Efficient Federated Learning Algorithm Design for Distributed Channel Estimation in Cell-Free Massive MIMO Systems

Distributed channel estimation (DCE) algorithm design is pivotal for exploiting the potential of cell-free massive multiple-input multiple-output (CF-mMIMO) systems, while reducing fronthaul costs and computational complexities inherent in conventional centralized algorithms. Most existing DCE algorithms utilize the linear minimum mean square error (LMMSE) estimator for its efficiency, but this method depends on precise channel covariance acquisition. To address these limitations, federated learning (FL)-based DCE algorithms, which use the widely adopted federated averaging protocol, have been developed for CF-mMIMO systems. However, in practical scenarios, small-scale fading at different access points often follows non-independent and identically distributed (non-IID) patterns. This non-IID nature causes existing FL-based DCE algorithms to suffer from model update variance during training, leading to slow convergence rates and poor inference performance. To address these challenges, we propose an efficient DCE algorithm built on a novel FL algorithm, specifically developed for this purpose, named Federated Variance Reduction (FedVR). Unlike federated averaging-based algorithms, FedVR can reduce the variance of model updates between access points during training, resulting in faster convergence rates and improved channel estimation accuracy. Additionally, we theoretically prove the convergence of the FedVR algorithm, and conduct extensive simulations to validate its efficacy.