Capacity of Nakagami-q (Hoyt) fading channels with channel side information

In this paper, we derive closed-form expressions for the channel capacity of a diversity reception system with maximal-ratio combining (MRC) or postdetection equal-gain combining (EGC) over a slowly varying Nakagami-q (Hoyt) fading channel under different adaptive transmission policies when the channel side information is available at the transmitter and the receiver. We consider the situation that the branches are independent and identically distributed (i.i.d.). We first derive three different canonical-form expressions for the probability density function (PDF) of the instantaneous combiner output signal-to-noise ratio (SNR) as a weighted sum of gamma PDFs. Then the channel capacity is obtained in different canonical forms as a weighted sum of channel capacities for single-branch systems in gamma fading environments.