Semiunitary Precoding for Spatially Correlated MIMO Channels

The focus of this paper is on spatial precoding in correlated multiantenna channels where the number of data-streams is adapted independent of the number of transmit antennas. Towards the goal of a low-complexity implementation, a statistical semiunitary precoder is studied where the precoder matrix evolves fairly slowly with respect to the channel evolution. While prior work on statistical precoding has focussed on information-theoretic limits, most of these computations result in complicated functional dependencies of the mutual information with the channel statistics that do not explicitly reveal the impact of statistics on performance. In contrast, estimates that are directly in terms of the channel statistics are obtained here for the relative mutual information loss of a semiunitary precoder with respect to a perfect channel information benchmark. Based on these estimates, matching metrics are developed that capture the degree of matching of a channel to the precoder structure continuously and allow ordering two matrix channels in terms of their mutual information performance. While these metrics are based on bounds, numerical studies are used to show that the proposed metrics capture the performance tradeoffs accurately. The main conclusion of this work is a simple-to-state fundamental principle in the context of signaling design for single-user MIMO systems: the best channel for the statistical precoder is the channel that is matched to it.