Ramp Sequence Analysis to Resolve Multi Target Scenarios for a 77-GHz FMCW Radar Sensor

Transcription

1 Ramp Sequence Analysis to Resolve Multi aget Scenaios o a 77-GHz FMCW Rada Senso K. Pouvoyeu 1, R. Fege 1, S. Schuste 1, A. Stelze 1,, L. Maue 3 1 Chistian Dopple Laboatoy o Integated Rada Sensos, Altenbege St. 69, A-44 Linz Institut o Communications and Inomation Engineeing, Altenbege St. 69, A-44 Linz 3 DICE GmbH & Co KG, Feistädte St. 4, A-44 Linz {k.pouvoyeu,.ege, s.schuste, a.stelze}@icie.jku.at, linus.maue@inineon.com Abstact Many pactical equency-modulated continuous-wave (FMCW) adas utilize consecutive upchips and/o downchips o the same amp slope to extact the desied ange and velocity inomation o the tagets. In this contibution it is demonstated that consecutive amp sequences povide only little moe inomation compaed to a non-consecutive sequence, but lead to a huge calculation complexity. Additional signiicant inomation on the taget states o a nonconsecutive sequence is gained by using the amp slope as a design paamete. he amp sequence distibuted ove a cetain peiod is tempoally aligned to a given point in time. State estimation is done by minimizing a cost unction. A signiicant advantage o a cost unction appoach is that ghost tagets ae suppessed diectly. Fo test puposes a 77-GHz FMCW ada pototype is used in an automotive envionment. Keywods: FMCW ada, data association, state estimation, tempoal alignment. 1 Intoduction Fo automotive applications the knowledge o ange and velocity o a taget is o impotance. Conventional FMCW ada systems use a sequence o consecutive amps utilizing identical amp slopes o the up- and downchips. Such amp sequences lead to a signiicant amount o calculation complexity. Especially o automotive applications computing powe is a vey limited esouce. heeoe the investigation o waveom design pinciples o automotive adas becomes moe and moe impotant. he use o dieent amp slopes is consideed in [1]. In this contibution the advantages o amp sequences consisting o a ew tens o chips is discussed in detail esulting in a ast and accuate ange as well as velocity estimation. FMCW Rada he well-known FMCW ada pinciple is summaized in this section. Fo an in-depth discussion it is eeed to [] and [3]..1 FMCW Pinciple An FMCW ada utilizes linea equency amps, also denoted as chips, as tansmit signal. he amp slope k o an FMCW chip is deined as B k =, (1) with B as the coveed bandwidth o the amp signal and as its duation. Fo B equal to zeo the ada is said to wok in the continuous wave (CW) mode. Fo an upchip the bandwidth is consideed to have a positive sign and a negative o a downchip. he tansmitted signal is mixed with the damped and delayed eplica etuned om a taget which geneates the intemediate equency (IF). In Fig. 1 the equency couse o a tansmit signal in the adio equency (RF) as well as in the IF is plotted o an upchip as well as o a downchip. he RF and IF ae sketched o a static and o a moving taget.. Measuement Equation he measuement equation o an FMCW ada descibes the impact o both, ange as well as velocity o a taget on the IF equency. he eect o ange-dopple coupling in chip adas is explained in [4]. Fo a complex-valued measuement signal the equency in the IF is calculated to Fig. 1 Fequency couse o an FMCW ada in the RF as well as in the IF. 48

2 s 1 1 Δ = = =, (6) N N with s as the sample ate and s as the sampling peiod o the analog/digital (A/D) convesion. Accoding to (6), the ange esolution Δ is calculated to s c 1 Δ = (7) B Fig. Ramp sequence consisting o two dieent amp pais with an identical cente equency as well as a CW mode. B + cv, () c c with c as the velocity o popagation o the electomagnetic wave, c as the cente equency o the chip signal, as well as and v as the taget ange and velocity. I only a eal-valued measuement signal is available the measuement equation is given by B + cv, (3) c c esulting in an inheent ambiguity between positive and negative equencies. he equency can e.g. be estimated by a ast Fouie tansom (FF). In this case the vaiance σ o the estimated equency o () is calculated to 1kwin σ = va{ ˆ}, (4) (π ) η N with N >> 1 as the numbe o samples, e.g. N = 14. In case o additive white noise (AWN) the signal to noise atio (SNR) η is usually deined as A η =, (5) σ n with A as the amplitude o the signal and σ n as the vaiance o the emaining noise. he deivation o (4) is shown in [5] o an FF based equency estimation. In [6] it is extended to take into account the windowing unction. Fo a Hanning window the windowing acto k win is calculated to k win =.34. Fo () and (3) it is assumed that the chip is linea enough so that non-linea phase distotion eects in the IF have no signiicant inluence..3 Fequency Resolution he tem esolution descibes the ability to sepaate two closely spaced tagets. he one-bin esolution in the equency domain Δ is given by and the velocity esolution Δv esults in c 1 Δ v =. (8) c Fo a bandwidth equal to zeo the ada is denoted as Dopple ada. 3 Ramp Sequence Design he main design paametes o an FMCW ada ae the bandwidth B o the chip signal, the chip duation, as well as the sample ate s o the A/D convesion. A classical vaiation in the signal geneation o an FMCW ada is to use upchips as well as downchips o state estimation puposes. 3.1 Ramp Slope as Design Paamete his section descibes how to use the bandwidth B and the chip duation as design paametes o a amp sequence. Othe ada paametes emain unchanged. Accoding to (4), the accuacy o the estimated equency is not inluenced by modiying the bandwidth o the chip signal. An upchip ollowed by a downchip with the same amp slope is denoted as amp pai. Such a amp pai can e.g. be geneated by a linea sweep unit that is based on a diect digital synthesize (DDS). he amp sequence itsel consists o a speciic numbe o amp pais. A shot epogamming time p between each amp pai is necessay to adjust the paamete setup o the DDS. A sketch o a amp sequence consisting o two dieent amp pais with an identical cente equency c as well as a CW mode is plotted in Fig.. 3. empoal Alignment he tem tempoal alignment descibes the mapping o local senso obsevation times to a common timeline. Fo a theoetical in-depth desciption o tempoal alignment techniques it is eeed to [7]-[9]. A single FMCW ada can not geneate seveal chip signals simultaneously. he tempoal alignment o seveal measuement chips o an FMCW signal sequence is discussed next. Fo a shot tempoal alignment time in the ange o some milliseconds a pope model assumption on the taget s motion o typical automotive scenaios is a constant velocity esulting in 49

3 Fig. 3 empoal alignment o a amp signal o the condition o a vitually ininite steep amp slope. = + v [ ], (9) [ a m with m as the ID o a speciic amp o the amp sequence, a [ as the aligned time o amp m which can be chosen abitay, and [ as the tempoally aligned ange. Fo a > the measuement is pedicted into the utue, and o a < the time is vitually tuned back. Based on (9) the time alignment o the estimated equency [ o amp m o a eal-valued signal is calculated to B[ [ = [ + c[ v c c B[ = c ( + v [ ) a + c[ v c B[ a [ = + c[ B[ v. c c + (1) heeoe, o caying out the tempoal alignment the cente equency c [ is vitually eplaced by a [ c[ c[ + B[. (11) Compaed to the oiginal measuement equations o () and (3) the tem caused by the Dopple shit o the equency is inluenced by the duation o the time shit multiplied by the amp slope, esulting in a modiied amp slope. Fo the condition c[ a [ = (1) B [ the time shited amp is vitually ininite steep. A gaphical intepetation o (1) o the condition o (1) is given in Fig Ramp Sequence Design Due to pactical limitations extemely steep amp slopes can not be geneated diectly since e.g. the intemediate equencies become vey lage with the additional poblem o an inceased noise bandwidth. Fig. 4 Poposed amp sequence in the time/equencydomain consisting o non-consecutive steep and lat amp pais. he sampling equency o the A/D convesion is esticted by technical easons esulting in the availability o only a vey limited numbe o sampling points o the downconveted amp signal o an extemely steep amp signal. Futhemoe, as shown in (4), the accuacy o the estimated equency depends diectly on the numbe o sample points as well as the squaed value o the chip duation. he amp sequence poposed in this contibution consists on one hand on steep amps and on the othe hand o amps with a signiicantly latte amp slope. Futhemoe, the steep upchip/downchip o the last/ist amp pai ulills condition (1). A visualization o the poposed amp sequence in the time/equency-domain is given in Fig. 4. he epesentation o the designed amp sequence in the ange/velocity-plane is discussed next. 4 Range/Velocity-Plane A single FMCW measuement o a taget implies an inheent ambiguity o the taget states in the ange/velocity-plane, descibed by (1). his ambiguity is esolved by taking into account a sequence o contempoay measuements. A gaphical intepetation o two tempoal aligned FMCW measuements o a taget epesented in the ange/velocity-plane is given in Fig. 5. he amplitude o the peak in the spectum is popotional to the ada coss section (RCS) o the detected taget. 4.1 Ramp Sequence in the Range/Velocity- Plane he poposed amp sequence consists o both steep and lat amps. he steep amps have a bandwidth o e.g. 1.4 GHz and a total duation o 1.4 ms. he time between the ist/last downchip/upchip ulills the condition o (1) esulting in a total duation o appoximately 77 ms. he total duation time o the amp sequence can be uthe educed using steepe amps with the necessity o vey ast A/D convetes (ADCs). 43

4 (a) (b) Fig. 5 wo tempoally aligned FMCW measuements o a taget epesented in the ange/velocity-plane. Advantageously, the ast sampling is only equied o a shot peiod o time and the gaps between the amp pais ae peectly suitable o data tanse and calculation puposes. As will be shown late the accuacy is not inceased signiicantly i the time between the ist and the last sequence ae totally illed up with steep amps. he total amount o eduction o amp pais esults in dastically educed computation powe equiements. Moe inomation with less computational eot can be gained by diectly alteing the amp slope. heeoe, the gaps between the ast amp pais ae used by amps with a duation o up to 4.96 ms. A vitual geneation o the lat amps based on the steep amps would take a huge amount o time which is not available in automotive scenaios. Each peak in the spectum o a chip in the IF epesents a line in the ange/velocity-plane. he intesection o seveal lines esolves the ambiguity poblem o ange and velocity. Resolving a taget with zeo velocity and zeo ange in the ange/velocity-plane is plotted in Fig. 6 o (a) ou steep amp pais and a positive tempoal alignment time, o (b) ou steep amp pais and a negative tempoal alignment time. An additional amp sequence with a amp duation o up to 4.96 ms is plotted in (c). A combination o the ist thee sequences is given in (d). he epesentation o 4 steep amp pais in the ange/velocity-plane is plotted in (e). he additional sequence o lat amps o (c) is added in () to the 4 steep amp pais o (e). 4. Eo Popagation o a Single aget In this subsection the inluence o the numbe o amp pais on the accuacy o the estimated state is investigated. he investigation is only done o a single taget scenaio without the poblem o coect data association. Data association is investigated in the next subsection. Fo a single taget the obsevation matix H o the amp sequence is given by B [1] a [1] c[1] + B[1] H =, (13) c c M M (c) (e) Fig. 6 Intesection o a taget with zeo velocity and zeo ange in the ange/velocity-plane. (a) ou steep amps o a >, (b) ou steep amp pais o a <, (c) additional lat amp sequence consisting o ou amp pais, (d) eight steep amp pais and additional lat amp sequence, (e) 4 steep amp pais, as well as () 4 steep amp pais and an additional lat amp sequence. with the numbe o ows o H equal to the numbe o amp signals o the pocessed amp sequence. Fo a least squaes appoach the states ange and velocity v ae calculated by = v 1 ( H H) H, (d) () (14) with as the vecto o the estimated equencies o the single taget. Assuming an identical standad deviation σ o the equency estimates the covaiance matix o estimated states is calculated to 1 q qv cov = σ ( H H) = σ, (15) v qv qvv with q and q vv as the nomalized vaiances o the ange and velocity estimates as well as q v = q v as the nomalized covaiance tem between ange and velocity. Nomalized standad deviations with espect to the numbe o steep amp pais ae plotted in Fig. 7 o (a) the ange estimate and in (b) o the velocity estimate. Futhemoe the nomalized standad deviations ae 431

5 estimate all anges as well as all velocities in a multi taget scenaio. A key poblem o this type o data usion is to assign a speciic peak in the spectum to a speciic taget in the multi taget scenaio. he peaks itsel ae detected by a constant alse alam ate (CFAR) algoithm as discussed e.g. in [1] and [11]. he vecto o IF equencies [ coesponding to the tagets o amp m is given by (a) [ [ [ ], [ m ] = (16) 1 K with 1 [ and [ as the estimated equency o the ist and second peak in the spectum. he state o a taget is given by the intesection o the tempoal aligned measuement equation (1) o the peaks o the same taget, but puely in the spectum this assignment is not possible. Futhemoe, the intesection o two lines om two dieent tagets esults in a so called ghost taget. o avoid this ambiguity the intesection poblem is eplaced by minimizing a cost unction. he minimal distance d [ (, o a speciic point in the ange/velocity-plane (, o peak n and amp m is calculated by 1 B[ dn[ (, = min ± n[ cv. (17) Δ c [ c (b) Fig. 7 Nomalized standad deviations with espect to the numbe o steep amp pais o ange estimate (a) as well as velocity estimate (b) with (solid line) and without (dashed line) an additional lat sequence consisting o ou amp pais. plotted i a lat amp sequence consisting o ou amp pais is added. Fo a single taget scenaio the numbe o amp pais has only a vey limited inluence on the total achievable accuacy. Hence little peomance is lost, but a huge amount o calculation powe is saved i only a limited numbe o amp pais, e.g. eight, ae used. 4.3 Resolving Multi aget Scenaio Fo automotive ada applications the goal is not necessaily to achieve the asymptotic best possible accuacy o ange and velocity estimates based on an ininite amount o measuements. Fa moe impotant o this type o applications is that both paametes o a taget ae estimated with an acceptable accuacy in a vey shot peiod o time, detecting potential theats as soon as possible. he oveall goal is to esolve the inheent ambiguities in the FMCW measuement equation and I only a eal-valued IF signal is available, both signs o the estimated equency must be consideed as a valid solution. he dieence between the expected equency and the measued equency n [ is nomalized by the one-bin esolution Δ to take into account the dieent accuacies depending on the dieent amp duations. he total vecto o minimal distances d[ (, is given by [ d [ d [ m ] d [ m ] = K (18) (, 1 (, ](, and the total minimal distance d min [ (, o chip m and a speciic point in the ange/velocity-plane is calculated to d = min( d[, d ). (19) min[ (, (, max he possibility o a miss is taken into account by a maximal distance d max. his maximal distance guaantees that a single miss can deteioate the cost unction only in a limited way. he cost unction J tot (, o a speciic point in the ange/velocity-plane (, is calculated by J, = d [, () tot ( min (, m with as a suitable nom, e.g. L 1 o L. A case example o esolving nine simulated tagets in the ange/velocityplane based on an L 1 cost unction using dieent amp sequences is plotted in Fig. 8. In (a) 4 amp pais, in (b) eight amp pais, and in (c) eight amp pais plus an additional latte amp sequence ae used. he 4 amp 43

6 (a) Fig. 9 Photo o the used 77-GHz FMCW ada pototype. (b) (c) Fig. 8 Cost unction o a simulated test scenaio consisting o nine tagets (white cicles). (a) 4 amp pais, (b) eight amp pais, (c) eight amp pais plus an additional latte amp sequence. pais show almost no dieence compaed to the eight amp pais. Adding the sequence o lat pais accoding to Fig. 6 (c) signiicantly impoves the cost unction, esulting in enhanced ghost taget suppession. 5 Applications Due to cost easons the available pocessing powe o automotive mass maket applications is vey limited. heeoe, the poposed amp sequence, only consisting o a vey limited numbe o amps, is peectly suitable o this type o application. Fo automotive applications two equency bands ae eseved: GHz o long ange ada (LRR) and GHz o shot ange ada (SRR) applications. he esolvability o multi taget situations is a key issue o both LRR as well as SRR GHz FMCW Rada Pototype he used 77-GHz ada pototype, pesented in [1] and [13], is suitable o both equency bands. Basically it consists o ou boads: RF ontend phased locked loop (PLL) & DDS boad ampliie & ADC boad baseband boad Sampled aw data om the ADCs ae tanseed to a conventional PC via a USB. connection ealized by a micocontolle (UC). Signal pocessing itsel is diectly done within the Matlab envionment. A photo o the 77- GHz FMCW ada pototype is shown in Fig. 9. he LRR speciications ae complied o implementation puposes o the pesented amp sequence. A summay o the basic paametes o the ada pototype is given in able Automotive Envionment Fo measuement puposes a test ca is equipped with the ada pototype o Fig. 9. Data stoage and uthe 433

7 able 1 Paamete set o the 77-GHz FMCW ada pototype. symbol value unit desciption c 76.5 GHz cente equency s 1 MHz sample equency B 14 MHz total bandwidth 1-4 ms amp duation p μs pogamming time 77 GHz ada pocessing is done by a laptop within the ca. A photo o the 77-GHz FMCW ada pototype mounted on a test ca is shown in Fig Conclusion A key issue o automotive applications is a ast esolving o multi taget scenaios as well as detection and elimination o any ghost tagets. In this contibution it is demonstated that popely designed amp sequences o an FMCW ada, consisting o only a vey limited numbe o amp pais, ae useul o this pupose. he basic design consideations o amp sequences ae discussed in detail. All measuements o a complete sequence ae tempoal aligned to a speciic point in time. At this point in time the multi taget scenaio is esolved. he ange and velocity estimation o a multi taget scenaio is done by using a cost unction. A 77-GHz ada pototype is used o test puposes in an automotive scenaio. Acknowledgment he authos would like to thank Alexande Fische and Hebet Jäge om DICE GmbH o thei continuous suppot. Reeences [1] H. Rohling and M.-M. Meinecke, Waveom Design Pinciples o Automotive Rada Systems, in Poc. CIE Intenational Coneence on Rada on CD- Rom, Beijing, China, Oct , 1. [] A. G. Stove, "Linea FMCW Rada echniques," IEE Poc. F Rada Signal Pocessing, vol. 139(5), pp , 199. [3] M. I. Skolnik, Rada Handbook, nd ed. New Yok, NY: McGaw-Hill Publishing Company, 199. [4] R. Fitzgeald, Eect o Range-Dopple Coupling on Chip Rada acking Accuacy, IEEE ansactions on Aeospace and Electonic Systems (AES), vol. 1, no. 4, pp , July, Fig. 1 Photo o the 77-GHz FMCW ada pototype mounted on a test ca. [5] S. M. Kay, Fundamentals o Signal Pocessing - Estimation heoy, Uppe Saddle Rive, NJ: Pentice- Hall, [6] S. Schuste, S. Scheiblhoe, and A. Stelze, he Inluence o Windowing on Bias and Vaiance o DFbased Fequency and Phase Estimation. IEEE ansactions on Instumentation and Measuements (IM). (to be published) [7] H. B. Mitchell, Multi-Senso Data Fusion. Belin: Spinge, 7. [8] D. L. Hall and S. A. H. McMullen, Mathematical echniques in Multisenso Data Fusion. nd ed. Nowood, MA: Atech House, 4. [9] R. P. S. Mahle, Statistical Multisouce-Multitaget Inomation Fusion. Nowood, MA: Atech House, 7. [1] H. Rohling and R. Mende, OS CFAR peomance in a 77GHz Rada Senso o Ca Application, in Poc. CIE Intenational Coneence on Rada, Peking, China, Oct. 8-1, 1996, pp [11] A. Ludlov, Paxiswissen Rada und Radasignalveabeitung. 3 d ed. Baunschweig: Vieweg,. [1] C. Wagne, A. Hadee, R. Fege, A. Fische, A. Stelze, and H. Jaege, A 77-GHz FMCW Rada System based on an RF ontend manuactued in a Silicon-Gemanium echnology, IASED Intenational Coneence on Antennas, Rada, and Wave Popagation, Baltimoe, Mayland, USA, Apil 16-18, 8. [13] A. Hadee, C. Wagne, R. Fege, and A. Stelze, An FPGA based ada system with a 77GHz FMCW RF ont-end, Intenational Rada Symposium (IRS), Woclaw, Poland, May. 1-3,