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

Abstract: 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, they can effectively mitigate the multiplicative fading effect. However, this also induces signal bouncing between the two active RISs that cannot be ignored. This phenomenon is termed as the "inter-excitation" effect and is characterized in the received signal by proposing a feedback-type model. 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 penalty dual decomposition (PDD) algorithm. Finally, simulation results indicate that it proposed scheme outperforms benchmark schemes with single active RIS and double passive RISs in terms of achievable rate. Furthermore, the results demonstrate that the proposed scheme can enhance the WSR by 30\% compared to scenarios that do not take this effect into account when the maximum amplification gain is 40 dB. Additionally, the proposed scheme is capable of achieving high WSR performance at most locations where double active RISs are deployed between the BS and the users, thereby providing greater flexibility in their positioning.