@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.

@inproceedings{Perez-Cruz2008a,
title = {Optimal Precoding for Digital Subscriber Lines},
author = {Perez-Cruz, Fernando and Rodrigues, Miguel R. D. and Verdu, Sergio},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4533270},
isbn = {978-1-4244-2075-9},
year = {2008},
date = {2008-01-01},
booktitle = {2008 IEEE International Conference on Communications},
pages = {1200--1204},
publisher = {IEEE},
address = {Beijing},
abstract = {We determine the linear precoding policy that maximizes 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 squared error (MMSE). The optimal linear precoder can be computed by means of a fixed- point equation as a function of the channel and the input constellation. We show that diagonalizing the channel matrix does not maximize the information transmission rate for nonGaussian inputs. A full precoding matrix may significantly increase the information transmission rate, even for parallel non-interacting channels. We illustrate the application of our results to typical Gigabit DSL systems.},
keywords = {Bit error rate, channel matrix diagonalization, Communications Society, Computer science, digital subscriber lines, DSL, Equations, fixed-point equation, Gaussian channels, least mean squares methods, linear codes, matrix algebra, MIMO, MIMO communication, MIMO Gaussian channel, minimum mean squared error method, MMSE, multiple-input multiple-output communication, Mutual information, optimal linear precoder, precoding, Telecommunications, Telephony},
pubstate = {published},
tppubtype = {inproceedings}
}

We determine the linear precoding policy that maximizes 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 squared error (MMSE). The optimal linear precoder can be computed by means of a fixed- point equation as a function of the channel and the input constellation. We show that diagonalizing the channel matrix does not maximize the information transmission rate for nonGaussian inputs. A full precoding matrix may significantly increase the information transmission rate, even for parallel non-interacting channels. We illustrate the application of our results to typical Gigabit DSL systems.