A Unified Framework for Radar Signal Sorting and Recognition

Abstract

Radar signal sorting (RSS) and radar emitter recognition (RER) constitute foundational yet challenging operations in electronic reconnaissance, where RSS aims to accurately segregate interleaved radar pulse streams and RER aims to recognize their originating emitters. Existing methods typically address RSS and RER as separate processes within a sequential streaming framework, which neglect the inherent interdependence and collaborative potential between them, thereby resulting in error accumulation and performance bottleneck. In this paper, we redefine the radar signal sorting and recognition (RSSR) problem from an integrated modeling perspective, decomposing it into three sub-problems, i.e., signal pattern detection, signal pattern extraction, and detection result integration. In order to effectively solve these problems, we propose a novel Unified Framework inspired by Object Detection (UFiOD). Firstly, an end-to-end neural network is constructed to simultaneously optimize the regression of signal temporal occurrence regions and the recognition of signal categories. Then, a template matching algorithm is designed to extract corresponding pulses from the regions based on the signal categories. Finally, an integration algorithm based on temporal correlation and direction of arrival (DOA) fuses the detection results to generate object-level sorting and recognition conclusions. We extensively validate the effectiveness of the proposed method on simulation datasets. It demonstrates robust performance under various interleaving scenarios, including the interleaving of homogeneous radar emitters. Notably, it exhibits impressive capability for handling unknown signals, further highlighting its practical utility.

1. Introduction

Radar signal sorting (RSS) and radar emitter recognition (RER) [1,2,3] are critical steps in electronic reconnaissance. RSS aims to separate the pulses of individual radar emitters from intercepted radar signals, while RER aims to recognise the emitters based on the parameters and tracks of deinterleaved radar signals [4,5]. The effectiveness of RSS and RER significantly influences the performance of subsequent tasks, e.g., threat assessment, jamming decision-making, etc. [6].

Existing RSS methods primarily fall into three categories: pulse repetition interval (PRI)-based [7,8,9,10,11,12], clustering-based [13,14,15,16,17,18,19], and deep learning-based [20,21,22,23,24,25,26,27,28,29,30,31,32,33,34]. Early RSS methods are primarily based on PRI estimation, e.g., cumulative difference histogram [7], sequence difference histogram [8,9], and PRI transform [10], which struggle to maintain effectiveness when PRI exhibits wide variation ranges or complex modulation types. Later, in order to improve radar signal sorting performance through the effective utilization of multi-dimensional pulse parameters, clustering methods based on pulse description words (PDWs) emerge. However, these methods rely heavily on prior information and tend to perform poorly when dealing with multifunction radars or complex radar feature sets. RER methods are mainly divided into library matching-based [35,36], machine learning-based [37,38,39], and deep learning-based [40,41,42,43,44,45]. Early RER methods mainly rely on library matching, which lack flexibility and fail in dealing with unknown emitters. Machine learning-based methods attempt to capture intra-pulse characteristics, but they are constrained by limited feature representation capability.

Recent advances in deep learning have driven the widespread application of neural networks for RSS and RER. Refs. [33,34] first convert radar signals into images via some transformation operations, and then adopt image detection models to locate waveform patterns for indirect radar signal sorting. Refs. [21,22,23,31] employ semantic segmentation techniques to classify individual pulses in converted images, and subsequently aggregates pulses belonging to the same category as the deinterleaving result of corresponding emitter. Refs. [24,25] construct graph-based representations for intercepted radar pulses and employ graph neural networks (GNNs) for deinterleaving. Ref. [40] employs convolutional neural networks (CNNs) to extract the feature of image converted from PDWs parameters for recognition. Ref. [43] utilizes recurrent neural networks (RNNs) to capture the characteristics of each PDWs parameters in pulse streams, and employs the attention mechanism to achieve information fusion. Although these deep learning-based methods show promise in independently tackling RSS and RER, there is still a critical gap in developing joint optimization frameworks that integrate both RSS and RER simultaneously to avoid error accumulation and performance bottleneck.

In this paper, we present a new definition for radar signal sorting and recognition (RSSR): tightly couple the radar signal sorting and recognition processes to leverage their mutual validation and feedback to achieve better results, and simultaneously generate the sorting and recognition conclusions. In order to complete RSSR effectively, we propose a novel modeling paradigm, as shown in Figure 1. Specifically, we define the signal tracks or mode lines of a radar emitter under a specific work mode during a single dwell as ‘signal pattern’, and decompose RSSR into three sub-problems: signal pattern detection, signal pattern extraction, and detection result integration. In order to address these problems, we propose a novel unified framework inspired by object detection (UFiOD). Different from [33,34], our framework borrows the idea of image detection but performs targeted modeling tailored to signal characteristics and task requirements, and then decomposes the RSSR problem and conducts unified optimization in the signal pattern detection stage. Firstly, a signal pattern detection model, which consists of a backbone, a multi-scale feature fusion neck, and a multi-task head, is constructed to predict the temporal occurrence regions and categories of signal patterns in an end-to-end manner. Subsequently, a template matching algorithm is employed to extract the signal patterns from the detected regions. Finally, the object-level radar signal sorting and recognition conclusions are obtained by integrating the detection results based on temporal correlation and DOA.

The contributions of this paper can be summarized as follows:

• We redefine RSSR and propose a novel modeling paradigm, which decomposes RSSR into three sub-problems, i.e., signal pattern detection, signal pattern extraction, and detection result integration.
• We propose a novel unified neural network for signal pattern detection, which outputs the temporal occurrence regions and categories of signal patterns in an end-to-end manner.
• We propose a template matching algorithm and temporal correlation and DOA-based integration algorithm to bridge the detection results to object-level sorting and recognition conclusions.
• The proposed method offers a novel solution pipeline for RSSR, which could open a new research direction.

The rest of this paper is organized as follows. Section 2 describes the related work, including radar signal sorting, radar emitter recognition and image object detection. Section 3 introduces the proposed method, including problem formulation and specific approach. Section 4 gives the experimental settings and results analysis of the proposed method. Finally, Section 5 concludes this paper.

2. Related Work

2.1. Radar Signal Sorting

The goal of radar signal sorting is to separate the interleaved pulse streams and obtain the signal trajectories of individual radar emitters. Existing radar signal sorting methods can generally be categorized into three types: PRI-based methods, clustering-based methods, and deep learning-based methods.

Early radar signal sorting methods are often based on PRI estimation. The cumulative difference histogram [7] employs a cumulative time of arrival (TOA) difference histogram to provide possible PRI estimations with minimal computational effort. The sequence difference histogram (SDIF) [8] determines the PRI using a sequence difference histogram. By deriving an optimal detection threshold for the SDIF histogram, the algorithm’s efficiency is significantly improved. However, SDIF is susceptible to jittered PRI, which could lead to missing batch. To address this issue, ref. [9] proposes an improved SDIF algorithm that uses overlapping PRI bins to detect signals with jittered PRI, and further introduces dynamic sequence searching to enhance the algorithm’s timeliness and effectiveness. Ref. [10] proposes an improved algorithm for the PRI estimation process, which employs overlapped PRI bins with shifting time origins to improve the robustness in handling jittered pulses. Ref. [11] proposes an enhanced PRI deinterleaving histogram method based on pulse correlation, which incorporates the mean filter and interquartile range algorithm to refine the estimated PRI values, making it more suitable for handling pulses with significant PRI fluctuations. Ref. [12] models the signal trajectory of each emitter as a renewal or counting process, which derives the theoretical performance lower bound, and proves that the proposed algorithm approaches this theoretical limit.

Due to the flexibility of modern radar systems and complexity of electromagnetic environments, the range of PRI variation has increased, and its variation patterns have become more complicated. As a result, methods based on PRI estimation are no longer sufficient. To improve deinterleaving performance by leveraging the multi-dimensional parameters of PDWs, clustering-based methods have been developed. Ref. [13] proposes a two-step clustering approach, where the first clustering is performed in the frequency-pulse width (F-PW) plane, followed by a second clustering based on the initial clustering results combined with optimal transport distance. Ref. [14] introduces an adaptive density peak clustering method, named subspace decomposition-based adaptive density peak clustering (SD-ADPC), which adaptively determines optimal cluster centers to address the issue that existing clustering methods heavily rely on prior knowledge. Ref. [15] first models interleaved radar pulses using the limited penetrable visibility graph, then combines the label propagation algorithm and density peak clustering to group signals from the same emitter, effectively mitigating the problem of increasing batch in multifunction radar signal sorting. MRTSC [16] considers whether the modulation type and parameters of candidate working modes are known, and designs three corresponding algorithms to achieve improved adaptability and reduce dependence on prior information. Ref. [17] employs Bézier curves to model frequency variations of intercepted pulses. These curve-based spatial distributions are used as the new features and processed via a density-based spatial clustering method to obtain the deinterleaving results. Ref. [18] proposes an improved clustering algorithm-based on the artificial bee colony (ABC). The algorithm accelerates the convergence by dynamically adjusting the search step and incorporating a ranking-based probabilistic selection mechanism. Ref. [19] presents a dynamic modified chaotic particle swarm optimization algorithm (DMCPSO), which enhances the diversity of particle swarm by introducing chaotic search, thereby avoiding premature convergence and falling into local optimum.

Clustering-based methods heavily rely on prior information and demonstrate limited effectiveness when radar features become more complex. Therefore, recent approaches introduce DNNs to model and solve the problem of radar signal sorting. Ref. [20] proposes a radar signal sorting method based on a denoising autoencoder, which learns the patterns and regularities of pulse sequences from the same emitter and generates clean, deinterleaved pulse sequences. Ref. [28] introduces RNNs to explore semantic patterns in radar signals, which predicts potentially arriving pulses based on existing ones and performs effective deinterleaving even under noisy conditions. Ref. [29] develops a prediction model-based on long short-term memory (LSTM) that utilizes predicted pulses for deinterleaving. Ref. [26] presents a multi-task deep learning model for radar signal sorting and PRI modulation recognition. Based on CNNs, the model exploits the interdependencies between these two tasks and improves the accuracy of both tasks simultaneously. Ref. [27] constructs a hierarchical deep learning model that captures temporal patterns and semantic correlations among pulses in multifunction radar signals. Based on this model, an iterative and parallel pulse deinterleaving method are introduced, achieving effective signal separation. Ref. [30] proposes a recursive deinterleaving network (RDN) of deep TOA mask (DTM), which captures both local and global contextual information of radar pulses and classifies them effectively. Some approaches [24,25] model interleaved pulse streams as graphs and apply graph-based solutions for deinterleaving. ResGCN-RSS [24] constructs a graph structure using the k-nearest neighbors (KNN) algorithm and builds a residual graph convolutional network for feature learning, achieving effective deinterleaving. Ref. [25] first applies self-organizing maps (SOM) to capture the spatial distribution of intercepted signals and constructs a graph based on SOM nodes, and then designs a three-layer weighted residual graph convolutional network (WRGCN) to predict deinterleaving results. Additionally, this method generates pseudo-labels using SOM, which pretrains the model on these pseudo-labels and finetunes using a limited number of true labels, significantly improving model generalization in few shot scenarios. Inspired by image segmentation and image object detection, several methods [21,22,23,31] adopt pulse level recognition to perform radar signal sorting. Ref. [21] develops a radar signal sorting method based on semantic segmentation, which takes TOA differences as input and classifies each pulse based on its semantic type. Ref. [22] converts PDWs features of intercepted signals into sequential images and applies a U-Net-based image segmentation model for radar signal sorting. Ref. [23] generates the 2D images based on PRI transform. These images visualize the variation patterns of PRI, and a segmentation model is performed on the images to obtain the signal sorting results. SOLOv2 [46] constructs the mimetic image mapping and visualizes the interleaved pulse sequence as mimetic point graph. An instance segmentation model is then employed to segment the mimetic point graph at pixel level, thereby achieving radar signal sorting. Ref. [34] proposes a deinterleaving method based on object detection, which uses pulse amplitude (PA) and TOA to synthesize the image that represents the amplitude patterns, and then leverages an object detection model to detect these patterns. However, all these methods first convert the radar pulse signals into images using some transformation approaches, and then perform radar signal sorting using image processing methods. As a result, they are inevitably prone to information leakage during the data conversion process and mismatching between cross-domain tasks. In contrast, the proposed method in this paper draws inspiration from image processing but is specifically designed based on the characteristics of radar pulse signals and the requirements of the processing tasks. It provides a unified solution to both radar signal sorting and radar emitter recognition without suffering from information leakage or task mismatch.

2.2. Radar Emitter Recognition

Radar emitter recognition aims to identify the type of radar emitter based on deinterleaved signal parameters or trajectories. Existing methods for radar emitter recognition can generally be categorized into three groups: library matching-based methods, machine learning-based methods, and deep learning-based methods.

Early radar emitter recognition methods are often implemented based on library matching [35,36], which is commonly referred to as the emitter library, threat library, radar library, or pre-flight data library. These methods are simple and intuitive, but lack adaptability and struggle to handle unknown signals. With the development of radar systems, radar signals have become increasingly complex, and the phenomenon of parameter overlapping has become more prominent. As a result, some methods attempt to introduce machine learning techniques to further explore signal features to assist in recognition. Ref. [37] utilizes image processing methods to extract shape features from the time-frequency distribution of radar signals, and performs radar emitter recognition based on these features. Ref. [38] employs the support vector machine (SVM) and KNN classifier for recognition. Ref. [39] extracts various new features from the choi-williams distribution (CWD) image and subsequently applies pattern recognition methods for recognition.

With the rapid development of deep learning, deep neural networks (DNNs) have demonstrated increasingly powerful capabilities in feature extraction. Some approaches introduce DNNs to extract high dimensional features from raw signals, further improving recognition performance. Ref. [40] converts PW, radio frequency (RF), and PRI into 3D images through data preprocessing, and then employs CNNs for recognition. Ref. [41] maps radar pulses into symbols at different levels, which can be regarded as a form of radar language, and then applies LSTM for recognition. Ref. [42] introduces an additional projection step on top of the standard DNNs or gated recurrent units (GRUs), significantly enhancing the recognition performance. Ref. [43] utilizes GRUs to capture waveform features across different dimensions of the pulse streams. An attention mechanism is then applied to fuse features and effectively reduce the impact of noise, thereby improving the robustness of recognition. Ref. [47] proposes a radar work mode recognition method based on dual-scale feature extraction. It adopts a hybrid architecture combining CNNs and LSTM to effectively explore the temporal characteristics of the signal for improved recognition performance. Ref. [48] presents a hybrid model that integrates CNNs and transformers. CNNs is employed to extract local features from radar pulse streams, while transformer captures long-term dependencies in the temporal domain, thereby enabling effective recognition of radar work modes.

2.3. Image Object Detection

Image object detection, as one of the fundamental tasks in computer vision, aims to identify and localize all visual objects in the images by predicting their categories and spatial positions. R-CNN [49] is a classical object detection method, where deep neural network is used to replace handcrafted feature extraction and significantly improves the representation of semantic features from region proposals. To avoid redundant feature computation caused by overlapping region proposals, subsequent methods such as SPP-Net [50], Fast R-CNN [51], and Faster R-CNN [52] are proposed, bringing substantial improvements in both speed and performance. Following this, a series of improvements based on Faster R-CNN are developed, including FPN [53] and Cascade R-CNN [54]. These methods typically define a set of anchor boxes, i.e., some rectangular frames at various scales, and then predict categories and location offsets of objects based on the image features within the anchor boxes.

However, some methods eliminate the setting of anchor boxes and directly predict categories and locations. For example, YOLO series methods [55,56,57,58] make direct predictions based on grid cells in the feature maps, significantly enhancing detection efficiency. SSD [59] improves detection performance across objects of different sizes by leveraging multi-scale feature pyramids.

3. Methodology

3.1. Problem Formulation

In this paper, we revisit RSS and RER, and give a new definition for RSSR: tightly couple the radar signal sorting and recognition processes to leverage their mutual validation and feedback to achieve better results, and simultaneously generate the sorting and recognition conclusions. Based on this definition, we propose a novel modeling paradigm for RSSR, and divide RSSR into three sub-problems:

• signal pattern detection: it aims to find out the temporal occurrence regions and categories of potential signal patterns from interleaved radar signals, i.e., the regression of signal temporal occurrence regions and recognition of signal patterns within the regions.
• signal pattern extraction: it focuses on extracting signal patterns from the detected temporal occurrence regions according to the corresponding categories, i.e., extracting pulses that belong to corresponding signal patterns.
• detection result integration: it is dedicated to associating and integrating the detected signal patterns, i.e., merging the signal patterns that originate from the same radar emitter.

where signal pattern is defined as the signal tracks or mode lines of a radar emitter under a specific work mode during a single dwell.

Specifically, given a set of radar signal pulses:

$$X={[x_1,\dots ,x_i,\dots ,x_N]}^T\in {\mathbb{R}}^{N\times d}$$

(1)

where $x_i\in {\mathbb{R}}^d$ represents the PDWs feature vector for the i-th pulse, and N, d are denoted as the number of radar pulses and PDWs feature dimension respectively.

According to above definition, assuming that the detection model $f_{\theta }(·)$ has been trained, signal pattern detection can be formulated as:

$$\{[T{S}_1,T{E}_1,CL{S}_1],\dots ,[T{S}_M,T{E}_M,CL{S}_M]\}=f_{\theta }\left(X\right)$$

(2)

where $\{[T{S}_1,T{E}_1,CL{S}_1],\dots ,[T{S}_M,T{E}_M,CL{S}_M]\}$ represents the detection results. For example, $[T{S}_m,T{E}_m,CL{S}_m]$ denotes the result of m-th signal pattern, where the start and end temporal points of its occurrence are $T{S}_m$ and $T{E}_m$, and the signal pattern category within this region is $CL{S}_m$.

Since the category of the signal pattern within the temporal region has been determined, it becomes straightforward to design an adapted template based on the specific parameters and characteristics of the signal pattern. Then, we use a signal pattern template matching algorithm to extract the pulses of corresponding signal patterns from the detected temporal regions.

The obtained signal pattern detection and extraction results are not yet sufficient to support the formation of complete sorting and recognition conclusions. Finally, we introduce a simple integration algorithm that considers temporal correlation and DOA to quickly merge the detected signal patterns, and generate the object-level radar signal sorting and recognition conclusions.

3.2. Signal Pattern Detection

In order to find out the temporal occurrence regions and categories of potential signal patterns in interleaved radar signals, we propose an end-to-end neural network as signal pattern detection model inspired by image object detection [55,56,57,58]. The proposed model architecture is shown in Figure 2. Specifically, it consists of a backbone, a multi-scale feature fusion neck, and a multi-task head, which are formed by stacking four base modules, i.e., ConvModule1D, CSPDarknetModule1D, SPPFModule1D, and Detection Head. We built these modules inspired by standard image object detection modules.

ConvModule1D is a basic convolution module, which is shown in Figure 3a. ConvModule1D is composed of a Conv1d, a BatchNorm1d, and a SiLU, and is also employed to compose the CSPDarknetModule1D, SPPFModule1D, and Detection Head. For CSPDarknetModule1D, since it forms the main body of the backbone and multi-scale feature fusion neck, we aim to make it as lightweight as possible to meet the real-time processing requirements in the field of radar signal processing. Based on this consideration, we only stack one bottleneck construction while retaining multi-level residual connections, ensuring efficiency while maintaining the accuracy of feature extraction and optimization stability, as shown in Figure 3b. As for SPPFModule1D, we mainly fuse the 1D features of different pooling scales to obtain the final high-dimensional features rich in semantics, as shown in Figure 3c.

The multi-task head consists of three detection heads, where each contains a regression branch and recognition branch, as shown in Figure 4. The regression branch is responsible for regressing temporal regions based on the multi-scale fused features, while the recognition branch predicts the category.

After feeding an interleaved signal normalized by min-max normalization into signal pattern detection model, it undergoes processing through backbone and multi-scale feature fusion neck, resulting in three features. Based on them, several anchor points are set as the centers of the predicted regions. Then, the features are fed into the multi-task head to regress the left and right distances for each anchor point and predict the categories of signal patterns within each region. Thus, the predicted temporal regions and categories can be determined. For the setup of anchor points, we treat the features as 1D number lines and set the anchor points with an interval of 0.5.

Additionally, positive and negative samples assignment and non-maximum suppression operations are required for the predictions to obtain the final detection results. Except for the IoU (Intersection over Union) calculation method, we follow the standard settings of object detection. Based on the 1D attribute of temporal regions, we design a unique IoU calculation method. For example, the IoU calculation for region $A=[T{S}_a,T{E}_a]$ and $B=[T{S}_b,T{E}_b]$ is defined as follows:

$$\mathrm{IoU}(A,B)={\displaystyle \frac{A\cap B}{A\cup B}}$$

(3)

where $A\cap B$ denotes the common intersection between region A and B, while $A\cup B$ represents the entire union of the two regions:

$$A\cap B=\max (\min (T{E}_a,T{E}_b)-\max (T{S}_a,T{S}_b),0)$$

(4)

$$A\cup B=\max (T{E}_a,T{E}_b)-\min (T{S}_a,T{S}_b)$$

(5)

In terms of the training loss, it consists of the recognition loss and regression loss. For an input signal X, assuming it contains M signal patterns, the recognition loss can be expressed as:

$${\mathcal{L}}_{cls}={\displaystyle \frac{1}{M}}{\displaystyle \sum _{i=1}^M}\mathrm{BCE}\left(PrCL{S}_i,TrCL{S}_i\right)$$

(6)

$$\begin{array}{cc}\hfill {\mathcal{L}}_{cls}=-{\displaystyle \frac{1}{M}}{\displaystyle \sum _{i=1}^M}& [TrCL{S}_i·\log \left(PrCL{S}_i\right)+\hfill \\ \hfill & (1-TrCL{S}_i)·\log (1-PrCL{S}_i)]\hfill \end{array}$$

(7)

where $\mathrm{BCE}(·,·)$ denotes the binary cross-entropy loss. $PrCL{S}_i$ and $TrCL{S}_i$ are the predicted probability and true label for i-th signal pattern respectively. The regression loss is composed of the IoU between the predicted and true regions:

$${\mathcal{L}}_{reg}={\displaystyle \frac{1}{M}}{\displaystyle \sum _{i=1}^M}\left(1-\mathrm{IoU}\left(PrRe{g}_i,TrRe{g}_i\right)\right)$$

(8)

where $PrRe{g}_i=[PrT{S}_i,PrT{E}_i]$ denotes the predicted region of i-th signal pattern and $TrRe{g}_i=[TrT{S}_i,TrT{E}_i]$ denotes the true region of i-th signal pattern.

Finally, the loss is composed of a weighted average of the recognition loss and regression loss:

$$\mathcal{L}={\mathcal{L}}_{cls}+\lambda \ast {\mathcal{L}}_{reg}$$

(9)

where $\lambda$ is a hyperparameter to control the intensity of the recognition loss and regression loss.

3.3. Signal Pattern Extraction

After obtaining the temporal regions and categories of signal patterns, the next step is to extract pulses of signal patterns to get measurement information, such as DOA, PRI, etc. Since the detection results already include the temporal regions and categories of signal patterns, we propose a signal pattern template matching algorithm to extract the corresponding pulses in an efficient manner.

Firstly, based on the categories of detected signal patterns in the temporal regions, the signal templates are designed according to the corresponding signal parameters and characteristics. Then, it matches each pulse in the temporal regions with the templates in order of TOA. If the match is successful, the pulse is extracted and locked with the corresponding template element, preventing it from participating in subsequent matches. If not, the pulse is discarded. This process is repeated cyclically until all pulses in the regions are matched or all template elements are locked. Finally, the extracted pulses serves as the output signal patterns. The algorithm can be expressed as:

$$Si{g}_m={[\dots ,x_j,\dots ]}^T=\varphi \left([T{S}_m,T{E}_m,CL{S}_m]\right)$$

(10)

where $\varphi \left(·\right)$ represents the signal patterns template matching algorithm, $Si{g}_m$ is the m-th signal pattern, and $x_j$ is the pulse belonging to the signal pattern.

3.4. Detection Result Integration

In this stage, we have obtained the processing results of intercepted signal patterns. What remains to form the complete radar signal sorting and recognition conclusions is to merge these signal patterns. In order to solve this problem, we design an integration algorithm that determines whether two signal patterns should be merged into the same object based on their temporal correlation and DOA.

Specifically, if two signal patterns which are predicted to be the same radar model have non-conflicting temporal correlation and similar DOA, they are merged into the same object. Otherwise, they are classified as two separate objects. By applying this rule to all detected signal patterns in a cyclic manner, the object-level radar signal sorting and recognition conclusions can be obtained. The algorithm can be expressed as:

$$\{\dots ,[Ob{j}_k\leftarrow Si{g}_m,CL{S}_m],\dots \}=\psi \left(\{\dots ,[Si{g}_m,CL{S}_m],\dots \}\right)$$

(11)

where $\psi \left(·\right)$ represents the integration algorithm, and $Ob{j}_k$ denotes the object to which the m-th signal pattern belongs. The overall workflow of the proposed method is illustrated in Algorithm 1.

Algorithm 1 The workflow of the proposed UFiOD

Input: a set of interleaved radar pulses $X={[x_1,\dots ,x_i,\dots ,x_N]}^T\in {\mathbb{R}}^{N\times d}$

Output: The object-level radar signal sorting and recognition conclusions $Ob{j}_1,\dots ,Ob{j}_k,\dots ,Ob{j}_K$

1: Use signal pattern detection model to predict the temporal occurrence regions and categories of potential signal patterns, i.e., $[T{S}_1,T{E}_1,CL{S}_1],\dots ,[T{S}_M,T{E}_M,CL{S}_M]$ 2: Use the template matching algorithm to extract the complete signal pattern, i.e., $[Si{g}_1,CL{S}_1],\dots ,[Si{g}_M,CL{S}_M]$ 3: Use the integration algorithm to find the radar emitter associated with each signal pattern, i.e., $\dots ,[Ob{j}_k\leftarrow Si{g}_m,CL{S}_m],\dots$ 4: return $Ob{j}_1,\dots ,Ob{j}_k,\dots ,Ob{j}_K$

4. Experiments and Results

4.1. Simulation Dataset

We construct our simulation dataset based on the settings shown in

Table 1. Simulation settings of radar signals.

Radar	Mode	RF (GHz)	PW ($\mathsf{\mu }$s)	PA (dB)	DOA (°)	PRI ($\mathsf{\mu }$s)	Pulse Num
A	1	3.2	5.9∼6.1	10∼15	36∼40	32∼52	500
		stable	jittered	wobulated + jittered	\	D&S	\
B	1	3.6∼5.5	3.7∼4.3	14∼16	34∼38	35∼41	500
		D&S	jittered	wobulated + jittered	\	D&S	\
	2	3.0	5.0	8∼10	34∼38	45	500
		stable	stable	wobulated + jittered	\	stable	\
	3	1.6∼2.4	6.8∼7.2	18∼21	34∼38	12	200
		stagger	jittered	jittered	\	stable	\
C	1	1.9∼3.5	5.0∼7.2	13∼15	35∼39	8	200
		D&S	D&S + jittered	wobulated + jittered	\	stable	\
D	1	2.8∼6.0	2.9∼4.3	10∼20	37∼41	34∼48	500
		sliding	D&S + jittered	wobulated + jittered	\	D&S	\
	2	5.0	7.8∼8.4	9∼13	37∼41	80	1000
		stable	jittered	wobulated + jittered	\	stable	\
E	1	1.2∼4.8	8.0	11∼13	33∼37	38	500
		D&S	stable	jittered	\	stable	\
	2	3.9∼6.0	6.0∼6.8	10∼12	33∼37	70∼85	1000
		D&S	jittered	jittered	\	D&S	\

, which contains five categories of radar emitters in total. Each radar emitter encompasses one to three work modes (i.e., one to three signal patterns). The PDWs features exhibit various modulation types, including stable, jittered, stagger, sliding, dwell and switch (D&S), etc. Within the simulation dataset, there is not only the interleaving between radar emitters and noise or different radar emitters, but also the interleaving between the same radar emitter. Moreover, the pulse number of each signal pattern is not strictly fixed in practice, which is designed to simulate the uncertainties in real-world scenarios. We simulate 20,000 train samples, 4000 val samples, and 4000 test samples. Each sample is an interleaved radar pulse sequence with a fixed number of 5120 pulses, composed of signals from two to four radar emitters and some background noise. The five descriptors of noise are randomly distributed within predefined ranges. As a result, nearly all signals are contaminated by superimposed noise, significantly increasing the difficulty of signal sorting and recognition. The pulse overlap probability of the dataset ranges from 6.9% to 33.7%, with an average value of 17.2%. The SNR is calculated via the formula $\mathrm{SNR}=10{\log }_{10}\left({\displaystyle \frac{N_{\mathrm{signal}}}{N_{\mathrm{noise}}}}\right)$, yielding values spanning −11 dB to 6 dB with a mean of −1.42 dB. For the distribution of interleaving complexity, 14.4% of samples contain no interleaved emitters, 50.2% feature pairwise interleaving of two emitters, 30.3% involve three interleaved emitters, and the remaining 5.1% correspond to four interleaved emitters.

4.2. Experimental Settings

Since DOA is not served as the inherent attribute of signal patterns, UFiOD only uses TOA, RF, PW, and PA as inputs, treating them as 1D 4-variable data for processing. DOA information is further utilized during detection results integration. For the training settings of UFiOD, we employ the adam optimizer with initial learning rate of 0.01, incorporating a cosine learning schedule. The weight decay is 0.0005, and the momentum is 0.9. We set the training stage as 20 epoches, and the batch size is 128. The model from the last epoch is uniformly used for validation and testing. Our experiments are conducted on a high-performance deep learning server which is equipped with an AMD EPYC 7763 (2.45 GHz) and an NVIDIA A100 GPU (80.0 GB).

4.3. Detection Results

In this part, we primarily provide the detection results of the proposed UFiOD, including the accuracy of region regression and category recognition. We adopt ‘recall’ and ‘precision’ as evaluation metrics, where recall is used to measure how many real signal patterns UFiOD can detect, while precision measures how many of the detected signal patterns are correct. Notably, during the evaluation process, a signal pattern is considered correct only if both its temporal occurrence region and category are accurately identified. Additionally, we conduct extra experiments to analyze the effectiveness of the multi-scale feature fusion mechanism. Furthermore, we employ a radar simulator to transmit the predefined signal waveforms specified in this paper within a realistic electromagnetic environment and conduct experiments on practically intercepted data. The experimental results are shown in

Table 2. The detection performance of proposed method.

Methods	Metric	Radar A	Radar B	Radar C	Radar D	Radar E	Avg
UFiOD-F1	Recall	93.58%	95.01%	98.41%	82.12%	85.81%	90.99%
	Precision	95.87%	98.94%	99.11%	96.88%	96.34%	97.43%
UFiOD-F2	Recall	92.72%	93.32%	95.21%	90.21%	91.45%	92.58%
	Precision	96.93%	97.58%	98.19%	95.88%	96.19%	96.95%
UFiOD-F3	Recall	94.14%	92.54%	89.94%	94.69%	94.92%	93.25%
	Precision	95.63%	98.30%	96.98%	96.04%	97.33%	96.86%
UFiOD	Recall	96.89%	98.29%	98.59%	98.36%	98.14%	98.05%
	Precision	97.81%	98.98%	99.36%	98.94%	97.97%	98.61%
UFiOD*	Recall	97.72%	99.18%	98.74%	98.51%	99.29%	98.69%
	Precision	94.67%	95.95%	96.31%	95.82%	96.14%	95.78%

. UFiOD-Fx denotes detection with only the x-th backbone feature, which does not require the multi-scale feature fusion neck. In contrast, UFiOD employs three multi-scale features fused through the multi-scale feature fusion neck. UFiOD^* denotes the results on real radar data. The results demonstrate that features at different scales exhibit varying adaptability to signal patterns of different durations. For example, UFiOD-F1 utilizes large-scale feature, which achieves better performance for emitters with short-duration signal patterns, e.g., RadarB and RadarC. UFiOD-F3, leveraging small-scale feature, performs better for emitters with long-duration signal patterns, e.g., RadarD and RadarE. UFiOD adopts multi-scale features and achieves the highest performance. For real radar data, the interference caused by noise is limited, whereas prominent disturbances originate from irrelevant signals. Distinct from random noise, these interfering signals possess intact waveform envelopes and can generally be separated by the model. However, they are prone to misclassification, which results in high recall yet slightly degraded precision on real radar data.

4.4. Comparison with Existing Methods

In this experiment, we focus on evaluating and analyzing the performance of radar signal sorting and identification. In order to make a fair comparison with existing methods, we reproduce the simulation dataset following the benchmark settings of ResGCN [24], and conduct the experiment on this dataset using pulse-level accuracy as the evaluation metric. Specifically, based on the final sorting and identification results, we calculate the proportion of pulses which are of both correct sorting and identification outcomes. Notably, existing methods only evaluate the correctness of sorting, while our method simultaneously validates both sorting and identification results, making our evaluation protocol more challenging. The experimental results are shown in

Table 3. Comparison with existing methods.

Methods	Radar 1	Radar 2	Radar 3	Radar 4	Acc.	T./s
ABC-K [18]	66.40%	45.03%	99.75%	74.60%	71.45%	2.56
PSO-K [19]	72.80%	44.27%	99.25%	73.48%	72.45%	5.66
CNet [15]	0%	100%	0%	51.08%	37.77%	5.61
ADPC [14]	0%	60.49%	18.75%	90.58%	56.61%	0.08
SVM [60]	68.00%	90.91%	68.75%	97.14%	81.20%	0.07
SOFM [61]	74.00%	37.98%	60.50%	87.93%	65.10%	4.62
DBSCAN [62]	0%	71.71%	0%	100%	42.93%	0.24
ResGCN [24]	95.72%	91.98%	94.72%	96.50%	94.73%	1.55
UFiOD (Ours)	97.05%	94.64%	96.03%	97.78%	96.38%	0.53

, which demonstrates that the proposed method achieves the highest accuracy across most emitters, showing strong competitiveness. A key factor contributing to the success of proposed method lies in its ability to accurately predict the regions and categories of signal patterns, thereby it could effectively identify the corresponding pulses. Furthermore, the proposed method exhibits excellent real-time performance, primarily due to the fact that most computations occur during the signal pattern detection process. As an end-to-end neural network, UFiOD leverages GPU acceleration to achieve significant speedup.

4.5. Ablation Study

In this experiment, we aim to conduct an effectiveness analysis for the affects of the missing pulse ratio and involved hyperparameters of the proposed method. During the experiment, all other settings remain consistent, except for the variable of interest. In the following parts, we provide a detailed analysis for the missing pulse ratio and the involved hyperparameter $\lambda$.

Discussion on the missing pulse ratio: due to the presence of varying degrees of missing pulse in practical electromagnetic environments, the accuracy of radar signal sorting methods may be affected. In order to validate the robustness of the proposed method under missing pulse conditions, we simulate scenarios with different missing pulse rates and conduct experimental analysis accordingly. In this experiment, the missing pulse ratio is increased from 0% to 60% in an increment of 10%. As shown in Figure 5, the overall accuracy (including radar signal sorting and recognition accuracy) gradually decreases with the increase of missing pulse ratio. It is worth noting that when the missing pulse ratio is below 50%, the overall accuracy is only slightly affected. However, when the missing pulse ratio reaches 60%, the accuracy drops sharply. This is because the proposed method relies on capturing the intrinsic characteristics of signals by detecting the waveform pattern of the signal. When the missing pulse ratio becomes severe, the original waveform pattern of the signal is lost, leading to a rapid decline in the effectiveness of the proposed method. Nevertheless, when the missing pulse ratio does not interfere with the judgment of the signal waveform pattern, the proposed method demonstrates strong robustness.

Discussion on the hyperparameter $\lambda$: the hyperparameter $\lambda$ plays a crucial role in controlling the balance between the recognition and regression components in the training loss. In order to select an appropriate value of $\lambda$ for better optimization of the entire framework, we investigate the effectiveness of UFiOD under different $\lambda$ values in this part. We conduct extensive experiments on the simulated dataset to evaluate the detection performance of UFiOD under various $\lambda$ values, and the detailed results are presented in

Table 4. The discussion on the hyperparameter $\lambda$.

$\mathit{\lambda }$	Metric	Radar A	Radar B	Radar C	Radar D	Radar E	Avg
5	Recall	94.25%	96.83%	95.70%	96.01%	96.67%	95.89%
	Precision	97.99%	99.04%	99.28%	99.00%	97.99%	98.66%
10	Recall	96.42%	97.17%	97.65%	97.82%	97.34%	97.28%
	Precision	97.58%	98.86%	99.67%	99.08%	98.14%	98.67%
15	Recall	96.89%	98.29%	98.59%	98.36%	98.14%	98.05%
	Precision	97.81%	98.98%	99.36%	98.94%	97.97%	98.61%
20	Recall	96.22%	97.80%	98.27%	98.46%	97.51%	97.65%
	Precision	97.19%	98.62%	98.93%	98.33%	97.59%	98.13%
25	Recall	96.08%	97.03%	97.69%	97.51%	97.04%	97.07%
	Precision	96.99%	98.04%	98.28%	97.60%	96.99%	97.58%

. The results show that the hyperparameter $\lambda$ has a certain impact on UFiOD. When $\lambda =5$, the recall drops significantly, which is due to insufficient weight on the regression loss, leading to inaccurate region regression. When $\lambda$ is set to 10, 15, 20, or 25, UFiOD exhibits similar performance. Finally, by taking both recall and precision into account, we choose 15 as the default value of $\lambda$ in practice.

Discussion on the setup of anchor points: anchor points are the centers of the predicted regions, whose configuration affects the accuracy of region prediction in UFiOD. A small interval setting would generate a large number of anchor points, leading to additional computational overhead, while a large interval significantly reduces the number of anchor points, thereby negatively impacting the accuracy of region regression. In order to find a suitable interval for the setup of anchor points, we conduct supplementary experiments on the simulated dataset to evaluate UFiOD’s detection performance under different anchor points configuration. The detailed results are presented in

Table 5. The discussion on the setup of anchor points.

Interval	Recall	Precision	T./s
0.1	98.11%	98.68%	2.31
0.5	98.05%	98.61%	0.47
1.0	90.23%	94.38%	0.29
1.5	86.41%	92.72%	0.21
2.0	83.94%	91.44%	0.18

. The experimental results show that the configuration of anchor points has a significant impact on UFiOD. When the interval is set to 0.1, UFiOD achieves relatively good performance, but the high computational cost results in an inference time of 2.31 seconds per sample. When the interval is set to 0.5, UFiOD achieves a better balance between the performance and efficiency. When the interval is set to 1.0, 1.5, or 2.0, UFiOD performs poorly, as the sparse anchor points are insufficient to accurately regress the object regions. Finally, considering both performance and efficiency, we choose 0.5 as the default interval for the setup of anchor points in practical.

Discussion on backbone depth: backbone depth plays a crucial role in the feature extraction capability of the model. In order to select an optimal backbone depth for overall framework optimization, this section investigates the practical performance of the algorithm under various backbone depth configurations. Notably, the depth is defined as one combined unit consisting of a ConvModule1D and CSPDarknetModule1D. Since backbones of arbitrary depths always require final semantic aggregation, the terminal unit composed of a ConvModule1D, CSPDarknetModule1D, and SPPFModule1D is excluded from depth counting. Ablation experiments are conducted on the simulation dataset to evaluate detection performance under multiple backbone depth settings, with detailed experimental results summarized in

Table 6. The discussion on the setup of backbone depth.

Backbone Depth	Recall	Precision
3	83.01%	87.44%
6	98.05%	98.61%
9	98.19%	98.46%

. Experimental results reveal that backbone depth imposes a significant impact on model performance. An excessively shallow backbone leads to insufficient feature extraction, failing to fully exploit high-level semantic information and fine-grained features from input data, which causes obvious degradation in precision and recall. In contrast, an overly deep backbone drastically increases model parameters while bringing negligible performance gains. After comprehensively balancing detection accuracy and parameter overhead, a value of six is finalized as the default engineering setting for backbone depth in this work.

4.6. Subjective Experimental Results

In this experiment, we present subjective results of the proposed method. From original input to signal pattern detection and extraction results, and ultimately to object-level sorting and recognition conclusions, the processing procedure of the proposed method is visualized from the perspective of PDWs features. In order to facilitate the presentation of the processing results to readers, we provide the time-sequential variation diagrams for each descriptive feature of PDWs. It is worth noting that in visualizing the detection results, we use the time-sequential variation diagram of DTOA, in order to provide a clearer representation of the original signal handled by the proposed method as well as the generated results. For visualization in other stages, we adopt the time-sequential variation diagram of PRI, as these stages have already acquired the capability to extract signal pulses, making it possible to calculate the PRI, and thereby better illustrate the processing outcomes.

Visualization of the deinterleaving for heterogeneous radar emitters: in this part, we conduct the visualization for the scenario involving interleaved heterogeneous radar emitters. The result is shown in Figure 6. From Figure 6b,c, we can see that the proposed method successfully separates different signal patterns, including the cases of intersection and covering. Each detected temporal interval accurately contains a signal pattern, and the category of the signal pattern in that interval is predicted with high confidence. The signal pattern extraction algorithm successfully extracts the corresponding pulses of the identified signal pattern category from the detected intervals. As shown in the time-sequential variation diagram of PRI, the clear periodicity exhibited by the extracted pulses confirms the accuracy of the extraction. Finally, the proposed method groups the signal patterns into three distinct objects based on temporal correlation and DOA, as shown in Figure 6d. This subjective result demonstrates that the proposed method is capable of effectively separating and identifying signal patterns from heterogeneous radar emitters in interleaved scenarios.

Visualization of the deinterleaving for homogeneous radar emitters: in this part, we focus on visualizing the scenario involving interleaved homogeneous radar emitters. In the context of formation flight scenarios, the radar signals from co-type emitters often intersect, and the similarity in their parameters and waveform patterns can make it difficult for signal sorting algorithms to separate pulses from different co-type emitters. In order to demonstrate the robustness of the proposed method in such situations, this experiment simulates a scenario in which two targets with the same radar model transmit the same signal pattern and generate signal interleaving. The detection results, extraction results, and object-level conclusions of the proposed method are then presented, as shown in Figure 7. The proposed method demonstrates robust capabilities in identifying complete signal patterns, even in the presence of interleaved identical signal patterns, please refer to Figure 7c for details. The proposed method succeeds in this task by relying on the detection of complete signal patterns for sorting, rather than simply classifying similar parameters or waveforms. This enables the proposed method to effectively distinguish two co-type signal patterns that are interleaved, thus, preventing missing batch. From Figure 7d, the proposed method achieves the object-level inference for homogeneous radar emitters based on temporal correlation and DOA. This subjective result demonstrates that the proposed method is capable of effectively separating and identifying signal patterns from homogeneous radar emitters in interleaved scenarios.

Visualization of the deinterleaving for unknown signals: in this part, we mainly aim to demonstrate the proposed method’s capability in deinterleaving unknown signals. Firstly, we construct simulated unknown signal based on the settings in

Table 7. Simulation settings of unknown radar signals.

Radar	Mode	RF (GHz)	PW ($\mathsf{\mu }$s)	PA (dB)	DOA (°)	PRI ($\mathsf{\mu }$s)	Pulse Num
Unknown	1	3.1∼5.0	5.4∼6.5	13∼21	36∼40	36∼44	500
		D&S	D&S + jittered	wobulated + jittered	\	D&S	\

, which is different from the known signals shown in Table 1 in terms of their parameters and transformation styles. Secondly, we introduce minor modifications to the proposed method to enable preliminary adaptability for unknown signals. Specifically, we set a rejection threshold (e.g., 70%). Signal patterns with recognition confidence below this threshold are rejected as ‘unknown’. Surprisingly, in the signal pattern detection stage, the proposed UFiOD is able to detect all potential signal patterns, even those that are not present during training, demonstrating its strong generalization capability. For known signal patterns that appear during training, the proposed UFiOD is able to make recognitions with very high confidence. In contrast, for unknown patterns not seen during training, UFiOD makes incorrect recognitions with relatively low confidence. Thus, a simple rejection threshold can endow UFiOD with the ability to distinguish unknown signal patterns. During signal pattern extraction, we employ k-means clustering on PDWs features of rest pulses after extracting known signals, and extract pulses of dominant clusters in the regions. Additionally, in order to investigate the sensitivity of our method to the rejection threshold, we conduct experiments under various threshold configurations. Furthermore, we also adopt the OpenMax open-set recognition strategy [45] to replace the threshold-based rejection strategy, and the experimental results are presented in Figure 8. As the rejection threshold rises, signal patterns with moderate recognition confidence are rejected. Such samples contain both hard known signals and unknown signals. Consequently, the known recognition accuracy gradually increases while the unknown rejection accuracy declines. By contrast, lowering the rejection threshold retains moderately confident signal patterns, leading to a drop in known recognition accuracy and a continuous rise in unknown rejection accuracy. Hence, the performance of the threshold-based rejection strategy is sensitive to rejection threshold. Furthermore, the introduced OpenMax strategy is threshold-free and sustains consistently high known recognition accuracy and unknown rejection accuracy. It demonstrates that the proposed method can work compatibly with current open-set recognition strategies to improve the overall model robustness. The subjective results for unknown signals are shown in Figure 9. From Figure 9c, the proposed method successfully separates the unknown signal, which is attributed to the robust ability of UFiOD to capture underlying waveform regularities. This subjective result indicates that the proposed method has a certain capability of separating and identifying unknown signal patterns in interleaved scenarios.

5. Conclusions

In this paper, we propose a novel solution pipeline for RSSR, where RSSR is divided into three sub-problems: signal pattern detection, signal pattern extraction, and detection result integration. In order to address these problems, we propose a novel unified framework inspired by object detection (UFiOD). For signal pattern detection, we construct an end-to-end neural network to output the temporal occurrence regions and categories of potential signal patterns. In order to extract signal patterns from the detected temporal regions, we propose a template matching-based extraction algorithm to extract the corresponding signal pulses. In order to form complete radar signal sorting and recognition conclusions, we further propose a temporal correlation and DOA-based integration algorithm that efficiently merges the detected signal patterns into object-level sorting and recognition conclusions. In the future, we will further study open-set recognition technologies to better address the challenges posed by unknown signals. We hope this paper could bring some novel perspectives and insights to the research community.