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arxiv: 2606.17801 · v1 · pith:I2QMF6SYnew · submitted 2026-06-16 · 📡 eess.SP

Joint Direction-of-Arrival and Range Estimation for Millimeter-Wave Uniform Linear Array Radar

Necati Kagan Erkek , Zeynep Gul Pehlivanli This is my paper

Pith reviewed 2026-06-26 23:10 UTC · model grok-4.3

classification 📡 eess.SP
keywords direction-of-arrival estimationrange estimationmillimeter-wave radaruniform linear arrayFFT77 GHzspatial phase modelsinc waveform
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The pith

A 77 GHz uniform linear array radar uses FFT processing on spatial phase samples to jointly estimate target direction and range.

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

The paper develops an FFT-based framework for monostatic uniform linear array radar at 77 GHz that estimates both direction-of-arrival and range from a single set of measurements. It starts from a narrowband sinusoidal waveform to build a spatial phase model, selects an aliasing-free element spacing of 0.97 mm, and sizes the array at 58 elements to reach 2 degree boresight resolution. Numerical tests confirm accurate recovery of a lone target at 30 degrees as well as multiple simultaneous targets. Replacing the waveform with a 1 GHz sinc-modulated signal extends the same array to two-dimensional localization with roughly 0.15 m range resolution. Simulations further map how additive Gaussian noise, wider spacing, and target decorrelation shift the observed FFT peaks.

Core claim

An FFT-based direction-of-arrival and range-estimation framework for a monostatic uniform linear array operating at 77 GHz is presented. A narrowband sinusoidal waveform is used to derive the spatial phase model, determine an aliasing-free inter-element spacing, and select the aperture required to obtain a boresight angular resolution of 2 degree. The resulting design uses an element spacing of 0.97 mm and 58 antenna elements, corresponding to an aperture length of 56.42 mm. Numerical results show accurate angular estimation for a single target at 30 degree and for multiple simultaneous targets. The analysis is further extended to two-dimensional localization by replacing the narrowband wave

What carries the argument

FFT applied to the spatial phase samples collected across the 58-element array, converting phase-progression patterns into distinct spectral peaks at the true target angles.

If this is right

  • The 58-element design delivers 2 degree angular resolution at boresight.
  • A 1 GHz sinc waveform on the same array yields approximately 0.15 m range resolution.
  • Additive complex Gaussian noise, larger element spacing, and target decorrelation each shift or broaden the DOA spectral peaks in measurable ways.
  • Multiple targets produce separate, identifiable peaks when their angles differ sufficiently.

Where Pith is reading between the lines

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

  • Real-world tests could check whether the predicted peaks survive indoor multipath or mutual coupling between elements.
  • The same phase-model approach might be reused at other carrier frequencies by simply rescaling the element spacing to maintain the alias-free condition.
  • Integrating Doppler processing on successive pulses could add velocity estimation without changing the spatial FFT step.
  • The 0.15 m range cell size suggests the method could support coarse mapping of extended objects such as vehicles.

Load-bearing premise

The narrowband far-field spatial phase model derived from the sinusoidal waveform remains valid for the chosen 0.97 mm spacing and 58-element aperture, with no significant near-field effects, multipath, or hardware imperfections altering the FFT peaks.

What would settle it

An experiment that places a single known target at 30 degrees in front of the 58-element array and measures whether the dominant FFT peak falls more than one bin away from the predicted location.

Figures

Figures reproduced from arXiv: 2606.17801 by Necati Kagan Erkek, Zeynep Gul Pehlivanli.

Figure 1
Figure 1. Figure 1: The array contains N antenna elements displaced along the x-axis, with uniform separation dx. The figure depicts nine elements only for illustration; the designed array contains the number of elements derived in Section III-B. A point target is located at range d and angular position θ with respect to boresight [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Path-length difference between adjacent ULA elements. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FFT magnitude versus estimated angle for a single target. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FFT magnitude versus estimated angle for multiple targets. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: Magnitude response versus range after wideband compression. [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Three-dimensional representation of range-compressed data for a [PITH_FULL_IMAGE:figures/full_fig_p005_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Range-compressed data for a decorrelated target. [PITH_FULL_IMAGE:figures/full_fig_p005_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: Aliased FFT magnitude versus estimated angle for excessive antenna [PITH_FULL_IMAGE:figures/full_fig_p005_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Magnitude and range-domain representation for the decorrelated [PITH_FULL_IMAGE:figures/full_fig_p006_12.png] view at source ↗
read the original abstract

An FFT-based direction-of-arrival (DOA) and range-estimation framework for a monostatic uniform linear array (ULA) operating at 77 GHz is presented. A narrowband sinusoidal waveform is used to derive the spatial phase model, determine an aliasing-free inter-element spacing, and select the aperture required to obtain a boresight angular resolution of 2 degree. The resulting design uses an element spacing of 0.97 mm and 58 antenna elements, corresponding to an aperture length of 56.42 mm. Numerical results show accurate angular estimation for a single target at 30 degree and for multiple simultaneous targets. The analysis is further extended to two-dimensional localization by replacing the narrowband waveform with a 1 GHz sinc-modulated signal, which provides an approximate range resolution of 0.15 m. Additional simulations quantify the effects of additive complex Gaussian noise, increased antenna spacing, and target decorrelation on the DOA response.

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

2 major / 2 minor

Summary. The manuscript presents an FFT-based framework for joint DOA and range estimation with a 77 GHz monostatic ULA. A narrowband sinusoidal waveform is used to derive an aliasing-free inter-element spacing of 0.97 mm and select a 58-element aperture of 56.42 mm for 2° boresight resolution. Numerical simulations demonstrate accurate single-target (30°) and multi-target angular estimation; the approach is extended to joint range-angle localization by substituting a 1 GHz sinc waveform (0.15 m range resolution). Additional simulations examine additive complex Gaussian noise, increased spacing, and target decorrelation.

Significance. If the far-field narrowband model remains valid, the work supplies a low-complexity FFT pipeline for mmWave radar that directly yields both angle and range from the same array. The explicit design formulas for spacing and aperture, together with the noise/decorrelaton test suite, constitute a practical contribution. The simulations are a strength in that they quantify performance degradation under realistic impairments rather than claiming ideal conditions only.

major comments (2)
  1. [Numerical results] The numerical results section reports accurate FFT peaks for the chosen 0.97 mm / 58-element geometry but does not state the simulated target range(s). At 77 GHz the 56.42 mm aperture produces a Fraunhofer distance of ~1.63 m; any target inside this boundary violates the plane-wave assumption underlying the spatial phase model (derived in the narrowband section) and can shift or broaden the observed peaks. This directly affects the central accuracy claims.
  2. [Two-dimensional localization extension] The wideband extension replaces the sinusoid with a 1 GHz sinc waveform for range estimation but retains the same spatial phase model without re-derivation or validation. Range-angle coupling across the 58 elements is therefore unexamined and could degrade the joint localization performance reported in that section.
minor comments (2)
  1. The abstract states that 'increased antenna spacing' is simulated, yet the specific spacing values, the resulting aliasing threshold, and the corresponding figures are not cross-referenced in the text.
  2. Notation for the array response vector and the FFT bin indexing should be made consistent between the derivation and the simulation figures to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify important aspects of the far-field assumption and the wideband extension. We address each major comment below and indicate planned revisions to improve the manuscript.

read point-by-point responses

  1. Referee: [Numerical results] The numerical results section reports accurate FFT peaks for the chosen 0.97 mm / 58-element geometry but does not state the simulated target range(s). At 77 GHz the 56.42 mm aperture produces a Fraunhofer distance of ~1.63 m; any target inside this boundary violates the plane-wave assumption underlying the spatial phase model (derived in the narrowband section) and can shift or broaden the observed peaks. This directly affects the central accuracy claims.

    Authors: We agree that the absence of explicit target ranges leaves the far-field validation incomplete. The simulations underlying the reported FFT peaks were performed with targets placed at distances satisfying the Fraunhofer criterion (greater than ~1.63 m). We will revise the Numerical Results section to state the specific ranges employed and add a short verification that the plane-wave model remains valid, thereby directly addressing the concern about potential peak shifts or broadening. revision: yes

  2. Referee: [Two-dimensional localization extension] The wideband extension replaces the sinusoid with a 1 GHz sinc waveform for range estimation but retains the same spatial phase model without re-derivation or validation. Range-angle coupling across the 58 elements is therefore unexamined and could degrade the joint localization performance reported in that section.

    Authors: The spatial phase model is derived under the narrowband approximation at the 77 GHz carrier; the 1 GHz bandwidth corresponds to a fractional bandwidth of only ~1.3 %, which supports retaining the same array response for the joint estimation. We nevertheless recognize that range-angle coupling merits explicit discussion. In the revision we will add a paragraph examining the validity of the approximation for the reported sinc-based range estimation and its implications for the observed localization performance. revision: partial

Circularity Check

0 steps flagged

No significant circularity; standard array formulas and direct simulation

full rationale

The paper derives the spatial phase model directly from the narrowband sinusoidal waveform under far-field plane-wave assumptions, then computes inter-element spacing (to avoid aliasing) and aperture length (for 2° resolution) using standard wavelength-based formulas at 77 GHz. These are not fitted to any outputs. Numerical results are generated by applying the model in simulation; the sinc-waveform extension for range is a direct substitution without re-derivation or parameter fitting. No self-citations, uniqueness theorems, or ansatzes are invoked. The derivation chain is self-contained against external benchmarks and does not reduce any claimed result to its inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on conventional array signal processing assumptions and calculated parameters; no new entities are introduced.

free parameters (1)
  • Element count and aperture length
    58 elements and 56.42 mm aperture chosen to meet the 2 degree boresight resolution target using standard array factor formulas.
axioms (1)
  • domain assumption Narrowband far-field assumption produces a linear spatial phase progression across the ULA that FFT can resolve without aliasing when spacing is below lambda/2.
    Invoked to derive the aliasing-free spacing of 0.97 mm and to justify the FFT-based estimator.

pith-pipeline@v0.9.1-grok · 5700 in / 1375 out tokens · 39960 ms · 2026-06-26T23:10:50.364338+00:00 · methodology

discussion (0)

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Reference graph

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