Reconfigurable holographic surfaces (RHSs) constitute a promising technique of supporting energy-efficient communications. In this paper, we formulate the energy efficiency maximization problem of the switch-controlled RHS-aided beamforming architecture by alternately optimizing the holographic beamformer at the RHS, the digital beamformer, the total transmit power and the power sharing ratio of each user. Specifically, to deal with this challenging non-convex optimization problem, we decouple it into three sub-problems. Firstly, the coefficients of RHS elements responsible for the holographic beamformer are optimized to maximize the sum of the eigen-channel gains of all users by our proposed low-complexity eigen-decomposition (ED) method. Then, the digital beamformer is designed by the singular value decomposition (SVD) method to support multi-user information transfer. Finally, the total transmit power and the power sharing ratio are alternately optimized, while considering the effect of transceiver hardware impairments (HWI). We theoretically derive the spectral efficiency and energy efficiency performance upper bound for the RHS-based beamforming architectures in the presence of HWIs. Our simulation results show that the switch-controlled RHS-aided beamforming architecture achieves higher energy efficiency than the conventional fully digital beamformer and the hybrid beamformer based on phase shift arrays (PSA). Moreover, considering the effect of HWI in the beamforming design can bring about further energy efficiency enhancements.

翻译：可重构全息表面（RHS）是一种支持高能效通信的潜在技术。本文针对开关控制型RHS辅助波束成形架构，通过交替优化RHS上的全息波束成形器、数字波束成形器、总发射功率以及各用户的功率分配比，构建了能效最大化问题。具体而言，为处理这一复杂的非凸优化问题，我们将其分解为三个子问题。首先，采用所提出的低复杂度特征分解（ED）方法优化RHS单元系数（负责全息波束成形），以最大化所有用户的本征信道增益之和；其次，通过奇异值分解（SVD）方法设计数字波束成形器以支持多用户信息传输；最后，在考虑收发机硬件损伤（HWI）影响的情况下，交替优化总发射功率与功率分配比。我们从理论上推导了存在HWI时基于RHS的波束成形架构的频谱效率和能效性能上界。仿真结果表明，相较于传统全数字波束成形器及基于移相阵列（PSA）的混合波束成形器，开关控制型RHS辅助波束成形架构能实现更高的能效。此外，在波束成形设计中考虑HWI效应可进一步提升能效。