@article{Perez-Cruz2010a,
title = {MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation},
author = {Perez-Cruz, Fernando and Rodrigues, Miguel R. D. and Verdu, Sergio},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5429131},
issn = {0018-9448},
year = {2010},
date = {2010-01-01},
journal = {IEEE Transactions on Information Theory},
volume = {56},
number = {3},
pages = {1070--1084},
abstract = {In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input-multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean-square error (MMSE). The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For non-Gaussian inputs, a nondiagonal precoding matrix in general increases the information transmission rate, even for parallel noninteracting channels. Whenever precoding is precluded, the optimal power allocation policy also satisfies a fixed-point equation; we put forth a generalization of the mercury/waterfilling algorithm, previously proposed for parallel noninterfering channels, in which the mercury level accounts not only for the non-Gaussian input distributions, but also for the interference among inputs.},
keywords = {Collaborative work, Equations, fixed-point equation, Gaussian channels, Gaussian noise channels, Gaussian processes, Government, Interference, linear precoding, matrix algebra, mean square error methods, mercury-waterfilling algorithm, MIMO, MIMO communication, MIMO Gaussian channel, minimum mean-square error, minimum mean-square error (MMSE), multiple-input-multiple-output channel, multiple-input–multiple-output (MIMO) systems, Mutual information, nondiagonal precoding matrix, optimal linear precoder, optimal power allocation policy, optimal precoding, optimum power allocation, Phase shift keying, precoding, Quadrature amplitude modulation, Telecommunications, waterfilling},
pubstate = {published},
tppubtype = {article}
}

In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple-input-multiple-output (MIMO) Gaussian channels with arbitrary input distributions, by capitalizing on the relationship between mutual information and minimum mean-square error (MMSE). The optimal linear precoder satisfies a fixed-point equation as a function of the channel and the input constellation. For non-Gaussian inputs, a nondiagonal precoding matrix in general increases the information transmission rate, even for parallel noninteracting channels. Whenever precoding is precluded, the optimal power allocation policy also satisfies a fixed-point equation; we put forth a generalization of the mercury/waterfilling algorithm, previously proposed for parallel noninterfering channels, in which the mercury level accounts not only for the non-Gaussian input distributions, but also for the interference among inputs.