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arxiv: 2606.13036 · v1 · pith:QLKHGM2Pnew · submitted 2026-06-11 · 💻 cs.IT · math.IT

Active Sensing-assisted UAV Communications with Jittering: Framework and Performance Analysis

Guangji Chen , Long Shi , Qingqing Wu , Qiaoyan Peng , Caihong Kai This is my paper

Pith reviewed 2026-06-27 05:54 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords UAV communicationsactive sensingjitteringangle-of-arrival estimationachievable ratebeam misalignmentintegrated sensing and communication
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The pith

Two-stage active sensing allows UAV communication rates to approach the jitter-free upper bound at high transmit power.

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

The paper develops a framework where a ground station uses active sensing to estimate the angle of arrival at a jittering UAV before transmitting data. Two schemes are compared: one that uses data signals for sensing throughout and one that dedicates an initial stage to pure sensing signals. Closed-form rate expressions reveal a tradeoff governed by the time split between stages, and optimal allocation is derived. The analysis shows that both schemes lose no performance relative to perfect alignment when transmit power is high enough, and identifies when one scheme beats the other via a simple threshold.

Core claim

By employing maximum likelihood estimation of the angle of arrival in the first stage and then using that estimate for beamforming in the second stage, the achievable rate of the ground-to-UAV link can be expressed in closed form. The optimal fraction of time for the sensing stage that maximizes the average rate is obtained in semi-closed form. A sufficient condition with threshold structure determines when using information-bearing signals for sensing throughout outperforms dedicating the first stage to deterministic sensing signals. As transmit power grows large, the rate gap to the jitter-free case vanishes for both schemes.

What carries the argument

The two-stage framework with communication-oriented and sensing-oriented schemes that trade sensing accuracy against communication time via time allocation.

If this is right

  • The performance loss of both schemes relative to the jitter-free upper bound approaches zero as transmit power increases.
  • A threshold-based condition determines when the communication-oriented scheme outperforms the sensing-oriented scheme.
  • The optimal time allocation between stages that maximizes the overall rate is available in semi-closed form.
  • Closed-form expressions for achievable rates and Cramér-Rao bounds are derived for both schemes.

Where Pith is reading between the lines

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

  • The threshold condition suggests a simple switching rule implementable in hardware without solving optimization problems each time.
  • Real-world UAV tests could check how well the single AoA parameter model holds when wind introduces additional jitter sources.
  • The framework points toward integrated sensing and communication designs where the same signals serve both purposes without dedicated sensing slots.

Load-bearing premise

The jitter-induced beam misalignment is fully captured by a single angle-of-arrival parameter whose statistics are known in advance.

What would settle it

Measure the achievable rate at increasing transmit powers and check whether the gap to the jitter-free rate goes to zero; if it plateaus at a positive value, the asymptotic claim is false.

Figures

Figures reproduced from arXiv: 2606.13036 by Caihong Kai, Guangji Chen, Long Shi, Qiaoyan Peng, Qingqing Wu.

Figure 1
Figure 1. Figure 1: Illustration of the system model with UAV jittering. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: An active sensing-assisted communication framework. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Achievable rate versus the variance of AoA. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Achievable rate versus the number of active sensors. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 5
Figure 5. Figure 5: Illustration of the optimal time allocation. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 8
Figure 8. Figure 8: Illustration of the impact of antenna deployment. [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

Providing reliable communication for unmanned aerial vehicles (UAVs) via existing cellular networks is crucial for enabling the rapid growth of the low-altitude economy. However, UAV jittering significantly degrades communication quality due to induced beam misalignment. Inspired by recent advances in integrated sensing and communication, we propose a novel two-stage active sensing-assisted communication framework tailored for ground-to-UAV links with jittering. Specifically, two schemes are conceived to leverage sensing for enhancing communication performance, namely the communication-oriented scheme and the sensing-oriented scheme. For the sensing-oriented scheme, deterministic signals are employed in the first stage to facilitate angle-of-arrival (AoA) acquisition at the UAV side, followed by pure communication service in the second stage by using the estimated AoA. In contrast, the communication-oriented scheme employs Gaussian information-bearing signals throughout both stages, with AoA estimation relying on Gaussian random signals. For both schemes, we provide maximum likelihood estimators for AoA, along with analytical results characterizing the Cram\'er-Rao bound. To capture the performance limit, closed-form expressions for the achievable rates of the two schemes are derived, unveiling a fundamental tradeoff between sensing and communication quality across the two stages by tuning the time allocated to the first stage. The optimal time allocation that maximizes the overall rate is obtained in semi-closed-form. Based on these results, we unveil a sufficient condition under which the communication-oriented scheme outperforms the sensing-oriented scheme, which admits an interesting threshold-based structure. Asymptotic analysis demonstrates that the performance loss of the proposed schemes relative to the jitter-free upper bound approaches zero in the high transmit power regime.

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 paper proposes a two-stage active sensing-assisted framework for ground-to-UAV communications under jittering, introducing a communication-oriented scheme (using Gaussian signals throughout) and a sensing-oriented scheme (deterministic signals for AoA estimation followed by communication). It derives ML AoA estimators and associated Cramér-Rao bounds for both, closed-form achievable rate expressions that trade off sensing and communication time, the semi-closed-form optimal time allocation maximizing the overall rate, a sufficient condition (with threshold structure) for when the communication-oriented scheme outperforms the sensing-oriented one, and an asymptotic result that the performance loss relative to the jitter-free upper bound vanishes as transmit power grows large.

Significance. If the closed-form rate expressions and asymptotic limits are rigorously justified without unaccounted residuals, the work supplies concrete analytic tools for balancing sensing and communication in jitter-affected UAV links, including a practical threshold rule for scheme selection. The explicit ML estimators, CRBs, and high-SNR vanishing-loss result are strengths that could inform ISAC designs in cellular networks.

major comments (2)
  1. [Section on achievable rate derivation (likely IV)] The transition from the ML AoA estimator (and its CRB) to the closed-form achievable rate expressions assumes that estimation error leaves no residual phase/amplitude misalignment in the second-stage communication rate; this is load-bearing for both the rate formulas and the high-power asymptotic claim that loss to the jitter-free bound approaches zero. The received-signal model must be shown to admit exact closed-form rates post-estimation without additional error terms.
  2. [Asymptotic analysis and sufficient condition sections (likely V)] The sufficient condition for communication-oriented scheme superiority (with its threshold-based structure) and the asymptotic analysis both rest on the single random AoA parameter fully capturing jitter misalignment with known statistics; if the underlying channel model admits time-varying AoA within a stage or unmodeled amplitude fluctuations, both the CRB-based performance characterization and the high-SNR limit would deviate from the stated jitter-free upper bound.
minor comments (2)
  1. [Section II] Notation for the two schemes and time-allocation parameter τ could be introduced more explicitly in the system model to improve readability before the rate derivations.
  2. [Throughout] A few instances of inconsistent capitalization in section headings and equation references appear; these are minor but should be standardized.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below with clarifications on the model and derivations.

read point-by-point responses

  1. Referee: [Section on achievable rate derivation (likely IV)] The transition from the ML AoA estimator (and its CRB) to the closed-form achievable rate expressions assumes that estimation error leaves no residual phase/amplitude misalignment in the second-stage communication rate; this is load-bearing for both the rate formulas and the high-power asymptotic claim that loss to the jitter-free bound approaches zero. The received-signal model must be shown to admit exact closed-form rates post-estimation without additional error terms.

    Authors: The closed-form rates explicitly incorporate misalignment: after obtaining the ML estimate in stage 1, the stage-2 beamformer uses the estimate, so the effective gain is a deterministic function of (true AoA - estimate). The achievable rate is the expectation of log(1 + SNR * |effective gain|^2) over the joint distribution of true AoA and estimate; this expectation evaluates in closed form under the array response and Gaussian noise model. The CRB enters only to characterize estimator variance for the sufficient condition, not to approximate the rate itself. The high-SNR limit follows because CRB ~ 1/P, so misalignment variance vanishes and the rate converges to the jitter-free bound. A clarifying remark will be added to Section IV. revision: partial

  2. Referee: [Asymptotic analysis and sufficient condition sections (likely V)] The sufficient condition for communication-oriented scheme superiority (with its threshold-based structure) and the asymptotic analysis both rest on the single random AoA parameter fully capturing jitter misalignment with known statistics; if the underlying channel model admits time-varying AoA within a stage or unmodeled amplitude fluctuations, both the CRB-based performance characterization and the high-SNR limit would deviate from the stated jitter-free upper bound.

    Authors: Section II explicitly models jitter via a single random AoA drawn from a known distribution that is constant over the two-stage frame (block model). Under this model the single parameter fully captures misalignment, the CRB is tight, the rate expressions and threshold condition are exact, and the high-SNR convergence holds. Time-varying AoA or amplitude fluctuations would require a different channel model outside the paper's scope. revision: no

Circularity Check

0 steps flagged

No circularity; derivations are independent analytic results from standard signal models

full rationale

The paper's central results consist of ML AoA estimators, CRB expressions, closed-form achievable rates, optimal time allocation, a threshold-structured sufficient condition for scheme comparison, and high-SNR asymptotic limits, all obtained by direct manipulation of the assumed received-signal model (single random AoA with known statistics, Gaussian or deterministic pilots). No equation reduces by construction to a fitted input, self-cited premise, or renamed known result; the jitter-free upper bound is an external reference point, not an internal tautology. Any self-citations are peripheral and non-load-bearing.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The derivations rest on standard wireless channel models (additive Gaussian noise, far-field plane-wave assumption for AoA) and on the premise that jitter statistics are known; no new entities are postulated and no parameters appear to be fitted to data inside the reported results.

axioms (2)
  • domain assumption Received signal follows a standard far-field array response model with additive white Gaussian noise whose variance is known.
    Invoked to obtain the ML estimator and Cramér-Rao bound for AoA.
  • domain assumption Jitter statistics (distribution of angle deviation) are known a priori and stationary across the two stages.
    Required for the rate expressions and the threshold condition to be computable in closed form.

pith-pipeline@v0.9.1-grok · 5829 in / 1563 out tokens · 23382 ms · 2026-06-27T05:54:07.360363+00:00 · methodology

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Reference graph

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