Computationally Efficient Unsupervised Deep Learning for Robust Joint AP Clustering and Beamforming Design in Cell-Free Systems

In this paper, we consider robust joint access point (AP) clustering and beamforming design with imperfect channel state information (CSI) in cell-free systems. Specifically, we jointly optimize AP clustering and beamforming with imperfect CSI to simultaneously maximize the worst-case sum rate and minimize the number of AP clustering under power constraint and the discrete constraint of AP clustering. Through transformations, the intractable simultaneous optimization of continuous and discrete variables is reduced to optimizing only the sparsity of the continuous variables, facilitating a computationally efficient unsupervised deep learning algorithm. In addition, to further reduce the computational complexity, a computationally effective unsupervised deep learning algorithm is proposed to implement robust joint AP clustering and beamforming design with imperfect CSI in cell-free systems. Numerical results demonstrate that the proposed unsupervised deep learning algorithm achieves a higher worst-case sum rate under a smaller number of AP clustering with computational efficiency.

I. Introduction

Recently, cell-free systems have received significant attentions [1], [2]. By connecting all access points (APs) to a central processing unit (CPU) via backhaul links, cell-free systems allow multiple APs to simultaneously collaborate to serve users within the network coverage area, which could overcome many of the interference issues that appear in cellular networks [3], [4]. In particular, the work in [5] derived the achievable spectral efficiency expressions of four uplink implementations for cell-free systems. Reference [6] investigated the hybrid beamforming design of reconfigurable intelligent surface (RIS)-assisted cell-free systems, in which some recent advancements in RIS-assisted cell-free systems can be seen in the survey in [7]. By introducing deep reinforcement learning (DRL), [8] realized the beamforming design of cell-free systems with better performance. Based on graph neural network (GNN), [9] proposed an Edge-GNN to achieve the beamforming design for cell-free systems, where experimental results demonstrated that Edge-GNN scales well on different numbers of APs and users. Nevertheless, popular beamforming design in cell-free systems generally assumes that all APs in the network coverage area serve users simultaneously [10], [11]. This appears to be impractical as long-range APs serving users consume precious power and bandwidth resources while contributing little useful power due to high path losses [12]. To solve the above problem, a practical solution is to allow a subset of APs to serve users, which can also be called AP clustering. Consequently, joint AP clustering and beamforming is uniquely designed for cell-free systems to improve both the sum rate and the practicality.