A simple approach to error probability with binary signaling over generalized fading channels with maximal ratio combining and noisy channel estimates

In this letter, we study the performance of binary signaling on generalized fading channels with maximal ratio combining (MRC) and imperfect channel estimates. With the assumption of the channel estimate being corrupted by a complex Gaussian random variable, an expression for the average probability of error is provided in the form of a simple single integral which involves the moment generating function of the normalized signal-to-noise ratio corresponding to the case of ideal MRC. Various examples are given to illustrate the usefulness of the derived expression under various fading conditions with different distributions, and with a possible correlation between the diversity branches.