Scrutinizing the average error probability for Nakagami fading channels

The ultimate goal of the present paper is to provide mathematical tools for dealing with the complicated average error probability (AEP) in Nakagami fading channels. This is useful for analytical investigations as well as alleviating computational effort in simulations or on-line computations. We hence thoroughly analyze the mathematical structure of the AEP over Nakagami fading channels. First, the AEP is re-parameterized to obtain a mathematically concise form. The main contributions are then as follows. An ordinary differential equation is set up, which has the AEP as a solution. By this approach, a new representation of the AEP is found, which merely needs integration over a broken rational function. This paves the way to numerous amazing relations of the AEP, e.g., to the Gaussian hypergeometric and the incomplete beta function. Moreover, monotonicity and log-convexity are demonstrated. Finally, asymptotic expansions of the AEP are given.