A Study on Stepped Frequency Radar by Using Intra-Pulse Phase Coded Modulation

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Eustace Harrell
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1 Proeedigs of the World ogress o Egieerig ad omputer Siee 28 WES 28, Otober 22-24, 28, Sa Fraiso, USA A Study o Stepped Frequey Radar by Usig Itra-Pulse Phase oded Modulatio. Fuushima ad. Hamada Abstrat I radar system, for detetig targets i the strog bagroud lutters, separatio of the target requires high rage ad ross-rage resolutio i the system. The high rage resolutio is obtaied by utilizig shorter pulses ad widebad-fm pulses, therefore, a expesive widebad reeiver should be implemeted. The alterative system to ahievig high rage resolutio without usig widebad reeiver is the stepped frequey (SF radar sheme performed sytheti rage profile (SRP proessig. The iple of this radar is that the ehoes of stepped frequey pulses are sythesized i the frequey domai to give the shorter pulses i the time domai thorough the IDFT. The SF radar auses some problems due to the Doppler shift whe it is applied to detet movig targets. I partiular, if the system assumes the fixed sytheti badwidth ad the target veloity, the ifluee of Doppler shift is greatly affeted by the duratio of the observatio time, whih is determied by the frequey step umber ad the pulse repetitio iterval. I this paper, we propose the phase oded stepped frequey (PSF radar with usig itra-pulse phase oded modulatio o eah SF pulse. It aims to realize the required sytheti badwidth by fewer frequey steps. The effetiveess of the PSF radar performig the Doppler ompesatio is proved eve uder low sigal-to-oise (SR irumstaes. Idex Terms Stepped frequey radar, Phase oded modulatio, Sytheti badwidth proessig I. ITRODUTIO The reeived eho sigals of radar (e.g. groud searh radar otai both the target ad bagroud lutter sigals. The bagroud lutter sigals, suh as refletios by groud, strutures, vegetatios ad so o, iterfere with the detetio of the targets. Hee it is eessary to separate the target sigal from bagroud lutter sigals with high spatial resolutio as well as rage ad/or ross-rage resolutio [1][2]. The aim of our study is foused o the improvemet of the rage resolutio. The straightforward approah for that purpose utilizes short duratio pulses ad widebad-fm pulses. This arrow pulse system has to realize ompliate system arhiteture, the, it results i higher implemetatio ost due to a widebad reeiver usage. The stepped frequey (SF radar performed sytheti rage-profile (SRP proessig has bee proposed to ahieve high rage resolutio without usig widebad reeiver[3]. The iple Mausript reeived July 22, 28; revised August 8, 28.. Fuushima is with the Shool of Itegrated Desig Egieerig, Graduate Shool of Siee ad Tehology, Keio Uiversity, Yoohama, Japa( fuushima@z2.eio.jp.. Hamada is with the Departmet of System Desig Egieerig, Siee ad Tehology, Keio Uiversity, Yoohama, Japa. of this radar is that the ehoes of stepped frequey pulses are sythesized i terms of Fourier trasform domai. This eables us to obtai short pulses i the time domai. I the previous study [4][5], we have evaluated the performae of SF radar i the detetio of statioary targets by both the omputer simulatios ad the experimets usig atual targets i a atual field. The obtaied results verified the effetiveess of SF radar to ahieve the rage-profile of targets. For the ase of movig targets, o the other had, the Doppler shift auses some problems that degrade both the preisio i the deteted target loatio ad the pea promiee of target sigal after proessig. I partiular, if the system assumes the fixed sytheti badwidth ad the target veloity, the ifluee of Doppler shift is greatly affeted by the observatio time iterval, whih is determied by the frequey step umber ad the pulse repetitio iterval. The approate Doppler ompesatio is a possible way to avoid the above degradatios i SRP proessig. The method by Hara et al.[6] gives oe way to Doppler ompesatio. However, exat estimatio of the target veloity is a diffiult tas i the low sigal-to-oise (SR irumstae. Oe way to overome this problem is to shorte the duratio i observatio to mitigate the effet of target s movig. This orrespods to reduig the umber of pulses. I otrast with reduig the umber of pulses, we mae the effetive badwidth of eah pulse wider to eep the sythesized badwidth approximately same, beause the sythesized badwidth is determied by the produt of the umber of SF pulses ad the effetive badwidth i eah pulse. From the viewpoits of the pea detetio, the pea power dereases aordig to the redutio of the umber of pulse. The phase oded modulatio is used for the ovetioal SF radar as a itra-pulse modulatio to get the sigal proessig gai for the purpose to mae up for the pea power redutio. This id of system is alled the PSF radar, ad studied i [7] ad [8]. The system i [7] has to use relatively wider istataeous reeived badwidth, ad the study i [8] does ot osider the Doppler ompesatio. We propose the PSF radar with the Doppler ompesatio, the badwidth of whih is arrower. The method uses the Doppler ompesatio based o the estimatio by reeived eho sigal. This report disusses a improved method givig high performae i target detetio eve i low SR irumstaes. This paper is orgaized as follows. The rage resolutio of uoded pulse radar is preseted i Setio II. The iple of movig target detetio of SF radar ad its problems are preseted i Setio III. The harateristi of itra-pulse phase oded SF radar is preseted i Setio IV. The results ISB: WES 28

2 Proeedigs of the World ogress o Egieerig ad omputer Siee 28 WES 28, Otober 22-24, 28, Sa Fraiso, USA of simulatio of proposed ad ovetioal SF with PSF are give i Setio V. The olusio is give i Setio VI. II. RAGE RESOLUTIO OF PULSE RADAR The rage resolutio, deoted by R, of pulse radar is defied as a futio of pulse width τ i the time domai as t D R = (1 2 where is the speed of light. The required reeiver badwidth B P i the frequey domai ad the pulse width τ i the time domai are related by B P = 1/τ, the (1 a be writte by DR =. (2 2B P As taig the wider reeiver badwidth B P, the pulse width τ is gettig shorter, the the rage resolutio is improved. (atrasmitted pulses ad reeived pulses i the time domai. III. STEPPED FREQUEY RADAR SF radar is ow as a tehique to ahieve high rage resolutio profile by usig SRP proessig. The basi oept of this radar is that the several arrow badwidth pulses of whih eter frequey is haged step by step durig eah pulses are sythesized. The mehaism of SF radar is firstly desribed ad the problems assoiated to detetig movig target i SF radar are metioed below. A. Sytheti Rage Profile Proessig The SRP proessig of stepped frequey radar osists of the followig proesses. 1 Trasmittig a series of stepped frequey pulses with stepwise time-varyig arrier frequey. We deote f as the step frequey width at eah pulse. 2 Sythesizig these badwidths of reeived pulses i the frequey domai for attaiig effetive broad badwidth. 3 arryig out IDFT for the sythesized badwidth. The obtaied rage resolutio by these proesses is higher tha that give by (2. I the followig, we explai the SRP proessig by usig a simple model ad the system arhiteture of it. osider the statioary target model whih exists i rage R from radar, ad R is assumed to satisfy / < T where T is the pulse repetitio iterval. Fig.1 shows the SRP proessig with frequey step umber. The eah pulse is trasmitted at differet arrier frequey, stepped up by spaig f from the first frequey f as show i Fig.1(a. Therefore the trasmitted th pulse sigal S (t (=,1,,-1 is expressed as ìa exp[ j( 2p ( f t + f ] S( t = í ; T t T + t (3 î ; otherwise where A is the amplitude ad ϕ is the iitial phase of the trasmitted pulses. ow, we assume that the trasmitted sigal is refleted by the statioary target loated i rage R, the the reeived sigal U (t(=,1,,-1 is expressed by ì A' expê jç2p ( f + D f è U ( t = í î ; ; æ T + otherwise æ ö çt - + f è ø ø t < T + + t (4 (breeived pulses i the frequey domai. (Sythesized badwidth ad resulted rage resolutio. Fig. 1. Priiple of SF radar by usig SRP proessig. where A is the amplitude of the reeived pulses. osider the referee sigal W (t (=,1,,-1 whih has the same frequey ad iitial phase as S (t, but W (t is defied over the iterval of t Î [T, (+1T ] as follows W ( t = B exp[ j( 2p ( f t + f ] ; T t < ( + 1 T. The the video sigal V (t (=,1,,-1 is defied as * V ( t = U ( t W ( t ì = í î ù A" exp ê - ( f ; T + t < T + + t, ; otherwise where W * (t is the omplex ojugate of W (t ad A is A multiplied by B. The disrete video sigal V( (=,1,,-1, sampled with the same spaig as the trasmitted pulse width from (6, is expressed as arryig out IDFT for data of V( obtaied, the resultat sigal of IDFT, P( (=,1,,-1 is give as ù " ê (5 (6 V ( = A exp -. (7 P 1-1 ( = åv ( 1 = = -1 å = A"exp ê- A" æ = expç - f è ù expê ö ø -1 å = æ expê ç è ù ù expê ö ù - Df ø ISB: WES 28

3 Proeedigs of the World ogress o Egieerig ad omputer Siee 28 WES 28, Otober 22-24, 28, Sa Fraiso, USA Fig. 2 Flowhart of SRP proessig. æ 1- expê ç A" æ ö è = expç - f è ø æ 1- expê ç è A" æ ö æ ö ù = expç - f expê jp ç - Df ( -1 è ø è ø æ p æ siêp ç - Df siê ç - Df è ø è ø ad the amplitude of P(, P( is give as æ si " êp ç - Df A ( è ø P =. (9 p æ siê ç - Df è ø P( taes the maximal value at p = Df, (1 ad the rage R from radar to the target is obtaied by R = p. (11 2Df For iteger p, the rage resolutio R of the SRP proessig is give by D R =, (12 2Df = 2BSF where B SF is the sythesized badwidth of SF radar (= f. This equatio meas that the R depeds o the sythesized badwidth, amely f. Whe the f equals B P, the rage resolutio is improved by the fator of 1/ ompared to R i (2 as show i Fig.1(. Fig.2 shows the flow of the SRP proessig, where the rage bi orrespods to the pulse width τ. I pratie, the data are itegrated at eah rage bi i the frequey domai. The IDFT is arried out for data stepped of eah rage bi, ad we aquire the high rage resolutio profile o required area. B. Problem of Movig Target s Detetio ö ù - Df ø - Df ø (8 For (4, if the relative veloity of target is ot zero (v,, the reeived eho sigal U (t (=,1,,-1 refleted by the movig target is rewritte as ì æ æ 2 ( ( R - vt ö A' exp ê jç2p f çt - + f è è ø ø U ( t = í 1 æ ö 1 æ ö (13 ; ç T + t < ç T + + t 1 + 2v è ø 1 + 2v è ø î ; otherwise where R ad v are the iitial rage of target from radar ad the relative veloity agaist the radar respetively. I the same sese of (7, sampled versio V( (=,1,,-1 of (13 is desribed as V ê = A"exp ê- expê ( = A"exp - T. Beause of Doppler shift of the seod expoetial term i (14, performig SRP proessig for data of V( obtaied from (14, the deteted target rage is ot orret ad also, the target pea is weaeed ad is diffused. These degradatios by Doppler shift deped o the target veloity v ad the observatio time that is the futio of the frequey step umber ad the pulse repetitio iterval T. For reduig the Doppler shift, it is effetive to perform SRP proessig withi less observatio time. IV. ITRA-PULSE PHASE ODED SF RADAR The SF radar realizes broad istataeous badwidth for overig the required sytheti badwidth i less time iterval ad with fewer frequey steps (lower, but it is ot eough power to detet target after performig SRP proessig. I otrast, itra-pulse phase oded SF (PSF radar is a tehique for reduig the Doppler shift by ahievig the required sytheti badwidth i less time iterval, ad utilizes the sigal gai obtaied by pulse ompressio of itra-pulse phase oded (P radar for improvig the SR. A. harateristi of Phase odig P radar ireases the effetive badwidth by hagig the itra-phase of trasmitted pulse sigal. If the pulse is modulated by ode sequee of legth M, a uoded pulse of width τ is divided ito M bits of idetial duratio τ, suh that τ=m τ. Eah divided pulse is alled subpulse. The eah bit is assiged with a speifi ode phase value ϕ m (m=1,2,,m, e.g. the phases of 13-elemet Barer ode (M=13 are [ π π π π ]. The rage resolutio of P radar deoted by R P is defied as t DR P = =, (15 2 2BP where τ is the duratio of oe bit of ode (=τ/m, B P is the resultat badwidth of phase oded subpulse of P radar, ad these are related by B P =1/τ. B. Rage Resolutio of PSF æ 2v ç - T è ù 2v ù (14 ombiig SF ad P proessig, the trasmitted PSF sigal a be desribed as ø ISB: WES 28

4 Proeedigs of the World ogress o Egieerig ad omputer Siee 28 WES 28, Otober 22-24, 28, Sa Fraiso, USA [ ] ì Am exp j( 2p ( f t + f S( t = í ; T + ( m -1 t t T + ( m -1 t (16 î ; otherwise where m is the mth ode for the th subpulse, i.e. m =exp(jϕ m. The PSF sythesized badwidth B PSF depeds o P ad SF harateristis, whih is expressed as BPSF = Df =. (17 t Hee, the rage resolutio of PSF radar is desribed as (18, whih is the PSF radar versio of (12. t D RPSF = = =. (18 2BPSF 2Df 2 Hee, if the sythesized badwidth of SF ad PSF radar is the same, the PSF subpulse badwidth is larger tha that of SF pulse (e.g. B PSF =M B SF, the PSF waveform overs the required sytheti badwidth usig fewer frequey step umber. By reduig the observatio time iterval durig a oheret proessig, it is effetive to mitigate the degradatio by target s movig. V. SIMULATIO RESULTS I this setio, we ompare the detetio performae of SF with PSF radar usig 13bit-Barer ode for itra-pulse phase oded modulatio. A. Results of statioary target ad Movig target The target is assumed as a poit refletive target loated i the iitial rage 45m apart from the radar. The parameters of simulatio are show i Table I. The amplitude i the figures is the ormalized value to the video sigal amplitude A i (6. Fig.3 (a ad (b show the SRP proessig result of SF ad PSF radar respetively, for zero target veloity (v=, the deteted targets are loated at the orret rage beause these are o Doppler shift. Fig.3( ad (d show the results of SF ad PSF radar respetively, for the ase whe the target veloity is ot zero (v=3m/s. The deteted target rages of SF ad PSF radar are 49.4m ad 453.1m respetively, so the Doppler shift auses iorret target rage estimates as show i these results. omparig Fig.3( ad (d, the target pea of SF broadeed due to Doppler shift, though target pea of PSF is ot so deviated. I iple, the rage error that orrespods to the target veloity ours durig the pulse width ad the subpulse width i SF ad PSF Table I Parameters of simulatio. System parameter SF PSF (13bit-Barer 1 st trasmitted frequey (f 36GHz 36GHz Istataeous reeived badwidth 1MHz 13MHz Stepped-frequey width ( f 1MHz 13MHz Step umber ( Pulse width (τ 1μs 1μs Subpulse width (τ 1/13μs Pulse repetitio iterval (T 1μs 1μs IDFT poit umber Sytheti badwidth ( f 512MHz 57MHz Rage resolutio (theoretial value.293m.296m (a SF (R =45m, v=m/s, SR= (b PSF (R =45m, v=m/s, SR= Deteted target rage : 49.4m Deteted target rage : 453.1m ( SF (R =45m, v=3m/s, SR= (d PSF (R =45m, v=3m/s, SR= Fig. 3 Target detetio results without Doppler ompesatio. ISB: WES 28

5 Proeedigs of the World ogress o Egieerig ad omputer Siee 28 WES 28, Otober 22-24, 28, Sa Fraiso, USA (a SF (R =45m, v=3m/s, SR=dB (b PSF (R =45m, v=3m/s, SR=dB ( SF (R =45m, v=3m/s, SR=-1dB (d PSF (R =45m, v=3m/s, SR=-1dB Fig. 4 Target detetio results without Doppler ompesatio with WG. respetively. With respet to the redutio of target pea, it is remarable that SF radar has the lower pea value tha that of PSF. This a be ivestigated that the smaller umber of pulse mitigates the redutio i the pea value. This meas the effet of the Doppler shift a be suppressed by reduig the observatio time. Fig.4 shows the SRP proessig results i the additive white Gaussia oise (WG ase. Fig.4 (a ad (b show the results for the ase of SR=dB. The, ( ad (d show the results for SR=-1dB, whih meas target sigal is uder oise level before sigal proessig. Aordig to these figures, it is evidet that the target detetio auray of PSF radar is better tha SF radar espeially i the low SR irumstae. However, the iorret target rage is ot ompesated yet. B. Effet of Doppler ompesatio This setio disusses the target detetio performaes of SF ad PSF with the ompesatio for the Doppler. I [6], the Doppler ompesatio has bee proposed usig the target veloity v al estimated by the reeived data. The ompesatio is performed usig target veloity alulated from the IDFT of phase differee futio. The futio is the produt of the digital video sigal V( ad the α-shifted omplex ojugate digital video sigal V * (+α. Here the sample umber of IDFT is -α. The optimal shift value α opt that the veloity resolutio is miimized is /2. Fig.5 shows the results of SF ad PSF with Doppler ompesatio for eah SR, where the target veloity is 3m/s iboud ad the iitial target rage is 45m. The simulatio parameters are show i figures. The alulated Table II Results of alulatio for the target veloity Figure System SR (db alulated Veloity v al (m/s Deteted Rage (m 5 - (a SF (b PSF ( SF (d PSF (e SF (f PSF veloities ad deteted target rages are show i Table II. We a observe preise estimatio results. As show i Fig.5 (a to (d, ompesatig Doppler shift, the target is deteted at the orret rage of target (45m. However, the estimatio by the SF for the lower SR does ot give orret rage as show i Fig.5 (e, beause it ould ot preisely ompesate Doppler shift due to oise. O the other had, the results of PSF at lower SR show preise rage estimatio as show i Fig.5 (f. VI. OLUSIO The high rage resolutio SF radar for movig targets has bee disussed. For ovetioal SR radar with sythesized rage profile proessig improves the rage resolutio, but the degradatio i estimatio of the positio ad pea height by target movig is the problem. To overome the problem, we use the wider istataeous badwidth pulse to eep the rage resolutio ad redue the observatio time, whih orrespods to the umber of frequey steps. I additio to usig the wider badwidth pulse, the ode modulatio is ISB: WES 28

6 Proeedigs of the World ogress o Egieerig ad omputer Siee 28 WES 28, Otober 22-24, 28, Sa Fraiso, USA (a SF (R =45m, v=3m/s, SR= (b PSF (R =45m, v=3m/s, SR= ( SF (R =45m, v=3m/s, SR=dB (d PSF (R =45m, v=3m/s, SR=dB (e SF (R =45m, v=3m/s, SR=-1dB (f PSF (R =45m, v=3m/s, SR=-1dB Fig.5 Target detetio results with usig Doppler ompesatio. adopted as the itra-pulse modulatio to avoid degradatio i the pea height. The simulatio results show that the proposed PSF method suppresses the degradatio i target sigals suffiietly, with respet to the Doppler shift eve i the low SR irumstaes. I additio, it is show that higher preisio i rage estimatio a be ahieved with the Doppler ompesatio. The preisio i the target veloity estimatio is ot so superior i PSF radar as i SF radar, beause SF uses small umber of pulses proessed. This would be solved i further researh. REFEREES [1] B. Edde, Radar, Pretie Hall, ew Jersey, [2] G. Stimso, Itrodutio to Airbore Radar, SiTeh Publishig, ew Jersey, [3] D. R. Weher, High Resolutio Radar, 2d ed., pp , Arteh House, Bosto, [4]. Fuushima, ad T. Yamaoa, Rage Profile Measuremet o Sytheti Badwidth Radar, IEIE Tras. ommu.(japaese Editio, Vol.J89-B, o.6, pp , Ju 26. [5]. Fuushima, Experimetal osideratio o the sytheti rageprofile proessig by stepped-frequey radar, IEEE TEO27, pp.1-4, 3 Ot-2 ov. 27. [6] T. Hara, T. Seiguhi, I. hiba ad S. Wadaa, Doppler frequey tolerat sytheti badwidth radar, IEIE Tras. ommu.(japaese Editio, Vol.J89-B, o.7, pp , July 26. [7] M. A. Temple, K. L. Sitler, R. A. Raies ad J. A. Hughes, High rage resolutio (HRR improvemet usig sytheti HRR proessig ad stepped-frequey polyphase odig, IEE Pro. Radar Soar avig., Vol.151, o.1, pp.41-47, February 24. [8] Ji Kai, Wag Wei-dog ad Wag Dog-Ji, The Study o a ew Radar Waveform with High Rage Resolutio, ISP 4 Pro., pp , Aug. 31-Sept. 4, 24. ISB: WES 28

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