Generalized MGF of Inverse Gaussian Distribution with Applications to Wireless Communications

Abstract

This correspondence considers the inverse Gaussian distribution, which is a tractable and accurate alternative to the log-normal distribution that represents not only shadowing in wireless communications but also turbulence in free-space optical communications. We first derive the generalized moment generating function (G-MGF) of the inverse Gaussian distribution, and then make use of the derived formula to effectively analyze several performance metrics, such as area under the receiver operating characteristics (ROC) curve, average error rate, outage probability, etc. Finally, we provide some numerical results to corroborate the accuracy of our evaluations.