Capacity of Correlated Multi - Input Multi - Output Channels Using the Virtual Channel Representation

The study of capacity of a randomly varying multi-input multi-output (MIMO) channel with independent and identically distributed entries by Telatar [7] and Foschini and Gans [8] has led to considerable interest in the question of capacity scaling under realistic channel assumptions. Initial work by Chuah et al. [9] had showed that capacity scaling is possible in correlated channels with a Kronecker product correlation model. Recently the capacity scaling problem was addressed using a physical scattering environment inspired by a virtual channel representation of MIMO channels. Modeling the virtual matrices as k-diagonal matrices it was shown that the ratio k N determines whether capacity scaling is possible or not. Attempting to generalize the capacity scaling results obtained using the k-diagonal random channels, we show in this thesis that capacity scaling is possible if and only if the number of entries with non-zero variance in the channel matrix grows at a rate O(N ). If the number of channel entries with non-zero variance grows at o(N), then capacity scales sub-linearly which results in capacity per dimension vanishing in the limit. We then show that the capacity random variable centered about its mean and normalized by the square-root of its variance converges weakly to a standard Gaussian random variable. Our work also addresses the issue of convergence to random matrix theory results and shows that convergence is dependent on the received signal-to-noise ratio. For completion, we relate the recent results on the statistics of ordered eigenvalues of MIMO channels which display a distinct power law behavior.