Probability of error for equal-gain combiners over Rayleigh channels: some closed-form solutions

The probability of error of a general equal-gain combiner (EG) in closed form is 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 for the probability of error of the EG combiner with two or three branches operating over a Rayleigh-fading channel.