Optimum power allocation for parallel gaussian channels with arbitrary input distributions

Angel Lozano, Antonia M. Tulino, Sergio Verdú

Research output: Contribution to journalArticlepeer-review

394 Scopus citations


The mutual information of independent parallel Gaussian-noise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signaling constellations with limited peak-to-average ratios (m-PSK, m-QAM, etc.) are used in lieu of the ideal Gaussian signals. This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum mean-square error (MMSE) proves key to solving the power allocation problem.

Original languageEnglish (US)
Pages (from-to)3033-3051
Number of pages19
JournalIEEE Transactions on Information Theory
Issue number7
StatePublished - Jul 2006

All Science Journal Classification (ASJC) codes

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


  • Channel capacity
  • Gaussian channels
  • Minimum mean-square error (MMSE)
  • Mutual information
  • Power allocation
  • Waterfilling


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