Analysis of diversity and multiplexing tradeoff for multi-antenna systems with covariance feedback

We study a single-user multi-antenna system with perfect channel state information (CSI) at the receiver and imperfect CSI at the transmitter. The common downlink transmission model is assumed with one or more uncorrelated receive antennas and correlated transmit antennas. Zheng and Tse (see IEEE Transactions on Information Theory, Jan., 2002) discussed the tradeoff between diversity advantage and multiplexing gain for the asymptotic high SNR regime. At low and mid-range SNR values the connection between the multiplexing gain and diversity is not cleared. We extend our results for the optimal power allocation in MISO and MIMO systems with covariance feedback in order to characterize the multiplexing gain in small and mid-range SNR regions. We give analytical results for the case in which the optimal transmit covariance matrix has rank 1 the equivalent to the multiplexing gain. In addition to this, we discuss the outage capacity and its optimization for the MISO and MIMO case. We provide an asymptotic result for the outage probability which enables us to measure the impact of correlation on the outage probability.