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Matrix-monotonic optimization: Part II: multi-variable optimization

Matrix-monotonic optimization: Part II: multi-variable optimization
Matrix-monotonic optimization: Part II: multi-variable optimization
In contrast to Part I of this treatise [1] 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 (MUMIMO) 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.
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 II: multi-variable optimization. IEEE Transactions on Signal Processing. (In Press)

Record type: Article

Abstract

In contrast to Part I of this treatise [1] 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 (MUMIMO) 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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Accepted/In Press date: 29 October 2020

Identifiers

Local EPrints ID: 444823
URI: http://eprints.soton.ac.uk/id/eprint/444823
ISSN: 1053-587X
PURE UUID: bcdd7378-57a0-43f6-bdf9-c5d3889cfdf1
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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