Reconfigurable intelligent surface (RIS) has emerged as a cost-effective and energy-efficient technique for 6G. By adjusting the phase shifts of passive reflecting elements, RIS is capable of suppressing the interference and combining the desired signals constructively at receivers, thereby significantly enhancing the performance of communication system. In this paper, we consider a green multi-user multi-antenna cellular network, where multiple RISs are deployed to provide energy-efficient communication service to end users. We jointly optimize the phase shifts of RISs, beamforming of the base stations, and the active RIS set with the aim of minimizing the power consumption of the base station (BS) and RISs subject to the quality of service (QoS) constraints of users and the transmit power constraint of the BS. However, the problem is mixed combinatorial and non-convex, and there is a potential infeasibility issue when the QoS constraints cannot be guaranteed by all users. To deal with the infeasibility issue, we further investigate a user admission control problem to jointly optimize the transmit beamforming, RIS phase shifts, and the admitted user set. Specifically, we first decompose the original non-convex problem into several rank-one constrained optimization subproblems via matrix lifting. A difference-of-convex (DC) algorithm is then developed to solve each decomposed subproblem. The proposed AO framework efficiently minimizes the power consumption of wireless networks as well as user admission control when the QoS constraints cannot be guaranteed by all users. To further address the complexity-sensitive issue for practical implementation, we propose an alternative low-complexity beamforming and RISs phase shifts design algorithm based on zero-forcing (ZF) to enable the green cellular networks.

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