The University of Southampton
University of Southampton Institutional Repository

A unified MIMO optimization framework relying on the KKT conditions

A unified MIMO optimization framework relying on the KKT conditions
A unified MIMO optimization framework relying on the KKT conditions
A popular technique of designing multiple-input multiple-output (MIMO) communication systems relies on optimizing the positive semidefinite covariance matrix at the source. In this paper, a unified MIMO optimization framework based on the Karush-Kuhn-Tucker (KKT) conditions is proposed. In this framework, with the aid of matrix optimization theory, Theorem 1 presents a generic optimal transmit covariance matrix for MIMO systems with diverse objective functions subject to various power constraints and different levels of channel state information (CSI). Specifically, Theorem 1 fundamentally reveals that for a diverse family of MIMO systems, the optimal transmit covariance matrices associated with different objective functions under various power constraints can be derived in a unified generic water-filling-like form. When applying Theorem 1 to the case of multiple general power constraints, we firstly equivalently transform multiple power constraints into a single counterpart by introducing multiple weighting factors based on Pareto optimization theory. The optimal weighting factors can be found by the proposed modified subgradient method. On the other hand, for the imperfect MIMO system with statistical CSI errors, we firstly address the non-convexity of the robust optimization problem by following the idea of alternating optimization. Finally, our numerical results verify the optimal solution structure in Theorem 1 and the global optimality of the proposed modified subgradient method, as well as demonstrate the performance advantages of the proposed alternating optimization algorithm.
Convex optimization, Karush-Kuhn-Tucker conditions, MIMO communications, positive semi-definite matrix optimization
0090-6778
7251-7268
Gong, Shiqi
56c61a3c-ffb4-4f08-a817-9cd4d073c6ad
Xing, Chengwen
2477f24d-3711-47b1-b6b4-80e2672a48d1
Jing, Yindi
ecdc560b-f047-424d-836c-b36161380e25
Wang, Shuai
eb3d7a29-f75a-409f-8cdb-c6b4cdea165e
Wang, Jiaheng
56bfdc95-c203-4204-bc18-764e686642ba
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1
Gong, Shiqi
56c61a3c-ffb4-4f08-a817-9cd4d073c6ad
Xing, Chengwen
2477f24d-3711-47b1-b6b4-80e2672a48d1
Jing, Yindi
ecdc560b-f047-424d-836c-b36161380e25
Wang, Shuai
eb3d7a29-f75a-409f-8cdb-c6b4cdea165e
Wang, Jiaheng
56bfdc95-c203-4204-bc18-764e686642ba
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1

Gong, Shiqi, Xing, Chengwen, Jing, Yindi, Wang, Shuai, Wang, Jiaheng, Chen, Sheng and Hanzo, Lajos (2021) A unified MIMO optimization framework relying on the KKT conditions. IEEE Transactions on Communications, 69 (11), 7251-7268. (doi:10.1109/TCOMM.2021.3102641).

Record type: Article

Abstract

A popular technique of designing multiple-input multiple-output (MIMO) communication systems relies on optimizing the positive semidefinite covariance matrix at the source. In this paper, a unified MIMO optimization framework based on the Karush-Kuhn-Tucker (KKT) conditions is proposed. In this framework, with the aid of matrix optimization theory, Theorem 1 presents a generic optimal transmit covariance matrix for MIMO systems with diverse objective functions subject to various power constraints and different levels of channel state information (CSI). Specifically, Theorem 1 fundamentally reveals that for a diverse family of MIMO systems, the optimal transmit covariance matrices associated with different objective functions under various power constraints can be derived in a unified generic water-filling-like form. When applying Theorem 1 to the case of multiple general power constraints, we firstly equivalently transform multiple power constraints into a single counterpart by introducing multiple weighting factors based on Pareto optimization theory. The optimal weighting factors can be found by the proposed modified subgradient method. On the other hand, for the imperfect MIMO system with statistical CSI errors, we firstly address the non-convexity of the robust optimization problem by following the idea of alternating optimization. Finally, our numerical results verify the optimal solution structure in Theorem 1 and the global optimality of the proposed modified subgradient method, as well as demonstrate the performance advantages of the proposed alternating optimization algorithm.

Text
TCOM2021-Nov - Author's Original
Download (1MB)
Text
TCOM_KKT_FINAL - Accepted Manuscript
Download (3MB)

More information

Accepted/In Press date: 28 July 2021
e-pub ahead of print date: 5 August 2021
Published date: 1 November 2021
Additional Information: Publisher Copyright: © 1972-2012 IEEE.
Keywords: Convex optimization, Karush-Kuhn-Tucker conditions, MIMO communications, positive semi-definite matrix optimization

Identifiers

Local EPrints ID: 450581
URI: http://eprints.soton.ac.uk/id/eprint/450581
ISSN: 0090-6778
PURE UUID: 3463af11-25a3-4d3d-8cf0-186f6fedf0dd
ORCID for Lajos Hanzo: ORCID iD orcid.org/0000-0002-2636-5214

Catalogue record

Date deposited: 04 Aug 2021 16:34
Last modified: 13 Aug 2022 04:11

Export record

Altmetrics

Contributors

Author: Shiqi Gong
Author: Chengwen Xing
Author: Yindi Jing
Author: Shuai Wang
Author: Jiaheng Wang
Author: Sheng Chen
Author: Lajos Hanzo ORCID iD

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×