Unitary Space–Time Constellation Design Based on the Chernoff Bound of the Pairwise Error Probability

Unitary space-time constellation design is considered for noncoherent multiple-antenna communications, where neither the transmitter nor the receiver knows the fading coefficients of the channel. By employing the Clarke's subdifferential theorem of the sum of the kappa largest singular values of a unitary matrix, we present a numerical optimization procedure for finding unitary space-time signal constellations of any dimension. The Chernoff bound of the pairwise error probability is used directly as a design criterion. The constellations are found by performing gradient descent search on a family ldquosurrogaterdquo functions that converge to the maximum pairwise error probability. The comp…