In this paper, we characterize the performance metrics of a multiuser multipolarized antenna system in a Rayleigh fading channel. We start by formulating a downlink system model that features a multiuser scenario in the presence of additive noise and a multipolarized antenna system; this is followed by evaluation of the outage probability in closed form. This is done by deriving the cumulative distribution function (CDF) of the signal-to-interference-plusnoise ratio using the approach of the ratio of indefinite quadratic forms. We thereby characterize the gradient of this CDF with respect to the combining vectors. Eventually, we obtain the optimum combining vectors by minimizing the outage probability via interior-point optimization technique. Simulation and theoretical results of our analysis are closely matched, which validates our analysis. Our findings suggest that the performance of the triple polarized antenna is better than that of the dual polarized antenna system for low signal-to-noise ratio (SNR) values in terms of outage probability; this situation, however, reverses for high SNR value.

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