Novel simple bounds on the probability of error for EGC and MRC diversity receivers over α-μ fading

Abstract

In this paper, we propose novel simple-to-calculate lower and upper bounds on the probability of error for dual-branch equal-gain combining (EGC) and maximal ratio combining (MRC) diversity receivers with α-μ fading and linear modulations. For deriving such bounds, we derive lower and upper bounds for the cumulative distribution function (CDF) of the sum of two independent and non identically distributed α-μ random variables (RVs). The CDF bounds are given in the form of finite series of normalized incomplete Gamma functions and, unlike many in the literature, do not require any look up tables or solving transcendental equations to be obtained. We present extensive numerical results for different combinations of the parameters α and μ and show that the proposed bounds on the CDF and the probability of error are very tight when compared to the exact quantities.