Vertical Federated Learning-Based Distributed Hybrid Precoding for Cell-Free Massive MIMO

In cell-free massive multiple-input multiple-output (MIMO) systems, centralized learning-based hybrid precoding needs to train a global model with large datasets collected from all access points (APs), which results in huge system overhead for information exchange and model training. To mitigate the above overhead, this paper proposes a vertical federated learning-based distributed hybrid precoding (VFL-DHP) scheme, in which the global model is divided into multiple local models, and the training of local models is performed in parallel at each AP with the same goal of maximizing sum rate. During the local model training, each AP uses its own channel state information (CSI) for hybrid precoding design, thus avoiding CSI exchange among APs. Specifically, a phase recovery network is designed for solving the analog precoder, and the digital precoder is obtained by interference cancellation. Numerical simulation results not only demonstrate the effectiveness of VFL-DHP, but also indicate that the spectral efficiency of VFL-DHP is very close to that of centralized fully-digital precoding scheme.