Configuring Intelligent Reflecting Surface With Performance Guarantees: Optimal Beamforming

• Published in: IEEE journal of selected topics in signal processing Vol. 16; no. 5; pp. 967 - 979
• Main Authors: Zhang, Yaowen, Shen, Kaiming, Ren, Shuyi, Li, Xin, Chen, Xin, Luo, Zhi-Quan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Approximation; Approximation algorithms; approximation ratio; Array signal processing; Beamforming; global optimum; Intelligent reflecting surface (IRS); linear time algorithm for discrete beamforming; Mathematical analysis; Optimization; Performance evaluation; Quadratures; Receivers; Reconfigurable intelligent surfaces; Signal processing algorithms; Signal to noise ratio; Transmitters
• ISSN: 1932-4553; 1941-0484
• DOI: 10.1109/JSTSP.2022.3176479

This work proposes linear time strategies to optimally configure the phase shifts for the reflective elements of an intelligent reflecting surface (IRS). Specifically, we show that the binary phase beamforming can be optimally solved in linear time to maximize the received signal-to-noise ratio (SNR). For the general <inline-formula><tex-math notation="LaTeX">K</tex-math></inline-formula>-ary phase beamforming, we develop a linear time approximation algorithm that guarantees performance within a constant fraction <inline-formula><tex-math notation="LaTeX">(1+\cos (\pi /K))/2</tex-math></inline-formula> of the global optimum, e.g., it can attain over 85% of the optimal performance for the quadrature beamforming with <inline-formula><tex-math notation="LaTeX">K=4</tex-math></inline-formula>. According to the numerical results, the proposed approximation algorithm for discrete IRS beamforming outperforms the existing algorithms significantly in boosting the received SNR.