even without channel information at transmitter.