1. Lecture 7,8: Diversity Aliazam Abbasfar

2. Outline Diversity types Diversity combining

3. Diversity Relying on a single channel Deep fade disrupts communication All modulations perform very badly in fading P e Decays linearly with SNR Solution : diversity Multiple independent channels for communication Micro-diversity : multipath fading Time, frequency, spatial, polarization, … Macro-diversity : shadowing Network management

4. Time diversity Sending bits again in different times Same bits experience different fades Repetition code + Interleaving Interleaver spread > Coherence time (T c ) L = # of repetition Diversity branches Less likely to be in deep fade all the time Rate reduction penalty Coded systems Diversity, and Coding gain

5. Frequency diversity Sending data over different frequency bands at the same time Bandwidth separation > Coherence bandwidth (W c ) 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

6. Case study : GSM

7. Spatial (antenna) diversity Sending/receiving bits to/from multiple antennas Antennas are separated enough to ensure un- correlated channels Transmit/Receive diversity 10 / /2 antenna separation No rate reduction or bandwidth penalty Polarization diversity Multipath channel have uncorrelated polarizations No spatial separation

8. Diversity combining Selection(switch) diversity Simplest type Pick 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

9. Switch diversity Best branch selection Need L receivers to monitor SNRs Switch to another branch when SNR is less than a threshold (SNR 0 ) 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

10. 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

11. Switch and stay Switch to another branch when SNR falls bellow a threshold Less sensitive to noise Outage probability can be as good as best branch selection

12. Maximal Ratio Combining (MRC) Combine branches linearly Find linear coefficients to maximize SNR Optimum coefficients : h i * Co-phase the branches Branches with high SNR have higher weights SNR =  SNR i = ‖ h ‖ 2 SNR avg E[ SNR] = L SNR avg ‖ h ‖ 2 Chi-square distribution BER

13. Maximal Ratio Combining (MRC) P e Upperbound At high SNR Achieves full diversity order

14. Equal Gain Combining (EGC) Co-phase the branches and add them Simpler receiver (No variable gain) Small performance degradation 1 dB of power penalty

15. Diversity gain – Array/Coding gain

16. Ch. 7 Goldsmith Ch. 3 Tse Reading