In this work, two problems associated with a downlink multi-user system are considered with the aid of intelligent reflecting surface (IRS): weighted sum-rate maximization and weighted minimal-rate maximization. For the first problem, a novel DOuble Manifold ALternating Optimization (DOMALO) algorithm is proposed by exploiting the matrix manifold theory and introducing the beamforming matrix and reflection vector using complex sphere manifold and complex oblique manifold, respectively, which incorporate the inherent geometrical structure and the required constraint. A smooth double manifold alternating optimization (S-DOMALO) algorithm is then developed based on the Dinkelbach-type algorithm and smooth exponential penalty function for the second problem. Finally, possible cooperative beamforming gain between IRSs and the IRS phase shift with limited resolution is studied, providing a reference for practical implementation. Numerical results show that our proposed algorithms can significantly outperform the benchmark schemes.
翻译:在这项工作中,在智能反射表面(IRS)的帮助下,考虑了与下链接多用户系统有关的两个问题:加权和加权反向最大化和加权最低反向最大化。对于第一个问题,建议采用新的DOUBL Monible 双向优化化(DOMALO)算法,方法是利用矩阵多重理论,使用复杂的球体、多重和复杂的斜体分别引入波形矩阵和反射矢量,包括固有的几何结构以及所需的限制。然后,根据Dinkelbach型算法和第二个问题平滑的指数性惩罚功能,制定平滑的双倍交替优化算法(S-DOMALO)算法。最后,研究在IRS和有限分辨率的IRS阶段转换之间可能形成合作收益,为实际执行提供参考。数字结果显示,我们提议的算法可以大大超过基准计划。