On the capacity of vector Gaussian channels with bounded inputs

Borzoo Rassouli, Bruno Clercks

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

3 Citations (Scopus)

Abstract

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.
Pages4030-4035
Number of pages6
Volume2015-September
ISBN (Electronic)9781467364324
DOIs
Publication statusPublished - 2015 Sep 9
EventIEEE International Conference on Communications, ICC 2015 - London, United Kingdom
Duration: 2015 Jun 82015 Jun 12

Other

OtherIEEE International Conference on Communications, ICC 2015
CountryUnited Kingdom
CityLondon
Period15/6/815/6/12

Fingerprint

Probability density function
Antennas

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Networks and Communications

Cite this

Rassouli, B., & Clercks, B. (2015). On the capacity of vector Gaussian channels with bounded inputs. In 2015 IEEE International Conference on Communications, ICC 2015 (Vol. 2015-September, pp. 4030-4035). [7248954] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICC.2015.7248954

On the capacity of vector Gaussian channels with bounded inputs. / Rassouli, Borzoo; Clercks, Bruno.

2015 IEEE International Conference on Communications, ICC 2015. Vol. 2015-September Institute of Electrical and Electronics Engineers Inc., 2015. p. 4030-4035 7248954.

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

Rassouli, B & Clercks, B 2015, On the capacity of vector Gaussian channels with bounded inputs. in 2015 IEEE International Conference on Communications, ICC 2015. vol. 2015-September, 7248954, Institute of Electrical and Electronics Engineers Inc., pp. 4030-4035, IEEE International Conference on Communications, ICC 2015, London, United Kingdom, 15/6/8. https://doi.org/10.1109/ICC.2015.7248954
Rassouli B, Clercks B. On the capacity of vector Gaussian channels with bounded inputs. In 2015 IEEE International Conference on Communications, ICC 2015. Vol. 2015-September. Institute of Electrical and Electronics Engineers Inc. 2015. p. 4030-4035. 7248954 https://doi.org/10.1109/ICC.2015.7248954
Rassouli, Borzoo ; Clercks, Bruno. / On the capacity of vector Gaussian channels with bounded inputs. 2015 IEEE International Conference on Communications, ICC 2015. Vol. 2015-September Institute of Electrical and Electronics Engineers Inc., 2015. pp. 4030-4035
@inproceedings{216e63e2175c424fbbf550a15711b9b6,
title = "On the capacity of vector Gaussian channels with bounded inputs",
abstract = "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.",
author = "Borzoo Rassouli and Bruno Clercks",
year = "2015",
month = "9",
day = "9",
doi = "10.1109/ICC.2015.7248954",
language = "English",
volume = "2015-September",
pages = "4030--4035",
booktitle = "2015 IEEE International Conference on Communications, ICC 2015",
publisher = "Institute of Electrical and Electronics Engineers Inc.",

}

TY - GEN

T1 - On the capacity of vector Gaussian channels with bounded inputs

AU - Rassouli, Borzoo

AU - Clercks, Bruno

PY - 2015/9/9

Y1 - 2015/9/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84953708896&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84953708896&partnerID=8YFLogxK

U2 - 10.1109/ICC.2015.7248954

DO - 10.1109/ICC.2015.7248954

M3 - Conference contribution

AN - SCOPUS:84953708896

VL - 2015-September

SP - 4030

EP - 4035

BT - 2015 IEEE International Conference on Communications, ICC 2015

PB - Institute of Electrical and Electronics Engineers Inc.

ER -