Qiang Guo, Pulong Nan, and Jian Wan*

    College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

    Abstract: For the multi-mode radar working in the modern electronic battlefield, different working states of one single radar are prone to being classified as multiple emitters when adopting traditional classification methods to process intercepted signals, which has a negative effect on signal classification. A classification method based on spatial data mining is presented to address the above challenge. Inspired by the idea of spatial data mining, the classification method applies nuclear field to depicting the distribution information of pulse samples in feature space, and digs out the hidden cluster information by analyzing distribution characteristics. In addition, a membership-degree criterion to quantify the correlation among all classes is established, which ensures classification accuracy of signal samples. Numerical experiments show that the presented method can effectively prevent different working states of multi-mode emitter from being classified as several emitters, and achieve higher classification accuracy.

    Keywords: multi-mode radar, signal classification data mining, nuclear field, cloud model, membership.

    DOI: 10.21629/JSEE.2016.05.09

    1. Introduction

    As one of the key technologies in radar reconnaissance systems, radar signal classification has been paid extensive attention to in the past few decades [1]. Classification methods separate and identify the intercepted signals emitted from different radars, the accuracy of which determines the effectiveness of the operation strategies in electronic warfare. Electromagnetic environments, nevertheless, have the tendency to worsen because of the appearance of modern radars with multiple functions and working states. One of the challenging difficulties that radar reconnaissance systems need to overcome is to effectually classify multimode radar signals. According to the requirements in electronic warfare, multi-mode radars usually adjust working states and emit the pulses with varying parameters [2]. As a result, the signals from one emitter are easy to be classified as multiple emitters, which is called “increasing-batch”.

    Previous studies on signal classification lay emphasis on feature-based algorithms, among which time-of-arrivalbased (TOA-based) classification is most commonly used. Popular algorithms include TOA histograms [3,4] and pulse repetition intervals (PRI) spectrum [5,6], plane transform [7,8], Kalman filter tracking [9], and hidden Markov model method [10]. Though TOA-based methods are capable of classifying the pulses with jittered and staggered PRI, it is hard to accomplish effective signal classification in case of enormous pulse density and massive lost pulses. Besides, multi-parameter methods have been applied in radar signal classification. Except for regular pulse description words (PDW), various intra-pulse features (include time-frequency features [11 – 17], similarity features [18], complexity features [19,20], fractal features [21], cumulant features [22]) have been researched and extracted in recent years. On the basis of extracted feature parameters, scholars apply several neural network methods [16,23], support vector machine (SVM) [12,24], clustering methods [25 – 29] and cloud model [30,31] to radar signal classification. The methods mentioned above can effectually classify ordinary radar signals on the condition of low signal-to-noise ratio (SNR), overlapping feature spaces and lacking of a priori knowledge. However, the “increasing-batch” problem inevitably arises when processing multi-mode radar signals. Deserved to be mentioned, a multi-mode signal sorting method [2] presented by Zhao et al. combines breadth first search neighbor (BFSN) clustering with data fusion and gain certain effect.

    In order to address the “increasing-batch” problem, we make an attempt to introduce the spatial data mining method based on nuclear field and cloud model into multimode radar signal classification. As a particular form of data field, nuclear field can simulate data interaction more reasonably. For the feature parameters of intercepted radar signals, nuclear field transforms quantitative data to qualitative concepts by depicting the distribution characteristics [32]. Further, hidden cluster information is dug out according to the spatial concepts. On this basis, we are supposed to quantify the correlation among all classes using cloud model membership, so that the transition from spatial concepts to spatial knowledge is accomplished, which provides strong support for the solution of the “increasingbatch” problem and multi-mode radar signal classification at high accuracy.

    In the rest parts of this paper, involved theories are discussed in Section 2 and Section 3. In Section 4, the proposed classification method is experimentally evaluated. Conclusions are given in Section 5.

    2. Clustering information acquisition based on nuclear field 

    For the radar pulses intercepted in a complex electromagnetic environment, the parameter samples in feature space tend to distribute randomly and uncertainly,  which results in negative impacts on signal classification. Inspired by the concept of field in physics, we regard the feature space as data field. Simultaneously, each parameter sample is viewed as a data target that radiates energy to the space and influences other parameters around. Considering that the short-range field has prominent advantages on the presentation of clustering characteristics of data targets, the paper employs the nuclear field model to sufficiently analyze the interaction of all parameter samples, with the purpose to acquire more accurate cluster information.

    2.1 Establishment of potential field

    Assume that there are K data targets vk (k = 1, 2, . . .,K) on behalf ofK radar pulse samples in feature space. Corresponding position vectors are vk (k = 1, 2, . . .,K). If all data targets are viewed as particles with mass who radiate energy to feature space, then the formed nuclear field, at position v, has the potential function:

where ϕi(v) denotes the potential function of the ith data target at position v, mi (i = 1, 2, . . .,K) denotes the mass of each data target and satisfies the normalization conditionis the Euclidean distance between vi and v, σ is the influence factor used to control the actuating range of data targets [33]. Fig. 1 gives an example of nuclear field, in which every isopotential line connects the points with the same potential values and all isopotential lines set up the potential field. The local maximal potential values surrounded by isopotential lines are called potential centers. On account that the local maxima, generally, locates at the barycenters of similar data clusters, we consider potential centers as the cluster centers of parameter samples [32].

    2.2 Potential center extraction

    Once the potential field is derived, we are supposed to dig out the hidden cluster information of parameter samples by analyzing the revealed distribution characteristics deeply. As the initial clustering information, the number and positions of cluster centers are significant to the clustering correctness. The paper, therefore, extracts the potential centers in potential field to locate the cluster centers and determine the number of classes.

According to (1), the original potential value at v is represented as

where r = vi − v. We extract the point with the maximal potential value as the first potential center. In order to eliminate the influence of determined centers on the extraction of rest potential centers, it is necessary to remove the present center and update the potential function before extracting the next potential center. The updating formula is as follows:

where L is the total number of potential centers in the potential field, cl is the lth potential center formally extracted, r = cl − v; ϕl(v) is the potential value at v after the influence of the lth potential center is eliminated and ϕl−1(v) is the potential value at v after the influence of the (l − 1)th potential center is eliminated. After iteration calculations, we derive all L potential centers as well as their position vectors, according to which both cluster centers and the number of classes are determined.

2.3 Dynamic clustering

    The determination of initial clustering information provides positive conditions for the clustering process. On this basis, data targets are to be allocated to different classes. The data targets in feature space interact with each other, and will move close to different cluster centers under the guidance of the distribution information in the potential field.

At time t, the field intensity at vi can be obtained according to (1):

and the field force acting on data target vi can be computed as

In (4) and (5), rij (t) = vj(t) − vi(t). If Δt is small enough, the movement of data targets within [t, t + Δt] is considered to be an uniformly accelerated motion. Let the initial velocity vector be 0, then the position vector of vi at t+Δt is

where a(t)(vi) is the instantaneous acceleration of vi at time t. The data object vi is guided by the field force to move towards where the potential value is larger until it reaches one of the cluster centers or some termination conditions set by users are satisfied. Additionally, Δt is adaptively selected during iteration: 

where f represents temporal resolution and is usually set to 100, E(t) is the norm of field intensity at time t, E = [E(t1), E(t2), · · ·] is the vector containing all field intensity derived in completed iteration process.

    2.4 Clustering procedures

    The clustering information acquisition of radar signal samples based on the nuclear field is detailed as follows:

    (i) Input the data targets corresponding to parameter samples.

    (ii) Data targets radiate energy into parameter space, and the potential field is formed.

    (iii) Partition the potential field by Cartesian grid (grid scale is) and grid points are regarded as candidates of the clustering center.

    (iv) Compute the potential values of all grid points according to (i).

    (v) Obtain initial clustering information by extracting potential centers in turn. Related details are specified in Section 2.2.

    (vi) On the basis of initial clustering information, dynamic clustering is completed under the guidance of field forces.

    3. Judgment criterion based on cloud model membership 

    The data targets in feature space are clustered into different classes in the last section. However, it is still difficult to judge which classes belong to the same emitter when multi-mode radar signals exist. Therefore, we attempt to establish a judgment criterion based on cloud model to measure the correlation of classes and resolve the “increasing-batch” problem.

    3.1 Cloud model

    The cloud model organically combines the fuzziness in fuzzy set theory and the randomness in probability theory, and appears to be an effective tool used for performance evaluation. The cloud model represents a concept via digital eigenvalues, namely expectation (Ex), entropy (En) and hyper entropy (He). Ex is the barycenter of cloud. En measures the granularity of concept, reflecting the acceptable range of qualitative concept.He measures the condensation degree of cloud droplets, reflecting the randomness of the droplets representing qualitative concept [34].

    In the cloud model, digital eigenvalues are known for a given concept. The smaller En the data element has, the closer it is to Ex. Then appearance chance of cloud droplet is greater and corresponding concept is more certain. Thus the acceptable data scope is smaller. Conversely, the data are far away from Ex. Then the appearing chance of cloud droplet is smaller and corresponding concept is more uncertain. Thus, the acceptable data scope is larger. Fig. 2 gives relevant schematic diagram.

    As can be seen from Fig. 2, the cloud droplets in data space of U can be divided into three categories, namely the basic elements in [Ex−En,Ex+En], the peripheral elements in [Ex−2En,Ex−En]∪[Ex+En,Ex+2En] and the inferior peripheral elements in [Ex − 3En,Ex −2En]∪[Ex+2En,Ex+3En]. The contribution of basic elements to qualitative concept accounts for 68.26%; the contribution of peripheral elements to qualitative concept accounts for 27.18%; the contribution of inferior peripheral elements to qualitative concept accounts for 4.3%. To conclude, overwhelmingmajority of elements distribute in [Ex − 3En,Ex+ 3En], which is called “3En” principle [32].

    3.2 Establishment of the judgment criterion If we take every parameter sample in feature space as a cloud droplet, then the cloud comprised of all cloud droplets is the qualitative representation of spatial data. For every class derived in Section 2, we employ backward cloud generator to calculate the digital eigenvalues of cloud droplets in different dimensions:

correspond to different parameter dimensions respectively. vpqk represents the kth parameter of the qth target in the pth class. m and l are the number of classes and the number of data targets in the pth class (p = 1, 2, . . .,m; q = 1, 2, . . ., l). Then the cloud models for different parameter dimensions are generated using the forward cloud generator:

where Enk and He2 k are the expectation and variance of generated random numbers for the kth parameter dimension, respectively. And the membership is derived using 

where μp2 (vp1q) is the membership of the qth data target in the p1th class to the p2th class; vp1qk is the kth parameter of the qth data target in the p1th class; Exp2k is the expectation of cloud droplets in the p2th class for the kth parameter dimension; En p2k is the random number for the kth parameter that generated by the forward cloud generator using the data targets in the p2th class. (p1 = 1, 2, . . .,m; p2 = 1, 2, . . .,m). Let the membership mean of the p1th class to the p2th class be

    The membership mean quantifies the correlation between any two of classes, which provides reliable spatial knowledge for the solution of the “increasing-batch” problem. On the basis of the cluster results and membership mean above, we can accomplish the judgment as follows:

    (i) Set the membership threshold εμ and the DOA threshold εDOA;

    (ii) IfΔ = |ExDOA(p1)− ExDOA(p2)| > εDOA, then consider that two cluster-classes come from different emitters;

    (iii) If Δ  εDOA and Eμp1p2  εμ, then consider two cluster-classes as different work modes of one radar emitter;

    (iv) If Δ  εDOA and Eμ p1p2 < εμ, then consider that two cluster-classes come from different emitters

    4. Experiments and results analysis

    To evaluate the classification accuracy and effectiveness of the proposed method, simulation experiments involving a set of radar pulses are to be accomplished. The signals in pulse sample set are emitted from four radars, including two multi-mode radars and two single-mode radars. Taking the stability and robustness of parameters into account, we extract radio frequency (RF), pulse width (PW) and direction of arrival (DOA) as feature parameters of pulse samples. Detailed parameter setting is listed in Table 1. Fig. 3 illustrates the distribution of parameter samples in threedimensional feature space.

    4.1 Initial settings

    4.1.1 Influence factor σ

    As a parameter used to control actuating range, influence factor σ has prominent effect on the distribution of potential field. Therefore, it is crucial to select an appropriate influence factor σ. In [2], an optimizing method based on potential entropy is applied to the determination of σ. Let the potential value of data targets {v1, v2, . . . , vn} be Ψ1, Ψ2, . . . , Ψn. The potential entropy is defined to be

where is a normalized factor and the potential entropy satisfies . Hψ measures the uncertainty of the potential field. So, all we need to do is to search an influence factor that minimizes the potential entropy. That is to say, the uncertainty is minimized to guarantee the distribution performance of the potential field. In Fig. 4, the curve of potential entropy shows that the σ corresponding minimal potential entropy is 0.14.

    4.1.2 Membership threshold εμ

    The “3En” principle provides theoretical support for the setting of εμ. For two classes satisfying Δ < εDOA, the membership between two classes in DOA dimension is relatively large. Therefore, we put more weight on the membership in DOA-dimension when setting εμ. Let x1 = Ex + En, which is the boundary between basic elements and peripheral elements, be the reference parameter in DOA dimension and let x2 = Ex + 2En, which is the boundary between peripheral elements and inferior peripheral elements, be the reference parameter in RF dimension and PW dimension. Then we derive the membership threshold using (13):

    4.1.3 Other parameters

    Let the scale of Cartesian grid be √2σ; in partition clust√ering, the moving step length of data objects is set to be

    4.2 Classification process

    In order to facilitate the processing, we normalize the feature parameters of pulse samples first. Following the clustering procedures in Section 2.3, pulse samples correspond to data targets, the radiation of which forms the potential field. Then partition the feature space adopting Cartesian grid. The potential values at all grid points are to be computed according to (1). The projections of threedimensional potential field on different two-dimensional planes are shown in Fig. 5. Taking the projection of potential field on PW-RF plane as an example. Fig. 6 illustrates the process of potential center extraction. The number of clustering centers turns out to be 8.

    On the basis of determined clustering centers and the hidden information in the potential field, the dynamic clustering of data targets are accomplished. According to the judgment criterion, the classification results are derived. Simultaneously, the same parameter sample set is classified using the method based on cloud model and the covering algorithm[30], which has some similarities with the proposed method and can achieve some effects. For convenience of observation, the comparison of classification results are given by Fig. 7 in RF-PW planes. Table 2 and Table 3 list the classification accuracy.

    As can be seen from classification results, the method in [30] classifies three working states of Radar 1 as two emitters. The “increasing-batch” problem, as a consequence, causes low classification accuracy. The proposed classification method can not only resolve the “increasing-batch” problem occurring in multi-mode radar signal classification, but also obtain higher classification accuracy than the method based on the cloud model and the covering algorithm.

    4.3 Results analysis

    For any point in the potential field, the potential is closely related to the energy radiation of every data target. As a result, the potential field can sufficiently represent the distribution characteristics of radar pulse samples, which directly affect the classification performance. In other words, all pulse samples exert their individual influence on classification results. Therefore, the dynamic clustering process based on the nuclear field is capable of acquiring more accurate clustering results in comparison traditional clustering methods. Besides, the established judgment criterion involving the cloud model provides reliable correlation information for the solution of the “increasing-batch” problem.

    5. Conclusions

    The paper presents a new classification method used to solve the “increasing-batch” problem in multi-mode radar signal classification. The classification method involving spatial data mining not only attaches importance to the role of each pulse sample, but eliminates the adverse effect caused by uncertain and random distribution of pulse samples at the same time. As a consequence, more dependable clustering and belonging information are obtained. It has been proved that the proposed method succeeds in preventing different working states of one emitter from being classified as multiple emitters, and can ensure high classification accuracy simultaneously.

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