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Frame-Induced Doppler Self-Ambiguity in SiriusXM Satellite Signals for Passive Radar

Khalid El-Darymli, Christoph H. Gierull, Ryan A. English, Tony Laneve

arXiv:2609.09393v1eess.SP

TL;DR

Deterministic SDARS TDM framing can create self-ambiguity that complicates passive radar processing, while real-data evidence at extended Doppler offsets has been limited. This paper relates XM/SXM FSP repetition to Doppler-replica spacing, tests the expected behavior with frame-accurate simulation and SXM-8 direct-path data, and finds a persistent Doppler comb. The results motivate frame-aware processing, although the simulation cannot represent undocumented proprietary signal features.

  • Problem

    Deterministic SDARS TDM framing can produce discrete Doppler replicas during extended-Doppler, long-CPI passive radar processing, and the impact using real satellite data had not previously been reported to the authors’ knowledge.

    Source: §I · p. 1

  • Method

    The paper links XM/SXM TDM framing to expected Doppler-replica spacing and checks the analysis with frame-accurate simulation and real SXM-8 direct-path measurements.

    Source: §I · p. 1

  • Results

    Pronounced replicas at XM FSP repetition-frequency spacings appear in SXM-8 measurements, in close agreement with theory and frame-accurate simulation.

    Source: §VI · p. 3, §VIII · p. 4

  • Takeaways & Limitations

    The Doppler comb is an intrinsic XM/SXM waveform property, independent of payload content, and motivates frame-aware passive-radar processing.

    Source: §VII · p. 4

    The XM/SXM waveform is proprietary, so the simulator uses publicly available patent and decoder documentation and cannot represent undocumented operational signal features.

    Source: §VII · p. 4

Abstract

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Satellite Digital Audio Radio Service (SDARS) signals are attractive illuminators of opportunity for passive radar due to their continuous geostationary coverage and relatively high effective radiated power. However, the deterministic time-division multiplexed (TDM) framing employed by these waveforms introduces inherent self-ambiguity that can constrain coherent integration and detection performance. This paper analyzes the self-ambiguity function (SAF) of the XM/SiriusXM (SXM) waveform and explicitly links the observed Doppler periodicity to the repetition of the fast synchronization preamble (FSP) embedded in the TDM master frame. A frame-accurate XM TDM signal simulation is used to establish the expected ambiguity behavior, which is then validated experimentally using real direct-path data collected from the SXM-8 satellite. Results demonstrate pronounced and persistent Doppler replicas at integer multiples of the XM FSP repetition frequency, forming a deterministic Doppler ``comb'' (grating-lobe structure) that spans Doppler extents relevant to GEO-based passive radar operation with multi-second coherent processing intervals.

I. INTRODUCTION

SDARS signals offer continuous GEO coverage and relatively high effective radiated power for passive radar, but deterministic TDM framing can create Doppler replicas that complicate long-CPI processing. This paper links XM/SXM frame structure to expected replica spacing and validates the behavior with simulation and SXM-8 measurements.

I. INTRODUCTION

  • SDARS downlinks are attractive passive-radar illuminators because GEO satellites provide continuous transmission, wide-area coverage, and relatively high effective radiated power.Passive radar typically forms range–Doppler products by correlating surveillance and reference (direct-path) channels over a coherent processing interval.Source: §I · p. 1
  • Deterministic SDARS TDM framing can produce discrete Doppler replicas during multi-second coherent processing, potentially masking weak target returns at extended Doppler offsets.The paper identifies real-data analysis of this framing effect at extended Doppler offsets as previously unreported to the authors’ knowledge.Source: §I · p. 1
  • The paper explicitly links XM/SXM TDM framing to the expected Doppler-replica spacing in the self-ambiguity function.SXM-8 broadcasts the legacy XM-format waveform and is described as representative of current operational SDARS transmissions.Source: §I · p. 1, Figure 1 · p. 1
  • The paper experimentally validates persistent frame-induced Doppler replicas across extended Doppler extents using real SXM-8 direct-path measurements.The study also uses a frame-accurate XM TDM simulation to verify the expected ambiguity behavior.Source: §I · p. 1

A. XM, Sirius, and SXM Overview

Following the XM–Sirius merger, operational SXM satellites continue to transmit the legacy XM waveform, so its TDM framing governs the signal analyzed in this work.

A. XM, Sirius, and SXM Overview

  • Operational SXM satellites retain the legacy XM waveform, including its modulation, framing, and synchronization, to preserve backward compatibility with legacy receivers.Accordingly, the XM TDM frame structure governs the signal behavior analyzed in this work.Source: A. XM, Sirius, and SXM Overview · p. 2

B. Key TDM Parameters

The section provides key SDARS waveform and framing parameters for XM/SXM and Sirius, with Sirius included for contextual comparison.

B. Key TDM Parameters

  • The key SDARS TDM and waveform parameters are summarized for XM/SXM and Sirius, with Sirius parameters provided for contextual comparison.The supplied material does not provide the table’s individual parameter values.Source: B. Key TDM Parameters · p. 2
  • Sirius uses a distinct fast-synchronization repetition frequency of 3670 Hz, implying Doppler replicas at substantially larger offsets than XM/SXM.Source: B. Key TDM Parameters · p. 2
  • The XM TDM master-frame schematic depicts repeated FSPs that induce Doppler periodicity in the self-ambiguity function.Source: Figure 3 · p. 2

III. XM TDM FRAME STRUCTURE AND EXPECTED DOPPLER PERIODICITY

The XM TDM frame repeats fast synchronization preambles, producing Doppler replicas whose locations follow the FSP repetition frequency. The replicas are intrinsic to the waveform, independent of payload content, and become more visible as coherent processing intervals lengthen.

III. XM TDM FRAME STRUCTURE AND EXPECTED DOPPLER PERIODICITY

  • Each 432 ms XM/SXM master frame contains 205 fast synchronization preambles, each 64 bits long, interspersed with payload data and padding.Source: §III · p. 2
  • Repeated FSPs produce discrete Doppler replicas in the ambiguity function, independent of payload content.Source: §III · p. 2
  • Replica visibility and masking impact increase with CPI length as coherent processing increases Doppler resolution and reinforces deterministic periodic components.Source: §III · p. 2
  • The section defines equivalent bistatic velocity from Doppler frequency using the carrier centre frequency and the speed of light.Source: §III · p. 2

IV. SELF-AMBIGUITY FUNCTION FRAMEWORK

The self-ambiguity function (SAF) characterizes a waveform’s intrinsic delay–Doppler response. For periodically framed XM/SXM signals, temporal repetition produces discrete Doppler replicas that can dominate the ambiguity surface during long coherent integration.

IV. SELF-AMBIGUITY FUNCTION FRAMEWORK

  • The SAF characterizes a waveform’s intrinsic delay–Doppler response and governs its sidelobe structure and masking behavior in correlation-based processing.In practice, it is computed from sampled data over a finite coherent processing interval and visualized by magnitude.Source: §IV · p. 2
  • Periodic temporal repetition in XM/SXM creates discrete Doppler replicas that can dominate the ambiguity surface under long coherent integration.Source: §IV · p. 2
  • Fig. 4 is a block diagram of the frame-accurate XM TDM signal simulation.Source: Figure 4 · p. 3

V. XM TDM SIGNAL SIMULATION

A frame-accurate simulator uses publicly available patent and decoder documentation to model XM TDM elements relevant to ambiguity behavior. Its simulated SAF shows a Doppler comb whose replica locations closely match predictions.

V. XM TDM SIGNAL SIMULATION

  • The simulator implements documented TDM framing, channel coding, interleaving, QPSK modulation, and root-raised-cosine filtering to reproduce frame-induced ambiguity structure.It uses publicly available patent literature and decoder documentation, without claiming access to proprietary implementation details.Source: §V · p. 3
  • With a 3 s CPI and fFSP ≈474.5 Hz, the expected Doppler-replica velocity spacing is approximately 60.7 m/s.Source: §V · p. 3
  • The simulated SAF exhibits a deterministic Doppler comb, with observed replica locations closely matching the predicted locations.Zoomed views highlight the grating-lobe structure induced by frame repetition.Source: §V · p. 3

VI. EXPERIMENTAL DATA AND SAF RESULTS

Direct-path data from SXM-8 were processed to form measured SAFs, which showed pronounced Doppler replicas at spacings consistent with the XM FSP repetition frequency. Zoomed views confirm close agreement between prediction and measurement.

VI. EXPERIMENTAL DATA AND SAF RESULTS

  • The SXM-8 (B) direct-path signal was recorded on June 21, 2023, and SAF products used a 3 s CPI with approximately 2 minutes of data incoherently summed.Source: §VI · p. 3
  • Measured SAFs show pronounced Doppler replicas at spacings consistent with the XM FSP repetition frequency, with zoomed views confirming close agreement between prediction and measurement.Source: §VI · p. 3
  • The simulated SAF captions describe a 3 s CPI and zoomed views of the deterministic replica comb, with dashed lines marking expected harmonics and showing close agreement with simulation.Source: Figure 5 · p. 3, Figure 6 · p. 3

VII. DISCUSSION

The XM/SXM FSP repetition produces a stable Doppler comb independent of payload content, increasingly prominent with longer coherent processing intervals. The discussion also identifies an unexplained measured delay offset and the simulator’s proprietary-waveform boundary.

VII. DISCUSSION

  • Frame-induced replicas are intrinsic to XM/SXM and form a stable Doppler comb at integer multiples of the FSP repetition frequency, independent of payload content and increasingly prominent with longer CPIs.Source: §VII · p. 4
  • The direct-path SAF has ambiguity energy at ±2.736 km delay, about −22.8 dB relative to the main response and above the ≈−60 dB noise floor; its origin remains uncertain despite recurrence across datasets.Source: §VII · p. 4
  • The simulator is limited to publicly documented waveform features and cannot represent undocumented proprietary features, though the observed delay offset does not affect replica spacing.Source: §VII · p. 4
  • At replica harmonics, the Doppler comb can elevate sidelobes and mask weak target responses, motivating frame-aware processing; detection and false-alarm impacts remain future work.Source: §VII · p. 4

VIII. CONCLUSION

The conclusion links XM/SXM TDM structure to expected Doppler-replica spacing and reports close agreement across theory, frame-accurate simulation, and SXM-8 (B) direct-path data. It identifies frame-aware processing as important and ambiguity mitigation and target detection as foundations for further study.

VIII. CONCLUSION

  • Theory, frame-accurate simulation, and SXM-8 (B) direct-path measurements from June 21, 2023 showed close agreement on expected Doppler-replica spacing.Source: §VIII · p. 4
  • The results highlight the need for frame-aware passive radar processing and provide a foundation for ambiguity-mitigation and target-detection studies.Source: §VIII · p. 4
  • Fig. 7 sums approximately 2 minutes of SXM-8 (B) direct-path data using 3-s CPIs, with Eq. (5) expected harmonic locations marked.Source: Figure 7 · p. 4
  • Fig. 8 zooms around selected replicas, where the dashed lines show close agreement between theory and experiment.Source: Figure 8 · p. 4
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