Enhanced Direction-Sensing Methods and Performance Analysis in Low-Altitude Wireless Network via a Rotating Antenna Array

Feng Shu; Jiangzhou Wang; Jiatong Bai; Jinbing Jiang; Maolin Li; Minghao Chen; Wan Choi; Yan Wang

arxiv: 2603.20784 · v5 · pith:XGDLVWLWnew · submitted 2026-03-21 · 📡 eess.SP

Enhanced Direction-Sensing Methods and Performance Analysis in Low-Altitude Wireless Network via a Rotating Antenna Array

Jinbing Jiang , Feng Shu , Minghao Chen , Jiatong Bai , Maolin Li , Yan Wang , Jiangzhou Wang , Wan Choi This is my paper

Pith reviewed 2026-05-21 10:57 UTC · model grok-4.3

classification 📡 eess.SP

keywords direction of arrival estimationrotating antenna arraylow-altitude wireless networkRoot-MUSICCramer-Rao lower boundspatial spectrum searchpre-rotation initialization

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The pith

A pre-rotation step followed by iterative greedy search lets a rotating antenna array sense emitter directions more accurately and with lower complexity than recursive rotation methods.

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

The paper develops an enhanced direction-sensing approach for low-altitude wireless networks that uses a mechanically rotating antenna array to counteract signal loss from narrow antenna beams. It introduces a pre-rotation initialization that tests a few candidate orientations to pick the one with highest received power, then fixes the array there and runs an iterative greedy spatial-spectrum search that adds up prior sampling covariance matrices at each step. This accumulation steadily lowers estimation error while avoiding the repeated full eigendecompositions required by earlier recursive rotation techniques. Simulations show the new method reaches the derived Cramer-Rao lower bound on mean-squared error, whereas the baseline does not because it never accumulates samples across rotations.

Core claim

The central claim is that the PRI-IGSS framework, consisting of a power-based pre-rotation to candidate directions, mechanical fixation at the initial Root-MUSIC estimate, and subsequent iterative greedy search with cumulative variance matrices, yields lower mean-squared error than RR-Root-MUSIC and attains the CRLB derived under a simplified instantaneous-rotation model.

What carries the argument

The PRI-IGSS framework, which pre-rotates the array normal to a small set of candidates to maximize sensing energy, locks the array at the best initial direction, and then performs iterative greedy spatial-spectrum search while summing all previous sampling covariance matrices with the current one.

If this is right

Direction estimation error decreases monotonically with each added iteration because the accumulated covariance matrices provide more effective samples.
Computational cost drops because only one initial Root-MUSIC run plus low-cost greedy searches are needed instead of repeated full eigendecompositions at every rotation.
The method can be used in any scenario where a single array can be mechanically reoriented between short sensing bursts without continuous motion.
The CRLB serves as a tight benchmark only when the simplified rotation model holds; real mechanical dynamics would require a modified bound.

Where Pith is reading between the lines

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

The same pre-rotation-plus-accumulation idea could be tested on other array geometries or in environments with moving emitters.
Adding a model of rotation dynamics into the CRLB derivation would produce a more practical performance limit for hardware implementations.
The reinforcement-learning motivation for the greedy search suggests that learned policies could further shrink the search range in future versions.

Load-bearing premise

The performance bound assumes the array can be rotated to any new orientation instantaneously with no mechanical settling time, friction, or vibration that would change its actual pointing direction while samples are being collected.

What would settle it

A hardware experiment or simulation that includes finite rotation settling time and small orientation jitter during each sensing interval; if the measured mean-squared error then exceeds the derived CRLB while the method still outperforms RR-Root-MUSIC, the claim would be falsified.

Figures

Figures reproduced from arXiv: 2603.20784 by Feng Shu, Jiangzhou Wang, Jiatong Bai, Jinbing Jiang, Maolin Li, Minghao Chen, Wan Choi, Yan Wang.

**Figure 2.** Figure 2: Illustration of the geometric relationship for the r [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Flowchart of the proposed low-complexity enhanced d [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 4.** Figure 4: Illustration of the spatial distribution of the diffe [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: Convergence curves of the proposed low-complexity m [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 8.** Figure 8: RMSE versus SNR of the proposed methods when [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 6.** Figure 6: Convergence curves of the proposed low-complexity m [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 9.** Figure 9: RMSE versus the elevation angle θ for the proposed methods when SNR = -5 dB. 0 30 60 90 120 150 180 10-2 10-1 100 101 102 [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

**Figure 10.** Figure 10: RMSE versus the elevation angle θ for the different number of candidate pre-rotation direction with SNR = 5 dB. successfully achieved by the proposed PRI-IGSS over the PRI and RR-Root-MUSIC. In [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗

read the original abstract

Due to the directive property of each antenna element, the received signal power can be severely attenuated when the emitter deviates from the array boresight, which will lead to a severe degradation in sensing performance along the corresponding direction. Although existing rotatable array sensing methods such as recursive rotation (RR-Root-MUSIC) can mitigate this issue by iteratively rotating and sensing, several mechanical rotations and repeated eigendecomposition operations are required to yield a high computational complexity and low time-efficiency. To address this problem, a pre-rotation initialization with recieve power as a rule is proposed to signifcantly reduce the computational complexity and improve the time-efficiency. Using this idea, a low-complexity enhanced direction-sensing framework with pre-rotation initialization and iterative greedy spatial-spectrum search (PRI-IGSS) is develped with three stages: (1) the normal vector of array is rotated to a set of candidates to find the opimal direction with the maximum sensing energy with the corresponding DOA value computed by the Root-MUSIC algorithm; (2) the array is mechanically rotated to the initial estimated direction and kept fixed; (3) an iterative greedy spatial-spectrum search or recieving beamforming method, moviated by reinforcement learning, is designed with a reduced search range and making a summation of all previous sampling variance matrices and the current one is adopted to provide an increasiong performance gain as the iteration process continues. To assess the performance of the proposed method, the corresponding CRLB is derived with a simplified rotation model. Simulation results demonstrate that the proposed PRI-IGSS method performs much better than RR-Root-MUSIC and achieves the CRLB in term of mean squared error due to the fact there is no sample accumulation for the latter.

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

PRI-IGSS adds a power-based pre-rotation step and covariance accumulation to cut rotations versus RR-Root-MUSIC, but the CRLB and MSE claims sit inside an idealized instantaneous-rotation model.

read the letter

The main point is that this paper gives a practical tweak for direction finding with rotating arrays on low-altitude platforms. It uses received power to pick a short list of candidate orientations first, then runs a greedy spatial-spectrum search over a narrowed range while summing covariance matrices from each step. That pipeline is the concrete new piece relative to the RR-Root-MUSIC baseline they cite, and it looks like it trims both the number of mechanical moves and the repeated eigendecompositions. The simulations they report show lower MSE and closer approach to their CRLB, which is consistent with the extra sample accumulation they get and the other method does not. The motivation around boresight attenuation and the need for fewer rotations is clear and directly tied to UAV-type scenarios. The CRLB derivation is also laid out under their rotation model, which at least lets them make a quantitative comparison. The soft spot is the rotation model itself. It treats each repositioning as instantaneous and error-free, leaving out settling time, vibration, or friction that would appear in real hardware. Both the bound and the Monte Carlo runs live inside that idealization, so the claim that PRI-IGSS reaches the CRLB could shrink once those effects are added. Simulation details such as exact search-range sizes, number of trials, or how the free parameters were chosen are not fully visible here, which makes it harder to judge robustness. Overall this is a solid incremental step inside the rotatable-array DOA literature rather than a broad advance. It is aimed at people working on array processing for drone or low-altitude networks who care about trading mechanical moves for computation. A reader in that niche would find the algorithm description and the performance numbers useful. The work is coherent enough on its own terms to go to peer review; an editor should send it out so referees can check the model assumptions and the simulation setup against the claims.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a pre-rotation initialization with iterative greedy spatial-spectrum search (PRI-IGSS) framework for direction-of-arrival estimation using a rotating antenna array in low-altitude wireless networks. It uses received power to select candidate directions for initial Root-MUSIC DOA computation, mechanically rotates the array to this estimate, and then performs an iterative greedy search or beamforming step (motivated by reinforcement learning) over a reduced range while accumulating covariance matrices from prior samples. A CRLB is derived under a simplified rotation model, and Monte Carlo simulations are reported to show that PRI-IGSS outperforms RR-Root-MUSIC and attains the CRLB in MSE, attributed to the absence of sample accumulation in the baseline method.

Significance. If the reported MSE gains and CRLB attainment hold under realistic mechanical constraints, the PRI-IGSS approach could meaningfully improve computational efficiency and time performance for DOA sensing where element directivity causes attenuation. The pre-rotation initialization and covariance accumulation strategy constitute a practical algorithmic contribution over purely recursive rotation baselines. The idealized rotation model, however, restricts the immediate applicability of the performance claims to real hardware.

major comments (2)

[CRLB derivation] CRLB derivation (performance analysis section): The bound is obtained from a simplified rotation model that assumes instantaneous mechanical repositioning. This assumption is load-bearing for the central claim that PRI-IGSS reaches the CRLB, because unmodeled effects such as settling time, friction, or vibration-induced orientation errors during each sensing interval would add extra noise to the array manifold and increase the effective estimation variance. An explicit statement of the rotation parameters used in the Fisher information matrix or a sensitivity study under non-ideal dynamics is required to support the attainment result.
[Comparison with RR-Root-MUSIC] Method comparison and simulation results: The statement that RR-Root-MUSIC fails to reach the CRLB 'due to the fact there is no sample accumulation for the latter' is internally consistent only within the chosen model. It is unclear why the same accumulation of prior covariance matrices cannot be applied to RR-Root-MUSIC under identical rotation assumptions; the manuscript should clarify the precise algorithmic distinction in sample usage and confirm that the reported MSE gap is not an artifact of unequal processing of the received snapshots.

minor comments (2)

[Abstract] Abstract contains multiple typographical errors: 'signifcantly' (significantly), 'recieve' (receive), 'develped' (developed), 'movitated' (motivated), 'increasiong' (increasing), and 'in term of' (in terms of).
[Notation] Ensure consistent notation for DOA, CRLB, and covariance matrices across the algorithmic description and performance analysis sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point by point below, providing clarifications and indicating the revisions made.

read point-by-point responses

Referee: [CRLB derivation] CRLB derivation (performance analysis section): The bound is obtained from a simplified rotation model that assumes instantaneous mechanical repositioning. This assumption is load-bearing for the central claim that PRI-IGSS reaches the CRLB, because unmodeled effects such as settling time, friction, or vibration-induced orientation errors during each sensing interval would add extra noise to the array manifold and increase the effective estimation variance. An explicit statement of the rotation parameters used in the Fisher information matrix or a sensitivity study under non-ideal dynamics is required to support the attainment result.

Authors: We agree that the CRLB derivation relies on a simplified model with instantaneous repositioning. In the revised manuscript, we have added an explicit statement of the rotation parameters (angular velocity and sensing interval duration) used when constructing the Fisher information matrix. A full sensitivity study under non-ideal effects such as settling time or vibration would require new modeling and hardware experiments outside the present scope; we therefore note this as a limitation for future work while maintaining that the CRLB attainment holds under the stated idealized assumptions. revision: partial
Referee: [Comparison with RR-Root-MUSIC] Method comparison and simulation results: The statement that RR-Root-MUSIC fails to reach the CRLB 'due to the fact there is no sample accumulation for the latter' is internally consistent only within the chosen model. It is unclear why the same accumulation of prior covariance matrices cannot be applied to RR-Root-MUSIC under identical rotation assumptions; the manuscript should clarify the precise algorithmic distinction in sample usage and confirm that the reported MSE gap is not an artifact of unequal processing of the received snapshots.

Authors: We thank the referee for highlighting this point. The key algorithmic distinction is that RR-Root-MUSIC performs recursive mechanical rotations at every iteration, so each snapshot is collected under a different array orientation and the associated steering vectors differ; prior covariance matrices therefore cannot be summed directly without explicit compensation for the changing manifold. In PRI-IGSS the array is pre-rotated once to the initial direction and then held fixed during the iterative greedy search, permitting direct accumulation of covariances from identical orientations. We have revised the manuscript to state this distinction clearly and confirm that the reported MSE results reflect equivalent snapshot counts processed according to each algorithm's native procedure. revision: yes

Circularity Check

0 steps flagged

No significant circularity; CRLB derivation and MSE claims are independent of the algorithm under test

full rationale

The paper derives a CRLB under an explicitly stated simplified rotation model and then reports Monte Carlo results showing the proposed PRI-IGSS estimator reaches that bound while RR-Root-MUSIC does not, attributing the difference to sample accumulation. This is a conventional efficiency check inside a fixed statistical model; the CRLB expression is obtained from the Fisher information matrix of the observation model and does not embed the PRI-IGSS procedure or any fitted parameter from the algorithm itself. No equation reduces to a prior result by definition, no self-citation supplies a load-bearing uniqueness theorem, and the simulations are generated under the same model used for the bound, which is the expected behavior for an efficient estimator rather than a circular construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The method rests on standard far-field plane-wave and narrowband assumptions plus a simplified mechanical rotation model; no new physical entities are postulated.

free parameters (2)

number of pre-rotation candidate directions
Chosen to trade off initial search cost against probability of landing near the true DOA; exact count not stated in abstract.
reduced search range size after pre-rotation
Determines the computational saving of the iterative greedy stage; value selected heuristically.

axioms (2)

domain assumption Received signal power is maximized when the array normal aligns with the emitter direction
Invoked to justify the pre-rotation initialization rule using receive power.
domain assumption Mechanical rotation can be treated as instantaneous for CRLB derivation
Stated as part of the simplified rotation model used to obtain the performance bound.

pith-pipeline@v0.9.0 · 5871 in / 1484 out tokens · 34815 ms · 2026-05-21T10:57:09.595527+00:00 · methodology

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discussion (0)

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the corresponding CRLB is derived with a simplified rotation model... Simulation results demonstrate that the proposed PRI-IGSS method performs much better than RR-Root-MUSIC and achieves the CRLB

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