Capacity-optimal structured linear dispersion codes for correlated MIMO channels

Abstract

In this paper, our analysis is based on a unitarily equivalent eigen-domain representation of correlated MIMO fading channels. The eigen-domain channel matrix has statistically independent entries and the non-uniform powers of its entries capture the channel correlation structure. Capacity and pairwise error probability (PEP) analysis is greatly simplified in the eigen-domain. In particular, the capacity-achieving input covariance matrix is diagonal in the eigen-domain, and the PEP bounds reveal the interaction between the code and the channel in spatio-temporal signal space dimensions. Furthermore, the achievable spatial multiplexing gain and diversity are constrained by the number of dominant channel entries in the eigen-domain. Using insights from the capacity and PEP analysis, we propose a characterization of capacity-optimal linear dispersion codes via a family of structured code generator matrices. These are parameterized by three unitary matrices, that determine the space-time structure of the codes, and a diagonal power-shaping matrix. The role of these matrices in controlling code performance is discussed and illustrative numerical results are presented.