Design optimization of linear precoders for complex vector gaussian channelswith finite alphabet inputs

We study the design optimization of linear precoders that maximize the mutual information in complex-valued vector Gaussian channels under finite alphabet inputs. It is well known that mutual information of a vector channel with discrete constellation source is a highly nonlinear and no concave function of the linear precoder matrix G, thereby complicating the precoder design optimization. In this paper, we show that the mutual information is a concave function of W = G
^h
H
_h
HG, where H is the complex-valued channel matrix and superscript "h" represents conjugate transpose. We further propose an iterative algorithm for solving the globally optimal linear precoder G. Illustrative results show that the proposed iterative algorithm is very robust and efficient for global convergence.