Evaluation of symbol error probability using a new tight Gaussian Q approximation

In wireless communication systems, various performance metrics requires an evaluation of the Gaussian Q function. However, it is challenging to obtain a closed approximation to the Gaussian Q function in vicinity of small arguments. In this context, this paper portrays a tight approximation to the Gaussian Q function using the Gauss-Legendre numerical integration technique. This can be effectively used towards the computation of symbol error probability (SEP) integrals of different modulation techniques over fading channels. The framework provides an excellent agreement in contrast to the existing methods for SEP computation in Nakagami-m fading channels for all possible values of fading parameter. The model operates well for both higher and lower input arguments of the signal to noise ratios (SNRs). Furthermore, for performance evaluation in Nakagami-m fading channel, this approximation is used to derive the analytical solution for the SEP integrals in general rectangular and non-rectangular quadrature amplitude modulation (QAM).