Performance analysis of MIMO systems in spatially correlated fading using matrix-monotone functions

The average performance of a single-user MIMO system under spatially correlated fading and with different types of CSI at the transmitter and with perfect CSI at the receiver was studied in recent work. In contrast to analyzing a single performance metric, e.g. the average mutual information or the average bit error rate, we study an arbitrary representative of the class of matrix-monotone functions. Since the average mutual information as well as the average normalized MSE belong to that class, this universal class of performance functions brings together the information theoretic and signal processing performance metric. We use Löwner's representation of operator monotone functions in order to derive the optimum transmission strategies as well as to characterize the impact of correlation on the average performance. Many recent results derived for average mutual information generalize to arbitrary matrix-monotone performance functions, e.g. the optimal transmit strategy without CSI at the transmitter is equal power allocation. The average performance without CSI is a Schur-concave function with respect to transmit and receive correlation. In addition to this, we derive the optimal transmission strategy with long-term statistics knowledge at the transmitter and propose an efficient iterative algorithm. The beamforming-range is the SNR range in which only one data stream spatially multiplexed achieves the maximum average performance. This range is important since it has a simple receiver structure and well known channel coding. We entirely characterize the beamforming-range. Finally, we derive the generalized water-filling transmit strategy for perfect CSI and characterize its properties under channel correlation.