[論文レビュー] Performance Analysis of Cell-Free Massive MIMO under Imperfect LoS Phase Tracking

Noor ul Ain, Lorenzo Miretti+2 more|arXiv (Cornell University)|Jan 16, 2026

Advanced MIMO Systems Optimization被引用数 0

ひとこと要約

tldr: This paper introduces a realistic model for imperfect LoS phase tracking in cell-free massive MIMO, derives a linear MMSE channel estimator under phase errors, and proposes centralized and distributed MMSE beamformers using a virtual uplink model to assess spectral efficiency bounds.

ABSTRACT

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 extit{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.

研究の動機と目的

• Motivate understanding of how imperfect LoS phase tracking affects cell-free mMIMO performance.
• Develop a realistic Rician fading model where LoS phases are imperfectly estimated and attenuated by a phase-error penalty.
• Derive a tractable linear MMSE channel estimator that encompasses perfect phase knowledge and unknown phase as limiting cases.
• Introduce a virtual uplink model to enable centralized and distributed MMSE beamforming under phase uncertainty.
• Provide ergodic spectral efficiency bounds (UatF and OER) to fairly evaluate performance under realistic tracking limitations.

提案手法

• Model LoS channels as a Rician process rotated by imperfect phase estimates and attenuated by a phase-error penalty ρ_error.
• Derive a conditionally linear MMSE channel estimator that handles non-Gaussian pilot observations and phase uncertainty.
• Introduce a virtual uplink with augmented noise covariance to enable tractable MMSE beamforming design.
• Obtain centralized beamformers using a closed-form MMSE expression incorporating phase-error covariances.
• Obtain distributed beamformers via a Team MMSE framework with a coupled set of local optimizations and a linear system for combining vectors.

(a)

実験結果

リサーチクエスチョン

• RQ1 How do imperfect LoS phase tracking and phase estimation errors influence channel estimation accuracy in cell-free mMIMO?
• RQ2 Can a tractable linear MMSE estimator unify perfect-phase and unknown-phase scenarios under partial LoS phase knowledge?
• RQ3 How can centralized and distributed MMSE beamformers be designed and analyzed under phase uncertainties?
• RQ4 What are the resulting ergodic spectral efficiency bounds under imperfect LoS phase tracking?
• RQ5 Do partial LoS phase knowledge and phase-tracking accuracy meaningfully improve performance over no-phase knowledge?

主な発見

• Imperfect LoS phase tracking can be effectively captured by a phase-noise penalty ρ_error that scales the deterministic LoS component and rotates its phase.
• The proposed conditionally linear MMSE estimator subsumes perfect-phase (Bayesian MMSE) and completely unknown-phase (zero-mean) cases as corollaries.
• A virtual uplink model enables tractable centralized and distributed MMSE beamforming by incorporating estimation error covariance into additive noise.
• Centralized beamformers incorporate phase-error covariances and yield closed-form expressions; distributed beamformers follow a Team MMSE approach with a solvable linear system for combining vectors.
• Numerical results show substantial performance gains with partial phase tracking over no-phase knowledge, with robustness stronger in centralized designs and better under higher Rician factors for distributed designs.

(b)