Performance Analysis of Cell-Free Massive MIMO under Imperfect LoS Phase Tracking

Abstract: We study the impact of imperfect line-of-sight (LoS) phase tracking on the performance of cell-free massive MIMO networks. Unlike prior works that assume perfectly known or completely unknown phases, we consider a realistic regime where LoS phases are estimated with residual uncertainty due to hardware impairments, mobility, and synchronization errors. To this end, we propose a Rician fading model where LoS components are rotated by imperfect phase estimates and attenuated by a deterministic phase-error penalty factor. We derive a linear MMSE channel estimator that captures statistical phase errors and unifies prior results, reducing to the Bayesian MMSE estimator with perfect phase knowledge and to a zero-mean model in the absence of phase knowledge. To address the non-Gaussian setting, we introduce a virtual uplink model that preserves second-order statistics of channel estimation, enabling the derivation of tractable centralized and distributed MMSE beamformers. To ensure fair assessment of the network performance, we apply these beamformers to the true uplink model and compute the spectral efficiency bounds available in the literature. Numerical results show that our framework bridges idealized assumptions and practical tracking limitations, providing rigorous performance benchmarks and design insights for 6G cell-free networks.