PaperlayerView exact revision on arXiv

Source-linked AI summary

Koopman-Predictive Coefficient Tracking for Vehicle-Mounted Monostatic ISAC

Anh Tuyen Le, Xiaojing Huang, Y. Jay Guo

arXiv:2609.37327v1eess.SP

TL;DR

In vehicle-mounted monostatic ISAC, vibration can make SI-channel coefficients change within an adaptation period, while cancellation must preserve delayed sensing echoes. KP-SIC predicts a coefficient trajectory from recent snapshots and combines it with adaptive correction; simulations report improved SI suppression over conventional FASIC-WL-NLMS.

  • Problem

    Vibration can change SI-channel coefficients within an adaptation period, causing conventional adaptive filters to lag while monostatic ISAC must preserve delayed sensing echoes.

    Source: §I · p. 1

  • Method

    KP-SIC uses recent effective SI-channel coefficient snapshots to predict a sample-varying trajectory for the next period, with adaptive correction of residual errors and unstructured variation.

    Source: §I · p. 1, §III · p. 3

  • Results

    KP-SIC improves SI suppression by 6.3–10.2 dB over conventional FASIC-WL-NLMS and recovers 60–74% of the prediction gain available to a non-causal bound.

    Source: §I · p. 2

  • Takeaways & Limitations

    The observation window should span sufficient vibration cycles to identify dominant modes, providing a practical window-sizing condition for vibration-aware tracking.

    Source: §I · p. 2

    When unstructured variation becomes dominant, the Koopman forecast is no longer reliable, although WL-NLMS correction absorbs most forecast error in the tested range.

    Source: D. Unstructured variation · p. 6

Abstract

from arXiv · show

This paper studies predictive coefficient tracking for digitally generated self-interference cancellation (SIC) in vehicle-mounted monostatic integrated sensing and communication (ISAC) systems. In such systems, the canceller must suppress strong transmitter leakage and nearby unintended reflections while preserving delayed sensing echoes. On mobile platforms, mechanical vibration from engines, rotors, or nearby structures can induce quasi-periodic variation in the self-interference (SI) channel. The optimal cancellation coefficients may then vary within one adaptation period, causing the applied coefficients of a conventional adaptive filter to lag behind the moving SI channel and increasing the residual SI. To address this problem, we propose a Koopman-predictive SIC (KP-SIC) module that augments a conventional adaptive filter with a predicted coefficient trajectory. KP-SIC uses recent effective SI-channel coefficient snapshots to identify structured vibration-induced dynamics and predict a sample-varying coefficient sequence for the next adaptation period. The predicted coefficients place the canceller closer to the expected time-varying optimum, while the adaptive filter corrects residual prediction errors and unstructured variation. For evaluation, the module is integrated with a widely linear normalized least mean-square (WL-NLMS) filter under a flexible analog SIC (FASIC) framework. Simulations show that KP-SIC improves SI suppression by $6.3$--$10.2$~dB over conventional FASIC-WL-NLMS once the observation window spans at least about $1.5$ vibration cycles. Compared with a non-causal performance bound, KP-SIC achieves $60$--$74\%$ of the available prediction gain.

I. INTRODUCTION

Vehicle-mounted monostatic ISAC must cancel strong leakage and nearby reflections without removing delayed sensing echoes, while vibration can make the SI channel change within an adaptation period. KP-SIC predicts coefficient trajectories from recent channel snapshots and combines that forecast with adaptive correction.

I. INTRODUCTION

  • Monostatic ISAC cancellation must suppress direct leakage and nearby reflections while preserving delayed echoes that carry sensing information.The cancellation structure can shape the waveform through its coefficient vector and effective delay span.Source: §I · p. 1
  • Vibration can make SI-channel coefficients vary within an adaptation period, so conventional filters lag and leave higher residual SI even when their cancellation basis adequately represents static paths.The SI variation can contain structured spectral components at tens to hundreds of hertz plus smaller unstructured variation.Source: §I · p. 1
  • KP-SIC predicts a sample-varying coefficient trajectory from recent effective SI-channel snapshots, while the adaptive filter corrects prediction errors and unstructured variation.The module is demonstrated with FASIC and a WL-NLMS correction filter.Source: §I · p. 1
  • 6.3–10.2 dB better SI suppression than conventional FASIC-WL-NLMS, with 60–74% of the predictive gain available from the non-causal bound.The gains occur once the observation window spans sufficient vibration cycles to identify dominant modes.Source: §I · p. 2

II. SIGNAL MODEL

The signal model represents SI as a time-varying effective coefficient vector over a transmit-derived basis, alongside useful receive signals and noise. It explains how vibration-driven channel changes make reactive coefficient tracking lag within an adaptation period.

II. SIGNAL MODEL

  • The received signal includes SI from direct leakage and nearby reflections, useful target echoes and remote communication signals, and receiver noise.The SI path model uses delayed transmit waveforms with time-varying complex path gains.Source: §II · p. 2
  • Vibration-induced path gains combine quasi-periodic sinusoidal phase variation with an unstructured component.The sinusoidal phase depths depend on displacement relative to carrier wavelength; σv sets the strength of the unstructured variation.Source: §II · p. 2
  • A selected transmit-derived basis approximates SI with effective coefficients h[n] and an orthogonal projection error ξ[n], while its delay span governs which transmit-correlated components can be represented.For monostatic ISAC, the span should cover leakage and nearby reflections while avoiding unnecessary overlap with delayed target echoes.Source: §II · p. 2
  • Under the stated orthogonality conditions, the coefficient vector minimizing the SI-dependent residual power equals h[n].The useful receive signal and receiver noise are assumed uncorrelated with the local transmit basis.Source: §II · pp. 2–3
  • Conventional filters update coefficients from measured residuals, but coefficients can lag when the optimum moves within an adaptation period.Increasing step size can shorten response time but amplifies gradient noise; prediction can keep coefficients closer to the expected optimum while adaptation corrects mismatch.Source: §II · p. 3

III. KOOPMAN-PREDICTIVE SIC TRACKING

KP-SIC augments the digital canceller by combining a Koopman-predicted coefficient component with an adaptive correction. It estimates recent effective SI-channel snapshots and forecasts a sample-varying trajectory for the next adaptation period.

III. KOOPMAN-PREDICTIVE SIC TRACKING

  • Applied coefficients combine a Koopman-predicted component wK[n] with an adaptive correction Δw[n].The forecast captures structured SI-channel variation; the correction addresses forecast errors and unstructured variation, and setting wK[n] = 0 recovers conventional adaptive cancellation.Source: §III · p. 3
  • A block least-squares stage estimates effective SI-channel coefficient snapshots from reconstructed precancellation samples and the known basis.The reconstruction uses the known applied cancellation waveform under an ideal, calibrated auxiliary-chain assumption.Source: §III · p. 3
  • The Koopman forecast predicts the next period’s sample-varying coefficient trajectory, while WL-NLMS updates the adaptive correction at every sample from the measured residual.The forecast uses the snapshot sequence rather than a single snapshot.Source: §III · p. 3

A. Forecast branch

The forecast branch maps recent transformed coefficient snapshots into a predicted coefficient trajectory for the next adaptation period. It identifies a low-rank linear model of a lifted snapshot history using dynamic mode decomposition.

A. Forecast branch

  • Recent snapshots are transformed using a Gram-matrix weighting so squared Euclidean coefficient error corresponds to average residual SI power.The weighting accounts for correlation among cancellation-basis functions.Source: A. Forecast branch · p. 3
  • A lifted state stacks the d most recent transformed snapshots, with conjugate entries to represent improper complex variation in widely linear cancellation.The delay depth d supplies temporal memory to the forecast.Source: A. Forecast branch · p. 3
  • Dynamic mode decomposition identifies a low-rank linear model for lifted-state evolution from shifted matrices formed from a window of snapshots.The window W yields K = W − d + 1 lifted states.Source: A. Forecast branch · p. 3
  • The forecast fits modal amplitudes jointly over a sliding window, predicts the next lifted state, then selects and transforms its leading entries into predicted effective coefficients.Eigenvalues above the chosen magnitude threshold are projected onto the unit circle to avoid artificial forecast growth; the predicted coefficients are applied over the next period.Source: A. Forecast branch · pp. 3–4

B. FASIC integration with WL-NLMS

KP-SIC supplies a sample-varying Koopman forecast while WL-NLMS adapts only the correction, so the filter tracks residual coefficient error rather than the full SI-channel vector.

B. FASIC integration with WL-NLMS

  • The FASIC basis uses delayed direct and conjugate EMP branches to represent transmitter I/Q imbalance, PA distortion, and multipath SI coupling.The applied coefficient combines the forecast and adaptive correction; only the correction is updated sample by sample.Source: B. FASIC integration with WL-NLMS · p. 4
  • The WL-NLMS correction is updated from the measured residual, with µ setting the step size and ϵ preventing division by small input power.Under the stated orthogonality conditions, the correction minimizing SI-dependent residual power is defined from this update.Source: B. FASIC integration with WL-NLMS · p. 4
  • KP-SIC changes the adaptation target from the full effective SI-channel vector to the remaining error after prediction.The Koopman forecast captures structured variation, while WL-NLMS corrects prediction errors and unstructured variation.Source: B. FASIC integration with WL-NLMS · p. 4

A. Simulation setup

The waveform-level evaluation uses a specified FASIC-WL-NLMS configuration and a simulated SI channel with structured vibration and unstructured variation.

A. Simulation setup

  • The simulations use a 3.5 GHz QPSK waveform and a 144-coefficient WL-EMP canceller, with 512-sample adaptation periods and a 48-period Koopman window.Runs span 240 periods, with the first 60 excluded from steady-state statistics; results generally average six realizations.Source: A. Simulation setup · p. 4
  • The simulated SI channel has three paths, −35 dB passive isolation, and two vibration tones; the sweep covers 10–400 Hz for a 1 ms adaptation period.Phase depths are 0.25 and 0.10 rad, and the unstructured-motion component has nominal strength σv = 0.02 rad.Source: A. Simulation setup · p. 4
  • SI suppression is the ratio of received SI power before cancellation to total residual power after the RF combiner; the non-causal bound uses the optimal coefficient sequence.Fig. 2 plots residual power normalized to received SI power at fv = 0.05, averaged over 50 transmit-data realizations, with a vertical marker for the abrupt channel change.Source: A. Simulation setup · p. 4, Figure 2 · p. 5

B. Convergence behavior

KP-SIC improves steady-state cancellation over conventional FASIC-WL-NLMS and recovers cancellation faster after an abrupt SI-channel change.

B. Convergence behavior

  • 34.7 dB below received SI is reached by the assisted scheme, versus 25.7 dB for conventional FASIC-WL-NLMS and 38.0 dB for the non-causal bound.After the Koopman forecast activates, residual power falls a further 5 dB; results average 50 transmit-data realizations at fv = 0.05.Source: B. Convergence behavior · p. 5
  • Both schemes initially lose cancellation to a similar level after the abrupt channel change.The change is introduced at adaptation period 150 to represent an environmental event not predictable from past snapshots.Source: B. Convergence behavior · p. 5
  • 1.8 ± 1.2 adaptation periods are required for the assisted loop to return to the common pre-change conventional level, versus 6.7 ± 2.4 for the conventional loop.The path gains undergo an unpredictable magnitude-0.3 and random-phase change; the assisted loop remains above the conventional loop throughout the transient in every realization.Source: B. Convergence behavior · p. 5

C. Variation rate

KP-SIC’s performance depends on choosing an observation window long enough to resolve vibration modes. With a window spanning at least about 1.5 vibration cycles, it outperforms conventional tracking across the sweep and recovers a substantial share of the non-causal prediction gain.

C. Variation rate

  • For fv ≥0.05, KP-SIC improves suppression by 6.3–10.2 dB, with its largest gain at fv = 0.1.At fv = 0.1, the channel changes within an adaptation period but remains predictable from recent coefficient snapshots.Source: C. Variation rate · p. 5
  • With the original window, fv = 0.01 spans only 0.5 cycle and leaves suppression 1.8 dB below conventional tracking, while fv = 0.05 spans 2.4 cycles and resolves the modes.The assisted scheme’s suppression is non-monotonic in fv because the observation window determines whether modes can be identified.Source: C. Variation rate · p. 5
  • At Wfv ≳1.5, the matched-window scheme gains 1.7 dB at fv = 0.01 and 7.9–10.1 dB from fv = 0.03 to 0.2 over the conventional loop.At fv = 0.4, the rate approaches the snapshot Nyquist rate, so window sizing does not remove the decline.Source: C. Variation rate · p. 5
  • The non-causal bound stays near 38.2 dB; from fv = 0.05 to 0.2, available prediction gain widens from 12.7 to 16.5 dB, and KP-SIC recovers 74% and 60%, respectively.The recovered gains are 9.4 dB at fv = 0.05 and 9.9 dB at fv = 0.2.Source: C. Variation rate · pp. 5–6

D. Unstructured variation

As unstructured SI variation increases, KP-SIC’s advantage over conventional FASIC-WL-NLMS declines because past snapshots become less predictive of future coefficient changes. WL-NLMS correction keeps the assisted loop near conventional performance over the tested range.

D. Unstructured variation

  • At σv = 0, KP-SIC improves suppression by 10.9 dB, but its advantage falls to 0.3 dB at σv = 0.2 rad and 0.6 dB below conventional tracking at the strongest variation.The reduction accompanies increasingly unpredictable future coefficient variation.Source: D. Unstructured variation · p. 6
  • When unstructured variation dominates, the Koopman forecast becomes unreliable, but WL-NLMS absorbs most forecast error and the assisted loop approaches conventional adaptive operation within the tested range.KP-SIC is most effective when SI-channel variation contains structured motion identifiable from snapshot history.Source: D. Unstructured variation · p. 6

V. CONCLUSION

The conclusion presents KP-SIC as a predictive coefficient-tracking module for vehicle-mounted monostatic ISAC. In FASIC with WL-NLMS correction, it improves SI suppression and offers a practical observation-window sizing guideline.

V. CONCLUSION

  • KP-SIC improves suppression by 6.3–10.2 dB over conventional FASIC-WL-NLMS and recovers 60–74% of the prediction gain available to a non-causal bound.It predicts next-period cancellation coefficients from structured vibration-induced SI-channel evolution, reducing the adaptive filter’s tracking burden.Source: §V · p. 6
  • The observation window should span sufficient vibration cycles to identify dominant modes, providing a practical window-sizing guideline for vibration-aware SIC.Future work includes imperfect auxiliary transmit chains, real-time Koopman implementation, measured platform-vibration validation, and wideband ISAC waveforms.Source: §V · p. 6
Loading 2609.37327v1…