Further Results on the Dirac Delta Approximation and the Moment Generating Function Techniques for Error Probability Analysis in Fading Channels

In this article, we employ two distinct methods to derive simple closed-form approximations for thestatistical expectations of the positive integer powers of Gaussian probability integral Eg [Qp ( bWg )]withrespect to its fading signal-to-noise ratio (SNR) g random variable. In the first approach, we utilize theshifting property of Dirac delta function on three tight bounds/approximations for Q(.) to circumvent theneed for integration. In the second method, tight exponential-type approximations for Q(.) are exploited tosimplify the resulting integral in terms of only the weighted sum of moment generating function (MGF) ofg. These results are of significant interest in the development of analytically tractable and simple closedformapproximations for the average bit/symbol/block error rate performance metrics of digitalcommunications over fading channels. Numerical results reveal that the approximations based on theMGF method are much more versatile and can achieve better accuracy compared to the approximationsderived via the asymptotic Dirac delta technique for a wide range of digital modulations schemes andwireless fading environments.