1. Diversity
Lecture 7

2. Diversity
Fading hurts the reliability of the system (we saw 30dB possible power penalty).
Reliability is increased by providing more signal paths that fade independently.
Diversity can be provided across time, frequency , space and polarization.
Macro-diversity vs. Micro-diversity
Macro-diversity: Combat shadowing
Micro-diversity: Combat small scale fading (Rayleigh fading)

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 t
Multiple paths unlikely to fade simultaneously

4. SNR Improvement Using Diversity
assuming
represents SNR for each path or brunch.
and
Then, for Rayleigh fading channel
The probability the path SNR less than specific threshold
The probability that SNR of all paths less than specific threshold is given by
Then, SNR improvement using diversity is given by

5. SNR Improvement Using Diversity

6. Rayleigh Flat Fading Channel

7. Rayleigh vs. AWGN

8. Typical Error Event

9. Using Diversity Deep Fades Become RarerL L

10. Performance

11. Diversity Combining Algorithms
There are three primary combining algorithms:
Selection combining (SC),
Maximal ratio combining (MRC),
Equal gain combining (EGC).
Received signal
Received signal power
Noise power

12. Selection Combining (SC)
Let the instantaneous SNR in any one of the branches Zk
Picking the output or branch having the highest value of the SNR expressed as
Then

13. MRC and EGC

16. Time Diversity
Time diversity can be obtained by interleaving and coding over symbols across different coherent time periods.
Coding alone is not sufficient!

17. Antenna Diversity

18. Receive Diversity Receive has more than one antenna.
Same as repetition coding in time diversity, except that there is a further power gain.
Optimal reception is via match filtering (receive beamforming).

19. Diversity Performance (BPSK)

20. Transmit Diversity

21. Space-time Codes
Transmitting the same symbol simultaneously at the antennas doesn’t work.
Using the antennas one at a time and sending the same symbol over the different antennas is like repetition coding.
More generally, can use any time-diversity code by turning on one antenna at a time.
Space-time codes are designed specifically for the transmit diversity scenario.

22. Alamouti Scheme

23. Examples of Diversity Approaches
Time-domain equalization (eg. GSM)
Direct-sequence spread spectrum (eg. IS-95 CDMA)
Orthogonal frequency-division multiplexing OFDM (e.g a and LTE)

24. Summary Fading makes wireless channels unreliable.
Diversity increases reliability and makes the channel more consistent.
Smart codes achieves the diversity gain while minimizing rate loss