A low ML-decoding complexity, full-diversity, full-rate MIMO precoder

Precoding for multiple-input, multiple-output (MIMO) antenna systems is considered with perfect channel knowledge available at both the transmitter and the receiver. For 2 transmit antennas and QAM constellations, a precoder that is approximately optimal (with respect to the minimum Euclidean distance between points in the received signal space) among real-valued precoders based on the singular value decomposition (SVD) of the channel is proposed. The proposed precoder is obtainable easily for arbitrary QAM constellations, unlike the known complex-valued optimal precoder by Collin et al. for 2 transmit antennas which is in existence for 4-QAM alone and is extremely hard to obtain for larger QAM constellations. The proposed precoding scheme is extended to higher number of transmit antennas on the lines of the E-d_min precoder for 4-QAM by Vrigneau et al.. The proposed precoder has an ML-decoding complexity of O(√M) as against the E-d_min precoder´s complexity of O(M√M) (M = 4). Compared with the recently proposed X- and Y - precoders, the error performance of the proposed precoder is significantly better. The proposed precoder provides full-diversity for QAM constellations and this is supported by simulation plots of the word error probability for 2 × 2, 4 × 4 and 8 × 8 systems.