TY - JOUR
T1 - Matrix-Monotonic Optimization-Part I
T2 - Single-Variable Optimization
AU - Xing, Chengwen
AU - Wang, Shuai
AU - Chen, Sheng
AU - Ma, Shaodan
AU - Poor, H. Vincent
AU - Hanzo, Lajos
N1 - 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.
PY - 2021
Y1 - 2021
N2 - Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for the matrix variables of matrix-variable 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 multiple-input 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 matrix-monotonic optimization framework can be used for deriving the optimal structures of the optimal matrix variables.
AB - Matrix-monotonic optimization exploits the monotonic nature of positive semi-definite matrices to derive optimal diagonalizable structures for the matrix variables of matrix-variable 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 multiple-input 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 matrix-monotonic optimization framework can be used for deriving the optimal structures of the optimal matrix variables.
KW - Matrix-monotonic optimization
KW - majorization theory
KW - optimal structures
KW - transceiver optimization
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U2 - 10.1109/TSP.2020.3037513
DO - 10.1109/TSP.2020.3037513
M3 - Article
AN - SCOPUS:85100538797
SN - 1053-587X
VL - 69
SP - 738
EP - 754
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
M1 - 9256999
ER -