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\title{Multi-Resolution Spectrograms Detection of LPI RADAR with Time-Frequency Attention augmented YOLO}

\name{Reihan Mazouz$^{1,3}$, José Picheral$^{1}$, Abigael Taylor$^{2}$, Jonathan Bosse$^{2}$, Sylvie Marcos$^{1}$, Chakib Belafdil$^{3}$}


\address{%
{\small
$^{1}$L2S, CentraleSupélec, Université Paris-Saclay, France \quad
\small
$^{2}$DEMR, ONERA, Université Paris-Saclay, 91120 Palaiseau, France \\
\small 
$^{3}$ATOS ORIGIN, 80 Quai Voltaire, 95870 Bezons, France
% \small
% \texttt{\{reihan.mazouz, jose.picheral, sylvie.marcos\}@l2s.centralesupelec.fr}\\
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% \texttt{\{abigael.taylor, jonathan.bosse\}@onera.fr, chakib.belafdil@atos.net}
}
}



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%  {A. Reihan Mazouz, B. José Picheral \sthanks{Thanks to XYZ agency for funding.}}
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\begin{abstract}
Detecting Low Probability of Intercept (LPI) radar signals in congested spectral environments remains a difficult challenge, as fixed-resolution spectrograms cannot simultaneously capture fine temporal and spectral details. We present \emph{TF-Attn-YOLO}, a YOLO-based detector augmented with time–frequency attention blocks (\emph{TF-Attn}) that emphasize informative spectro-temporal patterns while reducing complexity. To overcome the resolution trade-off, we leverage multi-resolution spectrograms processed jointly within the detector. Experiments on a large simulated LPI dataset show consistent gains in detection probability at low SNR, improved time–frequency localization, and more reliable waveform discrimination compared to single-resolution baselines\footnote{Code is available at 
\url{https://github.com/rmL2S/TF-Attn-YOLO-ICASSP}}.

\end{abstract}



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\begin{keywords}
YOLO, Time Frequency Attention, Low Probability of Interception, Radar, Multi-Resolution Spectrograms
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\section{Introduction}
\label{sec:intro}

In modern electronic warfare, passive radar interception is critical for threat identification and countermeasure deployment. Interceptors operate without prior knowledge of waveforms and must separate radar energy from noise and interference in a fully blind setting. The challenge is acute with \emph{Low Probability of Intercept} (LPI) radars, which deliberately reduce detectability via low-power emissions, spread-spectrum modulation, frequency agility, and adaptive waveforms \cite{pace2009detecting}. 
% While a matched filter at the radar receiver can coherently recover energy, these same design choices hinder interception by an external listener.


Time–frequency (TF) analysis provides a natural framework for radar signal interception, with short-time Fourier transform (STFT) being widely used in Radio Frequency (RF) processing for their intuitiveness and computational efficiency. Yet, the Heisenberg uncertainty principle enforces a trade-off between temporal and frequency resolution: short windows improve timing accuracy but blur frequency content, while long windows have the opposite effect. This limitation is particularly critical for LPI radars, whose waveforms exhibit high variability in duration, bandwidth, and modulation type \cite{stove2004low}. Hence, single-resolution spectrogram can not reliably capture all the relevant structures, making multi-resolution more suitable for robust detection.

Conventional LPI detection approaches include energy detectors (e.g., GLRT), geometric analysis (Hough/Radon), cyclostationary methods, and track-before-detect families such as HMMs or particle filtering \cite{pace2009detecting}. Effective under controlled assumptions, they often degrade in cluttered, interference-prone, low-SNR regimes.

Recent studies report that deep learning methods are more robust in less controlled environments \cite{deshmukh2020comparison, reihan2024low}. By learning directly from time–frequency images, they offer a powerful alternative to hand-crafted features. Among existing architectures, YOLO \cite{redmon2016you, terven2023comprehensive} has proven particularly effective for object detection and has recently shown promise in radar spectrogram analysis \cite{zhu2024yolo, sarkar2024radyololet}, including LPI interception \cite{ma2024low}. Beyond detection, YOLO’s bounding boxes inherently provide waveform characterization (time of arrival, duration, bandwidth, and carrier frequency) while its class scores enable modulation recognition. This unified detection–characterization–classification capability makes YOLO especially well suited for passive LPI radar interception.

Motivated by the challenge of exploiting information across multi-resolution spectrograms, we propose \emph{TF-Attn-YOLO}, a lightweight detector for passive LPI interception, with three main contributions:  
(1) a detection model that integrates novel \emph{time–frequency attention} (TF-Attn) module to boost detection and classification while keeping complexity low;  
(2) multi-resolution strategies that mitigate the inherent trade-off between temporal and spectral resolution;  
(3) a comprehensive evaluation on a large-scale LPI dataset spanning diverse waveforms, bandwidths, durations, interference, and SNRs.

\section{Related Work}
\label{sec:related}

Recent advances in deep learning have driven progress in RF signal detection, especially where traditional fixed-resolution methods fall short. One line of research bypasses spectrograms by learning directly from raw I/Q (in-phase and quadrature) samples. STFNet~\cite{yao2019stfnets} introduces learnable STFT kernels to extract frequency-selective features, while other works apply multi-scale convolutions on I/Q streams using dilated filters or progressively larger kernels to capture multiple resolutions~\cite{cui2024multi,8683630}. Hybrid designs such as IQFormer~\cite{10729886} combine time-domain and spectro-temporal information through parallel raw I/Q and STFT branches. However, these architectures are mainly evaluated on frame-level classification tasks, and do not perform dense time–frequency localization of individual signals.

Beyond raw I/Q modeling, spectrogram-based methods pursue multi-resolution representations that better express features appearing at different temporal and spectral scales. Models such as SLNet \cite{SLNet2023} and the CNN–RNN architecture of \cite{8979431} aggregate information across resolutions and improve robustness. Yet, these methods also remain focused on classification of entire acquisitions rather than explicit detection of multiple signals within dense spectra (i.e., heavily populated time–frequency scenes with overlapping emissions and interferences). In contrast, one-stage object detection models such as YOLO are designed for TF localization in such complex settings, but to the best of our knowledge they have not yet been applied to multi-resolution spectrograms.



In parallel, time–frequency attention mechanisms have been explored in speech enhancement~\cite{zhang2022time}, modulation recognition~\cite{lin2022learning}, and fault diagnosis~\cite{ding2022novel}. While effective, these modules often introduce substantial computational overhead. \cite{cai2024tf} addressed this limitation with TF-SepConvs, a lightweight design. Inspired by this, we propose \emph{TF-Attn}, and to our knowledge \emph{TF-Attn-YOLO} is the first integration of a time–frequency attention block into an object detection framework. Notably, the most recent YOLOv12~\cite{tian2025yolov12} also introduces an attention-centric design in the spatial domain, highlighting the growing relevance of attention mechanisms in modern detectors.

\section{Methodology}

\noindent\textbf{Signal model and spectrogram representation -}
We address the passive detection and classification of heterogeneous RF signals in congested spectral environments. 
The received baseband signal is modeled as 
\(
x(t)=\sum_{i=1}^N s_i(t)+\eta(t),
\)
where each \(s_i(t)\) denotes an unknown waveform (e.g., radar pulse, communication burst, or LPI emission), and \(\eta(t)\) is additive white Gaussian noise modeling the receiver’s thermal noise.  

A common representation is the STFT. We denote by \(S^{(r)}\!\in\!\mathbb{R}^{H_r\times W_r}\) the noise-normalized spectrogram at resolution \(r\), where \(H_r\) is the number of \emph{frequency} bins and \(W_r\) the number of \emph{time} frames. It is computed as
\[
S^{(r)}[m,k] = \frac{1}{\sigma_\eta^2}
\left| \sum_{n=0}^{L_r-1} x[n+m\,h_r]\; w_r[n]\; e^{-j 2\pi k n / L_r} \right|^2,
\]
with analysis window \(w_r[n]\) of length \(L_r\) and hop size \(h_r\). 
Here \(k\in\{0,\dots,H_r-1\}\) indexes frequency bins and \(m\in\{0,\dots,W_r-1\}\) indexes time frames, 
and \(\sigma_\eta^2\) denotes the variance of the additive noise.

Since the detection will be performed directly on spectrograms, the next step is to design an architecture that can exploit their time--frequency structure.

\medskip
\noindent\textbf{TF-Attn block -}
The TF-Attn module, illustrated in the block of Fig.~\ref{fig:full_architecture}, enhances spectro-temporal representation between convolutional downsampling operations. It applies depthwise convolutions along each axis, reduces channels via $1{\times}1$ point-wise projections, and aggregates axis-specific context through global pooling and broadcast interactions \cite{kim2021broadcasted}. A residual shortcut stabilizes deeper stacks. The corresponding equations are:
\setlength{\jot}{2pt}
\[
\begin{array}{ll}
\mathbf{U}_F        = \mathrm{DW}_{k_f\times 1}(\mathbf{F}), \quad &
\mathbf{U}_T        = \mathrm{DW}_{1\times k_t}(\mathbf{F}) \\[2pt]
\mathbf{V}_F        = \mathrm{PW}_{C\to C/2}(\mathbf{U}_F), \quad &
\mathbf{V}_T        = \mathrm{PW}_{C\to C/2}(\mathbf{U}_T) \\[2pt]
\mathbf{C}_F        = \mathrm{PW}(\mathrm{GAP}_F(\mathbf{V}_F)), \quad &
\mathbf{C}_T        = \mathrm{PW}(\mathrm{GAP}_T(\mathbf{V}_T)) \\[2pt]
\tilde{\mathbf{V}}_F= \mathbf{V}_F \oplus \mathbf{C}_F, \quad &
\tilde{\mathbf{V}}_T= \mathbf{V}_T \oplus \mathbf{C}_T \\[2pt]
\mathbf{H}          = \mathrm{Concat}(\tilde{\mathbf{V}}_F,\tilde{\mathbf{V}}_T), \quad &
\mathbf{F}_{\text{out}} = \mathbf{H} + \mathbf{F}
\end{array}
\]
where $\mathbf{F}\in\mathbb{R}^{B\times C\times F\times T}$ is the input (batch, channels, frequency, time),  
PW = pointwise convolution, DW = depthwise convolution,  
$\mathrm{GAP}_F/\mathrm{GAP}_T$ = global average pooling along the subscripted axis,  
$\mathrm{Concat}$ denotes channel-wise concatenation, and  
$\oplus$ denotes element-wise addition with broadcasting along singleton dimensions \cite{kim2021broadcasted}. All convolutional operators (DW and PW) are implemented as Conv-BatchNorm-SiLU, for brevity, BatchNorm and SiLU are omitted from the equations.

TF-Attn can be seamlessly integrated into the YOLO architecture.


\medskip
\noindent\textbf{Overall architecture -}
As illustrated in Fig.~\ref{fig:full_architecture}, TF-Attn-YOLO follows the standard YOLOv11 pipeline: features from the backbone are propagated through the neck (feature pyramid) and into the standard detection head. The main departure lies in replacing conventional C3k2 modules by TF-Attn blocks, strategically inserted before each downsampling stage. 
This placement allows the network to highlight informative time–frequency patterns before downsampling, thereby retaining discriminative structures while preserving the efficiency of the YOLO pipeline.


\begin{figure}[t]
    \centering
    \includegraphics[width=0.8\linewidth]{figures/icassp_architecture.png}
    \caption{TF-Attn-YOLO overall architecture.}
    \label{fig:full_architecture}
\end{figure}

\medskip
\noindent\textbf{Multi-resolution strategies -}
Given that LPI radar emissions exhibit diverse durations, bandwidths, and modulations, relying on a single spectrogram resolution is inadequate. We therefore introduce $R$ multi-resolution spectrograms $\{S^{(r)}\}$ and investigate two alternative strategies (Fig.~\ref{fig:comparison}).
 

\textbf{First}, a \emph{Joint Multi-Resolution} strategy with a unique YOLO model (Joint-MR). All spectrograms are upsampled by nearest-neighbor interpolation to a common size 
$(H =\max_r H_r,\, W=\max_r W_r)$ 
and concatenated along the channel dimension. The resulting multi-channel tensor is then processed by a single TF-Attn-YOLO, with redundant predictions removed by non-maximum suppression (NMS), a standard post-processing step that keeps only the most confident box in overlapping regions.  

\textbf{Second}, a \emph{Decoupled Multi-Resolution} strategy with parallel YOLO models (Decoupled-MR). Each resolution is processed independently by its own TF-Attn-YOLO model trained only at this resolution. The predictions from all resolutions are then concatenated and merged via the same NMS procedure.  


\begin{figure}[t]
    \centering
    \includegraphics[width=\linewidth]{figures/icassp_block_diagram.png}
    \caption{Comparison of the multi-resolution strategies. Here only 3 resolutions for simplification.}
    \label{fig:comparison}
\end{figure}


\section{Experiments}

\noindent\textbf{Dataset \footnote{Due to the sensitive nature of LPI radar, the dataset is not publicly released, a simplified simulator is provided on our GitHub.} and setup -}  
We evaluate our model on a large-scale synthetic dataset of 100k RF scenarios simulating congested electromagnetic environments with up to 7 radar emitters and 3 telecom emitters per scene. The received signal spans \(T=32.768\,\mu s\) at \(F_s=4\) GHz (bandwidth \(B=2\) GHz). Each scenario is transformed into $R=5$ spectrograms using STFT windows of \(\{128,256,512,1024,2048\}\) samples\footnote{The STFT is computed with a square window and no overlap. This is an arbitrary choice, and alternative configurations (e.g., Hann windows, overlapping frames) could equally have been adopted.}, providing complementary resolutions while preserving the same total number of time–frequency bins ($256\times256$).  

Although the focus of this work is on the detection of LPI radar emissions, the simulator also includes conventional radars and telecom signals, which act as sources of interference. Signal types comprise radar pulses (unmodulated, LFM/NLFM, polyphase, polytime, FSK) and communication bursts (BPSK), with SNRs sampled in \([-15,20]\) dB. 

Training follows settings with Adam, a cosine learning rate schedule (\(10^{-3}\)), mixed precision, batch size 64, and up to 200 epochs with early stopping. An NVIDIA H100 NVL GPU (96GB) was used for train and evaluation.  

\medskip
\noindent\textbf{Results -}  
We evaluate detection probability ($P_d$) at fixed false-alarm rate, counting a prediction correct if $\mathrm{IoU}\ge 0.5$, where the Intersection over Union (IoU) measures the overlap between predictions and ground-truth. Class-confidence thresholds are tuned per model to meet\footnote{In the LPI context, a higher $P_{fa}$ is justified to avoid misses.} $P_{fa}=1\%$. Notice that all methods (single/multi-resolution) use TF-Attn-YOLO models with adjusted first layer to match input size and equivalent capacity ($\approx$8.5M parameters), so that performance differences reflect the strategy itself rather than model size.


As shown in Fig.~\ref{fig:recall_snr}, multi-resolution strategies clearly outperform single-resolution baselines across SNR. Among them, the Joint-MR strategy yields the strongest improvements, with pronounced gains at low SNR, precisely where LPI signals operate. At high SNR, however, detection probability does not fully reachs $100\%$. This is partly due to the extreme density of our simulated scenes.

% Sensitivity to very short pulses is also limited, since with an input of $(1024{\times}1024{\times}5)$ and detection heads starting at $P_4$, the effective stride constrains responsiveness to tiny time–frequency footprints. Extending detection to lower pyramid levels (e.g., $P_3$) would likely improve small-pulse recall, but we did not adopt this due to the significant computational overhead and our focus beyond ultra-short classical radar pulses.

TF localization quality follows the same trend. Using the survival curve $S(\tau)=\tfrac{P_d(\mathrm{IoU}\ge \tau)}{P_d(\mathrm{IoU}\ge 0.5)}$, the Joint-MR strategy retains 41\% of matches at $\mathrm{IoU}=0.95$ versus 35\% for the Decoupled-MR strategy, yielding sharper estimates of bandwidth, duration, and carrier frequency (Fig.~\ref{fig:example_spectrum}). For classification (Fig.~\ref{fig:confusion}), average per-class accuracy improves by $+6.6\%$ with Joint-MR over Decoupled-MR, with the largest gains on polyphase-coded signals ($+67\%$ for Frank, $+24\%$ for P3).

Regarding efficiency, the Joint-MR strategy is more compute-intensive than a single-resolution model because inference starts from the largest canvas $(H,W)$; to keep parameter count matched ($\approx$8.5M), channel widths are reduced. In contrast, the Decoupled-MR strategy is $5\times$ heavier computationally (one model per resolution) and requires costlier post-processing to merge $5\times$ more candidate boxes.

Overall, Joint-MR consistently delivers the best results. An intuitive explanation is that processing all resolutions jointly within a single detector allows the model to exploit complementary cues: fine time details from high-resolution spectrograms and fine frequency details from low-resolution ones. The network learns to balance temporal and spectral information directly during feature extraction, leading to superior detection, sharper localization, and more reliable classification compared to treating resolutions independently.




\begin{figure}[t]
    \centering
    \includegraphics[width=0.85\linewidth]{figures/pd_snr_icassp.png}
    \caption{\(P_d\) vs.\ SNR at \(P_{fa}=1\%\).}
    \label{fig:recall_snr}
\end{figure}

\begin{figure}[t]
    \centering
    \includegraphics[width=0.8\linewidth]{figures/icassp_spectrum_example3.png}
    \caption{Example detection on a $128\times512$ spectrogram. Ground truth (green), predictions (red), labels indicate classes.}
    \label{fig:example_spectrum}
\end{figure}

\begin{figure}[t]
    \centering
    \includegraphics[width=\linewidth]{figures/icassp_confusion_matrix.png}
    \caption{Row-normalized confusion matrix for both multi-resolution methods.}
    \label{fig:confusion}
\end{figure}


\section{Ablation Study}

To assess the efficiency of our proposed TF-Attn-YOLO design, we compare it against state-of-the-art YOLO baselines on the small (\emph{s}) variants, reported in Table~\ref{tab:single_res_s_only}. Despite having fewer parameters and lower FLOPs than any YOLO counterparts, TF-Attn-YOLOs achieves the best accuracy, with $0.28$/$0.18$ mAP50/50-95. Here, \emph{mAP50} denotes the mean Average Precision (mAP) computed at an IoU threshold of 0.5, while \emph{mAP50-95} averages the mAP over multiple IoU thresholds ranging from 0.5 to 0.95 in steps of 0.05. This metric jointly evaluates detection, localization, and classification performance, and is widely used in computer vision benchmarks.  
It is worth noting that the absolute mAP values in Table~\ref{tab:single_res_s_only} appear relatively low. This is explained by the fact that performance is reported after averaging over all SNR conditions, including extremely low SNR levels.

\begin{table}[!ht]
\centering
\caption{Small (s) variants of state of the art YOLO and TF-Attn-YOLO on a $256{\times}256$ spectrogram. Times are mean forward latency on 100 iterations without NMS. Inference latency measured on an NVIDIA H100 and CPU.}
\label{tab:single_res_s_only}
\small
\resizebox{\linewidth}{!}{%
\begin{tabular}{lrrrrrr}
\hline
Label & Params (M) & FLOPs (G) & H100 [ms] & CPU [ms] & mAP50 & mAP50--95 \\
\hline
YOLOv8s       & 11.14 & 9.18 & 0.53  & 12.81 & 0.24 & 0.14 \\
YOLOv9s       & \textbf{7.29} & 8.77 & 0.80 & 13.88 & 0.26 & 0.17 \\
YOLOv10s      & 8.08  & 7.95 & 0.61 & 10.47 & 0.24 & 0.15 \\
YOLOv11s      & 9.43  & 6.91 & 0.57  & 11.87 & 0.24 & 0.15 \\
YOLOv12s      & 9.26  & 6.90 & 0.72 & 12.32 & 0.23 & 0.14 \\
TF-Attn-YOLOs & 7.55  & \textbf{5.59} & \textbf{0.49} & \textbf{9.23} & \textbf{0.28} & \textbf{0.18} \\
\hline
\end{tabular}%
}
\end{table}

To further analyze the design of our proposed attention mechanism, we evaluate different TF-Attn block variants under comparable capacity, as shown in Table~\ref{tab:tfsep_ablation}.
% The baseline TFSepConv~\cite{cai2024tf} block already improves over plain convolutions. Introducing the TFA block of Lin~\cite{lin2022learning} increases localization accuracy (mAP50-95 = 0.484), but with higher complexity. 
Our TF-Attn design achieves the best trade-off between precision and computation and obtain the best mAP50 and mAP50-95.  
In this ablation, multi-resolution spectrograms are used as input which explain the higher mAP. 

\begin{table}[!ht]
\centering
\caption{Effect of TF-Attn-block designs with multi-resolution input ($1024{\times}1024{\times}5$).}
\label{tab:tfsep_ablation}
\small
\resizebox{\linewidth}{!}{%
\begin{tabular}{lrrrr}
\hline
Model & Params (M) & FLOPs (G) & mAP50 & mAP50:95 \\
\hline
TFA~\cite{zhang2022time}   & 7.70 & 14.88 & 0.43 & 0.36 \\
TFA~\cite{lin2022learning} & 8.61 & 17.66 & 0.57 & \textbf{0.48} \\
TFSepConv~\cite{cai2024tf} & 8.44 & 16.66 & 0.54 & 0.43 \\
TF-Attn (ours)             & 8.45 & 16.78 & \textbf{0.58} & \textbf{0.48} \\
\hline
\end{tabular}%
}
\end{table}



% \section{Discussion}

% Two limitations are noteworthy. (i) Sensitivity to very small/short pulses is reduced. With an input of $(1024,1024,5)$ and detection heads starting at $P_4$, the effective stride limits responsiveness to tiny TF footprints. Extending detection to lower pyramid levels (e.g., $P_3$) would improve small-object recall, but we did not adopt this given our focus beyond ultra-short classical radar pulses and the substantial compute cost. (ii) At high SNR, detection probability does not saturate at $100\%$. This stems from the extreme density of our simulated scenes, heavy overlap and crowding induce assignment conflicts and occasional NMS suppression, leaving a small tail of misses even in favorable conditions.


\section{Conclusion}
\label{sec:conclusion}

By combining spectrograms from multiple STFT resolutions and integrating TF-Attn blocks into a YOLO-based model, the proposed approach achieves consistent detection improvements across all SNR regimes while reducing computational cost. It also provides more precise time–frequency localization, enabling accurate signal characterization (bandwidth, duration, carrier frequency, and time of arrival), while enhancing waveform classification. Overall, these results underline the effectiveness of multi-resolution processing and time–frequency attention for LPI signal detection.



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