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Matrix-monotonic optimization: Part I: single-variable optimization

Matrix-monotonic optimization: Part I: single-variable optimization
Matrix-monotonic optimization: Part I: single-variable optimization
Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for the matrix variables of matrixvariable optimization problems. Based on the optimal structures derived, the associated optimization problems can be substantially simplified and underlying physical insights can also be revealed. In our work, a comprehensive framework of the applications of matrix-monotonic optimization to multipleinput multiple-output (MIMO) transceiver design is provided for a series of specific performance metrics under various linear constraints. This framework consists of two parts, i.e., Part-I for single-variable optimization and Part-II for multi-variable optimization. In this paper, single-variable matrix-monotonic optimization is investigated under various power constraints and various types of channel state information (CSI) condition. Specifically, three cases are investigated: 1) both the transmitter and receiver have imperfect CSI; 2) perfect CSI is available at the receiver but the transmitter has no CSI; 3) perfect CSI is available at the receiver but the channel estimation error at the transmitter is norm-bounded. In all three cases, the matrixmonotonic optimization framework can be used for deriving the optimal structures of the optimal matrix variables.
1053-587X
Xing, Chengwen
2477f24d-3711-47b1-b6b4-80e2672a48d1
Wang, Shuai
eb3d7a29-f75a-409f-8cdb-c6b4cdea165e
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Ma, Shaodan
54d32a4d-e4e9-44a1-bf2e-62c6ba018ff2
Poor, H. Vincent
2450f17a-1b3d-4eef-ba7e-111f75631764
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1
Xing, Chengwen
2477f24d-3711-47b1-b6b4-80e2672a48d1
Wang, Shuai
eb3d7a29-f75a-409f-8cdb-c6b4cdea165e
Chen, Sheng
9310a111-f79a-48b8-98c7-383ca93cbb80
Ma, Shaodan
54d32a4d-e4e9-44a1-bf2e-62c6ba018ff2
Poor, H. Vincent
2450f17a-1b3d-4eef-ba7e-111f75631764
Hanzo, Lajos
66e7266f-3066-4fc0-8391-e000acce71a1

Xing, Chengwen, Wang, Shuai, Chen, Sheng, Ma, Shaodan, Poor, H. Vincent and Hanzo, Lajos (2020) Matrix-monotonic optimization: Part I: single-variable optimization. IEEE Transactions on Signal Processing. (In Press)

Record type: Article

Abstract

Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for the matrix variables of matrixvariable optimization problems. Based on the optimal structures derived, the associated optimization problems can be substantially simplified and underlying physical insights can also be revealed. In our work, a comprehensive framework of the applications of matrix-monotonic optimization to multipleinput multiple-output (MIMO) transceiver design is provided for a series of specific performance metrics under various linear constraints. This framework consists of two parts, i.e., Part-I for single-variable optimization and Part-II for multi-variable optimization. In this paper, single-variable matrix-monotonic optimization is investigated under various power constraints and various types of channel state information (CSI) condition. Specifically, three cases are investigated: 1) both the transmitter and receiver have imperfect CSI; 2) perfect CSI is available at the receiver but the transmitter has no CSI; 3) perfect CSI is available at the receiver but the channel estimation error at the transmitter is norm-bounded. In all three cases, the matrixmonotonic optimization framework can be used for deriving the optimal structures of the optimal matrix variables.

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Matrix_Monotonic_Opt_Single - Accepted Manuscript
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Accepted/In Press date: 29 October 2020

Identifiers

Local EPrints ID: 444822
URI: http://eprints.soton.ac.uk/id/eprint/444822
ISSN: 1053-587X
PURE UUID: 0ff87fc1-a484-4453-9c0f-d28a9e92c2e0
ORCID for Lajos Hanzo: ORCID iD orcid.org/0000-0002-2636-5214

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Date deposited: 05 Nov 2020 17:34
Last modified: 05 Nov 2020 17:34

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Contributors

Author: Chengwen Xing
Author: Shuai Wang
Author: Sheng Chen
Author: Shaodan Ma
Author: H. Vincent Poor
Author: Lajos Hanzo ORCID iD

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