Approximating the outage capacity of asymmetric 2×2 dual-polarized MIMO at high SNR

We present an outage probability analysis for asymmetric dual-polarized channels, where the elements of the channel gain matric are represented by independent nonidentical complex Gaussian distributions. We apply a moment generating function method to derive statistics associated with the determinant of the desired asymmetric random matrices. Using a two-step distribution model to characterize the mutual information we provide outage capacity approximates for various asymmetric channel realizations that are parameterized by the co-polarized power ratio, the cross-polarization discrimination ratio, and sub-channel Rician K-factors. Deriving an exact outage capacity formulation is made difficult by the inherent asymmetry of the model. The Lognormal and the Gamma distributions are assumed for mutual information exponent and the Weibull and Normal distributions are used to represent the mutual information. Contrary to current notions regarding the use of Gaussian approximations for mutual information, more accurate results are obtained using the Weibull distribution. We also show that partially-correlated channel gains typical of dual-polarized antennas negligibly impact the outage probabilities reported for the uncorrelated cases.