Some remarks on the Dirac delta function approximation for ASER analysis of digital modulations over fading channels

Abstract

In this article, we apply two distinct methods to obtain simple closed-form approximations for the average symbol error rate (ASER) performance metric of a broad class of coherent digital modulations in a myriad of fading environments (with/without diversity), which are known to be analytically involved as they require evaluation of the expectation of the Gaussian Q-function and/or its integer powers. In the first approach, we exploit the shifting property of Dirac delta approximations of the Q-function to circumvent the need for integration. In the second approach, we introduce tight exponential-type approximations for the Q-function that directly lead to the development of closed-form expressions for the ASER in terms of only the moment generating function (MGF) of the received signal-to-noise ratio (SNR) random variable. Numerical results reveal that our proposed solutions based on the MGF method are much more versatile and can yield better accuracy compared to our approximations derived via the Dirac delta approximation technique.