Robust Max-Min Energy Efficiency for RIS-Aided HetNets With Distortion Noises

The energy efficiency (EE) of femtocells is always limited by the surrounding radio environments in heterogeneous networks (HetNets), such as walls and obstacles. In this paper, we propose to deploy reconfigurable intelligent surfaces (RISs) to improve the EE of femtocells. However, perfect channel state information is more difficult to obtain due to the passive characteristics of RISs and non-cooperative relationship between different tiers. Besides, the low-cost transceivers and reflecting units suffer nontrivial hardware impairments (HWIs) due to the hardware limitations of practical systems. To this end, we investigate a realistic robust beamforming design based on max-min fairness for an RIS-aided HetNet under channel uncertainties and residual HWIs. The joint optimization of transmit beamforming vectors of femto base stations (FBSs) and the phase-shift matrices of RISs is formulated as a non-convex problem to maximize the minimum EE of the femtocell subject to the constraints of the maximum transmit power of FBSs, the quality of service of users, and unit modulus phase-shift constraints of RISs. We develop an iterative block coordinate descent-based algorithm which exploits the semi-definite relaxation, the S-procedure, and the singular value decomposition method. Simulation results reveal that the proposed algorithm outperforms existing algorithms in terms of fairness, EE, and outage probability.