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arxiv: 2507.02385 · v3 · pith:C4MF3K7Snew · submitted 2025-07-03 · 📡 eess.SP

Parameter estimation of range-migrating targets using OTFS signals from LEO satellites

Tong Ding , Luca Venturino , Emanuele Grossi This is my paper

Pith reviewed 2026-05-19 06:55 UTC · model grok-4.3

classification 📡 eess.SP
keywords OTFS modulationrange migrationparameter estimationLEO satellitesintegrated sensing and communicationdelay-Doppler domainsparse responsemaximum likelihood estimation
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The pith

OTFS signals from LEO satellites produce a sparse target response in the delay-Doppler domain whose support depends on initial range and range rate.

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

This paper develops a communication-centric integrated sensing and communication system that uses orthogonal time-frequency space signals from low Earth orbit satellites to estimate parameters of high-speed targets that experience range migration. It derives a new input-output model for the echo when ideal rectangular shaping filters are used, showing that the target response has a sparse structure in the delay-Doppler domain determined by the target's initial range and range-rate. Range migration causes a specific structured spread in this response that is characterized explicitly and differs from earlier models. An approximate maximum likelihood estimator is proposed that uses block orthogonal matching pursuit for coarse estimation and a bank of matched filters for refinement, with an iterative extension for handling multiple targets.

Core claim

The paper establishes that for high-speed targets with range migration, the echo in an OTFS system with ideal rectangular shaping filters exhibits a sparse structure in the delay-Doppler domain. The support of this sparse response is set by the initial range and the range-rate of the target. Range migration produces a structured spread around this support, which the authors characterize in detail and show to be different from previous models. This model underpins an approximate implementation of the maximum likelihood estimator for the target's initial range, range-rate, and amplitude.

What carries the argument

The novel input-output model that maps the high-speed target's echo to a sparse response in the delay-Doppler domain, with support fixed by initial-range and range-rate and a characterized spread due to range migration.

If this is right

  • Coarse information on the target response can be obtained efficiently using a block orthogonal matching pursuit algorithm.
  • Refinement of the estimates uses a bank of matched filters over a smaller initial-range and range-rate region.
  • The single-target estimator extends to multiple targets through iterative estimation, reconstruction, and cancellation of dominant echoes.
  • Numerical examples demonstrate the estimation performance of the proposed method.

Where Pith is reading between the lines

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

  • The model might enable better integration of sensing and communication in satellite networks by exploiting the sparsity for lower complexity processing.
  • If the assumptions hold in practice, this approach could reduce computational demands compared to exhaustive search methods for parameter estimation.
  • Extending the model to account for non-ideal filters or time-varying range-rates would test its robustness in more realistic scenarios.

Load-bearing premise

The model relies on the use of ideal rectangular shaping filters and the assumption of constant range-rate motion over the observation interval.

What would settle it

Simulate or measure the received OTFS signal from a target with known initial range and range-rate using rectangular filters; if the energy in the delay-Doppler domain does not concentrate in the predicted sparse support locations accounting for the range migration spread, the model would be falsified.

Figures

Figures reproduced from arXiv: 2507.02385 by Emanuele Grossi, Luca Venturino, Tong Ding.

Figure 1
Figure 1. Figure 1: System geometry. and operates with a carrier frequency c/λ, where λ is the carrier wavelength; the emitted waveform is specified by the underlying communication protocol and cannot be modified to adjust the radar needs. The radar receiver aims to estimate the initial range (delay), range-rate (Doppler shift), and amplitude of high-speed targets illuminated by the communication trans￾mitter; it may be mount… view at source ↗
Figure 2
Figure 2. Figure 2: |Φ[k, l]| vs k = 0, . . . , N − 1 and l = 0, . . . , M − 1 for Cases 1, 2, and 3, when B = 4, N = M = 64, and ideal shaping filters are employed. for b = 0, . . . , B − 1, where lb,int ∈ {0, 1, . . . , M − 1}, kint ∈ {0, 1, . . . , N − 1}, and lb,fra, kfra ∈ (−0.5, 0.5]. Then, from (23) and (27) we have Φ[k, l] = 1 B B X−1 b=0 e −i2π  k−kint−kfra B  bD N B  k − kint − kfra N  × DM  −  l − lb,int − lb… view at source ↗
Figure 3
Figure 3. Figure 3: RMSEr (left), RMSErr (center), and NRMSEα (right) versus B = 1, 2, 4, 8, 16, 32, 64, 128 for SNR = 10, 20, 30 dB, when a high- or low-speed target is present and ideal shaping filters are employed. Both the ML and the proposed estimator are considered for comparison. 0 5 10 15 20 25 30 10-1 100 101 102 Ideal Rectangular 0 5 10 15 20 25 30 10-2 10-1 100 101 Ideal Rectangular 0 5 10 15 20 25 30 10-3 10-2 10-… view at source ↗
Figure 4
Figure 4. Figure 4: RMSEr (left), RMSErr (center), and NRMSEα (right) versus SNR for B = 4, 8, 16, when a high-speed target is present and the proposed estimator is employed. Both ideal and rectangular shaping filters are considered. during the OTFS frame is v¯maxNT = 136 m, corresponding to about 7 times the range resolution Rr; the initial range d and the range-rate v are randomly generated, while a Swerling I fluctuation m… view at source ↗
Figure 5
Figure 5. Figure 5: RMSEr (left), RMSErr (center), and NRMSEα (right) versus v¯min, when rectangular filters are used, SNR = 15 dB, and v¯max = ¯vmin+1 km/s. The proposed estimator is implemented for B = 1, 2, 4, 8, 16. For comparison, the performance of the estimators presented in [20] and [28] is also evaluated. 0 5 10 15 20 25 30 100 101 Proposed Single target bound Target 1 Target 2 Target 3 0 5 10 15 20 25 30 10-1 100 10… view at source ↗
Figure 6
Figure 6. Figure 6: RMSEr (left), RMSErr (center), and NRMSEα (right) versus SNR2, when rectangular filters are used, P = 3 high-speed targets are present, B = 16, and SNR1/SNR2 = SNR2/SNR3 = 10. The performance of the proposed CLEAN-based estimator and the corresponding single-target performance bound are reported. rectangular filters achieve estimation performance that closely approximates that of the ideal filters. Finally… view at source ↗
Figure 7
Figure 7. Figure 7: |F [k, l]|/σω vs k = 0, . . . , N − 1 and l = 0, . . . , M − 1 at the first (top), second (middle), and third (bottom) iteration of the CLEAN procedure, when rectangular filters are employed, P = 3 high-speed targets are present, B = 16, SNR1 = 30 dB, SNR2 = 20 dB, and SNR3 = 10 dB. avoids exhaustive search in the delay-Doppler domain. If combined with the CLEAN algorithm, the proposed procedure can also h… view at source ↗
read the original abstract

This study investigates a communication-centric integrated sensing and communication system that utilizes orthogonal time-frequency space (OTFS) modulated signals emitted by low Earth orbit satellites to estimate the parameters of space targets experiencing range migration, hereinafter referred to as high-speed targets. Leveraging the signal samples produced by off-the-shelf OTFS demodulators, we derive a novel input-output model for the echo generated by a high-speed target when ideal and rectangular shaping filters are employed. Our findings reveal that the target response exhibits a sparse structure in the delay-Doppler domain, whose support is determined by the target initial-range and range-rate. Range migration induces a structured spread of this response, which is explicitly characterized in the paper and differs from that in previous models. We propose an approximate implementation of the maximum likelihood estimator for the target initial-range, range-rate, and amplitude. The estimation process first obtains coarse information on the target response using a block orthogonal matching pursuit algorithm, followed by a refinement step based on a bank of matched filters focused on a smaller initial-range/range-rate region. The proposed single-target procedure is extended to multiple targets via iterative estimation, reconstruction, and cancellation of dominant echoes. Finally, numerical examples are provided to evaluate the estimation performance.

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 manuscript derives a novel input-output model for echoes from high-speed range-migrating targets illuminated by OTFS signals transmitted from LEO satellites. Under the assumptions of ideal rectangular shaping filters and constant range-rate motion, the target response is shown to be sparse in the delay-Doppler domain with support set by initial range and range-rate; range migration produces an explicitly characterized structured spread that differs from prior models. An approximate maximum-likelihood estimator is constructed via block orthogonal matching pursuit for coarse support recovery followed by a bank of matched filters for refinement of initial range, range-rate, and amplitude; the single-target procedure is extended to multiple targets by iterative cancellation. Numerical examples evaluate estimator performance.

Significance. If the derived input-output model and the associated estimator are accurate under the stated assumptions, the work provides a concrete advance for communication-centric ISAC in satellite systems by supplying a tailored delay-Doppler characterization of range migration that can be exploited by standard OTFS demodulator outputs. The explicit sparse structure and the block-OMP-plus-matched-filter architecture constitute a practical algorithmic contribution that could be directly implemented in LEO-based sensing pipelines.

major comments (2)
  1. [Input-output model derivation] The central input-output model (derived in the section presenting the echo signal model) rests on ideal rectangular shaping filters and strictly constant range-rate during the observation interval. Because the claimed sparse support and the structured spread induced by range migration are obtained directly from these assumptions, the manuscript must supply either a first-order perturbation analysis or Monte-Carlo trials that quantify estimator degradation when realistic pulse-shaping roll-off or quadratic range terms from LEO acceleration are introduced.
  2. [Numerical examples] In the numerical results section, the reported RMSE curves for range-rate and initial range are presented without comparison to the Cramér-Rao bound or to a conventional range-Doppler matched filter that ignores the derived sparse structure. Without such benchmarks it is impossible to determine whether the observed performance gain is attributable to the novel model or simply to the increased computational effort of the two-stage procedure.
minor comments (2)
  1. [Notation and model] Notation for the delay-Doppler grid indices and the range-migration spread parameters should be introduced once in a dedicated table or equation block rather than redefined inline in multiple sections.
  2. [Abstract and introduction] The abstract states that samples are taken from off-the-shelf OTFS demodulators while the model assumes ideal rectangular filters; a short clarifying sentence in the introduction would resolve the apparent tension.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address each major comment below and outline the revisions planned for the manuscript.

read point-by-point responses

  1. Referee: [Input-output model derivation] The central input-output model (derived in the section presenting the echo signal model) rests on ideal rectangular shaping filters and strictly constant range-rate during the observation interval. Because the claimed sparse support and the structured spread induced by range migration are obtained directly from these assumptions, the manuscript must supply either a first-order perturbation analysis or Monte-Carlo trials that quantify estimator degradation when realistic pulse-shaping roll-off or quadratic range terms from LEO acceleration are introduced.

    Authors: We agree that the derivation relies on ideal rectangular shaping filters and constant range-rate, as stated in the manuscript. To strengthen the work, we will add Monte-Carlo trials in the revised numerical section that evaluate estimator degradation under realistic pulse-shaping roll-off factors and under quadratic range variations that model LEO acceleration effects. These simulations will quantify performance sensitivity while preserving the core model derivation under the stated assumptions. revision: yes

  2. Referee: [Numerical examples] In the numerical results section, the reported RMSE curves for range-rate and initial range are presented without comparison to the Cramér-Rao bound or to a conventional range-Doppler matched filter that ignores the derived sparse structure. Without such benchmarks it is impossible to determine whether the observed performance gain is attributable to the novel model or simply to the increased computational effort of the two-stage procedure.

    Authors: We acknowledge the value of additional benchmarks. In the revision we will include RMSE comparisons to the Cramér-Rao bound derived under the paper's signal model and to a conventional range-Doppler matched filter that does not exploit the sparse delay-Doppler structure. These additions will help isolate the contribution of the proposed model and estimator. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained under explicit filter and motion assumptions; no reduction to fitted inputs or self-citation chains

full rationale

The input-output model is obtained by direct substitution of ideal rectangular shaping filters and constant range-rate kinematics into the standard OTFS modulation and demodulation equations; the resulting sparse delay-Doppler support and structured range-migration spread follow algebraically from those substitutions without any parameter fitted to the target data inside the paper. The subsequent approximate ML estimator is constructed as a two-stage procedure (block-OMP coarse search followed by a bank of matched filters) whose steps are defined by the derived model itself rather than by any quantity that was previously estimated from the same observations. No load-bearing premise is justified solely by a self-citation whose authors overlap with the present work, and the paper does not rename an existing empirical pattern or smuggle an ansatz through prior work. The derivation therefore remains independent of its own outputs and is falsifiable against external benchmarks once the rectangular-filter and constant-range-rate assumptions are relaxed.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central model rests on the assumption of ideal rectangular shaping filters and constant range-rate motion; no explicit free parameters or new invented entities are introduced in the abstract description.

axioms (2)
  • domain assumption Ideal and rectangular shaping filters are employed at transmitter and receiver.
    Stated in the abstract as the condition under which the novel input-output model is derived.
  • domain assumption Target range-rate is constant during the observation interval.
    Implicit in the definition of range migration and the support of the sparse response.

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Reference graph

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