Optimal linear code design in improving BER for MIMO systems with MMSE receivers

In this paper, we present a design method of a type of linear codes which achieves full transmission data rate for multiple-input multiple-output (MIMO) communication systems under a flat-fading environment. The channel information is unknown to the transmitter but known at the receiver. Our design targets at the use of a simple receiver for which a minimum mean square error (MMSE) equalizer is employed and minimizes the averaged bit error probability when transmitted signal is selected from a Q-PSK constellation. It is shown that the optimum code must have the structure such that a) the unfolded coding matrix is unitary and b) the individual coding matrices are trace-orthogonal. Simulation results confirm that our optimally designed codes are indeed superior in performance compared to other codes.