Bayesian learning for pilot decontamination in cell-free massive MIMO

Pilot contamination (PC) arises when the pilot sequences assigned to user equipments (UEs) are not mutually orthogonal, eventually due to their reuse. In this work, we propose a novel expectation propagation (EP)-based joint channel estimation and data detection (JCD) algorithm specifically designed to mitigate the effects of PC in the uplink of cell-free massive multiple-input multiple-output (CF-MaMIMO) systems. This modified bilinear-EP algorithm is distributed, scalable, demonstrates strong robustness to PC, and outperforms state-ofthe-art Bayesian learning algorithms. Through a comprehensive performance evaluation, we assess the performance of Bayesian learning algorithms for different pilot sequences and observe that the use of non-orthogonal pilots can lead to better performance compared to shared orthogonal sequences. Motivated by this analysis, we introduce a new metric to quantify PC at the UE level. We show that the performance of the considered algorithms degrades monotonically with respect to this metric, providing a valuable theoretical and practical tool for understanding and managing PC via iterative JCD algorithms.