Linear precoder for codeword error minimization in MIMO systems with channel estimation errors

We propose a precoder design to minimize the codeword error rate of multiple-input multiple-output (MIMO) systems in the presence of channel estimation errors. Our proposed scheme only requires knowledge of the second-order statistics of the channel, noise and the estimation errors; an estimate of the instantaneous channel state information (CSI) is not required. Compared to the instantaneous CSI requirement, our assumption is more practical since obtaining an accurate CSI is challenging if the channel fluctuates rapidly, while the channel statistics are likely to remain unchanged for a much longer period. Furthermore, the feedback overhead from the receiver to the transmitter is greatly reduced. When compared to the case without transmit preceding, our proposed design achieves a significant improvement in error performance: (i) for a real 2 × 2 MIMO system with 4-PAM modulation and at codeword error rate of 104, our proposed precoder design achieves coding gains of up to 6 dB and (ii) for a real 4 × 4 MIMO system with BPSK modulation and at codeword error rate of 104, coding gains of up to 6.5 dB can be achieved.