Minimum symbol error probability MIMO design under the per-antenna power constraint

Approximate minimum symbol error probability transceiver design of single user MIMO systems under the practical per-antenna power constraint is considered. The upper bound of a lower bound on the minimum distance between the symbol hypotheses is established. Necessary conditions and structures of the transmit covariance matrix for reaching the upper bound are discussed. Three numerical approaches (rank zero, rank one, and permutation) for obtaining the optimum precoder are proposed. When the upper bound is reached, the resulting design is optimum. When the upper bound is not reached, a numerical fix is used. The approach is very simple and can be of practical use.