On the Dirac Delta Approximation and the MGF Method for ASER Analyses of Digital Communications over Fading Channels

Two distinct methods are applied to derive tighter closed-form approximations for the average symbol error rate (ASER) of a multitude of coherent and differentially coherent digital modulations (with/without diversity) in different fading environments. The first approach relies on the Dirac delta function approximation of a generalized function g(x)=x^c-1 exp(-ax) to eliminate the need for integration, while the second method exploits a tight exponential-type approximation for the Gaussian probability integral to express the ASER in terms of only the moment generating function (MGF) of received signal-to-noise ratio (SNR) random variable.