Wireless Communications and Mobile Computing

Volume 2017 (2017), Article ID 9403590, 9 pages

https://doi.org/10.1155/2017/9403590

## Frequency-Hopping Transmitter Fingerprint Feature Classification Based on Kernel Collaborative Representation Classifier

Institute of Information and Navigation, Air Force Engineering University, Xi’an, Shaanxi 710077, China

Correspondence should be addressed to Ping Sui; moc.361@nixgninuwiz

Received 15 June 2017; Accepted 27 August 2017; Published 9 October 2017

Academic Editor: Donatella Darsena

Copyright © 2017 Ping Sui et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Noncooperation frequency-hopping (FH) transmitter fingerprint feature classification is a significant but challenging issue for FH transmitter recognition, since not only is it sensitive to noise but also it has the nonlinear, non-Gaussian and nonstability characteristics, which make it difficult to guarantee the classification in the original signal space. To address these problems, a method of frequency-hopping transmitter fingerprint feature classification based on kernel collaborative representation classifier is proposed in this paper. First, the noise suppression pretreatment of the FH transmitter signal is carried out by using the wave atoms frame method. Then, the nuances of the FH transmitters in the feature space are characterized by the surrounding-line integral bispectra features. And finally, incorporating the kernel function, a classifier which can generalize a linear algorithm to nonlinear counterpart is constructed for the final transmitter fingerprint feature classification. Extensive experiments on real-world FH transmitter “turn-on” transient signals demonstrate the robust classification of our method.

#### 1. Introduction

Frequency-hopping (FH) signals are generated by varying the carrier frequencies according to a certain hopping pattern, which is typically pseudo-random. Due to their inherent capability of low interception, good confidentiality, and strong anti-interference, FH signals have become an important tactical means of antireconnaissance and anti-jamming in military communication.

FH transmitter identification is a traditional significant but challenging issue in the electromagnetic war domain, especially under serious noise and noncooperation conditions. Due to the individual nuances of FH transmitters, there exist the inherent features, which can be used to identify the transmitter individuals. This inherent feature based on the individual nuances can be called the fingerprint of the transmitters.

Benefiting from the nuances among the transmitters, a number of studies using transient response features were emphatically researched to achieve the identification. Xu [1] combined the maximum correlation processing with time-dependent statistical method to realize the FH signal recognition. Eric et al. [2] proposed the MUSIC method based on signal direction information to sort the FH signals. Luo et al. [3] used the transient response feature of the transmitting power amplifiers to obtain the recognition results. However, when it comes to the condition of serious noise and complicated electromagnetic environment, especially when the transmitters are noncooperative, the practical classification of such methods is not ideal. In recent years, with the advantage of insensitivity to noise and outperform of classification, some methods based on sparse representation have been rapidly developed in various fields of signal classification. In the early studies, the sparse representation of the training data can be found via the -minimization problem. However, this problem is proved to be an NP-hard problem [4]. Fortunately, theoretical results show that if the sparsely code solution of the training data is sparse enough, then the solution of and -minimization problems is equivalent [5, 6]. Therefore, Wright et al. [7] proposed a sparse representation-based classifier (SRC), in which sparse representation problem can be addressed by the -minimization optimization. Although there are lots of fast numerical algorithms that have been proposed for the -minimization optimization, it is still very computationally demanding. In contrast, Zhang et al. [8] argued both theoretically and empirically that collaborative representation classifier (CRC) based on the -minimization is significantly more computationally efficient and can result in similar performance compared with the SRC. And also Yang et al. [9] proposed a relaxed collaborative representation model, which is simple but very competitive with the state-of-the-art classification method. Thus, CRC has been widely used for the research of signal classification, and a recent study has shown that CRC is more efficient than the SRC without sacrificing the classification accuracy. However, CRC is conducted in the original signal space rather than the nonlinear high dimensional feature space; thus the effectiveness of CR for the classification is difficult to be guaranteed in the original signal space when it is used to describing the nonlinear, non-Gaussian and nonstability feature of the FH transmitter fingerprints.

Above all, there are still some issues that have not yet been properly addressed, in particular, () the influence of noise. Fingerprints of the FH transmitter are so subtle and seriously sensitive to noise; () effectiveness of classification: a recent study has shown that CR is a promising regularization framework for signal classification. However, it is conducted in the original signal space rather than the nonlinear high dimensional feature space so that the effectiveness of the classification is difficult to be guaranteed.

To address these issues, in this paper, an effective FH transmitter fingerprint feature classification method based on kernel collaborative representation classifier is proposed. Firstly, we denoise the signal data by wave atoms frame instead of the traditional wavelet-based method. Secondly, utilizing the surrounding-line integral bispectra analysis, we extract the fingerprint features of the FH transmitters by their real-world “turn-on” transient signals. Finally, the kernel collaborative representation classifier by introducing the kernel function was used to realize the classification results. The main advantages of our method include the following: () the data noises are especially inevitable in electric environment. Our noise suppression method based wave atoms frame outperforms the traditional wavelet-based denoising method; () instead of the CRC, which is conducted in the original signal space, our method generalizes the linear CRC to its nonlinear counterpart by using the kernel function, and in this way, the fingerprint features belonging to the same class can be easily separated. Experiments on real-world FH “turn-on” transient signals demonstrate the effectiveness and high classification of our method.

The rest of this paper is organized as follows. The theories of wave atoms frame and CRC are expounded in Section 2. Then Section 3 describes the procedures of noise suppression and the details of the proposed KCRC method. Section 4 demonstrates the experimental results and analyzes the classification performance. Finally, Section 5 concludes the paper.

#### 2. Preliminaries

This section starts with a succinct description of the wave atoms and offers insight into its implementation. And then some previous works in classification are introduced. In this part, we present the traditional sparse representation method first and then give the collaborative representation-based classifier and its deficiencies.

##### 2.1. Wave Atoms Frame

In a general signal processing problem, the wave atoms are represented as , with subscript , where and index is a point in phase-space aswhere are two constants, the position vector is the center of , and the wave vector determines the centers of both bumps of as in frequency plane.

Let and be as in (1) for some . The elements of a frame of wave packets are called wave atoms for all when

Consider the localization condition; one-dimensional wave atoms can be obtained by constructing the frequency domain tightly support symmetric ; and deal with it by two-dimensional scaling and translation as follows [10]:where , . The function is an appropriate real-valued, bump function with a support interval length of and it satisfied . And by combining dyadic dilates and translating on the frequency axis one-dimensional wave atoms can be noted asTo preserve the orthonormality of the , the profile needs to be asymmetric in addition to all the other properties, in the sense that for , with itself being supported on .

Considering is a Hilbert transform, the orthogonal basis and its dual orthogonal basis can be defined as

It is easy to see that the recombinationprovides basic functions with two bumps in the frequency plane, symmetric with respect to the origin, and, hence, the directional wave packets. Together and form the wave atom frame and may be denoted jointly as . If the frame is tight, there areThen we have the two-dimensional wave atoms transform coefficient as [10]

##### 2.2. Collaborative Representation-Based Classifier

Assume that the training data set is represented as , where is the number of classes, is the collection of the data points for class , and is the total number of training data. Then the sparse representation of a new test data can be found via the -minimization problem aswhere denotes the -norm which is defined to be the number of nonzero elements in a vector. Generally, a sparse solution via the -minimization is more robust and facilitates the consequent classification of the test data . However, this problem (9) is proved to be an NP-hard problem [4]. Fortunately, theoretical results show that if the solution obtained is sparse enough, then the solution of the and -minimization problems is equivalent [5, 6]. Therefore, in SRC [7], the test data can be sparsely coded by the -minimization problem asAlthough the -minimization problem is extensively studied and lots of numerical algorithms have been proposed, it is still a computationally demanded problem. In contrast, Zhang et al. [8] verified both empirically and theoretically that -minimization based classifier relying on collaborative representation can result in in a similar performance. The collaborative representation of can be written asThen the classifier based on collaborative representation is ruled as

Compared with the -minimization based sparse representation, extensive experimental results in [8] demonstrate that the -minimization base collaborative representation is more computationally efficient.

#### 3. Proposed Method

As for FH transmitters, there will be many actual and significant transient states during its work. Some of these transitions are from the system itself, such as “turn-on/off” instantaneous changes and mode switch of the transmitters; others are from the outside interference, which is accidental and does not exist for every transmitter. And these transitions which reflect the characteristics of the transient states contain a wealth of individual nuances information of the FH transmitters. Based on the analysis above, in order to fully characterize individual nuances of the FH transmitters, we choose the instantaneous “turn-on” response of the FH signals to calculate the fine features for the final transmitter classification.

##### 3.1. Noise Suppression

The FH signals collected in the actual environment often have noise and clutter interference. In order to effectively reduce the influence of external disturbances on the feature extraction of transient signals, our method performs the noise reduction pretreatment on the collected transient signals firstly.

At the present time, one-dimensional signal noise suppression is mainly based on the wavelet analysis. Due to the nonstationarity of the transient signals of FH transmitter, the traditional wavelet-based denoising algorithms can reduce some noise, but they blur the signal information at the same time. In contrast, experimental results in [11] demonstrate that wave atoms frame is more significantly denoising efficient without sacrificing more signal accuracy. Therefore, in this paper, we use the wave atoms frame to carry out the denoising result of the “turn-on” transient FH signal.

Let be the source “turn-on” signal, and the additive noise, which follows the Gaussian distribution, and also they are uncorrelated; then we have the observed signal as

Wave atoms frame is a special two-dimensional wave pocket deformation and is usually used for image and other two-dimensional signal denoising. Thus, we construct a virtual observation matrix for the by adding white noise. where obey the Gaussian distribution. In matrix , the signal between the lines is determined by the nuances characteristics of the FH transmitter; the information correlation is strong at all times. When is random noise, the correlation is weak.

Sampling the virtual observation matrix at , the number of sampling points is ; obtain its discrete form as

In this way, the matrix can be treated as a two-dimensional signal matrix for noise reduction. The effective information in is equivalent to the vertical texture feature of the two-dimensional image. And then we can use the superiority of wave atoms frame for two-dimensional texture information expression to obtain the denoising result ; the final denoising one-dimensional signal can be written as

##### 3.2. Feature Extraction

Compared with the traditional first-order and second-order spectrums, high-order spectrum can extract more significant features of nonstationary, non-Gaussian and nonlinear signals. In this paper, we extract the surrounding-line integral bispectra features to characterize the fingerprints of the FH transmitters in the feature space. The bispectrum of noise suppression data is defined aswhere is the three-order cumulant of . After obtaining the bispectrum, we use the surrounding-line integral bispectra analysis method to process the bispectral estimation result. As shown in Figure 1, the integral path is a square centered around the origin, and each point represents a bispectral estimate.