MIMO Systems With Restricted Pre/Post-Coding—Capacity Analysis Based on Coupled Doubly Correlated Wishart Matrices

Many practical communication systems have some form of restricted precoding or postcoding, such as antenna selection, selection combining, beam selection, and limited feedback precoding, to name a few. The capacity analysis of such systems is, in general, difficult and previous works in the literature provide results only for certain simplified cases. This paper derives a novel approach to analyze the capacity for such systems under a very generic setting. The results are based on asymptotic closed-form expressions for the second-order statistics and joint distributions of eigenvalues for a set of coupled, doubly correlated Wishart matrices. A tight approximation to the joint distribution of the eigenvalues in the non-asymptotic regime is also proposed. These results are then used to show that the system capacity can be approximated as the largest element of a correlated Gaussian vector. Showing that this is equivalent to the problem of finding the distribution of sum of lognormals, we propose a novel approach to characterize its distribution. As an application, the capacity for an antenna selection system and a limited feedback precoding system is compared with their respective approximations. This paper also demonstrates how the results can be used to design the precoding codebook in limited feedback systems.