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Reliable Near-Field Multi-User Positioning Informed by Two-Stage MUSIC
Jiaying Li, Haifeng Wen, Changsheng You, Yuanwei Liu, Hong Xing
TL;DR
Coherent NLoS propagation complicates near-field multi-user positioning because existing approaches estimate and associate paths, adding overhead and possible error while lacking reliability guarantees. MUSIC-Net embeds two-stage MUSIC in an end-to-end learning framework to recover LoS positions without explicit NLoS estimation or path/source association, and combines it with SCP for guaranteed confidence sets. It achieves lower MPER and tighter SCP-calibrated prediction regions than existing benchmarks.
Problem
Coherent LoS/NLoS multipath makes near-field positioning difficult, while existing methods require costly path estimation and association and generally lack reliability guarantees.
Method
MUSIC-Net embeds two-stage MUSIC into end-to-end learning to estimate LoS-related features and surrogate distance, while SCP constructs statistically guaranteed position sets for all users.
Results
MUSIC-Net achieves lower MPER than existing benchmarks and tighter SCP-calibrated prediction regions in coherent multi-path environments.
Takeaways & Limitations
The framework provides accurate LoS localization and reliable uncertainty quantification without explicit NLoS parameter estimation or path/source association.
Abstract
from arXiv · showhide
Near-field localization is a promising technique for high-resolution multi-user positioning in future wireless systems, but its performance is often degraded by scattering-induced coherent propagation. Existing near-field localization methods, which require separate parameter estimation and path/source association, suffer from high computation overhead and accumulated errors, and usually do not provide any guarantee on reliability. In this paper, we propose \emph{MUSIC-Net}, an end-to-end near-field positioning deep learning (DL) framework informed by two-stage MUltiple SIgnal Classification (MUSIC) in mixed line-of-sight (LoS) and non-LoS (NLoS) multi-path scenarios, which embeds the two-stage MUSIC objects into training to isolate the LoS-related signal subspace and to identify a surrogate distance. The proposed framework directly recovers multi-user positions without the need for involved NLoS parameter estimation or path/source association. Furthermore, we introduce split conformal prediction (SCP) to move beyond point-estimation-based positioning towards statistically guaranteed (confidence) set estimation for all users. Numerical results show that the proposed MUSIC-Net achieves lower mean positioning error (MPER) than existing benchmarks and yields tighter SCP-calibrated prediction regions, demonstrating both accurate LoS localization and efficient uncertainty quantification (UQ) in coherent multi-path environments.
I. INTRODUCTION
Near-field multi-user positioning offers high-resolution direction and distance estimation but becomes difficult under coherent LoS/NLoS scattering. MUSIC-Net combines two-stage MUSIC-informed learning with split conformal prediction to provide accurate positioning and statistically guaranteed uncertainty sets.
- Near-field localization estimates both direction of arrival and source distance, unlike far-field methods that mainly resolve angular information.This capability follows from spherical wavefronts in the radiative near-field regime.
- Coherent NLoS paths distort the LoS-induced subspace, making conventional localization demanding or impossible.The difficulty arises when LoS and NLoS paths associated with one user are highly coherent.
- Existing coherent-source methods estimate path parameters and then associate paths with sources, adding computation and potentially accumulating positioning errors.The paper motivates directly targeting LoS parameter estimation instead.
- MUSIC-Net estimates the LoS-related subspace and surrogate distance while preserving two-stage MUSIC interpretability, avoiding explicit NLoS estimation and path/source association.Its end-to-end framework directly supports multi-user positioning in coherent multi-path conditions.
- Split conformal prediction constructs confidence sets with statistically guaranteed true-position coverage for all users.SCP provides model-agnostic, distribution-free, and training-free uncertainty quantification beyond point estimates.
- MUSIC-Net achieves the lowest MPER across SNR regimes and the tightest prediction regions among benchmarks.These results support accurate localization and efficient uncertainty quantification in coherent multi-path environments.
A. System Model
The system models uplink near-field observations from multiple single-antenna users received by a ULA, with each user contributing one LoS path and possibly coherent NLoS paths plus noise. The received covariance therefore contains LoS, NLoS, cross-correlation, and noise components.
- The uplink system uses an access point with a uniform linear array to localize multiple users in the radiative near-field.Users are single-antenna devices, and the array receives their narrowband signals.
- The near-field condition is r < 2D^2/λ, where D is the array aperture and λ is the carrier wavelength.The aperture is D = (M̃ − 1)d, with d denoting antenna spacing.
- A near-field steering vector represents a target user through its direction of arrival and distance.The user and antenna positions determine the geometric relationship underlying the steering vector.
- Each user has one LoS propagation path and L_k ≥ 0 NLoS paths generated by scatterers, with independent transmitted signals over T time slots.The received signal also includes additive white Gaussian noise.
- The received covariance decomposes into LoS, NLoS, cross-correlation, and noise terms.In practice, the true covariance is approximated using the sample covariance matrix formed from observations.
B. Reliable Multi-User Positioning
The positioning objective is to estimate all users’ LoS-related direction and distance parameters while treating NLoS parameters as nuisance variables. The framework seeks confidence sets that jointly cover all true user positions with probability at least 1 − α.
- The target parameters are the direction and distance of every user’s LoS path.The number of users K is assumed known, while NLoS parameters are treated as nuisance parameters.
- Direct application of MUSIC to the sample covariance works mainly in LoS-only or LoS-dominant settings.In coherent multi-path scenarios, NLoS and cross-correlation terms deteriorate the LoS-only subspace structure and bias estimated positions.
- The proposed scheme constructs confidence sets for user positions that jointly cover all K true positions with probability at least 1 − α.The coverage probability is defined over the joint distribution of test and calibration data.
III. TWO-STAGE MUSIC INFORMED MUSIC-NET
MUSIC-Net is a deep learning framework informed by the two-stage MUSIC algorithm for near-field multi-user positioning with multiple coherent NLoS paths.
- MUSIC-Net uses two-stage MUSIC to inform a deep learning framework for near-field multi-user positioning under coherent NLoS propagation.
A. Motivation
Two-stage MUSIC reduces near-field localization’s joint angle-range search to sequential DoA and distance searches, but coherent NLoS paths prevent direct reuse of its standard subspace estimation.
- Two-stage MUSIC: The method assumes a covariance structure dominated by LoS paths, enabling signal- and noise-subspace decomposition through eigenvalue decomposition.This approximation represents the covariance as the sum of LoS steering-vector contributions and σ2I.
- Two-stage MUSIC: Standard two-stage MUSIC decomposes joint angle-range localization into one-dimensional DoA and distance searches.The DoA search uses a surrogate distance, followed by distance estimation based on the estimated DoAs.
- Limitation: Unknown NLoS parameters fundamentally alter the covariance structure, disabling direct estimation of the noise subspace required by two-stage MUSIC.Consequently, the conventional algorithm cannot be trivially adapted to coherent multi-path multi-user localization.
B. MUSIC-Net Training
MUSIC-Net replaces unavailable conventional subspace and surrogate-distance estimates with two trainable modules, then feeds their outputs into two-stage MUSIC for multi-user position recovery.
- Architecture: MUSIC-Net uses a LoS feature extractor and surrogate distance estimator to produce an estimated subspace and surrogate distance from the input SCM.These outputs substitute for the estimated noise subspace and surrogate distance used in standard two-stage MUSIC.
- Inference: The framework preserves the two-stage MUSIC pipeline while estimating LoS-related structure before DoA and distance searches.The resulting inference procedure outputs estimated DoAs and user positions for all users.
- Training: The chosen subspace-distance loss avoids alternatives described as sensitive to received-signal SNR and potentially prone to poor generalization.The paper contrasts it with SCM-fitting and affine-invariant-distance losses.
- Training: Training jointly minimizes multiple objectives for subspace learning and surrogate-distance estimation, with λ balancing losses from NLoS noise and distance estimation.The subspace loss compares the learned and target LoS-induced signal subspaces.
- Limitation: Inference produces point estimates of user positions but initially provides no robustness guarantee against uncertainty in MUSIC-Net outputs.The framework therefore augments these point estimates with confidence sets in the subsequent uncertainty-quantification stage.
A. Preliminary
Split conformal prediction calibrates prediction sets from held-out data using nonconformity scores and an empirical quantile under exchangeability.
- SCP formulation: SCP uses an i.i.d. calibration dataset of feature-label pairs to evaluate predictive conformity.Each calibration example receives a score through a model-associated nonconformity function.
- SCP formulation: The nonconformity score measures how poorly a label conforms to its corresponding feature.SCP uses these calibration scores to determine the prediction-set threshold.
- Prediction set: For target mis-coverage level α, SCP forms a confidence set containing labels whose scores do not exceed the empirical quantile q̂1−α.The set is constructed for a newly observed test feature.
- Coverage: Exchangeability of calibration and test examples yields a proven marginal coverage guarantee for the SCP prediction set.The guarantee depends on the stated exchangeability assumption.
B. Uncertainty Quantification for MUSIC-Net
For MUSIC-Net, SCP calibrates position errors on held-out data, converts each estimate into a circular region, and provides joint coverage for all users under exchangeability.
- Calibration: The calibration set contains samples with SCMs and ground-truth LoS DoA-distance parameters for the users.These data support post-hoc calibration of MUSIC-Net’s position estimates.
- Calibration: The nonconformity score compares estimated and ground-truth user positions after optimal permutation matching.The matching uses a permutation-based method such as the Hungarian algorithm.
- Confidence regions: Each predicted confidence region is a circle centered at the estimated user position with radius given by the empirical quantile q̂1−α.The same calibrated construction is applied to each estimated user position.
- Coverage guarantee: Under exchangeability, the predicted regions satisfy a joint coverage guarantee for all users.The proposition establishes simultaneous inclusion of every true user position with probability at least 1−α.
V. EXPERIMENT RESULTS
The experiments evaluate MUSIC-Net for near-field multi-user localization under mixed LoS/NLoS multipath, comparing point-estimation accuracy and SCP prediction-region tightness with benchmark schemes. MUSIC-Net achieves the strongest reported positioning and uncertainty-quantification results across the evaluated settings.
- Experimental setup: The evaluation uses uplink near-field localization with 25 ULA antennas at 1 GHz, randomly varying 1–4 users and enforcing minimum angular separation.The dataset contains 1.25×10^5 samples, with separate training, calibration, and test splits for SCP.
- Compared methods: The benchmarks include 2D MUSIC, Two-phase MUSIC, NF-SubspaceNet, and DCD-MUSIC, evaluated through indirect-LoS and direct-LoS approaches.Indirect-LoS schemes estimate and associate all paths before selecting LoS parameters, whereas direct-LoS schemes target the LoS-positioning objective directly.
- Point estimation: MUSIC-Net outperforms all other methods in MPER across the entire SNR range.Direct-LoS baselines generally outperform indirect-LoS counterparts, consistent with accumulated errors from path estimation and post-processing.
- Uncertainty quantification: MUSIC-Net produces a much smaller predicted region covering the true location than the benchmark schemes in a typical sample.The regions are constructed for all users using the SCP procedure.
- Uncertainty quantification: MUSIC-Net yields the smallest SCP radius among the benchmarks while satisfying the prescribed coverage level.Increasing the target coverage level 1 −α enlarges the prediction set.
VI. CONCLUSION
The paper concludes that MUSIC-Net combines two-stage MUSIC with learned LoS feature and distance estimation for reliable near-field multi-user positioning in coherent multipath environments. SCP adds statistically covered prediction regions, while experiments report lower MPER and tighter regions than existing benchmarks.
- Conclusion: MUSIC-Net is an end-to-end DL framework informed by two-stage MUSIC for near-field multi-user positioning in mixed LoS and NLoS multipath environments.The framework integrates a LoS feature extractor and a surrogate distance estimator with two-stage MUSIC.
- Conclusion: Subspace-distance-based losses directly recover LoS user positions without redundant NLoS parameter estimation or subsequent path/source association.This design targets the LoS-positioning objective while avoiding additional multipath-processing steps.
- Conclusion: SCP augments point estimates with prediction regions that provide statistical joint coverage guarantees for all users.The resulting regions quantify uncertainty in MUSIC-Net inference.
- Conclusion: MUSIC-Net achieves lower MPER than existing benchmarks and tighter SCP-calibrated prediction regions.The reported results support accurate LoS localization and reliable UQ in coherent multipath environments.