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On the Design of an Optimal Multi-Tone Jammer Against the Wiener Interpolation Filter

Corentin Fonteneau

TL;DR

An analytical proof is provided showing that a multi-tone jamming waveform composed of $L/2+1$ tones is sufficient to render the Wiener-filter-based anti-jamming module completely ineffective.

Abstract

In the context of civilian and military communications, anti-jamming techniques are essential to ensure information integrity in the presence of malicious interference. A conventional time-domain approach relies on computing the Wiener interpolation filter to estimate and suppress the jamming waveform from the received samples. It is widely acknowledged that this method is effective for protecting wideband systems against narrowband interference. In this work, this paradigm is questioned through the design of a $K$-tone jamming waveform that is intrinsically difficult to estimate assuming a $L$-tap Wiener interpolation filter. This design relies on an optimization procedure that maximizes the analytical Bayesian mean squared error associated with the jamming waveform estimate. Additionally, an analytical proof is provided showing that a multi-tone jamming waveform composed of $L/2+1$ tones is sufficient to render the Wiener-filter-based anti-jamming module completely ineffective. The analytical results are validated through Monte Carlo simulations assuming both perfect knowledge and practical estimates of the correlation functions of the received signal.

On the Design of an Optimal Multi-Tone Jammer Against the Wiener Interpolation Filter

TL;DR

An analytical proof is provided showing that a multi-tone jamming waveform composed of tones is sufficient to render the Wiener-filter-based anti-jamming module completely ineffective.

Abstract

In the context of civilian and military communications, anti-jamming techniques are essential to ensure information integrity in the presence of malicious interference. A conventional time-domain approach relies on computing the Wiener interpolation filter to estimate and suppress the jamming waveform from the received samples. It is widely acknowledged that this method is effective for protecting wideband systems against narrowband interference. In this work, this paradigm is questioned through the design of a -tone jamming waveform that is intrinsically difficult to estimate assuming a -tap Wiener interpolation filter. This design relies on an optimization procedure that maximizes the analytical Bayesian mean squared error associated with the jamming waveform estimate. Additionally, an analytical proof is provided showing that a multi-tone jamming waveform composed of tones is sufficient to render the Wiener-filter-based anti-jamming module completely ineffective. The analytical results are validated through Monte Carlo simulations assuming both perfect knowledge and practical estimates of the correlation functions of the received signal.
Paper Structure (27 sections, 6 theorems, 85 equations, 6 figures)

This paper contains 27 sections, 6 theorems, 85 equations, 6 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Received signal
  4. General architecture of the anti-jamming module
  5. Analytical performance of the anti-jamming module
  6. Analytical solution of the Wiener interpolation filter $\mathbf{w}^{\star}$
  7. Analytical BMSE of the interference estimate $\hat{i}^{\star}(\boldsymbol{\alpha},\boldsymbol{\omega})$
  8. Blind estimation of the Wiener interpolation filter $\mathbf{w}^{\star}$
  9. Design of an Optimal Multi-Tone Jammer
  10. Optimization problem
  11. Optimization for $K=1$ tone
  12. Optimization for $K=2$ tones
  13. Optimization for $3\leq K<\frac{L}{2}{+1}$ tones
  14. Optimization for $K\geq\frac{L}{2}{+1}$ tones
  15. Simulation results
  16. ...and 12 more sections

Key Result

Theorem 1

The Wiener interpolation filter $\mathbf{w}^{\star}$ for a multi-tone jammer in DSSS systems is expressed as, where,

Figures (6)

  • Figure 1: Architecture of the anti-jamming module.
  • Figure 2: Estimation of a 4-tone jammer in a QPSK-DSSS system by Wiener filtering ($SNR=-15\, \mathrm{dB}$, $JSR=25\, \mathrm{dB}$).
  • Figure 3: Increase in error ratio obtained with the help of the optimizer.
  • Figure 4: Jamming waveform optimisation for $K=6$ tones and $L=16$.
  • Figure 5: Empirical BMSE of the interference estimate ($SNR=-15\, \mathrm{dB}$, $JSR=25\, \mathrm{dB}$).
  • ...and 1 more figures

Theorems & Definitions (12)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Corollary 2.1
  • proof
  • Theorem 3
  • proof
  • Proposition 1
  • proof
  • ...and 2 more