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arxiv: 2504.03963 · v2 · submitted 2025-04-04 · 📡 eess.SP

FMCW Radar Interference Mitigation based on the Fractional Fourier Transform

Christian Oswald , Franz Pernkopf This is my paper

Pith reviewed 2026-05-22 20:50 UTC · model grok-4.3

classification 📡 eess.SP
keywords FMCW radarinterference mitigationfractional Fourier transformchirp signalssignal separationradar signal processingdiscrete FrFT
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The pith

The discrete fractional Fourier transform compresses FMCW radar interference chirps into isolated peaks that can be zeroed out.

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

This paper proposes using the discrete fractional Fourier transform to detect and remove mutual interference in frequency modulated continuous wave radar. Linear chirp interference concentrates into compact peaks after a suitable rotation in the fractional domain, enabling simple zeroing that leaves the desired target echoes intact. The method includes an efficient implementation for multiple interferers that exploits the angle-additivity property of the transform and reduces the complexity of applying several rotation angles in sequence. On a synthetic I/Q-modulated dataset the approach improves mean squared error, signal-to-interference-plus-noise ratio, error vector magnitude, and detection scores over reference methods. The design targets hardware deployment because the core operations remain straightforward and fast.

Core claim

Interference chirps in FMCW radar are detected and mitigated by compression and zeroing in the fractional domain using the discrete fractional Fourier transform; an efficient multi-interferer implementation follows from generalizing the multi-angle centered discrete fractional Fourier transform and applying consecutive transforms via the angle-additivity property.

What carries the argument

The discrete fractional Fourier transform (DFrFT) with its angle-additivity property, which rotates signals so that linear chirps concentrate into removable peaks while the target signal stays distributed.

If this is right

  • Hardware implementation becomes feasible because the algorithm relies on simple consecutive transforms and peak zeroing.
  • Multiple simultaneous interferers can be suppressed by applying a sequence of DFrFTs whose angles are chosen to compress each chirp in turn.
  • Performance gains appear in mean squared error, signal-to-interference-plus-noise ratio, error vector magnitude, true positive rate, false alarm rate and F1-score on synthetic I/Q data.
  • The target echo remains usable after mitigation because only the compressed interference peaks are zeroed.

Where Pith is reading between the lines

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

  • If rotation angles can be estimated directly from received data, the same compression step could support adaptive, real-time interference removal without prior knowledge of interferer parameters.
  • The chirp-compression idea might transfer to other systems that transmit linear frequency sweeps, such as certain sonar or automotive sensing setups.
  • Validation on recorded rather than purely synthetic waveforms would test whether the assumed peak compactness survives realistic propagation effects and receiver noise.

Load-bearing premise

Interference appears as distinct linear chirps that become compact peaks after a suitable fractional Fourier transform rotation, allowing clean separation from the desired signal by simple zeroing without distorting the target echo.

What would settle it

A measurement or simulation in which the interference does not form isolated compact peaks after the chosen DFrFT rotation or in which zeroing those peaks removes substantial energy from the target echo.

Figures

Figures reproduced from arXiv: 2504.03963 by Christian Oswald, Franz Pernkopf.

Figure 1
Figure 1. Figure 1: FMCW radar signal processing chain with our proposed interference [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example of an FMCW radar signal with four objects and two interferences. The signal has been padded using the technique introduced in Sec. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: DFrFT Magnitudes with angles α of signals in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Examples of RD-maps. (a) interfered RD-map (b) corresponding ground truth RD-map (c) interference mitigated RD-map using our method (d) interference mitigated RD-map using zeroing with perfect interference detection. (e-h) object detection maps as retrieved by a CFAR object detector when applied to RD-maps (a-d). Gray, red, orange and green bins correspond to true negatives, false negatives, false positive… view at source ↗
Figure 5
Figure 5. Figure 5: (a) STFT of a radar signal with an incomplete interference (b) Magnitudes of the corresponding interference and ground truth signals after a DFrFT with αˆ ≈ 45◦. The signals have been normalized and padded with the technique described in Sec. V-C. a requirement for our approach based on multiple consecutive DFrFTs. C. Incomplete Interferences Interferences have a certain starting and ending time, which are… view at source ↗
Figure 6
Figure 6. Figure 6: Interference component from Fig. 2 with [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Empirical cumulative density functions (ECDFs) of all evaluated metrics per range-Doppler map. The oracle methods are drawn with dashed lines. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Performance of our method for different Nα. Note that we zoomed into relevant portions of the ECDFs to better resolve close-by curves. [6] F. Jin and S. Cao, “Automotive radar interference mitigation using adaptive noise canceller,” IEEE Transactions on Vehicular Technology, vol. 68, no. 4, pp. 3747–3754, 2019. [7] J. Rock, W. Roth, M. Toth, P. Meissner, and F. Pernkopf, “Resource￾efficient deep neural net… view at source ↗
read the original abstract

In this paper, we propose a novel method for frequency modulated continuous wave (FMCW) radar mutual interference mitigation (IM) based on the discrete fractional Fourier transform (DFrFT). Interference chirps are detected and mitigated by compression and zeroing in the fractional domain. We provide an efficient implementation that can deal with multiple interferers, where we perform consecutive DFrFTs utilizing its angle-additivity property. For that purpose, we generalize and reduce the computational complexity of the multi-angle centered discrete fractional Fourier transform [1]. Our algorithm is designed to be simple and fast such that it can be implemented in hardware. We evaluate our algorithm on a synthetic I/Q-modulated dataset and outperform reference methods in terms of the mean squared error, signal-to-interference-plus-noise ratio, error vector magnitude, true positive rate, false alarm rate and F1-score.

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

3 major / 2 minor

Summary. The paper proposes a method for FMCW radar mutual interference mitigation using the discrete fractional Fourier transform (DFrFT). Interference chirps are detected and mitigated via compression and zeroing in the fractional domain. An efficient implementation for multiple interferers is given by generalizing the multi-angle centered DFrFT and exploiting angle-additivity. The algorithm is evaluated on a synthetic I/Q-modulated dataset and reported to outperform reference methods on MSE, SINR, EVM, TPR, FAR, and F1-score.

Significance. If the separability assumption and generalization hold beyond the evaluated cases, the approach could yield a simple, low-complexity, hardware-suitable mitigation technique for radar systems. Credit is due for the explicit use of angle-additivity to handle multiple interferers and the claimed complexity reduction in the multi-angle DFrFT implementation. The exclusive reliance on synthetic data without parameter-selection details or hardware validation limits the assessed significance.

major comments (3)
  1. [§ on detection and mitigation by compression and zeroing] § on detection and mitigation by compression and zeroing: the central premise that interference chirps become compact, isolated peaks after DFrFT rotation (allowing clean zeroing without target distortion) is invoked without an analytic bound on required angle separation or ablation on chirp-rate mismatch; this assumption is load-bearing for the claimed mitigation performance.
  2. [§5 (Evaluation)] §5 (Evaluation): all reported gains in MSE, SINR, EVM, TPR, FAR, and F1-score are obtained exclusively on synthetic I/Q data; no description is given of how the fractional angle α is selected, nor any analysis of robustness to real-world noise, hardware impairments, or angle estimation errors.
  3. [§ on efficient implementation] § on efficient implementation: while angle-additivity is used for consecutive DFrFTs on multiple interferers, the manuscript provides no quantitative verification that the generalized multi-angle centered DFrFT preserves the claimed complexity reduction when the optimal angles differ substantially.
minor comments (2)
  1. Clarify in the text how the fractional order is discretized and whether the same α is used for detection versus mitigation.
  2. [References] Add a reference or brief derivation for the claimed complexity reduction of the generalized multi-angle DFrFT relative to [1].

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for the thorough and constructive review of our manuscript. We address each major comment point by point below, with clear indications of planned revisions to the manuscript.

read point-by-point responses

  1. Referee: [§ on detection and mitigation by compression and zeroing] the central premise that interference chirps become compact, isolated peaks after DFrFT rotation (allowing clean zeroing without target distortion) is invoked without an analytic bound on required angle separation or ablation on chirp-rate mismatch; this assumption is load-bearing for the claimed mitigation performance.

    Authors: We acknowledge that the separability assumption in the fractional domain is central to the method and would benefit from additional theoretical support. In the revised manuscript, we will add a derivation of an analytic bound on the minimum angle separation required for reliable isolation of interference peaks from target signals, drawing on the known concentration properties of linear chirps under DFrFT rotation. We will also include an ablation study that systematically varies chirp-rate mismatch between interferers and targets to quantify any resulting degradation in mitigation performance. revision: yes

  2. Referee: [§5 (Evaluation)] all reported gains in MSE, SINR, EVM, TPR, FAR, and F1-score are obtained exclusively on synthetic I/Q data; no description is given of how the fractional angle α is selected, nor any analysis of robustness to real-world noise, hardware impairments, or angle estimation errors.

    Authors: The current evaluation is performed exclusively on the synthetic dataset described in Section 5. In the revision, we will expand Section 5 to provide an explicit description of the α-selection procedure, which relies on a coarse estimate of the dominant interference chirp rate followed by a fine search around the estimated angle. We will further add Monte-Carlo simulations that inject additive white Gaussian noise at varying SNR levels and quantify performance sensitivity to errors in the estimated fractional angle. Hardware impairments and real-world validation lie outside the present scope and would require new experimental campaigns. revision: partial

  3. Referee: [§ on efficient implementation] while angle-additivity is used for consecutive DFrFTs on multiple interferers, the manuscript provides no quantitative verification that the generalized multi-angle centered DFrFT preserves the claimed complexity reduction when the optimal angles differ substantially.

    Authors: We will strengthen the complexity claims by adding both asymptotic analysis and empirical timing results for the generalized multi-angle centered DFrFT. These results will cover cases in which the optimal fractional angles for different interferers differ by up to 0.5 radians, demonstrating that the computational savings from angle-additivity remain intact and that the overhead of angle reordering is negligible. revision: yes

standing simulated objections not resolved
  • Hardware validation and experimental results on physical FMCW radar systems subject to real hardware impairments.

Circularity Check

0 steps flagged

No significant circularity; method uses standard FrFT properties

full rationale

The paper proposes an FMCW radar interference mitigation algorithm that applies the discrete fractional Fourier transform (DFrFT) to compress interference chirps for detection and zeroing, then uses angle-additivity for multiple interferers. This relies on well-known mathematical properties of the FrFT rather than any derivation that reduces to its own inputs. The generalization of the multi-angle centered DFrFT is referenced to [1] as an implementation step but is not load-bearing for the core claims, which are supported by direct empirical evaluation (MSE, SINR, EVM, TPR, FAR, F1) on a synthetic I/Q dataset against reference methods. No equations define a quantity in terms of itself, no fitted parameters are relabeled as predictions, and no uniqueness theorem or ansatz is smuggled via self-citation. The approach is self-contained and externally falsifiable via the reported metrics.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach depends on the standard properties of the fractional Fourier transform and the assumption that interference chirps localize to compact support after rotation; no new entities are postulated and the only adjustable element is the fractional angle chosen per interferer.

free parameters (1)
  • fractional angle alpha
    Selected to compress each interference chirp into a narrow peak in the fractional domain; value is not reported as fitted from data in the abstract.
axioms (1)
  • standard math The discrete fractional Fourier transform satisfies angle-additivity, allowing consecutive transforms to handle multiple distinct angles without recomputing the full operator each time.
    Invoked to enable efficient multi-interferer processing.

pith-pipeline@v0.9.0 · 5669 in / 1368 out tokens · 45445 ms · 2026-05-22T20:50:26.801051+00:00 · methodology

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Reference graph

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