In this paper, the problem of designing a linear precoder for Multiple-Input
Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude
Modulation (QAM) is addressed. First, a novel and efficient methodology to
evaluate the input-output mutual information for a general Multiple-Input
Multiple-Output (MIMO) system as well as its corresponding gradients is
presented, based on the Gauss-Hermite quadrature rule. Then, the method is
exploited in a block coordinate gradient ascent optimization process to
determine the globally optimal linear precoder with respect to the MIMO
input-output mutual information for QAM systems with relatively moderate MIMO
channel sizes. The proposed methodology is next applied in conjunction with the
complexity-reducing per-group processing (PGP) technique, which is
semi-optimal, to both perfect channel state information at the transmitter
(CSIT) as well as statistical channel state information (SCSI) scenarios, with
high transmitting and receiving antenna size, and for constellation size up to
M=64. We show by numerical results that the precoders developed offer
significantly better performance than the configuration with no precoder, and
the maximum diversity precoder for QAM with constellation sizes M=16, 32, and
 64 and for MIMO channel size 100×100
