SEP Performance of Cross QAM Signaling with MRC over Fading Channels and its Arbitrarily Tight Approximation

The exact average symbol error probability (SEP) of the cross quadrature amplitude modulation signal in a single-input multiple-output system over independent but not necessarily identical fading channels is derived. The maximal-ratio combining (MRC) is considered as the diversity technique, and the average SEP is obtained by using the moment generating function (MGF) method. The obtained closed-form SEP expression is presented in terms of a finite sum of single integrals with finite limits and an integrand composed of a finite product of elementary functions. In addition, the arbitrarily tight approximations with the form of a sum of constant coefficient exponential functions for Gaussian Q-function and the generalization of its Craig's form are proposed by applying the composite rectangle and Simpson numerical integration rules, respectively. The proposed approximations are simple and accurate enough even with only a few terms of exponential functions, and they are particularly suitable for applications of averaging Q-function and the generalized Q-function over the fading distributions. As a result, the closed-form approximations of the SEP over the AWGN channel and fading multichannels are expressed as a finite sum of exponential functions and a finite sum of MGFs, respectively, such that it is convenient and rapid to evaluate the SEP performances. Both the simulation results and the approximations show excellent agreement with the exact analytical expressions.