This letter investigates the joint active and passive beamforming optimization for intelligent reflecting surface (IRS) aided multiuser multiple-input multiple-output systems with the objective of maximizing the weighted sum-rate. We show that this problem can be solved via a matrix weighted mean square error minimization equivalence. In particular, for the optimization of the passive IRS beamforming, we first propose an iterative algorithm with excellent performance based on the manifold optimization. By using the matrix fractional programming technique to obtain a more tractable object function, we then propose a low complexity algorithm based on the majorization-minimization method. Numerical results verify the convergence of our proposed algorithms and the significant performance improvement over the communication scenario without IRS assistance.

翻译：本信调查智能反射表面(IRS)辅助多用户多输入多输出输出系统的联合主动和被动波束优化,目的是最大限度地实现加权总和。我们表明,这个问题可以通过矩阵加权平均平均差错最小化等值来解决。特别是,为了优化被动IRS波束成型,我们首先提出一种基于多重优化的具有出色性能的迭代算法。我们通过使用矩阵分数编程技术获得一个更可伸缩的物体功能,然后根据主要化-最小化方法提出一种低复杂性算法。数字结果验证了我们提议的算法的趋同,以及在没有IRS协助的情况下对通信情景的重大性能改进。