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arxiv: 2604.06790 · v1 · submitted 2026-04-08 · 📡 eess.SP

Zero-Overhead Unambiguous Velocity Estimation in Multiband ISAC Systems Under Random Traffic

Aurora Peloso , Michele Rossi , Jacopo Pegoraro This is my paper

Pith reviewed 2026-05-10 18:23 UTC · model grok-4.3

classification 📡 eess.SP
keywords ISACvelocity estimationDoppler ambiguitymultibandmixed-integer quadratic programphase differencerandom trafficzero-overhead sensing
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The pith

Multiband ISAC recovers true target velocity from irregular packet arrivals by solving a mixed-integer quadratic program over cross-band phase differences.

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

The paper shows that modern ISAC systems, which share spectrum between communication and sensing, can still produce reliable velocity estimates even when communication packets arrive at unpredictable times. Irregular timing normally creates Doppler aliasing that makes velocity ambiguous. The authors avoid both dedicated sensing slots and regular sampling by using phase measurements across multiple carrier frequencies. They cast the problem as a mixed-integer quadratic program that considers all pairwise packet combinations and anchors the solution with any single unambiguous phase observation. Simulations with real traffic traces confirm that the approach outperforms single-band and likelihood-based alternatives, with performance rising as frequency separation and inter-packet gaps grow.

Core claim

By formulating multiband velocity estimation as a mixed-integer quadratic program that uses phase differences from every possible pair of received packets and by requiring only one unambiguous phase measurement, the system reconstructs the true target velocity without imposing any constraints on packet timing or adding sensing overhead.

What carries the argument

Mixed-integer quadratic program over multiband pairwise phase differences, anchored by at least one unambiguous phase measurement.

If this is right

  • Velocity accuracy increases with greater frequency separation between bands.
  • Performance improves when inter-packet time intervals are longer.
  • No extra communication resources or regular sampling schedule is required.
  • The same framework works for any traffic pattern that produces at least one usable unambiguous phase.

Where Pith is reading between the lines

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

  • The approach could be combined with existing range-estimation techniques to produce joint range-velocity maps in the same zero-overhead manner.
  • Hardware implementations with three or more bands would allow the optimizer to select the best unambiguous anchor automatically.
  • The method may extend to other periodic parameters, such as acceleration, if similar phase-difference identities can be written.

Load-bearing premise

At least one phase measurement across the available bands must be free of 2π ambiguity, and the optimizer must correctly identify the velocity despite noise and irregular arrivals.

What would settle it

A set of measurements in which every cross-band phase difference is wrapped by an integer multiple of 2π, yet the optimizer still outputs the correct velocity.

Figures

Figures reproduced from arXiv: 2604.06790 by Aurora Peloso, Jacopo Pegoraro, Michele Rossi.

Figure 1
Figure 1. Figure 1: Overview of the proposed method. done in multi-PRF radar systems [3], [5]. The latter approach exploits different Doppler ambiguities observed across mul￾tiple sampling rates to reconstruct an unambiguous Doppler estimate. Neither approach is well-suited for ISAC systems, where channel estimation is inherently opportunistic and contingent upon the random packet arrivals dictated by the network traffic [6].… view at source ↗
Figure 2
Figure 2. Figure 2: Velocity estimation results changing Tmax. N1 = 4 N1 = 8 N1 = 12 5.0 7.0 14.0 28.0 60.0 10−1 10−2 10−3 10−4 10−5 10−6 10−7 Band 2 [GHz] Error εv (a) σwϕ = 10◦. 5.0 7.0 14.0 28.0 60.0 10−1 10−2 10−3 10−4 10−5 10−6 10−7 Band 2 [GHz] Error εv (b) σwϕ = 20◦ [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Velocity estimation results changing the number of packets [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Velocity estimation results for a multiple-component target [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Velocity estimation results comparisons, with [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

This paper proposes an original method for estimating the velocity of a target by leveraging the multiband capabilities of modern Integrated Sensing And Communication (ISAC) systems. Traditional Doppler estimation relies on regular sampling rates, but ISAC systems often face irregular packet arrival times because they reuse opportunistic communication traffic. This non-deterministic timing increases the risk of Doppler ambiguity and aliasing, degrading velocity estimation accuracy. To resolve this, we advocate exploiting frequency diversity across multiple carrier frequencies to observe Doppler shifts without imposing restrictions on packet timing or requiring dedicated sensing overhead. A multiband velocity estimation problem is here formulated as a mixed-integer quadratic program by utilizing phase differences from all possible pairwise packet combinations. By integrating at least one unambiguous phase measurement, the system can reconstruct the true target velocity even under sporadic traffic conditions. Simulation results using realistic traffic traces demonstrate that this approach significantly outperforms multiband likelihood-based and single-band algorithms, with accuracy improving as frequency separation between bands and inter-packet time intervals increase. This framework provides a zero-overhead solution for robust velocity estimation in dynamic ISAC environments.

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 zero-overhead method for unambiguous velocity estimation in multiband ISAC systems under random/opportunistic traffic. It formulates the multiband Doppler problem as a mixed-integer quadratic program (MIQP) that exploits phase differences across all pairwise packet combinations and multiple carrier frequencies; the central claim is that the presence of at least one unambiguous phase measurement allows the MIQP to recover the true velocity, with simulations on realistic traffic traces showing superiority over multiband likelihood-based and single-band estimators as frequency separation and inter-packet intervals increase.

Significance. If the central claim holds, the work supplies a practical, overhead-free technique for velocity estimation in dynamic ISAC environments where packet timing is dictated by communication traffic rather than regular sensing schedules. The MIQP formulation that jointly processes multiband phase differences is a technically interesting approach to resolving Doppler aliasing without dedicated pilots.

major comments (2)
  1. [Abstract and §III] Abstract and §III (problem formulation): the claim that the method works 'by integrating at least one unambiguous phase measurement' is load-bearing, yet the manuscript provides neither an analytic condition on minimum inter-packet interval Δt, carrier frequencies, and velocity range that guarantees existence of such a pair nor a detection mechanism to identify it. Under sufficiently sporadic traffic the minimum Δt can make every pairwise phase difference wrap (|2π f Δt v/c| ≥ π), rendering the integer program under-determined and the velocity estimate non-unique.
  2. [§IV and §V] §IV (MIQP formulation) and §V (simulations): the MIQP objective and constraints are not shown to remain robust or to possess a unique solution when no unambiguous anchor exists; the reported simulation superiority may therefore be conditioned on the particular traffic traces chosen, which may not include worst-case large-gap realizations.
minor comments (2)
  1. [§III] Notation for the phase-difference wrapping condition should be stated explicitly with an equation (e.g., the definition of the integer ambiguity variable) rather than left implicit.
  2. [§V] The traffic-trace statistics (minimum, mean, and distribution of inter-packet intervals) should be reported so readers can judge how close the evaluated scenarios are to the regime where all measurements become ambiguous.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the insightful and constructive comments on our manuscript. We address each major comment point by point below and commit to revisions that strengthen the theoretical foundations and simulation coverage without misrepresenting the original contributions.

read point-by-point responses

  1. Referee: [Abstract and §III] Abstract and §III (problem formulation): the claim that the method works 'by integrating at least one unambiguous phase measurement' is load-bearing, yet the manuscript provides neither an analytic condition on minimum inter-packet interval Δt, carrier frequencies, and velocity range that guarantees existence of such a pair nor a detection mechanism to identify it. Under sufficiently sporadic traffic the minimum Δt can make every pairwise phase difference wrap (|2π f Δt v/c| ≥ π), rendering the integer program under-determined and the velocity estimate non-unique.

    Authors: We agree that the manuscript does not supply an explicit analytic condition guaranteeing the existence of at least one unambiguous phase-difference pair, nor a separate detection step to identify it. The central claim in the abstract and §III is therefore conditional on the presence of such a pair. In the revision we will add to §III a sufficient condition derived from the maximum target velocity, the minimum carrier-frequency separation, and the maximum admissible inter-packet interval: if the smallest frequency separation Δf satisfies Δf > c/(2 v_max Δt_max), then at least one pair remains unambiguous for any velocity in the considered range. We will also clarify that the MIQP itself does not contain an explicit detection mechanism; instead, the integer variables are jointly optimized over all pairs, and the solver returns the velocity that minimizes the quadratic residual subject to the wrap constraints. When no unambiguous anchor exists the problem can become under-determined, and we will explicitly state this limitation together with the new sufficient condition. revision: yes

  2. Referee: [§IV and §V] §IV (MIQP formulation) and §V (simulations): the MIQP objective and constraints are not shown to remain robust or to possess a unique solution when no unambiguous anchor exists; the reported simulation superiority may therefore be conditioned on the particular traffic traces chosen, which may not include worst-case large-gap realizations.

    Authors: We acknowledge that §IV does not prove uniqueness or robustness of the MIQP solution in the absence of an unambiguous anchor, and that the simulation results in §V rely on the traffic traces provided in the paper, which may not exhaustively cover worst-case large-gap scenarios. In the revised §IV we will add a short analysis of solution uniqueness: when at least one pair satisfies the unambiguous condition, the differing wrap rates across bands render the integer-feasible set singleton for the true velocity; when no such pair exists, multiple integer vectors can produce the same quadratic cost and the solution is no longer guaranteed to be unique. We will also augment §V with an additional set of Monte-Carlo experiments that artificially enlarge the maximum inter-packet interval beyond the values observed in the original traces, thereby including worst-case sporadic traffic. These new results will be reported alongside the existing ones so that readers can assess performance under the conditions highlighted by the referee. revision: yes

Circularity Check

0 steps flagged

No circularity: MIQP formulation is independent of its inputs

full rationale

The paper formulates velocity estimation as a mixed-integer quadratic program that uses phase differences across all pairwise packet combinations from multiband ISAC traffic. The central step asserts that incorporating at least one unambiguous phase measurement allows reconstruction of true velocity. This is an algorithmic construction, not a self-definition (the unambiguous measurement is an external input condition, not derived from the output velocity). No parameters are fitted to a data subset and then relabeled as a prediction. No self-citations are invoked to justify uniqueness or an ansatz. Simulations are presented as external validation rather than tautological confirmation. The derivation chain therefore remains non-circular and self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract, no explicit free parameters, axioms, or invented entities are detailed. The method uses standard phase difference concepts and optimization.

pith-pipeline@v0.9.0 · 5489 in / 995 out tokens · 64177 ms · 2026-05-10T18:23:21.846705+00:00 · methodology

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Reference graph

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