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Specific Radar Emitter Recognition Based on Wavelet Packet Transform and Probabilistic SVM

Specific Radar Emitter Recognition Based on Wavelet Packet Transform and Probabilistic SVM
Specific Radar Emitter Recognition Based on Wavelet Packet Transform and Probabilistic SVM

Abstract —Radar emitter recognition plays an important role in military automated command and control system. It is a com p osite task that involves radar signal interce p tion, modulation recognition, features extraction and classification. In this p ap er, a wavelet p acket transform is used for feature extraction of unintentional modulation on pulse (UMOP). Then specific radar emitter recognition is achieved by a probabilistic SVM (PSVM). Exp eriments on simulation and actual radar data verify the correctness and validity of this method.

I. I NTRODUCTION HE radar emitter recognition seems to be the one of most difficult tasks in electronic support measures (ESM) and electronic intelligence (ELINT) systems. Specific radar emitter recognition can recognize different radars of the same type, which seems to be the highest level in modern

information warfare. Conventional recognition approaches,

which separate the received pulses into individual emitter group, are usually based on the use of pulse parameters such as direction-of-arrival (DOA), radio frequency (R F ), time-of-arrival (TOA), pulse width (PW), pulse repetition interval (PRI), called pulse descriptor word (PDW). These features are efficient in simple emitter environment. However, in modern radar systems, the threat environment has changed dramatically and more sophisticated waveforms have been used. To identify radar emitters in high density and high interleaving environment, we need to explore the detailed structure inside each pulse, called unintentional modulation on pulse (UMOP) [1]. The UMOP features provide important information to perform specific emitter identification (SEI) [2, 3], especially for radar emitters. Usually, radar interceptors search targets both in frequency domain and spatial domain. The received pulses of one certain radar are discontinuous and limited. An effectual method for emitter recognition is achieved by using individual pulse. As demonstrated [2] the features of waveform amplitude and frequency are combined to a feature vector. Then a linear discriminant analysis (LDA) based feature selection is utilized for choosing a subset of the original predictive variables. Anderson [4] uses the multiresolution analysis method to aid the classification of radar pulse in the Specific emitter identification (SEI) problem. Gillespie and Atlas [5] use the class-dependent time-frequency representations (TF Rs) for radar transmitter Manuscript received January 15, 2009.

L. Li, H.B. Ji and L. Wang are with the School of Electronic Engineering, Xidian University, Xi’an, 710071, PR China (e-mail: lilin@https://www.doczj.com/doc/684898885.html,; hbji@https://www.doczj.com/doc/684898885.html,; leiwang@https://www.doczj.com/doc/684898885.html,).

identification. F urthermore, many classifiers are applied to specific radar emitter recognition, such as neural network [6], attribute measure [7], support vector machines [8], etc. And in [9] minimum description length (MDL) criterion and competitive learning algorithm is used for online clustering of radar emitter.

In this paper, we propose a wavelet packet transform and probabilistic SVM-based specific radar emitter recognition. The remainder of this paper is organized as follows. Section II

presents various types of UMOP features and the radar signal

model. Section III discusses the specific radar emitter recognition, including preprocessing, feature extraction and classification. Section IV is the experiments and results. And then the conclusions are drawn in Section V. II. T HE UMFO F EATURES The UMOP features of radar emitter signals represent the characters of individual radar accurately. The extraction of UMOP features is the key problem of specific radar emitter recognition. The UMOP features can be classified as follows: 1) Frequency drifting Because of the difference in process, ageing and temperature, the output frequency of frequency source is different from the nominal frequency. And the output frequency may drift in the pulse [10]. When radar works at different frequency, the relative deviation is invariable, and the absolute deviation varies with the working frequency. So the frequency drifting is unique and stationary, and it can be regarded as the UMOP feature for radar signals with the same type and modulation. 2) Pulse envelope Pulse modulator is a key device for pulsed radar system. The ideal pulse envelope is a rectangle with stable frequency. However, because of the inevitable spurious parameters, such as distribution capacitance and lead inductance, and the continual varying of work voltage and current, the output envelope of the pulse modulator is not a rectangle [11]. Pulse modulator will generate stable and specific form of pulse envelope. The pulse envelope is invariant with the working frequency. 3) Phase noise Phase noise can be measured in the frequency domain, and is expressed as a ratio of signal power to noise power in a

1Hz bandwidth at a given offset ωΔ from the center

frequency 0ω, which is defined as follow [12] Specific Radar Emitter Recognition Based on Wavelet Packet

Transform and Probabilistic SVM

Lin Li, Hongbing Ji, Member, IEEE , and Lei Wang

T

Proceedings of the 2009 IEEE

International Conference on Information and Automation

June 22 -25, 2009, Zhuhai/Macau, China

{}()0,110log sideband total carrier P Hz L P ωωω+Δao

Δ=?????

(1) Because of the phase noise, there are sidebands around the

center frequency 0ωof the output spectrum of an oscillator. Suppose the unintentional phase modulation is ()sin 2n t f t ?απ=. Where α is the modulation index, n f is offset frequency. Then the output signal can be written as follow: ()()()()()

000()sin 2sin 2sin 2cos sin 2cos 2sin sin 2n n n U t A f t f t A f t f t A f t f t παππαππαπ=+=+ (2) Using Bessel function expansion for (2), under the

condition of 1α<<, we can obtain

()()

()000()sin 2sin 2()2

sin 2()2

n n A

U t A f t f f t A f f t αππαπ≈+++? (3)

So the phase noise ()t ? will cause two sidebands at

0f f ±. This result is consistent with (1).

4) Spurious output

There are various spurious outputs in the radar waveform accompanied with the emission of useful signal [13]. F or example, because of the use of nonlinear devices, the frequency synthesizer always generates many spurious frequency components [14]. Suppose the input signals are ()111sin s a t ω= and ()222sin s a t ω=, we can obtain the

output signal

()()()()()

()()

()2

3

011221231222021211122222112221212121233311221

sin sin 21

cos 2cos 22

cos()cos()1

sin 3sin 34

out s k k s s k s s k s s k k a a k a t a t k a t a t k a a t a a t k a t a t ωωωωωωωωωω=+++++++=++++?++??+?++"

" (4)

Except for the useful signals 12()ωω+and 12()ωω?, there are many spurious signals, such as 12()m n ωω+, 0,1,2,;0,1,2,m n =="".

Besides the frequency synthesizer, the radiation, crosstalk and leakage of frequency sources in the emitter, power ripple and vibration will cause different kinds of spurious outputs. Although these spurious outputs can be reduced by different filters, a unique and stationary spurious signal will be generated because of the specific devices and coupling circuit.

F rom the analysis above, the UMOP features consist of envelope, frequency and phase modulations. Therefore, the k th received pulse of one radar can be expressed as

0()()exp{(()())}()k k k I k U k k x t A a t j t t n t τφτφτφ=??+?++ (5) Where, 1,,P k N ="?0,1,,1t N =?". N is the signal length, k A is the amplitude of the pulse, ()a t is the specific envelope shape of this radar and k τ is the time delay. ()I

t φ

represents the intra-pulse intentional modulation, such as linear frequency modulation (LF M), binary phase shift keying (BPSK), frequency shift keying (F SK), etc. ()U t φ

represents the intra-pulse unintentional modulations. And ()k n t are narrowband gauss noises.

III. S PECIFIC R ADAR E MITTER R ECOGNITION

F ig.1 shows the flow chart of the specific radar emitter recognition in this paper. As the development of electronic technical, modern radars usually have various intra-pulse intentional modulations with different modulation parameters. The UMOP features may vary with the intentional modulation. So the intentional modulation classification and normalization should be achieved in the preprocessing process. The specific radar emitter recognition is executed for radar emitters with the same type of waveform and parameters. Then the feature extraction is achieved by wavelet packet transform and the maximum selection of decomposition bi-tree. F inally, the specific radar emitter classification and recognition is accomplished by the method of probabilistic SVM.

A. Preprocessing

Intentional modulation recognition is the foundation of specific radar emitter recognition. A number of methods have been proposed for modulation recognition of radar signals such as Ref. [15, 16].

Normalization is another important task for specific emitter recognition. It can avoid the influence of common parameters to simplify the recognition process. For pulses with the same modulation type, specific emitter recognition is affected by signal amplitude, delay and frequency, which are corresponding to amplitude normalization, time normalization and frequency normalization, respectively. As shown in Fig.2, because of the background noise and

DOA, the pulse energies differ with each other greatly, even two sequential pulses. F irst the amplitude normalization limits the amplitude of pulse to [1,1]? with linear or non-linear transform.

Samples A m p l i t u d e

(a)

Samples A m p l i t u d e

(b)

Fig.2 Two sequential pulses received from one radar

Time normalization, viz. pulse aligning should be

accomplished before frequency normalization. Here, we use a

correlative method according to the following procedure [17]:

1. Rank the pulses into a descending order k x , 1,

,P k N =" based on signal-to-noise ratio (SNR).

2. F or 2,

,P k N =", calculate ()()()j j k t

c x t x t ττ=?|, where 1,2,,2N τ=" an

d 1,2,,1j k =?".

3. Time shift of the k th pulse is given by

11

?arg max ()k k j j c τ

ττ?==|

4. Shift the k th pulse circularly ?k τ samples.

Frequency normalization is achieved by the cancellation of intentional modulation parameters, viz. demodulation. After the three normalizations above, we obtain the UMOP signal

()()exp{()}

()k U k z t a t j t n t φ′≈+ (6)

Because all the intentional modulation parameters of the pulses to be processed in Fig.1 are the same, so the parameters estimation errors can not influence the recognition of specific radar emitters.

B. Wavelet packet transform Wavelet transform, also known as multiresolution analysis is linear time-frequency analysis method. The Morlet-Grossmann definition [18] of the continuous wavelet transform (CWT) for a 1-D signal 2()()x t L R ∈ is

(,)()t b W a b x t dt a ?+∞??∞

?§·=¨??1

(7) where (

)t ? is the analyzing wavelet, (0)a > is the scale parameter and b is the position parameter. It is computationally impossible to analyze a signal using all wavelet coefficients, so one may wonder if it is sufficient

to pick a discrete subset to be able to reconstruct a signal from the corresponding wavelet coefficients. This method is the

discrete wavelet transform (DWT).

The orthonormal basis set in 2()L R of the DWT can be

represented as

2,(,)2()()2j j n j j n Z t k t φ∈-??°°

=??°°ˉ? (8) The reconstruction of any signal x of finite energy can be achieved by the formula

,,(

),()j n

j n j n x t x t φ

φ∞∞

=?∞=?∞

=

¢2|| (9)

DWT is conventionally achieved by repeating application of two filtering operations, high frequency detail superimposed on low-frequency components. The decomposition process is repeat performed to the low-frequency sub-band to compose the next level of the hierarchy. As shown in F ig.3, the discrete wavelet packet transform (DWPT) is an extension of DWT, which repeat the decomposition both in the low-frequency and the high-frequency sub-bands. A number of methods based on DWPT have been proposed for signals feature extraction,

such as Ref. [19, 20, 21]. The DWPT can be represented as

122(2)(2(2)j j n n u

w t k h u k t u ??=?? (10) 1212(2)(2(2)j j n n u

w t k g u k t u ?+?=?? (11) where j is the scale index, k is the translation index, h is the lower-pass filter and the is a high-pass filter with ()(1)(1)r g k h r =??. 1

U 1

1U

2U 2

2

U 32

U 0

3U 13U 23U 33U 4

3U 53U 6

3U 7

3U 0

2U 0

1U

Fig.3 The diagram of three levels wavelet packet transform

Let the length of a sampled signal is 02n N =, the

decomposition sub-spaces by the mirror filter can be written as

221111

00,,,0,,2k k k j j j j U U U j n k +?++=⊕=="" (12) We can obtain 02n j ? complete orthogonal basis vectors of

the sub-pace k j U by the mirror filter. The orthogonal basis set can be represented as {},()j k u n , where ,,j k n u is called

wavelet packets or wavelet atoms.

The essential of DWPT is that it splits the signal to time-frequency localized information by a filter process, and it is possible to combine the different levels of decomposition in order to achieve the optimum time-frequency representation of the original signal. The wavelet packet energy is very useful features for signal and image recognition. The wavelet packet energy can be calculated as

2,,211()N

j k j k n E u n N ==| (13)

C. Probabilistic SVM

SVM was proposed as an effective machine learning approach by Vapnik and Cristianini [22, 23]. This method is a statistical learning method with a good performance, and it is easier to implement than neural networks. The SVM method was successfully applied to various problems including signal classification, modulation recognition, image recognition, etc.

A SVM is used for classification of only two-class problems. A separating hyperplane is obtained by calculating the maximum distance to the closest data points of the training set. These closest data points are called as Support Vectors (SVs). Usually, the data points cannot be linearly separated. In this state, these data points can be transformed to a high dimensional space by using a nonlinear transformation. The nonlinear transformations are performed by using variable kernel functions, such as sigmoid, polynomial, linear, Gaussian radial basis function (RBF), etc. These kernel functions define an inner product in high dimensional space. A kernel function can be given as below:

(,)()()Kernel x x d x d x ′′=? (14)

where ()d x is a mapping from low dimension input space

to a high dimensional space for each input data point x . The

decision function of a SVM is given as:

1

()(,)K

i i i i i f x a y Kernel x x b ==+| (15)

where K is the number of data points, {1,1}i y ∈? is the class label of training point i x . i a is Langrangian multiplier and can be found by solving a quadratic programming

problem with linear constraints [22]. Constructing a classifier to produce a posterior probability is very useful in practical recognition situations [24, 25]. In radar context, the received pulse may be an interference signal or may belong to a new class. So, this pulse should be rejected which is not considered in the standard SVM. F urthermore, posterior probabilities are also required for decision fusion with other classifiers. F irst, Vapnik uses a method which maps the output of SVMs to probabilities by decomposing the feature space into a direction orthogonal to the separating hyperplane. In [24], Platt suggests a method for fitting the posterior probabilities (1)P y f = with a parametric model directly. It uses a parametric form of sigmoid:

1

(1)1exp()

P y f Af B ==

++ (16)

As long as 0A <, the monotonicity of (16) is assured. Here it assumes that the output of the SVM is proportional to the log odds of a positive example. The parameters A and B are found by minimizing the negative log likelihood of the training data, which is a cross-entropy error function:

min log()(1)log(1)i i i i i

t p t p ?+??| (17)

where i t are defined as

1

2

i i y t +=

(18) and i p are the output probabilities defined as

1

1exp()

i i p Af B =

++ (19)

The minimization in (17) is a two-parameter minimization problem, and it can be performed using any number of optimization algorithms.

After the process of probabilistic SVM, we can obtain the posterior probability of radar emitter recognition. The next task is to estimate the generalized confidence. We suppose that the posterior probability of a radar pulse belonging to the k th class is ()k P H (1,2,,)k C =!, where C is the class number of the training set. ()k P H ′ are the posterior

probabilities by descending sorting of ()k P H . 1()P H ′ and 2()P H ′ are the maximum and the second maximum posterior

probabilities, respectively. There are several methods for generalized confidence estimation based on posterior probability, such as:

Method 1. Use the maximum posterior probability, viz.

1()()s F x P H ′= (20)

Method 2. Use the difference between the maximum and

the second maximum posterior probabilities, viz. 12()()()s F x P H P H ′′=? (21) Method 3. Use the normalized difference between the

maximum and the second maximum posterior probabilities, viz.

()121()()()()s F x P H P H P H ′′′=? (22) Method 4. Use the negative entropy of all C posterior probabilities, viz. 2()()log ()s k k k F x P H P H ′′=| (23) Method 5. Use the selective measurement, viz. ()11()()1()s k k F x P H P H ≠′′=?∏ (24) F or the five generalized confidence estimation methods, we set different reject thresholds. If the generalized confidence is less than the threshold Th , the pulse required for classification is regarded as an unknown class not belonging to the database.

(),(),s s

F x Th accepted

F x Th rejected ≥-?

<ˉ (25) The five generalized confidence estimation methods use different posterior probability information. So we can fusion the decision results by a voting scheme.

IV. E XPERIMENTS A ND R ESULTS

In this section, we discuss the performance of the proposed method by numerical experiments. First, the simulation data consists of three radars with sinusoid waveform. We generate 200 pulses for each one with different SNRs and initial phases. As shown in Fig.4.(a) and (b), the pulse envelope and frequency drifting are different form each other, but the differences are very slight. The sampling frequency Fs is 1.

Samples A m p l i t u d e

(a)

-3

Samples F r e q u e n c y ( x F s )

(b)

Fig.4 The pulse envelope and frequency drifting of the three radars

Usually, the spurious output and the phase noise have same UMOP characteristics. Here, we use a sinusoid interference ()sin 2n t f t ?απ= to simulate the phase noise or the spurious output. The parameters are [0.011, 0.012, 0.0013]α= and [0.01, 0.01, 0.01]n f =.

In this experiment, we use 120 pulses of each radar for

training and 80 for testing. Fig.5 shows the correct rate (CR)

versus the dimension reduced by principle component

analysis (PCA). The DWPT filter type is sym5 and the

decomposition level is 7. The SNR is 0 dB. The thresholds of the five methods for generalized confidence estimation introduced in Section III.A are set to {}0.5,0.3,0.6,0.2,0.3?. These reject thresholds have a direct relation with the recognition performance, which need to be selected according to the false-alarm probability. The principle of voting is that the minority is subordinate to the majority. It can be found that the correct rate tends to be stable while the dimension larger than 10. The experiment results in this section are the

average of Monte-Carlo experiments for 20 runs.

Dimensions

Fig.5 Correct recognition rate vs. dimensions

Table I shows the correct rates using different DWPT filters. The decomposition level is 7, feature dimension is 20. It can be found that the recognition performances of the eight DWPT filters are almost the same.

As shown in F ig.2, the actual received pulses are single-tone frequency signals. The sampling frequency is about 200 MHz. There are 7 radars with the same type and function. Each one has 50 pulses, and the total pulse number

is 350. As mentioned in Section II, because of the background noise and DOA, the pulses’ SNR differ with each other greatly, even two sequential pulses. The SNRs of these pulses are higher than 15 dB. In this experiment, the training set consists of 6 radars with 30 pulses for each one. So, the total pulses number of training set is 180. The testing set consists of the residual pulses, viz. 6 known radars with 20 pulses for each one and the unknown radar with 50 pulses. The correct

rates and false reject rates using different DWPT filters are shown in Table II, where the decomposition level is 8 and

feature dimension is reduced to 50 by PCA. The thresholds

for rejection are the same as the first experiment above. The

correct rate and false reject rate (FRR) are defined as

correct recognition samples

test samples except unknown classes

CR = 100%N N × (26)

FRR = 100%false rejected samples

test samples N N × (27)

respectively. From the experiment result, we can find that all of the eight DWPT filters can obtain good recognition performances. The correct rates are greater than 94%, and the false reject rates are less than 3%. TABLE I

C ORRECT R ATES U SING

D IFFERENT DPWT F ILTERS FOR S IMULATION

D ATA DWPT filter

type

SNR 10dB SNR 5dB SNR 0dB db3 87.6% 84.1% 78.3% db5 87.5% 84.5% 78.2% db7 87.4% 84.4% 77.9% sym3 87.6% 84.5% 78.4% sym5 87.5% 84.6% 78.3% sym7 87.5% 84.5% 77.7% coif1 87.4% 84.4% 77.8% coif2 87.3% 84.3% 77.2% We analyze three wavelet families: Daubechies (db), Symlets (sym) and Coiflets (coif).

V.C ONCLUSIONS

In this paper, we studied the application of discrete wavelet packet transform and probabilistic SVM for specific radar emitter recognition. Experiments on simulation and actual radar signals verify the correctness and validity of this method. Applied to different data, the performances of different DWPT filters are variable. But the differences of correct rates are slight. The reasonable thresholds for rejection are very important in the proposed method. In Section IV, we choose the thresholds mainly depend on experience. The method may be improved by an automatically learning algorithm for the thresholds selection. Furthermore, the selection of decomposition level of DWPT is another problem which is not considered in this paper. Higher decomposition level means that larger computational burden is needed, but the increase of correct rate is not always guaranteed. These problems need to be further investigated to improve the stability and validity of the proposed method.

A CKNOWLEDGMENT

The authors wish to thank the Editor and reviewers for their valuable comments and good suggestions.

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TABLE II

C ORRECT R ATES AN

D F ALS

E R EJECT R ATES U SING D IFFERENT DPWT

F ILTERS FOR A CTUAL D ATA

DWPT filter type CR FRR

db3 95.1%

2.5%

db5 95.1%

2.5%

db7 94.4%

2.7%

sym3 95.6%

2.4%

sym5 95.6%

2.5%

sym7 94.9%

2.5%

coif1 95.2%

2.4%

coif2 95.1%

2.6%

We analyze three wavelet families: Daubechies (db), Symlets (sym) and Coiflets (coif).

6、多普勒天气雷达原理与应用

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