## 2010 |

## Journal Articles |

Perez-Cruz, Fernando; Rodrigues, Miguel R D; Verdu, Sergio MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation Journal Article IEEE Transactions on Information Theory, 56 (3), pp. 1070–1084, 2010, ISSN: 0018-9448. Abstract | Links | BibTeX | Tags: 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 @article{Perez-Cruz2010a, title = {MIMO Gaussian Channels With Arbitrary Inputs: Optimal Precoding and Power Allocation}, author = {Fernando Perez-Cruz and Miguel R D Rodrigues and Sergio Verdu}, 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. |

## 2008 |

## Inproceedings |

Perez-Cruz, Fernando; Rodrigues, Miguel R D; Verdu, Sergio Optimal Precoding for Digital Subscriber Lines Inproceedings 2008 IEEE International Conference on Communications, pp. 1200–1204, IEEE, Beijing, 2008, ISBN: 978-1-4244-2075-9. Abstract | Links | BibTeX | Tags: 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 @inproceedings{Perez-Cruz2008a, title = {Optimal Precoding for Digital Subscriber Lines}, author = {Fernando Perez-Cruz and Miguel R D Rodrigues and Sergio Verdu}, 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. |

Rodrigues, Miguel R D; Perez-Cruz, Fernando; Verdu, Sergio Multiple-Input Multiple-Output Gaussian Channels: Optimal Covariance for Non-Gaussian Inputs Inproceedings 2008 IEEE Information Theory Workshop, pp. 445–449, IEEE, Porto, 2008, ISBN: 978-1-4244-2269-2. Abstract | Links | BibTeX | Tags: Binary phase shift keying, covariance matrices, Covariance matrix, deterministic MIMO Gaussian channel, fixed-point equation, Gaussian channels, Gaussian noise, Information rates, intersymbol interference, least mean squares methods, Magnetic recording, mercury-waterfilling power allocation policy, MIMO, MIMO communication, minimum mean-squared error, MMSE, MMSE matrix, multiple-input multiple-output system, Multiple-Input Multiple-Output Systems, Mutual information, Optimal Input Covariance, Optimization, Telecommunications @inproceedings{Rodrigues2008, title = {Multiple-Input Multiple-Output Gaussian Channels: Optimal Covariance for Non-Gaussian Inputs}, author = {Miguel R D Rodrigues and Fernando Perez-Cruz and Sergio Verdu}, url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=4578704}, isbn = {978-1-4244-2269-2}, year = {2008}, date = {2008-01-01}, booktitle = {2008 IEEE Information Theory Workshop}, pages = {445--449}, publisher = {IEEE}, address = {Porto}, abstract = {We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleo-utput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr.}, keywords = {Binary phase shift keying, covariance matrices, Covariance matrix, deterministic MIMO Gaussian channel, fixed-point equation, Gaussian channels, Gaussian noise, Information rates, intersymbol interference, least mean squares methods, Magnetic recording, mercury-waterfilling power allocation policy, MIMO, MIMO communication, minimum mean-squared error, MMSE, MMSE matrix, multiple-input multiple-output system, Multiple-Input Multiple-Output Systems, Mutual information, Optimal Input Covariance, Optimization, Telecommunications}, pubstate = {published}, tppubtype = {inproceedings} } We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleo-utput (MIMO) Gaussian channels with arbitrary (not necessarily Gaussian) input distributions, by capitalizing on the relationship between the gradient of the mutual information and the minimum mean-squared error (MMSE) matrix. We show that the optimal input covariance satisfies a simple fixed-point equation involving key system quantities, including the MMSE matrix. We also specialize the form of the optimal input covariance to the asymptotic regimes of low and high snr. We demonstrate that in the low-snr regime the optimal covariance fully correlates the inputs to better combat noise. In contrast, in the high-snr regime the optimal covariance is diagonal with diagonal elements obeying the generalized mercury/waterfilling power allocation policy. Numerical results illustrate that covariance optimization may lead to significant gains with respect to conventional strategies based on channel diagonalization followed by mercury/waterfilling or waterfilling power allocation, particularly in the regimes of medium and high snr. |