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 two transmit antennas and QAM constellations, a real-valued precoder which 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

for two 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
${\bf E}-d_{\min}$
precoder for 4-QAM by Vrigneau

which is an extension of the complex-valued optimal precoder for 4-QAM. The proposed precoder's ML-decoding complexity as a function of the constellation size
$M$
is only
${\cal O}(\sqrt {M})$
while that of the
${\bf E}-d_{\min}$
precoder is
${\cal O}(M\sqrt {M})(M=4)$
. Compared to the recently proposed
$X$
- and
$Y$
-precoders, the error performance of the proposed precoder is significantly better while being only marginally worse than that of the
${\bf E}-d_{\min}$
precoder for 4-QAM. It is argued that the proposed precoder provides full-diversity for QAM constellations and this is supported by simulation plots of the word error probability for 2
$\,\times\,$
2, 4
$\,\times\,$
4 and 8
$\,\times\,$
8 systems.