### 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 language | English |
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Title of host publication | 2015 IEEE International Conference on Communications, ICC 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 4030-4035 |

Number of pages | 6 |

Volume | 2015-September |

ISBN (Electronic) | 9781467364324 |

DOIs | |

Publication status | Published - 2015 Sep 9 |

Event | IEEE International Conference on Communications, ICC 2015 - London, United Kingdom Duration: 2015 Jun 8 → 2015 Jun 12 |

### Other

Other | IEEE International Conference on Communications, ICC 2015 |
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Country | United Kingdom |

City | London |

Period | 15/6/8 → 15/6/12 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Networks and Communications

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

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 -