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Micro-Doppler Sensing for UAV Flight-State Estimation in ISAC Networks

Henglin Pu, Lu Su, Zhu Han, Athina P. Petropulu, Husheng Li

arXiv:2610.21225v1eess.SP

TL;DR

Conventional ISAC UAV studies mainly estimate position and bulk velocity, leaving rotor dynamics and orientation less characterized. This paper uses OFDM-ISAC micro-Doppler measurements, first locally and then across multiple stations, to estimate rotor rate and rotor-axis state; simulations and experimental measurements demonstrate the feasibility of the sensing pipeline.

  • Problem

    Most existing ISAC-based UAV studies focus on position and bulk velocity, providing limited information about rotor dynamics and orientation.

    Source: §I · p. 1

  • Method

    The framework extracts rotor-rate and view-dependent bandwidth features at individual stations, then fuses bandwidths across stations to estimate rotor-axis direction and Doppler scale.

    Source: B. Contributions of the Present Work · p. 3, §IV · p. 6

  • Results

    Three geometrically diverse views support local recovery of rotor-axis coordinates and unknown Doppler scale; an estimation example reports pitch RMSE of 8.68° and rotor rate of 99.56 revolutions/s against a prescribed 100 revolutions/s.

    Source: B. Contributions of the Present Work · p. 3, C. Multi-Station Rotor-Axis Estimation · p. 10

  • Takeaways & Limitations

    The demonstrated framework adds rotor-rate and rotor-axis sensing to UAV monitoring beyond position and bulk-velocity sensing.

    Source: §VII · p. 13

    Within the analyzed motion conditions, observations approaching residual-phase coherence or range-migration limits require improved motion compensation or integration over multiple shorter CPIs.

    Source: E. Observation Time and Motion… · p. 11

Abstract

from arXiv · show

Integrated sensing and communication (ISAC) provides a promising foundation for low-altitude unmanned aerial vehicle (UAV) monitoring. However, most existing studies focus primarily on position and bulk velocity, thus providing limited information about UAV rotor dynamics and orientation. To address this limitation, this paper develops an orthogonal frequency-division multiplexing (OFDM)-ISAC framework that exploits UAV micro-Doppler signatures to estimate operational states, including rotor rate and rotor-axis orientation, thereby providing richer UAV state information beyond conventional ISAC localization and velocity sensing. The framework progresses from single-station micro-Doppler sensing to multi-station rotor-axis estimation. At each base station, micro-Doppler signatures are first extracted and used to estimate the rotor rate. The framework is then extended to a distributed ISAC network, where view-dependent micro-Doppler signatures from multiple sensing directions are fused to estimate the common rotor-axis direction. Since the fusion relies on Doppler-bandwidth features rather than complex channel phases, inter-station carrier-phase synchronization is not required. We show that three geometrically diverse views can locally identify both the rotor-axis direction and the unknown rotor-tip-speed scale. In addition, a feature-aware radar equation bridges blade radar cross section (RCS), sensing range, transmit power, and observation duration to micro-Doppler detection and rotor-rate estimation accuracy. The effects of residual motion and range migration on the coherent processing interval (CPI) are also analyzed. Simulations and experimental measurements validate the proposed framework and demonstrate the feasibility of rotor-rate estimation and multi-station rotor-axis sensing.

I. INTRODUCTION

The paper addresses the limited rotor-state information in conventional ISAC UAV sensing by using blade micro-Doppler signatures. It develops single-station rotor-rate estimation and multi-station rotor-axis sensing, alongside analysis of sensing feasibility.

I. INTRODUCTION

  • Rotor-induced micro-Doppler features provide information about rotor dynamics, while multiple views can constrain the common rotor-axis direction and blade-tip-speed scale.Weak, aspect-dependent blade returns and range-dependent power loss make reliable feature extraction a practical challenge.Source: §I · p. 1

A. Review of Existing Works

  • Prior UAV-oriented cooperative ISAC work largely addressed detection, localization, tracking, and classification; three-dimensional rotor-axis estimation remained largely unexplored.The paper targets this gap using view-dependent Doppler bandwidths rather than individual scattering-center reconstruction.Source: A. Review of Existing Works · p. 2

B. Contributions of the Present Work

  • The framework combines local rotor-feature extraction with multi-station fusion to estimate rotor dynamics and attitude-related states without inter-station carrier-phase synchronization.It also investigates geometric observability and practical sensing feasibility.Source: B. Contributions of the Present Work · pp. 2–3
  • The OFDM-ISAC signal model incorporates UAV translation, rotor geometry, blade RCS, body attitude, and blade rotation to characterize features for rotor-rate and orientation sensing.The harmonic structure supports rotor-rate estimation, while the time-varying micro-Doppler span supports orientation sensing.Source: B. Contributions of the Present Work · p. 3
  • Three geometrically diverse views support local recovery of two rotor-axis coordinates and an unknown Doppler scale; the work also derives local Fisher information and identifies ill-conditioned station geometries.It characterizes required observation time as a function of blade RCS, sensing distance, transmit power, and hardware parameters, and reports prototype validation in single- and multi-station configurations.Source: B. Contributions of the Present Work · p. 3

C. Organization of the Paper

  • The paper proceeds from system modeling and single-station estimation to multi-station rotor-axis estimation, sensing-feasibility analysis, and numerical and experimental results.The distributed system model assumes local feature extraction and fusion, with sufficiently small measurement-time offsets relative to rotor-axis variation.Source: C. Organization of the Paper · p. 3, §II · p. 3

A. Transmitted OFDM Signal Model

The section specifies the OFDM sensing waveform and models UAV kinematics and blade reflections. The resulting view-dependent Doppler span links blade rotation to measurable rotor-axis constraints.

A. Transmitted OFDM Signal Model

  • An OFDM station transmits symbols over N subcarriers with spacing ∆f; the useful symbol duration is Tu = 1/∆f, and the total interval includes the cyclic prefix.For K coherent symbols, the CPI is KTs and nominal Doppler resolution is 1/TCPI.Source: A. Transmitted OFDM Signal Model · p. 3

B. UAV Kinematics and Reflection Channel

  • The UAV model represents body attitude by a rotation matrix and blade scatterers by their positions along rotating blades, with the rotor axis determined by body attitude.Rotor angular velocity has a signed convention: positive denotes right-hand rotation about the positive body-frame z-axis.Source: B. UAV Kinematics and Reflection Channel · pp. 3–4
  • The channel model includes UAV-body and distributed blade-scattering returns, with blade coefficients accounting for propagation loss, antenna gains, polarization mismatch, shadowing, and aspect-dependent blade RCS.The model’s phase contains information about UAV position, attitude, rotor locations, and blade rotation.Source: B. UAV Kinematics and Reflection Channel · p. 4
  • The maximum rotor-induced Doppler magnitude defines the micro-Doppler half-bandwidth, which varies across stations because each line of sight projects the shared rotor motion differently.The blade-tip speed characterizes the maximum Doppler extent of the distributed blade return; it does not assume scattering occurs only at the tip.Source: B. UAV Kinematics and Reflection Channel · p. 4

C. Received OFDM Signal and Feature Mapping

The processing chain forms a range-focused slow-time signal, suppresses bulk Doppler and body/clutter components, then extracts rotor-rate and bandwidth features. The bandwidth measurements provide inputs for multi-station fusion without inter-station carrier-phase coherence.

C. Received OFDM Signal and Feature Mapping

  • After cyclic-prefix removal and an N-point DFT, the station estimates channel coefficients on active resource elements, transforms them to delay, and selects a range gate around the localized UAV.The resulting slow-time signal contains body return, blade-induced components, residual in-gate clutter, and receiver noise.Source: C. Received OFDM Signal and Feature… · pp. 4–5
  • After bulk-Doppler compensation and body/clutter suppression, time–frequency processing extracts rotor rate from periodic spectral structure and rotor bandwidth from Doppler boundaries.For approximately identical, uniformly spaced blades, the dominant spectral spacing is the blade-pass frequency Bqfr,q.Source: C. Received OFDM Signal and Feature… · p. 5
  • The view-dependent half-bandwidth is a measurement of rotor-axis direction and rotor-tip-speed scale, and bandwidth-based fusion does not require carrier-phase coherence among distributed RF front ends.The extracted bandwidths serve as local measurements for the multi-station estimator.Source: C. Received OFDM Signal and Feature… · p. 5

D. Estimation Formulation

The formulation defines single-station rotor-feature estimation, multi-station recovery of rotor axis and Doppler scale, and the sensing conditions needed for usable measurements.

D. Estimation Formulation

  • Single-station processing estimates rotor rates and projected micro-Doppler bandwidths despite residual body, clutter, and receiver-noise components.The model includes residual leakage and noise in the processed signal.Source: D. Estimation Formulation · p. 5
  • Across a fusion interval, stations use bandwidths and their LoS vectors to estimate a common rotor axis and Doppler scale, while rotation about that axis remains unobservable.The model assumes approximately common rotor axes and tip speed during the interval.Source: D. Estimation Formulation · p. 5
  • Blade echoes must provide sufficient feature energy, and the feasibility analysis relates transmit power and observation duration to detection and estimation accuracy under residual-motion and range-migration constraints.The formulation also accounts for link parameters over intervals where range and those parameters are approximately constant.Source: D. Estimation Formulation · p. 5
  • The study assumes prior UAV detection and cross-station association, available station positions and LoS vectors, and approximately stable dominant rotor motion within each processing window.Source: D. Estimation Formulation · p. 5

III. SINGLE-STATION MICRO-DOPPLER FEATURE ESTIMATION

Each station suppresses body and clutter returns, extracts a view-dependent micro-Doppler bandwidth, and estimates rotor rate from periodic envelope structure. The section also distinguishes ideal coherent information bounds from practical estimation performance.

A. Body Suppression and Bandwidth Extraction

  • Body-suppression processing applies an MTI filter to the range-focused sequence, reducing stationary clutter and quasi-static body returns while also attenuating near-zero-Doppler components.Slow-time differencing before the inverse DFT is an equivalent implementation because the operations are linear.Source: A. Body Suppression and Bandwidth… · p. 5
  • The time–frequency spectrum is searched around a tracked blade ridge, with a local noise floor removed before expanding the interval to contain 95% of residual energy.A short median filter suppresses isolated extraction errors, and the measured half-bandwidth can be expressed as projected blade-tip velocity.Source: A. Body Suppression and Bandwidth… · pp. 5–6

B. Rotor-Rate Estimation

  • The estimator finds rotor rate from periodic envelope structure by selecting a smoothed spectral peak and testing subharmonic candidates with a harmonic-comb score.The BPF is associated with repeated blade scattering, and spectral magnitudes do not reveal the sign of rotor angular velocity.Source: B. Rotor-Rate Estimation · p. 6
  • The coherent-component Cramér–Rao bound describes ideal local information but does not establish that the practical envelope-spectrum estimator attains it.Multiple blades, aspect-dependent amplitudes, peak selection, and coherence loss can cause threshold errors outside the local bound.Source: B. Rotor-Rate Estimation · p. 6
  • A single station supplies rotor rate and projected blade-tip speed but cannot separate true tip-speed scale from rotor-axis geometry.Source: B. Rotor-Rate Estimation · p. 6

IV. MULTI-STATION ROTOR-AXIS ESTIMATION

The multi-station estimator fuses view-dependent bandwidth measurements to infer a common rotor axis and Doppler scale, accounting for extraction error and station geometry.

IV. MULTI-STATION ROTOR-AXIS ESTIMATION

A. Joint Rotor-Axis and Doppler-Scale Estimation

  • The weighted least-squares fit models bandwidth-extraction errors, which arise from noise, finite Doppler resolution, blade flashing, and imperfect spectral-edge estimation.Independent zero-mean Gaussian errors are a working model for weighted estimation and local performance analysis; equal weights are used when station-specific variances are unavailable.Source: A. Joint Rotor-Axis and Doppler-Scale… · pp. 6–7
  • For each candidate axis, the estimator profiles the minimizing Doppler scale analytically and searches over an azimuth–elevation grid.When rotor rate and effective blade-tip radius are known, the scale can instead be fixed.Source: A. Joint Rotor-Axis and Doppler-Scale… · p. 7

B. Local Identifiability and Accuracy

Local identifiability requires sufficiently diverse station geometry, while the section defines local accuracy bounds and an axis-error measure.

B. Local Identifiability and Accuracy

  • At least three scalar bandwidth measurements are necessary to identify the two local axis coordinates and unknown scale, but three stations are insufficient when their LoS directions are nearly parallel.Local identifiability requires rank(H) = 3; nearly parallel views make the information matrix poorly conditioned.Source: B. Local Identifiability and Accuracy · p. 7
  • The local covariance and mean-squared angular-error bounds provide lower-bound measures for estimator accuracy.The reported estimator-RMSE and local-CRB curves correspond to the section’s equations.Source: B. Local Identifiability and Accuracy · p. 7
  • Because a and −a yield identical bandwidths, the simulation evaluates acute axis error rather than a signed-axis difference.Source: B. Local Identifiability and Accuracy · p. 7

C. Axial-Rotation Ambiguity

Bandwidth fusion identifies the common rotor-axis direction, but rotation about that axis remains unobservable. The sensing-feasibility analysis relates blade RCS and link conditions to whether weak blade returns can be measured.

C. Axial-Rotation Ambiguity

  • Rotation about the common rotor axis leaves every bandwidth measurement unchanged, so the method estimates axis direction and Doppler scale rather than complete attitude.Resolving the missing attitude component would require an additional body-fixed feature, such as a distinguishable arm or rotor hub, beyond the waveform’s range resolution.Source: C. Axial-Rotation Ambiguity · p. 7

A. Blade RCS and Link Budget

  • Blade RCS varies with viewing aspect; the rectangular-plate model is illustrative, and quantitative system design requires calibrated blade RCS.The model approximates the blade as a thin rectangular plate under a physical-optics approximation.Source: A. Blade RCS and Link Budget · p. 7
  • Received monostatic power depends on component RCS and link conditions, with range entering through an R^4 denominator.For fixed conditions, doubling range requires approximately 12 dB additional transmit power; a 10 dB RCS reduction requires 10 dB additional power at the same range.Source: A. Blade RCS and Link Budget · pp. 7–8
  • Usable micro-Doppler links must meet task-specific thresholds, and every station used for rotor-axis estimation needs a usable bandwidth measurement as well as geometric rank.Blade-feature extraction depends on the weaker dynamic blade RCS after body and clutter suppression, unlike body detection, which is governed by body RCS.Source: §V · p. 7, A. Blade RCS and Link Budget · p. 8

B. Required Observation Time

Observation duration is set by detection, local rotor-rate accuracy, and a minimum blade-pass cycle count. The energy-based duration is an ideal benchmark, not a guarantee of practical estimator accuracy.

B. Required Observation Time

  • The ideal coherent-processing benchmark accumulates blade-echo SNR with observation duration, but it assumes matched processing that exploits the modeled return energy.Directly summing uncompensated phase-modulated samples does not achieve the benchmark gain, and using only some harmonics requires substituting their available power.Source: B. Required Observation Time · p. 8
  • The duration needed for a specified accumulated blade-feature SNR is an ideal detectability benchmark; detecting a harmonic alone does not guarantee accurate bandwidth extraction.The separate rotor-rate duration is a local accuracy benchmark, not a sufficient guarantee that the practical estimator reaches its target RMSE.Source: B. Required Observation Time · p. 8
  • At long range or low power, detection dominates required duration and produces R^4/(Pt,mσb,m) scaling; at short range or high power, the cycle requirement sets a floor.Depending on operating parameters, local rotor-rate accuracy can also limit duration.Source: B. Required Observation Time · p. 9

C. Motion-Limited Coherent Integration

The section bounds coherent integration by residual phase error and range migration, then compares the observation required for sensing with those motion limits.

C. Motion-Limited Coherent Integration

  • Residual translation can move the echo across range bins, so range migration supplies a separate duration limit from residual-phase coherence.The range-migration constraint limits displacement to a fraction of the range resolution.Source: C. Motion-Limited Coherent Integration · p. 9
  • A single-CPI operating point is feasible only when the required observation duration fits within the motion limit and its coherent-loss effect is included in the link margin.Otherwise, the body track must update delay and bulk Doppler over shorter CPIs; longer-term combination is possible, but its fusion algorithm is outside this work.Source: C. Motion-Limited Coherent Integration · p. 9
  • Residual phase error and range migration jointly set the maximum usable duration of a single coherent processing interval.The design relationship combines the observation time required by blade RCS, range, and transmit power with these motion-dependent limits.Source: C. Motion-Limited Coherent Integration · p. 9

VI. NUMERICAL AND EXPERIMENTAL RESULTS

The evaluations test single-station rotor-rate estimation, multi-station rotor-axis recovery, and the link conditions for observing weak blade returns. Simulations and measurements support the processing pipeline, while the link analysis shows that rotor sensing has stricter range requirements than body detection.

A. Simulation Setup

  • The evaluations use 28 GHz, a 0.1 m rotor radius, and a 60-revolutions/s rotor rate unless otherwise stated; statistical multi-station results average 1,000 trials.The three stations and UAV positions are specified for the statistical evaluation, while signal-level and hardware configurations are described separately.Source: §VI · p. 9, A. Simulation Setup · p. 10

B. Single-Station Rotor-Frequency Estimation

  • The weighted harmonic-comb estimator’s rotor-frequency MSE decreases toward the many-cycle local CRB as SNR increases, while low-SNR frequency-selection errors produce large errors.The comparison uses a 0.512 s observation; the local bound does not describe the low-SNR error regime.Source: B. Single-Station Rotor-Frequency… · p. 10

C. Multi-Station Rotor-Axis Estimation

  • The three-station signal-level simulation recovered the imposed pitch motion with 8.68° RMSE and estimated a 99.56-revolutions/s rotor rate against the prescribed 100 revolutions/s.The remaining pitch error was attributed mainly to finite Doppler resolution, aspect-dependent blade returns, bandwidth-extraction errors, and locally unfavorable viewing geometry.Source: C. Multi-Station Rotor-Axis Estimation · p. 10
  • At low bandwidth uncertainty, the joint axis-and-scale estimator’s simulated RMSE closely follows its local CRB; increasing uncertainty produces departures from the bound.Fixing the Doppler scale improves accuracy, but joint estimation remains necessary when effective blade radius or tip speed is unknown.Source: C. Multi-Station Rotor-Axis Estimation · p. 10

D. Sensing Range and Power Requirements

  • Rotor-feature and rotor-axis estimation require higher post-processing SNR than body detection, making their achievable sensing ranges substantially shorter at the same transmit power.The weakest participating station can limit the common sensing range because each station must provide a usable bandwidth measurement.Source: Figure 6 · p. 10, D. Sensing Range and Power Requirements · p. 11

E. Observation Time and Motion Limitations

Observation duration depends on blade-return energy and must fit within motion-limited coherent processing intervals. Hardware experiments demonstrate single-station rotor-rate sensing and three-station recovery of rotor-axis changes across measured configurations.

E. Observation Time and Motion Limitations

  • In the energy-limited regime, required observation time rises with range and falls with transmit power or blade RCS, while short-range or high-power operation approaches a 41.7 ms cycle-limited floor.Transmit power and blade RCS play equivalent roles through their product Ptσb in the energy-limited regime.Source: E. Observation Time and Motion… · p. 11
  • The Fig. 7 residual-phase and range-migration planes mark whether the required observation fits within one CPI; points near or beyond either boundary require improved motion compensation or shorter CPIs.The range-migration plane applies under the assumed motion conditions.Source: E. Observation Time and Motion… · p. 11

1) Single-Station Rotor-Rate Estimation:

  • After MTI suppressed strong near-zero-Doppler returns, the single-station experiment estimated a rotor rate of approximately 59.6 Hz from a two-blade rotor operating near 60 Hz.About 12 blade passages occurred in 0.1 s, and the measured spectrum showed the corresponding harmonic structure.Source: Figure 9 · p. 11, 1) Single-Station Rotor-Rate Estimation · p. 12

2) Multi-Station Rotor-Axis Estimation:

VII. CONCLUSION

  • The paper concludes that micro-Doppler sensing can provide rotor-rate and rotor-axis information beyond conventional UAV position and bulk-velocity sensing.The proposed framework also relates blade RCS, range, transmit power, and observation duration while accounting for motion-induced coherence and range-migration constraints.Source: §VII · p. 13
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