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.
Matrix-monotonic optimization, majorization theory, optimal structures, transceiver optimization
738-754
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
1 February 2021
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
(2021)
Matrix-monotonic optimization: Part I: single-variable optimization.
IEEE Transactions on Signal Processing, 69, , [9256999].
(doi:10.1109/TSP.2020.3037513).
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.
Text
Matrix_Monotonic_Opt_Single
- Accepted Manuscript
Text
TSP2021-Feb-1
- Version of Record
Restricted to Repository staff only
Request a copy
More information
Accepted/In Press date: 29 October 2020
e-pub ahead of print date: 11 November 2020
Published date: 1 February 2021
Additional Information:
Funding Information:
Manuscript received May 5, 2020; revised August 27, 2020 and September 29, 2020; accepted October 22, 2020. Date of publication November 11, 2020; date of current version February 1, 2021. The associate editor coordinating the review of this article and approving it for publication was Prof. Stefano Tomasin. The work of Chengwen Xing was supported in part by the National Natural Science Foundation of China under Grants 61671058, 61722104, and 61620106001, and in part by Ericsson. The work of Shaodan Ma was supported in part by the Science and Technology Development Fund, Macau SAR (File no. 0036/2019/A1 and File no. SKL-IOTSC2018-2020), and in part by the Research Committee of University of Macau under Grant MYRG2018-00156-FST. The work of H. Vincent Poor was supported by the U.S. National Science Foundation under Grant CCF-1908308. The work of Lajos Hanzo was supported in part by the Engineering and Physical Sciences Research Council projects EP/N004558/1, EP/P034284/1, EP/P034284/1, EP/P003990/1 (COALESCE), of the Royal Society’s Global Challenges Research Fund Grant and in part by the European Research Council’s Advanced Fellow Grant QuantCom. (Corresponding author: Shuai Wang.) Chengwen Xing is with the School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China, and also with the Department of Electrical and Computer Engineering, University of Macau, Macao, S.A.R. 999078, China (e-mail: xingchengwen@gmail.com).
Publisher Copyright:
© 1991-2012 IEEE.
Keywords:
Matrix-monotonic optimization, majorization theory, optimal structures, transceiver optimization
Identifiers
Local EPrints ID: 444822
URI: http://eprints.soton.ac.uk/id/eprint/444822
ISSN: 1053-587X
PURE UUID: 0ff87fc1-a484-4453-9c0f-d28a9e92c2e0
Catalogue record
Date deposited: 05 Nov 2020 17:34
Last modified: 18 Mar 2024 02:36
Export record
Altmetrics
Contributors
Author:
Chengwen Xing
Author:
Shuai Wang
Author:
Sheng Chen
Author:
Shaodan Ma
Author:
H. Vincent Poor
Author:
Lajos Hanzo
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