Schur-convexity of the Symbol Error Rate in Correlated MIMO Systems with Precoding and Space-time Coding

This paper analyzes the symbol error rate (SER) of spatially correlated multiple-input multiple-output (MIMO) systems with linear precoding, space-time block codes, and long-term statistical channel state information at the transmitter. Majorization theory and the notion of Schur-convexity is used to show how the SER depends on the signal-to-noise ratio (SNR), on the transmit and receive correlation, and on the choice of precoder. Depending on these conditions, the Chernoff bound on the SER is shown to be Schur- convex (i.e., increasing with the amount of correlation) with respect to the receive correlation, while it is Schur-convex at high SNR and Schur-concave (i.e., decreasing with increasing amount of correlation) at low SNR with respect to the transmit correlation. These properties are inherited by the exact SER, as shown analytically and illustrated numerically.QC 2011110