Reconfigurable intelligent surface (RIS) technology has gained widespread recognition for its ability to significantly enhance communication performance between base stations (BS) and users in blind spot areas. This paper investigates the energy efficiency (EE) of an RIS-assisted multi-cell communication system, incorporating a measurement-based empirical RIS power consumption model. Exploiting only statistical channel state information (CSI), we aim to maximize the overall EE of the system. An alternating optimization (AO) algorithm is proposed for joint optimization of the transmit beamforming vectors at the BSs and the RIS phase shift matrix. To circumvent the challenges arising from the discrete relationship between the power consumption of positive-intrinsic-negative (PIN) diode-based reflecting elements and their phase shifts, we introduce a continuous function to approximate the relationship. With this approximation, the complex circle manifold (CCM) technique is applied to optimize the continuous RIS phase shifts, which are then quantized within a discrete set. Then, to further reduce the complexity of the AO algorithm, a sub-optimal algorithm is proposed. In this algorithm, the statistical maximum ratio transmission beamforming is employed at each BS, which decouples the design of BS beamforming vectors from the design of BS transmit power and RIS phase shifts. Given the BS beamforming vectors, the BS transmit power and RIS phase shifts are then designed using the quadratic transformation and CCM techniques. Simulation results show that the proposed algorithm achieves near-optimal EE while offering guidance on PIN diode encoding to balance phase resolution and power consumption in practical RIS design.

Reconfigurable intelligent surface (RIS) technology has gained wide recognition for its ability of enhancing the performance of wireless communication systems. This paper investigates the energy efficiency (EE) of a discrete phase shift RIS-assisted multi-cell communication system. Assuming that only statistical channel state information is available, we maximize the EE under a practical measured-based RIS power consumption model. Approximating the discrete measured-based RIS power consumption model by a continuous differentiable function, the problem is addressed by jointly optimizing the transmit beamforming at the base stations and the RIS phase shift matrix, by using fractional programming and complex circle manifold techniques. Simulation results demonstrate that the proposed algorithm can effectively achieve near-optimal EE performance and low RIS power consumption.