Linear Precoding Gain for Large MIMO Configurations With QAM and Reduced Complexity

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 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 technique to both perfect channel state information (CSI) at the transmitter as well as statistical CSI (Statistical CSI) scenarios, with large transmitting and receiving antenna sizes, and for constellation size up to M = 64. We show by the numerical results that the precoders developed offer significantly better performance than the configuration with no precoder as well as the maximum diversity precoder for QAM with constellation sizes M = 16, 32, and 64 and for MIMO channel size up to 100 × 100.