Diversity Lecture 7

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)

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

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

SNR Improvement Using Diversity

Rayleigh Flat Fading Channel

Rayleigh vs. AWGN

Typical Error Event

Using Diversity Deep Fades Become Rarer L L

Performance

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

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

MRC and EGC

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

Antenna Diversity

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).

Diversity Performance (BPSK)

Transmit Diversity

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.

Alamouti Scheme

Examples of 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)

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