Linear minimum-distance precoding for MIMO systems using quadrature amplitude modulation

The criterion of maximizing the minimum Euclidean distance under the transmit power constraint is investigated in this paper for multiple-input multiple-output (MIMO) spatial multiplexing systems. With a real-valued constraint on the precoding matrix, a new low-complexity construction algorithm is proposed for arbitrary number of data streams and rectangular quadrature amplitude modulation (QAM) input. Feasible precoding matrices are constructed with distinctive ranks dropping from full rank to rank one, where the full-rank precoder is generated through an iteration mechanism, and the rank-one precoder is obtained by a parameterized matrix associated with the particular modulation level of QAM constellation. In addition, the other rank-deficient precoders are formally constructed by a combination of two sub-precoders from lower dimensional space. The achievable minimum distance is also presented in closedform expression for the proposed precoder, and simulation results validate the efficiency of the proposed precoder as compared with the traditional cross-form precoder.