Active reconfigurable intelligent surface (RIS) has attracted significant attention in wireless communications, due to its reflecting elements (REs) capable of reflecting incident signals with not only phase shifts but also amplitude amplifications. In this paper, we are interested in active RIS-aided interference channels in which $K$ user pairs share the same time and frequency resources with the aid of active RIS. Thanks to the promising amplitude amplification capability, activating a moderate number of REs, rather than all of them, is sufficient for the active RIS to mitigate cross-channel interferences. Motivated by this, we propose a power-aware sparse reflect beamforming design for the active RIS-aided interference channels, which allows the active RIS to flexibly adjust the number of activated REs for the sake of reducing hardware and power costs. Specifically, we establish the power consumption model in which only those activated REs consume the biasing and operation power that supports the amplitude amplification, yielding an $\ell_0$-norm power consumption function. Based on the proposed model, we investigate a sum-rate maximization problem and an active RIS power minimization problem by carefully designing the sparse reflect beamforming vector. To solve these problems, we first replace the nonconvex $\ell_0$-norm function with an iterative reweighted $\ell_1$-norm function. Then, fractional programming is used to solve the sum-rate maximization, while semidefinite programming together with the difference-of-convex algorithm (DCA) is used to solve the active RIS power minimization. Numerical results show that the proposed sparse designs can notably increase the sum rate of user pairs and decrease the power consumption of active RIS in interference channels.

翻译：主动可重构智能表面(RIS)因其反射单元(RE)不仅能对入射信号进行相位调控，还能实现幅度放大，在无线通信领域引起了广泛关注。本文研究主动RIS辅助的干扰信道，其中$K$个用户对在主动RIS辅助下共享相同的时频资源。得益于其优越的幅度放大能力，主动RIS无需激活全部RE，仅需启用适度数量的RE即可有效抑制跨信道干扰。基于此，我们针对主动RIS辅助干扰信道提出了一种功率感知的稀疏反射波束赋形设计，通过灵活调整激活RE数量来降低硬件与功耗成本。具体而言，我们建立了功率消耗模型，该模型中仅激活的RE消耗支撑幅度放大的偏置与运行功率，由此得到$\ell_0$-范数功率消耗函数。基于所提模型，我们通过精心设计稀疏反射波束赋形向量，分别研究了和速率最大化问题与主动RIS功率最小化问题。为求解这些问题，我们首先用迭代重加权$\ell_1$-范数函数替代非凸的$\ell_0$-范数函数。随后采用分数规划求解和速率最大化问题，而结合半定规划与凸差算法(DCA)求解主动RIS功率最小化问题。数值结果表明，所提出的稀疏设计能显著提升用户对的和速率，并降低干扰信道中主动RIS的功耗。