Robust waterfilling for approximately gaussian inputs

Wei Cao, Alex Dytso, Michael Fauss, Gang Feng, H. Vincent Poor

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

2 Scopus citations


This paper investigates the power allocation problem for parallel Gaussian channels from an information-theoretic perspective with the aim of maximizing the sum of mutual informations (i.e., an achievable data rate). If all the inputs are Gaussian, it is well-known that the waterfilling policy provides an optimal solution. For arbitrary input distributions, a generalization of waterfilling, so-called mercury/waterfilling, provides an optimal power allocation in terms of the minimum mean square errors (MMSEs). However, the difficulty of obtaining closed-form analytical expression of the MMSE often makes the computation of mercury/waterfilling solution challenging. This paper proposes a robust waterfilling power allocation (RPA) policy for parallel Gaussian channels when the input distributions are close to Gaussian distributions in the Kullback-Leibler divergence (relative entropy). First, it is shown that the proposed policy results in water levels that are close to the optimum in a well-defined sense. Second, tight bounds for the loss in achievable rate are given. This bounded loss property makes the proposed power allocation policy robust and approximately optimal. Both aspects are illustrated by means of different simulation setups. Finally, the RPA is argued to be scalable with the number of users on the account of the fact that it inherently uses the classical low complexity waterfilling.

Original languageEnglish (US)
Title of host publication2019 IEEE Global Communications Conference, GLOBECOM 2019 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728109626
StatePublished - Dec 2019
Event2019 IEEE Global Communications Conference, GLOBECOM 2019 - Waikoloa, United States
Duration: Dec 9 2019Dec 13 2019

Publication series

Name2019 IEEE Global Communications Conference, GLOBECOM 2019 - Proceedings


Conference2019 IEEE Global Communications Conference, GLOBECOM 2019
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Hardware and Architecture
  • Information Systems
  • Signal Processing
  • Information Systems and Management
  • Safety, Risk, Reliability and Quality
  • Media Technology
  • Health Informatics


  • Approximately Gaussian input
  • Power allocation
  • Robust optimization
  • Waterfilling


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