Gradient of mutual information in linear vector Gaussian channels

This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 52; no. 1; pp. 141 - 154
Main Authors: Palomar, D.P., Verdu, S.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2006
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Channels
Closed-form solution
Covariance matrix
De Bruijn's identity
Derivatives
divergence
Electrical engineering
Estimation theory
Exact sciences and technology
Exact solutions
Gaussian
Gaussian channels
Gaussian noise
Information theory
Information, signal and communications theory
Joints
Mathematical analysis
Mathematical models
minimum mean-square error (MMSE)
multiple-input multiple-output (MIMO) channels
Mutual information
nonlinear estimation
precoder optimization
Robustness
Signal to noise ratio
Signaling
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Transmission and modulation (techniques and equipments)
Vectors
Vectors (mathematics)
MIMO system
Non linear estimation
precoder optimization
Gaussian channel
Transmission channel
Linear channel
nonlinear estimation
minimum mean-square error (MMSE)
Optimization
Mean square error
divergence
Gaussian noise
multiple-input multiple- output (MIMO) channels
De Bruijn's identity
Mutual information
Information theory
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Description
Summary:This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information theory and estimation theory. Generalizing the fundamental relationship recently unveiled by Guo, Shamai, and Verdu/spl acute/, we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output. Gradients and derivatives with respect to other parameters are then found via the differentiation chain rule.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2005.860424