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

Abstract

In this letter, we propose novel, accurate approximation for the Gaussian <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {F}$ </tex-math></inline-formula> distribution. Lastly, the analysis is justified with the help of Monte-Carlo simulations.