Impact of Correlation on Linear Precoding in QSTBC Coded Systems with Linear MSE Detection

In this paper, we study a wireless multiple-input multiple-output system in a Rayleigh flat-fading environment with correlation among the transmit antennas. We assume that the receiver has perfect CSI and the transmitter only knows the correlation matrix. The transmitter employs a quasi-orthogonal space-time block code in combination with a linear precoder; the receiver uses a linear MMSE detector. We analyze the optimal transmit precoding strategy that minimizes the average sum MSE at the receiver. We show that, as expected, the optimal precoding directions coincide with the eigenvectors of the transmit correlation matrix. The optimal power allocation, however, only supports at most 2 directions at all SNRs independent of the number of transmit antennas, which correspond to the 2 largest eigenvalues of the transmit correlation matrix. We characterize this optimal power allocation by the necessary and sufficient optimality conditions. At high SNRs, the optimal allocation approaches equal power on the two supported modes. At low SNRs, the weaker mode is dropped and the precoding matrix becomes single-mode beamforming. We provide a closed-form expression characterizing this low-SNR range. Numerical simulations confirm our theoretical analysis.