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arxiv: 2604.08160 · v1 · submitted 2026-04-09 · 📡 eess.SP

Joint Range-Angle Estimation in Near-Field ISAC System using Uniform Circular Array

Lorenzo Zaniboni , Mark F. Flanagan This is my paper

Pith reviewed 2026-05-10 17:56 UTC · model grok-4.3

classification 📡 eess.SP
keywords near-field ISACuniform circular arrayrange-angle estimationCRLBmaximum likelihood estimationOFDMmonostatic sensingbeamforming
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The pith

A 0.5 m radius for a uniform circular array best balances joint range-angle estimation accuracy and received signal strength in near-field ISAC.

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

This paper develops a continuous-time channel model for near-field integrated sensing and communication that includes per-element delays, Doppler shifts, and spherical wavefront effects under OFDM signaling. Using a uniform circular array at the base station for monostatic sensing of a single user equipment, it derives a closed-form Cramer-Rao lower bound on joint range-angle estimation, designs an optimal transmit beamformer with Riemannian gradient descent, and formulates a maximum likelihood estimator. Monte Carlo results demonstrate that while larger array radii improve the theoretical bound, they reduce received SNR and can cause the practical estimator to degrade. Among tested sizes the 0.5 m radius sustains the highest SNR across distances and therefore yields the best combined estimation and communication performance.

Core claim

The authors show that the uniform circular array's rotational symmetry creates an angle-invariant near-field region. Building on the wideband channel model, the closed-form CRLB tightens with increasing radius while the received SNR at the base station falls because of spherical-wave geometry; the maximum-likelihood estimator therefore reaches its best operating point at an intermediate radius of 0.5 m rather than at the largest aperture evaluated.

What carries the argument

The continuous-time wideband channel model that embeds per-element delay, Doppler, and spherical wavefront geometry for OFDM signaling, which directly supplies the closed-form CRLB, the Riemannian beamformer, and the joint range-angle ML estimator.

If this is right

  • Increasing UCA radius reduces the CRLB on range and angle estimates.
  • The same radius increase lowers received SNR at any fixed user distance.
  • The ML estimator can fall below its convergence threshold when SNR drops too far.
  • Joint estimation and communication performance peaks at an intermediate radius rather than the maximum aperture.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same radius-dependent SNR penalty may appear in other array geometries or carrier frequencies not examined in the simulations.
  • An adaptive system that adjusts effective aperture size according to estimated distance could exploit the trade-off in real time.
  • Hardware validation of the predicted SNR degradation would directly test whether the continuous-time model captures the dominant propagation effects.

Load-bearing premise

The continuous-time channel model that adds per-element delay, Doppler shifts, and spherical wavefront geometry accurately represents the real wideband near-field propagation environment under OFDM.

What would settle it

A hardware measurement campaign that records received SNR versus distance for uniform circular arrays of several radii; if SNR does not fall with larger radius or if the ML estimator achieves lower error at radii larger than 0.5 m, the reported aperture-SNR trade-off would be contradicted.

Figures

Figures reproduced from arXiv: 2604.08160 by Lorenzo Zaniboni, Mark F. Flanagan.

Figure 1
Figure 1. Figure 1: Schematic of the system model. captures the phase and amplitude response of each element at position (d, θ), is a(d, θ) = e j 2π λ d √ Na h e −j 2π λ r1 , . . . , e−j 2π λ rNa i ∈ C Na×1 . (2) Since the transmitter (Tx) and receiver (Rx) are co-located (monostatic), the same vector a(d, θ) describes both the Tx and Rx array responses. Unlike the ULA geometry studied in [5], [6], the rotational symmetry of … view at source ↗
Figure 2
Figure 2. Figure 2: RMSE values of d at the BS for different values of UCA radius R. -70 -60 -50 -40 -30 -20 -10 SNR [dB] 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 A n gle R M S E [°] 400m 300m 200m 150m 100m 75m 50m 25m 10m R = 0.5 m (RMSE) R = 1.0 m (RMSE) R = 2.0 m (RMSE) R = 5.0 m (RMSE) R = 0.5 m (CRLB) R = 1.0 m (CRLB) R = 2.0 m (CRLB) R = 5.0 m (CRLB) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: RMSE values of θ at the BS for different values of UCA radius R. throughout the evaluated range. The threshold effect of ML estimators [13] refers to the phenomenon whereby, below a critical SNR, the likelihood surface contains multiple compet￾ing local minima and outlier estimates dominate, causing the RMSE to far exceed the CRLB regardless of the estimator implementation. At d = 10 m the range RMSE alrea… view at source ↗
Figure 4
Figure 4. Figure 4: Achievable rate (solid) and optimal rate (dashed) vs. SNR for different [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

This paper studies joint range-angle estimation and communication in the NF ISAC systems, where the BS serves a single UE whose position is simultaneously estimated via monostatic sensing. Unlike the ULA, the UCA provides an angle-invariant NF region due to its rotational symmetry. To capture the full wideband NF propagation environment, we develop a continuous-time channel model incorporating per-element delay, Doppler shifts, and spherical wavefront geometry under OFDM signaling. Building on this model, we derive the closed-form CRLB for joint range-angle estimation of the UE position, design an optimal transmit beamformer via Riemannian gradient descent, and formulate a joint range-angle ML estimator. Monte Carlo simulations confirm a fundamental aperture-versus-SNR trade-off in NF-ISAC: while a larger UCA radius tightens the CRLB, it simultaneously reduces the received SNR at any given distance, pushing the maximum likelihood estimator below its convergence threshold and degrading practical performance. Among the evaluated configurations, R = 0.5 m achieves the best joint estimation and communication performance at the BS} by sustaining the highest received SNR throughout the evaluated range.

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.

Referee Report

1 major / 2 minor

Summary. The manuscript studies joint range-angle estimation and communication in near-field ISAC systems with a uniform circular array (UCA) at the base station. It develops a continuous-time channel model incorporating per-element delay, Doppler shifts, and spherical wavefront geometry under OFDM signaling. Building on this model, the authors derive a closed-form CRLB for joint range-angle estimation of the UE, design a transmit beamformer via Riemannian gradient descent, and formulate a joint ML estimator. Monte Carlo simulations demonstrate an aperture-SNR trade-off, concluding that a UCA radius of R = 0.5 m achieves the best joint estimation and communication performance by sustaining the highest received SNR.

Significance. If the channel model holds, the work usefully quantifies the aperture-SNR trade-off in NF-ISAC with UCAs and supplies a closed-form CRLB together with a Riemannian beamformer as practical tools for system design. The explicit identification of an optimal radius provides concrete guidance for array sizing in monostatic NF-ISAC.

major comments (1)
  1. [Abstract and Simulation Results] Abstract and Simulation Results section: the central claim that R = 0.5 m yields the best joint performance rests entirely on Monte Carlo runs driven by the proposed continuous-time NF channel model. Because the model (per-element delay, Doppler, spherical wavefront) is not cross-validated against measured channels or full-wave EM simulation, inaccuracies in wideband effects such as mutual coupling could alter the received-SNR curves and change which radius ranks highest.
minor comments (2)
  1. [Abstract] The abstract would benefit from stating the number of Monte Carlo trials performed and the exact set of radii evaluated, so that the robustness of the R = 0.5 m optimum can be assessed directly.
  2. [Notation and Figures] Notation for range, angle, and array radius should be checked for consistency across the CRLB derivation, beamformer design, and simulation figures.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the constructive feedback on the channel model validation. We address the concern point by point below and outline targeted revisions to clarify assumptions and limitations without altering the core theoretical contributions.

read point-by-point responses

  1. Referee: [Abstract and Simulation Results] Abstract and Simulation Results section: the central claim that R = 0.5 m yields the best joint performance rests entirely on Monte Carlo runs driven by the proposed continuous-time NF channel model. Because the model (per-element delay, Doppler, spherical wavefront) is not cross-validated against measured channels or full-wave EM simulation, inaccuracies in wideband effects such as mutual coupling could alter the received-SNR curves and change which radius ranks highest.

    Authors: We agree that the central claim relies on Monte Carlo simulations under the proposed continuous-time near-field channel model, which incorporates per-element delay, Doppler, and spherical wavefront geometry but does not include empirical cross-validation. This modeling approach follows standard first-principles derivations used in the near-field ISAC and massive MIMO literature for analyzing fundamental trade-offs. Mutual coupling and other wideband effects are neglected under the ideal isotropic element assumption, as is common in theoretical CRLB and beamforming studies. To address the referee's concern, we will revise the manuscript by: (1) expanding Section II (Channel Model) with an explicit subsection on modeling assumptions and limitations, including the omission of mutual coupling; (2) adding a paragraph in the Simulation Results section noting that the R = 0.5 m optimum is obtained under these ideal conditions and that coupling could quantitatively shift the curves, though the qualitative aperture-SNR trade-off driven by geometry and path loss is expected to persist. We believe these clarifications strengthen the paper while preserving its scope as a theoretical contribution. revision: partial

standing simulated objections not resolved
  • Empirical cross-validation of the continuous-time NF channel model against measured channels or full-wave EM simulations, as this requires new experimental campaigns and hardware measurements outside the theoretical scope of the current work.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper develops a continuous-time NF channel model incorporating per-element delay, Doppler, and spherical wavefronts under OFDM, then derives the closed-form CRLB for joint range-angle estimation directly from that model, designs the transmit beamformer using standard Riemannian gradient descent, and formulates the joint ML estimator. Monte Carlo simulations using the same model evaluate the aperture-SNR trade-off and identify R = 0.5 m as optimal. None of these steps reduce by construction to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations; each mathematical step (CRLB derivation, optimization, estimator) is independent of the final simulation ranking. The paper is self-contained against its internal benchmarks with no equations that force the claimed result tautologically.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on a domain-standard continuous-time NF channel model whose accuracy is assumed rather than independently validated in the abstract.

axioms (1)
  • domain assumption The continuous-time channel model incorporates per-element delay, Doppler shifts, and spherical wavefront geometry under OFDM signaling.
    This model is invoked as the foundation for the CRLB derivation and ML estimator.

pith-pipeline@v0.9.0 · 5491 in / 1245 out tokens · 66446 ms · 2026-05-10T17:56:44.956335+00:00 · methodology

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Reference graph

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