Impact of mismatched statistics on correlated MIMO capacity

Many recent works that study the impact of spatial correlation on the performance of multi-input multi-output (MIMO) systems assume a separable (also known as the Kronecker) model where the variances of channel entries, upon decomposition onto the transmit and the receive eigen-bases, admit a separable form. If the true statistics of the channel coefficients are non-separable, the separability assumption leads to a flattening and spreading of the degrees of freedom (DoF) in the channel, and hence results in misleading estimates of capacity - an observation consistent with many measurement campaigns. Towards understanding this observation, we first elucidate the importance of channel power normalization, an often-ignored notion, in the capacity analysis of correlated channels. Using tools from random matrix theory, we characterize the mismatch in estimating capacity with the separable model, and thus provide a theoretical underpinning behind many measurement-based observations.