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Diversity

Diversity. Lecture 6. Announcement. Project proposals: due on Monday, May 06. 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.

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Diversity

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  1. Diversity Lecture 6

  2. Announcement • Project proposals: due on Monday, May 06.

  3. 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 and space, polarization. • Macro-diversity vs. Micro-diversity • Macro-diversity: Combat shadowing • Micro-diversity: Combat small scale fading (Rayleigh)

  4. Tb 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 t Multiple paths unlikely to fade simultaneously

  5. Rayleigh Flat Fading Channel

  6. Rayleigh vs. AWGN

  7. Typical Error Event

  8. 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

  9. Selection Combining (SC) • Picking the output or branch having the highest value of the SNR expressed as where, the instantaneous SNR in any one of the branches Zk

  10. Maximal Ratio Combining (MRC) • We are seeking a set of weights g’s so that the output SNR is maximized • In other words, the out SNR of the MRC algorithm is the sum of the individual SNRs from the M branches.

  11. Equal Gain Combining (EGC) • If the gain factors are all equal, the output SNR of the EG combiner becomes

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

  13. Example: GSM • Amount of time diversity limited by delay constraint and how fast channel varies. • In GSM, delay constraint is 40ms (voice).

  14. Simplest Code: Repetition

  15. Geometry • For BPSK • Is a sufficient statistic (match filtering). • Reduces to scalar detection problem

  16. Deep Fades Become Rarer

  17. Performance

  18. Antenna Diversity

  19. 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).

  20. Diversity Performance (BPSK)

  21. Transmit Diversity

  22. 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.

  23. Alamouti Scheme

  24. Frequency Diversity Approaches: • Time-domain equalization (eg. GSM) • Direct-sequence spread spectrum (eg. IS-95 CDMA) • Orthogonal frequency-division multiplexing OFDM (e.g. 802.11a and LTE)

  25. 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

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