Multiple-input multiple-output Gaussian channels: Optimal covariance for non-Gaussian inputs

Miguel R.D. Rodrigues, Fernando Pérez-Cruzy, Sergio Verdú

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations


We investigate the input covariance that maximizes the mutual information of deterministic multiple-input multipleoutput (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 fixedpoint 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.

Original languageEnglish (US)
Title of host publication2008 IEEE Information Theory Workshop, ITW
Number of pages5
StatePublished - 2008
Event2008 IEEE Information Theory Workshop, ITW - Porto, Portugal
Duration: May 5 2008May 9 2008

Publication series

Name2008 IEEE Information Theory Workshop, ITW


Other2008 IEEE Information Theory Workshop, ITW

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Electrical and Electronic Engineering


  • Gaussian noise
  • MMSE
  • Multiple-input multiple-output systems
  • Mutual information
  • Optimal input covariance


Dive into the research topics of 'Multiple-input multiple-output Gaussian channels: Optimal covariance for non-Gaussian inputs'. Together they form a unique fingerprint.

Cite this