MIMO gaussian channels with arbitrary inputs: Optimal precoding and power allocation

Fernando Perez-Cruz, Miguel R.D. Rodrigues, Sergio Verdú

Research output: Contribution to journalArticlepeer-review

170 Scopus citations


In this paper, we investigate the linear precoding and power allocation policies that maximize the mutual information for general multiple- inputmultiple-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.

Original languageEnglish (US)
Article number5429131
Pages (from-to)1070-1084
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - Mar 2010

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Gaussian noise channels
  • Minimum mean-square error (MMSE)
  • Multiple-inputmultiple-output (MIMO) systems
  • Mutual information
  • Optimum power allocation
  • Precoding
  • Waterfilling


Dive into the research topics of 'MIMO gaussian channels with arbitrary inputs: Optimal precoding and power allocation'. Together they form a unique fingerprint.

Cite this