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UW-OCDM for Low-Altitude UAV Communication and Cooperative Sensing

Yi Tao, Zhen Gao, Ziwei Wan, Yuezu Lv, Hua Wang, Kaibin Huang, Sheng Chen

arXiv:2608.21050v1eess.SPcs.IT

TL;DR

High-mobility UAV networks need communication and sensing despite severe Doppler and rapidly varying, doubly-selective channels. The paper proposes UW-OCDM with shared communication and cooperative-sensing procedures, and reports reliable communication and localization with low-complexity equalization and reduced reference-sharing overhead.

  • Problem

    High-speed UAV mobility creates severe Doppler and fast time-varying, doubly-selective channels that challenge reliable communication and sensing.

  • Method

    The framework embeds a deterministic UW into OCDM for synchronization, Doppler compensation, sparse channel estimation, and locally constructed multi-static sensing dictionaries.

  • Results

    The framework demonstrates reliable communication and localization in highly dynamic UAV scenarios while retaining low-complexity FDE and reducing transmit-reference sharing overhead.

  • Takeaways & Limitations

    A deterministic UW can support both communication reception and cooperative sensing without requiring real-time exchange of full payload-dependent transmit references.

Abstract

from arXiv · show

Integrated sensing and communications (ISAC) is a key enabler for uncrewed aerial vehicles (UAVs) in the low-altitude economy. This paper proposes an ISAC waveform that embeds a unique word (UW) into orthogonal chirp division multiplexing (OCDM), termed UW-OCDM, together with corresponding communication reception and cooperative sensing schemes for high-mobility UAV scenarios. For communication, the embedded UW enables timing synchronization and Doppler estimation and compensation without requiring a separate synchronization sequence. A sparse spatio-temporal channel estimation method exploits the common channel support across multiple receive antennas and consecutive UW observations to support reliable data demodulation. For sensing, the deterministic UW serves as a shared prior that allows distributed base stations to construct sensing dictionaries locally without exchanging random payload symbols in real time. A hierarchical multi-target detection and tracking algorithm integrates direct-path interference suppression, kinematic prediction, multi-candidate screening, off-grid refinement, residual verification, and successive interference cancellation for robust localization with reduced search complexity. Simulation results demonstrate reliable communication and localization in highly dynamic UAV scenarios, while the proposed framework retains low-complexity frequency-domain equalization and reduces transmit-reference sharing overhead and multi-static localization complexity.

I. Introduction

Low-altitude UAV networks require integrated communication and sensing despite severe Doppler, fast time variation, and doubly-selective fading. The paper addresses these demands with a UW-OCDM framework that reuses a deterministic unique word across synchronization, reception, and cooperative sensing.

  • Motivation: High-speed UAV mobility causes severe Doppler shifts and fast time-varying channels that challenge both data transmission and sensing localization.
  • Motivation: Doubly-selective fading shortens channel coherence time, destroys waveform orthogonality, and triggers inter-carrier interference.
  • Motivation: Independent designs for synchronization, channel estimation, demodulation, and localization would increase reference-signal overhead and complicate reliable module-level performance.
  • Proposed framework: UW-OCDM embeds a deterministic unique word into OCDM, whose quadratic-phase chirp structure provides improved Doppler robustness and a reusable signal reference.
  • Communication reception: The communication receiver uses the UW for timing synchronization, Doppler estimation and compensation, and sparse spatio-temporal channel estimation before data demodulation.
  • Cooperative sensing: Distributed base stations use the known UW and system parameters to construct sensing dictionaries locally, while hierarchical detection and tracking combines prediction, refinement, verification, and interference cancellation.

B. Multi-Static Cooperative Sensing Model

The sensing model uses one transmitting base station, its receive array, and distributed receiving base stations to localize multiple UAV targets from bistatic delays and spatial signatures. The surrounding OCDM construction supplies the chirp-based signal structure used by the proposed waveform.

  • Multi-Static Cooperative Sensing Model: BS-A transmits a downlink signal that illuminates UAV targets, while BS-A and distributed base stations receive their scattered echoes for cooperative sensing.
  • Multi-Static Cooperative Sensing Model: The sensing network comprises BS-A with an N (A)rx-element ULA and I distributed receiving base stations, each using a single omnidirectional antenna.
  • Measurement signatures: Distributed receivers primarily observe bistatic delay, whereas BS-A additionally preserves monostatic delay and array spatial response associated with target bearing.
  • Measurement signatures: The cooperative localization model uses delay and spatial signatures from the sensing observations, which also contain superposed echoes, direct-path interference, and receiver noise.
  • OCDM preliminaries: OCDM is a Fresnel-transform multicarrier scheme using mutually orthogonal linear-frequency-modulation chirps, with N orthogonal sub-chirps spanning the synthesized signal bandwidth.

B. Proposed UW-OCDM Waveform Design

UW-OCDM embeds a deterministic UW into OCDM by reserving Fresnel-domain resources and synthesizing the time-domain tail. The design trades communication efficiency against UW processing and observation benefits.

  • Waveform construction: UW-OCDM replaces the data-dependent symbol tail with a deterministic UW sequence for integrated communication and sensing.The adopted UW is a unit-power QPSK sequence.
  • Waveform construction: The Fresnel-domain sub-chirps are partitioned into data and UW-generating sets, with uniformly interleaved UW resources producing a data payload followed by a deterministic UW.The data and UW-generating sets have sizes Nd = N − Ng and Ng, respectively.
  • UW synthesis: UW synthesis solves a linear tail constraint using a minimum ℓ2-norm solution obtained through the right Moore-Penrose pseudoinverse.The constraint is formed by subtracting the data contribution from the desired UW tail.
  • Implementation: The pseudoinverse depends only on waveform dimensions and index sets, so it is computed offline; online generation costs O(N log N + NgNUW) per antenna and symbol.No matrix inversion or pseudoinverse update is required online.
  • Resource trade-off: Increasing NUW enlarges the ISI-free observation window, whereas increasing Ng provides more synthesis freedom but reduces the number of data-bearing sub-chirps and net spectral efficiency.The choices of NUW and Ng jointly determine processing gain and communication efficiency.
  • Implementation: PAPR mitigation is handled in the BS-A transmit chain, and clipping must limit distortion of the deterministic UW.Input backoff, digital predistortion, clipping, and filtering are identified as mitigation options.

A. UW-Assisted Timing Synchronization

The receiver synchronizes UW-OCDM symbols by sliding cross-correlation, then uses aligned, ISI-free UW observations to estimate and compensate Doppler. Shared phase structure across antennas and observations supports robust estimation.

  • Timing synchronization: UW correlation assumes the channel is approximately quasi-static within one UW, enabling the receiver to distinguish UW contributions during synchronization.For the stated 5 GHz, 40 MHz, 256-sample, 150 km/h setting, the maximum phase drift is approximately 0.028 rad.
  • Timing synchronization: The receiver evaluates a multi-antenna timing statistic by accumulating correlation energies across receive antennas and UWs, then accepts the strongest valid peak above γsyn.The accepted peak determines the estimated UW-OCDM symbol starting index.
  • Observation alignment: After alignment, absolute stream samples are indexed by aligned UW-OCDM symbols, and consecutive UW observations are extracted for Doppler estimation.The mapping is nabs(b,n) = ℓ̂start + bN + n.
  • ISI-free observation: The first Lmax samples of each selected UW are discarded, leaving G = NUW − Lmax samples in an ISI-free observation window.This removes data-induced ISI caused by the multipath delay spread.
  • Doppler estimation: Separated ISI-free UW observations differ primarily by a common LoS Doppler phase rotation because path delays remain stable while complex gains may vary.The phase is common across antennas, UW pairs, and samples under the adopted pairwise model.
  • Doppler estimation: The global cross-correlation phase ∠ρglobal is the maximum-likelihood estimate of the accumulated phase difference under the adopted disturbance model.The estimate maximizes Re{ρglobal e^−jφ} modulo 2π.
  • Doppler compensation: The estimated Doppler is used to de-rotate each symbol, after which the ISI-free UW segment is passed to spatio-temporal joint channel estimation.This completes the timing-frequency alignment before subsequent communication processing.
  • Doppler estimation: Increasing the number of accumulated UW observations improves noise suppression, but the maximum Doppler estimation range is governed by the single-step interval DN Ts.The accumulated phase must remain below π to avoid phase ambiguity.

C. MMV-OMP-Based Joint Channel Estimation

The receiver estimates a sparse MIMO channel by exploiting common path delays across antennas and consecutive UW observations, then uses the resulting representative CIR for low-complexity frequency-domain equalization and demodulation.

  • The channel-estimation model concatenates Doppler-compensated, ISI-free UW observations across receive antennas and symbols.A global observation matrix and horizontally concatenated Toeplitz UW convolution submatrices form the MMV compressed-sensing problem.
  • Joint row-sparsity models common path-delay support across receive antennas and consecutive UW observations despite varying complex path gains.MMV-OMP identifies the shared support before estimating channel coefficients.
  • Phase alignment combines adjacent UW-pair estimates into a representative CIR for subsequent receiver processing.The representative CIR is used under a post-compensation symbol-wise quasi-static approximation.
  • The receiver applies an MMSE frequency-domain equalizer, inverse DFT, and DFnT decoupling before extracting payload symbols and QAM-demodulating the recovered bits.The equalization stage remains low-complexity, while inverse DFT and DFnT transforms retain O(N log N) complexity.
  • Although equalization is low-complexity, total receiver complexity exceeds LS-based CP-OFDM because MMV-OMP requires iterative correlations and support-restricted LS updates.

V. Multi-Static UAV Sensing and Localization

The cooperative sensing framework uses deterministic UW signatures to build local sensing dictionaries at distributed base stations and suppress direct-path interference before localization.

  • The local dictionary maps candidate positions to geometry-dependent delay and Doppler signatures, including a full space-time atom at BS-A.Delay atoms are constructed using the Fourier time-shifting property and frequency-domain delay factors.
  • Each cooperative base station reconstructs local sensing atoms from the deterministic UW and stored system configuration without acquiring per-symbol payload data.Random-payload coherent sensing would require real-time transmit-reference sharing or local decoding.
  • Direct-path energy can be tens of decibels stronger than scattered UAV echoes, so direct-path interference suppression is applied independently at each receiving base station.The suppression uses atoms derived from known station geometry or a calibrated direct channel.
  • The cleaned residuals are projected onto local orthogonal subspaces before sequential multi-target searches to reduce subspace mismatch.

B. Iterative Coarse-to-Fine Multi-Target Localization

Localization proceeds hierarchically from tracked-target prediction and global coarse acquisition to candidate-wise fine search, adaptive region expansion, and off-grid refinement.

  • The algorithm prioritizes previously tracked targets by extrapolating their positions and ordering them by normalized matching scores.Strong tracked targets are scheduled before weaker ones, followed by a global-acquisition attempt.
  • Predicted candidates enter local refinement directly, while failed verification or unscheduled attempts invoke global coarse-grid acquisition.
  • Global searches exclude neighborhoods around previously accepted positions and retain up to Mc spatially separated peaks through nonmaximum suppression.
  • Candidate extraction stops when no retained peak remains or the largest score falls below γth.
  • Boundary-adjacent spectral peaks trigger successive region expansions until the peak leaves the boundary or the maximum expansion level is reached.This addresses prediction or coarse-grid errors that place a peak outside the initial search region.
  • Axis-wise parabolic interpolation performs off-grid refinement to reduce residual spatial discretization error.

4) Candidate Verification and Interference Cancellation:

Candidates are admitted to tracking and successive interference cancellation only after multi-base-station residual verification, linking accepted positions to track updates or new-track initialization.

  • Each candidate is temporarily added to the active dictionary, its least-squares coefficients are computed, and the resulting transient residual is evaluated.
  • The joint residual-reduction ratio compares aggregate multi-base-station residual energy before and after temporary candidate inclusion.
  • Only candidates satisfying the residual-reduction threshold ξth proceed to final selection and acceptance.If no candidate passes, the algorithm follows its fallback or termination procedure.
  • An accepted candidate updates its associated track or initializes a new track with zero velocity when no association exists.
  • Accepted candidates retain their temporary dictionaries, coefficients, and residuals for SIC, so only candidates that consistently reduce multi-BS residual energy enter cancellation.

C. Computational Complexity Analysis

The localization search uses coarse acquisition followed by candidate-wise fine refinement, with prediction-based tracking reducing computation during stable operation.

  • Complexity Evaluation: Coarse acquisition requires O(NcoaNc) operations, while refining candidates requires O(NfineNloc) operations per candidate.The coarse search uses the first BS-A receive antenna and distributed BS observations.
  • Complexity Evaluation: A conservative upper bound combines global acquisition and at most Mc + 1 local refinements over Kmax attempts.The bound accounts for prediction failure and global fallback.
  • Stable Tracking: During stable tracking, updating Q verified tracks has dominant complexity O(QNfineNloc) because prediction-based candidates bypass global acquisition.This reduces repeated coarse searches when predictions pass verification.
  • Coarse-to-Fine Localization: The algorithm performs DPI suppression, kinematic prediction, candidate screening, refinement, verification, and SIC across up to Kmax attempts.Established tracks are prioritized before coarse or prediction-based candidate processing.

VI. Simulation Results

Simulations evaluate UW-OCDM communication under high mobility and compare power constraints, resource allocations, and channel-estimation strategies. The results favor relaxed amplitude constraints, equispaced UW allocation, and two-UW spatio-temporal estimation.

  • Simulation Setup: The simulated system uses 5 GHz carrier frequency, 40 MHz bandwidth, 16-QAM payloads, and three distributed sensing BSs.BS-A transmits to the UAV, while BS-A and the distributed BSs receive cooperative sensing echoes.
  • UW Sub-Chirp Power Constraints: At Ath = 2, severe amplitude limiting increases CE NMSE, while Ath = 16 yields the best NMSE and BER within the evaluated settings.Clip suffers the greatest distortion under the severe limit; relaxing the constraint is therefore adopted without additional clipping.
  • UW Resource Index Allocation: Fully random UW allocation severely degrades CE NMSE and BER, whereas equispaced allocation is adopted for UW-OCDM because its quadratic phase suppresses repetitive behavior.Random clusters and gaps worsen UW-generation conditioning and reduce payload power under equal total transmit power.
  • Channel Estimation: Two-UW ST-MMV-OMP achieves lower CE NMSE and BER than single-UW spatial MMV-OMP, while MMV-OMP outperforms full-dimensional estimators.The comparison attributes the gain to temporal coupling and joint support recovery across observations.

3) Channel Estimation Performance:

The channel-estimation and sensing evaluations compare waveform, velocity, and localization configurations. Results support UW-assisted estimation, off-grid refinement, SIC, and receive-array processing, while accuracy remains deployment-geometry dependent.

  • Mobility Robustness: Across 0–300 km/h, both UW-OFDM and UW-OCDM maintain favorable BER because dominant LoS Doppler is estimated from adjacent UWs and compensated before equalization.At high SNR, NMSE gradually degrades with velocity as residual Doppler becomes more pronounced after compensation.
  • Waveform Performance Comparison: UW-OCDM achieves lower NMSE and BER than CP-OCDM, practical CP-OFDM, and ideal CP-OFDM, while retaining the best high-SNR performance among evaluated practical schemes.The results attribute complementary gains to OCDM modulation, the deterministic UW reference, and sparse MMV channel estimation.
  • 3D Trajectory Tracking Performance: Estimated positions closely follow two ground-truth UAV trajectories over 80 epochs without track loss or evident error accumulation.Track association remains correct through changes in direction, altitude, and random RCS fluctuations.
  • Scope Boundary: Localization accuracy varies with BS-target geometry, and topology optimization is outside the paper’s scope.The adopted deployment is representative rather than optimized; dictionaries can be reconstructed for other BS coordinates.
  • Ablation Study on Localization Performance: Reducing the BS-A receive array from 8 to 4, 2, and 1 antennas increases RMSE and consistently decreases detection success rate.The ablation confirms the spatial-discrimination gain provided by the receive array.

3) Localization Baseline Comparison:

The proposed localization method is compared with ablations and representative baselines using detection success rate, 3D localization RMSE, and clock-offset robustness. At higher SNR, it achieves lower average RMSE and higher average detection success rate while maintaining a favorable performance–complexity balance.

  • Evaluation setup: The evaluation compares target detection success rate and 3D localization RMSE against ablations and representative localization baselines.The ablations include off-grid refinement, successive interference cancellation, and receive-array components.
  • Complexity comparison: ROI-CML-SIC, FG-JCML, and SRR incur different search or estimation costs through full-grid searches, candidate-pair processing, or active-set screening.Stable tracking with the proposed method requires O(QNfineNloc), with fallback using the smaller dimension Ncoa.
  • Performance comparison: As SNR increases, the proposed method achieves lower average RMSE and higher average target detection success rate.At low SNR, noise dominates target echoes and no consistent performance ordering appears.
  • Performance comparison: The observed performance is consistent with kinematic prediction, multi-candidate screening, adaptive ROI expansion, off-grid refinement, residual verification, and SIC.These processing stages jointly support multi-target localization under the evaluated conditions.
  • Clock-offset robustness: Residual inter-BS clock offsets perturb geometry-dependent delays in the sensing dictionary, increasing localization error and reducing success rate as offsets grow.At SNR 25 dB, degradation is negligible for σclk ≤0.1Ts, while pronounced degradation occurs near half a sampling interval.
  • Clock-offset robustness: Fully asynchronous operation requires joint clock-position estimation, defining a synchronization boundary for the cooperative localization method.The impact of clock offsets depends on sampling rate, SNR, and BS-target geometry.
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