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.

翻译：本文研究了非理想视距（LoS）相位跟踪对无蜂窝大规模MIMO网络性能的影响。与先前假设相位完全已知或完全未知的研究不同，我们考虑了一个更现实的场景：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，其中视距分量受到非理想相位估计的旋转，并受到确定性相位误差惩罚因子的衰减。我们推导了一种线性MMSE信道估计器，该估计器能够捕捉统计相位误差并统一先前的相关结果：在相位知识完全已知时退化为贝叶斯MMSE估计器，在相位知识完全缺失时退化为零均值模型。针对非高斯场景，我们引入了一个虚拟上行链路模型，该模型保留了信道估计的二阶统计特性，从而能够推导出易于处理的集中式和分布式MMSE波束成形器。为确保对网络性能的公平评估，我们将这些波束成形器应用于真实上行链路模型，并计算了文献中已有的频谱效率界。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建立了桥梁，为6G无蜂窝网络提供了严格的性能基准和设计启示。