New, Simple and Accurate Approximation for the Gaussian Q Function With Applications

In this letter, we propose novel, accurate approximation for the Gaussian Q function which is expressed as the sum of simple exponentials. To do so, we use the composite Gauss quadrature numerical integration method incorporating a special mid point rule. The nuances on the accuracy as well as an insight on the tractability of the proposed approximation is exhaustively presented in this letter. We show that this approximation facilitates the symbol error probability of square quadrature amplitude modulation technique over the versatile Fluctuating Beckmann fading model and the practical Fisher-Snedecor F distribution. Lastly, the analysis is justified with the help of Monte-Carlo simulations.

Automated summary

We propose a novel and accurate approximation method for the Gaussian Q function, which expresses it as a sum of simple exponentials. By using the composite Gauss quadrature numerical integration method incorporating a special midpoint rule, we exhaustively analyze the accuracy and tractability of this approximation. We demonstrate the application of this approximation in the symbol error probability of square quadrature amplitude modulation technique, considering the versatile Fluctuating Beckmann fading model and practical Fisher-Snedecor F distribution. Our analysis is supported by Monte-Carlo simulations.