Beamforming Design for Double-Active-RIS-aided Communication Systems with Inter-Excitation

In this paper, we investigate a double-active-reconfigurable intelligent surface (RIS)-aided downlink wireless communication system, where a multi-antenna base station (BS) serves multiple single-antenna users with both double reflection and single reflection links. Due to the signal amplification capability of active RISs, the mutual influence between active RISs, which is termed as the "inter-excitation" effect, cannot be ignored. Then, we develop a feedback-type model to characterize the signal containing the inter-excitation effect. Based on the signal model, we formulate a weighted sum rate (WSR) maximization problem by jointly optimizing the beamforming matrix at the BS and the reflecting coefficient matrices at the two active RISs, subject to power constraints at the BS and active RISs, as well as the maximum amplification gain constraints of the active RISs. To solve this non-convex problem, we first transform the problem into a more tractable form using the fractional programming (FP) method. Then, by introducing auxiliary variables, the problem can be converted into an equivalent form that can be solved by using a low-complexity penalty dual decomposition (PDD) algorithm. Finally, simulation results indicate that it is crucial to consider the inter-excitation effect between active RISs in beamforming design for double-active-RIS-aided communication systems. Additionally, it prevails over other benchmark schemes with single active RIS and double passive RISs in terms of achievable rate.