Matrix-monotonic optimization - Part II: Multi-variable optimization
Xing,Chengwen1,2; Wang,Shuai1; Chen,Sheng3,4; Ma,Shaodan5; Poor,H. Vincent6; Hanzo,Lajos3
Source PublicationIEEE Transactions on Signal Processing
AbstractIn 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.
Keywordmatrix-monotonic optimization MIMO multiple matrix-variate optimizations
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Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorWang,Shuai
Affiliation1.School of Information and Electronics,Beijing Institute of Technology,Beijing,100081,China
2.The Department of Electrical and Computer Engineering,University of Macau,Macao S.A.R.,999078,Macao
3.School of Electronics and Computer Science,University of Southampton,Southampton,430205,United Kingdom
4.The King Abdulaziz University,Jeddah,21422,Saudi Arabia
5.Department of Electrical and Computer Engineering,State Key Laboratory of Internet of Things for Smart City,University of Macau,Macao,Macao S.A.R.,999078,Macao
6.Department of Electrical Engineering,Princeton University,Princeton,08544,United States
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Xing,Chengwen,Wang,Shuai,Chen,Sheng,et al. Matrix-monotonic optimization - Part II: Multi-variable optimization[J]. IEEE Transactions on Signal Processing,2021,69:179-194.
APA Xing,Chengwen,Wang,Shuai,Chen,Sheng,Ma,Shaodan,Poor,H. Vincent,&Hanzo,Lajos.(2021).Matrix-monotonic optimization - Part II: Multi-variable optimization.IEEE Transactions on Signal Processing,69,179-194.
MLA Xing,Chengwen,et al."Matrix-monotonic optimization - Part II: Multi-variable optimization".IEEE Transactions on Signal Processing 69(2021):179-194.
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