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

In this article, we are interested in active reconfigurable intelligent surface (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 reflecting elements (REs) rather than all of them is sufficient for the active RIS to mitigate the cross-channel interferences. Motivated by this, we propose a power-aware sparse reflect beamforming (SRB) 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 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula>-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 SRB vector. To solve these problems, we first replace the nonconvex <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula>-norm function with an iterative reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-norm function. Subsequently, we employ fractional programming to solve the sum-rate maximization and utilize semidefinite programming combined with the difference-of-convex algorithm (DCA) to address the active RIS power minimization both of which are proven to converge well. Numerical results show that the proposed sparse designs can notably increase the sum rate of user pairs and decrease the power consumption of the active RIS in interference channels.