  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.
