Bounding the ergodic capacity of asymmetric 2×2 dual-polarized channels

We consider asymmetric MIMO channel models in an analysis of ergodic capacity for multi-polarized MIMO systems. Using Jensen's inequality we derive an upper bound for various asymmetric channel realizations that are parameterized by the co-polarized power ratio, cross-polarization discrimination measures, and subchannel Rician K-factors. Computation of a lower bound is complicated by the inherent asymmetry in the model, which prevents use of existing random matrix theories developed for Wishart matrices and Quadratic forms of Gaussian vectors. A lower bound is derived based on Minkowski's inequality and an approximation is also proposed that is shown numerically to be close to the lower bound.