Analytical expression of average detection probability for a linear MMSE combiner in cognitive radio networks

Abstract

This paper derives the theoretical average detection probability of the Fusion Center (FC) with linear minimum mean square error (MMSE) combiner. We consider a centralized cooperative multiple-input multiple-output (MIMO) antenna based reporting network. We assume the sensing channel as an additive white Gaussian noise (AWGN) and the reporting channel as an independent and identically distributed (IID) Rayleigh fading channel. To obtain the average detection probability of FC, average the statistical distribution of output signal-to-interference-plus-noise ratio (SINR) of MMSE combiner and the detection probability of FC over AWGN channel which is a generalized Marcum Q-function. We arrive at a closed form expression of average detection probability by making some approximations in the output SINR distribution where it involves hypergeometric function with two matrix arguments which in turn expressed as an infinite series of zonal polynomials.