Performance Analysis of Wireless Systems from the MGF of the Reciprocal of the Signal-to-Noise Ratio

A class of wireless problems is characterized by the availability of the moment generating function (MGF) of the reciprocal of the signal-to-noise ratio. We show how to compute the average error rates and outage probability in this case. The result allows a simple, accurate numerical calculation of the average error rate by using the Gauss-Legendre numerical quadratures. We also derive the exact bit error rate of multihop relays for the special case where the fading index of each hop is an odd multiple of one-half.