On the capacity of vector Gaussian channels with bounded inputs

Borzoo Rassouli, Bruno Clerckx

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

3 Citations (Scopus)


The capacity of a multiple-input multiple-output (MIMO) identity channel under the peak and average power constraints is investigated. The approach of Shamai et al. is generalized to the higher dimension settings to derive the necessary and sufficient conditions for the optimal input probability density function. This approach prevents the usage of the identity theorem of the holomorphic functions of several complex variables which seems to fail in the multi-dimensional scenarios. It is proved that in the spherical coordinates, the magnitude and phases of the capacity-achieving distribution are mutually independent and its support is a finite set of hyper-spheres where the points are uniformly distributed on them. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough (e.g. massive MIMO), the capacity has a closed form solution and constant amplitude signaling at the peak power achieves it. Finally, it will be observed that in a discrete-time memoryless Gaussian channel, the average power constrained capacity, which results from a Gaussian input distribution, can be closely obtained by an input where the support of its magnitude is a discrete finite set.

Original languageEnglish
Title of host publication2015 IEEE International Conference on Communications, ICC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781467364324
Publication statusPublished - 2015 Sept 9
EventIEEE International Conference on Communications, ICC 2015 - London, United Kingdom
Duration: 2015 Jun 82015 Jun 12

Publication series

NameIEEE International Conference on Communications
ISSN (Print)1550-3607


OtherIEEE International Conference on Communications, ICC 2015
Country/TerritoryUnited Kingdom

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


Dive into the research topics of 'On the capacity of vector Gaussian channels with bounded inputs'. Together they form a unique fingerprint.

Cite this