This paper investigates the interference nulling capability of reconfigurable intelligent surface (RIS) in a multiuser environment where multiple single-antenna transceivers communicate simultaneously in a shared spectrum. From a theoretical perspective, we show that when the channels between the RIS and the transceivers have line-of-sight and the direct paths are blocked, it is possible to adjust the phases of the RIS elements to null out all the interference completely and to achieve the maximum $K$ degrees-of-freedom (DoF) in the overall $K$-user interference channel, provided that the number of RIS elements exceeds some finite value that depends on $K$. Algorithmically, for any fixed channel realization we formulate the interference nulling problem as a feasibility problem, and propose an alternating projection algorithm to efficiently solve the resulting nonconvex problem with local convergence guarantee. Numerical results show that the proposed alternating projection algorithm can null all the interference if the number of RIS elements is only slightly larger than a threshold of $2K(K-1)$. For the practical sum-rate maximization objective, this paper proposes to use the zero-forcing solution obtained from alternating projection as an initial point for subsequent Riemannian conjugate gradient optimization, and shows that it has a significant performance advantage over random initializations. For the objective of maximizing the minimum rate, this paper proposes a subgradient projection method which is capable of achieving good performance at low complexity.

翻译：本文调查了在多用户环境中可重新配置智能表面(RIS)的干扰无效能力,在多用户环境中,多个单安诺纳收发器在共享频谱中同时进行通信。从理论角度看,我们表明,当RIS和收发器之间的渠道有直观观察线,直接路径被堵时,可以调整RIS元素的阶段,完全消除所有干扰,并在总美元用户干涉渠道中实现最大自由度(DoF)KK$(DoF),条件是RIS元素的数量超过某些取决于$K$的有限限值。对于任何固定频道实现的频道,我们将干扰问题视为可行性问题,并提出交替预测算法,以有效解决由此产生的非 Connovx问题。 数字结果显示,拟议的交替预测算法可以取消所有干扰,如果IS元素的数量仅略大于2K(K-1美元)的阈值。对于实际的总和最大值目标取决于$$美元。对于任何固定频道实现的有限值值,本文件提议在初始预测中采用最优化的预测方法,从而逐步实现最大幅度的升级的升级的升级的升级的绩效。