On the Capacity of Vector Gaussian Channels With Bounded Inputs

Borzoo Rassouli, Bruno Clercks

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The capacity of a deterministic multiple-input multiple-output (MIMO) 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
JournalIEEE Transactions on Information Theory
VolumePP
Issue number99
DOIs
Publication statusPublished - 2016

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Probability density function
Antennas
scenario
performance
time

Keywords

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

ASJC Scopus subject areas

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

Cite this

On the Capacity of Vector Gaussian Channels With Bounded Inputs. / Rassouli, Borzoo; Clercks, Bruno.

In: IEEE Transactions on Information Theory, Vol. PP, No. 99, 7585061, 2016.

Research output: Contribution to journalArticle

Rassouli, Borzoo ; Clercks, Bruno. / On the Capacity of Vector Gaussian Channels With Bounded Inputs. In: IEEE Transactions on Information Theory. 2016 ; Vol. PP, No. 99.
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