On the Capacity of Vector Gaussian Channels with Bounded Inputs

Borzoo Rassouli, Bruno Clerckx

Research output: Contribution to journalArticlepeer-review

19 Citations (Scopus)


The capacity of a deterministic multiple-input multiple-output channel under the peak and average power constraints is investigated. For the identity channel matrix, 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 the support of the capacity-achieving distribution is a finite set of hyper-spheres with mutual independent phases and amplitude in the spherical domain. Subsequently, it is shown that when the average power constraint is relaxed, if the number of antennas is large enough, the capacity has a closed-form solution and constant amplitude signaling at the peak power achieves it. Moreover, 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. Finally, we investigate some upper and lower bounds for the capacity of the non-identity channel matrix and evaluate their performance as a function of the condition number of the channel.

Original languageEnglish
Article number7585061
Pages (from-to)6884-6903
Number of pages20
JournalIEEE Transactions on Information Theory
Issue number12
Publication statusPublished - 2016 Dec

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Vector Gaussian channel
  • discrete magnitude
  • peak power constraint
  • spherical symmetry

ASJC Scopus subject areas

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


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