1. Diversity

2. Outline Introduction to Diversity Receiver Diversity
Combining Techniques
Performance of Diversity in Fading
Selection Combining
Maximal Ratio Combining
MGF Approach to MRC Performance
EGC
Transmit Diversity

3. Introduction to Diversity
Basic Idea
Send same bits over independent fading paths
Independent fading paths obtained by time, space, frequency, or polarization diversity
Combine paths to mitigate fading effects Tb
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 simultaneously t

4. Realization of independent fading paths
Space diversity
Polarization diversity
Angle (pattern) diversity
Frequency diversity
Time diversity

5. Receiver Diversity System Model
Coherently combine the independent fading paths
S(t) multiplied by a random complex amplitude term
Suppose no fading
so that , noise PSD N0/2 on each branch and pulse shaping such that BTs=1.
Then each branch has the same SNR:
Set
Then the received SNR after combination:
Array gain: SNR increase in the absence of fading

6. Receiver Diversity System Model
With fading
More favorable distribution of , increase and Pout
Average probability of error
Outage probability
Diversity gain: change in BER slope
The average probability of error
Diversity order: M
how the slope of average probability of error as a function of average SNR changes with diversity.

7. Array/Diversity gain
Array gain is from noise averaging (AWGN and fading)
Diversity gain is change in BER slope (fading)

8. Receiver Diversity ——Combining Techniques
Selection Combining
Fading path with highest gain used
Maximal Ratio Combining
All paths cophased and summed with optimal weighting to maximize combiner output SNR
Equal Gain Combining
All paths cophased and summed with equal weighting

9. Selection Combining Analysis and Performance
CDF of
PDF of
Differentiating relative to
For Rayleigh fading, the average SNR on the ith branch as
The 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 of
Differentiating relative to
Average 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.
Outage
Probability

12. MRC and its Performance
With MRC, gS=gi for branch SNRs gi
Optimal technique to maximize output SNR
Yields dB performance gains
Distribution of gS hard to obtain
Standard average BER calculation
Hard to obtain in closed form
Integral often diverges
MGF Approach

13. EGC EGQ simpler than MRC Harder to analyze
Performance about 1 dB worse than MRC

14. Transmit Diversity
With channel knowledge, similar to receiver diversity, same array/diversity gain
Without channel knowledge, can obtain diversity gain through Alamouti scheme: works over 2 consecutive symbols

15. Alamouti Alamouti code h11 h12 Transmitter 1, S1 Receiver 1, Y1 h21
Tx1
Tx2
Time k
k+1

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
Function
GUI interface
Original reference
S. M. Alamouti, A Simple Transmit Diversity Technique for Wireless Communications, IEEE Journal on Select Areas in Communications, vol. 16, no. 8, Oct

20. Alamouti code-Time domain
Before coding
Data1
Data2
Data3
Data4
Data5
Data6
Transmitter 1
OFDM symbol
After coding
and framing
Preamble Tx1
-Preamble Tx2*
Data 1,1
-Data 2,1*
Data 1,n
-Data 2,n*
Transmitter 1
OFDM symbol
Transmitter 2
Preamble Tx2
Preamble Tx1*
Data 2,1
Data 1,1*
Data 2,n
-Data 1,n*
OFDM symbol

21. Total data sub-carrier
Frequency domain
Frequency
Frequency
F 1,1
F 2,1
-F 2,1*
F 1,1*
F 1,96
F 2,96
-F 2,96*
F 1,96*
Time
Time
Total data sub-carrier
192
Total pilots 8 DC 1
FFT size
256

22. Main Points
Diversity overcomes the effects of fading by combining fading paths
Diversity 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 approach
EGC easier to implement than MRC: hard to analyze.
Performance about 1 dB worse than MRC
Transmit diversity can obtain diversity gain even without channel information at transmitter.