Results for Integrals Involving m-th Power of the Gaussian Q-function Over Rayleigh Fading Channels with Applications

Exact-form results are presented for integrals involving higher-order power of the one dimensional Gaussian Q-function over identical and nonidentically distributed multichannel Rayleigh fading with maximal ratio combining (MRC). The formulas known in the literature for the average of the 1st and 2nd powers are shown as special cases. The derived results herein are then used to obtain new expressions for the average error performance of differentially encoded quadri-phase shift-keying signals over identical as well as nonidentically distributed multi-channel Rayleigh fading.