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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)5145-5161
Number of pages17
JournalIEEE Transactions on Communications
Volume72
Issue number8
DOIs
Publication statusPublished - 2024

Keywords

  • Complex matrix derivatives
  • hybrid analog-digital system
  • intelligent reflecting surface
  • matrix-variate optimization
  • special structure constraints

Fingerprint

Dive into the research topics of 'A Framework on Complex Matrix Derivatives With Special Structure Constraints for Wireless Systems'. Together they form a unique fingerprint.

Cite this