### Abstract

The capacity of a Multiple-Input Multiple-Output (MIMO) channel in which the antenna outputs are processed by an analog linear combining network and quantized by a set of threshold quantizers is studied. The linear combining weights and quantization thresholds are selected from a set of possible configurations as a function of the channel matrix. The possible configurations of the combining network model specific analog receiver architectures, such as single antenna selection, sign quantization of the antenna outputs or linear processing of the outputs. An interesting connection between the capacity of this channel and a constrained sphere packing problem in which unit spheres are packed in a hyperplane arrangement is shown. From a high-level perspective, this follows from the fact that each threshold quantizer can be viewed as a hyperplane partitioning the transmitter signal space. Accordingly, the output of the set of quantizers corresponds to the possible regions induced by the hyperplane arrangement corresponding to the channel realization and receiver configuration. This connection provides a number of important insights into the design of quantization architectures for MIMO receivers; for instance, it shows that for a given number of quantizers, choosing configurations which induce a larger number of partitions can lead to higher rates.^{1}

Original language | English (US) |
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Title of host publication | 2018 IEEE International Symposium on Information Theory, ISIT 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1355-1359 |

Number of pages | 5 |

Volume | 2018-June |

ISBN (Print) | 9781538647806 |

DOIs | |

State | Published - Aug 15 2018 |

Event | 2018 IEEE International Symposium on Information Theory, ISIT 2018 - Vail, United States Duration: Jun 17 2018 → Jun 22 2018 |

### Other

Other | 2018 IEEE International Symposium on Information Theory, ISIT 2018 |
---|---|

Country | United States |

City | Vail |

Period | 6/17/18 → 6/22/18 |

### Fingerprint

### Keywords

- Capacity
- Hybrid analog-digital receiver
- MIMO
- One-bit quantization
- Sphere packing

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

### Cite this

*2018 IEEE International Symposium on Information Theory, ISIT 2018*(Vol. 2018-June, pp. 1355-1359). [8437510] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2018.8437510

**On MIMO Channel Capacity with Output Quantization Constraints.** / Khalili, Abbas; Rini, Stefano; Barletta, Luca; Erkip, Elza; Eldar, Yonina C.

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

*2018 IEEE International Symposium on Information Theory, ISIT 2018.*vol. 2018-June, 8437510, Institute of Electrical and Electronics Engineers Inc., pp. 1355-1359, 2018 IEEE International Symposium on Information Theory, ISIT 2018, Vail, United States, 6/17/18. https://doi.org/10.1109/ISIT.2018.8437510

}

TY - GEN

T1 - On MIMO Channel Capacity with Output Quantization Constraints

AU - Khalili, Abbas

AU - Rini, Stefano

AU - Barletta, Luca

AU - Erkip, Elza

AU - Eldar, Yonina C.

PY - 2018/8/15

Y1 - 2018/8/15

N2 - The capacity of a Multiple-Input Multiple-Output (MIMO) channel in which the antenna outputs are processed by an analog linear combining network and quantized by a set of threshold quantizers is studied. The linear combining weights and quantization thresholds are selected from a set of possible configurations as a function of the channel matrix. The possible configurations of the combining network model specific analog receiver architectures, such as single antenna selection, sign quantization of the antenna outputs or linear processing of the outputs. An interesting connection between the capacity of this channel and a constrained sphere packing problem in which unit spheres are packed in a hyperplane arrangement is shown. From a high-level perspective, this follows from the fact that each threshold quantizer can be viewed as a hyperplane partitioning the transmitter signal space. Accordingly, the output of the set of quantizers corresponds to the possible regions induced by the hyperplane arrangement corresponding to the channel realization and receiver configuration. This connection provides a number of important insights into the design of quantization architectures for MIMO receivers; for instance, it shows that for a given number of quantizers, choosing configurations which induce a larger number of partitions can lead to higher rates.1

AB - The capacity of a Multiple-Input Multiple-Output (MIMO) channel in which the antenna outputs are processed by an analog linear combining network and quantized by a set of threshold quantizers is studied. The linear combining weights and quantization thresholds are selected from a set of possible configurations as a function of the channel matrix. The possible configurations of the combining network model specific analog receiver architectures, such as single antenna selection, sign quantization of the antenna outputs or linear processing of the outputs. An interesting connection between the capacity of this channel and a constrained sphere packing problem in which unit spheres are packed in a hyperplane arrangement is shown. From a high-level perspective, this follows from the fact that each threshold quantizer can be viewed as a hyperplane partitioning the transmitter signal space. Accordingly, the output of the set of quantizers corresponds to the possible regions induced by the hyperplane arrangement corresponding to the channel realization and receiver configuration. This connection provides a number of important insights into the design of quantization architectures for MIMO receivers; for instance, it shows that for a given number of quantizers, choosing configurations which induce a larger number of partitions can lead to higher rates.1

KW - Capacity

KW - Hybrid analog-digital receiver

KW - MIMO

KW - One-bit quantization

KW - Sphere packing

UR - http://www.scopus.com/inward/record.url?scp=85052436299&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85052436299&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2018.8437510

DO - 10.1109/ISIT.2018.8437510

M3 - Conference contribution

AN - SCOPUS:85052436299

SN - 9781538647806

VL - 2018-June

SP - 1355

EP - 1359

BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018

PB - Institute of Electrical and Electronics Engineers Inc.

ER -