Micro-Doppler Effect Analysis and Feature Extraction in ISAR Imaging With Stepped-Frequency Chirp Signals

Transcription

1 Miro-Doppler Effet Analysis and Feature Extration in ISAR Imaging With Stepped-Frequeny Chirp Signals The MIT Faulty has made this artile openly available. Please share how this aess benefits you. Your story matters. Citation As Published Publisher Ying Luo et al. Miro-Doppler Effet Analysis and Feature Extration in ISAR Imaging With Stepped-Frequeny Chirp Signals. Geosiene and Remote Sensing, IEEE Transations on : IEEE. Institute of Eletrial and Eletronis Engineers Version Final published version Aessed Tue Sep 11 17:53:21 EDT 2018 Citable Link Terms of Use Detailed Terms Artile is made available in aordane with the publisher's poliy and may be subjet to US opyright law. Please refer to the publisher's site for terms of use.

2 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 4, APRIL Miro-Doppler Effet Analysis and Feature Extration in ISAR Imaging With Stepped-Frequeny Chirp Signals Ying Luo, Qun Zhang, Senior Member, IEEE, Cheng-wei Qiu, Member, IEEE, Xian-jiao Liang, and Kai-ming Li Abstrat The miro-doppler m-d effet indued by the rotating parts or vibrations of the target provides a new approah for target reognition. To obtain high range resolution for the extration of the fine m-d signatures of an inverse syntheti aperture radar target, the stepped-frequeny hirp signal SFCS is used to synthesize the ultrabroad bandwidth and redue the requirement of sample rates. In this paper, the m-d effet in SFCS is analyzed. The analytial expressions of the m-d signatures, whih are extrated by an improved Hough transform method assoiated with time frequeny analysis, are dedued on the range-slow-time plane. The implementation of the algorithm is presented, partiularly in those extreme ases of rotating vibrating frequenies and radii. The simulations validate the theoretial formulation and robustness of the proposed m-d extration method. Index Terms Hough transform HT, inverse syntheti aperture radar ISAR, miro-doppler m-d effet, stepped-frequeny hirp signal SFCS, time frequeny analysis. I. INTRODUCTION THE MICROMOTION dynamis of an objet or strutures on the objet may indue frequeny modulations on the returned signal, whih generate sidebands of the target s Doppler frequeny shift, whih is alled the miro-doppler m-d effet [1] [4]. Miro-Doppler features an be regarded as a unique signature of an objet with movements, providing additional information for the lassifiation, reognition, and identifiation of the objet. On the other hand, the existene of m-d effet may ontaminate the inverse syntheti aperture radar ISAR image of the main body and bring great diffiulties to the image interpretation [1] [9]. Therefore, it is neessary to separate and extrat the m-d signals from the returns of the main body. Sine Chen introdued it into the radar imaging in 2000 [1], the m-d effets, whih widely exist in the radar targets e.g., a Manusript reeived Marh 27, 2009; revised June 4, First published Deember 4, 2009; urrent version published Marh 24, This work was supported in part by the National Natural Siene Foundation of China under Grant and Grant and in part by the Natural Siene Foundation Researh Program of Shaanxi Provine under Grant 2007F28. Y. Luo, X. Liang, and K. Li are with the Institute of Teleommuniation Engineering, Air Fore Engineering University, Xi an , China. Q. Zhang is with the Institute of Teleommuniation Engineering, Air Fore Engineering University, Xi an , China, and also with the Key Laboratory of Wave Sattering and Remote Sensing Information Ministry of Eduation, Fudan University, Shanghai , China zhangqunnus@ gmail.om. C. Qiu is with the Researh Laboratory of Eletronis, Massahusetts Institute of Tehnology, Cambridge, MA USA. Color versions of one or more of the figures in this paper are available online at Digital Objet Identifier /TGRS heliopter with rotating rotors, a ship with sanning antennas, et., have attrated great researh attention in aurate target identifiation. High-resolution time frequeny tehniques have been developed to extrat these time-varying m-d signatures [3], [5], and the adaptive hirplet presentation for m-d features from the target with rotating parts is studied in [6]. The empirial-mode deomposition is utilized to estimate aurate parameters of the rotating parts and fous the image of the main body in [7]. The image proessing algorithms have also been introdued for the separation of the m-d features, suh as the Radon transform [8] and the Hough transform HT [9], [10]. Furthermore, some literature has reported the appliation of the m-d effet in automati target reognition, e.g., the geometrial feature extration of wheels [11], the miromotion feature extration of heliopters [5], the urban sensing and indoor sensing [12], the gait and ativity analyses of pedestrians [1] [3], [5], [6], [11], [13], et. The m-d signatures desribe the fine miromotion features of a radar target. To more effetively exploit the m-d signatures of an ISAR target, the broad-bandwidth transmitted radar signal is neessary to obtain high range resolution. The hirp train with stepped arrier frequenies, i.e., the stepped-frequeny hirp signal SFCS, is one kind of effetive signals for obtaining high-resolution downrange profiles of targets. The main advantage of this signal is that the atual instantaneous bandwidth of the radar is quite small, ompared to the total proessing bandwidth, whih allows the transmission of waveforms with extremely wide overall bandwidth without expensive hardware to support the wide instantaneous bandwidth [14]. Thus, this kind of signals an be utilized to introdue imaging apability to existing narrow-bandwidth radar [15]. In ontrast to the stepped-frequeny signal, the SFCS possesses longer detetion distane and lower grating lobes in the range response by means of replaing the fix-frequeny subpulses with hirp subpulses [16]. However, due to the frequeny-stepped proessing, it is sensitive to the radial veloity of the target. When a target ontains miromotion strutures, the movements of these strutures will modulate the high-resolution range profile HRRP and exhibit different m-d harateristis from the traditional hirp signal. Most of the present studies fous on the m-d effets with single-frequeny signals and hirp signals [1], [6] [9]. Although the m-d effets with SFCS are briefly disussed in our previous work [17], detailed analyses of the m-d effets and the algorithm for m-d signature extration are not studied, whih motivates this paper /$ IEEE

3 2088 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 4, APRIL 2010 In this paper, we first analyze the m-d signatures and investigate the range profile s migration and wrapping in SFCS in Setion II. Partiularly, we disuss the m-d effets indued by rotation and vibration in detail and dedue the analytial expressions of the m-d signatures on the range-slow-time plane sine the rotating and vibration dynamis are the most ommon miromotions in radar targets. Then, we propose an algorithm based on an improved HT and time frequeny analysis for the m-d signature extration in Setion III. Due to the range profile s migration and wrapping, the m-d signal of a rotating or vibrating satterer on the target no longer satisfies the sinusoidal funtion on the range-slow-time plane. As a result, the HT method for sinusoid detetion and estimation in [9] is not suitable for the m-d signature extration in SFCS. In this setion, we onstrut new HT equations and assoiate with the time frequeny analysis to extrat the m-d signatures of the rotating or vibrating parts with different moving periods and radii. Different from [9], whih fouses on the imaging for targets with large-radius and low-frequeny rotating parts suh as heliopters, this paper mainly deals with the m-d signature extration for the rotating or vibrating parts with extreme frequenies very high or very low and radii that are larger/smaller than the range resolution. Simulations are presented in Setion IV, and more disussions are presented in Setion V. In addition, it should be mentioned that the deramping method [18] is utilized to synthesize the HRRP for simpliity in this paper. In fat, the analyses of m-d effet and the signature extration method an easily be extended to imaging systems utilizing other HRRP synthesis methods, suh as the timedomain synthesis [19] and the frequeny-domain synthesis [20]. Furthermore, onsidering the small size of general ISAR target and the narrow bandwidth of the hirp subpulses, we assume that the length of target in line of sight LOS is shorter than the oarse range resolution of SFCS. Thus, ompliated extration proessing of HRRP from redundant data an be avoided, and the analyses of m-d effet are simplified. II. m-d EFFECT ANALYSIS In this setion, we first introdue the HRRP synthesis tehnique with SFCS and then analyze the m-d effets indued by the miromotions, partiularly the rotating motion and the vibrating motion. A. HRRP Synthesis With SFCS The SFCS transmitted by the radar is made up of a series of bursts, eah of whih onsists of a sequene of hirp subpulses of stepped arrier frequeny. Fig. 1 shows the variety of the signal frequeny in a burst. Suppose that the ith subpulse of a burst transmitted by the radar is U i t =ut it r exp j2πf 0 + iδft it r +jθ i, 0 i N 1 1 where ut =rett/t 1 expjπμt 2 is a hirp with μ and T 1 being its frequeny modulation slope and time duration, Fig. 1. Frequeny variety in a burst of SFCS. respetively; f 0 + iδf is the arrier frequeny; T r and N denote the subpulse repetition interval and number of subpulses in a burst, respetively; and θ i is the initial phase. B 1 = μt 1 stands for the bandwidth of the subpulse, whih should be equal to or a bit larger than the stepped frequeny value Δf to avoid the interspaes in the syntheti spetrum. Assuming a target of a point satterer with unit sattering oeffiient, the eho of the ith subpulse from the target is t itr 2R/ st, i=ret exp jπμt it r 2R/ 2 T 1 exp j2πf 0 + iδft it r 2R/+jθ i 2 where R is the distane between the target and the radar, and is the wave propagation veloity. The deramping is performed by multiplying the eho signal with the omplex onjugate of the referene signal [18], and the referene point an be hosen among the satterers with the strongest sattering oeffiients on target. The referene signal an be written as t itr 2R 0 / s 0 t, i=ret exp jπμt it r 2R 0 / 2 T ref exp j2πf 0 + iδft it r 2R 0 /+jθ i 3 where R 0 is the distane between the referene point and the radar, T ref is the duration of the referene signal, whih is a bit larger than T 1. After the deramping proessing, it yields s t, i =st, is 0t, i t itr 2R/ = ret T 1 exp j 4πμ exp t it r 2R 0 R Δ j 4π f 0 + iδfr Δ exp j 4πμ 2 R2 Δ where R Δ = R R 0. Replaing t it r 2R 0 / by t, applying the Fourier transform to 4 with respet to t, and removing the Residual Video Phase RVP, one an obtain S ω, i =T 1 sin T 1 ω + 4πμ R Δ exp j 4π f 0 + iδf R Δ. 5 4

4 LUO et al.: MICRO-DOPPLER EFFECT ANALYSIS AND FEATURE EXTRACTION 2089 Thus, the HRRP peaks at k =Φ i = 4π Δf R Δ0 4π f 0T r v 8π ΔfiT rv 9 Fig. 2. Nonrigid target with miromotion. It an be found that the peak value of S ω, i appears at ω = 4πμR Δ /, and in fat, it is the oarse range profile of the point target reated by the ith subpulse exatly. N subpulses will reate N oarse range profiles. Assuming the length of target in LOS to be shorter than the oarse range resolution /2B 1, the range profile of the target obtained by hirp subpulse will have only one peak at ω = 4πμR Δ /. Therefore, keeping ω = 4πμR Δ / and taking the Fourier transform of these oarse range profiles with respet to i, one an obtain Sk=C n sin k+ 4πΔf R Δ exp j 4πf 0 R Δ where C n is a onstant. From 6, it an be found that the peak value of Sk appears at k = 4πΔf R Δ /, i.e., the HRRP is obtained. Divide k by 4πΔf/, and then, the loation of the satterer in the range an be saled. Eah burst reates an HRRP. By transmitting a number of bursts and taking the Fourier transform to the HRRPs with respet to slow time, the ISAR image of the target an be ahieved [17]. B. Miromotion Signatures in SFCS In many ases, the radar target annot be regarded as a rigid objet, e.g., a heliopter with rotating rotors and a bird with wings beating. When a target ontains miromotion parts, the existene of miromotions will affet the synthesis of the HRRP and bring in m-d effet. As shown in Fig. 2, point P is the referene point, and point Q is a miromotion satterer with the veloity v relative to P along the LOS. Sine the duration of a burst is very short, v an be onsidered as a onstant in burst time approximately. The distane between P and Q at the initial time of a burst is R Δ0. Due to the movement of Q, in a burst time, R Δ in 4 should be rewritten as 6 R Δ = R Δ0 + it r v. 7 Generally, the displaement of Q in a burst annot exeed the oarse range resolution. Therefore, 5 an be rewritten as S ω, i =T 1 sin T 1 ω + 4πμ R Δ0 + it r v exp j 4π f 0 + iδfr Δ0 + it r v T 1 sin T 1 ω + 4πμ R Δ0 exp j 4π f 0 + iδfr Δ0 + it r v. 8 where Φi = 4πf 0 + iδfr Δ0 + it r v/ is the phase term in 8. From 9, one an see that the first term on the right side denotes the initial loation of the point during the burst time, the seond term demonstrates that the loation of Q in the HRRP has an offset proportional to v, and the last term is the oupling term between the veloity and the stepped frequeny, whih is negligibly small, ompared with the first two terms e.g., when f 0 =35 GHz, T r =1 μs, i =1, Δf =5 MHz, v =20 m/s, and R Δ0 =5 m, the value of this term is only , whereas the values of the first and seond terms are and , respetively. However, this term may make the peaks of the HRRP seriously expanded, partiularly when v is quite large. Ignoring the last term, 9 is rewritten as k = 4π Δf R Δ0 4π f 0T r v 10 and 10 denotes the peak loation of Q in the HRRP. The loation of Q in range an be obtained by dividing 10 by 4πΔf/, i.e., r = R Δ0 + f 0 T r v/δf. 11 Beause the HRRP is obtained by N-point Fourier transform, the value range of k is within [ π, π].ifv is too large, k in 10 may exeed this sope, and the peak loation of the HRRP may wrap and appear on the other side of the referene point. That is to say, to avoid the wrapping of the HRRP, k must satisfy the following ondition: k <π 12 i.e., 4Δf <r< 4Δf. 13 Equation 13 demonstrates that the peak loation of the miromotion point is limited to the unambiguous range window. Thus, v must also satisfy 1 f 0 T r 4 +Δf R Δ0 <v< 1 f 0 T r 4 Δf R Δ0. 14 When the movement of the miromotion point does not satisfy the onditions of 12 14, due to the wrapping of the HRRP, the peak loation of the miromotion point in the HRRP will be determined by ˆr =mod r + 4Δf, 2Δf 4Δf where moda, b returns the remainder of a divided by b. C. Miro-Doppler Signatures of Rotation and Vibration 15 In order to more profoundly omprehend the m-d effet in SFCS, we take further analyses of the m-d signatures indued

5 2090 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 4, APRIL 2010 Fig. 3. Target with rotating or vibration satterers. by rotating and vibrating parts in a radar target. The rotation and vibration are the most ommon kinds of miromotions in the radar targets, e.g., a heliopter with rotating rotors, a ship with sanning antennas, and a truk with vibrating surfae indued by a running engine. As shown in Fig. 3, when the miromotion satterer Q is taking the rotation or vibration motion around C with the rate ω 0 =2πΩ and radius ρ, the distane between Q and the referene point P in LOS is expressed as Rt m =R Q + ρ osω 0 t m + θ 0 16 where R Q indiates the distane between the rotating enter C and the referene point, θ 0 is the initial phase, and t m is the slow time, i.e., the transmitting time of eah burst. The veloity of the point relative to the radar is vt m =R t m = ρω 0 sinω 0 t m + θ Aording to 10, the HRRP of Q peaks at kt m = 4π Δf Rt m 4π f 0T r vt m = 4πΔf R Q + ρ 1+ω0 2 f 0 2T r 2 /Δf 2 osω 0 t m + θ 0 + φ 18 where φ = aros1/ 1+ω 2 0 f 2 0 T 2 r /Δf 2. When kt m satisfies the ondition in 12, the loation of the point in range is rt m =Rt m +f 0 T r vt m /Δf = R Q + ρ 1+ω0 2f 0 2T r 2 /Δf 2 osω 0 t m + θ 0 + φ. 19 If kt m does not satisfy the ondition in 12, the HRRP will be wrapped, and aording to 15, the loation of the point in range is ˆrt m =mod R Q + ρ 1+ω0 2f 0 2T r 2 /Δf 2 osω 0 t m + θ 0 + φ+ 4Δf, 2Δf 4Δf. 20 It an easily be found that 19 is just a subset of 20 under the ondition in 12. Therefore, 20 desribes the m-d effet in SFCS indued by the rotation and vibration. From 19 and 20, three onlusions an be drawn. 1 When the miromotion parameters of the rotating/ vibrating satterer satisfy the ondition in 12, the m-d signatures of the rotating/vibrating satterer appears to be a sinusoidal urve on the range-slow-time plane. The frequeny of the sinusoid is equal to the rotating or vibrating rate of the satterer. Divide the amplitude of the sinusoid by 1+ω 2 0 f 2 0 T 2 r /Δf 2, and then, the radius of the rotation or vibration ρ is obtained. 2 Sine rt m in 19 annot reah its maximum when Rt m in 16 reahes its maximum, owing to the phase shift φ, it means that, at the moment of the sinusoid maximum, the rotating/vibrating satterer does not reah the maximum distane from the referene point. 3 When the miromotion parameters of the rotating/ vibrating satterer fail to satisfy the ondition in 12, the m-d signature of the rotating/vibrating satterer appears to be a wrapped sinusoidal urve on the range-slow-time plane. The frequeny of the urve is equal to the rotating or vibrating rate of the satterer. These harateristis of the m-d effet are different from that in hirp signals. In hirp signals, the sinusoid on the rangeslow-time plane would never be wrapped, and the amplitude of the sinusoid is equal to the radius of the rotating or vibrating satterer [9]. In addition, the sinusoid rest also means that the rotating or vibrating satterer is reahing the maximum distane from the referene point at the moment. These differenes between the SFCS and hirp signal result from the range profile s migration in 10 and the wrapping of the HRRP in 15. III. MICRO-DOPPLER FEATURE EXTRACTION Sine the urves on the range-slow-time plane ontain the miromotion information of the target, we an extrat the m-d signatures by deteting the parameters of these urves. The HT has been reognized as one of the most popular methods for the detetion of line segments. It was first introdued by Hough [21] and was later improved to detet analytial urves [22], [23]. The major advantage of the HT is its robustness to noise and disontinuities in the pattern to be deteted. In general, the HT an be used to extrat the urves feature with the following basi priniple: the parameters a 1,a 2,...,a N are used to represent the urve, and eah parameter aumulator simply ounts the number of points x i,y i fitted into the urve equation fa 1,a 2,...,a N,x i,y i =0. 21 The aumulator, whih ontains the loal maxima in the HT spae, may orrespond to the presene of a urve. The m-d effets indued by different forms of miromotions appear as different urves on the range-slow-time plane. If the analytial expressions of the urves are obtained, the parameters of the m-d features an be extrated by HT by onstruting orresponding transform equations. In the following, we take the rotation and vibration as examples to disuss the m-d extration algorithm. Aording to 20, the parameters R Q,ρ,ω 0,θ 0 have determined the urve s equation on the range-slow-time plane. We onstrut the HT equation as follows.

6 LUO et al.: MICRO-DOPPLER EFFECT ANALYSIS AND FEATURE EXTRACTION 2091 First, 20 is rewritten in the equivalent form ˆrt m + 4Δf + M 2Δf = R Q + ρ 1+ω0 2f 0 2T r 2 /Δf 2 osω 0 t m i.e., + θ 0 + φ+, M=0, ±1, ±2, Δf R Q =ˆrt m +M 2Δf ρ 1+ω0 2f 0 2T r 2 /Δf 2 osω 0 t m + θ 0 + φ. 23 Aording to the assumption that the length of the target in LOS is shorter than the oarse range resolution /2B 1, i.e., /4B 1 <R Q </4B 1, and B 1 Δf, it yields 4Δf <R Q < 4Δf. 24 Therefore, 23 an be rewritten as R Q =mod ˆrt m ρ 1+ω0 2f 0 2T r 2 /Δf 2 osω 0 t m + θ 0 + φ+ 4Δf, 2Δf 4Δf. 25 Let A = ρ 1+ω0 2f 0 2T r 2 /Δf 2, Ω=ω 0 /2π, and ζ = θ 0 + φ, and we have R Q =mod ˆrt m A os2πωt m + ζ + 4Δf, 2Δf 4Δf. 26 Thus, the detetion of urves on the range-slow-time plane is transformed to the peak value detetion in the parameters R Q,A,Ω,ζ spae by utilizing the HT aording to 26. The implementation of the HT is given as follows: Step 1 Set up a disrete aumulator matrix A R Q,A,Ω,ζ, where R Q [R Q min,r Q max ], A [A min,a max ], Ω [Ω min, Ω max ], and ζ [ζ min,ζ max ] are within the prospetive value sales. Zeroize matrix A. Step 2 Apply the HT to all the points on the rangeslow-time plane whose module values are greater than a ertain threshold, i.e., alulate the urves ˆR Q, Â, ˆΩ, ˆζ in the HT spae orresponding to the point ˆrˆt m, ˆt m on the range-slow-time plane aording to 26, and then apply A ˆR Q, Â, ˆΩ, ˆζ =A ˆR Q, Â, ˆΩ, ˆζ Step 3 Searh the loal maxima in the HT spae, and their oordinates A R Q,A,Ω,ζ are the parameters of the urves on the range-slow-time plane. The rotating or vibrating rate of the miromotion satterer ω 0 =2πΩ an be obtained from the parameters deteted by HT. The rotating or vibrating enter an be identified from the parameter R Q. The radius ρ an also be estimated using the following: ρ = A/ 1+ω0 2f 0 2T r 2 /Δf The auray of R Q and A is mainly dependent on the range resolution of the HRRP, and the auray of Ω and ζ is determined by the set interval between the adjaent disrete elements in [Ω min, Ω max ] and [ζ min,ζ max ], respetively. The more aurate the Ω and ζ, the more the omputer storage and omputational time required. Generally, the algorithm previously presented an extrat the m-d signatures from most of the targets with rotating or vibrating parts, suh as the horizontal rotors on a heliopter and the rotating antenna on a ship. However, two speial situations must be taken into onsideration. A. When A</4NΔf In this situation, the amplitude of the urve is less than half of the range resolution. This situation also widely exists in radar target, e.g., a truk with vibrating surfae indued by a running engine or a person with hest flutuation indued by breathing. When A</4NΔf, the urve will appear as a straight line on the range-slow-time plane, and the m-d signatures annot diretly be extrated by HT. Supplementary proessing is needed before the implementation of the HT. Reonsider 8; when letting ω = 4πμR Δ0 /, the HRRP an be synthesized by applying fast Fourier transform FFT to the right side of 8 with respet to i. Ignoring the influene of the oupling term between v and i, the result of FFT is approximately obtained, i.e., Sk =C n sin k + 4πΔf R Δ0 + 4π f 0T r v exp j 4π f 0R Δ0 29 where C n is a onstant. Aording to 16 and 17, it an be obtained as Sk, t m =C n sin k + 4πΔf Rt m + 4π f 0T r vt m exp j 4π f 0Rt m. 30 Beause A</4NΔf, Sk, t m appears as a straight line on the range-slow-time plane; hene, we have the peak loation of Sk, t m at k = 4πΔfRt m / 4πf 0 T r vt m / C n 31 where C n is a onstant. Let k = C n, and take the derivative to the phase term of the right side of 30 in terms of t m. Then, the

7 2092 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 4, APRIL 2010 variane of the instantaneous frequeny of Sk, t m k=c with n respet to t m is obtained as lt m = 1 2π ψ t m = 2 f 0ρω 0 sinω 0 t m + θ It an be found that lt m is a sinusoidal funtion. Therefore, the m-d signatures an be extrated by analyzing Sk, t m k=c in the joint time frequeny domain first and n then utilizing the HT to detet the urve on the time frequeny plane. Similarly, lt m will also be wrapped if lt m > BRF/2, where the BRF is the burst repetition frequeny, i.e., the sample frequeny in slow-time domain. Therefore, the urve on the time frequeny plane is depited as ˆltm =mod 2 f 0ρω 0 sinω 0 t m + θ 0 + BRF 2,BRF BRF Then, the HT equation an be dedued aordingly as mod ˆltm A sin2πωt m + ζ,brf =0 34 where A =2f 0 ρω 0 /, Ω=ω 0 /2π, and ζ = θ 0. Thus, the m-d signature extration is equivalent to the peak value detetion in the parameters A, Ω,ζ spae. Sine Sk, t m k=c is a sine frequeny modulation signal, onsidering the defiient time frequeny onentration n of short-time Fourier transform STFT and the rossterm interferene in quadrati time frequeny distribution suh as Wigner-Ville distribution WVD and Smoothing Pseudo WVD, we hoose the Gabor transform to analyze Sk, t m k=c. Gabor transform has been reognized as one of n the best methods to represent pattern signals, owing to its perfet time resolution, frequeny resolution, and the absene of ross-term interferene [24]. Hene, analyzing Sk, t m k=c n with Gabor transform ould give many advantages to the following HT proessing. B. When the Rotating or Vibrating Rate Is Extraordinarily High When BRF is given in a radar system, the higher the rotating or vibrating rate, the less the slow-time-domain samplings of the urve in a yle. If the number of samplings in a yle is too low, the detetion apability of the HT will be depressed, and the parameters of the urve annot aurately be extrated. Simulation results have demonstrated that the number of samplings in a yle should be larger than to ensure preise detetion ability of the HT. For example, in a radar system with BRF = 200 Hz, the parameters of the urve are diffiult to diretly be deteted from the range-slow-time plane when the rotating or vibrating rate is higher than 20 Hz. Please refer to the simulations in Setion IV-C3. Furthermore, when the value of v inreases, the value of the third term in 9 inreases aordingly and more seriously expands the peaks in the HRRP. Therefore, some supplementary proessing are also neessary when extrating the m-d signatures of miromotion parts with high rotating or vibration rates, suh as the tail rotors on a heliopter or missile. Fig. 4. Range profile s migration and wrapping. Aording to the analysis in Setion II, the HRRP of the miromotion satterer is synthesized by taking FFT to 8 with respet to i. When the value of v is quite large, the oupling term between v and i will more signifiantly affet the HRRP, and the Fourier transform is not suitable to desribe the m-d signatures. From 9, the linear relationship between k and i an be observed when assuming v to be a onstant approximately in a burst time. Considering that k is the instantaneous frequeny of S ω, i in 8 at ω = 4πμR Δ /, S ω, i ω= 4πμRΔ / is an approximate linear frequeny modulation LFM signal. Taking time frequeny analysis to S ω, i ω= 4πμRΔ /,itwill appear as a segment of straight line on the time frequeny plane. Sine it is a simple LFM signal, the STFT is ompetent to analyze it without ross-term interferenes. After taking the STFT to S ω, i ω= 4πμRΔ / of eah burst, the orresponding time frequeny planes an be obtained, and a new frequeny-slow-time plane an be onstruted by stithing up these planes in order. On that new plane, the m-d signatures of rotating or vibrating satterers also appear as the urves depited by 20, but the slow-time sampling number in a yle has inreased to N times. Therefore, the HT an then be arried out to aurately extrat the m-d signatures aording to 26. The aforementioned algorithm is just for the m-d signature extration of rotation and vibration. Nevertheless, if other miromotions an be depited by ertain analytial expressions, one an also extrat their m-d signatures by onstruting their respetive HT equations. IV. SIMULATIONS In this setion, we verify the theoretial derivation and the proposed m-d extration method using simulated data. The simulations are omposed of three parts: 1 simulations to validate the range profile s migration and wrapping; 2 simulations to validate the m-d signatures indued by rotation; and 3 simulations of m-d signature extration. Simulation results of vibration are not presented, beause it is very lose to the ase with rotation. A. Validation of the Range Profile s Migration and Wrapping The parameters of the transmitted radar signal are f 0 = 35 GHz, T r = μs, Δf = MHz, N =64, and the total bandwidth B = 300 MHz. Four miromotion satterers are at the same loation with the distane from the referene point R Δ0 =5 m but with different instantaneous veloities. Aording to 14, it an easily be alulated that v 36 m/s, m/s to avoid the range profile s wrapping.

8 LUO et al.: MICRO-DOPPLER EFFECT ANALYSIS AND FEATURE EXTRACTION 2093 Fig. 5. Miro-Doppler signatures indued by rotation. a Curves of the satterers 2 Hz, 2 m and 5 Hz, 2 m on the range-slow-time plane. b Curves of the satterers 2 Hz, 2 m and 8 Hz, 2 m on the range-slow-time plane. The -dotted and -dotted dashed urves are determined by 20 when the motion parameters of the satterer are 2 Hz, 2 m and 8 Hz, 2 m, respetively. As shown in Fig. 4, the peak loations of the satterers in the HRRP are different from eah other beause of their different instantaneous veloities. In partiular, the profile s wrappings are validated in Fig. 4b. When v is 19 m/s lose to the ritial point m/s, the peak of the satterer in the HRRP is split and appears at both sides of the HRRP. When v exeeds the limited value of 14, suh as 60 m/s, the orresponding peak of the satterer is wrapped and appears at the right side of the peak of the satterer with v = 15 m/s. It an also be observed that the peaks are more and more seriously expanded versus the horizontal axis with the inrease in v. B. Validation of m-d Signatures Indued by Rotation The parameters of the transmitted radar signals are given as follows: f 0 =10GHz, T r = μs, Δf = MHz, N = 64, BRF = 200 Hz, and the total bandwidth B = 300 MHz. The range resolution of HRRP is Δ R =0.5m. Two satterers both rotate around one enter with the distane from the referene point R Q = 3 m. The radii are both 2 m, and the initial phase θ 0 are both π/2. As shown in Fig. 5a, when the rotating rate is 2 and 5 Hz, respetively, it an be alulated that k max = <πaording to 18, whih satisfies the onditions limited by 12. The magnifying oeffiient of the sinusoid s amplitude 1+ω0 2f 0 2T r 2 /Δf 2 is and , respetively. Hene, the amplitude of the sinusoid in Fig. 5a is the rotating radius multiplied by 1+ω0 2f 0 2T r 2 /Δf 2, whih is and m, respetively. In the simulation, the satterer with a rotating rate of 5 Hz was set to reah the ritial position with the largest distane in LOS from the referene point at t m =0.05 s, 0.25 s, 0.45 s,... Taking t m =0.25 s into onsideration, although the satterer has moved to the furthest position in LOS from the referene point, the orresponding sinusoid on the range-slow-time plane has not reahed the rest at the moment, suh as point A shown in Fig. 5a. The phase shift φ an be alulated as aording to 18. As a result, the sinusoid rests at the position indiated by point B in Fig. 5a. When the rotating rate of the satterer 5 Hz, 2 m inreases up to 8 Hz, it an be alulated that k max = >π. Therefore, the sinusoid will be wrapped as shown in Fig. 5b. For the sake of validating the orretness of 20, we draw the TABLE I CURVE PARAMETERS DIRECTLY OBTAINED VIA HT FROM THE RANGE-SLOW-TIME PLANE urves depited by the equation on the range-slow-time plane using the -dotted and -dotted dashed lines. It an be observed that the urves determined by 20 oinide well with the simulation results. C. Validation of m-d Signature Extration Algorithm The parameters of the transmitted radar signals are the same as those in Setion IV-B. In this setion, the effetiveness of the m-d signature extration algorithm is validated in Setions IV- C1 IV-C3, and the robustness of the algorithm is disussed in Setion IV-C4. 1 Detet Curves Using HT on the Range-Slow-Time Plane Diretly Under the Most Common Conditions: Assume that two satterers are both rotating around one enter with the distane from the referene point R Q = 3 m. The radii are both 2 m, and the rotating rates are 2 and 8 Hz, respetively. The initial phase θ 0 are both π/2. The orresponding urves on the rangeslow-time plane have been shown in Fig. 5b. The parameter pairs R Q,A,Ω,ζ deteted by HT are shown in Table I. It an be found that the rotating rates of the two satterers and the value of R Q are aurately obtained. The average value of parameter A is about 4.75 and 17 m, respetively. Aording to 28, the radii of rotating satterers are and m, whih agree quite well with the set value of 2 m. 2 Detet Curves When A</4NΔf: Assume that two satterers rotate around the enter with the distane from the referene point R Q = 3 m. The radii are both 0.05 m, and the rotating rate is 2 and 4 Hz, respetively. The initial phase θ 0 are both 0 rad. It an be alulated that A 1 =0.1160, A 2 =0.2153, and /4NΔf =0.25, whih satisfy A 1 </4NΔf and A 2 </4NΔf. Beause the amplitudes are smaller than

9 2094 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 4, APRIL 2010 Fig. 6. Miro-Doppler signature extration when A</4NΔf. a Curves on the range-slow-time plane appear to approximately be a straight line. b Sinusoidal urve obtained by applying the Gabor transform to the row of straight lines. TABLE II CURVE PARAMETERS OBTAINED VIA HT WHEN A<C/4NΔf Fig. 7. Miro-Doppler signature extration when the rotating rate is extraordinarily high. a Blurry urves on the range-slow-time plane. b STFT result of S ω, i in 8 at ω = 4πμR Δ /. It appears to be segments of straight lines on the time frequeny plane. New frequeny range-slow-time plane onstruted by stithing up the planes of all the bursts in order. half-range resolution, the urves appear to be a straight line approximately, as shown in Fig. 6a. In this ondition, the HT is unable to detet the parameters from the range-slow-time plane. Extrating the row of straight line, taking interpolations for four times, and then implementing Gabor transform to the row, the sinusoidal urves are obtained as shown in Fig. 6b. The synthesis window in the Gabor transform is a Gaussian window. The number of Gabor oeffiients in time is 100, and the degree of oversampling is 20. Then, the HT an be implemented to obtain the parameters A, Ω,ζ, and the results are shown in Table II. It an be observed in Table II that the rotating rates are aurately deteted as Ω=2and 4 Hz. The average values of parameter A are about and 84.75, respetively. Aording to 34, the rotating radii are alulated as ρ = A /2f 0 2πΩ = m and m, whih are quite lose to the set value of 0.05 m. In fat, the errors are mainly dependent on the frequeny resolution of the Gabor transform. 3 Detet Curves When the Rotating or Vibrating Rate Is Extraordinarily High: Assume that two satterers both rotate around one enter with the distane from the referene point R Q = 3 m. The radii are both ρ =1m, and the rotating rates are the same at 20 Hz. The initial phase θ 0 is 0 and π/2, respetively. The magnifying oeffiient of the sinusoid s amplitude is 1+ω 2 0 f0 2T r 2 /Δf 2 = , i.e., A = aording to 28. The urves on the range-slow-time plane are shown in Fig. 7a. The urves are very blurry beause of the high rotating rates; as a result, the parameters of the urves annot exatly be deteted by the HT from the range-slow-time plane, as shown in Table III. It an be found that the deteted parameters fail to fit to the set values. Fig. 7b shows the STFT result of S ω, i in 8 at ω = 4πμR Δ /. It an be seen that S ω, i ω= 4πμRΔ / is an approximate LFM signal on the time frequeny plane, i.e., the i k plane. Stithing up the planes of all the bursts in order, a new frequeny-slow-time plane an be onstruted, as shown in Fig. 7. For larity of the figure and ease of omprehension, Fig. 7 presents just a part of the new plane from 0 to 0.1 s in the slow time, and the frequeny

10 LUO et al.: MICRO-DOPPLER EFFECT ANALYSIS AND FEATURE EXTRACTION 2095 TABLE III CURVE PARAMETERS OBTAINED VIA HT FROM THE RANGE-SLOW-TIME PLANE WHEN THE ROTATING RATE IS EXTRAORDINARILY HIGH TABLE IV CURVE PARAMETERS OBTAINED VIA STFT AND HT WHEN THE ROTATING RATE IS EXTRAORDINARILY HIGH axis is transformed to the range axis for onsisteny with Fig. 7a. Thus, the urves in Fig. 7 are more obvious, and the HT an be utilized to detet the parameters exatly. The deteted parameters R Q,A,Ω,ζ of the two urves are given in Table IV and fit well to the set values. 4 Robustness Disussion: In atual situations, the miromotion parts are always masked by the target s body. As a result, the indued m-d signals are ontaminated by the target body s returns. In the proessing of m-d feature extration, these body returns must be onsidered as noise, beause they will bring in mistakes. Meanwhile, for simpliity, we have assumed the target onsists of point satterers with unit sattering oeffiients. However, for a rotating target with a large radius or high frequeny in real-world situations, it is highly possible that the baksattering oeffiients have timevarying omplex values. In the following, we further study the performane of the proposed algorithm in these situations. SNR: After suffiiently aurate translation ompensation, the body satterers an be onsidered as miromotion satterers with zero rotating frequeny approximately; therefore, the orresponding urves on the range-slow-time plane or the frequeny-slow-time plane appear to be straight lines. Aording to the differene between the m-d urves and the body s straight lines, a primary and simple noise suppression method is designed as follows: assuming that the data matrix on the range-slow-time plane or the frequeny-slow-time plane ism with X Y points, the straight-line-removing proessing an be expressed as M x, y = Mx, y 1 Y Mx, y M Y 35 Y y=1 where M Y is a 1 Y vetor with all elements equal to one. Then, the HT an be implemented to M x, y for m-d feature extration. As shown in Fig. 8a, the simulation onditions are the same as those in Setion IV-C1, and the body s returns are added with SNR = 20 db. It an be found that the m-d urves are relatively very weak and that the HT may have errors when deteting the parameter pairs of urves. The result of the noise suppression proessing is shown in Fig. 8b. Applying the HT to this figure, the parameter pairs an aurately be deteted. However, similar with many other algorithms, the m-d extration algorithm presented herewith annot effetively work when the noise is overwhelming. As shown in Fig. 8, when the SNR dereases to 30 db, the noise suppression does not effetively work, so that the urve with a frequeny of 8 Hz an no longer be deteted by HT. In this ase, it is neessary to improve the noise suppression algorithm in future works. When A</4NΔf or the rotating rate is extraordinarily high, the Gabor transform or the STFT needs to be implemented before the HT. In these ases, the body s returns will bring in adverse effets beause of the limitation of the time frequeny resolution. Therefore, the antinoise ability of the algorithm will be degraded to some extent. In partiular, for the STFT, the multiomponent signal of the body s returns will seriously ontaminate the m-d urves on the frequeny-slow-time plane. Fig. 9 shows the robustness of the proposed algorithm when A</4NΔf. The simulation onditions are the same as those in Setion IV-C2, and SNR = 16 db. The results of Gabor transform and the noise suppression proessing are shown in Fig. 9a and b, respetively, and the HT an aurately detet the parameters of the urves. Fig. 10 shows the robustness of the algorithm when the rotating rate is extraordinarily high. The simulation onditions are the same as those in Setion IV-C3, and SNR = 10 db. Applying the HT to Fig. 10, the m-d features an suessfully be extrated. Time-varying omplex sattering oeffiients: It is highly possible that the sattering oeffiients are time-varying omplex values if the rotating satterers have large radii or high frequenies. When the rotating satterers have large radii, we diretly detet the urves from the range-slow-time plane; therefore, the time-varying omplex sattering oeffiients just lead to the varying moduli of the urves. When the rotating rates of the satterers are extraordinarily high, we detet the urves on the frequeny range-slow-time plane after taking the STFT to eah burst and stithing up the time frequeny planes in order, and in eah burst time, the sattering oeffiients an be onsidered as onstants approximately. In suh ase, the timevarying omplex sattering oeffiients also just lead to the varying moduli of the urves on the frequeny range-slowtime plane. Due to the robustness of the HT to the disontinuities of the pattern, the adverse effets of the urves varying moduli are very limited. Fig. 11 shows the urves on the range-slow-time plane, where the simulation onditions are the same as those in Setion IV-C1. The moduli and phases of sattering oeffiients randomly vary within [0, 1] and [0, 2π], respetively. Applying the HT to Fig. 11, the parameter pairs of the urves an aurately be deteted. Fig. 12 shows the urves on the frequeny range-slow-time plane, where the simulation onditions are idential to those

11 2096 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 4, APRIL 2010 Fig. 8. Robustness validation of the proposed algorithm under different SNRs when deteting urves on the range-slow-time plane. a Curves and straight lines orrespond to the miromotion satterers and the body satterers on the range-slow-time plane, respetively. The straight lines are onsidered as noise when extrating the m-d features. The SNR is 20 db. b Result of the noise suppression proessing when SNR = 20 db. Result of the noise suppression proessing when SNR = 30 db. Fig. 9. Robustness validation when A</4NΔf and SNR = 16 db. a Result of Gabor transform. b Result of the noise suppression proessing. Fig. 10. Robustness validation when the rotating rate is extraordinarily high and SNR = 10 db. a Blurry urves orrespond to the miromotion satterers, and straight lines orrespond to the body satterers on the range-slow-time plane. b New frequeny range-slow-time plane onstruted by stithing up the STFT results of all the bursts in order. Result of the noise suppression proessing. in Setion IV-C3. The moduli and phases of sattering oeffiients also randomly vary within [0, 1] and [0, 2π], respetively. Applying the HT to Fig. 12, the parameter pairs of the urves an also aurately be deteted. From these analyses and simulations, it an be found that the proposed algorithm possesses good antinoise performane and robustness to the time-varying omplex sattering oeffiients. Fig. 11. Curves with time-varying omplex sattering oeffiients on the range-slow-time plane. V. D ISCUSSION AND CONCLUSION The m-d information has been verified to be very useful for radar target identifiation and reognition. In this paper, the m-d effets in SFCS radar have been investigated, and an algorithm for m-d signature extration has been proposed.

12 LUO et al.: MICRO-DOPPLER EFFECT ANALYSIS AND FEATURE EXTRACTION 2097 using simulated data at present. In our future work, we will introdue the algorithm to the real data proessing. Fig. 12. Curves with time-varying omplex sattering oeffiients on the frequeny range-slow-time plane after taking the STFT. The proposed m-d signature extration method is mainly based on the HT to detet the parameters of the urves on the rangeslow-time plane or the frequeny-slow-time plane. It is known that, when using the HT to detet patterns, the omputer storage and the omputational time exponentially grow with the number of dimensions in the parameter spae [22]. The HT that we utilized here is a four-parameter mapping when using the HT on the range-slow-time plane diretly under the most ommon onditions or when the rotating rate is extraordinarily high or a three-parameter mapping [when A < /4N Δf]. In our simulation, the omputation time for obtaining the parameter pairs A, Ω,ζ in Setion IV-C2 was approximately 175 s on a personal omputer with an Intel Pentium Dual T GHz proessor, whereas that for obtaining the parameter pairs R Q,A,Ω,ζ from Fig. 7 was approximately 1311 s. In order to redue the omputation ost for real-time appliations, some supplementary proessing for speeding up the omputation of the algorithm an be used, e.g., the fast method presented in [25] to detet fixed-period sinusoids based on the HT by deomposing the parameters into two groups and estimating them in turn an be extended to detet urves in this paper. The parallel proessing tehnique an also be used to aelerate the omputation of the HT. It is mentioned that the main purpose of this paper is the m-d effet analysis and signature extration in SFCS radars. In fat, based on the m-d signature extration, the final ISAR image of the target body an be improved after eliminating the urves from the range-slow-time plane. The elimination algorithm for hirp radars has been disussed in our previous work [9], and it an also be extended to fous a lear body image in SFCS radars. Of ourse, onsidering the m-d harateristi differenes between the hirp radar and the SFCS radar, the algorithm should be modified aordingly. For example, in this paper, the Gabor transform and STFT are adopted before the HT, and therefore, how the signals in range-slow-time domain ould be reonstruted after urves eliminated from the time frequeny domain will be a subjet for further researh. The ISAR imaging algorithm based on the m-d signature extration will be onsidered in a separate paper. The simulations in Setion IV have validated the auray of m-d effet analysis and the effetiveness of the proposed signature extration algorithm. Due to the lak of the required real data, we an just examine the performane of the algorithm REFERENCES [1] V. C. Chen, Analysis of radar miro-doppler signature with time frequeny transform, in Pro. Stat. Signal Array Proess., Poono Manor, PA, 2000, pp [2] V. C. Chen, Miro-Doppler effet of miromotion dynamis: A review, Pro. SPIE, vol. 5102, pp , Apr [3] V. C. Chen, F. Li, S. S. Ho, and H. Wehsler, Miro-Doppler effet in radar: Phenomenon, model, and simulation study, IEEE Trans. Aerosp. Eletron. Syst., vol. 42, no. 1, pp. 2 21, Jan [4] T. Sparr and B. Krane, Miro-Doppler analysis of vibrating targets in SAR, Pro. Inst. Elet. Eng. Radar Sonar Navig., vol. 150, no. 4, pp , Aug [5] T. Thayaparan, S. Abrol, E. Riseborough, L. Stankovi, D. Lamothe, and G. Duff, Analysis of radar miro-doppler signatures from experimental heliopter and human data, IET Radar Sonar Navig., vol. 1, no. 4, pp , Aug [6] J. Li and H. Ling, Appliation of adaptive hirplet representation for ISAR feature extration from targets with rotating parts, Pro. Inst. Elet. Eng. Radar Sonar Navig., vol. 150, no. 4, pp , Aug [7] X. Bai, M. Xing, F. Zhou, G. Lu, and Z. Bao, Imaging of miromotion targets with rotating parts based on empirial-mode deomposition, IEEE Trans. Geosi. Remote Sens., vol. 46, no. 11, pp , Nov [8] L. Stankovi, I. Djurovi, and T. Thayaparan, Separation of target rigid body and miro-doppler effets in ISAR imaging, IEEE Trans. Aerosp. Eletron. Syst., vol. 42, no. 4, pp , Ot [9] Q. Zhang, T. S. Yeo, H. S. Tan, and Y. Luo, Imaging of a moving target with rotating parts based on the Hough transform, IEEE Trans. Geosi. Remote Sens., vol. 46, no. 1, pp , Jan [10] S. He, Y. F. Zhu, H. Z. Zhao, J. X. Zhou, and F. Qiang, Analysis of rotating strutures for stepped frequeny radar, in Pro. Int. Conf. Radar, 2008, pp [11] A. Ghaleb, L. Vignaud, and J. M. Niolas, Miro-Doppler analysis of wheels and pedestrians in ISAR imaging, IET Signal Proess., vol. 2, no. 3, pp , Sep [12] P. Setlur, M. Amin, and F. Ahmad, Urban target lassifiations using time frequeny miro-doppler signatures, in Pro. 9th Int. Symp. Signal Proess. Appl., 2007, pp [13] Y. Kim and H. Ling, Human ativity lassifiation based on miro- Doppler signatures using a support vetor mahine, IEEE Trans. Geosi. Remote Sens., vol. 47, no. 5, pp , May [14] Q. Zhang and Y. Q. Jin, Aspets of radar imaging using frequenystepped hirp signals, EURASIP J. Appl. Signal Proess., vol. 2006, no. 13, pp , [15] A. Freedman, R. Bose, and B. D. Steinberg, Thinned stepped frequeny waveforms to furnish existing radars with imaging apability, IEEE Aerosp. Eletron. Syst. Mag., vol. 11, no. 11, pp , Nov [16] N. Levanon and E. Mozeson, Nullifying ACF grating lobes in steppedfrequeny train of LFM pulses, IEEE Trans. Aerosp. Eletron. Syst., vol. 39, no. 2, pp , Apr [17] Q. Zhang, Y. S. Zeng, Y. Q. He, and Y. Luo, Avian detetion and identifiation with high-resolution radar, in Pro. IEEE Radar Conf., Rome, Italy, May 26 30, 2008, pp [18] H. Shimpf, A. Wahlen, and H. Essen, High range resolution by means of syntheti bandwidth generated by frequeny-stepped hirps, Eletron. Lett., vol. 39, no. 18, pp , Sep [19] R. T. Lord and M. R. Inggs, High resolution SAR proessing using stepped-frequenies, in Pro. IEEE IGARSS, Singapore, Aug. 1997, vol. 1, pp [20] D. J. Rabideau, Nonlinear syntheti wideband waveforms, in Pro. IEEE Radar Conf., Long Beah, CA, May 2002, pp [21] P. V. C. Hough, Methods and means for reognizing omplex patterns, U.S. Patent , De. 18, [22] D. H. Ballard, Generalization the Hough transform to detet arbitrary shapes, Pattern Reognit., vol. 13, no. 2, pp , [23] D. S. Mkenzie and S. R. Protheroe, Curve desription using the inverse Hough transform, Pattern Reognit., vol. 23, no. 3/4, pp , Mar [24] S. Qian and D. Chen, Disrete Gabor transform, IEEE Trans. Signal Proess., vol. 41, no. 7, pp , Jul [25] Z. Changhun and S. Ge, A Hough transform-based method for fast detetion of fixed period sinusoidal urves in images, in Pro. 6th Int. Conf. Signal Proess., 2002, pp

13 2098 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 48, NO. 4, APRIL 2010 Ying Luo was born in Hunan, China, in He reeived the M.S. degree in eletrial engineering, in 2008, from the Institute of Teleommuniation Engineering, Air Fore Engineering University AFEU, Xi an, China, where he is urrently working toward the Ph.D. degree in eletrial engineering. He is urrently with the Radar and Signal Proessing Laboratory, Institute of Teleommuniation Engineering, AFEU. His researh interests inlude signal proessing and ATR in SAR and ISAR. Cheng-wei Qiu M 06 was born in Zhejiang, China, on Marh 9, He reeived the B.Eng. degree from the University of Siene and Tehnology of China, Hefei, China, in 2003 and the Ph.D. degree from the Joint Ph.D. Program between the National University of Singapore, Singapore and the L Éole Supérieure d Életriité SUPELEC, Gif-sur-Yvette, Frane, in Sine 2009, he has been a Postdotoral Fellow with the Researh Laboratory of Eletroni, Massahusetts Institute of Tehnology, Cambridge, MA. He has authored more than 40 journal papers and one book hapter, and has given a few invited talks at onferenes. His researh interests inlude the eletromagneti wave theory of omplex media e.g., hiral, anisotropi, and bianisotropi materials, invisibility loaks, metamaterials, and imaging. Dr. Qiu was the reipient of the SUMMA Graduate Fellowship in Advaned Eletromagnetis in 2005; the IEEE AP-S Graduate Researh Award in 2006; the Young Sientist Travel Grant in Japan in 2007; the Travel Grant for Metamaterial 07 in Rome, Italy; and the URSI Young Sientist Award in Qun Zhang M 02 SM 07 reeived the M.S. degree in mathematis from Shaanxi Normal University, Xi an, China, in 1988 and the Ph.D. degree in eletrial engineering from Xidian University, Xi an, in He was a Researh Engineer from 2001 to 2003 and a Researh Fellow from 2005 to 2006 with the Department of Eletrial and Computer Engineering, National University of Singapore, Singapore. He is urrently a Professor with the Teleommuniation Engineering Institute, Air Fore Engineering University, Xi an, and an Adjunt Professor with the Key Laboratory of Wave Sattering and Remote Sensing Information Ministry of Eduation, Fudan University, Shanghai, China. He has authored more than 100 papers on journals and onferene proeedings. His researh interests inlude signal proessing, lutter suppression, and its appliation in SAR and ISAR. Dr. Zhang is a Senior Member of the Chinese Institute of Eletronis CIE; a Committee Member of the Radioloation Tehniques Branh, CIE; and a member of the Signal Proessing Counil of Shaanxi, China. He was also a Vie Co-Chair of the Tehnial Program Committee of Workshop for Spae, Aeronautial and Navigational Eletronis in He was the reipient of the First-Grade and the Seond-Grade Prizes of Shaanxi Natural Siene Exellent Aademi Paper in 2006 and 2008, respetively. Xian-jiao Liang was born in Hunan, China, in She is urrently working toward the M.S. degree in eletrial engineering in the Institute of Teleommuniation Engineering, Air Fore Engineering University, Xi an, China. Her researh interests inlude signal proessing in SAR and ISAR. Kai-ming Li reeived the M.S. degree in eletrial engineering from the Institute of Teleommuniation Engineering, Air Fore Engineering University AFEU, Xi an, China, in He is urrently with the Radar and Signal Proessing Laboratory, Institute of Teleommuniation Engineering, AFEU. His researh interests inlude signal proessing and ATR in SAR and ISAR.