Rank-deficient dispersive covariance MIMO precoders

Recent research for multiple input, multiple output (MIMO) systems has utilized the linear structure of linear dispersion codes (LDCs) to construct precoders with partial transmitter channel knowledge. In this paper, we build upon a coding structure known as dispersive covariance coding (DCC) derived in R. Hayes and J.J. Caffery (2005) for precoding scenarios in which statistical channel covariance knowledge is present at the transmitter. Previous work on DCCs has focused on special full-rank cases where code parameters were fixed. In this paper, we relax DCC parameter selection and design DCC codes with improved design flexibility such that any desired number of channel modes can be excited by the precoder. Unlike previous full-rank DCCs, we prove that our new DCCs are rank-deficient. Through theory and numerical simulation, we quantify the system´s resulting loss in capacity. Furthermore, we develop useful distance metrics which illustrate the relationship between the full-rank and rank-deficient precoders