Matrix-monotonic optimization: Part II: multi-variable optimization
Matrix-monotonic optimization: Part II: multi-variable optimization
In contrast to Part I of this treatise (Xing, 2021) that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization problems associated with multiple matrix variables. It is revealed that matrix-monotonic optimization still works even for multiple matrix-variate based optimization problems, provided that certain conditions are satisfied. Using this framework, the optimal structures of the matrix variables can be derived and the associated multiple matrix-variate optimization problems can be substantially simplified. In this paper several specific examples are given, which are essentially open problems. Firstly, we investigate multi-user multiple-input multiple-output (MU-MIMO) uplink communications under various power constraints. Using the proposed framework, the optimal structures of the precoding matrices at each user under various power constraints can be derived. Secondly, we considered the optimization of the signal compression matrices at each sensor under various power constraints in distributed sensor networks. Finally, we investigate the transceiver optimization for multi-hop amplify-and-forward (AF) MIMO relaying networks with imperfect channel state information (CSI) under various power constraints. At the end of this paper, several simulation results are given to demonstrate the accuracy of the proposed theoretical results.
MIMO, matrix-monotonic optimization, multiple matrix-variate optimizations
179-194
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
3 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 II: multi-variable optimization.
IEEE Transactions on Signal Processing, 69, , [9257097].
(doi:10.1109/TSP.2020.3037495).
Abstract
In contrast to Part I of this treatise (Xing, 2021) that focuses on the optimization problems associated with single matrix variables, in this paper, we investigate the application of the matrix-monotonic optimization framework in the optimization problems associated with multiple matrix variables. It is revealed that matrix-monotonic optimization still works even for multiple matrix-variate based optimization problems, provided that certain conditions are satisfied. Using this framework, the optimal structures of the matrix variables can be derived and the associated multiple matrix-variate optimization problems can be substantially simplified. In this paper several specific examples are given, which are essentially open problems. Firstly, we investigate multi-user multiple-input multiple-output (MU-MIMO) uplink communications under various power constraints. Using the proposed framework, the optimal structures of the precoding matrices at each user under various power constraints can be derived. Secondly, we considered the optimization of the signal compression matrices at each sensor under various power constraints in distributed sensor networks. Finally, we investigate the transceiver optimization for multi-hop amplify-and-forward (AF) MIMO relaying networks with imperfect channel state information (CSI) under various power constraints. At the end of this paper, several simulation results are given to demonstrate the accuracy of the proposed theoretical results.
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Matrix_Monotonic_Opt_Multiple
- Accepted Manuscript
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TSP2021-Feb-3
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Accepted/In Press date: 29 October 2020
Published date: 3 February 2021
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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 3, 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 partially supported 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. (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).
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© 1991-2012 IEEE.
Keywords:
MIMO, matrix-monotonic optimization, multiple matrix-variate optimizations
Identifiers
Local EPrints ID: 444823
URI: http://eprints.soton.ac.uk/id/eprint/444823
ISSN: 1053-587X
PURE UUID: bcdd7378-57a0-43f6-bdf9-c5d3889cfdf1
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Date deposited: 05 Nov 2020 17:34
Last modified: 18 Mar 2024 05:15
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Author:
Chengwen Xing
Author:
Shuai Wang
Author:
Sheng Chen
Author:
Shaodan Ma
Author:
H. Vincent Poor
Author:
Lajos Hanzo
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