Optimality of proper signaling in Gaussian MIMO broadcast channels with shaping constraints

Christoph Hellings, Lorenz Weiland, Wolfgang Utschick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations

Abstract

Proper (i.e., circularly symmetric) Gaussian signals are known to be capacity-achieving in Gaussian multiple-input multiple-output (MIMO) broadcast channels with proper noise in the sense that the sum rate capacity under a sum power constraint is achievable with proper Gaussian signaling. In this paper, we generalize this statement by proving that the optimality of proper Gaussian signals also holds under a shaping constraint, i.e., a sum covariance constraint instead of a power constraint. Moreover, we show that not only the sum rate optimal point, but the whole capacity region can be achieved with proper Gaussian signals. Finally, we prove that the worst-case noise in a MIMO broadcast channel with shaping constraints is proper.

Original languageEnglish
Title of host publication2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3474-3478
Number of pages5
ISBN (Print)9781479928927
DOIs
StatePublished - 2014
Event2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 - Florence, Italy
Duration: 4 May 20149 May 2014

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Conference

Conference2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
Country/TerritoryItaly
CityFlorence
Period4/05/149/05/14

Keywords

  • Broadcast channels
  • capacity region
  • covariance constraints
  • dirty paper coding
  • multiuser MIMO systems
  • proper and improper signals

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