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Ray Antenna Array Achieves Uniform Angular Resolution Cost-Effectively for Low-Altitude UAV Swarm ISAC

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Ray antenna arrays give uniform angular resolution in every direction, and the paper applies that property to low-altitude UAV-swarm ISAC.

desk verdict A correct but idealized resolution theorem; the discrete-array gap needs quantifying before this is ready. read the letter →

arxiv 2505.10306 v1 pith:MOTVOQCR submitted 2025-05-15 eess.SP

Haoyu Jiang , Yong Zeng This is my paper · ORCID
classification eess.SP
keywords rayantennaarrayuniformangularresolutionintegratedsensingandcommunicationUAVswarmOFDMISACMUSICangleestimationbeampatternhybridbeamforming
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to establish that a ray antenna array (RAA) — $N$ simple uniform linear arrays (sULAs) of $M$ directly connected elements arranged radially — resolves targets with the same angular accuracy $\gamma_{\rm RAA}=\arcsin(2/M)$ no matter which direction they come from. If that holds, it removes the main blind spot of conventional uniform linear arrays, whose resolution degrades as a target moves toward endfire, and it does so without expensive phase shifters. The paper derives the beam pattern, designs the ray orientations and ray selection network, and gives a complete OFDM-ISAC sensing pipeline for low-altitude UAV swarms: MUSIC for angle-of-arrival, zero-forcing spatial filtering, and a 2-D Periodogram for delay and Doppler. Simulations against DFT-codebook hybrid beamforming show RAA keeping angle RMSE flat and communication rate higher while ULA fails as the swarm moves off-boresight.

What carries the argument

The load-bearing object is the Dirichlet kernel $H_M(x)=\frac{1}{M}\sum_{m=0}^{M-1}e^{j\pi m x}=e^{j\pi(M-1)x/2}\frac{\sin(\pi Mx/2)}{M\sin(\pi x/2)}$, evaluated at $x=\sin(\theta-\eta_n)$ for an sULA. Its zeros at $x=\pm 2/M$ make the first nulls of an aligned sULA symmetric in angle, independent of $\theta'$; in a ULA the same kernel appears at $\sin\theta-\sin\theta'$, so its zeros are not symmetric in angle. The ray selection network then chooses the strongest sULA outputs, so beamforming is replaced by spatial selection and no phase shifters are needed.

What would settle it

For $M=8$, take a target at $\theta'=0.15$ rad between the two nearest ray orientations $\eta_0=0$ and $\eta_1=\arcsin(2/8)\approx 0.2527$ rad. The selected sULA's nulls lie at $\theta=\pm 0.2527$ rad, so the distances from the target to the left and right nulls are approximately 0.4027 rad and 0.1027 rad, not both equal to the claimed $\gamma_{\rm RAA}=0.2527$ rad; measuring the actual two-target resolution at such off-grid angles against Theorem 1 would settle whether the discrete RAA really has constant resolution.

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Extended reading notes

Core claim

With an sULA aligned exactly to the desired direction $\theta'$, the paper proves (Theorem 1) that the RAA beam pattern is $M\sqrt{G(\theta-\theta')}\,|H_M(\sin(\theta-\theta'))|$, whose first nulls are at $\theta'\pm\arcsin(2/M)$; hence $\gamma_{\rm RAA}(\theta')\equiv\arcsin(2/M)$. The paper contrasts this with a ULA, whose pattern has the Dirichlet kernel in $\sin\theta-\sin\theta'$, giving $\gamma_{\rm ULA}(\theta')=\frac{1}{2}[\arcsin(\sin\theta'+2/M)-\arcsin(\sin\theta'-2/M)]$, which grows with $|\theta'|$. It then proves $\gamma_{\rm ULA}(\theta')\ge\gamma_{\rm RAA}$ with equality only at $\theta'=0$, so RAA has no worse and generally better angular resolution. Because each sULA covers only a small angular sector, the array can also use more directional elements and obtain higher beamforming gain, and the discrete orientation rule $\eta_n=n\arcsin(2/M)$ makes adjacent sULAs orthogonal.

Load-bearing premise

The constant-resolution formula assumes a target direction can always be matched exactly by the orientation of some sULA; the implemented RAA has only finitely many discrete orientations, so off-grid targets see an asymmetric main lobe whose resolution error the paper does not quantify.

Editorial extensions

If this is right

  • For a swarm near the array endfire, two targets separated by about $\arcsin(2/M)$ (about $0.9^\circ$ for $M=128$) remain resolvable with RAA, while a ULA of the same gain needs a larger separation and eventually cannot resolve them at all.
  • The communication rate no longer collapses for users far off-boresight, since the uniform beam pattern bounds inter-user interference in every direction rather than only near broadside.
  • The OFDM sensing pipeline (MUSIC angle estimation, zero-forcing spatial filtering, and 2-D Periodogram) gives separated delay-Doppler maps for each UAV with only $N_{\rm RF}\ll N$ radio-frequency chains.
  • Hardware cost drops because each sULA's elements are summed directly and the RSN uses switches instead of phase shifters; the paper quotes a commercial phase-shifter-switch example where RAA costs less than one percent of hybrid beamforming.
  • The price is physical size: RAA needs more antenna elements and a larger aperture than ULA, but the extra size is less problematic at millimeter-wave and terahertz wavelengths.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: with the discrete orientations actually implemented, the resolution should oscillate slightly as a target moves between two adjacent sULA orientations; computing that ripple and choosing whether extra rays are worth the added aperture is a natural follow-up.
  • Editorial inference: the same $\sin(\theta-\theta')$ versus $\sin\theta-\sin\theta'$ distinction suggests that other geometries, such as arc or cylindrical arrays, may inherit a form of uniform resolution while trading aperture size.
  • Editorial inference: the energy-based ray selection assumes all sULA outputs can be swept to pick the strongest; a compressed or fast-switching selection could lower the sweep overhead without changing the resolution theorem.
  • Editorial inference: near-field UAV targets would break the plane-wave assumption behind the Dirichlet-kernel nulls, so testing whether uniform resolution survives in near-field ISAC is the next regime worth checking.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper proposes the ray antenna array (RAA) as a cost-effective multi-antenna architecture for low-altitude UAV swarm ISAC. An RAA consists of a set of simple uniform linear arrays (sULAs) with distinct fixed orientations, each with its elements directly combined, plus a ray selection network (RSN) that connects a subset of sULAs to RF chains. The authors derive the array response model, analyze the beam pattern of a single sULA, and claim that RAA achieves direction-independent angular resolution γ_RAA(θ′) = arcsin(2/M) (Theorem 1). They compare this with the resolution of a conventional ULA (Theorems 2 and 3), concluding that RAA is never worse and is strictly better away from boresight. They then design an OFDM-ISAC sensing algorithm combining MUSIC-based AoA estimation, zero-forcing spatial filtering, and 2D Periodogram for delay/Doppler estimation, with simulations showing improved resolution and communication rate over ULA.

Significance. The uniform-angular-resolution property, if established for the actual discrete RAA, would be a genuinely useful contribution: it would provide a phase-shifter-free array that maintains good angular resolution for targets far from boresight, which is directly relevant to low-altitude UAV swarm sensing. The paper's analytical formulas for the sULA beam pattern and the ULA/RAA resolution comparison are clean and self-consistent under the stated idealizing assumptions. The proposed receive processing chain (MUSIC + ZF + 2D Periodogram) is complete and the simulation study is reasonably extensive. The strengths of the paper are its closed-form beam-pattern analysis for the idealized continuously rotatable sULA, the explicit comparison theorems for ULA, and the concrete algorithm and numerical demonstrations.

major comments (3)
  1. [§IV.A, Theorem 1 vs. Eq. (18)] Theorem 1 is proved by setting the sULA orientation η exactly equal to the desired direction θ′ in Eqs. (8), (12), and (16). However, the designed RAA in Eq. (18) has only discrete orientations η_n = n arcsin(2/M). For a target at an arbitrary θ′, the RSN selects the nearest sULA with offset δ = θ′ − η_n, 0 < |δ| ≤ arcsin(2/M)/2. The response at θ′ is then reduced by up to |H_M(sin(δ_max))| ≈ 0.64 (about −3.9 dB for M = 128), and the first nulls are at θ′ − (γ+δ) and θ′ + (γ−δ), asymmetric about θ′. The paper does not quantify this off-grid behaviour or prove that the uniform-resolution claim holds for the discrete RAA used in the simulations and algorithms; this is a load-bearing gap because uniform resolution is the paper's headline contribution.
  2. [§IV.A, after Eq. (18)] The assertion that RAA achieves higher beamforming gain than ULA by using directional antenna elements is stated to be 'rigorously proved in [38]', which is described as 'in preparation' and thus not available to the reader. Since higher beamforming gain is listed as one of the three main advantages of RAA and is used to explain the communication-rate results in Fig. 10, the proof should either be included in this paper or the claim should be explicitly presented as an assumption depending on the chosen element pattern models, rather than as an externally established fact.
  3. [Appendix A, proof of Theorem 3] The derivation of d²γ_ULA/dx² is not correct as written. The paper writes dγ_ULA/dx = 4x/(MΔ) and then concludes d²γ_ULA/dx² = 4/(MΔ), but Δ is a function of x through u = x+2/M and v = x−2/M, so the second derivative must include a term involving dΔ/dx. The conclusion γ_ULA(θ′) ≥ γ_RAA may still be true, but the proof in the appendix is incomplete and should be replaced with a correct convexity argument (e.g., showing that the second derivative of arcsin is positive on the relevant interval).
minor comments (5)
  1. [Eq. (38)] The MUSIC spectrum is written as P_MUSIC(θ) = 1/(h_s^H(θ) E_n E_n^H h_s(θ0)); the second factor h_s(θ0) appears to be a typo for h_s(θ), and the denominator should be the real quadratic form h_s^H(θ) E_n E_n^H h_s(θ).
  2. [Definition 1 and §IV.A] The definition of angular resolution as half the null-to-null mainlobe width is well-defined for symmetric beams, but the off-grid sULA patterns discussed above are asymmetric about θ′. Please clarify whether the resolution metric is meant to describe the width of the selected sULA's mainlobe or the achievable resolution for targets centred at an off-grid direction, and discuss the impact of asymmetry.
  3. [Eq. (46)] The definition of 'average missing shots' uses card(S_i^θ) − card(hat S_i^θ) but the condition card(S_i^θ) ≥ card(hat S_i^θ) is only stated to hold for small noise; please state explicitly what is counted when the estimated set is larger than the true set.
  4. [Throughout] There are several typographical and formatting issues, including inconsistent spacing in 'UA V' and the use of 'specturm' in figure captions; a careful proofread is recommended.
  5. [§VI, Fig. 10] For the RAA 'directional' case the element gain G_0 is set to 5.13 dB while ULA uses 0 dB, with the same total power; this is consistent with the paper's model but should be clearly stated as the mechanism for the RAA gain advantage, since the figure alone does not separate the effect of array architecture from that of the chosen element patterns.

Circularity Check

1 steps flagged · score 2.0 of 10

Theorem 1 is a parameter-free consequence of the array model, not a fitted or definitional prediction; the only self-referential support is the secondary beamforming-gain claim delegated to unpublished ref. [38].

  1. self citation load bearing [Section IV-A, paragraph after Theorem 1 (beamforming-gain claim; used in Fig. 10)]
    "Note that for RAA, each sULA is only responsible for a small portion of the whole angular range from [−ηmax,ηmax]. Therefore, different from the conventional antenna arrays where the antenna elements are shared by all beams or signal directions, we can use antenna elements with stronger directivity to enhance the overall beamforming gain as rigorously proved in [38]."

    The paper advertises enhanced beamforming gain as one of RAA's three main advantages and later attributes RAA's communication-rate gain (Fig. 10) to the same effect. The only proof offered is a citation to [38], an in-preparation paper by Z. Dong, Z. Zhou, and Y. Zeng, i.e., the same research group as the present paper. No derivation or external verification of the gain is given here, so this particular claim is supported by a self-citation rather than by evidence in the manuscript. This citation is not used in the derivation of Theorem 1, so the circularity is minor.

full rationale

The core derivation chain is self-contained. Theorem 1 follows by direct substitution from Eq. (16) and Definition 1: with η=θ′, the Dirichlet kernel H_M(sin(θ−θ′)) has first nulls at sin(θ−θ′)=±2/M, giving γ_RAA=arcsin(2/M). No fitted parameter is introduced and no empirical quantity is renamed as a prediction. Theorem 2 is the analogous ULA null equation sinθ−sinθ′=±2/M, and Theorem 3 is a calculus comparison of the two closed forms; both are independent of the self-citations. The only self-referential element is the beamforming-gain advantage, which is delegated to unpublished ref. [38] and used in the communication simulation; it does not affect the resolution theorems, so the appropriate score is 2 rather than higher. I also note a non-circular limitation: Theorem 1 assumes a continuously rotatable sULA (η_n=θ′), while the implemented orientation grid in Eq. (18) is discrete, so off-grid targets experience slightly asymmetric and attenuated mainlobes; this is an idealization/accuracy issue, not a circularity, and is therefore not scored as a circular step.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The central resolution theorem introduces no fitted constants; its main burden is the idealization of a continuous, exactly aligned sULA and a wide antenna element pattern. The communication-gain advantage additionally imports an unproved claim from the authors' unpublished companion paper, and the OFDM model uses standard ISAC assumptions (CP longer than max delay, constant Doppler per symbol).

assumptions (4)
  • domain assumption The antenna element radiation pattern G(ζ) is wide enough that it does not shift the first nulls of the sULA Dirichlet factor, i.e., θ_3dB is larger than the main lobe width considered.
    Used in the proof of Theorem 1 to locate the zeros of the beam pattern solely from H_M(sin(θ−θ′)). It is satisfied by the simulated M=128 and 0.3π beamwidth but is not guaranteed for small M or very narrow elements.
  • ad hoc to paper For every desired direction θ′ there is an sULA with orientation η_n = θ′.
    Eq. (16) and Theorem 1 define the beam pattern with η_n = θ′. The actual design in Eq. (18) has only discrete orientations η_n = n arcsin(2/M), so arbitrary directions fall between orientations and exact alignment is impossible.
  • ad hoc to paper Replacing wide-beam ULA elements with more directional elements having the same total radiated power yields higher peak beamforming gain without creating coverage holes.
    This underpins the communication-rate advantage in Fig. 10. The paper cites [38], which is in preparation, as the rigorous proof, so the statement is imported rather than derived here.
  • domain assumption The cyclic prefix is longer than the maximum path delay, and the Doppler phase is approximately constant within one OFDM symbol.
    Standard OFDM-ISAC assumptions used to derive Eq. (28) and the space-frequency-time tensor in Eq. (29). They are stated in Section V and are reasonable for the simulated parameters.

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Cite this review

Pith. "Pith review of Ray Antenna Array Achieves Uniform Angular Resolution Cost-Effectively for Low-Altitude UAV Swarm ISAC." pith.science (2026). https://pith.science/paper/MOTVOQCR

@misc{pith2026250510306,
  author       = {Pith},
  title        = {Pith review of: Ray Antenna Array Achieves Uniform Angular Resolution Cost-Effectively for Low-Altitude UAV Swarm ISAC},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MOTVOQCR}},
  note         = {Machine review of arXiv:2505.10306}
}
read the original abstract

Ray antenna array (RAA) is a novel multi-antenna architecture comprising massive low-cost antenna elements and a few radio-frequency (RF) chains. The antenna elements are arranged in a novel ray-like structure, where each ray corresponds to a simple uniform linear array (sULA) with deliberately designed orientation and all its antenna elements are directly connected. By further designing a ray selection network (RSN), appropriate sULAs are selected to connect to the RF chains for further baseband processing. RAA has three appealing advantages: (i) dramatically reduced hardware cost since no phase shifters are needed; (ii) enhanced beamforming gain as antenna elements with higher directivity can be used; (iii) uniform angular resolution across all signal directions. Such benefits make RAA especially appealing for integrated sensing and communication (ISAC), particularly for low-altitude unmanned aerial vehicle (UAV) swarm ISAC, where high-mobility aerial targets may easily move away from the boresight of conventional antenna arrays, causing severe communication and sensing performance degradation. Therefore, this paper studies RAA-based ISAC for low-altitude UAV swarm systems. First, we establish an input-output mathematical model for RAA-based UAV ISAC and rigorously show that RAA achieves uniform angular resolution for all directions. Besides, we design the RAA orientation and RSN. Furthermore, RAA-based ISAC with orthogonal frequency division multiplexing (OFDM) for UAV swarm is studied, and efficient algorithm is proposed for sensing target parameter estimation. Extensive simulation results demonstrate the significant performance improvement by RAA system over the conventional antenna arrays, in terms of sensing angular resolution and communication spectral efficiency, highlighting the great potential of the novel RAA system to meet the growing demands of low-altitude UAV ISAC.

Figures

Figures reproduced from arXiv: 2505.10306 by the authors.

Figure 1
Figure 1. An illustration of RAA-based ISAC for low-altitude UAV swarm. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The beam patterns for (a) RAA, where each curve represents the response of one sULA. (b) ULA, where each curve corresponds to one codeword in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. An illustration of conventional ULA-based ISAC for low-altitude UAV swarm. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The comparision of angular resolution of RAA versus the conventional [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: MUSIC specturm of (a) RAA (b) ULA with moderate AoAs [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 7
Figure 7. Figure 7: An example of Delay-Doppler maps of targets (a) without ZF beamforming, (b)-(f) with ZF beamforming [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: RMSE of AoA estimation beamforming is not performed, some of the targets may be buried in the noise, or overlapping with each other making them difficult to distinguish. With ZF beamforming, the delay and Doppler information of each target are shown in Fig. 7b-7f, resp…
Figure 9
Figure 9. Figure 9: Average missing shots of AoA estimation -40 -30 -20 -10 0 10 20 0 5 10 15 20 25 RAA directional RAA isotropic ULA directional ULA isotropic [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: Communication rate for RAA and ULA. between RAA and ULA w.r.t. different AoAs centroid. It can be seen that as the UAV swarm moving closer with increasing AoAs, the RMSE of ULA increases dramatically while that of RAA remains almost the same. This can be explained tha…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.