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, an approximately optimal (with respect to the minimum Euclidean distance between points in the received signal space) real-valued precoder based on the singular value decomposition (SVD) of the channel is proposed, and it is shown to offer a maximum-likelihood (ML)-decoding complexity of $\mathcal{O}(\sqrt{M})$ for square $M$-QAM. 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 with an ML-decoding complexity of $\mathcal{O}(M\sqrt{M})$ (M=4) and is extremely hard to obtain for larger QAM constellations. The proposed precoder's loss in error performance for 4-QAM in comparison with the complex-valued optimal precoder is only marginal. Our 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. which is an extension of the complex-valued optimal precoder for 4-QAM. Compared with the recently proposed $X-$ and $Y-$precoders, the error performance of our precoder is significantly better. It is shown that our precoder provides full-diversity for QAM constellations and this is supported by simulation plots of the word error probability for $2\times2$, $4\times4$ and $8\times8$ systems.