Probability of error for m-branch macroscopic selection diversity

Abstract

Diversity is a well known technique to mitigate the deleterious effects of the 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 (σ) of the lognormal component, the improvement decreasing as σ increases. In this paper a closed-form analytical solution is obtained for the performance of Mbranch macroscopic selection diversity. It has been found that a composite Rayleigh plus lognormal distribution can be accurately approximated by another log-normal distribution. The results indicate that for a BER of 10⁻³ and (σ = 9 dB, a 2-branch macroscopic diversity offers an improvement of 13 dB. Unlike microscopic diversity, the performance improvement of an Mbranch macroscopic system increases as σ increases. The results also show that, for the same number of branches, macroscopic outperforms microscopic diversity and the composite microscopic plus macroscopic systems.