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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.
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