On the design of minimum BER linear space-time block codes for MIMO systems equipped with MMSE receivers

In this paper, we consider the design of a full-rate linear space-time block code for coherent multiple-input multiple-output (MIMO) communication systems under a quasi-static Rayleigh flat-fading environment. Our design targets specifically at the use of a linear minimum mean-square error (MMSE) receiver that minimizes the asymptotic average bit error rate (BER) when the transmitted signal is selected from a 4-QAM constellation. This optimization problem is solved in two main stages: 1) a lower bound on the BER is first minimized, and 2) how this minimized lower bound can be achieved is then shown. By exploiting a rigorous convex optimization technique without any assumption on the code, we prove that individual unitary and trace-orthogonal structures are the necessary and sufficient conditions to assure the minimum asymptotic average BER with an MMSE detector. An algorithm is provided for an efficient generation of our codes, and simulation results confirm that our optimally designed codes are indeed superior in performance compared to some other commonly used codes.