We study the impact of imperfect line-of-sight (LoS) phase tracking on the uplink 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 \textit{phase-error penalty factor}. We derive a linear MMSE channel estimator that accounts for statistical phase errors and unifies prior results, reducing to the Bayesian MMSE estimator when phase is perfectly known and to a zero-mean model when no phase information is available. 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 virtual centralized and distributed MMSE beamformers. To ensure fair assessment of network performance, we apply these virtual beamformers to the operational uplink model that reflects the actual physical channel 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.

翻译：本文研究了非完美视距（LoS）相位跟踪对无蜂窝大规模MIMO网络上行链路性能的影响。与先前假设相位完全已知或完全未知的研究不同，我们考虑了一个更实际的场景：由于硬件损伤、移动性和同步误差，视距相位的估计存在残余不确定性。为此，我们提出了一种莱斯衰落模型，其中视距分量由非完美的相位估计进行旋转，并由一个确定的\textit{相位误差惩罚因子}进行衰减。我们推导了一种线性最小均方误差（MMSE）信道估计器，该估计器考虑了统计相位误差并统一了先前的相关结果：当相位完全已知时，它退化为贝叶斯MMSE估计器；当无相位信息可用时，则退化为零均值模型。针对非高斯场景，我们引入了一个虚拟上行链路模型，该模型保持了信道估计的二阶统计特性，从而能够推导出易于处理的虚拟集中式和分布式MMSE波束成形器。为确保对网络性能进行公平评估，我们将这些虚拟波束成形器应用于反映实际物理信道的操作上行链路模型，并计算了文献中可用的频谱效率界。数值结果表明，我们的框架在理想化假设与实际跟踪限制之间架起了桥梁，为6G无蜂窝网络提供了严格的性能基准和设计见解。