Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Noor Ul Ain, Lorenzo Miretti, Renato L. G. Cavalcante, Sławomir Stańczak

TL;DR

This work addresses the practical challenge of imperfect LoS phase tracking in cell-free massive MIMO by introducing a realistic Rician fading model with bounded phase estimation errors. It derives a conditionally linear MMSE channel estimator that smoothly interpolates between perfect-phase and no-phase knowledge, and develops centralized and distributed MMSE beamformers via a virtual uplink that incorporates estimation error covariance. Ergodic spectral efficiency bounds (UatF and OER) are computed to fairly assess performance under realistic phase uncertainty. Numerical results show substantial performance gains from partial LoS phase knowledge over completely unknown phases, with centralized beamforming offering robustness to large phase errors and distributed schemes performing near-optimal under moderate tracking accuracy, providing practical benchmarks for 6G deployments.

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.

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

TL;DR

This work addresses the practical challenge of imperfect LoS phase tracking in cell-free massive MIMO by introducing a realistic Rician fading model with bounded phase estimation errors. It derives a conditionally linear MMSE channel estimator that smoothly interpolates between perfect-phase and no-phase knowledge, and develops centralized and distributed MMSE beamformers via a virtual uplink that incorporates estimation error covariance. Ergodic spectral efficiency bounds (UatF and OER) are computed to fairly assess performance under realistic phase uncertainty. Numerical results show substantial performance gains from partial LoS phase knowledge over completely unknown phases, with centralized beamforming offering robustness to large phase errors and distributed schemes performing near-optimal under moderate tracking accuracy, providing practical benchmarks for 6G deployments.

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.
Paper Structure (16 sections, 4 theorems, 27 equations, 1 figure, 1 table)

This paper contains 16 sections, 4 theorems, 27 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. System and Channel Model
  3. Rician Channel under Imperfect Phase Tracking
  4. Channel Estimation
  5. Data Detection
  6. Uplink Signal Model
  7. General MMSE beamforming
  8. Virtual Uplink Model
  9. Centralized Beamforming
  10. Distributed Beamforming
  11. Ergodic Rates
  12. Use-and-then-forget (UatF) Bound
  13. Optimistic ergodic rate (OER) Bound
  14. Numerical Results
  15. Parameters and Setup
  16. ...and 1 more sections

Key Result

Lemma 1

Fix $\delta\in [0,\pi]$. Let $\varepsilon_{k,l}\sim\mathcal{U}[-\delta,\delta]$ and let $\bm{\tilde{h}}_{k,l}$ be independent of $\hat{\theta}_{k,l}$. Define Then, we have

Figures (1)

  • Figure 1: Comparison of ul SEs achieved for centralized and distributed beamforming under different LOS phase tracking scenarios. Fig \ref{['fig:cdf_mmse']}) CDF of per-user SE in centralized cell-free using OER bound \ref{['eq:se_oer']}. Fig \ref{['fig:cdf_tmmse']}) CDF of per-user SE in distributed cell-free using OER bound \ref{['eq:se_oer']}. In both (a) and (b), the black line refers to two cases from literature, the optimistic case where the phase is perfectly known (Cor. \ref{['cor:perfect']}), the pessimistic case where the phase is completely unknown (Cor. \ref{['cor:unknown']}), and the dotted lines represent our proposed model in Proposition \ref{['prop:LMMSE']} where the LoS phase is partially trackable with some error uniformly distributed as $\sim\mathcal{U}[-\delta,\delta]$. We compare for $\delta\in[0^{\circ},15^{\circ},30^{\circ},45^{\circ},180^{\circ}]$ with all the channels $\kappa=5$. Fig \ref{['fig:avg_ses']}) shows the average SE of the network versus phase uncertainty for centralized and distributed beamformers at different Rician factors $\kappa$ using UatF bound \ref{['eq:se_uatf']}. We plot for $\kappa\in[1,5,20,100]$ and $\delta\in[0^{\circ},15^{\circ},30^{\circ},45^{\circ},90^{\circ},180^{\circ}]$.

Theorems & Definitions (9)

  • Lemma 1
  • Remark 1
  • Definition 1: Conditionally Linear MMSE Estimator kay_1993
  • Proposition 1: Conditionally Linear MMSE channel estimator under imperfect phase tracking
  • Corollary 1
  • Corollary 2
  • Remark 2
  • Remark 3
  • Remark 4