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ISAR Multi-band Fusion Based onAttributed Scattering CenterYu Ning Feng Zhou* Lei LiuThe Ministry Key Laboratory of Electronic InformationCountermeasure and SimulationXidian UniversityXi'an, ChinaXueru BaiNational Laboratory of Radar Signal ProcessingXidian University,Xi’an, Chinafzhou@mail.xidian.edu.cnAbstract—High resolution Inverse synthetic aperture radarimaging is an important technique for aerospace targetsrecognition. Multi-band fusion method greatly improves the radarbandwidth without the increasing of hardware cost. TraditionalMulti-band fusion methods usually adopt damped exponentialmodel or geometrical theory of diffraction model, but these modelsare not precise enough, especially when the target is complex. Thispaper proposes a novel multi-band fusion method based onattributed scattering center model. Firstly, The ASCs of differentsubbands are extracted using zoom dictionary; Secondly, thevacant band is recovered; Finally, the coherence phase iscompensated, and the full-band signal is obtained. Compared withtraditional methods, the proposed method has higher rangeresolution.all-phase fast Fourier transform (apFFT) to estimate the constantphase and estimates the linear phase by correlating the imagesafter pulse compression. Then iterative adaptive approach (IAA)is performed to fuse multi-band signal.Keywords — Inverse synthetic aperture radar; Multi-bandFusion; Attributed scattering centerI.INTRODUCTIONInverse synthetic aperture radar (ISAR) imaging is asignificant approach to classify, recognize and surveillanceaerospace targets. The range resolution is a key indicator ofISAR imaging. A directly approach to improve range resolutionis increasing the bandwidth. However, it brings huge burden onhardware cost. An alternative method is to utilize several radarsworking in different frequencies [1]. After coherent processing,integrated wideband signal is obtained. The essence ofmulti-band fusion is extrapolating the vacant band betweenmeasurement subbands. Traditional multi-band fusion methodscan be classified into two categories. The first category isnon-parametric methods, which require no prior information oftargets. [2] proposes the amplification gapped-data amplitudeand phase estimation (GAPES) method. This method adoptsleast-squares (LS) technique to iteratively estimate the unknownfrequency spectrum. Simulation and measured data confirm itsefficiency, but improper initialization may let the method dropinto local optima. [3] models the phase deviations of differentradars as linear phase and constant phase. This method employsThis work was supported in part by the National Natural Science Foundationof China under Grant No. 61201283, No. 61471284, No. 61522114，612310107and by the NSAF under Grant No. U1430123; it was also supported by theFoundation for the Author of National Excellent Doctoral Dissertation of PRChina under Grant No. 201448, and by Program for New Century ExcellentTalents in University under Grant NCET-12-0916. This work was supported bythe Fundamental Research Funds for the Central Universities under Grant No.KJXX1601， No. 7214534206 and the Young Scientist Award of ShaanxiProvince under Grant No. 2015KJXX-19 and 2016KJXX-82. This work wassupported by the Postdoctoral Science Foundation of China under Grant2016M602775 and 2017M613076.The second category is parametric methods, which establishparametric models and solve relevant parameters. Comparedwith non-parametric methods, parametric methods employ richprior information and have more excellent performance.According to the model adopted, these methods can beclassified to two subclasses. The first subclass is based ondamped exponential (DE) model. [5] proposes a multi-bandfusion method based on all-pole model. This method buildsforward-prediction matrices for lower and upper subbands,respectively. Then, singular-value decomposition and Akaikeinformation criterion are adopted to estimate the number ofpoles and LS technique is adopted to solve model parameters.After compensating phase offset, the integrated frequency signalis gained. However, this method is hard to determine themodel-order in low signal to noise ratio (SNR). The secondsubclass employs geometrical theory of diffraction (GTD)model. [6] combines two measurement bands, and constructs afrequency dictionary to estimate back-scattering coefficientsusing fast sparse Bayesian learning algorithm. Making use ofback-scattering coefficients and full-band dictionary, theintegrated band signal is recovered. Moreover, dynamicdictionary decreases the computing burden.Even though those methods aforementioned have wellperformance in some situations, the range resolution is restrictedby the precision of DE model and GTD model, especially whenthe target is complex. This paper models the target using moreprecise attributed scattering center (ASC) model [7], and zoomdictionary is adopted to extract ASCs of different subbands. Weelaborately deduce the origin of coherence phase and utilizegenetic algorithm (GA) to calculate it. After compensating thecoherence phase, the integrated wideband signal is obtained.The remainder of this paper is organized as follows. SectionII derives multi-band signal fusion model. Section III introducesthe ASC model and the extraction method. Section IV shows themeans of compensating coherence phase between differentsubbands. Section V presents the fusing results and analyzes theperformance of the proposed method. Section VI concludes thepaper.

II.MULTI-BAND SIGNAL FUSION MODELEchoes of several radars working in different frequenciescan be composed into a wideband signal which has widerbandwidth. Without loss of generality, this paper takes tworadars as an example, and more radars are similar.Supposing two radars are located at S and S ，as shownin Fig. 1, the radar coordinate system of radar1 is (U ,V ,W )with origin S . The radar coordinate system of radar2 is(U ,V ,W ) with origin S . In (U ,V ,W ) , the distancebetween the target and radar1 is L1 . In (U ,V ,W ) , thedistance between the target and radar1 is L2 . Because thedistance between the radar and the target is much larger than thedistance between two radars, i.e. SS L1 and SS L2 .Thus, SP S P . P is any scatterer of target.PUS'Radar 2The difference frequency output of k radar skif isL tˆ 2 Rkl (t ) c skif (tˆ, tm ) kl rect Tpl 1 (5) 4 2 Rref 4 4 2exp j tˆ f kc R kl j 2 R kl R kl jc c cc V'U'Fig. 1 Multi-band signal fusion model.Assuming that two radars transmit pulse signal with thesame period Tp , the time of transmitting istm mT (m 0,1, ) , which is called as slow time. Fast time tˆcorresponds to the propagation time of electromagnetic waves,and t tˆ mT . The transmitted linear frequency modulation(LFM) signal is expressed as tˆskt (tˆ, tm ) rect T p(4)thW'Radar 1(3)is the pulse width of reference signal. Let*skif (tˆ, tm ) skr (tˆ, tm ) sref(tˆ, tm )L2V tˆ 2 Rref (t ) c sref (tˆ, tm ) rect Tref 2 1 ˆ exp j 2 f kc t 2 Rref c t 2 Rref (t ) c 2 R kl Rkl (t ) Rref , and de-chirping processing isL1Swhere Rkl (t ) is the instant distance between the lth scattererand the kth radar, and kl is the back-scattering coefficient ofthe lth scatterer in the kth radar. De-chirping processing isperformed to compress pulse. Let the references range of tworadars are all Rref , and the reference signal is shown in (3).where TrefTargetWL tˆ 2 Rkl (t ) c skr (tˆ, tm ) kl rect Tpl 1 (2)2 1 ˆ exp j 2 f kc t 2 Rkl (tm ) c t 2 Rkl (tm ) c 2 1 2 exp j 2 f kc t tˆ 2 (1)wherek is the kth radar, andk 1, 2 ， andrect (t ) 1, only if t 1 2 ，and f kc is central frequency of kthradar, and Tp is the pulse width. denotes the chirpacceleration term of an LFM waveform. For simplicity offormula derivation, two radars transmit signals of samewaveform only with different frequencies. In fact, samplefrequency, pulse width and chirp acceleration term may bedifferent. However, interpolation processing is able to handlethis problem.Assuming that the first-order Born approximation is satisfied,the target consists of L scatterers. Echoes of kth radar can beexpressed asDue to SP S P , R1l (t ) R2l (t ) is appropriate inenvelope, and it is simplified as Rl (t ) . However, the phase ismuch more sensitive to range bias than the envelope, soR1l (t ) R2l (t )inthephase.Phaseterm4 4 exp jf kc R kl j 2 R 2kl is independent of time, and itcc is simplified as exp j k . Thus, (5) is rewritten asL tˆ 2 Rl (t ) c skif (tˆ, tm ) l rect Tpl 1 (6) 4 2 Rref exp j tˆ R j klk c c The difference of the de-chirped echoes of two radars isL tˆ 2 Rl (t ) c sif (tˆ, tm ) l rect Tpl 1 4 2 Rref exp j tˆ R l j c c (7)where R l R1l (t ) R2l (t ) , 1 2 . Simplify the phase of(7), and the phase difference is as shown in (8).8 R 4 exp j R l tˆ j 2 ref R l j cc (8)

(8) reveals that the phase difference consists of linear phaseand constant phase, i.e.(9) exp j tˆ j 8 Rref4 R l , R l .cc2In order to figure out the coherent phase, it is necessary torepresent the signals as precise as possible. Traditional DEmodel and GTD model are no more appropriate, so ASC modelis introduced in this paper.where III. ATTRIBUTED SCATTERING CENTER MODEL ANDEXTRACTION TECHNIQUEThe ASC model [7] is proposed on the base of GTD model.The response of the ith ASC isTo reduce computation load, the scopes of x , y , L and should be as small as possible. We need to determine theseparameters using prior information as shown below.x xmin , xmax , y ymin , ymax , L 0, Lmax , 1 , 2 (14)After the scope is determined, OMP algorithm is applied tosolve parameters. However, high precise result requires a hugedictionary, and zoom dictionary is adopted to mitigate thiscontradiction. A huge spaced dictionary is constructed tocalculate parameters coarsely. Then, a refined dictionary isconstructed to obtain precise results. The gap of huge spaceddictionary is set as radar resolution, and the result is as preciseas the resolution. Supposing the result of the ith iteration isxi , yi , Li , i , the scopes of refined dictionary are shown below. i f 4 fEi ( f , ; ) Ai j exp j xi cos yi sin c (10) fc 2 f sinc Li sin i exp 2 f i sin c where Ai denotes the backscattered coefficient, i thefrequency dependence, f the radar frequency, f c the centralfrequency, the cross-range angle, xi and yi the range andcross-range locations, respectively. The remaining threeparameters i , Li and i determine the aspect dependenceof the scattering. According to these parameters, ASCs areclassified into localized ASCs and distributed ASCs.Compared with DE model and GTD model, ASC model ismore precise but its extraction technique is more complex.Conventional extraction techniques are classified intoimage-domain methods and frequency-domain methods.Image-domain methods extract ASCs in image domain afterdecoupling, but distributed ASCs may be divided into severallocalized ASCs by mistake. Frequency-domain methodsconstruct dictionaries based on signal model and calculate thebest reconstruction by Orthogonal Matching Pursuit (OMP).However, huge dictionaries need a lot of resources. In order tosolve these problems, zoom dictionary extraction technique [8]is adopted. The signal can be rewritten ass D σ(11)where s is the vectorization of measurements E ( f , ; ) Dis a redundant dictionary, and σ is a complex sparse vectorwhose element denotes the backscattering amplitude.D x, y, L, d1 , d2 ,where di di dias shown in (13)2dn 1 , dn (12)and d i is a combination of parameterstyty tt x xi x , xi x , y yi , yi 22 22 (15)t t tt L Li L , Li L , i , i 22 22 (16)where t x , t y , t L and t are the gaps of huge spaced dictionary.After the refined extraction, precise result is gained.With xi , yi , Li and i , the rest parameters i and ican be estimated easily. Finally, Ai is obtained by LS criterion.The flow of ASC extraction algorithm is shown in TABLE 1TABLE 1 FLOW OF ASC EXTRACTION ALGORITHMStep1: Construct huge spaced dictionary D1 x, y D2 L, ;Step2: Calculate coarse x , y , L , using OMP;Step3: According to the coarse result, Construct refineddictionary D3 x, y and D4 x, y ;Step4: Calculate refined x , y , L , using OMP;Step5: Construct dictionary D , D to figure out and ,then calculate A using LS;Step6: Calculate the residual energy . If is smaller thanthreshold , the algorithm stops. If not, go to Step2.IV. MULTI-BAND COHERENT PROCESSINGBefore multi-band signals are fused, coherent processing isnecessary. The ASC extractions of lower subband and uppersubband are expressed as EP ( f , ; ) and EQ ( f , ; ) ,respectively. We extrapolate the lower subband and uppersubband and obtain overlapped subband as indicated in Fig. 2.f1 j 4 fdi exp xi cos yi sin c 2 f sinc Li sin i c f2Lower subband(13)andVacant subbandf3f4Upper sunbandFig. 2 Multi-band signal extrapolation.The extrapolation subbands of lower subband and uppersubband are expressed as (17) and (18), respectively.

PiNP f 4 fU EP ( f , ; ) APi j U exp j xPi cos yPi sin fc i 1 Pc 2 fU sinc LPi sin Pi exp 2 f Pi sin c (17) QiNQ f 4 fVEQ ( f , ; ) AQi j V exp j xQi cos yQi sin fc i 1 Qc 2 fV sinc LQi sin Qi exp 2 f Qi sin c (18)where fU f1 , f3 , fV f 2 , f 4 and the subscript P and Qdenote the lower subband and upper subband, respectively. LetEU and EV indicate the lower subband signal and uppersubband signal between f 2 , f3 , respectively. According to (9),there exist linear phase and constant phase betweenEU and EV . On the basis of EV , we need to minimize thecost function JJ min , f3 tˆ f 2 EV A* EU exp j tˆ j (a)(b)Fig. 4 ASCs reconstruction results. (a) ASCs reconstruction of lower subband (b)ASCs reconstruction of upper subband.From Fig. 4, it can find that there is offset in range betweenlower subband and upper subband. The reason is that linearphase in frequency domain leads to position offset in imagedomain. We take 36th echo as an example, the real part of thesignal is demonstrated in Fig. 5 (a). GA is adopted to figure outthe coherence phase and the compensated signal is shown in Fig.5 (b). Upper subband and lower subband is well coherent.(19)where A* is the amplify difference between EU and EV .A* can be solved by normalization but and should befound by other approaches. Genetic algorithm (GA) [9] is aneffective method compared with traversal search. Withcoherence phase and amplification, lower subband and uppersubband are coherent. Then, ASCs of linked full band areextracted and full band signal are obtained. The flowchart ofmulti-band fusion based on ASC is shown in Fig. 3.Extract ASCs oflower subbandCompensatecoherence phase andamplification(a)(b)Fig. 5 The real part of the 36th echo. (a) Before coherence phase compensation(b) After coherence phase compensation.The full band 9.5 GHz 12.5 GHz fusion result is shown inFig. 6 (b). we compare fusion result with full band signal andthe maximum relative error of all the pixels is about 0.1.Because the reconstruction is quite similar with the real target,the result is very well.Extract ASCs ofupper subbandExtrapolate lowerand upper subbandExtract ASCs oflinked full bandCalculate coherenceObtain full bandphasesignalFig. 3 The flowchart of multi-band fusion based on ASC model.V.EXPERIMENTS AND ANALYSISThe first experiment adopts 10 simulated ASCs with radarwork frequency 9.5 GHz 12.5 GHz. The known lower subbandis 9.5 GHz 10.5 GHz and the known upper subband is 11.5GHz 12.5 GHz. linear phase 8 and constant phase 4 are added to lower subband. The ASCs extractionresults are shown in Fig. 4.(a)(b)Fig. 6 Multi-band fusion result. (a) True full band signal (b) Fusion result of fullband.In order to confirm the proposed method further, we use aplane electromagnetic data. The plane model is 16.2 m lengthand 17.7 m width and 3 m height, as shown in Fig. 7.

Fig. 7 Electromagnetic plane model.Lower subband is 10 GHz 11 GHz and upper subband is 12GHz 13 GHz. Gaussian white noise is added in this experimentwith SNR 10 dB. Linear phase 8 and constant phase 4 are added to lower subband. The ASCs extractionresult of lower subband and upper subband are shown in Fig. 8(b) and (d), respectively. From Fig. 8, it is significant that themain structure of the plane is extracted and the noise issuppressed.(a)(b)(c)(d)Fig. 9 Imaging results of multi-band fusion using PFA. (a) Imaging result oflower subband (b) Imaging result of upper subband (c) Imaging result ofmulti-band fusion (d) PSLF of the 52nd cross-rang cell.For measurable analysis, the peak side lobe ratio (PSLR) ofthe 52nd cross-rang cell is drawn in Fig. 9 (d). It is observed thatthe resolution in range is improved from 0.225 m to 0.08 m(with Hamming window). Additional, conventional methodbased on DE model and GTD model are unproductive in face ofsuch complex targets.CONCLUSIONThis paper proposes a novel multi-band fusion method basedon ASC model other than traditional DE model and GTD model.First, The ASCs are extracted in different bands based on zoomdictionary; Secondly, the vacant band is recovered byextrapolation; Finally, coherence phase is figured out, and thecoherent full band is obtained. Compared with traditionalmethods, the proposed method has higher range resolution,especially in complex situations. The simulation andelectromagnetic data confirm the efficiency of the proposedmethod.ACKNOWLEDGMENTThe authors would like to thank the anonymous reviewers fortheir valuable comments and helpful advices.REFERENCES(c)(d)Fig. 8 ASCs extraction results of plane model. (a) Original imaging result oflower subband using FFT (b) ASCs reconstruction of lower subband (c) Originalimaging result of upper subband using FFT (d) ASCs reconstruction of uppersubband.After the ASCs are extracted, coherence phase is solved usingGA. We adopt polar format algorithm (PFA) to image, and theimaging result of multi-band fusion is shown in Fig. 9 (c). Ascontracts, PFA imaging results of lower subband and uppersubband are shown in Fig. 9 (a) and (b), respectively.[1][2][3][4][5][6][7](a)(b)[8][9]X. Bai, F. Zhou, Q. Wang, M. Xing and Z. Bao, “Sparse SubbandImaging of Space Targets in High-Speed Motion,” IEEE Trans. Geosci.Remote Sens., vol. 51, no. 7, pp. 4144-4154, Jul. 2013.E. G. Larsson, P. Stoica, and J. Li, “Amplitude Spectrum Estimation forTwo-Dimensional Gapped Data,” IEEE Trans. Signal Processing, vol. 50,no. 6, pp. 1343-1354, Jun. 2002.J. Tian, J. Sun, G. Wang, Y. Wang et al., “Multiband Radar SignalCoherent Fusion Processing With IAA and apFFT,” IEEE Signal Process.Lett., vol. 20, no. 5, pp. 463-466, May 2013.Y. Zheng, S. Tseng and K. Yu, “Spectral Analysis of Periodically GappedData,” IEEE Trans. Aerosp. Electron. Syst., vol. 39, no. 3, pp. 1089-1097,Jul. 2003.K. M. Cuomo, J. E. Piou, and J. T. Mayhan, “Ultra-Wideband CoherentProcessing,” The Lincoln Laboratory Journal, vol. 10, no. 2, pp. 203-222,1997.H. Zhang and R. Chen, “Coherent Processing and SuperresolutionTechnique of Multi-Band Radar Data Based on Fast Sparse BayesianLearning Algorithm,” IEEE Trans. Antennas Propag., vol. 62, no. 12, pp.6217-6227, Dec. 2014.M. J. Gerry, L. C. Potter, I. J. Gupta et al., “A parametric model forsynthetic aperture radar measurements,” IEEE Trans. Antennas Propag.,vol. 47, no. 7, pp. 1179-1188, Jul. 199

Inverse synthetic aperture radar (ISAR) imaging is a significant approach subclass employs gto classify, recognize and surveillance aerospace targets. The range resolution is a key indicator of ISAR imaging. A directly approach to improve range resolution is increasing the bandwidth. .

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