An effcient approximation of Q(√x) function and general BER performance analysis

In this paper, a novel approximation for the Gaussian Q-function in the form of Q(√x) is presented. The proposed approximation is compared with other known closed-form approximations of the Q-function in terms of accuracy and applicability. This approximation can be effciently used to simplify intractable problems which do not have explicit solutions. The approximation of the generalized probability density function (PDF) using Gaussian fnite mixture components is utilized with the proposed approximation to derive a generalized closed-form expression for the Bit Error Rate (BER) for coherent modulation techniques. The derived expression is evaluated over Nakagami-m and Weibull fading channels. Monte Carlo simulation of the average BER expression is provided over Nakagami-m and Weibull fading channels in order to validate the derived expression. The derived average SER expression can be used by engineers to evaluate the BER performance for any coherent modulation technique and over any fading channel given that the fading channel statistics are modeled using Gaussian fnite mixture.