Interrupted-Sampling Repeater Jamming

• Interrupted-Sampling Repeater Jamming is a coherent jamming method that retransmits amplitude-scaled radar signal slices to generate false targets and contaminate matched-filter outputs.
• It exploits pulse compression and convolutional processing to produce spurious peaks that can mask or even exceed real target responses in radar ambiguity functions.
• Advanced countermeasures such as waveform-domain adaptive matched filtering, complementary signal sets, and deep learning approaches significantly enhance radar resilience against ISRJ.

Interrupted-Sampling Repeater Jamming (ISRJ) is a form of coherent electronic countermeasure in which a jammer periodically samples portions of an incoming radar signal, retransmits these amplitude-scaled and delayed slices toward the radar, and thus generates spurious, range-localized “false targets” and deceptive features in the matched-filter output. ISRJ exploits the convolutional processing inherent to pulse compression radars, contaminating the ambiguity function with partially matched, energy-accumulating segments that can exceed or mask true target responses. This capability challenges both radar detection and classification, necessitating advanced anti-jamming techniques that adapt to nonstationary jamming strategies without relying on explicit jammer parameter estimation (Su et al., 2023, Su et al., 19 Jan 2024, Li et al., 21 May 2025, Sun et al., 28 Nov 2025).

1. Physical Principles and Signal Model

ISRJ leverages digital radio-frequency memory (DRFM) hardware to intercept a radar’s transmitted waveform $s(t)$, slice it periodically at intervals $T_J$ with “on” durations $T_j$ (duty cycle $\varepsilon=T_j/T_J$), and retransmit the energy-coherent sub-pulses with delay $\tau_J$ and (possibly) modulation or frequency shifts. The canonical ISRJ signal model after retransmission is

$\jmath(t) = g(t)\,s(t)$

where $$g(t) = \sum_{n}\text{rect}\left(\frac{t-nT_J}{T_j}\right)$$ defines the periodic gating. The resulting received signal at the radar front-end is, in the direct-repeater case,

$x(t) = A_s\,s(t-\tau_s) + A_j\,\jmath(t-\tau_j)$

where $A_s$ and $A_j$ are amplitudes for the echo and jamming, respectively, $\tau_s$ the round-trip delay to the scatterer, and $\tau_j$ the jammer delay (Su et al., 2023, Su et al., 19 Jan 2024).

After matched filtering, ISRJ slices produce a convolution between $s(t)$ and sliced/repeated copies of $s(t)$, resulting in both peak suppression at the true target position (if the true echo and a jamming slice overlap) and grating-lobe–like false peaks at predictable offsets.

Extended ISRJ forms include:

• Interrupted-Sampling Repetitive Repeater Jamming (ISRRJ): repeated bursts yield clusters of false targets at fixed delays.
• Interrupted-Sampling Cyclic Repeater Jamming (ISCRJ): shifted cycles generate more complex cluster and shift patterns (Su et al., 19 Jan 2024).

2. Matched Filter Response and Limitations

The matched filter output in the presence of ISRJ is governed by the radar’s ambiguity function $\chi(t,\nu)$, yielding

$$x_o(t) = A_s\,\chi(t-\tau_s,0) + \sum_{q=-Q}^{Q} A_j\,A_q\,\chi(t-\tau_j,-q f_J)$$

where $f_J = 1/T_J$, and $A_q = T_j f_J\,\text{sinc}(\pi q f_J T_j)$ are ISRJ harmonic amplitudes. The jamming slices give rise to “partial matches” in the convolution, generating false targets with amplitudes sometimes comparable to (or capable of suppressing) real echoes, especially when the jamming duty cycle $\varepsilon$ is high (Su et al., 19 Jan 2024, Su et al., 2023).

Classical matched filtering cannot distinguish between energy from true echoes and that from ISRJ, as both are formed from the same or modulated versions of $s(t)$. Traditional electronic counter-countermeasure (ECCM) techniques typically require prior knowledge or online estimation of ISRJ parameters—e.g., duty cycle, repetition rate, or slice offset—which can be unreliable if the jammer adapts its mode (Su et al., 2023).

3. Impact on High-Resolution Range Profile (HRRP) and Recognition

ISRJ-induced distortion in HRRP manifests as periodic convolution artifacts associated with the jammer’s slice-and-retransmit protocol. In the frequency domain, ISRJ multiplies the clean HRRP spectrum $S(f)$ by a comb of rect function windows: $$J(f) = \sum_n \text{rect}\left(\frac{f-nT_f}{\tau_f}\right)$$ with $T_f = 1/\tau_s$ the comb spacing and $\tau_f$ the notch width. In the time domain, this equates to convolution with a periodic sinc-weighted impulse train, or “point spread function” (PSF): $$h(t) = \sum_{n=-\infty}^{\infty} A'\,\mathrm{Sinc}\left(\frac{n}{\tau_f T_f}\right)\,\delta\left(t-\frac{n}{T_f}\right)$$ Thus, the observed HRRP $y'(t)$ is given by $y(t) * h(t)$, leading to a washout of true target peaks and proliferation of false ones (Sun et al., 28 Nov 2025). This significantly degrades the performance of radar automatic target recognition (RATR) systems reliant on HRRP feature integrity.

4. Anti-ISRJ Techniques

4.1 Waveform-Domain Adaptive Matched Filtering (WD-AMF)

WD-AMF operates by recasting matched filtering into the waveform domain, where each contribution at integration variable $\mu$ is adaptively weighted according to local coherence growth: $$z_o(t) = \int_{-\infty}^{\infty} a^{(t)}(\mu)\,\upsilon^{(t)}(\mu)\,d\mu + \varsigma^{(t)}$$ with $a^{(t)}(\mu) \in \{0,1\}$ determined by a thresholded comparison of the estimated CWCF derivative against an adaptively set threshold, and $\varsigma^{(t)}$ a compensation term for SNR neutrality. This processing distinguishes true echo-like growth from jamming slices, acting like a dynamic bank of bandpass filters on the waveform domain (Su et al., 2023).

WD-AMF achieves >30 dB suppression of ISRJ-induced peaks, restores full main-lobe echo gain, and maintains low sidelobe levels, without prior ISRJ modeling. Its performance is robust across wide ranges of SNR, SJR, and jamming parameters, provided certain assumptions hold (e.g., constant-envelope slices, moderate Doppler) (Su et al., 2023).

4.2 Waveform-Domain Complementary Signal Sets (WDCSS)

WDCSS enhances WD-AMF by deploying a transmitter-side phase-coded set $\{s_i(t)\}$ with waveform-domain complementarity properties: $$\sum_{i=0}^{D-1} a_i(n+m) a_i^*(n) = 0\quad \forall m \neq 0$$ This ensures that only the true echo occupies the integrable region at $t=\tau_s$, while jamming slices are fully separable in the waveform domain. Construction employs column-orthogonal matrices (e.g., Walsh–Hadamard, cascaded Golay), enabling parameter-free ECCM operation—neither receiver nor transmitter requires knowledge of ISRJ timing or duty cycle. Under high-intensity ISRJ, WDCSS yields a peak-to-sidelobe ratio improvement of 30–40 dB over standard LFM and Golay waveforms (Su et al., 19 Jan 2024).

Performance for ISRRJ ($\eta=0.9$):

• LFM: main-lobe loss −10.5 dB, PSLR ≈ 19.9 dB
• Golay: main-lobe loss −57 dB, PSLR → −23.8 dB
• WDCSS: main-lobe preserved, PSLR ≈ 52.5 dB

4.3 GLWD-Based Time–Frequency Line Detection

To combat ISRJ in low SNR/multicomponent scenarios, processing in the Generalized Linear Canonical Wigner Distribution (GLWD) domain allows each linear-FM (LFM) signal to be mapped to an energy-concentrated straight line, while ISRJ artifacts remain fragmented. The proposed mobile long line segment detection (M-LLSD) exploits this property, emphasizing continuous long lines (targets) and suppressing short discontinuous segments (jamming). After GLWD detection, a filter mask in the short-time Fourier transform (STFT) domain reconstructs the de-jammed signal via inverse STFT (Li et al., 21 May 2025).

• SJR improvement factor (SJRIF) ≈13 dB (single ISRJ, SNR=–12 dB)
• Probability of detection 90% at SNR ≈–6 dB, exceeding classical energy-function and Max-TF methods by 3.6–4.5 dB

4.4 Prior Information-Guided Deep Learning

For HRRP-based recognition, explicit modeling of the ISRJ-induced PSF allows extraction of the jamming convolution kernel as prior information. Deep neural networks can then exploit this PSF via prior-guided feature interaction modules and hybrid cross-entropy/contrastive loss to maintain class separability even in the presence of ISRJ. This approach delivers state-of-the-art generalization on out-of-distribution jamming scenarios without sacrificing in-distribution accuracy (Sun et al., 28 Nov 2025).

Method	InD Accuracy	OOD Accuracy	SJR Suppression (Typical)
WD-AMF	–	–	>30 dB
WDCSS+WD-AMF	≈100% main lobe	–	30–40 dB (PSLR)
GLWD+M-LLSD	–	–	13 dB (SJRIF)
Prior-guided recognition	97.1–97.3%	84–89%	–

5. Practical Considerations, Limitations, and Extensions

Anti-ISRJ performance depends on waveform–domain separability, SNR, SJR, and Doppler dynamics.

• WD-AMF and WDCSS assume that jammer slices and true echo are temporally separable (|τ_j–τ_s|>T_j≥T_c). Overlap of jamming slices with the true echo slice erodes performance.
• Doppler shifts bias WD-AMF’s local coherence estimates unless compensated; extension to Doppler–robust processing is a research direction.
• WDCSS main lobe and PSLR robustness persist up to duty cycles ε ≈ 0.9; for higher duty cycles or overlapping slice scenarios, complementarity alone is insufficient.
• WDCSS matched filter is Doppler-sensitive, potentially limiting detection of high-velocity targets unless chip waveform or sequence design accounts for this constraint.
• GLWD-based processing achieves real-time implementability due to fast transforms, but neural module inference complexity and hardware implementation requirements (e.g., for real-time threshold updates in WD-AMF) must be addressed.
• Deep learning with PSF priors requires accurate PSF estimation and sufficient labeled data spanning ISRJ parameter space for robust generalization.

6. Summary and Outlook

Interrupted-Sampling Repeater Jamming presents a substantial challenge to modern radar target detection and recognition through its energy-coherent, partially matched echo injection. Suppression approaches founded on waveform-domain modeling (adaptive matched filtering, complementary sets), phase-coded design, and advanced time–frequency representations significantly enhance resilience—removing or reducing the impact of spurious jamming peaks without explicit jammer parameter knowledge (Su et al., 2023, Su et al., 19 Jan 2024, Li et al., 21 May 2025). Deep learning approaches guided by PSF priors enable robust recognition of targets even under severe ISRJ distortion (Sun et al., 28 Nov 2025). Further advances are anticipated in simultaneous Doppler–robust complementarity, joint waveform–algorithm co-design, and fully model-agnostic ECCM strategies.