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Localization in Multi-Panel Massive MIMO With Clock Asynchronism: A Unified Approach

Yuhao Zhang, Guangjin Pan, Musa Furkan Keskin, Carmen D'Andrea, Stefano Buzzi, Henk Wymeersch

arXiv:2610.12178v1eess.SPcs.ITmath.IT

TL;DR

Localization in multi-panel MIMO must accommodate mixed LoS/NLoS visibility and residual clock asynchronism, which limit earlier unified approaches designed for single-BS, tightly synchronized settings. UNILocMP combines model-based geometry and unsupervised channel charting for different visibility classes. Simulations report better performance than model-based and CC-based methods, approaching supervised fingerprinting, while multi-panel deployments improve performance over single-BS localization, especially with imperfect synchronization.

  • Problem

    Unified geometry-and-learning localization for multi-panel systems under mixed LoS/NLoS visibility and clock asynchronism remains underexplored, while the single-BS UNILocPro requires tight synchronization.

    Source: §I · p. 1

  • Method

    UNILocMP uses joint position and clock-bias estimation for multi-LoS users and unsupervised channel charting with clock-bias-aware dissimilarity and data augmentation for single/non-LoS users.

    Source: §I · p. 1

  • Results

    UNILocMP outperforms model-based and CC-based methods and approaches fully supervised fingerprinting; multi-panel localization performs better than single-BS localization, especially under imperfect synchronization.

    Source: B. Localization Performance Evaluation · p. 5, C. Comparison with Single-BS… · p. 5, §V · p. 6

  • Takeaways & Limitations

    The reported comparisons indicate that multi-panel CSI can provide additional geometric diversity and robustness against clock asynchronism.

    Source: C. Comparison with Single-BS… · p. 5, §V · p. 6

Abstract

from arXiv · show

In this work, we propose a unified localization framework, termed UNILocMP, that combines model-based geometry and channel charting (CC) for multi-panel massive multiple-input-multiple-output (MIMO) under clock asynchronism. Owing to the multi-panel architecture, users are classified into multi-line-of-sight (LoS) users, which maintain LoS links with at least two panels, and single/non-LoS users, which maintain a LoS link with only one panel or with none of the panels. For multi-LoS users, a joint position and clock bias estimation is developed; while for single/non-LoS users, an unsupervised CC model is trained with a two-stage data augmentation strategy, where a clock-bias aware dissimilarity metric is introduced. It is numerically validated that the proposed UNILocMP outperforms model-based and CC-based baselines and achieves acceptable performance compared with fully-supervised fingerprinting. Moreover, for a fixed total number of antennas, the multi-panel architecture significantly improves localization accuracy and robustness compared with a single-panel base station (BS) deployment, particularly in the presence of clock asynchronism.

I. INTRODUCTION

The introduction motivates unified localization for distributed multi-panel MIMO under mixed LoS/NLoS conditions and residual clock bias. The paper combines model-based geometry with channel charting, using simulations to evaluate the framework across synchronization conditions.

I. INTRODUCTION

  • UNILocMP combines model-based geometry and channel charting to handle heterogeneous panel visibility and clock asynchronism in multi-panel localization.It uses joint position and clock-bias estimation for multi-LoS users and a clock-bias-aware CC approach for single/non-LoS users.Source: §I · p. 1
  • Ray-tracing simulations show improved performance by exploiting complementary spatial information from multiple panels.The evaluation compares single-BS and multi-panel localization under perfect and imperfect synchronization.Source: §I · p. 2

II. SYSTEM MODEL

  • The system has spatially separated panels serving users over OFDM, with residual user-to-BS clock biases bounded by ±ǫ_max.The BS panels are assumed synchronized with one another.Source: §II · p. 2

A. Channel Model

  • Panel separation produces spatially nonstationary channels, so a user may have LoS visibility to only a subset of panels.The model assumes known user height and a high-SNR regime so CSI can be reliably estimated.Source: A. Channel Model · p. 2

B. Map Information

A coarse environment map supports visibility-aware localization by separating feasible user positions into per-panel LoS and NLoS regions.

B. Map Information

  • The map partitions the feasible position region according to whether each location has an LoS connection to each panel.It need not provide high-resolution geometric information; it primarily supplies a coarse feasible region and learning constraints.Source: B. Map Information · p. 2
  • A position is classified as multi-LoS when it has LoS connections to at least two panels.Source: B. Map Information · p. 2
  • Single/non-LoS positions have an LoS connection to only one panel or none.Source: B. Map Information · p. 2

III. MULTI-PANEL UNIFIED LOCALIZATION

UNILocMP first classifies users from CSI, then selects model-based estimation for multi-LoS users and a neural-network branch for the others. The multi-LoS estimator fits observed CSI to geometry-induced LoS channels while enforcing map-derived visibility constraints.

III. MULTI-PANEL UNIFIED LOCALIZATION

  • CSI-based classification routes multi-LoS users to model-based estimation and single/non-LoS users to a neural network.Source: §III · p. 2

A. CSI-Based User Identification

  • The per-panel LoS/NLoS identification mechanism is treated as external, with assumed accuracy p_I ∈ [0.5, 1].Prior mechanisms are reported to achieve up to 93%–100% accuracy.Source: A. CSI-Based User Identification · pp. 2–3

B. Model-Based Multi-Panel Localization

  • For multi-LoS users, the estimator directly fits observed CSI to analytical LoS channels across visible panels rather than matching extracted measurements alone.Map-derived visibility constraints enforce cross-panel geometric consistency and exclude infeasible positions.Source: B. Model-Based Multi-Panel Localization · p. 3
  • Panel-specific geometric parameters are computed from candidate user positions using the panel geometry.The ULA direction vector and speed of light are used in the geometric model.Source: B. Model-Based Multi-Panel Localization · p. 3

1) Joint Optimization

The joint optimization estimates user position and clock bias by minimizing mismatch between observed CSI and geometry-predicted LoS channels. It filters strong NLoS paths before forming the optimization objective.

1) Joint Optimization

  • Strong NLoS paths are filtered by excluding paths whose channel gain exceeds that of the shortest path before optimization.The remaining CSI is used to form the squared-Frobenius-norm discrepancy objective.Source: 1) Joint Optimization · p. 3
  • The channel gains for each panel’s LoS component are obtained by least squares, yielding a reduced concentrated-cost optimization problem.Source: 1) Joint Optimization · p. 3
  • The position-and-clock-bias objective is non-convex, and the feasible region may be non-convex or disconnected in complex environments.Grid search is described as prohibitively complex, motivating gradient-based optimization from an initial point.Source: 1) Joint Optimization · p. 3

2) Initial Point Acquisition

The initial position is obtained by multi-lateration using TDoA and AoA measurements from all visible LoS panels. A closed-form least-squares solution provides the starting position, from which an initial clock bias is derived.

2) Initial Point Acquisition

  • TDoA/AoA multi-lateration across all LoS panels supplies the initial position estimate.The method uses the estimated channel parameters for the user's visible LoS panels.Source: 2) Initial Point Acquisition · p. 3
  • The reference panel is the one with the highest overall channel gain; each other panel's shortest-path ToA is differenced against its ToA.The shortest-path ToA is selected for each panel before taking differences against the reference.Source: 2) Initial Point Acquisition · p. 3
  • A least-squares solution of the linear system gives the initial position, which is then used to obtain the initial clock bias.The position solution is derived in Appendix A; the initial clock bias is calculated from the initial position.Source: 2) Initial Point Acquisition · p. 3

C. CC-based Multi-Panel Localization

For single/non-LoS users, the CC model maps preprocessed CSI features to position. The input combines angle-delay CSI features from the panels after truncating delays to a clock-bias-expanded ToA range.

C. CC-based Multi-Panel Localization

  • A neural network maps CSI to position for single/non-LoS users.The antenna-frequency CSI is first transformed into the angle-delay domain, then truncated to delays within the ToA range expanded by εmax for clock bias.Source: C. CC-based Multi-Panel Localization · p. 3
  • The delay truncation extends the minimum and maximum ToA bounds by εmax to account for clock bias.The truncated angle-delay CSI is used to form the model input features.Source: C. CC-based Multi-Panel Localization · p. 3
  • Element-wise CSI amplitude and phase form each panel's feature vector, and the panel vectors are concatenated into the final input.The network estimates position from the concatenated input.Source: C. CC-based Multi-Panel Localization · pp. 3–4

1) Loss for CC

The CC objective combines pairwise, triplet, multi-LoS, and map-assisted losses. Its dissimilarity metric uses per-panel CSI signatures and clock-bias mitigation, with the bias estimate chosen according to user visibility.

1) Loss for CC

  • The CC loss combines pairwise distance preservation, triplet ordering, multi-LoS alignment to model-based estimates, and optimal-transport alignment to the single/non-LoS map region.The multi-LoS loss anchors the learned chart in global coordinates; the optimal-transport loss aligns identified single/non-LoS users with their region.Source: 1) Loss for CC · p. 4
  • The multi-panel CC redesigns the CSI dissimilarity and adds asynchronous-setting data augmentation to the inherited training principles.Its CSI is constructed jointly from spatially separated panels.Source: 1) Loss for CC · p. 4

2) Dissimilarity Metric with Clock Bias

  • Per-panel dissimilarity compares CSI signatures using fused GOSPA and Wasserstein metrics, then averages across panels.Each signature is a set of estimated channel-path positions derived from geometric relationships.Source: 2) Dissimilarity Metric with Clock Bias · p. 4
  • Before computing dissimilarity, estimated ToAs are corrected by subtracting the user's estimated clock bias or a clock-shift proxy.Multi-LoS users use the model-based clock estimate; single/non-LoS users use an alignment proxy, not an accurate clock estimate, because their LoS paths are insufficient.Source: 2) Dissimilarity Metric with Clock Bias · p. 4

3) Data Augmentation and Training Strategy

The two-stage training strategy targets clock-bias-induced feature variation. After CC training, random clock-bias perturbations generate augmented CSI samples that receive pseudo-labels and are used for further training.

3) Data Augmentation and Training Strategy

  • Clock bias and possible drift can make CSI features differ for samples from the same physical location, motivating a model trained on bias-invariant patterns.The stated goal is to make the neural network agnostic to clock bias and improve generalization.Source: 3) Data Augmentation and Training… · p. 4
  • The CC stage computes input features, dissimilarities, and multi-LoS model-based estimates, then trains the neural network with the multi-component loss.The resulting parameters are denoted Θ0.Source: 3) Data Augmentation and Training… · p. 4
  • The augmentation stage adds random clock-bias perturbations within [−εmax, εmax], pseudo-labels the resulting samples with the trained model, and further trains it using an MSE loss.The augmented dataset contains multiple perturbed samples per original CSI sample.Source: 3) Data Augmentation and Training… · p. 4

IV. NUMERICAL RESULTS

The numerical evaluation uses a street-canyon scenario with four rooftop panels spaced 7 m apart. Table I reports testing-set mean absolute error for localization methods in multi-panel MIMO.

IV. NUMERICAL RESULTS

  • Four rooftop antenna panels are uniformly spaced 7 m apart in the street-canyon evaluation.The deployment center is [0, −9, 57]T.Source: §IV · p. 4
  • The evaluated street-canyon scenario uses a rooftop deployment centered at [0, −9, 57]T.Source: §IV · p. 4
  • Table I reports testing-set MAE in meters for localization methods in the multi-panel MIMO scenario.Source: Table I · p. 5

A. System Parameters and Dataset Generation

The evaluation compares UNILocMP in ray-traced multi-panel settings under clock asynchronism and against a same-antenna single-BS deployment. UNILocMP outperforms model-based and CC-based methods, while multi-panel methods outperform their single-BS counterparts, with gains depending on deployment and visibility.

A. System Parameters and Dataset Generation

  • The multi-panel evaluation uses four 64-antenna panels, ray-traced CSI, and about 1,800 independently generated training and testing positions.The LoS/NLoS identifier is assumed ideal to isolate localization performance.Source: A. System Parameters and Dataset… · p. 5

B. Localization Performance Evaluation

C. Comparison with Single-BS Localization

  • All multi-panel methods outperform their single-BS counterparts, especially under imperfect synchronization; UNILocMP retains better performance than UNILocPro under clock bias.The comparison uses a single ULA with 256 antennas to match the multi-panel system’s total antenna count.Source: C. Comparison with Single-BS… · p. 5, Table II · p. 5, Figure 2 · p. 6
  • Multiple panels provide complementary geometric information and improve positioning accuracy and clock-bias robustness, but gains depend on panel placement and visibility.Source: C. Comparison with Single-BS… · p. 6

V. CONCLUSION

  • The conclusion characterizes UNILocMP as combining model-based localization for multi-LoS users with unsupervised channel charting for single/non-LoS users.It reports robust localization without ground-truth labels and calls for evaluation with real identification and measured data.Source: §V · p. 6

APPENDIX A

The appendix derives linear geometric relationships by eliminating intermediate distance terms and subtracting a reference-panel relation. The resulting equations combine relations across visible panels.

APPENDIX A

  • Substituting the earlier relation eliminates d_i^p and yields a linear equation.Source: Appendix A · p. 6
  • Subtracting the reference-panel relation from each other visible panel’s TDoA relation eliminates the shared norm term.Source: Appendix A · p. 6
  • The final relations combine the per-panel equations across all LoS-visible panels and the non-reference panels.Source: Appendix A · p. 6
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