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arxiv: 2604.21022 · v1 · submitted 2026-04-22 · 📡 eess.SP

The Radon Transform, True Time Delay Beamforming, and Ultra-Wideband Antenna Arrays (Invited Paper)

Tyler Ikehara , Ibrahim Pehlivan , Danijela Cabric , Thomas L. Marzetta This is my paper

Pith reviewed 2026-05-09 23:04 UTC · model grok-4.3

classification 📡 eess.SP
keywords Radon transformtrue time delay beamformingultra-wideband antenna arraysnear-field localizationspace-time signal processingsemblance detection6G FR3
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The pith

True time delay beamforming equals the Radon transform of space-time array measurements.

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

The paper establishes that true time delay beamforming for ultra-wideband signals in large antenna arrays is mathematically the same as taking the Radon transform of the received space-time data. This equivalence lets researchers apply techniques from computer tomography and seismic exploration to handle extreme bandwidth challenges in 6G FR3 operation, where conventional phase-shift methods suffer from beam squint. The approach uses Radon slowness filtering and semblance detection to remove far-field signals, partitions the array to estimate near-field arrival angles, locates sources by triangulation, and extracts individual envelopes by integrating along hyperbolic paths.

Core claim

True time delay beamforming is mathematically equivalent to taking the Radon transform of the space/time measurements. This equivalence permits the direct transfer of Radon transform techniques from tomography and seismology to ultra-wideband antenna array processing, specifically to remove far-field signals, estimate near-field source positions via subarray partitioning and triangulation, and extract individual signal envelopes by integration along hyperbolic trajectories.

What carries the argument

The mathematical equivalence between true time delay beamforming and the Radon transform of space/time measurements, which carries the argument by allowing reuse of Radon-based filtering and detection methods for array signals.

Load-bearing premise

The mathematical equivalence between true time delay beamforming and the Radon transform holds exactly under the wireless propagation model used for the array.

What would settle it

Compute both the true time delay beamformed output and the Radon transform of the same space-time data for a known source position and check if the results match exactly.

Figures

Figures reproduced from arXiv: 2604.21022 by Danijela Cabric, Ibrahim Pehlivan, Thomas L. Marzetta, Tyler Ikehara.

Figure 2
Figure 2. Figure 2: Block diagram describing the proposed method of [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Radon transform of the linear array space/time data [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A 251 element linear array receives data from five [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Plot of weighted semblance, S(px), as described in (6) with an arbitrary threshold ϵ = 0.2. If S(px) ≥ ϵ, the slowness filter will be H(px) = 0, and all other values of H(px) = 1. 8. The near-field region boundary of an array increases with the square of the array aperture [14], and a user who falls within the near-field region of the entire array can be in the far-field region of a sub-array. Therefore, b… view at source ↗
Figure 7
Figure 7. Figure 7: Inverse Radon transform of the slowness filtered data. [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Block diagram describing the sub-array based [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
read the original abstract

The FR3 band has emerged as the major focus of 6G wireless research. FR3 cellular operation presents the challenge of extreme bandwidth combined with physically large antenna arrays. In this regime, conventional phase-shift beamforming entails a loss of coherence (beam-squint), and has to be replaced by true time delay beamforming (TTD). It happens that TTD is mathematically equivalent to taking the Radon transform of the space/time measurements. We exploit fifty years of research in the application of the Radon transform to computer tomography and to seismic exploration to elucidate the workings of TTD. We use the Radon transform combined with semblance detection and Radon slowness filtering to remove far-field signals from the measured space/time signals from a linear array, leaving only near-field signals. In turn we partition the array into sub-arrays. For each sub-array we estimate, via the semblance Radon transform, the angles-of-arrival of the near-field signals. We then use triangulation to estimate the coordinates of the near-field sources. Finally we integrate the original space/time data along hyperbolic trajectories to extract the individual near-field signal envelopes.

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

3 major / 2 minor

Summary. The paper claims that true time delay (TTD) beamforming in ultra-wideband arrays for the FR3 band is mathematically equivalent to the Radon transform of space-time measurements. It exploits this equivalence, drawing on Radon methods from tomography and seismology, to suppress far-field signals via semblance detection and slowness filtering, estimate near-field angles-of-arrival through sub-array processing and triangulation, and extract near-field signals by integrating along hyperbolic trajectories.

Significance. If the equivalence is rigorously established and the Radon techniques transfer effectively to the electromagnetic propagation model, the work could provide a principled, cross-domain framework for beam-squint-free processing and near-field localization in wideband 6G arrays. The reuse of established semblance and Radon filtering methods offers a structured alternative to conventional phase-shift approaches.

major comments (3)
  1. [Abstract] Abstract: The assertion that TTD beamforming 'is mathematically equivalent to taking the Radon transform of the space/time measurements' is stated without a derivation, explicit mapping, or proof. This equivalence is load-bearing for the subsequent far-field suppression and near-field extraction steps and requires demonstration of how time-delay summation corresponds to Radon line integrals (including any normalization or geometry factors).
  2. [Abstract] Abstract: The manuscript employs the standard (linear) Radon transform for far-field removal but switches to hyperbolic integration for near-field signals. It does not verify whether the claimed equivalence holds under the wireless EM model, which includes spherical spreading loss, multipath, and frequency-dependent element patterns that are absent from the tomography and seismology contexts.
  3. [Abstract] Abstract: No error analysis, simulation results, or validation data are supplied to quantify the performance of semblance-based detection, far-field suppression, or triangulation accuracy, leaving the central claims without demonstrated quantitative support.
minor comments (2)
  1. Clarify the precise definition and implementation of the 'semblance Radon transform' and 'Radon slowness filtering' steps, including any parameter choices or thresholds.
  2. Specify the criteria for partitioning the array into sub-arrays and how sub-array size affects angle-of-arrival estimation accuracy.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their insightful comments, which have helped us improve the clarity and rigor of our manuscript. We address each of the major comments below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that TTD beamforming 'is mathematically equivalent to taking the Radon transform of the space/time measurements' is stated without a derivation, explicit mapping, or proof. This equivalence is load-bearing for the subsequent far-field suppression and near-field extraction steps and requires demonstration of how time-delay summation corresponds to Radon line integrals (including any normalization or geometry factors).

    Authors: We agree that an explicit derivation strengthens the paper. In the revised manuscript, we will include a dedicated subsection deriving the equivalence between TTD beamforming and the Radon transform. The time-delay summation in TTD corresponds directly to the line integrals in the Radon transform for a given slowness (or angle), with appropriate discretization and normalization factors that we will explicitly map out. revision: yes

  2. Referee: [Abstract] Abstract: The manuscript employs the standard (linear) Radon transform for far-field removal but switches to hyperbolic integration for near-field signals. It does not verify whether the claimed equivalence holds under the wireless EM model, which includes spherical spreading loss, multipath, and frequency-dependent element patterns that are absent from the tomography and seismology contexts.

    Authors: The switch is intentional and consistent with the propagation model: linear Radon for plane waves (far-field), hyperbolic for spherical waves (near-field). The core equivalence is in the delay-and-sum operation, which remains valid under the standard EM far/near field models for delays, though amplitudes are affected by spreading loss. We assume no multipath and ideal elements for this analysis, as is typical; we will add explicit discussion of these assumptions and their impact on the equivalence. revision: partial

  3. Referee: [Abstract] Abstract: No error analysis, simulation results, or validation data are supplied to quantify the performance of semblance-based detection, far-field suppression, or triangulation accuracy, leaving the central claims without demonstrated quantitative support.

    Authors: We recognize that quantitative validation would strengthen the claims. Although the manuscript emphasizes the theoretical framework, we will add a new section with simulation results in the revised version, including performance metrics for semblance detection, suppression of far-field signals, and accuracy of near-field triangulation under FR3 band conditions. revision: yes

Circularity Check

0 steps flagged

No circularity: equivalence to Radon transform drawn from external literature

full rationale

The paper states that TTD beamforming is mathematically equivalent to the Radon transform of space-time measurements and then reuses fifty years of established Radon methods from tomography and seismology. No parameters are fitted to a data subset and then renamed as a prediction of a related quantity. No load-bearing step reduces to a self-citation whose authors overlap with the present paper, nor is any uniqueness theorem imported from the authors' prior work. The central steps (slowness filtering, semblance detection, sub-array angle estimation, and hyperbolic integration) are applications of known Radon properties rather than tautological redefinitions of the paper's own inputs. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on one domain assumption: the exact equivalence of TTD beamforming to the Radon transform of space-time measurements. No free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption True time delay beamforming is mathematically equivalent to taking the Radon transform of the space/time measurements.
    Explicitly stated in the abstract as the foundational insight that enables reuse of tomography and seismic techniques.

pith-pipeline@v0.9.0 · 5518 in / 1420 out tokens · 29392 ms · 2026-05-09T23:04:44.567749+00:00 · methodology

discussion (0)

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