Novel Romberg approximation of the Gaussian Q function and its application over versatile κ − μ shadowed fading channel

Abstract

In this paper, we propose extremely accurate, generic, exponential based approximations for the Gaussian Q function. Precisely, we make use of the Romberg numerical integration technique which utilizes the Richardson extrapolation method. This method combines two trapezoidal based approximations thereby yielding accurate yet simple approximations for the Gaussian Q function. We extensively illustrate the significance of the proposed work by comparing it with several other approximations available in the open literature. To show the application of the proposed work in communication theory, as an instance, we further apply the six-term proposed approximation over the versatile κ−μ shadowed fading channel which facilitates the error performance metrics for several wireless communication systems. In addition, the analysis is solidified with the help of computer simulations.