Max-Min Energy Efficiency for RIS-aided HetNets with Hardware Impairments and Imperfect CSI

Abstract

Beamforming design is crucial to reconfigurable intelligent surface (RIS)-aided communication networks. However, most of the existing works assume ideal hardware and perfect channel state information (CSI), which are unrealistic assumptions in practical systems. In order to improve system robustness and user fairness, in this paper, we firstly study the max-min energy efficiency problem for RIS-aided heterogeneous networks under non-ideal hardware and imperfect CSI. Specifically, the joint optimization of transmit beamforming vectors of femto base stations (FBSs) and the phase shift matrices of RISs is formulated as a nonconvex problem to maximize the minimum energy efficiency of femtocells subject to the constraints of the maximum transmit power of FBSs, the maximum cross-tier interference power of macrocell users, the minimum rates of femtocell users, and unit modulus of RISs. To facilitate the design, we develop an iterative block coordinate descent-based algorithm which exploits the semidefinite relaxation, the S-procedure, the successive convex approximation method, and the singular value decomposition method. Simulation results demonstrate the superiority of the proposed algorithm.