SidraBhatti/vit-vvit-radar-modulation-recognition

Transformer-Based Models for Intrapulse Modulation Recognition of Radar Waveforms

Three transformer/CNN-based Automatic Modulation Recognition System (AMRS) architectures — ViT, Vicinity Vision Transformer (VViT), and a DCNN baseline — for recognizing phase-coded low-probability-of-intercept (LPI) radar waveforms from their STFT phase spectrum, evaluated down to extremely low SNR (−16 dB).

Role & Attribution

Sidra Ghayour Bhatti — first & corresponding author. Per the paper's CRediT statement: Writing – original draft, Visualization, Validation, Software, Methodology, Funding acquisition, Formal analysis, Conceptualization. Co-authored with Imtiaz Ahmad Taj and Aamer Iqbal Bhatti (Writing – review & editing, Validation, Supervision, Conceptualization/Methodology/Investigation) and Mohsin Ullah (Validation, Software, Methodology).

Fig. 1: Signal interception → STFT-based phase-spectrum feature extraction → cropping → training/testing → classification into six phase-coded waveform families (Barker, Frank, P1, P2, P3, P4).

Method

Why phase spectrum, not magnitude. Phase-coded waveforms are defined by their intrapulse phase-modulation pattern; the paper deliberately extracts the phase spectrum from the STFT of the intercepted signal (rather than the more common magnitude spectrum), since phase offset carries the discriminative information about which phase-coding scheme was used — magnitude-based approaches lose this.

Feature extraction pipeline. For each intercepted phase-coded signal: compute FFT to estimate carrier frequency f_c and its reciprocal T_c → derive an appropriately narrow STFT window size from T_c and sampling frequency F_s → slide the window across the signal, computing phase at each step → assemble a phase matrix → transform into an image and crop to the row corresponding to f_c (removing AWGN-dominated rows) → feed the cropped phase-spectrum image to the AMRS classifier.

Fig. 2: Full pipeline from data generation and AWGN injection (−16 dB to +8 dB) through the STFT phase-extraction loop to classification.

Three AMRS architectures compared, all trained on the same phase-spectrum images:

• ViT — standard Vision Transformer (Dosovitskiy et al., 2020): splits the phase-spectrum image into fixed-size patches, linearly embeds them with learnable position embeddings, and processes them with a standard transformer encoder (multi-head self-attention + MLP blocks).
• VViT (Vicinity Vision Transformer) — replaces standard softmax self-attention with Vicinity Attention, a linear-complexity mechanism that re-weights attention using a 2D Manhattan-distance-based locality bias between patches (feature reduction attention + feature preserving connection), built in a 4-stage pyramid structure — designed to scale linearly with sequence length instead of quadratically.
• DCNN — a deep convolutional baseline (32/64/96 filters across three conv layers, max-pooling, two fully-connected layers with dropout).

Six phase-coded waveform types are used: Barker (M=4,7,11,13), Frank (L=3,4,6), P1 (L=2,4), P2 (L=4,6), P3 (Nc=4,12,16), P4 (Nc=4,12,15) — 674 images per type across SNR from −16 dB to +8 dB (2 dB steps), 1326 test images total.

Results

Recognition accuracy (%) vs. SNR, per modulation type and architecture:

Modulation	Arch.	−16 dB	−12 dB	−8 dB	−4 dB	0 dB	4 dB	8 dB
Barker	ViT	91.6	97.5	100	100	100	100	100
Barker	DCNN	88	93	97	100	100	100	100
Barker	VViT	96	92	100	100	100	100	100
Frank	ViT	100	100	100	100	100	100	100
Frank	DCNN	99	100	100	100	100	100	100
Frank	VViT	100	100	100	100	100	100	100
P1	ViT	87.5	98.3	100	100	100	100	100
P1	DCNN	57	77	100	100	100	100	100
P1	VViT	75	100	100	100	100	100	100
P2	ViT	100	100	100	100	100	100	100
P2	DCNN	100	100	100	100	100	100	100
P2	VViT	83	100	100	100	100	100	100
P3	ViT	97.7	99	100	100	100	100	100
P3	DCNN	97	99	100	100	100	100	100
P3	VViT	100	100	100	100	100	100	100
P4	ViT	79.4	87.7	98.3	100	100	100	100
P4	DCNN	93	99	100	100	100	100	100
P4	VViT	94	100	100	100	100	100	100
Overall	ViT	92.7	97	99.7	100	100	100	100
Overall	DCNN	89	94.6	99	100	100	100	100
Overall	VViT	93	98	100	100	100	100	100

VViT achieves the highest overall accuracy (93%) at the most challenging SNR (−16 dB), followed by ViT (92.7%), both outperforming the DCNN baseline (89%). All three converge to 100% by −8 dB to 0 dB depending on waveform type.

Fig. 8: The proposed ViT and VViT architectures maintain higher accuracy than four state-of-the-art comparison methods (Wang et al. 2023b, Kim et al. 2023, Guo et al. 2022, Ma et al. 2022) particularly in the −12 dB to −6 dB range, where competing methods drop sharply while ViT/VViT/DCNN remain above ~88%.

Statistical validation: a Friedman test (χ²) followed by Nemenyi post-hoc pairwise comparisons confirmed the ranking differences among models are statistically significant (p = 1.73e⁻⁸), with critical difference (CD) = 2.49 used to determine which pairwise differences are significant.

Limitations (as stated in the paper)

The study assumes all threat emitter signals operate at the same carrier frequency (50 MHz) and focuses on single-component (not multi-component) intrapulse modulation recognition — both flagged as directions for future work.

Published: Bhatti, S.G., Taj, I.A., Ullah, M., & Bhatti, A.I. (2024). "Transformer-based models for intrapulse modulation recognition of radar waveforms." Engineering Applications of Artificial Intelligence, 136, 108989. doi.org/10.1016/j.engappai.2024.108989 (subscription required — not open access, so no PDF is included here; link only)

Citation

@article{bhatti2024transformer,
  author  = {Bhatti, Sidra Ghayour and Taj, Imtiaz Ahmad and Ullah, Mohsin and Bhatti, Aamer Iqbal},
  title   = {Transformer-based models for intrapulse modulation recognition of radar waveforms},
  journal = {Engineering Applications of Artificial Intelligence},
  volume  = {136},
  pages   = {108989},
  year    = {2024},
  doi     = {10.1016/j.engappai.2024.108989}
}