Estimation Techniques and Simulation Platforms for 77

Transcription

1 EPJ manuscrpt No. (wll be nserted by the edtor) Estmaton Technques and Smulaton Platforms for 77 GHz FMCW ACC Radars Al Bazz 1, Camlla Krnfelt 1, Alan Pden 1, Therry Chonavel 1, Phlppe Galaup 1, and Frantz Bodereau 2 1 Insttut TELECOM, TELECOM Bretagne, Lab-STICC, Technople Brest Irose CS 83818, Brest Cedex 3, France. e-mal: Frst-name.Famly-name@telecom-bretagne.eu 2 Autocruse, a TRW Automotve branch, Plouzan, France. e-mal: Frantz.Bodereau@trw.com the date of recept and acceptance should be nserted later Abstract. Ths paper presents two radar smulaton platforms that have been developed and evaluated. One s based on the Advanced Desgn System (ADS) and the other on Matlab. Both platforms are modeled usng homodyne front-end 77 GHz radar, based on commercally avalable monolthc mcrowave ntegrated crcuts (MMIC). Known lnear modulaton formats such as the frequency modulaton contnuous wave (FMCW) and three-segment FMCW have been studed, and a new varant, the dual FMCW, s proposed for easer assocaton between beat frequences, whle mantanng an excellent dstance estmaton of the targets. In the sgnal processng doman, new algorthms are proposed for the three-segment FMCW and for the dual FMCW. Whle both of these algorthms present the choce of ether usng complex or real data, the former allows faster sgnal processng, whereas the latter enables a smplfed front-end archtecture. The estmaton performance of the modulaton formats has been evaluated usng the Cramer-Rao and Barankn bounds. It s found that the dual FMCW modulaton format s slghtly better than the other two formats tested n ths work. A threshold effect s found at a sgnal-to-nose rato (SNR) of 12 db whch means that, to be able to detect a target, the SNR should be above ths value. In real hardware, the SNR detecton lmt should be set to about at least15 db. 1 Introducton accdents by the year of 2010 as compared to the rate n 1998 [1]. Despte safety efforts, rates only decreased In 2001 the European Unon member states set up the goal to halve the number of fataltes caused by road by 27%. Nowadays, most accdents are partly caused by human error or too long reacton tme on the part

2 2 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars of the drver [2], thus callng for percepton assstance. In ths area, ACC (Adaptve Cruse Control) radars are expected to play an mportant role. In 2005, the European Telecommuncatons Standards Insttute (ETSI) dd temporarly open the 24 GHz Other smulaton platforms have prevously been descrbed n the lterature, e.g. [5] where an all-matlab smulator s proposed. Ths smulator deals wth hardware desgn, algorthm testng and performance analyss. Another elaborated smulaton platform usng ADS band for Short-Range automotve Radars (SRR) [3]. How- s presented n [6] n order to smulate a phase-coded ever, snce the 24 GHz band s also used for other systems, e.g. rado astronomy and weather forecastng, ths band wll only be allowed for car radars untl 2013, when t s presumed that the hardware technology (MMICs, antennas, etc.) wll be mature enough to enable the development and producton of automotve radar modules at the GHz band. After2013, two bands are permanently allocated n Europe: one at GHz for LRRs and another at GHz for ultra wde band (UWB) short-range radars [4]. There are several advantages n movng from 24 to GHz: smaller sze and weght of the radar frontend, RF chp set ntegraton on a sngle chp, resultng n reduced losses and assembly costs, mproved dstance resoluton due to wder avalable bandwdth; and narrower antenna beam whch results n a better angular resoluton. In ths paper, we descrbe efforts to mprove the functonalty of the ACC system by smultaneously developng the modulaton format, detecton and estmaton algorthms, radar smulaton tools and radar archtecture. Ths s prmarly done by the development of two smulaton platforms usng ADS by Aglent Technologes and Matlab by Mathworks. CW radar sensor. In our work, the ADS-based platform allows the co-smulaton usng an envelope smulator for the 77 GHz radar front-end and a Data Flow smulator whch controls the dgtal sgnal processng at baseband. It also facltates a correct and detaled modellng of the ncluded components and sgnal analyss functons, such as spectrum analysers. The smulaton results obtaned from the ADS-based platform s compared to results obtaned from the Matlab-based platform, to ensure that correct and feasble results are obtaned. Furthermore, the Matlab platform allows us to establsh statstcal studes as well as the mplementaton and thorough testng of the algorthms to be used to detect and dentfy the targets. For the presented radar applcaton, the Cramer-Rao lower bound [7] and the Barankn bound [8] are used to calculate lower bounds of the mean square error for the dstance and relatve velocty estmaton of the detected targets. Then, the parameters estmated from data obtaned after Fourer transformaton s compared to the bounds. The nterest of these bounds s twofold. Frst, they supply a lmt to best achevable results for a gven waveform n terms not only of varance of the estmators, but also of detecton capablty. Second, they can

3 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 3 tell us how far a certan processng algorthm s from the bound, and whether t s worth lookng for a better one or not. Ths paper s arranged as follows: In secton II we present system requrements and dscuss the advantages and drawbacks of dfferent frequency modulaton formats. Further on, we ntroduce the Cramer-Rao and Barankn bounds to estmate the performance of the chosen modulaton formats, and fnally we present a comparson between the theoretcally calculated bounds and the practcal results. Secton III lays on a frst smulaton platform developed usng the ADS co-smulaton features, and a second platform usng Matlab, together wth a descrpton of the general archtecture of the radar system used throughout ths work. The results from the two smulaton platforms are compared and dscussed n Secton IV. In Secton V, we show the results from extensve smulatons to compare the effcency of two proposed FMCW waveforms. Fnally, n secton VI, we gve a concluson about the results presented n the paper. from the nstant of transmsson to the nstant of recepton of the pulse. For Frequency Shft Keyng (FSK) radar, two (or more) contnuous sgnals shfted n frequency are transmtted [9]. The sgnal returned after reflecton by the target s mxed wth the transmtted sgnal, and thereby we wll obtan the Doppler frequency whch allows the calculaton of the relatve velocty of the target. The phase dfference among the dfferent FSK levels determnes the target dstance. The man dsadvantage of FSK radar s that t can not dscrmnate fxed targets along the road, snce they mperatvely have the same relatve velocty wth respect to the radar. Moreover, targets wth a relatve velocty of zero (that s the same relatve velocty as the vehcle that carres the radar) wll return a Doppler frequency of zero, whch means that they are not detected. The Frequency Modulated Contnuous Wave (FMCW) prncple s to send a contnuous sgnal wth a lnear frequency modulaton [9]. The down-converted sgnal s referred to as the beat frequency. By varyng the lnear frequency modulaton (up slopes, down slopes, flats 2 FMCW waveforms for multtarget detecton etc.), on dstnct tme ntervals, several beat frequences are obtaned, and the dstance and relatve velocty data of the targets can readly be resolved. One advantage of For the detecton and parameter estmaton of targets, the radar modulaton format s the most mportant consderaton. In pulse doppler radars, the dstance to the target s gven by the measure of tme that has elapsed FMCW over FSK radar s that, thanks to the modulaton format, fxed targets wth dfferent dstances return dfferent beat frequences, even f ther relatve velocty s the same; hence they can be detected separately. The same goes for the targets that have a null relatve

4 4 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars velocty: snce ther dstances are not the same, ther beat frequences wll be dfferent, and thus the targets can be dstngushed accordng to ther dstance. When t comes to sgnal processng, FMCW radar does not add any dffcultes as compared to the FSK radar, but rather the challenge les n keepng the modulaton lnear n get detecton s obtaned from the beat frequences presented for each target on the up and down frequency slopes, respectvely. The beat frequences arse from the followng scheme: at a gven transmsson tme, say t, the nstantaneous frequency of the transmtted sgnal s f 0 + f m (t). When ths sgnal hts the target, t s shfted by the target s Doppler frequency, f d. Once re- order to correctly estmate the beat frequences. turned to the radar, the tmeτ = 2d c has elapsed, that s, Another waveform s the dgtal FMCW, obtaned by the combnaton of LFMCW and FSK Modulaton [10]. It has many advantages, such as the hgh dstance and relatve velocty resolutons, but ts man problem s the complexty of ts generaton. Gven the drawbacks of the FSK modulaton format as dscussed above, ths work s based on FMCW modulaton formats. the tme t took for t to travel to the target and back. Thus the sgnal returnng from the target nto the recever at tme t = t +τ s f 0 +f m (t) +f d. Ths sgnal s mxed wth the transmtted sgnal at that nstant, that s f 0 +f m (t +τ). Wrtten n another way, at tme t = t + τ, the transmtted sgnal wth the frequency f 0 +f m (t ) s mxed wth the receved sgnal wth frequencyf 0 +f m (t τ)+f d. Ths s llustrated n Fg. 1. Equaton (1) gves the beat frequences as a functon 2.1 FMCW of the target s relatve velocty v and dstance d [12] : f 0 + B f Transmtted sgnal : f 0 + f m(t) f d Receved sgnal : f 0 + f m(t τ) + f d f up = 2vf0 c 4Bd Tc f do = 2vf0 c + 4Bd Tc, (1) where c s the speed of lght and B the chrp bandwdth. f 0 t Once the beat frequences have been detected, the T 2 Fg. 1. Emtted FMCW waveform (sold lne) and receved waveform wth delay and doppler offset (dashed lne). τ dstance d to the target can be calculated usng (2) and ts relatve velocty, accordng to (3): d = Tc 8B (f up f do ) (2) When usng an FMCW modulaton format, the tar- v = c 4f 0 (f up +f do ), (3)

5 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 5 It s mportant to notce that n some cases beat frequences can be negatve, that s, the complex sgnal phase decreases wth tme. Thus, t s a must to fnd the correct sgn n order to correctly calculate the target s data. Fg. 2 shows the beat frequences for the up ramp and down ramp as a functon of dstance (0-200 m) and relatve velocty range ( 180 to +360 km/h). The relatve velocty for approachng vehcles s defned as Beat frequency (khz) d (m) v (km/h) 400 postve. Here we have set B = 600MHz. The hor- (a) Up ramp zontal plane n the graphs s the zero frequency plane; accordngly, every beat frequency that s found below 400 the horzontal plane actually has a negatve sgn. When consderng Fg. 2, one realzes that n-phase demodulaton,.e. usng only the real component of the sgnal, should be enough n the majorty of stuatons. Indeed, Fg. 2 shows that n most stuatons we have f up 0 andf do 0. Based on these assumptons, errors would Beat frequency (khz) v (km/h) d (m) occur for short dstance and postve relatve velocty (where f up 0) or negatve relatve velocty (where f do 0). For relatve veloctes consdered here, we (b) Down ramp Fg. 2. Beat frequences as a functon of dstance and relatve velocty. The beat frequency on the up ramp (a) s "nega- have error-free stuatons whenf up (d,v) > f up (0,v max ) tve" = n most cases, whle the down ramp (b) beat frequency s 2f 0v max c = f up t andf do (d,v) > f do (0, v mn ) = 2f0 vmn mostly "postve". The sgns have to be taken nto account n c = f do t. When f up and f do are outsde [ f up t,f up t ] and eq. (2) and (3). [ f do t,f do t ] respectvely, nphase demodulaton s unambguous. Whenf up [ f up t,f up t ] and f do [ f do t,f do t ], ambguty occurs. However, note that sgn ambgutes manly occur at short dstances, mplyng potentally dangerous stuatons. The FMCW format has some advantages over the FSK modulaton, as dscussed n the ntroducton. How- ever, t also suffers from drawbacks n a mult-target scenaro. Indeed, every target presents a beat frequency on each ramp, and the assocaton between the frequences on the up ramp and the down ramp can be complcated, due to the fact that beat frequences of targets can be ordered n a dfferent way on up and down ramps.

6 6 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars Consequently, more complex modulaton formats such as the ones proposed n [10], [14] and [16] must be consdered for multple target detecton. For these formats, smple dstance crtera or more sophstcated ones [13] can be consdered for the assocaton of beat frequences. a good estmate of relatve velocty) and the double down chrp modulaton formats (wth ts benefcal beat frequency assocaton), we propose a modulaton format, whch we call the "dual FMCW waveform". Ths modulaton format nvolves two successve FMCW waveforms wth slghtly dfferent slopes on the frst trangle as compared to the second trangle. The order of the beat frequences of the targets s thus mantaned between both up ramps as well as between both down ramps. Thus, the assocaton of the beat frequences s kept smple and the dstance-velocty ambguty s allevated, whle the varance of relatve velocty estmaton 2.2 Dual FMCW waveform Presentaton Reference [14] consders a waveform nvolvng n two (or more) successve down ramps wth slghtly dfferent slopes. The author shows that, for such a waveform, the order n whch targets beat frequences are arranged on the frst ramp s dentcal to ther order on the second ramp. Thus, the assocaton between the beat frequen- s kept small, thanks to the lmted slope dfference between the trangle ramps. The structure of the dual FMCW waveform s summarzed n Fg. (3). It s descrbed by means of four parameters: The carrer frequency (f 0 ) The modulaton bandwdth (B) The total duraton of the modulaton (T ) The duraton of the frst trangle (θ) ces from dfferent ramps s facltated and the ambguty of the smple FMCW s consderably allevated. Unfortunately, ths smple method of assocaton has a f 0 + B f problem, namely that t provdes a bad estmate of relatve velocty [14]. Nevertheless, the smplfed assocaton between beat f 0 θ 2 T θ 2 0 θ T t frequences s a great advantage of ths waveform and was kept n mnd n the desgn of a more advanced mod- Fg. 3. Dual FMCW waveform. ulaton format. Inspred by smple FMCW (whch gves Parameter estmaton for the dual FMCW waveform For ths dual FMCW waveform, we propose an algorthm where only the real part of the reflected sgnal

7 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 7 s needed 1. Thus, a smplfed radar front-end archtecture s also possble, compared to recevers wth nphase and quadrature demodulaton. Beat frequences of targets are obtaned by thresholdng the perodograms [15] of the demodulated sgnals of each ramp.f up k denotes the th detected frequency on the k th (k = 1,2) up ramp. The parameter estmaton s descrbed hereafter. In the frst step, snce the order of targets s ensured only between both up ramps and between both down ramps, we calculate the dstance and relatve velocty usng only up and down ramps respectvely: d up = (f up2 f up1 ) cθ(t θ) 4B(T 2θ) v up = c (T θ)f up2 θf up1 2f 0 T 2θ Up ramp estmatons (4) calculate an estmate for the frst trangle (up and down ramps) and for the second trangle (up and down ramps): d = (f do1 f up1 ) cθ 8B v = (f up1 +f do1 ) λ 4 Frst trangle estmatons d = (f do2 f up2 ) c(t θ) 8B v = (f up2 +f do2 ) λ 4 Second trangle estmatons (6) (7) The fnal estmate s gven by the mean of the estmates suppled by both trangles n (6) and (7). Ths algorthm, whch provdes us wth the relatve velocty at the targets, s summarzed n Fg. 4. d do = (f do2 f do1 ) cθ(t θ) 4B(2θ T) v do = c (T θ)f do2 θf do1 2f 0 T 2θ Down ramp estmatons (5) d up = (f up2 v up = c Calculate f up1 ) cθ(t θ) 4B(T 2θ) d do = (f do2 f do1 ) cθ(t θ) 4B(2θ T) v do = c (T θ)f up2 2f 0 T 2θ θf up1 (T θ)f do2 θf do1 2f 0 T 2θ Then, based on the rough estmaton suppled by (4) and (5), we search matches between the postve dstance and relatve velocty estmates on the up ramps and those on the down ramps, Ths way, we can dstngush whch of all beat frequences are assocated wth each target. So, for a gven target, we now know ts d = c 8B Search matches between postve up do (d, d ) and correspendng speeds Fnal estmates for target : [ θ(f do1 f up1 ) +(T θ)(f do2 [ v = c 4f 0 f up1 +f do1 +f up2 f up2 ) ] ] +f do2 beat frequences on each of the four ramps. Then we 1 Note that for a spectrum based on real sgnals, we have to test twce as many beat frequences on each ramp, as compared to a spectrum based on complex sgnals. Fg. 4. Algorthm for calculatng dstance and relatve velocty for dual FMCW waveform.

8 8 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 2.3 Three segment FMCW waveform f Another varant of the FMCW waveform was presented f 0 + B n [14], [16] and [17]. Ths modulaton format has one part where the transmtted waveform s kept at a fx frequency. The rest of the waveform s composed of an up ramp and a down ramp. The echoes returned durng f 0 the fxed part contan the Doppler frequences, whch t provdes us wth the nformaton on the targets relatve veloctes. Moreover, the Doppler frequences allow us to correctly assocate the beat frequences on the up and down ramps. An example of the three segment FMCW waveform s presented n Fg. 5, where f 0, B and T are kept equal to those of the double FMCW waveform. θ s set equal to T 3. 0 θ 2θ Fg. 5. Three segment FMCW waveform. d up = (f pure j f up k ) cθ 2B Up ramp dstance estmaton d do = (f do pure j f k ) cθ 2B Down ramp dstance estmaton T (8) (9) Parameter estmaton As for the case of the double FMCW, for the Threesegment FMCW waveform our algorthm allows the choce between the use of real or complex data processng (see footnote 1). Estmaton s based on the fact that Doppler frequences are gven on the fxed frequency part of the modulaton (hereafter calledf pure ), thus provdng the relatve veloctes of targets. Then, from the Doppler frequency nformaton t s easy to fnd all possble correspondng Doppler-dstance pars on the up and down ramps. The dstance estmaton s gven by (8) and (9). Then, we seek the best possble match between the dstances estmated on the up ramp and those estmated on the down ramp by mnmzng I =1 (dup d do σ() )2 over all the permutatons σ(.) of the set 1,..., I, where I s the number of targets. The assocaton thus made, the relatve velocty and dstance estmates of the targets can be performed usng the assocated beat frequences nsde the followng equatons: d = (f do f up ) cθ 4B v = (f up +f do ) c 4f 0 A summary of ths algorthm s shown n Fg. 6. (10)

9 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 9 Calculate d up = (f pure j f up k ) cθ 2B d do = (f do pure j fk ) cθ 2B square error of any estmate, s used. The estmate s calculated as a functon of SNR. In ths work, the Cramer- Rao lower bound, [7], and the Barankn bound, [8], [18] and [19], are consdered. The Cramer-Rao lower bound expresses a bound on the varance of estmators of a determnstc parameter. Search matches between postve up do d and d The bound states that the varance of any unbased estmator s at least as hgh as the nverse of the Fsher nformaton matrx [7]. Any lower bound represents a Mean calculate for every target l d l = (f do l f up l ) cθ 4B v l = (f up l +f do l ) c 4f 0 Square Error (MSE) that s below the MSE of any possble estmator. Thus, the hgher the lower bound, the better t characterzes the performance of a system. The bound proposed by Barankn s hgher than the Fg. 6. Algorthm of calculatng dstance and relatve velocty for Three segment FMCW waveform. 2.4 Performance Analyss Cramer-Rao lower bound for low SNR values. For hgh SNR values, t approaches the Cramer-Rao bound. In fact, the Cramer-Rao bound can be seen as a partcular case of the Barankn bound, where the test ponts used In order to further decde whch modulaton format s best, a performance analyss s carred out. Ths knd of analyss helps n determnng the standard devaton of the dstance and the relatve velocty as a functon of the sgnal to nose rato (SNR). The searched parameters (dstance, relatve velocty, etc.) are calculated from the returned down converted baseband sgnal. Ths sgnal s always embedded n nose and thus the parameters can not be determned exactly, but have to be estmated. To evaluate the performance of ths estmate, a statstcal bound, whch s a mnmal bound on the mean are the only true parameters. The Barankn bound contans more nformaton: t takes nto consderaton the secondary lobes of the ambguty functon [9], whereas the Cramer-Rao bound only consders the nformaton gven by the man lobe. By accountng for possble false detectons around sdelobe maxma at low SNR, the Barankn bound supples nformaton not only on estmaton varance, but also on detecton capablty: as the SNR decreases, a non detecton wll occur more frequently, thus possbly resultng n a break of the shape of the varance bound curve. On another hand, f an unbased estmator of a parameter ω exsts, then there exsts an unbased estmator that reaches the Barankn

10 10 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars bound. Thus, the Barankn bound s the best lower bound and n addton, t s achevable. For an unbased estmaton ˆω, the Barankn bound yelds [19]: σ 2 d = var( α 1f up1 +α 1 f do1 α 2 f up2 +α 2 f do2 ) cov( ˆω) L(Ω 1 T )L T, (11) where 1 = [1,...,1] T s a vector wth length M, and L s a M M matrx defned by: [ ] L = ω 1 ω ω 2 ω... ω M ω τ 1 τ τ 2 τ... τ M τ (12) =, ν 1 ν ν 2 ν... ν M ν where(ω ) =1,...,M s any set of test ponts andω s them M Barankn matrx. The entres ofω are gven σ 2 v = var(βf up1 +βf do1 +βf up2 +βf do2 ), where var(.) stands for the varance and α 1 = cθ 16B, α 2 = c(t θ) 16B, β = c 8f 0. Developng the rght hand terms, we get (15) (16) by: where Ω k,l = E[L(y,ω,ω k )L(y,ω,ω l )] (13) σd 2 = α2 1(σf 2 +σ 2 up1 f )+α 2 2(σ 2 do1 f +σ 2 up2 f ) do2 (17) σv 2 = β2 (σf 2 +σ 2 up1 f +σ 2 do1 f +σ 2 up2 f ), do2 because of the ndependence of the estmatons from L(y,ω,ω k ) = p(y ω k) p(y ω) (14) one ramp to the next. For the three-segment FMCW waveform we repeat and p(y ω) s the lkelhood of observaton y, gven the parameter vector ω. the same steps performed for the prevous waveform. Here (10) yelds : To acheve the Barankn bound, we must maxmze the rght sde of the nequalty (11). So, our am s to fnd a way to obtan the maxmum bound and to compare t wth the Cramer-Rao bound. σ 2 d = σ2 ( γf up +γf do ) σ 2 v = σ2 (ζf up +ζf do ) (18) wth: Approxmatons For the dual FMCW waveform, we can derve from (6) and (7) that the varanceσd 2 ofdandσ2 v ofv are: γ = cθ 4B β = c 4f 0 (19)

11 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 11 and lead to the relatons Numercal Illustratons σ 2 d = γ2 σ 2 f up +γ2 σ 2 f do (20) In Fg. 7 and Fg. 8 we dsplay the standard devaton curves of both waveforms, for the dstance and relatve σ 2 v = ζ2 σ 2 f up +ζ2 σ 2 f do Then, the correspondng Cramer-Rao bounds for d andv can be derved easly from (17) for the dual FMCW as follows: CRB(d) = α 2 1 (CRB(f up1 )+CRB(f do1 ))+ α 2 2 (CRB(f up2 )+CRB(f do2 )) CRB(v) = β 2 (CRB(f up1 )+CRB(f do1 )+ CRB(f up2 )+CRB(f do2 )), (21) where CRB(.) s the Cramer-Rao bound, and CRB(f) s gven by [15]: CRB(f) = σ 2 N 1 n=0 ( s(n) f )2, (22) where (s(n)) n=0,...,n 1 s the sampled sgnal wth frequencyf andσ 2 s the varance of the nose. For the three-segment FMCW, (20) leads to: velocty error respectvely, versus SNR. The standard devaton curves plotted here are those of perodogrambased estmatons and Barankn and Cramer-Rao bounds. We can see that for low SNRs, the Barankn bound s far above the Cramer-Rao bound, and t s more n accordance wth smulaton results. When the SNR s hgh, the Barankn bound reaches the Cramer-Rao bound, and both bounds are close to the perodogram performance. In practce, there s a strong threshold effect around 12 db both for dstance and relatve velocty estmatons. Below the threshold, performance s very poor. Ths expresses the fact that at low SNRs, false detecton often occurs. The threshold effect also appears on Barankn bounds, but at lower SNRs (around 5dB). Ths shows that perodogram-based estmators are qute far from optmal. For both dstance and relatve velocty estmaton, CRB(d) = γ 2 CRB(f up )+γ 2 CRB(f do ) the performance of the dual FMCW waveform s slghtly (23) better than that of the three-segment FMCW waveform. CRB(v) = ζ 2 CRB(f up )+ζ 2 CRB(f do ) As far as Barankn bounds are concerned, the analytcal formulas for fxed test ponts have been obtaned by usng Mathematca software. Snce they are very complcated, ther expresson s omtted here. Thus, from (17) and (20), we can calculate the standard devaton (std) of the dstance and relatve velocty errors from the standard devatons of beat frequences. For the fnal calculaton of the relatve velocty from the three-segment waveform, we do not use the pure frequency. An optmsaton based on the mean square error shows that the best results are obtaned when takng nto consderaton the up and down beat frequences only. Also, n Fg. 9, we can see that the absolute value of the beat frequency of the pure snusod part of the waveform s much lower n general than those of

12 12 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars RANGE STANDARD DEVIATION σ d (m) Barankn (Dual FMCW) Cramer Rao (Dual FMCW) Perodogram (Dual FMCW) Barankn (Three segment FMCW)) Cramer Rao (Three segment FMCW)) Perodogram (Three segment FMCW)) SNR (db) Fg. 7. Dual FMCW and Three-segment FMCW dstance peformance (d = 50 m,v = 80 km/h). SINUSOID STANDARD DEVIATION σ f (Hz) f pure Barankn Cramer Rao Perodogram f up f do SNR (db) Fg. 9. Frequency estmaton varance and bounds. Estmaton performance for beat frequences for a car (d = 50 m, v = 80 km/h). 3 ADS & Matlab platforms VELOCITY STANDARD DEVIATION σ v (km/h) Barankn (Dual FMCW) Cramer Rao (Dual FMCW) Perodogram (Dual FMCW) Barankn (Three segment FMCW)) Cramer Rao (Three segment FMCW)) Perodogram (Three segment FMCW)) SNR (db) Fg. 8. Dual FMCW and Three-segment FMCW relatve velocty performance (d = 50 m, v = 80 km/h). 3.1 Radar Archtecture To promote system smplcty and keep down the unt prce, the radar archtecture s homodyne. The general archtecture of the radar front-end s presented n Fg. 10, and Table I shows the values of the man parameters used to model the RF platform that contans the radar front-end. The 76.5 GHz sgnal s generated by a GHz Voltage-Controlled Oscllator MMIC (VCO), whch s modulated accordng to the chosen modulaton format. The VCO s followed by an MMIC ncludng a up and down ramps, resultng n a lower SNR (due to hgher mxer nose at low frequences), and thus n sgnfcantly hgher varance of the estmator. Moreover, snce the SNR of f pure s lower, t rsks beng closer to the threshold, and t s safer not to use t. multpler by sx, combned wth a medum-power amplfer (X6MPA). At the output of the X6MPA, the chrpmodulated 76.5 GHz sgnal s njected nto a power dvder, whch passes one part of the sgnal through a coupler to the antenna where t s to be transmtted, and the other part to the MMIC mxer to serve as the LO sgnal. Once the transmtted sgnal has passed through the

13 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 13 propagaton channel, t s reflected on the target (pedestran, motorcycle, car, truck, etc.) and propagated back and expresses the fact that at short dstances the target s not completely llumnated by the antenna beam. 10log 10 (d)+5 RCS car (db) = mn 20 20log 10 (d)+5 RCS truck (db) = mn 45 whereds the dstance. 3.3 Nose modellng (24) (25) to the antenna. After passng through the coupler, t s amplfed n a low nose amplfer (LNA), and then dvded nto ts quadrature components (I and Q) n a second coupler. These I and Q components are fnally downconverted n the MMIC mxers to generate the baseband beat frequences. 3.2 Modelng consderatons The antenna and propagaton channel are modelled accordng to the radar equaton. The delay of the propagaton to the target and back s also ncluded n the propagaton channel. Intally, only the lne-of-sght propagaton path s taken nto account, and f multple targets are present, they are consdered as transparent. Thus each target s reached by a sgnal propagatng along the lneof-sght path. Four types of targets are consdered n ths study: pedestran, motorcycle, car and truck. The model pa- One parameter whch s decsve for the choce of radar archtecture s the SNR. Experences from an earler generaton of ACC radar show that an SNR greater than 15 db s necessary n order to guarantee target detecton. Ths was also emphassed by the performance analyss of the dstance and relatve velocty estmaton of the waveforms presented n secton II D. The threshold rameters are the radar cross secton (RCS) and the Doppler found n smulatons s about12 db, whch makes the15 frequency shft assocated to each target s relatve velocty. Dfferent publcatons of RCS measurements at GHz, e.g. [20], [21], [22] and [23], show that the RCS of dfferent targets must be evaluated more thoroughly. However, n ths study we chose to use a fxed RCS value of 10 dbsm and 7 dbsm for the pedestran and the motorcycle, respectvely. For the two larger targets, an expresson obtaned expermentally s used. It s gven by (24) and (25) for cars and trucks respectvely, db requrement for practcal operaton of the radar reasonable. Thus, to obtan accurate SNRs from radar smulatons, the nose of the concerned components must be modelled properly. In the front-end, the followng nose sources are consdered: the phase nose (PN) of the VCO, the nose deteroraton n the X6 whch follows the formula 20log 10 (N) (where N s the multplcaton factor), the nose fgure (NF) of the MPA, the equvalent nose temperature at the antenna, the NF of

14 14 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars f = 12.75GHz+fm(t) fm, Tr X6 f=76.5 GHz+ 6fm(t) MIXER COUPLER f=76.5 GHz+ 6fm(t) VCO X6 MPA LNA V IF_I V IF_Q f=76.5 GHz+ 6fm(t)+fd Fg. 10. The general archtecture of the radar front-end, ncludng antenna, propagaton channel and target. the LNA and fnally the NF and1/f nose of the MMIC mxer. Table 1 shows the values of the man parameters used to model the RF platform. antenna propagaton channel and targets (as presented n Fg.11) are ncluded n the Analog/RF sub-system, referred to here as the "RF Platform". The I and Q baseband sgnals (.e. the sgnal contanng the beat frequences) are collected for further sgnal processng, as descrbed n secton II. In the ADS-based platform, bultn spectrum analyzers are used to capture the frequency spectrum on each ramp. Unfortunately, once the spectra are avalable, the ADS data dsplay offers lmted possbltes for detectng, sortng and assocatng the peaks of each spectrum. Hence, the peak-detecton-assocaton and target-dentfcaton algorthm s almost mpossble to mplement. The acqured sgnalsv IF _I (t) andv IF _Q (t) are therefor exported to Matlab for further processng. The radar front-end s descrbed n more detals n [24]. 3.4 ADS Implementaton To obtan a usable smulaton platform, the Advanced Desgn System (ADS) from Aglent Technologes was employed. ADS allows co-smulaton between ts bultn envelope and DSP smulators. Hence, the complete radar front-end, ncludng the antenna, the propagaton channel and the targets, s modelled usng the ADS bultn elements of the analog/rf schematc. Care s taken to represent all ncluded components as correctly as possble, accordng to ther specfcatons. These RF parts are smulated usng the bult-n envelope smulator. The envelope smulaton s launched from a baseband data flow (DF) controller that controls the flow of all mxed numerc and tmed sgnals for all dgtal sgnal processng (DSP) smulatons. The DF controller also manages the control voltage of the VCO where the modulaton waveform s appled. The DSP level of the ADS smulaton platform s presented n Fg.11. The front-end 3.5 Matlab Implementaton To verfy that the baseband sgnals generated by the ADS platform are correct, a Matlab-based platform has been developed. Ths platform also serves as a means to mplement and test the proposed algorthms, as well as to detect and dentfy the targets. It also allows statstcal studes. Snce the baseband sgnal bandwdth s

15 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 15 Table 1. Data of the radar front-end components. Component Parameter Value VCO(MMIC) Frequency Output power at 10 khz GHz +f m 5 dbm 75 dbc/hz Phase Nose at 100 khz at 1 MHz 100 dbc/hz 123 dbc/hz Multplcaton factor 6 Multpler-amplfer(MMIC) LNA Output power Nose fgure Gan Nose Fgure Converson loss at 1 khz 14.5 dbm 8 db 15 db 4.5 db 7.5 db 34 db Mxer(MMIC) Nose fgure at 10 khz at 100 khz 28 db 21 db at1mhz 17 db Couplers(durod) Losses Isolaton 3.2 db 40 db Transton (antenna) Losses 0.25 db Maxmal gan (G) 27 db Antenna Effectve area (RX) m 2 Propagaton path Nose temperature Losses (per unt area) Delay Doppler frequency Pedestran 290 K 10log 10(4πd 2 ) dbsm τ = d/c (s) 2vf 0/c (Hz) 10 dbsm Targets RCS (σ) Motorcycle 7 dbsm Car see equaton (24) Truck see equaton (25)

16 16 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars FMCW ramp : Control Voltage Tmed Expresson TmedSnk Acquston of IF_I sgnal TmedSnk Tmed Expresson Add RF Platform IF_I Vosc IF_Q R R TmedSnk Acquston of IF_Q sgnal Fg. 11. General smulaton platform, where the Data Flow smulaton tool controls the Envelope smulaton of the RF platform. very wde (B = 600 MHz), we drectly generate sgnals at the output of the mxer to avod huge vector manpulaton. We calculate the radar equaton (26) formulated here for non-fluctuatng targets, to determne the sgnal level for each target, takng nto account all parameters n Table 1. P r = P t G 2 λ 2 σ (4π) 3 d 4 (26) In eq (26), P t and P r are the transmtted and receved powers respectvely,g s the gan of the radar antenna, λ the mean wavelength of the sgnal, σ the RCS and d the dstance to the target. The values of parametersλ, G andσ are those gven n Table 1. The receved sgnal power depends on the dstance and the RCS of the targets. The mxer and VCO phase noses are calculated as n the ADS mplementaton, and nterpolated for all frequences. They are added n the Fourer doman of the sgnal: at each frequency a gaussan nose wth sutable varance s added. Accordng to the study of estmaton performance, we set the detecton threshold for beat frequences at SNR = 15 db. Beat frequences are obtaned from the local maxma of the perodogram stuated above the detecton threshold. Once the beat frequences are obtaned, the estmaton algorthms of detecton are appled usng (6), (7) and (10) for dual FMCW and three-segment FMCW waveforms, respectvely. 4 Smulaton results 4.1 Comparson of ADS and Matlab To compare the results of both smulaton platforms (ADS and Matlab), a three-target example s set up contanng a pedestran [15 m,+80 km/h] 2, a motorcycle [150 m, 10 km/h] and a truck [15 m, +10 km/h], where veloctes are relatve veloctes between the radar and the targets. The dual FMCW and three-segment FMCW 2 80 km/h s a relatve speed, whch means that the car s approachng the slowly movng pedestran at about 80 km/h.

17 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 17 modulaton formats are consdered wth a total duraton T = 5.12 ms. The frst up ramp spectra based on ADS and Matlab smulatons are shown n Fg. 12 and Fg. 13 respectvely. Complex data I + jq data were used n order to enhance the vsblty n the spectra. A Hammng wndow s used for perodogram smoothng [25]. Snce at the output of the mxer related to the beat frequency closest to the null frequency. Ths s done because ADS only accounts for a constant (worst case) nose level n a multtarget confguraton. Ths s not a problem wth Matlab, as shown n Fg. 14, where correlaton of mxer nose s fully taken nto account. Smlar results are obtaned wth other ramps of both FMCW formats. complex data are used, the beat frequences are all found at the correct sde of zero n the spectrum. Usng only the real part would lead to twce as many beat frequences at both postve and negatve frequences. Accordng to the theory, the three beat frequences should be Power (dbm) UP ramp Freq. (khz) Fg. 12. ADS Spectrum for frst ramp of dual FMCW waveform khz, khz and 43.1 khz for the pedestran, motorcycle and truck, respectvely. Table 2 shows the detected beat frequences from ADS and Matlab smulatons. The frequency resoluton depends on the nverse of the ramp duraton, leadng to a precson of about0.8 khz for the beat frequences. Ths shows that the results n Table 2 agree perfectly wth the theoretcal values. Table 2. Beat frequency comparson for the frst up ramp Power (dbm) UP ramp 1 Pedestran Motorcycle Truck Theory 33.2 khz khz 43.1 khz ADS 33.4 khz khz 43.0 khz Matlab 33.0 khz khz 42.7 khz Freq. (khz) Fg. 13. Matlab Spectrum for frst ramp of dual FMCW waveform. Fg. 12 and Fg. 13 yeld smlar results for ADS and Matlab. Here the nose level has been set equal for all frequences. It has been chosen equal to the nose level 4.2 Target detecton Once all spectra are calculated, the target detecton algorthm s mplemented and the target parameters are

18 18 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars UP ramp 1 s excellent, but t seems that the real case returns better values for relatve velocty. More generally we have Power (dbm) tested both approaches wth several examples. In some examples we obtan better results for the complex case, Freq. (khz) whle the real case gves better results n other examples. Yet, t proves that the proposed algorthm works Fg. 14. Matlab Spectrum of the frst ramp usng dual FMCW. All noses are taken nto account. estmated. For the dual FMCW usng complex data, results are shown n Table 3. Table 3. Results usng complex data Dstance Relatve velocty RCS SNR Type Detecton Motorcycle Yes Truck Yes Pedestran Yes for both cases. If the same smulaton example s used for the Three segment FMCW we wll realse, that for ths partcular example, we have another problem, namely that the motorcycle and the truck have the same magntude of relatve velocty ( 10 km/h and +10 km/h). Thus, for these two targets we should fnd the Doppler frequences 1.4 khz and +1.4 khz. If usng the real sgnal, each Doppler (and beat) frequency wll turn up on both sdes of zero n the spectrum. As the returned power The results obtaned when usng only the real part of the sgnal are presented n Table 4. Table 4. Results usng real part of data Dstance Relatve velocty RCS SNR Type Detecton Motorcycle Yes Truck Yes Pedestran Yes of the truck s about 37 dbm, whle that of the motorcycle s about 100 dbm, the former wll be completely hdden by the latter. Thus, we wll obtan fewer detected targets from pure Doppler frequences. However, ths wll not have any effect on the fnal detecton of targets and ther dstance and relatve velocty estmaton. Indeed, the pure Doppler frequency of the truck wll enter nto the algorthm as the pure frequency of the motorcycle, and t wll be used together wth the up and down ramp beat frequences of the motorcycle for the calculaton ofd up andd down respectvely. Fnally When comparng Table 3 wth Table 4, t s seen that, for both the real and the complex case, all targets are detected. For both cases, the estmaton of dstance the motorcycle s detected too, and ts parameters are correctly estmated. Here both targets have SNRs above the detecton threshold (15 db). More generally, f the

19 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 19 contrbutons of two targets nterfere on one ramp, t s stll possble to recover both of them, provded that each has a power level above the threshold on the perodograms. Note that ths does not sgnfcantly degrade estmaton performance, snce target contrbutons n the perodogram are narrow and the error remans smaller RANGE STANDARD DEVIATION σ d (m) mean std max std mn std than the Fourer transform resoluton. In fact, t can be calculated that the resultng error on dstance s less than 1 m and the error on relatve velocty less than 1 km/h. 5 Further experments In order to show that the conclusons hold for varous stuatons, we have consdered the estmaton performance bounds. We have plotted the maxmum and mnmum performance curves together wth the mean performance curves for all (d,v) couples wth d = 1, 50, 100, 150, 200 m and v = 180, 90, 0, 90, 180, 270, 360 km/h. Fg. 15 and 16 clearly show that a 15 db VELOCITY STANDARD DEVIATION σ v (km/h) SNR (db) (a) dstance mean std max std mn std SNR (db) (b) Relatve velocty Fg. 15. Mn, max and mean std for dstance and relatve velocty for dual FMCW for all 35 pars (d,v) wth d = 1, 50, 100, 150, 200 m and v = 180, 90,0,90,180,270,360 km/h. P fa = P(X > S) = = S 1 σ 2e u σ 2 du. [ e u σ 2 ] S = e S σ 2 S = e db σ2 10 db 10. (27) threshold above the nose level (SNR mnmum) s vald for all scenaros. In addton, for SNRs larger than 15 db, the standard devaton s always much lower than 1 m for dstance and1km/h for relatve velocty. Each frequency of the perodogram follows an exponental dstrbuton [26] [27]. Let us fx the detecton threshold equal tos, and denote the varance of the nose byσ 2 and the perodogram output at a certan frequency byx. In the absence of a target, the probablty of false alarm at ths frequency sp fa : So, for all then ponts of the perodogram, the total false alarm probablty s1 (1 P fa ) N. In Fg. 17 we have plotted the false alarm rate versus the threshold-to-nose rato. We have seen before that

20 20 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars RANGE STANDARD DEVIATION σ d (m) mean std max std mn std false alarm rate SNR (db) Threshold to nose rato VELOCITY STANDARD DEVIATION σ v (km/h) (a) dstance mean std max std mn std SNR (db) (b) Relatve velocty Fg. 16. Mn, max and mean std for dstance and relatve velocty for three-segment FMCW for all 35 pars (d,v) wth d = 1, 50, 100, 150, 200 and v = 180, 90,0,90,180,270,360. a 15 db threshold above the nose level s enough for a good estmaton of beat frequences. Now, from Fg. 17 we see that wth ths choce, the false alarm rate s neglgeable. In order to determne f I/Q complex data or the nphase-only processng s to be preferred, we have compared the estmaton standard devaton for a motorcycle and the 35 (d,v) pars gven above. The motorcycle has been chosen snce t s a target of partcular nterest due Fg. 17. False alarm rate as a functon of the threshold-to-nose rato. From left to rght: 1, 2 and 4 ramps wth 4096 samples per ramp. to ts low RCS, ts wde relatve velocty range and long dstance detecton requrement. The standard devatons are calculated for the estmates obtaned when the target s detected. For each (d, v) par, 100 experments have been carred out. The results are presented n tables 5 to 8. The dual FMCW outperforms the three-segment approach n most cases, but they both acheve good detecton and low estmaton varance. As expected, complex data processng acheves better detecton due to a 3 db processng loss wth nphase-only processng. Ths results n a detecton loss, as shown by the crosses (X) n the tables. In these tables, the frst column represents stuatons that would lead to ambguty when processng only nphase data wth the classcal FMCW (sngle trangle waveform). Unlke the classcal FMCW waveform that shows ambguty at short dstance and hght relatve speed (see secton 2.1), we see that, as expected, dual and three-segment FMCW waveforms do not suffer from

21 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars 21 any ambguty n the whole dstance and velocty ranges. Performance levels smlar to those n tables 5 to 8 are obtaned wth the ADS smulaton platform. Ths s because the same SNRs are observed for beat frequency spectra on both platforms. Table 5. Dstance and relatve velocty Standard Devaton for a motorcycle when usng complex data for the dual FMCW σ d (m) dstance (m) σv(km/h) e 52.9e 5 2.6e 2 3.4e 5 1.6e relatve velocty (km/h) 5.2e 43.6e 4 5.5e 1 6.4e 4 3.4e 4 2.2e 51.9e 2 1.9e 2 1.9e 2 2.5e e 44.5e 1 4.6e 1 4.1e 1 5.9e 1 4.9e 51.9e 5 3.3e 5 3.0e 5 3.1e e 44.7e 4 1.1e 3 7.3e 4 6.5e 4 4.1e 51.9e 2 2.9e 5 3.0e 2 3.0e e 44.5e 1 5.3e 4 6.3e 1 6.3e 1 Table 6. Dstance and relatve velocty Standard Devaton for a motorcycle when usng real data for the dual FMCW (X when detecton s not feasble on all ramps) σ d (m) dstance (m) σv(km/h) e 51.9e 5 2.6e 2 1.9e 2 X 180 relatve velocty (km/h) 4.9e 44.2e 1 5.5e 1 4.1e 1 X 1.9e 53.0e 2 3.0e 2 X X e 46.9e 1 7.0e 1 X X 3.2e 52.5e 5 2.1e 5 X X 0 7.8e 43.0e 4 9.0e 4 X X 2.3e 53.2e 2 3.5e 2 X X e 47.5e 1 6.7e 1 X X 4.5e 51.9e 2 1.9e 2 X X e 44.1e 1 4.2e 1 X X 3.4e 52.4e 5 2.6e 5 3.3e 2 X e 45.2e 4 7.0e 4 7.6e 1 X 3.7e 52.6e 5 3.3e 5 1.9e 2 X e 44.5e 4 4.1e 4 4.5e 1 X e 53.9e 5 1.9e 2 2.7e e 4 7.3e 45.9e 4 4.1e 1 5.2e 4 3.8e 4 3.2e 52.6e 5 2.2e 5 3.0e 2 2.6e 2 7.7e 46.5e 4 5.7e 4 6.9e 1 6.1e 1 3.6e 53.9e 5 3.2e 5 1.9e 2 4.9e 2 8.3e 49.0e 4 3.0e 4 4.6e Table 7. Dstance and relatve velocty Standard Devaton for a motorcycle when usng complex data for the three-segment FMCW σ d (m) σv(km/h) dstance (m) To ensure good detecton of the targets, we must fnd the mnmum transmted power P t that guarantees targets detecton. The results are summarzed n Fg. 18. relatve velocty (km/h) e 51.8e 53.9e 24.8e 56.0e 2 7.3e 43.7e 46.4e 11.3e e 55.3e 55.8e 55.9e 53.9e 2 7.9e 45.1e 47.2e 46.6e 46.4e 1 5.2e 54.4e 54.7e 51.0e 13.9e 2 1.1e 37.6e 38.5e 49.7e 16.5e 1 We can see that P t 21 dbm n all confguratons. For e 56.3e 52.3e 55.3e 26.7e 5 1.0e 31.0e 36.5e 48.6e 19.0e 4 fxed P t, the correspondng power densty at dstance d from the radar antenna s e 53.7e 56.0e 26.6e 56.4e 2 1.2e 31.0e 39.9e 11.1e e 55.4e 55.5e 53.3e 53.4e 2 1.0e 31.0e 39.7e 48.6e 46.4e 1 Power Densty = PG 4πd 2 (28) e 57.3e 56.5e 52.9e 55.1e 5 5.8e 47.9e 41.4e 35.4e 46.1e 4 where G s the antenna gan. For P t = 21 dbm, we get the power densty as a functon of d, plotted n Fg. 19. From ths fgure we can see that when a pedestran s at more than 40 cm from the radar, the power densty s below the recommended lmt (5mW/cm 2 ) for waves

22 22 Al Bazz et al.: Estmaton Technques and Smulaton Platforms for ACC Radars Power Densty ( mw / cm 2 ) Power Densty Recommended lmt wth frequences between 1.5 and 100 GHz, accordng to the recommendaton provded by the Amercan Natonal Standards Inttute (ANSI) n table 1 n [28]. So, the radar comples wth ths norm n any stuaton whence there s nobody closer than 40 cm from t. Swtchng off the radar when the car s stopped or at very low speed would brng further guarantee n terms of safety Dstance (m) Fg. 19. Receved power densty at dstance d for transmtted power P t = 21 dbm. Table 8. Dstance and relatve velocty Standard Devaton 6 Concluson for a motorcycle when usng real data for the three-segment FMCW (X when detecton s not feasble on all ramps) σ d (m) dstance (m) σv(km/h) e 5 4.4e 5 3.9e 2 2.7e 5 X 180 relatve velocty (km/h) 1.1e 3 1.6e 3 6.5e 1 4.2e 4 X 3.6e 5 4.6e 5 3.9e 5 X X e 4 5.6e 4 1.1e 3 X X 8.2e 5 3.1e 5 5.2e 5 8.8e 2 X 0 1.1e 3 4.8e 4 8.4e 4 6.5e 1 X 2.2e 5 3.4e 5 4.0e 5 5.3e 2 X e 4 6.2e 4 7.9e 4 8.7e 1 X 9.1e 5 6.5e 5 3.9e 2 X X e 3 9.5e 4 6.5e 1 X X 4.5e 5 5.0e 5 5.4e 5 X X e 4 7.5e 4 9.5e 4 X X We have developed and valdated two smulaton platforms for a lnear frequency modulaton, one based on ADS and the other based on Matlab. Three modulaton formats have been tested and new algorthms for dstance and relatve velocty estmaton have been proposed. The Cramer-Rao and Barankn bounds have been used to evaluate the performance of the estmated parameters, relatve velocty and dstance. Ths valdated e 54.00e 2 4.2e 5 3.2e 5 X 8.9e 4 6.5e 1 7.9e 4 5.5e 4 X the use of a 15 db SNR threshold for target detecton. It was found that the proposed dual FMCW modulaton P t (dbm) Pedestran Motorcycle car truck Dstance (m) Fg. 18. Necessary transmted power to ensure good detecton at dstance d. format offers slghtly hgher performance and low complexty n beat frequency assocatons compared to other strateges. The algorthms proposed allow the choce between usng real or complex data; whchever s used, the targets are detected. Thus, we see that t s possble to desgn low complexty 77 GHz ACC radar. Ths wll hopefully lead to a more wdespread use of ACC radars and help reduce car accdent rates.