Probability of error for M-branch macroscopic selection diversity

Diversity is a well known technique to mitigate the deleterious effects of the mobile radio channel as it can reduce the signal variability. However, the improvement in performance obtainable from the use of microscopic diversity is related to the standard deviation ( sigma ) of the log-normal component, the improvement decreasing as sigma increases. A closed-form analytical solution is obtained for the performance of M-branch macroscopic selection diversity. It has been found that a composite Rayleigh plus log-normal distribution can be accurately approximated by another log-normal distribution. The results indicate that for a BER of 10 ^-3 and sigma =9 dB, a 2-branch macroscopic diversity offers an improvement of 13 dB. Unlike microscopic diversity, the performance improvement of an M-branch macroscopic system increases as sigma increases. The results also show that, for the same number of branches, macroscopic outperforms microscopic diversity and the composite microscopic plus macroscopic systems.<>