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Permutation-Invariant Time-Frequency Segmentation and Parameter Estimation of Multiple Overlapping Interference Signals

Lucas Heublein, Christian Wielenberg, Christopher Mutschler, Felix Ott

arXiv:2610.02908v1eess.SP

TL;DR

Overlapping RF sources make it difficult to determine each emitter’s time–frequency occupancy and characteristics, while existing monitoring requires source-resolved outputs. PI-SCAN jointly predicts source-specific masks and properties through unordered slots and permutation-invariant assignment. Its results show a detection-versus-characterization trade-off, and evaluation is limited to a synthetic ray-tracing environment.

  • Problem

    Overlapping sources can obscure weaker emissions, while reliable spectrum awareness requires estimating each source’s count, occupancy, type, and physical characteristics.

    Source: §I · p. 1

  • Method

    PI-SCAN maps spectrograms to six unordered source slots containing objectness, type, physical properties, and source-specific masks, aligned to ground truth by Hungarian assignment.

    Source: §VI · pp. 11–12

  • Results

    74.8% F1 for the seven-task model versus 91.1% for objectness–type–mask prediction, revealing a trade-off between detection and comprehensive characterization.

    Source: §VI · p. 12

  • Takeaways & Limitations

    The reported results identify a trade-off between detection performance and comprehensive multi-parameter characterization.

    Source: §VI · p. 12

    Training and evaluation use synthetically generated signals in the considered Sionna ray-tracing environment, so generalization to real-world measurements is not established.

    Source: F. Limitations · p. 19

Abstract

from arXiv · show

Radio-frequency interference threatens satellite navigation, wireless communications, radar, and industrial sensing. Reliable operation therefore requires spectrum situational awareness to detect interference and determine the number, time-frequency occupancy, and characteristics of active sources. In realistic environments, multiple sources may overlap. Source-specific segmentation and characterization are therefore particularly challenging. In this paper, we propose PI-SCAN (Permutation-Invariant Segmentation, Characterization, and Assignment Network), a joint set-based learning framework for source-specific segmentation and characterization of overlapping interference signals. A logarithmic power spectrogram derived from complex IQ samples is mapped to six unordered prediction slots. For each slot, the model estimates objectness, interference type, center frequency, bandwidth, received signal strength, binary offset carrier (BOC) modulation, and a source-specific segmentation mask. Permutation-invariant Hungarian assignment aligns the predicted slots with the unordered ground-truth sources, while a weighted multi-task objective jointly optimizes the individual prediction tasks. The framework is evaluated using a ray-traced industrial environment containing mixtures of one to six simultaneously active interferers drawn from 94 waveform configurations across six interference classes. The full seven-task configuration achieves a detection F1-score of 74.8%, type and BOC accuracies of 97.3% and 98.4%, and mean absolute errors of 1.29MHz, 2.54MHz, and 3.19dB for center frequency, bandwidth, and signal strength. Using only objectness, type, and mask prediction increases the F1-score to 91.1%, highlighting the trade-off between detection and comprehensive characterization.

I. INTRODUCTION

The paper targets source-resolved monitoring of overlapping RF interference, where prior approaches generally lack joint per-source segmentation and physical characterization. PI-SCAN uses six unordered predictions and permutation-invariant assignment to associate source masks with estimated properties.

I. INTRODUCTION

  • Overlapping RF emitters can obscure weaker sources, so spectrum awareness must count, localize, classify, and characterize each source while preserving its mask-to-property association.Source-resolved outputs can also be combined with antenna-array or distributed-station measurements for direction-of-arrival estimation and emitter localization.Source: §I · p. 1

II. RELATED WORK

  • Prior approaches use recording-level labels, shared masks, or rectangular extents, leaving joint source-specific masks and comprehensive physical characterization insufficiently addressed.The related-work comparison includes multilabel recognition, localized technology predictions, and bounding-box detection of overlapping signals.Source: §I · p. 1, §II · p. 2

I. INTRODUCTION

  • PI-SCAN pairs a Sionna ray-traced multi-source dataset with a set framework for detecting, segmenting, and characterizing up to six overlapping sources.The authors also investigate MobileNetV2–U-Net and attention-based architectures, prediction objectives, and loss functions, including the detection-versus-characterization trade-off.Source: §I · pp. 1–2

A. Problem Formulation and Input Representation

  • Each composite spectrogram maps to six unordered source slots with attributes and masks; independent masks may overlap in the same bins, and Hungarian assignment aligns slots to sources.Inference uses predicted objectness scores to select active source slots.Source: A. Problem Formulation and Input… · p. 3, Figure 1 · p. 3

B. Method Overview

PI-SCAN processes normalized time–frequency representations through shared features and parallel characterization and segmentation branches, producing six joint source predictions. Its evaluated variants share a prediction interface while differing in feature extraction and refinement.

B. Method Overview

  • A shared encoder feeds global characterization heads and a skip-connected mask decoder; their outputs form six joint source predictions, with objectness selecting active slots at inference.The input is a normalized time–frequency representation, and the branches estimate source properties and source-specific masks.Source: B. Method Overview · p. 3, D. Network Architectures · p. 4

C. Pre-Processing

  • The input is a 512-by-512 log-PSD spectrogram computed with a 512-sample Blackman STFT window and 256-sample hop, then standardized per snapshot.At 40.5 MHz, the setup gives approximately 79.1 kHz frequency-bin spacing and 6.32 μs temporal hop.Source: C. Pre-Processing · pp. 3–4

D. Network Architectures

  • Both architectures retain the same six-slot heads and mask resolution, enabling controlled comparison of MobileNetV2–U-Net features against attention-based feature refinement.The first combines a pretrained MobileNetV2 encoder with a U-Net-style decoder; the second introduces attention while keeping the prediction interface and training procedure unchanged.Source: D. Network Architectures · p. 4

E. Joint Set-Based Segmentation and Characterization

F. Permutation-Invariant Source Assignment

Because source annotations and prediction slots are unordered, PI-SCAN constructs a pairwise assignment cost and uses Hungarian matching to associate active sources with prediction slots.

F. Permutation-Invariant Source Assignment

  • The six prediction slots and active ground-truth sources have no predefined correspondence, so training constructs a pairwise cost matrix for their assignment.Source: F. Permutation-Invariant Source… · p. 5
  • Hungarian matching selects an injective source-to-slot assignment; matched slots receive positive objectness targets and characterization and segmentation losses.Unassigned slots are treated as inactive.Source: F. Permutation-Invariant Source… · p. 5
  • Mask costs are excluded during the first 10% of training, then activated so spatial similarity contributes to source association.The warm-up prevents initially uninformative mask predictions from dominating assignment.Source: F. Permutation-Invariant Source… · p. 5

G. Multi-Task Training Objective

The training objective combines enabled task losses through configurable weights, allowing the same architecture to be trained with different combinations of prediction tasks.

G. Multi-Task Training Objective

  • A weighted multi-task objective combines the seven task-specific losses following permutation-invariant assignment.Source: G. Multi-Task Training Objective · pp. 5–6
  • Each task is enabled with a positive weight or excluded with zero weight, allowing alternative combinations of detection, classification, characterization, and segmentation objectives.Source: G. Multi-Task Training Objective · p. 6
  • The loss study changes one component at a time before testing selected cross-component combinations, keeping architecture, data split, training budget, and remaining losses fixed for individual alternatives.Source: G. Multi-Task Training Objective · p. 6

IV. EXPERIMENTAL SETUP

The experimental setup uses ray tracing to generate overlapping interference mixtures and evaluates them through spectrograms, source-specific masks, and parameter distributions. The dataset spans multiple jammer counts and waveform types, with examples illustrating how overlap complicates source attribution.

Simulation and signal generation

  • The simulated scene uses Sionna RT to model propagation and multipath in a metallic enclosure with shelving, exporting complex baseband IQ samples.The receiver is modeled as a single antenna, and sources transmit at 1.57542 GHz.Source: §IV · p. 6

Interference parameters

  • Snapshots contain one to six jammers from 94 waveform configurations spanning six interference classes and bandwidths from 0.5 to 40 MHz.Frequency shifts are constrained so at least 90% of each jammer’s occupied bandwidth remains in the observation band; signals are then propagated and superimposed.Source: §IV · pp. 6–7

Signal representation

  • Each 3.24 ms snapshot is represented by a 512-by-512 spectrogram, with 79.1 kHz frequency-bin spacing and 6.32 µs temporal hops.The spectrogram uses 512-sample segments and a 256-sample hop.Source: §IV · p. 6

Dataset statistics

  • The training set has about four times as many samples as the test set; overlapping cases are balanced across one to six jammers, while non-overlapping cases concentrate on one or two.Jammer types are imbalanced, and RSSI values span approximately −70 to −20 dBm, concentrated between −45 and −25 dBm.Source: Figure 2 · p. 6, Figure 3 · p. 6, §IV · p. 7

Exemplary samples

  • Figures 4–6 show mixtures of four or six interferers alongside source-specific masks, with strong signals sometimes obscuring weaker components.The masks isolate each source’s time-frequency support while preserving regions shared by multiple signals.Source: §IV · p. 7, Figure 4 · p. 7, Figure 5 · p. 7

Spectrogram and PSD examples

  • Welch power spectral density estimates show occupied frequency regions, but spectrally overlapping contributions merge and cannot be assigned unambiguously to individual interferers.The examples compare spectrograms with Welch estimates and ground-truth frequency boundaries.Source: §IV · pp. 7–8, Figure 7 · p. 8

V. EVALUATION

The evaluation compares task and loss choices under shared training conditions, then tests selected joint configurations using Hungarian source assignment. Detection improves when characterization objectives are reduced, while loss-function gains do not necessarily transfer across tasks.

A. Hardware and Training Setup

  • 100 training epochs use Adam, batch size 32, fixed random seeds, and deterministic cuDNN; reported results use MobileNetV2–U-Net without attention.The learning rate is reduced tenfold at epochs 60 and 80; preliminary experiments found this variant substantially outperformed the attention-based alternative.Source: A. Hardware and Training Setup · p. 8

B. Loss Elements

  • Using objectness, type classification, and mask prediction yields 91.6% F1, versus 91.1% with objectness and type classification alone; omitting signal-strength estimation raises F1 to 79.9%.Omitting bandwidth estimation slightly raises F1 to 73.2% but substantially reduces count, type, and BOC accuracy.Source: B. Loss Elements · p. 8

C. Loss Functions

  • 33.6% F1 with quality focal loss is below the 58.8% from varifocal loss; neither alternative outperforms the reference focal loss for objectness.Neither alternative center-frequency loss outperforms Huber; label smoothing performs almost identically to conventional cross-entropy for type classification.Source: C. Loss Functions · p. 9
  • 76.1% F1 with quantile signal-strength loss is the best overall loss-function result, while RSSI error rises from 3.35 dB to 3.56 dB.Quantile loss also improves type and BOC accuracy to 93.0% and 97.0%, and reduces frequency and bandwidth errors to 1.14 MHz and 1.97 MHz; Huber remains preferable when RSSI accuracy is prioritized.Source: C. Loss Functions · pp. 9–10
  • 72.5% F1 with Laplace NLL gives the best bandwidth-loss balance, while Tversky mask loss reaches 72.6% F1; signal-strength loss choice has the greater overall effect.Cauchy NLL lowers bandwidth error to 2.40 MHz, and focal BCE raises F1 to 71.1% while lowering BOC accuracy to 96.0%.Source: C. Loss Functions · p. 9

D. Joint Objective and Source Assignment

  • 74.8% F1 is achieved with all objectives; the objectness–type–mask configuration reaches 91.1% F1, while omitting signal-strength estimation offers the best detection–characterization compromise.Mask supervision supports source detection and assignment beyond segmentation, but improvements from individually favorable loss alternatives do not necessarily transfer to the joint objective.Source: Table IV · p. 10, D. Joint Objective and Source Assignment · p. 10

E. Comparison to Related Work

The proposed method is competitive with the strongest reference approach while producing source-specific masks and characterizing multiple overlapping signals. As source count and overlap increase, missed detections become more prominent, whereas inference remains fast across configurations.

F. Multi-Interference Characterization

  • 93.9% F1 for two overlapping sources falls to 74.6% for six, while type and BOC accuracies remain 95.2% and 96.5%.As source count rises, recall drops; qualitative masks retain distinguishable source signatures, though fragmentation, boundary deviations, and leakage become more pronounced at five and six sources.Source: Table VI · p. 11, F. Multi-Interference Characterization · p. 11, Figure 9 · p. 11

E. Comparison to Related Work

  • 91.1% F1 and 98.7% type accuracy make the reduced objectness–type–mask model competitive with RCJ while also producing source-specific masks.The complete model reaches 74.8% F1 and reports type and BOC accuracies plus frequency, bandwidth, and RSSI errors.Source: E. Comparison to Related Work · pp. 10–11

G. Inference Times

  • 8–9 ms per sample on GPU versus 240–260 ms on CPU; adding prediction elements or changing training losses introduces negligible inference overhead.Inference times are averaged over all test samples.Source: G. Inference Times · p. 11

VI. CONCLUSION

  • The seven-task model reaches 74.8% F1, while the objectness–type–mask configuration reaches 91.1%; GPU inference takes 8–9 ms per sample.Across two to six overlapping sources, F1 falls from 93.9% to 74.6%, while type and BOC accuracies remain above 95%.Source: §VI · p. 12

VII. APPENDIX

The appendix gives idealized conditions for spectral separability and shows why unrestricted, completely overlapping sources cannot be uniquely decomposed from a single-channel mixture. The results serve as representation-level limits, not guarantees for the learned model.

A. Spectral Separability and Identifiability

  • Under exact DFT-grid alignment, finite discrete supports, and a periodic Blackman window, sufficient support separation makes the windowed source supports pairwise disjoint.The condition is sufficient, not necessary, and applies to an idealized single-frame setting.Source: A. Spectral Separability and… · p. 14
  • With disjoint windowed supports, the noiseless mixture power spectrogram is binwise additive and contains no cross-source terms.This follows because at most one source contributes at each frequency bin.Source: A. Spectral Separability and… · p. 14
  • The separation condition is only an idealized resolution reference, not a general minimum center-frequency spacing or a performance bound for the learned model.Off-grid, broadband, time-varying, noisy, or leaky signals violate the stated assumptions.Source: A. Spectral Separability and… · pp. 14–15
  • Two unrestricted components that overlap completely in time and frequency cannot be uniquely decomposed from a single-channel mixture without structural assumptions or learned source priors.The same ambiguity remains after transforming the mixture into a spectrogram.Source: A. Spectral Separability and… · p. 15

B. Training and Source-Assignment Algorithm

Training converts each IQ recording into a normalized spectrogram and predicts six source slots. Hungarian assignment matches slots to valid sources, after which a weighted multi-task objective trains the matched predictions.

B. Training and Source-Assignment Algorithm

  • Each complex IQ recording becomes a centered, standardized two-sided power spectrogram, and valid sources are padded to six slots with padding ignored in matching and loss.Sources outside the selected observation bandwidth are discarded.Source: B. Training and Source-Assignment… · p. 15
  • For each mini-batch, Hungarian assignment finds a minimum-cost one-to-one match between predicted slots and valid ground-truth sources.During the first 10% of epochs, mask costs are excluded from matching to stabilize the prediction heads, although mask supervision remains active.Source: B. Training and Source-Assignment… · p. 15
  • Objectness loss covers all slots, while type, parameter, BOC, and mask losses apply only to matched source-slot pairs.The weighted multi-task objective is accumulated and used to update the model parameters.Source: B. Training and Source-Assignment… · p. 15

C. Evaluation Metrics

The evaluation assigns active prediction slots to unordered ground-truth sources before computing detection, characterization, and segmentation metrics. Several characterization and mask metrics are conditional on assigned pairs, so they must be interpreted alongside detection metrics.

C. Evaluation Metrics

  • Evaluation uses Hungarian assignment over active predictions, with disabled regression tasks excluded from the assignment cost.Objectness defines the active prediction set first; BOC and segmentation masks do not contribute to evaluation assignment.Source: C. Evaluation Metrics · p. 16
  • A valid detection requires a correct type and enabled continuous attributes within tolerances of 5 MHz for center frequency, 5 MHz for bandwidth, and 10 dB for signal strength.BOC correctness and mask overlap are evaluated separately and are not required for a valid detection.Source: C. Evaluation Metrics · p. 16
  • Count accuracy checks whether the number of active predictions exactly matches the ground-truth source count, even if assigned attributes are incorrect.Results are also stratified by source count and by whether ground-truth masks overlap in any active time-frequency bin.Source: C. Evaluation Metrics · pp. 16–17
  • Type and BOC accuracies are conditional on assigned pairs, so missed sources and unmatched predictions affect detection metrics rather than those accuracy denominators.Regression errors also cover assigned pairs only, regardless of whether they meet detection tolerances.Source: C. Evaluation Metrics · p. 17
  • Segmentation metrics are computed from masks thresholded at 0.5, and missed sources are excluded from conditional mask averages.If needed, ground-truth masks are resized with nearest-neighbor interpolation; empty-mask pairs receive IoU 1.Source: C. Evaluation Metrics · p. 17

D. Additional Multi-Interference Characterization Results

As source complexity increases, segmentation scores decline, although the principal time-frequency structures remain recovered. Qualitative examples show source-specific masks for overlapping signals, and RF-DETR provides a segmentation baseline without joint physical-parameter estimation.

D. Additional Multi-Interference Characterization Results

  • For two overlapping sources, predictions recover both a narrow frequency-varying trajectory and broad stationary bands, with minor boundary deviations and fragmentation.Predicted masks are displayed by Hungarian assignment to ground-truth sources, so slot indices need not match annotation order.Source: D. Additional Multi-Interference… · pp. 17–18
  • The principal time-frequency structures remain recovered across examples ranging from isolated chirps to dense combinations of broadband, narrowband, and nonlinear components.Disagreements occur mainly near mask boundaries and overlapping regions.Source: D. Additional Multi-Interference… · p. 18, Figure 14 · p. 18
  • IoU falls from 0.890 to 0.795 and Dice from 0.942 to 0.885 as source complexity increases in the Figure 14 examples.Precision declines from 0.969 to 0.869, while recall remains above 0.90 for all examples and specificity remains at least 0.985.Source: Table VII · p. 18, D. Additional Multi-Interference… · p. 18, Figure 14 · p. 18
  • RF-DETR achieves a segmentation F1-score of 0.912 on the same one-to-six-source dataset, but does not jointly estimate PI-SCAN’s source-specific physical characteristics.Its examples recover dominant broadband, narrowband, periodic, and chirped structures, with minor deviations around boundaries and weak or overlapping regions.Source: D. Additional Multi-Interference… · p. 18

E. RSSI-Based Evaluation

Center frequency has the lowest estimation error, while bandwidth error generally grows with the number of active sources and RSSI error is largest, with a U-shaped trend across reference RSSI. Sample-wise normalization is identified as making absolute signal-strength recovery more difficult.

E. RSSI-Based Evaluation

  • Center frequency has the lowest error, bandwidth error generally increases with source count, and RSSI error is largest and most widely distributed.The source-wise error plot shows absolute RSSI, bandwidth, and center-frequency errors across scenes with one to six sources.Source: E. RSSI-Based Evaluation · pp. 18–19, Figure 19 · p. 19
  • RSSI moving-average error rises for weak sources around −50 to −45 dB and strong sources around −30 to −25 dB, remaining lower in the intermediate range.The paper attributes this U-shaped pattern to regression toward the central RSSI range.Source: E. RSSI-Based Evaluation · p. 19, Figure 19 · p. 19
  • Sample-wise spectrogram normalization largely removes absolute amplitude information, making RSSI recovery more difficult despite retaining spectral information for frequency and bandwidth estimation.The authors identify normalization as the explanation for the weaker absolute signal-strength estimates.Source: E. RSSI-Based Evaluation · p. 19

F. Limitations

The model resolves at most six sources per spectrogram with the fixed set size, and larger mixtures require a larger set and retraining. Evaluation uses synthetic signals in one ray-traced environment, so generalization to real measurements is not established.

F. Limitations

  • With fixed set size S = 6, the model resolves at most six sources; additional sources may go undetected or merge into other predictions.The estimated source count saturates at six.Source: F. Limitations · p. 19
  • Supporting larger mixtures requires increasing S, extending the training data, and retraining, at the cost of added prediction-head, mask-decoder, and matching computation.Source: F. Limitations · p. 19
  • Training and evaluation use synthetic signals propagated in the considered Sionna ray-tracing environment, leaving generalization to real-world measurements unestablished.Receiver hardware, noise, propagation, and unseen waveforms may contribute to a simulation-to-real domain gap.Source: F. Limitations · p. 19
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