Performance analysis and side lobe suppression in radon- Fourier transform based on random pulse repetition interval

Transcription

1 COMPUTER MOELLING & NEW TECHNOLOGIES (11) Pefoance analysis and side lobe suppession in adon- Fouie tansfo based on ando pulse epetition inteval Abstact Qian Chen 1, 2*, Junhao Liu 2, Chaowei Fu 2, Haitao Wang 2 1 School of Infoation and Electonics, Beijing Institute of Technology, Beijing, 181, China 2 Shanghai Radio Equipent Reseach Institute, Shanghai, 29, China Received 1 June 214, In ode to solve the Blind Speed Side Lobe (BSSL) appeaed in Radon-Fouie Tansfo (RFT) ethod used fo di taget detection, a novel ethod of BSSL suppession is poposed in this pape. It is based on Rando Pulse Repetition Inteval (RPRI). The pocess of RPRI-RFT and the BSSL popeties ae descibed, the pefoance of coheent integation and the odulation noise of RFT algoith based on RPRI ae analysed in detail. Both the theoetical analysis and the nueical expeiental esults show that RPRI-RFT can be used to ipove signal-to-noise atio (SNR) and suppess BSSL effectively, and the influence of odulation noise of RPRI can be suppessed by the long-tie integation chaacteistic, thus significantly ipove the ability of low pulse epetition fequency ada to detect and easue long-ange wea high-speed ulti-tagets. Keywods: Blind Velocity Side Lobe, Radon-Fouie Tansfo, Rando Pulse Repetition Inteval 1 Intoduction With the developent of ada stealth technology, the ada coss section (RCS) of taget deceases shaply, weaening the enegy of ada echo and diinishing the ange of ada detection. Long-tie integation is an effective ethod to ipove the detection pefoance of di tagets [1-3]. With the incease of integation tie, howeve, the poble of acoss ange unit (ARU) wal will occu inevitably. Pefoing diectly conventional ethods of oving taget detection (MT) on highvelocity tagets, the enegy of tagets spead ove ultiple esolution units [4-6] and cannot be integated effectively. In this case, the incease of integation tie cannot ipove the pefoance of ada detection. Non-coheent integation and coheent integation ae two basic ethods fo long-tie integation. The foe ainly accuulates the enegy along with the otion tajectoy of tagets to solve the poble of ARU. As a typical algoith, the Hough Tansfo (HT) poposed by Calson does not need phase copensation, aing it easy to ipleent [7-9]. Howeve, without phase infoation, the enegy of taget cannot be accuulated copletely and this ethod cannot wo well in exteely low SNR scenaio [1]. The latte has dawn extensive attention fo acadeic counity and has been deeply investigated in ecently yeas, because of its bette integated gain in the field of di taget detection. Techniques fo ARU copensation in the long-tie coheent integation can be classified into two types. In the fist type, ARU copensation can be ipleented by shifting o expanding the envelope afte pulse copession [11]. In ode to guaantee the copensation pecision, intepolation in ange diension should be adopted, so the eoy cost is huge. In the second type, ARU copensation is ealized in the tansfo doain of the ange-pulse plane, such as Keystone tansfoation, achieving ARU copensation of constant-velocity tagets [12-14]. This ethod is fee of seaching opeation, but it cannot eliinate the ARU effect fo ultiple tagets with diffeent abiguity nube siultaneously. In ecent yeas, based on the coupling elationship between ange wal and opple fequency, Radon- Fouie Tansfo (RFT) is poposed to ealize the longtie coheent integation [15-17] by apping the echo pulse to the ange-opple plane. RFT concentating the enegy to a focused pea, ipoves the ada detection pefoance of di tagets. Howeve, because of the discete pulse sapling, finite ange esolution and liited integation tie, the BSSL still exists in the case of Low Pulse Repetition Fequency (LPRF). Since the BSSL would incease the atio of false ala and deteioate the detection pefoance, a syetical weighting ethod has been poposed to suppess the BSSL in RFT integation plane. The locations of BSSLs can be contolled via diffeent weighting functions, and the BSSLs can be eliinated by cobing the diffeent weighted RFT esults [16]. Howeve, BSSLs still cannot be eliinated copletely when the BSSLs appea siultaneously in both RFT outputs. Anothe ethod based on the design of pulse epetition inteval (PRI) has been poposed in Ref. [18]. By jointly pocessing the RFT outputs in two adjacent Coheent Pocessing Intevals (CPIs), iniu citeion is eployed between * Coesponding autho e-ail @qq.co 48 Matheatical and Copute Modelling

2 COMPUTER MOELLING & NEW TECHNOLOGIES (11) the two diffeent PRI to achieve BSSL suppession. It should be note that the algoith needs at least two CPIs, so that the integation tie is inceased twice and the ada efficiency is halved. A BSSL suppession ethod based on CLEAN algoith has been poposed in [19]. The pea position of echo envelope is fist obtained afte RFT opeation, and accoding to the elationship aong BSSL, velocity and ange, the positions of BSSL ae confied and eoved. And then the RFT pea will be deteined. Though the BSSL of one taget can be well estained, the taget cannot be detected when its ain lobe ovelaps the BSSL of anothe taget. In this pape, a novel RFT algoith based on Rando Pulse Repetition Inteval (RPRI) is poposed to suppess BSSL. And the pape is oganized as follows: the pinciple of RFT algoith is analysed, and the causes of BSSL of discete RFT ae pesented in section 2. In section 3, the RFT algoith based on RPRI is poposed, and the analyses about the odulation noise and BSSL suppession pefoance of RFT algoith ae pesented. In section 4, the siulation esults of the poposed ethod ae shown. Finally, the conclusions ae given out in section 5. 2 The chaacteistics of RFT 2.1 SIGNAL MOEL Suppose a linea fequency odulation (LFM) signal () pt is used by the ada tansitting, i.e., 2 P p( t) ect t T exp jπ t, (1) whee T P is the pulse duation, is the odulation fequency ate, and ect( ) is the ectangula function. Fo a point taget with the RCS of Swelling- type, the eceived echo signal can be witten as ˆ s ( tˆ, t ) A p t 2 t c exp j4πf t c, (2) c whee ˆt and t ( t T quic-tie and slow-tie espectively,, T is the PRI) denote the f c is the caie fequency, c epesents the light velocity and A is the aplitude of taget. It is supposed that the adial velocity of the taget is unifo. The instantaneous distance between ada and taget can be expessed as t vt whee is the initial distance fo ada platfo to taget, and v is the adial velocity of taget. Afte ange copession, the echo signal can be epesented as ˆ f c f v t c s,m ( tˆ, t ) Asinc B t 2 vt c exp j4π exp j4π c c, (3) whee A is the aplitude of baseband signal, B is the bandwidth of LFM signal. Fo the conventional MT ethod,echo envelop is supposed to be in the sae ange unit, and the coheent integation esults can be witten as S t v s t t vt t, (4) P(, ) ˆ T,M, exp j4π d CPI whee is the wavelength, S t v is the coheent P, integation esult in the ange-velocity plane. In equation (4), the pulse integation tie should satisfy T CPI, (5) vax whee is the ange esolution, and c B. 2 Howeve, in geneal cases, the aneuveing tagets cannot satisfy (5) duing the long integation tie, so ARU will appea, thus affecting the coheent integation of enegy. RFT algoith is a solution way to deal with the effect of ARU. Fo unifo velocity otion, it can be expessed as 2 vt 4πvt G, v s,m, texp j dt c, (6) Equation (6) shows that the echo envelope of each slow-tie is extacted along with the otion tac t v t, and the phase tes ae copensated based on the elationship between velocity and opple fequency. In contast, equation (4) shows that the saple points ae extacted in the sae ange cell fo diffeent pulse epetition inteval. Theefoe, RFT can integate the enegy of taget copletely, while MT cannot. Since otion tac of the taget is unnown befoe detection, two-diensional joint seaching of ange and velocity is equied in the RFT algoith. In pactical application, the discete fo of (6) can be ewitten as M 1 vt G, v s,m ound, exp j4π vt, (7) M 1 A sinc 2 B ( - )+ T ( v v ) c) exp j4π ( v v ) T whee M is the nube of integated pulses. The axiu of integation pea can be found by seaching in distance-velocity paaetes' plane, and the pea value can be witten as G, v A M. (8) 49 Matheatical and Copute Modelling

3 COMPUTER MOELLING & NEW TECHNOLOGIES (11) RFT BSSL CHARACTERISTICS Fo LPRI Pulse opple (P) ada, the accuulating gain of MT ethod (shown in (4)) at abiguous fequency point fd T, coesponding to the abiguous velocity v v vb, whee vb 2T is the blind velocity, is the sae with tue opple fequency point, the tue velocity cannot be ascetained. Fo RFT ethod fo equation (7), although phase fluctuation of abiguous velocity v can still be copensated copletely, only soe sapling units can be accuulated effectively accoding to the false otion tac of abiguous velocity v, if they ae in the sae t v t. ange unit with the eal otion tac The valid integation nube L of accuulated pulses, which satisfies the above condition, can be epesented as ound / v v T v v L. (9) M v v In this case, RFT esults can be ewitten as, AL G v 2A. (1) Thus, fo LPRI P ada, one ain accuulating pea and seveal BSSLs ae geneated in RFT output, and the Piay Lobe-to-Side Lobe Ratio (PSLR) is I M 2lg. (11) 2 Fo constant wavelength, BSSL is elevant with the abiguity nube, the nube of accuulated pulse M and the distance esolution. RFT pocessing can suppess the effect of MT ethod on velocity abiguity, and the suppession atio is I. But RFT still cannot esolve the velocity abiguity copletely. In the case of ultiple tagets, the phenoena of false alas will still exist when BSSLs exceed the theshold. 3 BSSL Suppession of RFT based on RPRI 3.1 PROCESS OF RPRI-RFT P ada with RPRI esolves the poble of velocity abiguity by adding ando jitte to unifo PRI, and it shows good pefoance in anti-inteception and antielectonic-jaing. In RPRI case, slow-tie t is ando, and it can be epesented as t T d ( ) T, (12) whee is a jitte of unifo distibution added to the aveage epetition inteval T, which satisfies.5.5. Then the discete expession of RPRI- RFT can be witten as M 1,M exp4πjv T d G, v s ound vt vd R,. (13) Copaing (13) with (7), thee ae two diffeences between RPRI-RFT and RFT. Fist, the envelope delay of the foe inceases with the ando jitte, which is elated to d instead of inceasing linealy with slowtie t. When vd R, the envelope delay jitte caused by RPRI is uch less than the ange esolution, and the RPRI can be consideed to have no influence on the sapling of envelope. In fact, the condition usually can be satisfied in eality. Secondly, the phase te of RPRI-RFT is not only elated to opple odulation, but exp 4πjvd, which also including a ando te intoduces ando noise coponent to the pocessing esult of RFT. Theefoe, RPRI-RFT is equivalent to Non-Unifo iscete Fouie Tansfo (NUFT) along the tac of ange igation. The Mean and G, v ae analysed as follows. vaiance of The Mean of RPRI-RFT is expessed as E G, v M 1 E s,m ound vt, vt d expj4π M 1 A E sinc2b - + T dv v c exp j4πv vt d. (14) M 1 A E ect - + T d v v exp j4πv vt d L1 A E exp j4πv v T d A x(, v) In (14), the condition suppoted the final appoxiate equation is vd, that is, the envelope jitte caused by RPRI is fa less than the ange esolution. As a esult, x(, v ) in equation (14) is witten as 5 Matheatical and Copute Modelling

4 COMPUTER MOELLING & NEW TECHNOLOGIES (11) x(, v) L1 E exp j4π ( v v)( T d ) ) L 1 exp j4π v v T / v v d v v T L1 v v T v v T Lsinc 2 v v LT / exp j2πv sinc 2 v vt / E exp j4π / sinc 4 / exp j4π / sinc 4 / v L 1 T / The vaiance of RPRI-RFT is expessed as,m 4πv T d M 1 G, v s ound vt R, expj LA sinc 2 B( ) 1 sinc 4 v v T 2 2 2,. (15). (16) In (16), when v v G, v, the ain integation pea of RPRI-RFT has no noise coponent. When v v, ound / L v v T, howeve, G, v becoes salle with inceasing the deviate degee of v fo v accoding to equation (9). Fo (15) and (16), it can be seen that both the ean and G, v have no elationship with the vaiance of nube of integated pulses M. Theefoe, the advantage of RPRI-RFT is that the aplitude of ain pea coesponding to taget paaete, v inceases with the sae popotion as M, while the vaiance of odulation noise coesponding to othe ange-velocity paaete points deceases when v deviates fo v. Although noise is intoduced by ando odulation, it is still estained afte RFT pocessing so that taget can be detected in low SNR when M eaches a cetain value. It can be seen fo Equation (18) that, the ipoveent of BSSL suppession is elated to the jitte and abiguity nube. Specifically when.5, the ean of BSSL is. The noise vaiance intoduced afte RPRI RFT is coputed to be G, v I 2 2 A 2 1 sinc (2 ). (19) In this case, PSLR of RPRI-RFT can be ewitten as 2 M 1lg. (2) sinc Equation (2) shows that, PSLR of RPRI-RFT can incease with the incease of M o the jitte, so the pefoance of PSLR can be ipoved effectively by M and. Foula (19) also shows that BSSL vaiance will educe when abiguity inceases, and howeve, BSSL vaiance cannot be copletely zeo even if =.5. Theefoe, in ode to eliinate BSSL, paaetes and M should be chosen easonably. 4 Nueical expeients Nueical siulations ae done to veify the above analysis. The paaetes of tagets and ada ae as follows: the ada caie fequency is 2.5 GHz; the signal bandwidth is 5MHz; the coplex sapling fequency is 1MHz; the pulse duation is 1μs; and aveage epetition fequency is 1 Hz. Thee tagets ae assued, and thei distance and velocity ae T 1(96, 68 /s), T 2(96, 62 /s) and T 3(94, 68 /s) espectively. 4.1 UNIFORM PRI PROCESSING 3.2 BSSL PROPERTIES OF RPRI-RFT Fo the case of v v, L M and,, E G v AM G, v, the ando odulation has no influence on the integation aplitude of RFT Piay lobe. The BSSL of RPRI-RFT output is ando, and its ean is witten as 2A E G, v sinc(2 ). (17) Copaed with (1), the ipoveent facto of BSSL fo RPRI-RFT can be witten as Ia sinc(2 ). (18) The ange wal does not occu when M = 32. Fo unifo PRI, the esult of MT is shown in Figue 1. Velocity abiguity has eeged on thee tagets so that the eal velocity cannot be obtained coectly. In addition, MT pocessing cannot distinguish T 1 fo T 2 in the sae distance and opple unit in Figue 1. FIGURE 1 MT esults of unifo PRI when M=32 51 Matheatical and Copute Modelling

5 COMPUTER MOELLING & NEW TECHNOLOGIES (11) The ARU effect becoe uch oe evident when M =124. The esults of MT and RFT ae shown in Figue 2. Figue 2(a) shows that MT pocessing cannot distinguish the thee tagets, because of ARU effect. Figue 2(b) shows that the tagets cannot be distinguished because of BSSL, in this case, the PSLR is I 6.2dB. (a) MT esults of.3 (a) MT esults (b) RPRI -RFT esults of.3 (b) RFT esults FIGURE 2 Results of unifo PRI when M = RESULT OF RPRI-RFT On the basis of unifo PRI, RPRI status is pesented, and the suppession of diffeent jittes on blind side lobe is analysed, which is shown in Figue 3: (1) When.3, MT shown in Figue 3(a) is diectly applied, and the velocity diension accods with noise distibution; (2) When.3, the RFT pocessing esults ae shown in Figue 3(b). The BSSL is futhe suppessed, and I 1 =1.9dB, which is 4.7dB highe than Figue 2(b); (3) When.5, the RFT pocessing esults ae shown in Figue 3(c). The BSSL of RFT is educed shaply, and the PSLR is I 1 =27.7dB. Fo the above siulation esults, it can be obseved that the noise does not affect distance esolution along the distance diension, and the effect of odulation noise is sall out of ange esolution unit afte RPRI-RFT pocessing; along the velocity diension, the ando odulation noise can be futhe suppessed, and the influence of odulation noise will be salle when a cetain pulse nube M is selected. (c) RPRI-RFT esults of.5 FIGURE 3 Results of RPRI at M =124 The following Figue 4 shows that PSLR values of diffeent jitte and the nube of accuulated pulse M coespond to the position of the fist side lobe. PSLR/dB =.5 =.48 =.45 = M FIGURE 4 PSLR value of diffeent α and M 52 Matheatical and Copute Modelling

6 COMPUTER MOELLING & NEW TECHNOLOGIES (11) Fo Figue 4, it shows that the PSLR can be ipoved to 2 db when M is oe than 6 and.45, and the PSLR can be ipoved to 3 db when M is oe than 1 and.48. These esults show diffeent ability to suppess of the BSLL at diffeent paaetes. 4.3 PERFORMANCE ANALYSIS OF RPRI-RFT IN LOW SNR P d FIGURE 5 Results of RPRI at M=124 and SNR=-2dB On the basis of section 4.2, Gaussian white noise is intoduced, and the input SNR is -2dB. Expeiental esults ae shown in Figue 5. Figue 5(a) shows that tagets ae subeged in noise afte MT pocessing. Figue 5(b) shows that signal enegy can be integated so that SNR can be ipoved substantially afte RPRI-RFT pocessing. Figue 4(c) shows that afte the incease of the PRI jitte, BSSL is subeged in noise, and the thee pecs of the tagets ae all uch highe than the noise bacgound when the pulse nube M is lage enough ( M =124),in this case, the output SNR is 2.7dB SNR/dB FIGURE 6 etection pefoance at diffeent input SNR In ode to analyse the detection pefoance at low input SNR, the esults ae given at diffeent input SNR of 1 Monte-Calo siulation expeients in Figue 6. With detection pobability P d =8% and a given constant false ala atio P f =1-6, Figue 6 shows that the needed input SNR is -34.3dB at RPRI-RFT ethod. Siulation esults illustate that RPRI-RFT can be well applied to esolve the poble of di taget detection and anti-velocity abiguity, theeby achieving accuate velocity and distance of tagets. 5 Conclusion (a) MT esults at.3 (b) RPRI-RFT esults at.3 Fo the detection of the high-velocity di taget, the poble of ARU in long coheent integation tie can be solved by RFT algoith. Howeve, BSSL of RFT algoith ay affect the detection when ultiple tagets exist in the obseved scene. Theefoe, a RFT algoith with RPRI odulation has been poposed to estain BSSL in this pape. The pocess of RPRI-RFT has been descibed and the BSSL popeties of RPRI-RFT have been analysed in details. The expeiental esults have shown that RPRI-RFT can effectively estain BSSL and the influence of odulation noise of RPRI can be suppessed by the chaacteistic of long-tie integation of RFT. Theefoe, the ability to detect long-ange and high velocity di tagets has been ipoved effectively by RPRI-RFT, and poved by the siulation esults. Acnowledgent This wo has been suppoted in pat by Shanghai Aeospace Technology Innovation Fund (Poject No. SAST21224). (c) RPRI- RFT esults at.5 53 Matheatical and Copute Modelling

7 COMPUTER MOELLING & NEW TECHNOLOGIES (11) Refeences [1] Solni M 22 Oppotunities in ada-22 Electonics and Counication Engineeing Jounal 14(6) [2] Cleetus G M 1976 Popeties of staggeed PRF Rada Spectal Coponents IEEE Tansaction of Aeospace and Electonic Syste 12(6) 8-3 [3] Vegaa oinguez L 24 Analysis of the digital MTI filte with ando PRI IEE Poceedings-F 14(2) [4] Baton K 24 Rada Syste Analysis and Modeling Beijing: Publishing House of Electonics Industy [5] Solni M 22 Intoduction to Rada Syste (3nd d) Colubus, OH: McGaw-Hill [6] Yuxi Zhang, Jinping Sun, Bingchen Zhang, Wen Hong 211 opple Abiguity Resolution Based on Copessive Sensing Theoy Jounal of Electonics & Infoation Technology 33(9) [7] Calson B, Evans E, Wilson S L 1994 Seach Rada etection and Tac with the Hough Tansfo Pat I: Syste Conception IEEE Tansactions on Aeospace and Electonic Systes 3(1) 12-8 [8] Calson B, Evans E, Wilson S L 1994 Seach Rada etection and Tac with the Hough Tansfo Pat II: etection Statistics IEEE Tansactions on Aeospace and Electonic Systes 3(1) [9] Calson B, Evans E, Wilson S L 1994 Seach Rada etection and Tac with the Hough Tansfo Pat III: etection Pefoance with Binay Integation IEEE Tansactions on Aeospace and Electonic Systes 3(1) [1] Richads M A 25 Fundaentals of Rada Signal Pocessing New Yo: McGaw-Hill [11] Wang Y M, Ma J G, Fu Q, Zhuang Z W 26 Reseach on integation detection of high-velocity oving taget Moden Rada 28(3) 24-7 (in Chinese) [12] Pey R P, ipieto R C, Fante R L 27 Coheent integation with ange igation using Keystone foatting In Poceedings of IEEE Rada Confeence [13] Su J, Xing M, Wang G, Bao Z 21 High-velocity ulti-taget detection with naowband ada IET Rada Sona and Navigation 4(4) [14] Zhang S S, Zeng T 25 i taget detection based on Keystone tansfo In Poceedings of IEEE Intenational Rada Confeence May [15] Xu J, Yu J, Peng Y, et al. 211 Radon-Fouie tansfo fo ada taget detection I: genealized opple filte ban IEEE Tansactions on Aeospace and Electonic Systes 47(2) [16] Xu J, Yu J, Peng Y-N, et al. 211 Radon-Fouie Tansfo fo Rada Taget etection, II: Blind Velocity Side lobe Suppession IEEE Tansactions on Aeospace and Electonic Systes 47(4) [17] Xu J, Yu J, Peng Y-N, et al. 212 Radon-Fouie tansfo fo ada taget detection III: Optiality and Fast Ipleentations IEEE Tansactions on Aeospace and Electonic Systes 48(2) [18] Li-chang Qian, Jia Xu, Wen-feng Sun, Ying-ning Peng 212 Blind Speed Side Lobe Suppession in Radon-Fouie Tansfo Based on Rada Pulse Recuence Inteval esign Jounal of Electonics & Infoation Technology 34(11) (in Chinese) [19] Lichang Qian, Jia Xu, Wenfeng Sun, et al. 212 CLEAN based blind velocity side lobe (BSSL) suppession in the Radon Fouie Tansfo (RFT) fo ulti-taget detection Poc. of 212 IEEE 12th Intenational Confeence on Copute and Infoation Technology 49-5 Authos Qian Chen, bon on Mach 16, 1975, China Cuent position, gades: pusuing his Ph.. degee in Beijing Univesity of Science and Technology. Univesity studies: B.S. degee fo Univesity of Electonic Science and Technology of China, in 1996, and the M.S. degee fo Shanghai Radio Equipent institute, in 1999, China. Expeience: He joined in the Shanghai Radio Equipent Reseach Institute in 1999, and has been a vice diecto. Scientific inteest: ae signal pocess, autoobile anti-collision and ada syste. He has been long engaged in shot-ange ada technology eseach. Junhao Liu, bon on Febuay 12, 1988, China Univesity studies: B.S. degee in counication engineeing fo Nanjing Univesity of Science & Technology, Nanjing, China, in 211. He eceived the M.S. degee in 214 fo Shanghai Acadey of Spaceflight Technology, Shanghai, China. Expeience: He joined Shanghai Radio Equipent Reseach Institute, China, in 214, whee he has been engaged in eseach on wea signal pocessing, and shot-ange ada syste. Chaowei Fu, bon on May 21, 1985,China Cuent position, gades: a eseache at Shanghai Radio Equipent Reseach Institute, China. Univesity studies: B.S. and M.S. degees in engineeing of signal and infoation pocessing fo Xidian Univesity, Xi'an, China, in 21. Scientific inteest: SAR Iaging and Signal pocessing. Haitao Wang, bon on August 13, 1978, China Cuent position, gades: senio enginee in Shanghai Radio Equipent Reseach Institute. Univesity studies: B.S. degee in Shandong Univesity, Jinan, Shandong, in 2. He eceived the M.S. degee in 23 fo Shanghai Acadey of Spaceflight Technology, Shanghai, China. Scientific inteest: ada signal pocessing, ada syste and Teahetz detection technology. 54 Matheatical and Copute Modelling