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 K-ary phase beamforming, we develop a linear time approximation algorithm that guarantees performance within a constant fraction (1+\cos(\pi/K))/2 of the global optimum, e.g., it can attain over 85% of the optimal performance for the quadrature beamforming with K=4. According to the numerical results, the proposed approximation algorithm for discrete IRS beamforming outperforms the existing algorithms significantly in boosting the received SNR.

翻译：这项工作提出线性时间战略, 以优化配置智能反射表面( IRS) 反射元素的相位移。 具体地说, 我们显示二进制波束在线性时间中可以优化解决, 以最大限度地实现收到的信号对噪音比率( SRR ) 。 对于一般 K- ary 相位化, 我们开发了线性时间近似算法, 保证在全球最佳常数分数(1 ⁇ cos (\ pi/ K)/2) 范围内的性能, 例如, 它可以达到 K=4 的二次相位形成最佳性能的85%以上。 根据数字结果, 离散IRS 的近似算法在提高接收的 SNR 时, 大大优于现有算法。