A Framework on Complex Matrix Derivatives With Special Structure Constraints for Wireless Systems

Xin Ju, Shiqi Gong*, Nan Zhao, Chengwen Xing, Arumugam Nallanathan, Dusit Niyato

*此作品的通讯作者

科研成果: 期刊稿件文章同行评审

4 引用 (Scopus)

摘要

Matrix-variate optimization plays a central role in advanced wireless system designs. In this paper, we aim to explore optimal solutions of matrix variables under two special structure constraints using complex matrix derivatives, including diagonal structure constraints and constant modulus constraints, both of which are closely related to the state-of-the-art wireless applications. Specifically, for diagonal structure constraints mostly considered in the uplink multi-user single-input multiple-output (MU-SIMO) system and the amplitude-adjustable intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) system, the capacity maximization problem, the mean-squared error (MSE) minimization problem and their variants are rigorously investigated. By leveraging complex matrix derivatives, the optimal solutions of these problems are directly obtained in closed forms. Nevertheless, for constant modulus constraints with the intrinsic nature of element-wise decomposability, which are often seen in the hybrid analog-digital MIMO system and the fully-passive IRS-aided MIMO system, we firstly explore inherent structures of the element-wise phase derivatives associated with different optimization problems. Then, we propose a novel alternating optimization (AO) algorithm with the aid of several arbitrary feasible solutions, which avoids the complicated matrix inversion and matrix factorization involved in conventional element-wise iterative algorithms. Numerical simulations reveal that the proposed algorithm can dramatically reduce the computational complexity without loss of system performance.

源语言英语
页(从-至)5145-5161
页数17
期刊IEEE Transactions on Communications
72
8
DOI
出版状态已出版 - 2024

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引用此

Ju, X., Gong, S., Zhao, N., Xing, C., Nallanathan, A., & Niyato, D. (2024). A Framework on Complex Matrix Derivatives With Special Structure Constraints for Wireless Systems. IEEE Transactions on Communications, 72(8), 5145-5161. https://doi.org/10.1109/TCOMM.2024.3379360