International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June 2009 Method to Improve Range and Velocity Error Uing De-interleaving and Frequency Interpolation or Automotive FMCW Radar Eugin Hyun, and Jong-Hun Lee Diviion o Advanced Indutrial Science & Technology, DGIST, Korea {braham, jhlee}@dgit.ac.kr Abtract In the paper, we propoe method to obtain the range and velocity with improved error depending on each ditance (long, middle, and hort) o the target or the automotive Frequency Modulation Continuou Wave (FMCW) radar. While target i in the long ditance, the range and velocity are roughly extracted, or near-range target with the high colliion probability, the de-interleaved method in the time domain and requency interpolation in the requency domain are applied to obtain more accurate range and velocity. Keyword: Automotive FMCW Radar, Frequency Interpolation, Velocity Error 1. Introduction 77GHz radar are already on the market a the active aety ytem to protect the driver and minimize damage o all road vehicle. The radar enor ytem are one o important element in automotive technology, becaue thee are virtually unaected by harh environmental condition uch a weather and light quality. The 77GHz FMCW radar are epecially eective and preently on the market a the aety ytem or high perormance automotive application [1][2][3]. In FMCW radar, a typical approach to extract range and velocity i to analyze the Fourier pectrum o the received beat ignal. The Fourier pectrum i uually determined by digital method uing the beat ignal ampled by ADC (Analog Digital Converter). However, ince accurate beat requency meaurement can be poible only up to requency tep determined by ADC ampling rate, the number o ampling, and chirp period, the tep ize o etimated range and velocity i limited. In thi paper, the main idea o the propoed method i to obtain range and velocity with dierent error depending on the ditance (long, middle, or hort) o the target rom the radar. The baic concept wa introduced in the previou paper [4]. While the range and velocity extracted uing only FFT or target in the long ditance, more accurate range and velocity can be obtained by de-interleaving method and requency interpolation or object in the middle and hort range zone. Section I provide the FMCW radar principle. In ection II, the propoed adaptive range proile algorithm will be decribed in detail. 2. Overview o FMCW Radar 11
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June, 2009 FMCW radar tranmit a requency-modulated continuou wave to meaure the range and velocity o the target. Figure 1 how requencie a a unction o time in the tranmitted ignal and received ignal or a tationary target [5][6]. Here, c i the center requency, B i the modulation bandwidth, and 0 i the tarting requency, and td i the delay time between tranmitted and received ignal. T i a chirp period which i one hal o PRI(Pule Repetition Interval). req. T Rx ignal Tx ignal B t d c 0 req. bd PRI time bu Figure 1. Tranmitted, received, and beat requencie a a unction o time or a moving target When the target i not tationary the received ignal will contain a Doppler hit term in addition to the requency hit due to the time delay t d. The beat requency i dierence between the tranmitted ignal and received ignal and the beat requencie or the up chirp and down chirp are denoted a repectively a bu and bd. The range beat requency r and the Doppler requency d are mathematically expreed a r bu bd / 2 and d bu bd / 2. The range beat requency r and Doppler requency d can be obtained by ignal proceing, and then the ditance and velocity o the target can be etimated a Equation (1) and (2). ct r R 2B (1) cd V 2 (2) c time In a FMCW radar, the ideal unambiguou range i ct / 2. In practice, however, the maximum range i normally elected a ewer than 10% o the unambiguou range [6]. Depending on the application, the maximum range and velocity are elected and then, the correponding ranging beat requency b max and Doppler d max are calculated. Thereore, the required ampling rate o ADC hould be 2( r max d max ). Typically, the range pectrum o the beat ignal ampled with requency i computed with N point DFT(Dicrete Fourier Tranorm) or every chirp period, 12
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June 2009 uing the FFT(Fat Fourier Tranorm) algorithm[7] a hown in Figure 2. Here, requency tep and N i the number o data ampled over chirp period T. i v N T t 1/ T N / 2 / N / 2 Figure 2. Data ample o beat ignal and dicrete requency pectrum The meaured beat requency error i expreed a dierence between the ideal beat requency in the continuou requency domain and the beat requency in the dicrete ideal FFT requency domain in Equation (3). Here, b i ideal beat requency, b i dicrete beat requency by FFT, and err i the beat requency error. The maximum error o beat requency i equal to / N. error (3) ideal b FFT b Thu, the range tep ize and velocity tep ize are equal to Equation (4) and (5), repectively. The maximum range error and velocity error alo are equal to R and V, repectively. I we can chooe longer chirp period, the velocity tep ize can be more diminihed but the range tep ize i not changed becaue requency tep ize i ixed a 1 /T. Thi limitation can be, however, overcomed uing more data ampled by multiple modulation period at the ame ampling rate[7]. I, or example, two chirp period are ued, then 2N data may be ampled and requency tep / 2 may be obtained. The limitation o range and velocity may be reolved with a proper choice o ample length. 13
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June, 2009 ct R 2B c V 2 2 c ct 2B c c N N (4) (5) 3. The propoed method In Figure 3, Car #0 ha a FMCW radar with a maximum range R max. We aume that Car #1 and Car #2 are moving in middle range zone and long range zone on the ame road lane, repectively. In thi cenario, while Car #0 can roughly detect the ditance rom Car #2, the range rom Car #1 hould be more accurately extracted becaue Car #2 ha a higher probability o colliion. We alo aume that Car #1 i moving into hort range zone. In the cae, more accurate range and velocity hould be obtained. R max Car #0 Car #1 Car #2 Short range zone Middle range zone Long range zone Figure 3. Scenario example to explain the propoed method I the maximum range i reduced by one hal o R max, the correponding maximum beat requency and required ampling rate can be hortened by hal. However, ince the number o data ampled in one chirp period i alo one hal o N, the maximum range error and velocity error are not changed by Equation (4) and (5). A above mentioned, iner range and velocity tep ize may be reolved uing ample over everal chirp period or FFT. However, thi method lead to a high computational complexity by increaing the number o data. In the paper, we propoed method to improve range and velocity error a the ditance (long, middle, or hort) o the target by uing de-interleaving method and requency interpolation a hown in Figure 4. In the example o Figure 3, or obtaining range and velocity o Car #2 in the long ditance, we ue FFT with N ample. Then, the maximum range error and velocity error are equal to Equation (4) and (5). Thi i reerred to a long-range detection. 14
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June 2009 I target(car #1) i located in the middle range zone, the maximum range to be detected and the correponding maximum beat requency in a FMCW radar are reduced by hal. Moreover, required ADC ampling rate can be reduced by hal. Amplitude N ample Beat ignal ADC ( ampling rate) T... time De-interleaved in time-domain N / 4 Sample Frequency Interpolation in requencydomain N Point R & V extraction De-interleaved in time-domain N / 2 N Sample Frequency Interpolation in requencydomain Point R & V extraction Frequency Spectrum N Point R & V extraction Short Range Detection Middle Range Detection Long Range Detection Figure 4. The concept o ignal proceing in the propoe method In a general radar ytem, however, the ADC ampling rate depend on the requirement o the application and initial ampling requency cannot be changed becaue o the hardware contraint o ytem implementation. For reducing the number o ample, we employ de-interleaving method in the time domain without changing ADC ampling rate. Figure 5 how that data ample o example o Figure 2 are down-ampled into N / 2 by de-interleaving method in order to adjut the maximum range to meet the middle-range detection. However, i N / 2 data are proceed uing FFT, the range tep ize and velocity tep ize are not changed becaue the required ADC ampling rate become alo one hal o by deinterleaving method. In the paper, or overcoming the limitation, we ue the requency interpolation uing zero padding FFT in the requency domain. Zero padding i ueul when the requency ampling i conidered to be too pare to provide a good repreentation o the 15
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June, 2009 continuou-requency etimation pectrum[8]. In middle-range detection o Figure 5, zero padding FFT with N point i ued to obtain ine range and velocity with 0.5 R and 0.5 V in comparion a the long-range detection. v N T t 1/ T N / 4 / 2N / 4 Figure 5. Example o middle range detection in the propoed method Latly, when the target ditance rom radar i very near in hort range zone, we mut extract an accurate range and velocity. Uing the ame method, we can reduce ampling rate and the number o ample, and then we can obtain the accurate range and velocity by the requency interpolation. Thi i reerred to a hort-range detection. 4. Simulation Reult We imulate thi algorithm uing Matlab. The detail propertie o FMCW radar, uch a the tranmitted bandwidth, the carrier requency, the chirp period, the PRI(Pule Repetition Interval), and the modulation requency, are hown in Table 1. The ampling requency o ADC i 2 MHz becaue the maximum range i 200 m and the maximum beat requency i 533 khz. 16
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June 2009 The imulation reult o long-, middle- and hort-range detection i hown in Table 2. For long-range detection, all 1000 data ampled during a chirp period are applied with 1024 point FFT to detect range up to maximum range 200 m. In middle- detection, the 1000 ample are de-interleaved into 500 in the time domain to obtain maximum range up to 100m and thee down-ampled data are computed by 1024 point FFT with zero padding. For hort-range detection, de-interleaved 250 ample in the time domain or maximum ditance 50m, are proceed with Fourier pectrum interpolation in the requency domain. Table 1. The propertie o FMCW radar Item Nomenclature Speciication Bandwidth B 200MHz Carrier requency 76.5GHz Chirp period T 0.5m PRI T 1m Modulation requency ADC ampling rate c m m 1kHz 2MHz We can know that the maximum range error and velocity error o hort-range detection are decreaed in comparion with them o the long-range detection. Table 2. The imulation reult o long range and middle-range detection Type Long-range detection Middle-range detection Long-range detection The maximum range 200m 100m 50m Number o ample de-interleaved 1000 500 250 in the time domain FFT point 1024 1024 1024 Frequency tep ize 1.95kHz 0.98kHz 0.49kHz Maximum range error 0.73m 0.36m 0.18m Maximum velocity error 13.8km/h 6.9km/h 3.4km/h Figure 6 how the imulation reult o long-, middle-, and hort-range detection or tationary target. The target range i 30m~50m. X-axi i target ditance and y-axi i error o detected range. We can know range error o the hort-range detection i lowet. 17
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June, 2009 Figure 6. The error o extracted range when tationary target in i 60m~90m (a) by long-range detection (b) by middle- range detection (b) by hort range detection Figure 7 how the imulation reult o long-, middle-, and hort-range detection or moving target. The range o moving target i 50m and the velocity i -100km/h ~ 100km/h. X-axi i target velocity and y-axi i error o detected velocity. We can alo know velocity error o the hort-range detection i lowet. 18
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June 2009 Figure 7. The error o extracted velocity when moving target range i 50m and it velocity i -100km/h~100km/h (a) by long-range detection (b) by middlerange detection (b) by hort range detection Next, we imulate the range proile with multi-target. We aume that the ditance o the range o target are 49.0m, 48.3m, 36.4m, 35.7m, and 35.0m. Figure 8 how the FFT reult o long-, middle-, and hort-range detection or thee ive target. X- axi i range o target and y-axi i normalized PSD(Power pectrum denity). While we cannot detect the exact range o the target by long- and middle-range detection, hort-range detection can provide ine range proile. That i, in hort-range detection, all range o ive target are extracted a 49.12m, 48.2m, 36.66m, 35.74m, and 34.82m, while only two target (49.12m and 36.66m) can be een by long-range detection. 19
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June, 2009 Figure 8. Normalized range proile extracted (a) by long-range detection (b) by middle range detection (c) by hort range detection 5. Concluion We propoed method to improve the range and velocity error a each range (long, middle, and hort) o the target or the automotive FMCW radar. For the target in the long ditance, the range i extracted with the coare range and velocity uing only FFT. For middle- and hort- range detection, the ampled data o beat ignal i de-interleaved in the time domain to adjut maximum beat requency to be detected, and then requency interpolation by zero padding FFT in the requency domain i ued to obtain more accurate range and velocity. Acknowledgement 20
International Journal o Signal Proceing, Image Proceing and Pattern Recognition Vol. 2, No. 2, June 2009 Thi work i upported by the baic reearch program o the Minitry o Education & Science Technology. Reerence [1] Hermann Rohling, Marc-Michael Meinecke, Waveorm Deign Principle or Automotive Radar Sytem [2] Hermann Rohling, Marc-Michael Meinecke, Waveorm Deign Principle or Automotive Radar Sytem, 2001 CIE International Conerence on Radar, IEEE, China, 2001, pp. 1-4. [3] SupplierBuine, Market report : Active Saety Sytem Report, SupplierBuine, 2007. [4] Eugin Hyun, Sang-Dong Kim, Chiho Park, Jong-Hun Lee, Automotive FMCW Radar with Adaptive Range Reolution, 2008 International Sympoium on Signal Proceing, Image Proceing and Pattern Recognition (SIP2008),China, 2008, pp. 130-133. [5] Graham M Brooker, Undertanding Millimetre Wave FMCW Radar, 1 t International Conerence on Sening Technology, IEEE, New Zealand, 2005, pp. 152-157. [6] Baem R. Mahaza, Radar Sytem Analyi and Deign Uing MATLAB, Chapman & Hall/CRC, 2005. [7] A. Wojtkiewicz, J. Miiurewicz, M. Nałecz, K. Jedrzejewki, K. Kulpa, Two-dimenional ignal proceing in FMCW radar, ta.elka.pw.edu.pl/~jmiiure/eptr_bae/lect_mcw/kk97m.pd [8] Petre Stoica, Randolph L. Moe, Introduction to Spectral Analyi, Prentice Hall, 1997. Author Eugin Hyun received the B.S. degree in electrical and electronic engineering rom Yeungnam Univeriity, Korea, in 1999, and obtained the M.S., and Ph.D. degree in electronic engineering rom Yeungnam Univeriity, Korea, in 2001 and 2005, repectively. From 1999 to 2005, he wa a Reearch Aitant with the VLSI laboratory, Yeungnam Univerity. Since 2005, he joined the Daegu Geongbuk Intitute o Science and Technology(DGIST), Daegu, Korea, a a enior reearch engineer. Hi primary reearch interet are the radar digital ignal proceing and deign o digtal ignal proceor. Jong-Hun Lee received the B.S. degree in electronic engineering rom SungKyunKwan Univerity, Korea, in 1996 and obtained the M.S. and Ph.D. degree in electrical and electronic and computer cience rom SungKyunKwan Univerity, Korea, in 1998 and 2002, repectively. From 2002 to 2005, he joined in the diviion o Telecom. Network, Samung Electronic Company a a Senior Reearch engineer. Since 2005, he ha joined in the diviion o advanced indutrial cience & technology, Daegu Gyeongbuk Intitute o Science & Technology (DGIST), Korea, a a enior reearch engineer. Hi primary reearch interet are the detection, tracking, recognition or radar (FMCW & UWB radar) and viion-baed vehicle enor. 21
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