Optimization of RIS-assisted Cell-free Massive MIMO Systems with Heterogeneous Graph Neural Networks under Imperfect Channel Estimation

A reconfigurable intelligent surface (RIS), composed of multiple passive reflecting elements, has emerged as a promising technology for enhancing wireless communications in future network generations. This study investigates a cell-free massive MIMO(CFMM)system integrated with an RIS, referred to as an RIS-assisted CFMM system, focusing on its performance under imperfect channel estimation and specifically addressing the challenge of pilot contamination. Recent advances in computing power have facilitated the widespread applications of deep learning in wireless networks, yielding remarkable results. Among these methods, heterogeneous graph neural networks (HetGNNs) have shown strong potential by effectively combining node information with topological structures. Leveraging these strengths, this work proposes a HetGNN architecture to optimize the RIS assisted CFMM system for maximizing the minimum uplink rate per user. Our approach jointly optimizes the phase shifts at the RIS and the data power control coefficients at user equipments (UEs) to improve overall system performance in uplink data transmission. However, traditional HetGNN architectures are not ideal for RIS-assisted CFMM systems, as they do not fully exploit interaction information among access points (APs), UEs, and RIS. To address this, we propose advanced HetGNN (Adv HetGNN) algorithms, which leverage detailed link information between APs, UEs, and RIS. Simulation results demonstrate the superior performance of the proposed HetGNN-based algorithms over conventional methods, with the Adv-HetGNN algorithms excelling in mitigating performance degradation caused by pilot contamination due to pilot sequence reuse.