arxiv: 2605.03389 · v1 · submitted 2026-05-05 · 📡 eess.SP

Recognition: unknown

Near-field Wideband Multi-User Localization using NFMR-Net

Pearl Hetul Shah , Srikar Sharma Sadhu , Praful D. Mankar

Authors on Pith no claims yet

Pith reviewed 2026-05-07 14:55 UTC · model grok-4.3

classification 📡 eess.SP

keywords near-field localizationmulti-userwidebanddeep learningMUSIC algorithmZadoff-Chu pilotsNFMR-Netchannel estimation

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The pith

NFMR-Net refines coarse near-field localization estimates from Zadoff-Chu pilots to outperform 2D MUSIC in multi-user scenarios.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a deep learning approach for localizing multiple users in the near-field region using wideband signals. It starts by using Zadoff-Chu sequences to reduce interference and estimate the channel matrix, from which the line-of-sight array response is extracted. Coarse range and angle estimates are obtained via parabolic interpolation and 2D MUSIC, then fed into NFMR-Net for refinement. A sympathetic reader would care because accurate near-field localization matters for applications like 6G communications and radar where far-field assumptions fail.

Core claim

The paper claims that the near-field music refinement network (NFMR-Net), consisting of separate sub-networks for range and angle, can refine coarse estimates derived from the LoS array response to achieve better localization performance than the conventional 2D MUSIC algorithm, as shown through numerical analysis.

What carries the argument

NFMR-Net, a neural network with separate sub-networks that takes the extracted LoS array response and coarse estimates as input to refine range and angle parameters.

Load-bearing premise

The line-of-sight array response extracted from the delay-tap energy profile of the multi-tap channel matrix estimated via Zadoff-Chu pilots is sufficiently accurate to serve as input for both coarse estimation and NFMR-Net refinement.

What would settle it

A simulation or measurement where the channel estimation has significant interference residuals or model mismatch, showing if the localization error remains lower than 2D MUSIC or not.

Figures

Figures reproduced from arXiv: 2605.03389 by Pearl Hetul Shah, Praful D. Mankar, Srikar Sharma Sadhu.

**Figure 1.** Figure 1: An Illustration of the System Model to detect a new path and obtain coarse estimates of its range, azimuth and elevation AoAs, and finally refines these estimates using damped Newton refinement method. Further, a twostage beamspace MUSIC method is proposed in [11] for nearfield localization using XL-MIMO systems. An optimally precompensated distance based codebook is applied enable 1D sequential search… view at source ↗

**Figure 2.** Figure 2: Proposed NFMR-Net pipeline. TABLE I SIMULATION PARAMETERS Parameter Symbol Value Carrier frequency fc 2.4 GHz Sample time Ts 5 × 10−9 s Delay resolution cTs 1.5 m Antenna spacing dA 0.5λ ULA size M 41 Fraunhofer distance dF 100 m Number of UEs K 3 Number of obstacles P 5 Absorption loss β 0.5 Pilot sequence length N 256 Number of transmissions T 4 Local range window ∆r 8 m Local angle window ∆w 10◦ SNR ran… view at source ↗

**Figure 3.** Figure 3: Scatter plots of range (left) and angle (right) parameters. view at source ↗

**Figure 4.** Figure 4: RMSE vs. SNR for range (left) and angle (right). view at source ↗

**Figure 5.** Figure 5: RMSE vs. N, for range (left) and angle (right), at SNR = 10 dB view at source ↗

read the original abstract

This paper proposes a deep learning based method for wideband near-field multi-user localization. In particular, the proposed approach utilizes the Zadoff-Chu (ZC) sequence based pilots to mitigate the inter-user interference, which in turn aids the estimation of the multi-tap channel matrix. From this channel matrix, we extract the line-of-sight (LoS) array response based on the delay-tap energy profile. The LoS delay-tap is further refined using parabolic interpolation to obtain the coarse estimate of range parameter. Next, the extracted LoS array response is used to obtain the coarse angle estimate using 2D MUSIC algorithm. These coarse estimates are further refined using the near-field music refinement network (NFMR-Net), which involves separate sub-networks for range and angle estimations. Through numerical analysis, the proposed NFMR-Net is demonstrated to outperform conventional 2D MUSIC algorithm.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

NFMR-Net adds a targeted neural refinement step on top of ZC pilots, parabolic interpolation, and 2D MUSIC for near-field multi-user localization, but the simulation results are too lightly documented to confirm the gains are reliable.

read the letter

The paper's core contribution is a hybrid pipeline: Zadoff-Chu pilots reduce inter-user interference to estimate the multi-tap channel, the LoS tap is picked from the delay energy profile and refined with parabolic interpolation for range, 2D MUSIC gives a coarse angle, and then NFMR-Net's two separate sub-networks refine both parameters. This specific two-branch refinement network for near-field range and angle is new relative to the cited baselines. The approach does a reasonable job of keeping the classical steps intact while adding a lightweight neural correction, which avoids throwing out established tools that already work for coarse estimation in wideband settings. Credit is due for targeting the practical issue of multi-user interference in near-field scenarios that matter for 6G positioning. The method stays grounded in standard signal-processing steps rather than claiming a full replacement. The main weakness is the evaluation. The abstract only states that numerical analysis shows NFMR-Net beats plain 2D MUSIC, with no error bars, no dataset description, no ablation on the network branches, and no comparison against stronger recent baselines. The stress-test point about LoS array response extraction is worth taking seriously: if the delay-tap selection or parabolic step introduces even modest distortion from finite ZC length, residual interference, or timing offsets, that error feeds directly into both MUSIC and the neural refinement. Without seeing the full simulation setup or sensitivity checks, it is difficult to know whether the reported improvement is robust or tied to clean extraction conditions. The paper is aimed at researchers working on near-field wireless localization and hybrid classical-DL methods for 6G. A reader already familiar with MUSIC and ZC sequences could pick up the NFMR-Net architecture as a concrete example to build on. I would send it to peer review so the authors can supply the missing simulation details, ablations, and checks on the extraction step; the idea is incremental but coherent enough to deserve referee time once the evidence is filled in.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes NFMR-Net, a hybrid deep-learning method for wideband near-field multi-user localization. Zadoff-Chu pilots are used to estimate the multi-tap channel matrix while mitigating inter-user interference; the LoS array response is extracted from the delay-tap energy profile, refined by parabolic interpolation for a coarse range estimate, and fed to 2D MUSIC for a coarse angle estimate. Separate sub-networks then refine the range and angle estimates. Numerical simulations are reported to show that NFMR-Net outperforms conventional 2D MUSIC.

Significance. If the numerical gains prove robust, the hybrid coarse-estimate-plus-refinement architecture could offer a practical route to improved accuracy in near-field wideband localization without abandoning established signal-processing primitives. The explicit use of ZC sequences for interference control and the separation of range and angle sub-networks are concrete design choices that could be reused in related 5G/6G positioning tasks.

major comments (2)

[Abstract / Numerical results] Abstract and numerical-results section: the central performance claim rests on unspecified numerical simulations that provide neither error bars, Monte-Carlo trial counts, dataset generation details, nor ablation studies on the LoS-extraction step. Without these, it is impossible to determine whether the reported improvement over 2D MUSIC is statistically significant or an artifact of idealized channel conditions.
[Proposed method] Proposed-method description (LoS array-response extraction): the pipeline assumes that the delay-tap energy profile obtained from ZC-based multi-tap channel estimates yields an accurate LoS array response even in the presence of finite-length ZC correlation sidelobes, delay spread, and possible timing/Doppler residuals. No analytic bound or sensitivity analysis is supplied to quantify how residual interference or tap-selection errors propagate into both the 2D MUSIC coarse estimate and the subsequent NFMR-Net inputs.

minor comments (1)

[Proposed method] Notation for the parabolic-interpolation step and the exact definition of the input feature vector to each NFMR-Net sub-network should be stated explicitly (e.g., as an equation) rather than described only in prose.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the positive assessment of the potential practical value of the hybrid architecture. We address each major comment below and indicate planned revisions.

read point-by-point responses

Referee: [Abstract / Numerical results] Abstract and numerical-results section: the central performance claim rests on unspecified numerical simulations that provide neither error bars, Monte-Carlo trial counts, dataset generation details, nor ablation studies on the LoS-extraction step. Without these, it is impossible to determine whether the reported improvement over 2D MUSIC is statistically significant or an artifact of idealized channel conditions.

Authors: We agree that the current description of the numerical results lacks sufficient detail for independent assessment of statistical significance. In the revised manuscript we will report the exact number of Monte-Carlo trials, include error bars (standard deviation across trials) on all curves, provide complete dataset-generation parameters (carrier frequency, bandwidth, array size, user locations, noise variance, and channel model), and add an ablation study isolating the contribution of the LoS-extraction and parabolic-interpolation steps. These additions will allow readers to judge whether the observed gains are robust. revision: yes
Referee: [Proposed method] Proposed-method description (LoS array-response extraction): the pipeline assumes that the delay-tap energy profile obtained from ZC-based multi-tap channel estimates yields an accurate LoS array response even in the presence of finite-length ZC correlation sidelobes, delay spread, and possible timing/Doppler residuals. No analytic bound or sensitivity analysis is supplied to quantify how residual interference or tap-selection errors propagate into both the 2D MUSIC coarse estimate and the subsequent NFMR-Net inputs.

Authors: ZC sequences are selected precisely because their ideal periodic autocorrelation minimizes sidelobes and inter-user interference; the multi-tap estimation step further exploits this property. We nevertheless acknowledge that the manuscript supplies neither an analytic error-propagation bound nor a dedicated sensitivity study. In the revision we will add a new subsection that derives a first-order bound on the perturbation of the extracted LoS vector due to finite-length correlation sidelobes and residual timing/Doppler errors, and we will complement it with Monte-Carlo sensitivity curves showing how these perturbations affect both the coarse 2D-MUSIC estimates and the final NFMR-Net accuracy under controlled levels of delay spread and synchronization error. revision: yes

Circularity Check

0 steps flagged

No circularity: NFMR-Net pipeline uses standard estimation tools plus independent neural refinement, with outperformance shown numerically

full rationale

The paper describes a processing chain starting from ZC-pilot channel estimation, LoS tap extraction via energy profile and parabolic interpolation, coarse 2D MUSIC angle estimation, and refinement by NFMR-Net sub-networks. The central claim of outperformance over 2D MUSIC is supported solely by numerical simulations rather than any closed-form derivation or fitted parameter that reduces to the input by construction. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing steps; the method remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The approach rests on standard near-field wideband channel assumptions and the effectiveness of ZC sequences for interference mitigation; the neural network itself introduces many implicit parameters whose values are learned from simulation data.

free parameters (1)

NFMR-Net weights and hyperparameters
Deep network parameters fitted during training on simulated channel data; exact architecture and training details not provided in abstract.

axioms (2)

domain assumption Zadoff-Chu sequences enable accurate multi-tap channel matrix estimation by mitigating inter-user interference
Invoked to justify extraction of LoS array response from the estimated channel.
domain assumption Delay-tap energy profile reliably identifies the LoS component in near-field wideband channels
Used to select the array response for subsequent MUSIC and refinement steps.

invented entities (1)

NFMR-Net no independent evidence
purpose: Refine coarse range and angle estimates from traditional methods
New deep learning architecture with separate sub-networks for range and angle; no independent evidence provided beyond numerical tests.

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Reference graph

Works this paper leans on

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