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DopplerGLRTNet for Radar Off-Grid Detection

Yadang Alexis Rouzoumka, Jean Pinsolle, Eugénie Terreaux, Christèle Morisseau, Jean-Philippe Ovarlez, Chengfang Ren

Abstract

Off-grid targets whose Doppler (or angle) does not lie on the discrete processing grid can severely degrade classical normalized matched-filter (NMF) detectors: even at high SNR, the detection probability may saturate at operationally relevant low false-alarm rates. A principled remedy is the continuous-parameter GLRT, which maximizes a normalized correlation over the parameter domain; however, dense scanning increases test-time cost and remains sensitive to covariance mismatch through whitening. We propose DopplerGLRTNet, an amortized off-grid GLRT: a lightweight regressor predicts the continuous Doppler within a resolution cell from the whitened observation, and the detector outputs a single GLRT/NMF-like score given by the normalized matched-filter energy at the predicted Doppler. Monte Carlo simulations in Gaussian and compound-Gaussian clutter show that DopplerGLRTNet mitigates off-grid saturation, approaches dense-scan performance at a fraction of its cost, and improves robustness to covariance estimation at the same empirically calibrated Pfa.

DopplerGLRTNet for Radar Off-Grid Detection

Abstract

Off-grid targets whose Doppler (or angle) does not lie on the discrete processing grid can severely degrade classical normalized matched-filter (NMF) detectors: even at high SNR, the detection probability may saturate at operationally relevant low false-alarm rates. A principled remedy is the continuous-parameter GLRT, which maximizes a normalized correlation over the parameter domain; however, dense scanning increases test-time cost and remains sensitive to covariance mismatch through whitening. We propose DopplerGLRTNet, an amortized off-grid GLRT: a lightweight regressor predicts the continuous Doppler within a resolution cell from the whitened observation, and the detector outputs a single GLRT/NMF-like score given by the normalized matched-filter energy at the predicted Doppler. Monte Carlo simulations in Gaussian and compound-Gaussian clutter show that DopplerGLRTNet mitigates off-grid saturation, approaches dense-scan performance at a fraction of its cost, and improves robustness to covariance estimation at the same empirically calibrated Pfa.
Paper Structure (17 sections, 26 equations, 2 figures)

This paper contains 17 sections, 26 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Signal Model in Slow-Time
  4. Doppler Parametrization: On-Grid vs Off-Grid
  5. Matched-Filter SNR and Whitening
  6. Classical GLRT-Based Detectors
  7. Normalized Matched Filter (Single Test)
  8. On-grid NMF (single bin) and Local Dense Scanning (NMF scan within one cell)
  9. Off-Grid GLRT Viewpoint (Continuous-Parameter NMF)
  10. Oracle Upper Bound
  11. DopplerGLRTNet: Neural Off-Grid detector via Amortized GLRT
  12. Training, Calibration, and Simulation Setup
  13. Experimental Results
  14. Baseline Detectors
  15. Gaussian Clutter: Off-Grid Saturation
  16. ...and 2 more sections

Figures (2)

  • Figure 1: Overview of DopplerGLRTNet. Training (top): a cell-constrained Doppler regressor outputs $\widehat{\theta}(\mathbf{u})\in D$ from whitened and energy-normalized slow-time data, optimized with $\mathcal{L}=\mathcal{L}_{\mathrm{CE}}+\lambda \mathcal{L}_{\delta}$ (Huber loss on the normalized offset for $H_1$ samples). Detection (bottom): the frozen network predicts $\widehat{\theta}$ and we compute a single GLRT/NMF-like score $T(\mathbf{u}; \boldsymbol{\phi})=|\mathbf{v}^{\mathsf H}(\widehat{\theta}(\mathbf{u}; \boldsymbol{\phi}))\, \mathbf{u}|^2$, followed by an empirical CFAR threshold calibration $\tau_{P_{fa}}$.
  • Figure 2: $P_{\mathrm{d}}$ versus matched-filter SNR at $P_{\mathrm{fa}}=10^{-2}$ for off-grid targets in the single Doppler cell $D_0$ ($m=16$, $\rho=0.5$). Whitening uses a global SCM fit on $H_0$ data, followed by energy normalization. Baselines: on-grid NMF, local scan in $D_0$ ($K=64$), oracle, and DopplerGLRTNet. (cGN: complex Gaussian clutter; cCGN: compound-Gaussian clutter; AWGN: additive white Gaussian noise.)