Joint Power Allocation and Passive Beamforming for RIS-Assisted Wireless Energy-Constrained Systems With Multi-User Scheduling

In this paper, we consider a reconfigurable intelligent surface (RIS)-assisted wireless communications system with multi-user scheduling, where a pilot-embedded data transmission is carried out from a selected user to an access point (AP) with the aid of an RIS. Specifically, by taking into account a transmit energy constraint, we propose a joint passive beamforming and power allocation optimization (JPB-PAO) scheme for the RIS-assisted wireless system, in which a problem of joint optimization on the pilot power, data power, and RIS's phase shifts is formulated for maximizing the achievable rate of the user-AP transmission. To this end, we propose a Dinkelbach and majorization-minimization (DMM) aided JPB-PAO (termed as DMM-JPB-PAO) scheme for the sake of obtaining a semi-closed form expression of the optimal RIS phase shifts, based on which a closed-form solution of power allocation is derived. Moreover, we adopt the widely used semidefinite relaxation (SDR) algorithm as a baseline to solve the JPB-PAO problem, which is referred to as the SDR-JPB-PAO. Numerical results show that our proposed DMM-JPB-PAO achieves almost the same achievable rate as the SDR-JPB-PAO at a much lower computational complexity. Meanwhile, DMM-JPB-PAO scheme yields a higher achievable rate than the passive beamforming optimization with fixed power allocation (PBO-FPA) scheme and the random passive beamforming with fixed power allocation (RPB-FPA) scheme.