Some closed-form solutions to the equal gain combiner over Rayleigh fading channels

In a typical land mobile radio system, the received signal usually suffers from multipath fading, severely degradating the service quality. Equal gain combiner (EGG) is a powerful means to combat multipath fading and has long been used in practice owing to its good performance and ease of implementation. Nevertheless, the error probability of the EGC in a closed form is still not available in the literature. By formulating the problem in the framework of signal detection and evaluating the probability of error directly from the characteristic function (CF) of the signal at the combiner output, we obtain closed form solutions to the probability of error for the EG combiner with two or three branches operating over a Rayleigh fading channel