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Efficient dual-scale generalized Radon-Fourier transform detector family for long time coherent integration

Suqi Li, Yihan Wang, Bailu Wang, Giorgio Battistelli, Luigi Chisci, Guolong Cui

TL;DR

This work tackles LTCI detection for moving targets by addressing RM and DFM with a dual-scale decomposition of motion parameters, enabling a cascade correction where RM is handled on a coarse search space and DFM on a fine space. The authors develop DS-GRFT and DS-KT-MFP detectors, showing that RM/DFM corrections can be factorized into a range-domain GIFT and a Doppler-domain GFT conditioned on coarse parameters, dramatically reducing computational load while preserving detection efficacy. The approach yields substantial complexity reductions (e.g., up to two orders of magnitude over FD-GRFT) and maintains comparable performance to standard GRFT and KT-MFP in multi-object scenarios, validated through simulations in a mmWave UAV surveillance context. Overall, the dual-scale strategy provides a practical pathway to efficient LTCI processing for moving targets in real-time radar systems, with flexible implementation options and demonstrated robustness in challenging scenarios.

Abstract

Long Time Coherent Integration (LTCI) aims to accumulate target energy through long time integration, which is an effective method for the detection of a weak target. However, for a moving target, defocusing can occur due to range migration (RM) and Doppler frequency migration (DFM). To address this issue, RM and DFM corrections are required in order to achieve a well-focused image for the subsequent detection. Since RM and DFM are induced by the same motion parameters, existing approaches such as the generalized Radon-Fourier transform (GRFT) or the keystone transform (KT)-matching filter process (MFP) adopt the same search space for the motion parameters in order to eliminate both effects, thus leading to large redundancy in computation. To this end, this paper first proposes a dual-scale decomposition of the target motion parameters, consisting of well designed coarse and fine motion parameters. Then, utilizing this decomposition, the joint correction of the RM and DFM effects is decoupled into a cascade procedure, first RM correction on the coarse search space and then DFM correction on the fine search spaces. As such, step size of the search space can be tailored to RM and DFM corrections, respectively, thus avoiding large redundant computation effectively. The resulting algorithms are called dual-scale GRFT (DS-GRFT) or dual-scale GRFT (DS-KTMFP) which provide comparable performance while achieving significant improvement in computational efficiency compared to standard GRFT (KT-MFP). Simulation experiments verify their effectiveness and efficiency.

Efficient dual-scale generalized Radon-Fourier transform detector family for long time coherent integration

TL;DR

This work tackles LTCI detection for moving targets by addressing RM and DFM with a dual-scale decomposition of motion parameters, enabling a cascade correction where RM is handled on a coarse search space and DFM on a fine space. The authors develop DS-GRFT and DS-KT-MFP detectors, showing that RM/DFM corrections can be factorized into a range-domain GIFT and a Doppler-domain GFT conditioned on coarse parameters, dramatically reducing computational load while preserving detection efficacy. The approach yields substantial complexity reductions (e.g., up to two orders of magnitude over FD-GRFT) and maintains comparable performance to standard GRFT and KT-MFP in multi-object scenarios, validated through simulations in a mmWave UAV surveillance context. Overall, the dual-scale strategy provides a practical pathway to efficient LTCI processing for moving targets in real-time radar systems, with flexible implementation options and demonstrated robustness in challenging scenarios.

Abstract

Long Time Coherent Integration (LTCI) aims to accumulate target energy through long time integration, which is an effective method for the detection of a weak target. However, for a moving target, defocusing can occur due to range migration (RM) and Doppler frequency migration (DFM). To address this issue, RM and DFM corrections are required in order to achieve a well-focused image for the subsequent detection. Since RM and DFM are induced by the same motion parameters, existing approaches such as the generalized Radon-Fourier transform (GRFT) or the keystone transform (KT)-matching filter process (MFP) adopt the same search space for the motion parameters in order to eliminate both effects, thus leading to large redundancy in computation. To this end, this paper first proposes a dual-scale decomposition of the target motion parameters, consisting of well designed coarse and fine motion parameters. Then, utilizing this decomposition, the joint correction of the RM and DFM effects is decoupled into a cascade procedure, first RM correction on the coarse search space and then DFM correction on the fine search spaces. As such, step size of the search space can be tailored to RM and DFM corrections, respectively, thus avoiding large redundant computation effectively. The resulting algorithms are called dual-scale GRFT (DS-GRFT) or dual-scale GRFT (DS-KTMFP) which provide comparable performance while achieving significant improvement in computational efficiency compared to standard GRFT (KT-MFP). Simulation experiments verify their effectiveness and efficiency.
Paper Structure (23 sections, 4 theorems, 83 equations, 6 figures, 4 tables, 4 algorithms)

This paper contains 23 sections, 4 theorems, 83 equations, 6 figures, 4 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Receival signal model
  4. RM and DFM effects
  5. GRFT detector family and its coupling effect of parameter search spaces
  6. Two implementations of GRFT detector and performance analysis
  7. GRFT detector in the time domain
  8. GRFT detector in frequency domain
  9. KT-MFP detector and connection to the GRFT detector
  10. Detection on single-scale search space
  11. Dual-scale GRFT detector family
  12. Generalized PC and MTD procedure
  13. Dual-scale decomposition of motion parameters
  14. Factorization of the GRFT detector
  15. Factorization of the KT-MFP detector
  16. ...and 8 more sections

Key Result

Proposition 1

Given the dual-scale decomposition in (Partition-Parameter) - (Definition-of-fine), the following holds: where: $A_4(\tau_n)\!\triangleq\!A'_2\! \, \exp\{j\pi B_r (\tau_n-2c_0/c)\}$; $\tilde{\mathbf{c}}_c\!\triangleq\![\tilde{c}_{0},\tilde{c}_{1,c},\cdots,\tilde{c}_{P,c}]$; $c_{p,f}\triangleq c_p- \tilde{c}_{p,c}$ for $p\!=\!1,\! \cdots\!,\! P$; $\kappa\triangleq 1-\frac{B_r}{2f_c}$; $\overline{w

Figures (6)

  • Figure 1: Dual-scale parameter decomposition.
  • Figure 2: Scenario of UAV surveillance via ICSR system.
  • Figure 3: (a) Range spectrum with slow-time before RM correction; (b) range spectrum with slow-time after coarse acceleration compensation; (c) range spectrum with slow-time after coarse acceleration and coarse velocity compensations; (d) range-Doppler spectrum after RM correction.
  • Figure 4: Estimation of target motion parameters: (a) maximum output of each range bin; (b) coarse acceleration and folding factor spectrum at range bin 1765; (c) fine acceleration and baseband velocity spectrum at bin-pair $(5,2)$ of (b); (d) coarse acceleration and folding factor spectrum at range bin 1613; (e) fine acceleration and baseband velocity spectrum at bin-pair $(5,2)$ of (d); (f) range-Doppler spectrum after target motion compensation.
  • Figure 5: Range-Doppler spectrum estimation: (a) TD-GRFT; (b) DS-GRFT.
  • ...and 1 more figures

Theorems & Definitions (16)

  • Remark 1
  • Definition 1
  • Remark 2
  • Definition 2
  • Remark 3
  • Remark 4
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • ...and 6 more