Configuring Intelligent Reflecting Surface With Performance Guarantees: Optimal Beamforming

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