Efficient radar target recognition using the MUSIC ...yu.ac.kr/~kkt/documents/cm.pdf · Efficient...

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 3, MARCH 2002 325

Efficient Radar Target Recognition Using the MUSICAlgorithm and Invariant Features

Kyung-Tae Kim, Dong-Kyu Seo, and Hyo-Tae Kim

Abstract—In this paper, an efficient technique is developed torecognize target type using one-dimensional range profiles. Theproposed technique utilizes the Multiple Signal Classification algo-rithm to generate superresolved range profiles. Their central mo-ments are calculated to provide translation-invariant and level -in-variant feature vectors. Next, the computed central moments aremapped into values between zero and unity, followed by a principalcomponent analysis to eliminate the redundancy of feature vectors.The obtained features are classified based on the Bayes classifier,which is one of the statistical classifiers. Recognition results usingfive different aircraft models measured at compact range are pre-sented to assess the effectiveness of the proposed technique, andthey are compared with those of the conventional range profilesobtained by inverse fast Fourier transform.

Index Terms—Feature extraction, radar signal processing, radartarget recognition, spectral analysis.

I. INTRODUCTION

RADAR target recognition is a very difficult task since theradar cross-section (RCS) of a target is highly dependent

on operating frequency and aspect angle. To solve this problem,it is essential to obtain efficient and robust features from theRCS of a target, and therefore, range profiles, inverse syntheticaperture radar (ISAR) images, natural frequencies, and time-frequency signatures have been used for this purpose.

Range profiles of complex radar targets are the most easilyobtainable feature vectors of the conventional radars. The rangeprofile shows the RCS distribution of a target along the radialdistance, which can provide information on the position andscattering strength of the target’s scattering centers at that as-pect [1]. One difficult problem with the range profile for usein target recognition is that it is highly aspect-dependent, anda large amount of data storage is required to provide adequatetarget recognition performance. Another problem is that its res-olution has a significant effect on the final recognition results,and the range profiles of low resolution cannot provide robustand reliable feature vectors for target recognition. ISAR im-

Manuscript received May 23, 2001. This work was supported by the KoreanAgency for Defense Development under Contract EM-44 and by the Ministryof Education of Korea under the BK 21 program.

K.-T. Kim is with the Department of Electrical Engineering and ComputerScience, Yeungnam University, Kyongsan, Kyongbuk, 712-749, Korea.

D.-K. Seo is with the Graduate School for Information Technology, PohangUniversity of Science and Technology, Pohang, Kyungpook 790-784, Republicof Korea (e-mail: [email protected]).

H.-T. Kim is with the Electrical and Computer Engineering Division, PohangUniversity of Science and Technology, Pohang, Kyungpook 790-784, Republicof Korea (e-mail: [email protected]).

Publisher Item Identifier S 0018-926X(02)02623-6.

ages show two-dimensional (2-D) RCS distribution of a targetin the down-range and cross-range domain [2]. Although theycan provide information about the 2-D position and strength ofthe scattering centers on the target, a sophisticated motion com-pensation algorithm to compensate for the translational and ro-tational motion of a moving target is needed to generate reli-able ISAR images [3]. In addition, a huge amount of memoryspace is necessary to store the ISAR images for many aspectsand target classes. Therefore, ISAR images may not be suitablefor real-time target recognition due to their computational com-plexity.

Natural frequencies extracted from the late time responsesof a target are aspect-independent, resulting in efficient featurevectors for target recognition [4]–[6]. However, for conventionalhigh-frequency operating radars, the energy of the resonancecontained in the late time portion of a signal is too small and iseasily corrupted by noise. This is because no significant naturalfrequencies are excited in terms of the target’s size and givenhigh-frequency band. Therefore, it may be impossible to ex-tract accurate natural frequencies of a target in a real situation.Recently introduced time-frequency signatures have some ad-vantages over the range profiles or natural frequencies: they areable to show both early time responses such as scattering centersand late time responses such as resonance in a time-frequencyplane [7]–[9]. However, they have a prohibitive memory spaceproblem as in ISAR images, and resonance responses may notbe identified in the time-frequency plane for the same reason asin natural frequencies.

Here, we consider range profiles as feature vectors for targetrecognition. Li and Yang [1] have developed a strategy based onrange profile and used matching scores as a decision rule thatutilizes normalized correlation coefficients. According to theiralgorithm, the matching score is defined as the maximum valueof the correlation coefficients for all linear translational shiftsbetween two range profiles. Therefore, their computationalcomplexity grows rapidly as the number of target classes andaspect angles increases, unless accurate information aboutthe target’s aspect is available. Moreover, the enhancementof range resolution for the improvement of recognition ac-curacy increases the number of translation shifts to obtain amatching score between two range profiles, resulting in anadditional computational cost. In view of target recognition,the matching score is robust against amplitude variations in therange profiles, but it is dominated by the strongest peak, whichdoes not always originate from the same target. In addition tothe above technique by Li and Yang, other correlation-basedtechniques have been proposed to compress the database fortarget recognition [10], [11].

0018-926X/02$17.00 © 2002 IEEE

326 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 50, NO. 3, MARCH 2002

Zyweck and Bogner [12] used the magnitude of the Fouriertransform of the preprocessed range profile to provide transla-tion-invariant feature vectors. The feature vector based on thistechnique is the same regardless of the location of the targetin the range window, so translational shifts, as in the case ofmatching scores, are not necessary. However, its dimension isstill very large for high-resolution range profiles, and a largeamount of storage is required to guarantee successful classifica-tion performance.

In this paper, we propose a recognition scheme based onthe superresolution range profiles of the Multiple Signal Clas-sification (MUSIC) algorithm and central moment features,which guarantee the translational invariance. Note that nearlyall methodologies for target recognition discussed earlier arebased on the range profiles obtained by conventional inversefast Fourier transform (IFFT). Of course, much research hasfocused on the improvement of range resolution throughsuperresolution techniques such as MUSIC [13], maximumlikelihood [14], maximum entropy method [15], and Prony[16], but studies about their application to target recognitionare rare. After the super-resolved range profiles are producedusing the MUSIC algorithm, each range profile is normalizedto its maximum amplitude in order to guarantee amplitude level(scattering strength) invariance. Next, central moment featuresof normalized range profiles are computed to provide transla-tional invariance. Therefore, the central moment feature vectorsof the normalized range profile have both the translation andlevel invariance, and hence they are dependent not on the posi-tion or overall amplitude level of the target response but only onits shape. Next, they are transformed into values between zeroand unity to have the same “weight” in the Euclidean featurespace. Next, the principal component analysis (PCA) is appliedin order to eliminate their redundancy, resulting in featurevectors of a much smaller dimension. The resulting smalldimensional features are combined with the Bayes classifier,based on the statistics of the data set. Experimental resultsusing five aircraft models measured at the Pohang Universityof Science and Technology (POSTECH) compact range facilityare presented to demonstrate the performance of the proposedtechnique. These results are compared with those of the rangeprofiles obtained by IFFT.

II. PROPOSEDSCHEME

A. Superresolved Range Profiles Using the MUSIC Algorithm

It was noted that a radar with higher range resolution canprovide not only better recognition performance but also bettertolerance to aspect variation, yielding significant advantage insaving memory space for establishing the database [17]. There-fore, it is crucial to enhance the range resolution for an efficienttarget recognition system. In a practical situation, however, thefrequency bandwidth of a radar system is often limited by sev-eral factors, and the range profiles obtained by IFFT often resultin a limited range resolution. In contrast, it is well known thatthe MUSIC algorithm provides superresolved range profiles ofa target compared with those of the conventional IFFT for thesame frequency bandwidth [13], [18]. Of course, the computa-tional complexity of the MUSIC algorithm is much larger than

IFFT, but recently, the MUSIC processing can be completedwithin a real time due to the emergence of high-speed proces-sors.

In the high-frequency region, the electric field backscatteredfrom a complex radar target can be modeled approximately bya sum of fields scattered from some dominant scattering centerson the target. Therefore, the measured high-frequency RCSatfrequency can be represented using undamped exponentialsas

(1)

where is the location of the th scattering center, is theassociated amplitude, is the number of scattering centers onthe target, is the measurement noise, is the number offrequency measurements, andis the speed of light.

Rewriting (1) in vector notation, it can be expressed as

(2)

where

In the above, is an data vector, is an matrix,is a direction vector of length is an 1 amplitude

vector, and is an 1 noise vector.To obtain superresolution range profiles using the MUSIC

algorithm, the covariance matrix of the received signalshould be estimated. If the noisesare assumed to be uncor-related and to have identical variance, the covariance matrix

is defined as

(3)

where is the identity matrix and denotescomplex conjugate transpose. Because the exact covariancematrix in (3) is an average over a number of snapshots butonly one snapshot is available in radar applications, a specialtechnique known as spatial smoothing preprocessing (SSP)may be used to estimate [19]. However, modified spatialsmoothing preprocessing (MSSP) has been shown to exhibit animproved performance over SSP in decorrelating signals fromvarious scattering centers [18].

Applying the MSSP, the covariance matrix can be estimatedas follows:

(4)

KIM et al.: EFFICIENT RADAR TARGET RECOGNITION 327

where

......

...

In (4), is the number of subarrays, is the subarray dimen-sion, is the exchange matrix, anddenotes complexconjugate. is the data vector of theth subarray of size ,as shown in Fig. 1.

It should be noted that, as shown in Fig. 1 and (4), the resolu-tion of the MSSP is reduced, since the effective bandwidth de-creases from to . In spite of this disadvantage, the MUSICalgorithm combined with the MSSP gives a much better perfor-mance than the conventional IFFT [18]. In the MSSP, the decor-relation effect is obtained at the expense of a reduced effectivebandwidth. If increases, the resolution of the MUSIC algo-rithm improves, but the decorrelation performance between sig-nals from different scattering centers is degraded. In contrast, as

decreases, the decorrelation performance improves, whereasthe resolution is degraded. Therefore, in terms of target recog-nition, there are some tradeoffs in choosing. That is, if islarge, the MUSIC algorithm can provide range profiles of highresolution but some dominant scattering centers may not be de-tected due to the degradation of the decorrelation performance,and vice versa.

Using the MUSIC algorithm, we can estimate the superre-solved range profile of a target as

(5)

where is the eigenvectors corresponding to the minimum(noise) eigenvalues of . Note that the MUSIC algorithmtakes advantage of the fact that the direction vector isorthogonal to the noise subspace consisting of noiseeigenvectors .

In (5), the selection of plays an important role in the stableoperation of the MUSIC algorithm. If the estimatedis lessthan true may miss some dominant scattering cen-ters on the target, whereas if it is greater than, spurious peaksmight appear. For an accurate estimation of, the information-based criteria such as Akaike information criterion and min-imum description length can be used [20], [21], but they arecomputationally intensive and furthermore they often fail to pre-dict accurate values of for noise-corrupted signals. On theother hand, from empirical studies in [18], a sharp spurious peakdid not appear even when the estimatedis larger than sincean orthogonality relationship between the direction vectorand noise eigenvectors still holds whenis larger than

.

B. Feature Extraction Based on Central Moments

Moments and functions of moments have been utilized as pat-tern features in a number of applications to achieve invariant

Fig. 1. Subarray configuration for the MSSP.

recognition of 2-D image patterns [22]–[26]. To guarantee thetranslation, scale, contrast, and rotation invariance, various mo-ments such as Hu moment invariants, Zernike moments, Le-gendre moments, and complex moments have been used in the2-D pattern recognition community [27]. However, in this study,we only need translational and scale (level) invariance to clas-sify one-dimensional (1-D) image (i.e., range profile) patterns.In 1-D pattern recognition, the level invariance can be accom-plished through an appropriate preprocessing proposed in thispaper, and the simple central moments satisfy the translationalinvariance [22].

For a fixed bandwidth and polarization, the range profile ofa target measured by the radar depends on the distance and as-pect between the radar and target. That is, for a fixed aspect,the returned signal from the target decays as it travels, and itsrange profile from a far-away target has the target responses withlow amplitude levels, and vice versa. However, in general, theoverall shape of the target response of a specific target does notchange with the distance when the aspect is fixed, and absoluteamplitude of target response has no significant meaning. There-fore, in order to construct the database for target recognition, weneed only to store the shapes of the range profiles as a functionof aspect rather than as a function of distance, resulting in signif-icant savings of computational resources. To meet this require-ment, the range profile of a target at each aspect is normalizedto its value of maximum peak (strongest scattering center), andtherefore the range profile does not depend on the distance butonly on the aspect. Furthermore, this normalization reduces theaspect dependence or weight of the signal levels of the target’sresponses. The overall amplitude levels of the range profileswithin the same target fluctuate with the aspect, and its levels atcertain aspects may be much higher than those at other aspects.This may cause a significant difference between the two rangeprofiles of a target at two different aspects even though theirrelative shapes are similar, yielding unwanted bias or weight inthe feature space domain. Using the above normalization, twosimilar-shaped range profiles of a target at two different aspectsguarantee their closeness in the Euclidean feature space eventhough their overall amplitude levels are quite different. Hence,for each target class, the features at various aspect angles arewell grouped together to form a cluster in the feature space do-main. As a result, the desired level invariance has been achieved


through this preprocessing, and the discrimination between dif-ferent target classes can be performed only by the shapes of nor-malized range profiles, not by their signal levels.

The th order central moments of a function are de-fined as

(6)

where

The central moments are projections onto sothat they become invariant under translation, but note that theyhave substantial redundancy since the monomialsare not orthogonal. In [27], the information redundancy ofthe geometric moments, which is equivalent to that of thecentral moments, was analyzed to show the ratio between theinformative part and redundant part as a function of momentorder . According to the results, the ratio decays exponentiallyas increases, and this implies that the information containedin the high-order central moments is already provided in thelower order central moments. This problem can be circum-vented by the use of orthogonal moments such as Zernikeor Legendre moments, which are based on the theory oforthogonal polynomials. However, in the presence of noise,the geometric moments, i.e., the central moments, are morerobust than the Zernike and Legendre moments [27]. Becausethe range profiles of a target are often corrupted by noise, thecentral moments may provide more stable features for targetrecognition than other orthogonal moments. Furthermore, theredundancy contained in the central moments can be effectivelyeliminated by the principal component analysis (PCA), to bediscussed later.

After the preprocessing and discrete sampling of the rangeprofile in (5), its th order central moment can be computed by

(7)

where

where is the normalized range profile after the prepro-cessing, is the number of range bin sampling, and is themaximum unambiguous range.

Note that the noise terms outside of the target response inthe range profile may have an effect on the final value of thecentral moments in (7). As the noise power contained in thereceived signal increases, spurious peaks due to noises appearin the range profile . In general, since the target responseis concentrated on a limited region of in the range profile,the remaining part of the range profile excluding the target re-sponse is often corrupted by noise, resulting in many spuriouspeaks. Therefore, the central moments from the noise-corrupted

range profile may be more unstable as the number of range binsampling increases, though the noise power contained in thereceived signal is negligibly small. This problem can be miti-gated using the range window around the target response. Be-cause the distance information from the radar to the target isavailable in any conventional radar, we select only the rangeprofile around the target response, and the s outside ofthe target response are set to zeros.

We also note that the magnitude of moments may grow expo-nentially with increasing order. This problem may cause thecentral moments with higher orders to be more sensitive to noiseor quantization error, resulting in unstable features, and can bemitigated by mapping the range valuesinto [0, 1] rather than[0, ]. This mapping can be achieved by choosing the resolu-tion of range bin sampling as , yielding

. Therefore, the magnitude of central moments de-cays exponentially with increasing order, and it may be lesssensitive to noise or quantization error.

Using the central moments in (7), the feature vectorcan berepresented as

(8)

where is the maximum order of central moments used toform a feature vector. The selection of is dependent on thespecific problem at hand. Note that there is no absolutely rightway of choosing optimum . For the feature extraction froma complex 2-D image, it is necessary to compute the momentsup to high orders since high-frequency spectral contents suchas edges and corners cannot be described only with low-ordermoments. However, the computational cost increases with anincrease in , but a too large value of does not im-prove classification accuracy. For example, seven different mo-ment invariants derived by Hu [22] are composed of central mo-ments only from zeroth to third order, which were successfullyapplied to classify 2-D image patterns. For representing a 1-Drange profile in this study, we think that a too large value ofmay add a computational burden without improving recognitionaccuracy because the central moments have more informationredundancy as the orderincreases. Furthermore, the higherorder moments are more sensitive to additive white Gaussiannoise (AWGN) [27]. From several experiments in this study, wefound that is sufficient for classifying 1-D range pro-files from different targets, but a smaller value may be enoughto guarantee the classification accuracy for range profiles withsmaller amplitude variations.

To design a classifier, it is necessary to construct a trainingdatabase containing feature vectors of many target classes andaspect angles. For target classes and aspects used fortraining, we can obtain the training databaseusing (8) as fol-lows:

......

...(9)

where and is a matrix.


Because the magnitudes of central moments obtained in (8)decrease rapidly as the order increases, the magnitude of ele-ment in also decreases rapidly asincreases for any fixed. However, the obtained central moments should have the same

“weight” in the Euclidean feature space irrespective of ordersfor improving classification accuracy. Therefore, we transformthe elements of into values between zero and unity to provideequal weight in each dimension of the feature space as follows:

(10)

where

minimum for a given

maximum for a given

and therefore the normalized training databaseis establishedas follows:

......

...(11)

Note that any test data for demonstrating the performance of theproposed technique in this paper will also be normalized using(10) from the training database.

C. Redundancy Reduction Using Principal ComponentAnalysis

As discussed earlier, the central moment features show moreredundant information as the orderincreases. The redundancycontained in the feature vectors often adds the computationalcost to the classifier stage without increasing recognition ac-curacy. To deal with this difficulty, the PCA is applied to thenormalized training database. With the PCA, the redundancycontained in the features can be effectively reduced, and further-more the dimensionality reduction can be achieved [28]. That is,the transformation based on the PCA is designed in such a waythat the data set may be represented by a reduced number of “ef-fective” features and yet retain most of the intrinsic informationcontent of the data.

Let be the th column vector of the normalized trainingdata matrix in (11)

(12)

Next, the sample mean vector and the sample covariancematrix can be obtained by

(13)

(14)

where is a 1 vector and is a matrix.Let the eigenvalues of be denoted by

and the associated

eigenvectors be denoted by . Then, thesample covariance matrix can be decomposed as follows:

(15)

where

Then, the transformation matrix can be constructed usingand is given by

(16)

where and are the eigenvectors corre-sponding to the largesteigenvalues. The remainingeigenvalues are negligibly small. Each feature vector of dimen-sion from both the training data set and the test data setcan be transformed into a new feature space of dimensionasfollows:

(17)

Note that the sample mean and sample covariance matrix arecomputed from the training data set only, and the same trans-form matrix is used for redundancy elimination in both trainingand test samples.

After the PCA, variances of high-order components of a newfeature vector are near zero since redundancy in the originalfeature space is removed. Therefore, high-order components inthe new feature vector can be ignored, and the original featurespace can be reduced to a new feature space whose dimensionis smaller than .

The compression ratio is dependent on how much re-dundant information is contained in the feature vectors. In thisstudy, the redundant information may increase as the maximumorder used to form a feature vector in (8) increases becausehigher order central moments have more redundancy. There-fore, the value of does not increase if is larger than acertain threshold because the number of largest eigenvalues of

no longer increases. We found that is the typ-ical threshold for the range profiles of the five targets used inthis study.

D. Bayes Classifier

We have now final training feature vectorsto design a classifier to classify a test feature

vector whose class is unknown. In this paper, one of thewell-known statistical methods, Bayes classifier, is selected toperform classification of .

The Bayes classifier is optimum in the sense of probabilityof error, and it is a parametric procedure [29]. Therefore, it re-quires the joint probability density function of the feature ofeach class as well as thea priori probability of each class. How-ever, such information is not available in general, and it shouldbe estimated from the training feature vectors. Usually, the dis-tribution of the training data set is assumed to be a multivariatenormal, and a priori probability of each class is the same. Wetake the above assumption for simplicity since the preprocessing


and feature extraction techniques mentioned in the previous sec-tions may provide the feature vectors to be well clustered acrossthe aspects. Hence the assumption of the multivariate normaldistribution may be valid.

Supposing that the training features have a multivariatenormal distribution and equal class probability, the Bayes ruledetermines the class of test feature vectoras

(18)

with

(19)

where and are the sample mean vector and sample co-variance matrix of class, respectively, andvaries from one to

since we have target classes.

III. A LGORITHM SUMMARY

So far, the proposed scheme for target recognition has beendiscussed in detail, and it is summarized as follows.

1) For target classes and aspects used for training,compute range profiles using the MUSIC spectrum esti-mator in (5).

2) Normalize each range profile using its maximum peak.3) Apply the range window to the normalized range profile

.4) Compute the central moments up to order using

(7) but with where the resolution of range binsampling is equal to .

5) Construct the training database.6) Map each element of into values between zero and

unity using (10), resulting in .7) Apply the PCA to the column vectors ofto obtain the

transformation matrix .8) With the use of , transform the column vectors of

into where .9) Design a Bayes classifier in (18) and (19) using the ob-

tained training feature vectors .10) For any target and aspect used for testing, perform Steps

1)–4), 6), and 8) to obtain the test feature vectorwhose class is unknown, and identify its class using thedesigned Bayes classifier in Step 9).

Note that the transformations of feature vectors in Steps 6) and8) are based on the training data samples only, and the sametransformations are applied to both the training and test featurevectors. In the proposed procedures described above, Step 1)can be replaced with range profiles from other superresolutionspectrum estimators or IFFT.

The computational bottleneck of the training phase occurs inSteps 1) and 7) because they need computationally intensiveeigendecomposition, and the major computational cost in thetesting phase comes from Step 1) only. In Step 1), the dimen-sion of the covariance matrix is , where is a sub-array dimension that we select, and the MUSIC algorithm re-quires the eigendecomposition of . Therefore, the selectionof subarray dimension is most important in reducing the com-putation time for both the training phase and the testing phase.

As decreases, the computation time may be reduced, but theresolution is degraded, and vice versa. For computational effi-ciency, IFFT can be used in Step 1) instead of MUSIC. How-ever, the MUSIC algorithm can provide range profiles of muchhigher resolution than those of the IFFT, and therefore the pro-posed technique can ensure the successful correct classificationrate even for a relatively small value of, as will be shown inthe next section.

IV. EXPERIMENTAL RESULTS

To demonstrate the proposed technique, we chose five dif-ferent aircraft models shown in Fig. 2. Their physical sizes areabout 1 m, and their RCS were measured at the POSTECH com-pact range facility. The frequency bandwidth of the measure-ments ranges from 8.3 to 12.3 GHz (X-band) with a 0.01-GHzincrement, yielding 401 frequency samples, and aspect anglesin the azimuth plane ranges from 30.2to 59.8 with respect tothe target’s head using a 0.4step, resulting in 75 aspects foreach target. The elevation angle of each target is fixed at 0.Both the horizontally transmitting–horizontally receiving (HH)and vertically transmitting–vertically receiving (VV) polariza-tions were used for the measurements.

Note that the size of each target at a frequency of 10 GHzis merely about 33 wavelengths, and therefore some small sub-structures on each target may be in the resonance region ratherthan in the high-frequency region. On the other hand, the sizeof an actual aircraft whose physical size is 30 m corresponds to1000 wavelengths at 10 GHz, and its substructures are strictly inthe high-frequency region. In addition, the range resolution ofthe measured 4-GHz bandwidth is 3.75 cm, and the response of atarget with 1 m dimension is represented only about 27 Fourierbins in the range profile domain. However, an actual target of30 m dimension corresponds to 800 Fourier bins for the samebandwidth. Therefore, the experimental setup in this study is avery difficult condition for target recognition compared to thatof a real situation consisting of an actual-sized target under anX-band operating radar.

Fig. 3 shows the RCS values for the five targets measured atthe POSTECH compact range. It is clearly observed from thisfigure that the RCS of each target is highly dependent on itsaspect angle. For example, Fig. 3(a) and (c) shows that the RCSaround the angle 35is much larger than other aspect regions.Furthermore, as previously mentioned, resonant-like scatteringat 9 and 12.3 GHz, which is independent of aspect angle, isseen in Fig. 3(d). Note that the absolute RCS levels of the fivetargets are all different, and Target 4 has much lower RCS valuesthan the others. Therefore, the absolute amplitude levels of therange profiles for the five targets are different, but the proposedtechnique in this paper uses their shapes only irrespective oftheir levels. Using the RCS data at an aspect of 30.2in Fig. 3,the normalized range profiles of the MUSIC algorithm and IFFTfor the five targets are shown in Fig. 4.

Before target recognition experiments, the data sets must bedivided into a training set and a test set. We have five targetclasses, and the data set from each target includes 75 aspects. So

(number of target classes) (number of aspects)


Fig. 2. Five aircraft models to demonstrate the proposed technique.

data sets must be subdivided with respect to their aspectsto form a training set and a test set. Assume the trainingdata set comes from uniform angle sampling with an in-crement of 1.6, corresponding to 19 aspects for eachtarget. Therefore, we have (number of target classes)

(number of aspects for training) data sets forconstructing the training database, and the remaining

data sets are reserved for testing. Hence thetraining set size is only % of the overall dataset, resulting in 74.67% for testing. Table I shows the sizes oftraining sets and test sets for three different angle incrementsused for training in this study. The experimental results to bedemonstrated later are based on one of the three data sets inTable I.

A. Effect of Subarray Dimension

As discussed earlier, the selection of the subarray dimensionis crucial to the stable operation of the MUSIC algorithm

and therefore to successful target recognition. Since the MSSPis used to estimate the covariance matrix , one can success-fully apply the MUSIC algorithm to this smoothed covariancematrix regardless of the coherence of the signals. However, thisrobustness comes at the expense of a reduced effective band-width. The number of subarrays is given by ,where is the number of frequency samples. Becauseisfixed in general, the increase of reduces the number of subar-rays , and therefore the decorrelation performance of MSSPis degraded. Further, the decrease ofreduces the effectivebandwidth, degrading the resolution of the MUSIC estimator.


(a)

(b) (c)

(d) (e)

Fig. 3. Angle versus frequency display of the RCS for the five targets at the fixed elevation angle 0: frequency bandwidth= 8:3–12:3 GHz with a frequencystep of 0.01 GHz, azimuth angle region= 30:2 –59:8 with an angle step of 0.4, and HH polarization. The color levels represent RCS values in dB. (a) Target1, (b) Target 2, (c) Target 3, (d) Target 4, and (e) Target 5.

On the other hand, the decorrelation performance is improved.For a target consisting of scattering centers, the number ofsubarrays must be greater than or equal to

in order to guarantee the successful decorrelation ofco-herent signals, and also must be at least 1. Therefore,the minimum number of frequency samplingis equal to 2[18]. The subarray dimension has been chosen such that theeffective bandwidth is about half the available bandwidth, i.e.,

, to ensure the required resolution in ISAR images[30].

To investigate the performance of the proposed technique interms of the subarray dimension, we utilized SET-1 to esti-mate the correct recognition rate, which is given by

Number of correct classificationsNumber of test samples

(20)

The polarization was chosen as HH, and was usedfor the MUSIC algorithm to estimate at least 30 scattering cen-ters on the target. When the number of scattering centers on the


(a)

(b) (c)

(d) (e)

Fig. 4. Normalized range profiles obtained by MUSIC and IFFT: frequency bandwidth= 8:3–12:3 GHz, aspect angle= 30:2 , and HH polarization. Thedashed lines come from the 401-point IFFT, and the solid lines come from the MUSIC algorithm withm = 134; L̂ = 30 andN = 401. (a) Target 1, (b) Target2, (c) Target 3, (d) Target 4, and (e) Target 5.

target is less than 30, spurious peaks may appear, but the majorportion of the spurious peaks can be effectively reduced by arange window of 3 m in length. was used to samplethe range profile of the MUSIC algorithm, and wasused to compute the central moments of the range profiles. Afterthe PCA, the largest seven eigenvalues are kept to produce thetransformation matrix , and therefore, the dimension of thefinal feature vector, is seven. Note that in the case of ,a large compression ratio of can beachieved via the proposed algorithm based on central moments

and PCA. The results of as a function of are shown inFig. 5.

In Fig. 5, the horizontal axis denotes the effective bandwidth, and the vertical axis denotes the correct recognition rate

. We performed the experiments based on three differentbandwidths, 2, 3, and 4 GHz, and the correspondings are

and , respectively. In the caseof the 2 GHz bandwidth, slowly decreases when islarger than the threshold 0.3. The respective threshold values of

for 3 and 4 GHz bandwidths are 0.4 and 0.5. For


TABLE ISUBDIVISION OF TRAINING AND TESTDATASETS(EQUIVALENT PERCENTAGESWITH RESPECT TO THEOVERALL DATA SIZE ARE GIVEN IN PARENTHESES)

Fig. 5. P versus effective bandwidthm=N display using the SET-1 and HHpolarization. The data with a 2 GHz bandwidth: 8.3–10.3 GHz,N = N =

201; L̂ = 30; p = 20, and l = 7. The data with a 3 GHz bandwidth:8.3–11.3 GHz,N = N = 301; L̂ = 30; p = 20, andl = 7. The datawith a 4 GHz bandwidth: 8.3–12.3 GHz,N = N = 401; L̂ = 30; p =

20, andl = 7.

TABLE IICONFUSIONMATRIX OF THE MUSIC ALGORITHM USING SET 2AND HH

POLARIZATION. THE SELECTED PARAMETERS ARE: BANDWIDTH = 8:3–12:3GHz,N = N = 401;m = 134; L̂ = 30; p = 20, AND l = 7 (OVERALL

CORRECTRECOGNITION RATE P = 99:64%)

values smaller than each threshold,reaches 100% irrespec-tive of bandwidth. Note that maintains 100% even for arelatively small since the MUSIC algorithm can providesuperresolved range profiles even for a small bandwidth. Thedecrease of when is larger than each threshold comesfrom the fact that , the number of subarrays, decreases as

increases, and this degrades the decorrelation performanceof the MSSP. Furthermore, as (i.e., bandwidth) decreases,the threshold decreases due to the decrease in the availablefor the same . The computational complexity increases with

TABLE IIICONFUSIONMATRIX OF THE MUSIC ALGORITHM USING SET 2AND VV

POLARIZATION. THE SELECTED PARAMETERS ARE: BANDWIDTH = 8:3–12:3GHz,N = N = 401;m = 134; L̂ = 30; p = 20 AND l = 7 (OVERALL

CORRECTRECOGNITION RATE P = 99:64%)

the increase of since the eigendecomposition of withthe size of is needed to compute the superresolvedrange profile of the MUSIC estimator. Considering the abovethree conflicting requirements of resolution, decorrelation, andcomputation time, we select the subarray dimensionsuchthat , which will be used for all later experiments.

Tables II and III show the confusion matrices of the proposedscheme using SET 2 in Table I. The polarizations in Tables II andIII are based on HH and VV, respectively, and the bandwidth of4 GHz is used, resulting in . Therefore, we selectedthe subarray dimension as in order to satisfy

. Note that only one incorrect classification is observed inboth tables, and the corresponding overall correct recognitionrate is %. This result confirms that theprevious assumption of the multivariate normal distribution ofthe training data set across the aspects is valid, and implies thatthe training features from different targets are well separatedfrom each other in the feature space.

Tables IV and V show the confusion matrices of the proposedscheme replacing Step 1) in Section III with the conventionalIFFT. The data set used for this experiment and associated pa-rameters are the same as in the previous experiment. Note thatthe results in Tables II and III are improved over those of Ta-bles IV and V due to the poor resolution of the IFFT.

B. Effect of Bandwidth

To investigate the performance of the proposed technique interms of bandwidth, we performed the classification experi-ments using SET 1, and its bandwidth is varied from 2 to 4 GHzwith a 1-GHz step. The selected bandwidths are 8.3–10.3 GHz,8.3–11.3 GHz, and 8.3–12.3 GHz, and associated fractionalbandwidths are 21.51%, 30.61%, and 38.83%, respectively.


TABLE IVCONFUSIONMATRIX OF THE IFFT USING SET 2AND HH POLARIZATION.

THE SELECTED PARAMETERS ARE: BANDWIDTH = 8:3–12:3 GHz,N = N = 401; p = 20 AND l = 7 (OVERALL CORRECT

RECOGNITION RATE P = 97:86%)

TABLE VCONFUSIONMATRIX OF THE IFFT USING SET 2AND VV POLARIZATION.

THE SELECTED PARAMETERS ARE: BANDWIDTH = 8:3–12:3 GHz,N = N = 401; p = 20 AND l = 7 (OVERALL CORRECT

RECOGNITION RATE P = 87:86%)

The polarization was chosen as VV. In addition, Step 1) in Sec-tion III was replaced with the IFFT, and the same classificationexperiments were performed. The results are shown in Fig. 6.

In Fig. 6, one can see that the performance of the proposedtechnique based on MUSIC or IFFT is very robust to the band-width variations. However, the results of the MUSIC are muchsuperior to those of the IFFT due to its increased resolution forthe same bandwidth.

C. Effect of Training Set Size

An efficient target recognition system should provide suffi-cient recognition accuracy even though the training set size issmall. The small size of the training set implies that the trainingdatabase can be efficiently compressed, and it provides signif-icant advantages in terms of memory storage and computationspeed.

Figs. 7 and 8 show the values versus the training set size forthe case of HH and VV polarizations, respectively. We used allthree data sets in Table I, i.e., SET 1, SET 2, and SET 3, and se-lected the bandwidth to be 4 GHz. In Figs. 7 and 8, the proposedscheme, whether it is combined with MUSIC or with IFFT, isrobust to the training set size, but the results of the MUSIC aresuperior to those of the IFFT. For the typical five targets usedin this study, values of the VV polarization are much morerobust to the training set size than those of the HH polariza-tion. From these figures, it is shown that the proposed techniquecombined with MUSIC can successfully identify different tar-gets only using the training data set consisting of 13.33% of theoverall data set.

Fig. 6. P versus fractional bandwidth display using SET 1 and VVpolarization. The parameters with a 2 GHz bandwidth: 8.3–10.3 GHz,N = N = 201;m = 67; L̂ = 30; p = 20, andl = 7. The parameterswith a 3 GHz bandwidth: 8.3–11.3 GHz,N = N = 301;m = 100; L̂ =

30; p = 20, andl = 7. The parameters with a 4 GHz bandwidth: 8.3–12.3GHz,N = N = 401;m = 134; L̂ = 30; p = 20, andl = 7. TheMUSIC and IFFT share the same parameters above, but the IFFT does notrequire the two parametersm andL̂.

D. Effect of Additive Noise

To evaluate the performance of the proposed scheme in anoisy environment, the measured RCS in Fig. 3 was contam-inated by AWGN to achieve the desired signal-to-noise ratio(SNR) from 0 to 40 dB with a 10-dB step. Note that the ac-tual noise level contained in the data may be somewhat higherthan the desired noise level since the measurement noise levelwas not considered in the process of noise addition. SET 1 witha 4-GHz bandwidth and HH polarization were used, and weperformed ten Monte Carlo simulations using ten independentAWGN at each SNR. The resultant tens are averaged to ob-tain more reliable results.

Fig. 9 shows the result of the proposed technique combinedwith MUSIC. The error bars around estimated values inFig. 9 mark one (estimated) standard deviation above and belowthe estimated values. The averaged s decrease, and theirstandard deviations increase slowly with the decrease of SNR.

is larger than 60% even when SNR is 0 dB.The result of the proposed technique combined with the IFFT

is presented in Fig. 10. We observe that the estimatedvaluesare significantly decreased for SNR levels below 20 dB, andtheir standard deviations are large. Comparing Figs. 9 and 10,it can be seen that the MUSIC algorithm is much more robustto noise than IFFT, and therefore has significant advantages ina noisy environment.

V. CONCLUSION

A new target recognition scheme based on range profiles hasbeen proposed and analyzed. The proposed scheme utilizes theMUSIC algorithm and central moments features in additionto the appropriate preprocessing. The proposed features havetranslation and level invariance, which are essential to suc-cessful target recognition based on range profiles. The Bayes


Fig. 7. P versus training set size display using SET 1, SET 2, SET 3,and HH polarization. The selected parameters for the MUSIC algorithm are:bandwidth= 8:3–12:3 GHz,N = N = 401;m = 134; L̂ = 30; p =

20, andl = 7. The MUSIC and IFFT share the same parameters above, but theIFFT does not require the two parametersm andL̂.

Fig. 8. P versus training set size display using SET 1, SET 2, SET 3,and VV polarization. The selected parameters for the MUSIC algorithm are:bandwidth= 8:3–12:3 GHz,N = N = 401;m = 134; L̂ = 30; p =

20, andl = 7. The MUSIC and IFFT share the same parameters above, but theIFFT does not require the two parametersm andL̂.

classifier recognizes target types using the proposed features,and the results show that the proposed scheme has significantadvantages in radar target recognition. For the stable operationof the algorithm, we have derived a criterion for selecting sub-array dimensions of the MSSP by considering three conflictingrequirements such as resolution, decorrelation, and computa-tion complexity. Moreover, in view of the bandwidth, trainingset size, and noise sensitivity, it was shown that the MUSICalgorithm outperforms the conventional IFFT at the cost ofcomputation time. The efficiency of the proposed algorithmcomes from two major facts: the superresolved range profilescaused by the MUSIC algorithm and small dimensional fea-tures caused by the central moments and PCA. It is well known

Fig. 9. P of MUSIC versus SNR display using SET 1 and HH polarization.The selected parameters for the MUSIC algorithm are: bandwidth= 8:3–12:3GHz,N = N = 401;m = 134; L̂ = 30; p = 20, andl = 7.

Fig. 10. P of the IFFT versus SNR display using SET 1 and HH polarization.The selected parameters for the IFFT are: bandwidth= 8:3–12:3 GHz,N =

N = 401; p = 20, andl = 7.

that range resolution is crucial to data compression across theangular domain and improvement of recognition accuracy. Inaddition, the small dimensional features can reduce memorystorage and computation time during the classification stage.

The proposed technique in this paper can be combined withrange profiles from other superresolution techniques, and com-bined with other classification techniques such as classical pat-tern classifiers and neural networks. These issues may be thearea of future research.

REFERENCES

[1] H. J. Li and S. H. Yang, “Using range profiles as feature vectors to iden-tify aerospace objects,”IEEE Trans. Antennas Propagat., vol. 41, pp.261–268, Mar. 1993.

[2] D. L. Mensa, High Resolution Radar Cross-Sec-tion Imaging. Norwood, MA: Artech House, 1991.

[3] D. R. Wehner,High Resolution Radar, 2nd ed. Boston, MA: ArtechHouse, 1994.


[4] E. Rothwell, D. P. Nyquist, K. M. Chen, and B. Drachman, “Radar targetdiscrimination using the extinction-pulse technique,”IEEE Trans. An-tennas Propagat., vol. AP-33, pp. 929–937, Sept. 1985.

[5] K. M. Chen, D. P. Nyquist, E. J. Rothwell, L. L. Webb, and B. Drachman,“Radar target discrimination by convolution of radar returns with extinc-tion pulses and single-mode extraction signals,”IEEE Trans. AntennasPropagat., vol. AP-34, pp. 896–904, July 1986.

[6] J. E. Moony, Z. Ding, and L. S. Riggs, “Robust target identification inwhite Gaussian noise for ultra wide-band radar systems,”IEEE Trans.Antennas Propagat., vol. 46, pp. 1817–1823, Dec. 1998.

[7] A. Moghaddar and E. K. Walton, “Time-frequency distribution analysisof scattering from waveguide cavities,”IEEE Trans. Antennas Prop-agat., vol. 41, pp. 677–680, May 1993.

[8] L. C. Trintinalia and H. Ling, “Interpretation of scattering phe-nomenology in slotted waveguide structures via time-frequencyprocessing,”IEEE Trans. Antennas Propagat., vol. 43, pp. 1253–1261,Nov. 1995.

[9] H. Kim and H. Ling, “Wavelet analysis of radar echo from finite-sizedtargets,”IEEE Trans. Antennas Propagat., vol. 41, pp. 200–207, Feb.1993.

[10] E. J. Rothwell, K. M. Chen, D. P. Nyquist, J. E. Ross, and R. Beber-meyer, “A radar target discrimination scheme using the discrete wavelettransform for reduced data storage,”IEEE Trans. Antennas Propagat.,vol. 42, pp. 1033–1037, July 1994.

[11] Q. Li, E. J. Rothwell, K. M. Chen, and D. P. Nyquist, “Radar target dis-crimination schemes using time-domain and frequency-domain methodsfor reduced data storage,”IEEE Trans. Antennas Propagat., vol. 45, pp.995–1000, June 1997.

[12] A. Zyweck and R. E. Bogner, “Radar target classfication of commercialaircraft,” IEEE Trans. Aerosp. Electron. Syst., vol. 32, pp. 598–606, Apr.1996.

[13] R. O. Schmidt, “Multiple emitter location and signal parameter estima-tion,” IEEE Trans. Antennas Propagat., vol. 34, pp. 276–280, Mar. 1986.

[14] J. Capon, “High resolution frequency-wavenumber spectrum analysis,”Proc. IEEE, vol. 57, pp. 1408–1418, Aug. 1969.

[15] E. K. Walton, “Far-field measurements and maximum entropy analysisof lossy material on a conducting plate,”IEEE Trans. Antennas Prop-agat., vol. 37, pp. 1042–1047, Aug. 1989.

[16] R. Carriere and R. L. Moses, “High resolution radar target modelingusing a modified Prony estimator,”IEEE Trans. Antennas Propagat.,vol. 40, pp. 13–18, Jan. 1992.

[17] H. J. Li, Y. D. Wang, and L. H. Wang, “Matching score properties be-tween range profiles of high-resolution radar targets,”IEEE Trans. An-tennas Propagat., vol. 44, pp. 444–452, Apr. 1996.

[18] H. Yamada, M. Ohmiya, Y. Ogawa, and K. Itoh, “Superresolution tech-niques for time-domain measurements with a network analyzer,”IEEETrans. Antennas Propagat., vol. 39, pp. 177–183, Feb. 1991.

[19] T. J. Shan, M. Wax, and T. Kailath, “On spatial smoothing for direc-tion-of-arrival estimation of coherent signals,”IEEE Trans. Acoust.,Speech, Signal Processing, vol. ASSP-33, pp. 806–811, Aug. 1985.

[20] M. Wax and T. Kailath, “Detection of signals by information theo-retic criteria,” IEEE Trans. Acoust., Speech, Signal Processing, vol.ASSP-33, pp. 387–392, Apr. 1985.

[21] M. Wax and I. Ziskind, “Detection of the number of coherent signals bythe MDL principle,” IEEE Trans. Acoust., Speech, Signal Processing,vol. 37, pp. 1190–1196, Aug. 1989.

[22] M.-K. Hu, “Visual pattern recognition by moments invariants,”IRETrans. Inform. Theory, vol. IT-8, pp. 179–187, Feb. 1962.

[23] S. A. Dudani, K. J. Breeding, and R. B. McGhee, “Aircraft identificationby moments invariants,”IEEE Trans. Comput., vol. C-26, pp. 39–45,Jan. 1977.

[24] A. Khotanzad and J.-H. Lu, “Classification of invariant image represen-tations using a neural network,”IEEE Trans. Acoust., Speech, SignalProcessing, vol. 38, pp. 1028–1038, June 1990.

[25] S. Paschalakis and P. Lee, “Pattern recognition in grey level images usingmoment based invariant features,” inInst. Elect. Eng. Image Processingand Its Applications, Conference Pub. 465, 1999, pp. 245–249.

[26] J. Flusser, T. Suk, and S. Saic, “Recognition of blurred images by themethod of moments,”IEEE Trans. Image Process., vol. 5, pp. 533–538,Mar. 1996.

[27] C. H. Jeh and R. T. Chin, “On image analysis by the methods of mo-ments,”IEEE Trans. Pattern Anal. Machine Intell., vol. 10, pp. 496–511,July 1988.

[28] S. Haykin,Neural Networks, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 1999.

[29] M. Friedman and A. Kandel,Introduction to Pattern Recognition, ser.Series in Machine Perception Artificial Intelligence: Imperial CollegePress, 1999, vol. 32.

[30] J. W. Odendaal, E. Barnard, and C. W. I. Pistorius, “Two-dimensional su-perresolution radar imaging using the MUSIC algorithm,”IEEE Trans.Antennas Propagat., vol. 42, pp. 1386–1391, Oct. 1994.

Kyung-Tae Kim was born in Taejon, Korea, onApril 15, 1970. He received the B.S., M.S., andPh.D. degrees in electrical engineering from theDepartment of Electrical Engineering, PohangUniversity of Science and Technology (POSTECH),Pohang, Kyungbuk, Korea, in 1994, 1996, and 1999,respectively.

From March 1999 to March 2001, he workedat the Electromagnetics Technology Laboratory,POSTECH, as a Research Fellow. From April 2001to February 2002, he worked as a Research Assistant

Professor, Electrical and Computer Engineering Division, POSTECH. He isnow on the faculty of the Department of Electrical Engineering and ComputerScience, Yeungnam University, Kyongsan, Kyungbuk, Korea. His primaryresearch interests include radar target recognition and imaging, array signalprocessing, spectral estimation, pattern recognition, neural networks, and RCSmeasurement and prediction.

Dong-Kyu Seoreceived the B.S. degree in electronic,electrical, and control engineering from Hongik Uni-versity, Seoul, Korea, in 1999 and the M.S. degreefrom the Department of Computer and Communica-tion Engineering, Pohang University of Science andTechnology (POSTECH), Pohang, Korea, in 2001,where he is currently pursuing the Ph.D. degree inelectrical engineering.

His research interests are in the areas of radartarget imaging and recognition, radar signalprocessing, pattern recognition using artificial

intelligence, and RCS measurement.

Hyo-Tae Kim received the B.S. and M.S. degrees inelectronics engineering from Seoul National Univer-sity, Seoul, Korea, in 1978 and 1982, respectively,and the Ph.D. degree in electrical engineering fromThe Ohio State University, Columbus, in 1986.

After his graduate work at the ElectroScience Lab-oratory, he joined the Faculty of Pohang Universityof Science and Technology, Pohang, Korea, wherehe is now a Professor. His research activity and in-terests are in the areas of antennas, EM scattering,EMI/EMC, and radar signal processing for imaging

and identification.

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