Power-Aware Sparse Reflect Beamforming in Active RIS-aided Interference Channels

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.