On the influence of the power profile on diversity combining schemes

The usage of multichannel receivers that are followed by diversity combining can significantly improve the performance of wireless communications links. In this paper, we investigate in some detail three popular techniques for diversity combining, namely maximal ratio combining (MRC), equal gain combining, and selection combining. The main goal is to investigate under which circumstances it can be guaranteed that a certain technique does indeed decrease the probability of error of a multichannel receiver. The analyzed fading model is quite general with the only assumption that fading gains are scaled exchangeable random variables. The crucial mathematical tool used to produce the results of this paper is the powerful theory of stochastic majorization. Among other results, it was shown that the average bit-error probability of the MRC receiver with equally distributed average powers always decreases with the addition of a new diversity branch if the total power is fixed.