Characterization of optimal input distributions for Gaussian-mixture noise channels

Hung V. Vu, Nghi H. Tran, Mustafa C Gursoy, Tho Le-Ngoc, S. I. Hariharan

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

Abstract

This paper addresses the characterization of optimal input distributions for the general additive quadrature Gaussian-mixture (GM) noise channel under an average power constraint. The considered model can be used to represent a wide variety of communication channels, such as the well-known Bernoulli-Gaussian and Middleton Class-A impulsive noise channels, co-channel interference in cellular communications, and cognitive radio channels under imperfect spectrum sensing. We first demonstrate that there exists a unique input distribution achieving the channel capacity and the optimal input has an uniformly distributed phase. By using the Kuhn-Tucker conditions (KTC) and Bernstein's theorem, we then demonstrate that there are always a finite number of mass points on any bounded interval in the optimal amplitude distribution. Equivalently, the optimal amplitude input distribution is discrete. Furthermore, by applying a novel bounding technique on the KTC, it is then shown that the optimal amplitude distribution has a finite number of mass points.

Original languageEnglish (US)
Title of host publication2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages32-35
Number of pages4
ISBN (Print)9781479965601
DOIs
StatePublished - Sep 10 2015
Event14th IEEE Canadian Workshop on Information Theory, CWIT 2015 - St. John's, Canada
Duration: Jul 6 2015Jul 9 2015

Other

Other14th IEEE Canadian Workshop on Information Theory, CWIT 2015
CountryCanada
CitySt. John's
Period7/6/157/9/15

Keywords

  • Capacity-achieving distribution
  • Discrete input
  • Gaussian-mixture channel
  • Shannon capacity

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Information Systems
  • Software

Fingerprint Dive into the research topics of 'Characterization of optimal input distributions for Gaussian-mixture noise channels'. Together they form a unique fingerprint.

  • Cite this

    Vu, H. V., Tran, N. H., Gursoy, M. C., Le-Ngoc, T., & Hariharan, S. I. (2015). Characterization of optimal input distributions for Gaussian-mixture noise channels. In 2015 IEEE 14th Canadian Workshop on Information Theory, CWIT 2015 (pp. 32-35). [7255146] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CWIT.2015.7255146