Beamforming Optimization for Hybrid Active-Passive RIS Assisted Wireless Communications: A Rate-Maximization Perspective

Reconfigurable intelligent surface (RIS) has evolved into a promising approach to significantly improve both spectral and energy efficiencies of wireless communications. Different from the traditional fully-passive and fully-active RISs, a novel hybrid RIS composed of both active and passive reflecting elements has recently emerged, which can leverage their combined advantages to effectively mitigate the RIS-induced multiplicative path loss. In this paper, we investigate a hybrid active-passive RIS assisted wireless system from a rate-maximization perspective. Specifically, we firstly consider the multi-antenna multi-user system and aim to maximize the system weighted sum rate (WSR) by jointly optimizing the transmit precoding matrices and the active-passive RIS reflection matrix. The optimal semi-closed-form solution to each subproblem is obtained by jointly exploring the activeness of constraints and leveraging the majorization-minimization (MM) technique. To gain more useful insights into the rate maximization, we also study the special single-antenna single-user scenario, in which it is revealed that both the optimal transmit beamsteering direction and the optimal phase shifts at the hybrid RIS are independent of actual reflection amplitudes of the hybrid RIS. Numerical results demonstrate the lower complexity and superior rate performance of our proposed algorithms as compared to the existing schemes adopting the fully-passive RIS. Moreover, it is revealed that the hybrid RIS can strike a flexible balance between the square-order beamforming gain of the fully-passive RIS and the power amplification gain of the fully-active RIS by adjusting the active/passive element allocation.