60 GHz FMCW Radar System with High Distance and Doppler Resolution and Accuracy

Transcription

1 Deparmen o Elecrical Engineering Sudenenadminisraie Den Dolech, 56 AZ Eindhoven.O. Box 53, 56 MB Eindhoven The eherlands hp://w3.ele.ue.nl/nl/ Auhor Li Wang Order issuer ro. Balus Group/Chair: Mixed-signal Micro Elecronics 6 GHz FMCW Radar Sysem wih High Disance and Doppler Resoluion and Accuracy Reerence Series: Maser graduaion paper, Elecrical Engineering Dae 3 Augus ro. Balus Copy holder The Deparmen o Elecrical Engineering o he Eindhoven Universiy o Technology acceps no reponsibiliy or he conens o M.Sc. heses or pracical raining repors

2 Graduaion paper 6GHz FMCW Radar Sysem wih High Disance and Doppler Resoluion and Accuracy Li Wang Signal rocessing Sysem Group, Deparmen o Elecrical Engineering Eindhoven Universiy o Technology and ESSI Deparmen, hilips Research l.wang.@suden.ue.nl Absrac This paper presens an algorihm or 6GHz FMCW radar deecion sysem providing precise disance and velociy measuremens. A digial simulaion environmen based on he radar hardware seup is buil o evaluae and demonsrae he applicabiliy and perormance o he deecion sysem under laboraory condiions. The sysem irs incorporaes a normal or general requency esimaion, based on which he Radar Cross Secion o deeced arges will be calculaed or urher processing. Then Consan False Alarm Rae (CFAR) Threshold algorihm is used or deecing radar arges in background ull o noises and relecions or which all parameers in he saisical disribuion are no known and may be non-saionary. Finally he Complex Specral hase Evoluion (CSE) mehod is applied as a ool o obain super Doppler and disance accuracy, which can provide or super-resoluion o requencies by examining he evoluion o he phase o he signal specrum over ime -shied windows. The uncionaliy o he sysem is demonsraed by simulaion based on he 6GHz FMCW radar hardware sysem and will also be esed on he real hardware sysem. The paper illusraes, ha he combinaion o advanced signal processing scheme wih a cos-eecive ron-end can provide high perormance microwave sensors. Index Terms CFAR rocessors, CSE, Doppler Eec, FMCW Radar, High Resoluion, High Accuracy C I. ITRODUCTIO OMMERCIAL high volume applicaions o microwave and millimerewave echnology, e.g. in he auomoive area, indusrial process conrol or public uiliies and household applicaions, require cos eicien sensor designs [], []. Under his condiion i is very imporan no only o consider he sensor hardware bu especially he sysem concep ha is a combinaion o advanced ron-end hardware and suiable sensor digial signal processing algorihms. Employing algorihms adaped o he given sensor, some criical uncionaliy can be ransormed rom he hardware o he soware level. This way, sensors wih excellen This projec was perormed in Elecronic Sysem & Silicon Inegraion Deparmen, hilips Research, Eindhoven, he eherlands, rom December, 9 o Augus,. uncionaliy can be se up based on a less sophisicaed and less expensive hardware. Furhermore, inelligen sensors require addiional algorihms e.g. or sel diagnosis and sel calibraion. The rapid developmen o processor echnology e.g. signal processors or RISC conrollers allow o implemening sophisicaed algorihms a moderae cos [3]. For a radar deecion sysem, he criical uncionaliy may be dieren or dieren applicaions. However, generally speaking, simulaneous arge range and velociy measuremen wih high resoluion and accuracy, which is virually unaeced by resricive condiions such as weaher and ligh, are always preerred and is he key o many imporan applicaions, i.e., such as in vehicle echnology, by he aid o high speed, disance accuracy and disance resoluion measuremen, he saey can be signiicanly raised. The 77 GHz FMCW radars are especially eecive and presenly on he marke as he saey sysem or high perormance auomoive applicaions [4] [5]; also in many public uiliies and household applicaions, high accuracy can help o improve he power eiciency. A radiional approach o range exracion is o use he. However, resuls give a low resoluion and accuracy since he ypical FMCW radar sysem has a narrow bandwidh and limied sample capabiliy. In order o improve he resoluion and accuracy capaciy, much research has been conduced wih high resoluion and accuracy algorihms such as AR (Auo-Regressive), MUSIC (MUlipe SIngnal Classiicaion), and ESRIT (Esimaion o Signal arameers by Roaional Invariance Technique) [6],[7]. However, since hese algorihms have a high compuaional complexiy, embedded high-perormance hardware is required o process he algorihms in real ime o apply hem ino radar. In his paper, we propose a range and velociy exracion scheme o 6GHz FMCW radar sysem wih high resoluion rely on he advanced ron-end hardware wih large requency sweep bandwidh, maximum o 6 GHz and high accuracy using a CSE (Complex Specral hase Evoluion) algorihm which can esimaing he requency o componens ha exis in a signal wih super accuracy, an order o magniude larger han he and independen o he requency bin. Based on he sysem design, his paper is organized as ollows: Secion II inroduces he background knowledge

3 Graduaion paper abou he heory and pracice principle o he FMCW radar and Doppler Eec. In Secion III, hardware and simulaion environmen or inal sysem perormance evaluaion will be described. Secion IV elaboraes our proposed deecion sysem in deail sep by sep and also he CFAR processor. Secion V will ocus on he accuracy improvemen, discussing possible soluions o increase he range and speed accuracy o he arges. In Secion VI, he inal deecion sysem scheme will be evaluaed in he simulaion environmen based on he hardware. Final conclusions will be drawn in Secion VII. Tx Rx a D Fig. Typical Doppler signal o CW radar a a D A. Inroducion II. FMCW RADAR AD DOLER EFFECT Wih he as developmen o emerging acive sensing radar echnology, i more and more covers he whole area o ransporaion and public uiliies and applicaions; even more is role is increasingly growing in wireless sensors echnology, especially in vehicle echnology, signiicanly raising is saey by he aid o speed, disance and disance resoluion measuremens. There are many ypes o radar used in sensors, bu his inroducion only covers radars in coninuous operaion, especially or he FMCW radar. The heory explained here is aided by he design and consrucion o radars which are buil ino sensors [8]. B. CW Doppler Radar According o he Doppler heory: i here is a coninuous signal (CW) ransmiing ransmier, i beams a signal wih requency a on a arge (or example a vehicle) and he arge has a relaive speed v r compared o he ransmier, hen he releced signal requency v is larger or smaller han a depending on wheher he arge is moving o or away rom he ransmier. The requency o he received signal is dieren rom he requency o he ransmied signal and called Doppler Frequency D. I can be calculaed rom: vr vr D D v a a vr () c where λ is he wavelengh and c is he speed o ligh and due o ransmiing and receiving, here is a acor o. Fig. shows a simple CW radar schemaic while Fig. shows he CW radar signal requency specrum. Tx CW power Oscillaor Display Ampliier D LF Fig. Block Scheme o a simple CW radar a a D or a Transmi signal Rx Received signal D C. FMCW Radar In case we plan o use he CW radar or disance measuremen, he ransmier requency is modulaed by a riangular signal [9]. The requency o he ransmier oscillaor is increased or decreased by some uncion. This uncion can be riangular, sawooh or sinusoidal in shape. In radars, in general, he irs wo are in use. Linear requency modulaion is used in he early years o radar echnology because o he simple modulaion process and will be used or explanaion and insrucion in he ollowing secions. This mehod uses a requency called chirp or he signal which changes linearly over ime. The goal is o esablish a simple sysem or disance measuremens, because here is dierence in requency only beween he radiaed and releced signal d in case o linear requency modulaion. ) Linear Modulaion or saic arge wih r Examine he ransmied and he received signal momenary requency which is based on Fig. 3, hen we can ge a requency dierence as ollow: a d R () ct Where T is he modulaion period duraion and R is he range o he arge. a d () Transmi Signal Fig. 3 Linear requency modulaion wihou Doppler Eec Received Signal ) Linear Modulaion or moving arge wih r In pracice, he releced signal includes wo requency dierences and heir sum gives he whole requency dierence d. One componen is he runime requency dierence τ relaed o he disance, he oher componen D comes rom he Doppler shi requency dierence D relaed o he speed. The wo componens are independen o each

4 AD converer 8 x x Graduaion paper 3 oher and ensure ha he arge disance and speed can have dieren values. () Transmi Signal a (-τ) ± D () wih ime-delay τ=r/c and swp is he modulaion requency bandwidh, which is deined by he ampliude o he signal or modulaion inside he ransmiing oscillaor driver bandwidh, T chirp is he ime period. D D a d d Fig. 4 Linear requency modulaion wih Doppler Eec Received Signal III. HARDWARE AD SIMULATIO In order o evaluae and demonsrae he applicabiliy and perormance o he deecion sysem under laboraory condiions, a digial simulaion environmen based on he sensor hardware seup is buil, as shown in Fig. 6. They have he same inpus (Iniial parameers) and oupus (received I/Q signals and a riangular modulaion signal as a rigger signal). And he inal oupus o he deecion sysem are he RCS (Radar Cross secion), R (Range) and V (Velociy) o arges which are deeced by he sysem. Examine Fig. 4 we can see he dieren requencies are vr a D, R ct d D (3) 3) Triangular modulaion or moving arge According o equaion (3), here is no possibiliy o disinguish he requency componens rom arge disance and speed. The classical soluion is where he measuremen indeinieness can be resolved wih he help o anoher chirp, which leads o a wo-variable equaion, when resolved we ge a value-pair or boh disance and relaive speed. As shown in Fig. 5, he requency o he irs chirp increases coninuously, his is called an up-chirp. Accordingly, he second chirp which always decreases is called a down-chirp. Thus he wo measuremens rom he wo chirps respecively can lead o he ollowing wo equaions: a d D ( ) R c T ( d d) R ct 4 a (4) a d D ( ) R vr ( d d) ct 4 swp B D B B D D T c hirp T R R c () a Fig. 5 Triangular modulaion wih Doppler Eec Transmi Signal () v Received Signal In Fig. 5, uniied signal schemes are presened, where a () is he modulaed radiaed signal, v () is he received signal v ()= Fig. 6 Diagram o he whole sysem. The hardware seup o he 6GHz FMCW sensor sysem is shown in Fig.7. The riangular volage signal is used as he inpu o he VCO o generae he FMCW radar ransmi signal hrough he requency modulaion o a 6GHz carrier wave and power ampliied, wih a sweep requency range up o 6 GHz. Wih a mixer, a par o he VCO signal is used as a sable local oscillaor (LO) o down conver he received signal o an inermediae requency. Then low pass iler is used o iler ou he high requency. Finally he obained received signal as well as he inpu riangular inpu signal is digiized hrough an AD converor or urher compuer based signal processing. V Signal generaor I signal Q signal pni pnq Ampliier Ampliier VCO Low-pass iler Low-pass iler Modulaed requency signal Mixer Ampliier Fig. 7 6 GHZ FMCW sensor sysem hardware seup wn Transmi signal Ampliier Receive signal The whole simulaion environmen has been buil based on he hardware seup in Fig.7. Two key issues during he simulaion are he addiive whie noise and pink noise which are brough ino he sysem by he ampliiers according o he real siuaion in he hardware seup. Tx Rx

5 Ampliude (db) Ampliude (db) ower/frequency (db/hz) Graduaion paper 4 ) Whie oise The disribuion o he whie noise or simulaion is Gaussian, wih Mean value: μ ( ) w ( ) = w ower specral densiy: ( ) Toal noise power or limied bandwidh As shown in Fig. 8 and Fig. 9, arbirary addiive whie noise can be generaed by simulaion wih dieren value o he requency bandwidh and he oise Figure (F) Whie noise es wih dieren requency resoluion bandwidh (bw) in requency domain : 6e+7 Y: -7 : 5.98e+7 Y: -36 : 5.9e+7 Y: bw=m(6db) bw=k(3db) bw=.m(5db) Frequency (Hz) x 7 Fig. 8 Whie noise wih dieren bandwidh bu same sysem oise Figure (F=) Whie noise es wih dieren noise igure (F) in requency domain : 6e+7 Y: : 6e+7 Y: -6.7 : 6e+7 Y: -6. : 6e+7 Y: Frequency (Hz) x 7 F=dB F=3dB F=5dB F= db Fig. 9 Whie noise wih dieren sysem noise igure bu same requency bandwidh ( = khz = 5 db) bw ( ) Fs ) ink oise ink noise is a signal wih a requency specrum such ha he power specral densiy is inversely proporional o he requency. So i can be obained by ilering he whie noise using a low pass iler whose ampliude response is inversely proporional o he requency. The iler [] can be designed wih he coeiciens as ollows 3 b() b() Z b(3) Z b(4) Z H( z) W( Z) 3 a() Z a(3) Z a(4) Z b = [ ]; a = [ ]; Final oise ower Specral Densiy Esimae via Welch mehod Frequency (Hz) whie noise pink noise inal noise Fig. The inal simulaed noise including whie noise and pink noise As shown in Fig., he inal noise which is added ino he simulaion environmen is composed by whie noise and pink noise. A. Inroducion IV. ROOSED TARGET DETECTIO SYSTEM A he end o he deecion processing, he oupu variables are he Radar cross secion (σ or RCS), Range or disance (R) and Speed o he arge (V). The whole deecion procedure is as shown in Fig.. Accordingly he power in a radar equaion (also see Table I) GGr r 3 4 ( 4 ) R (5) Then aer going hrough a mixer, he received signal s peak volage ampliude is Vpeak V rms G r con (6) r G G TABLE I ABBREVIATIOS I THE EQUATIOS Received signal power Transmied signal power Transmier anenna gain r Receiver anenna gain G con Conversion gain or he receiver R B. Deecion procedure RCS (Radar cross secion) Wavelengh o he carrier signal Range o he arge o be deeced ) Sep : eriod deecion A square rigger signal is used as a reerence signal o deec he received signal s period, i.e. calculae he T chirp, he ime period o he FMCW signal.

6 Graduaion paper 5 osiive par Received signal eriod deecion Trigger signal egaive par ) Sep : ariion Aer he period deecion, he received signal can be divided ino posiive par (up-chirp) and negaive par (down-chirp), as shown in Fig.. S is he posiive signal while S is he negaive signal in he irs period. 3) Sep 3: Averaging For a received signal wih Q periods, using averaging by Q imes o improve he SR, hen he S o he posiive signals S (i=,, Q) and i S o he negaive signals S (i=,, Q) are as ollows i Averaging Averaging S p Q Q i S Q i S Q i, S i (7) Window uncion RCS conversion CFAR Threshold Comparaor Frequency esimaion d, window Calculae he range and speed o he deeced arge Fig. The diagram o he whole deecion sysem swp T c h ir p Transmi Signal Window uncion RCS conversion CFAR Threshold Comparaor Frequency esimaion Received Signal S S S S S 3 S 3 Fig. The ransmi and receive signal 4) Sep 4: Windowing In order o decrease he specral leakage aer, a Hann window uncion is used beore. Here n is he lengh o he posiive or negaive signal in one period. S and S are he o he posiive and negaive signals aer a Hann window. w( n) Hann( n) Q S S w Si w Q, Q S S w Si w i Q i (8) 5) Sep 5: Using or Specrum Analysis FS ( S ), FS ( S ), W ( w) 6) Sep 6: RCS Conversion Then according o equaion, or each value, we can calculae he RCS or according o: 3 4 (4 ) R V r p, r G G G r The received signal s power can be esimaed hrough heir specrums respecively. For a speciic arge, he value o 3 (4 ) A= is consan, using his consan resuls G G G in: con r AR V A 4 p, n p, n pp con 4 R p, n FS, 7) Sep 7: Consan False Alarm Rae (CFAR) Threshold Use Consan False Alarm Rae (CFAR) hreshold processor o deec he peak o he RCS ( ) and hen ge he requencies accordingly:, which will be described in deail in Secion IV.C. 8) Sep 8: Frequency Esimaion There are hree possible soluions o improve he accuracy o he requency esimaion which will be discussed in he Secion V. W max

7 Graduaion paper 6 9) Sep 9: Final resul oupu Based on he Doppler equaion, we can obain he IF requency and Doppler requency as ollows i i D, ( ), And inally ge he range and speed o he arge i ctchirp Dc R, V 4 F swp C. CFAR Consan False Alarm Rae ) Inroducion The major ask o he deecion sysem is o observe he arges (cars, people and bikes) and o esimae heir parameers. To observe a arge is easy, i we know he background noise and relecions. In his case he releced signal can be compared wih a concree ixed limi value. I he releced signal is bigger han he limi, he arge signal rises rom he noise. However, in real pracice here is more disurbance and noise which varies in ime, place and inensiy, and he noise power is no known a any given locaion []. Thus a ixed hreshold deecion scheme canno be applied o he radar reurns in individual range cells i he alse alarm rae is o be conrolled. An aracive class o schemes ha can be used o overcome he problem o noise are he Consan False Alarm Rae (CFAR) processing schemes which se he hreshold adapively based on local inormaion o oal noise power. The hreshold in a CFAR scheme is se on a cell by cell basis using esimaed noise power by processing a group o reerence cells surrounding he cell under invesigaion []. Fig. 3 presens he general synhesis o CFAR. A window wih suiable lengh esimaes he average over a number o cells. In order o analyze he deecion perormance o a CFAR algorihm in homogeneous background noise, we assume ha he square-law deeced oupu or any range cell is exponenially disribued, wih probabiliy densiy uncion (pd): x ( x) exp( ) (9) Under he null hypohesis H o no arge in a range cell and homogeneous background, λ is he oal background noise power, which is denoed by µ. Under he alernaive hypohesis H o presence o a arge, λ is µ(+s), where S is he average signal-o-oal noise rae (SR) o a arge. This means ha we are assuming a Swerling I model or he radar reurns rom a arge and Gaussian saisics or he background []. We also assume ha he observaions in he +cells, including he cell under es, are saisically independen. Thereore or he cell under es he value o λ in equaion (9) is, ( S), D i () D cw under H under H and or he reerence cells surrounding he cell under he value o λ. In his case, he alse alarm probabiliy a is: [ Y S H ] ( x) dx, S T () a S Where T is he hreshold scalar parameer based on which we can modiy he value o he alse alarm probabiliy. As in our applicaion, he suiable deecion probabiliy d is.8 o 3.9, while he suiable alse alarm probabiliy a is (relaed o he sample size) wih he according SR needed o o db or a non lucuaing arge []. The exra SR is needed or arges o dieren swerling model [3]. Inpu Samples Square Law Deecor n n n Y n eighborhood eighborhood Calculaion o an esimae Z based on daa in he reerence window Cell under es Fig. 3 The general synhesis o CFAR processors Range Threshold Scalar T Comparaor Targe o Targe ) Applicaion In our applicaion, we use he OS (Ordered Saisics, irs inroduced by H.Rohling [4]) - CFAR processor which perorms relaively beer han ohers when here are muliple arges need o be deeced. Is scheme is shown in Fig. 4. The acor measuring he resuls depends on k compleely. adav Levanon [5], [6] used he OS-CFAR or he irs ime or he Weibull coeiciened sign series and hen deines he resuls analyically. Sor by ampliude Cell under es Range n n n Y n ( n) ( k ) () () Threshold Scalar T Fig. 4 The scheme o OS-CFAR processor Comparaor Targe The range samples are irs ordered according o heir magniudes, and he saisic Z is aken o be he kh larges sample, (see Fig.4):, Z () () ( n) ( k) Accordingly he pd k (z) o he random variable (k) is given by [7]: z k ( k) z k ( z) k [ e ] e k () Lasly he probabiliy o alse alarm can be shown: k a ( i) /( i T ) () i

8 RCS (db) RCS (db) Graduaion paper 7 3) erormance Tesing Consan k/ window Rae, Dieren window sizes 5 : 4.94 Y: : 6.3 Y: 9.7 Original daa window=6 window=3 window=64 window=96 window= Range (m) Fig. 5 Tesing resul or consan k/ window Rae=7/8, dieren window sizes, wo arges a R=5m, R=6m respecively. As shown in Fig.5, or consan k/ window Rae, wih he increase o he size o he window, he hreshold level is decreased. Aer comparing he series o he resuls in Fig.5, we choose window =64 while he lengh o ineres is 3 in he uure evaluaion es, in which case he hreshold no only can deec boh arges, bu also wih smaller alse deecion probabiliy. Thus he suiable rae or he window size o signal size is around 64/3 /5. Consan window sizes, Dieren k 5 : 4.94 Y: : 6.3 Y: 9.68 Original daa 4/3 7/3 8/3 3/ Range (m) Fig. 6 Tesing resul or consan window sizes, dieren value o k, wo arges a R=5m, R=6m respecively. In he legend, he rae is k/ window wih window =64. Also seen rom Fig.6, or consan window size, changing he value o k also will aec he hreshold level. However, on he opposie, he hreshold level will increase along wih he increase o he value o k. Compare he series o he resuls in Fig.6, we choose k/ window =8/3 or uure evaluaion es, also o make sure ha he hreshold no only can deec boh arges, bu also wih smaller alse deecion probabiliy. A. Inroducion V. RESOLUTIO AD ACCURACY There are wo key measuremens or a radar sysem, Range Resoluion and Accuracy, which are also easily o be conused wih each oher. The arge resoluion o radar [7] is is abiliy o disinguish beween arges ha are very close in eiher range or bearing. Weapons-conrol radar, which requires grea precision, should be able o disinguish beween arges ha are only yards apar while search radar is usually less precise and only disinguishes beween arges ha are hundreds o yards or even miles apar. Thus he precision o resoluion mainly depends on he requiremen o is real applicaion. Moreover, resoluion is usually divided ino wo caegories: range resoluion and bearing resoluion, in our case we are alking abou he range resoluion. Range Resoluion: is he abiliy o a radar sysem o disinguish beween wo or more arges on he same bearing bu a dieren ranges. The degree o range resoluion depends on he requency sweep range, he ypes and sizes o arges, and he eiciency o he receiver and indicaor. The requency sweep range swp is he primary acor in range resoluion. Thus in our case, or a FMCW radar sysem, he range resoluion is: c Rmin swp (3) Where c is he speed o ligh and swp is he sweep requency range o he FMCW radar signal. Thus we can obain a high precision o range resoluion hrough using a large range, i.e. swp =6 GHz resuls in a resoluion o.5m. Accuracy: is he degree o conormance beween he esimaed or measured posiion and/or he velociy o a plaorm a a given ime and is rue posiion or velociy. For he accuracy, because we calculae he inal value o he arge s range and velociy based on he IF requency esimaion according o he equaion (4), he precision o he accuracy is limied by he precision o he requency esimaion mehods. Such as i a normal is used or he requency esimaion, he accuracy depends on he requency sep o. ex wo main mehods or he requency esimaion will be discussed and compared in deail: ormal CSE algorihm B. ormal is a radiional approach o range exracion. However, is esimaion precision is limied by is requency sep which depends on he measuremen period T chirp. Because here are wo chirps also shown in Fig., one up-chirp and one down chirp, we have:

9 Ampliude Graduaion paper 8 min Tchirp (4) Then he accuracy o he range and velociy o he deeced arges are: min c Tchirp c dmin 4 swp swp (5) min c c min 4cw Tchirp cw (6) Where cw is he requency o our carrier wave, which is 6 GHz. For general esing condiion, when T chirp is.ms, he according min is KHz while he D is 4Hz or m/s in Table II. There lies a large gap, 5 imes dierence beween he Doppler Frequency and he minimum requency sep min we can deec. The possible soluion is o modiy he parameers value o he sysem, such as increase he value o T chirp o decrease he value o min. To obain he goal o min =4Hz, T chirp need o be increased o 5ms. However, i also brings more roubles han beneis. The reason is ha when we increase he T chirp and decrease min by 5 imes, which means he requency o he arges are also decreased by 5 imes, he arges will be eeced grealy by he / noise and make he deecion more diicul or need a larger SR value. TABLE II DOLER FREQUECY Speed m/s 5m/s m/s m/s D 4Hz Hz 4Hz 8Hz The Doppler requency D values are calculaed when λ=c/ cw based on equaion (). Insead o increasing he value o T chirp, anoher mehod is o use muliple periods o reconsruc he low requency signal (he Doppler requency) which will modiy he ampliude o he dc level o each period as shown in Fig.7. However, i is only useul when here is only one arge. I here is more han one arge, he received signal will be modulaed by oo many requency componens and canno disinguish rom each oher anymore. - signal dc level Time domain Fig. 7 Signal reconsrucion using muliple periods C. CSE ) Inroducion The Complex Specral hase Evoluion (CSE) algorihm was inroduced by Shor and Garcia [8] as a mehod o accuraely esimaing he requency o componens ha exis in a signal. The procedure o he CSE algorihm is depiced in block diagram orm in Fig.8. The mehod provides or super precision o requencies by examining he evoluion o he phase o he complex signal specrum over ime-shied windows. I is shown ha his analysis, when applied o a sinusoidal signal componen, allows or he precision o he rue signal requency wih orders o magniude greaer accuracy han he DFT. Furher, his requency esimae is independen o he requency bin and can be esimaed rom leakage bins ar rom specral peaks. The mehod is robus in he presence o noise or nearby signal componens, and is a undamenal ool in he ron-end processing or he audio compression echnology. S Windowing Fig. 8 The low diagram o CSE Shi Sample Muliply bin by bin Angle Frequency Esimaion S Windowing Conjugae ) Mehod The process can be described as ollows, as shown in Fig.8: an analysis is perormed irs on he signal o ineres and again on he same signal bu shied in ime by one sample. By muliplying he sample-shied specrum wih he complex conjugae o he iniial specrum, a requency dependen uncion is ormed rom which he exac values o he requency componens i conains can be deeced. The algorihm produces a graph wih a saircase-like appearance where he horizonal pars indicae he exac requencies o componens in he signal [9]. The widh o hese pars depends on he main-lobe widh o he window uncion. A wider main-lobe provides beer accuracy in requency ideniicaion as i produces a wider horizonal secion. Fig.9. shows he oupu rom he CSE process or a square wave and a uallc3 window or illusraion purposes. We can see rom Fig.9 ha here are clearly ideniiable horizonal sep-like secions which represen acual componens presen in he signal.

10 Ampliude Frequency Esimaion Error (%) Frequency Esimaion (Hz) Ampliude Graduaion paper 9 = Y=.36 :.58e+4 Y:.4 CSE Fig. 9 Oupu o he CSE process or a square wave o 64. Hz and a uallc3 window [9]. 3) erormance Tesing The Complex Specral hase Evoluion Mehod (CSE) is a echnique ha allows or he deecion o oscillaory componens in he requency specrum o a signal and gives improved requency resoluion when compared o he resoluion o a ypical ransorm-based analysis []. The perormance esing below will be compared beween he calculaions are done wih he Fas Fourier Transorm () and ha using CSE algorihm. Single signal componen Tesing parameers are: o Sample Frequency Fs=.8 MHz; o Sample umber =65; o umber =64; o Signal Frequency =388Hz; o Inpu daa wihou noise S sin( ) S S Time domain vecors Fig. Single signal componen in ime domain As shown in Fig. and Fig., S is he inpu daa wih signal requency componen 388Hz, while S is he same signal bu shied in ime by one sample, he inal requency esimaion using CSE is 388Hz compared o he esimaion using normal is 586Hz which is limied by he requency sep sep =F s / -=698 Hz also as shown in Fig.. The requency esimaion using CSE algorihm are much more precise han he s resul and is independen o he sample number Frequency domain (Hz) x 4 Fig.. Single signal componen requency esimaion by and CSE 8 x CSE Ideal Inpu requency (Hz) x 4 Fig. Frequency Sep Esimaion resuls comparison or single requency componen signal beween and CSE The requency esimaion error using CSE is calculaed as ollows, he maximum error is.% which is quie small already as shown in Fig.3: CSE Error ( ) % : Y: -.93 ideal Frequency bin Fig. 3 Frequency Esimaion Error using CSE Muliple signal componen While he esing discussion above ocuses on he applicaion o he CSE super-resoluion algorihm o a single signal componen, i works much more generally han ha, and can be used o resolve many signals componens so long as here is some separaion beween he signal requencies. When muliple signals are presen, he super-resoluion o he requencies is mos accurae near specral requency bins ha are dominaed by an individual signal componen, and he regions o he specrum ha are away rom he signal ceners

11 RCS RCS Speed (m/s) Speed (m/s) Disance (m) Ampliude Disance (m) Graduaion paper are generally remapped o he neares dominan signal requency. As shown in Fig.4 and Table III, he requency esimaion beween and CSE under he same condiions wih single signal componen wih 4 requency componens. TABLE III FREQUECY ESTIMATIO (HZ) Inpu value CSE The calculaion is based on he Fs=.8 MHz, =64, =698Hz. sep CSE Frequency domain (Hz) 3 4 x 5 Fig. 4 Frequency Esimaion resuls comparison or muliple requency componen signal beween and CSE 4) Conclusion Thus as long as here is some separaion beween he signal requencies, CSE can provide a very precise esimaion wih super-resoluion o requencies and is independen o he requency bin. In our applicaion, hrough a general and CFAR hreshold processing, we can obain he general requency bin esimaion or he arges and hen apply CSE algorihm or precise requency esimaion. VI. SYSTEM EVALUATIO To demonsrae he applicabiliy and perormance o he above menioned conceps and sysem, a high resoluion and precision Doppler/Disance measuremen based on he radar seup in Fig.7 is demonsraed using hardware simulaion ime. 5 disance (m) 5 (a) (b) Fig. 5 RCS/disance diagram (a) o arges (b) deeced peak ime..5 5 disance (m) Fig. 5 illusraes he resul o an evaluaion wih his algorihm. The received signal was corruped by a whie noise and pink noise based on he real hardware sysem noise. The sweep had a bandwidh o GHz, which can provide a resoluion o.3m, while he duraion was.ms. Two arges were simulaed. One arge was locaed a 5.m, moving as 5 owards he sensor wih a speed o 5.8m/s and RCS o dbsm. The oher arge a 3.m was moving slowly away wih -. m/s and RCS o dbsm. In he evaluaion resuling RCS/disance diagram, as shown in Fig.5 he wo arges can be ideniied and racked clearly. Fig.5a shows he RCS and disance o he wo moving arges while Fig.5b is he value o RCS/disance o he deeced arges by he algorihm. Fig.6 and Fig.7 show ha wo arges are deeced and racked very clearly using CSE. Targe a 3.m is moving away wih a average speed -.97 m/s while Targe a 5.m is moving oward he radar wih a average speed 5.79 m/s, which corresponds he simulaed siuaions Ideal CSE Time (s) 6 Targe 4 Ideal CSE Time (s) Fig. 6 Disance accuracy o he deeced arges Time (s) 3 Targe Targe Targe CSE Ideal CSE Ideal Time (s) Fig. 7 Speed accuracy o he deeced arges From Fig.6, we can ind he deeced disance value is almos he same wih he inpu simulaed value using CSE algorihm. The red line is he deeced value using CSE algorihm compared o he green doed line is he value using normal while he blue is he simulaed inpu value. Similarly, we can ind he speed accuracy using CSE algorihm is also very good. As shown in Fig.7, he red line sands or he deeced value using CSE compared o he green doed line is he value using normal while he blue one is he simulaed inpu value. Especially or he speed accuracy, he normal canno deec he speed smaller han 5 m/s under he same condiion while he CSE can deec he

12 Graduaion paper speed even only. m/s. Thus we ind he CSE algorihm is very promising wih high accuracy. So we can rely on he excellen perormance o he CSE algorihm o obain high accuracy while also can obain high resoluion rom he excellen hardware, i.e. when he sweep requency bandwidh is 6 GHz, he resoluion can achieve.5m. VII. COCLUSIO This paper presens a high-accuracy algorihm or 6 GHz FMCW radar or precise simulaneous measuremen o disance and velociy. A digial simulaion environmen based on he sensor hardware seup is buil o evaluae and demonsrae he applicabiliy and perormance o he deecion sysem under laboraory condiions. The sysem uses muliple periods o he FMCW signal o increase he SR by averaging. Wih he OS CFAR processors, we can deec he muliple arges in a noisy background or which all parameers in he saisical disribuion are no known and may be non-saionary. The novel CSE algorihm is discussed ha uses he evoluion o he phase o he signal specrum over ime-shied windows, leading o excellen accuracy or disance and velociy measuremens. Combined wih high resoluion provided by he advanced hardware, he paper demonsraes ha he advanced digial signal processing esablishes novel cos-eecive sraegies or high perormance FMCW radar sysems. ACKOWLEDGMET I would like o express my sinceres and warmes hanks o my supervisors Dr. Ir. aul T.M. van Zeijl and ro. Dr. Ir. Jean-aul Linnarz or heir dedicaed eors on my progress during he eleven and an hal monhs o my inernship and maser graduaion projec. ro. Dr. Ir. Jean-aul Linnarz gave me such a precious opporuniy ha I can do my inernship and coninued as my maser graduaion projec in hilips and augh me he cauious and precise aiude o he research. For almos one year, my daily coach, aul spen los o ime and energy o supervise my process and answer all he quesions deailedly and paienly. He always encouraged and helped me. His preciseness and grea kindness impressed me so grealy ha I believe I will always remember in my hear. In he meanime, I also would like o hank all he colleagues in our deparmen or heir guide, help and encouragemen. [5] H. Rohling, M.Meinecke, Waveorm Design rinciples or Auomoive Radar Sysems, CIE Inernaional Conerence on Radar, IEEE, China,, pp.-4. [6].Soica, R.L.Moses, Inroducion o Specral Analysis, renice Hall, 997. [7] E.Hyun, S.Kim, C.ark, J.Lee, Auomoive FMCW Radar wih Adapive Range Resoluion, FGC 8 second inernaional conerence, 8, pp [8] M.Baracskai, R.Horvah, Dr. F.Olah, HU ISS 48-78: HEJ Manuscrip no: TAR-746-A. [9] Lecure Scrip: Radar Sysem Engineering. Ediion WS 6/7. [] hp://ccrma.sanord.edu/sasp/sasp.hml [] A.Di Vio, G.Galai, R.Mura, Analysis and comparison o ow order saisic CFAR sysem, IEEE roceeding 4, 994, pp.9-5. [].. Gandhi, S.A. Kassam, Analysis o CFAR rocessors in onhomogeneous Background, IEEE Transacions, 988, pp [3] hp://en.wikipedia.org/wiki/chi-square_arge_models [4] H.Rohling, Radar CFAR Thresholding in Cluer and Muliple Targe Siuaions IEEE Transacions on Aerospace and Elecronic Sysems (ISS 8-95), vol. AES-9, July 983, p [5] Levanon,. -Shor, M. : Order saisic CFAR or Weibull background. IEE roceedings. 6/99. pp.57-6 [6] Levanon,. Deecion loss due o inerering arges in ordered saisic CFAR, IEEE Transacions on AES,/988, pp [7] hp:// [8] K. M. Shor and R. A. Garcia, Signal Analysis using he Complex Specral hase Evoluion (CSE) Mehod, Audio Engineering Sociey h Convenion, May 6, aris, France. [9] Wang, Jian and Healy, Ron and Timoney, Joe () ercepually Transparen Audio Waermarking o Real Audio Signals Based On The CSE Algorihm. In: s Irish Signals and Sysems Conerence, 3rd - 4h June, UCC, Cork, Ireland. [] D. J. elson and K. M. Shor. A channelized cross specral mehod or improved requency resoluion. roceedings o he IEEE-S Inernaional Symposium on Time-Frequency and Time-Scale Analysis, IEEE ress, Ocober 998 REFERECES [].Heide, Microwave and Millimerewave Sensor Sysems or Commercial Applicaions a 4, 6 and 77GHz, in MIO 97, Microwave and Opronics Conerence, Workshop on Commercial Radio Sensors and Communicaion Techniques, Sugar, Germany, 997 [] H.Ruser,.Heide, M.Vossiek, A.v.-Jena, V.Magori, and H.-R Trankler, A High-Sensiive Microwave-Ulrasound Sensor or Reliable Measuremen o Moion and Range, Eurosensors I, Warszawa, 997. [3] M.Vossiek, T.v.Kerssenbrock,.Heide, Signal rocessing Mehods or Millimerewave FMCW Radar wih High Disance and Doppler Resoluion, Microwave Conerence, 7 h European, 997. [4] SupplierBusiness, Marke repor: Acive Saey SysemRepor, Supplier Business, 7