FPGA Implementation of Pipelined CORDIC for Digital Demodulation in FMCW Radar

Transcription

1 FPGA Implementaton o Ppelned CORIC or gtal emodulaton n FMCW Radar Amrtakar Mandal, Rajesh Mshra Abstrat Now-a-days Radar Sgnal Proessng system s ganng a great deal o attenton or realzaton o on-hp programmable sgnal proessor or ts real tme applatons. Applaton spe systems are beng mplemented usng wde spetrum o gtal Sgnal Proessng (SP algorthms. Suh s the ase or COordnate Rotaton Igtal Computer (CORIC algorthm whh s turned out to be wdely researhed top n the eld o vetor rotated SP applatons. In ths paper we have desgned an applaton spe ppelned CORIC arhteture or dgtal demodulaton n low power, hgh perormane FMCW Radar. A omplex gtal Phase Loked Loop (PLL has been used or dgtal demodulaton. The FPGA mplementaton o CORIC based desgn s sutable beause o ts nherent hgh system throughput due to ts ppelned arhteture where lateny s redued n eah o the ppelned stage. Substantal amount o resoure utlzaton has been redued n proposed desgn. For better loop perormane o rst order omplex PLL durng demodulaton, the onvergene o the CORIC arhteture s also optmzed. Hardware syntheszed result usng Cadene desgn tools are presented. Index Terms FMCW Radar, CORIC, FPGA, SP, PLL, Loop perormane. P I. INTROUCTION HASE ETECTION s a wdely researhed top n radar demodulaton, espeally n low power oppler radar where aurate deteton s needed []. In general, radar system uses oherent osllator as a reerene requeny or oppler deteton. In analog demodulaton, Voltage Control osllator (VCO s used. But peret demodulaton s not possble wth the use o VCO as t suers to mantan lnearty over the desred requeny range []. In present deade, dgtal or mxed sgnal desgn based demodulator s wdely used or superor perormane. To ensure lnearty over the range o requeny, numerally ontrolled osllator s beng used. Phase deteton n ommunaton reever s very muh senstve to quantzaton nose. Ths knd o dstorton s basally due to bt resoluton. Eorts have been made to desgn a quantzaton error ree ppelned CORIC arhteture based dgtal demodulator on FPGA platorm. We have proposed a rst order omplex gtal Phase Loked Loop (PLL or eent demodulaton o radar sgnals. The teratve ormulaton o CORIC algorthm was rst Manusrpt reeved Marh 3, 3; revsed May, 3. Amrtakar Mandal and Rajesh Mshra are wth the Shool o Inormaton and Communaton Tehnology, Gautam Buddha Unversty, Greater Noda, U.P.- 38, Inda (e-mal: amrtkark@gmal.om; rmshra@gbu.a.n. developed by Jak E. Volder n 959 [3] or the multplaton, dvson and omputaton o trgonometr untons lke sne, osne, magntude and phase wth great preson. The key onept o CORIC algorthm s smply sht and adds. Although the same untons an be mplemented usng multplers, varable sht regsters or Multply Aumulator (MAC unts, but CORIC an mplement these untons eently whle savng enough slon area whh s onsdered to be a prmary desgn rtera n applaton spe on hp mplementaton where hgh perormane and low ost hardware solutons or SP are requred [4]. Ths knd o demodulator an be used n wde varety o reevers where real tme sgnal proessng s mportant [5]. Ths paper desgns rst order omplex PLL or I/Q hannel Radar demodulator usng ppelned CORIC arhteture. In dgtal PLL, an adjustable loal sne wave generator and phase detetor s requred. The CORIC oers the opportunty to alulate the desred trgonometr omputaton n a smple and eent way. ue to the smplty o the nvolved operatons, the CORIC realzaton o omplex PLL s very well suted or on-hp hardware desgn and ts mplementaton. The analyss o varous error soures s neessary or optmal desgn o system usng the CORIC proessor. In SP systems, sgnals are requred to be quantzed and represented n xed word-length. A lmted word-length results n the round-o nose and degradaton o Sgnal-to-Quantzaton Nose Rato (SQNR perormane [6,7]. In general, larger the dynam range o the sgnals, more severe s the round-o nose. To redue the omputaton error, a proessor desgner mght smply nrease the number o teratons and that wll be a huge wastage o proessng tme and power. Thereore, exat omputaton o word-length s neessary or desgnng an arhteture or CORIC. I word-length s larger, the omputatonal speed o CORIC redues sgnantly [8,9]. On the other hand, we mplement wth smaller word-length, the desgn wll suer rom danger o overlow. To desgn an optmal applaton spe CORIC proessor or a hgh perormane sgnal proessng, the hoe o word-length and number o teratons n error analyss are needed to be taken nto onsderaton. In ths paper, both the problems o overlow and quantzaton nose have been addressed adequately or the desgn proess. The remander o ths paper proeeds as ollows. In seton II, the onventonal CORIC algorthm s brely revewed.

2 esgn o ppelned CORIC and desgn related ssues have been dsussed n seton III. Evaluaton and analyss o omputatonal error has been dsussed n seton IV. In seton V and VI, omplex sgnal proessng through CORIC has been explaned or demodulaton purpose. In seton VII, Hardware synthess result has been dsussed and onluson may be ound n seton VIII. II. REVIEW OF CORIC ALGORITHM The theory o CORIC omputaton s to deompose the desred rotaton angle nto the weghted sum o a set o predened elementary rotaton angles. Eah o them an be aomplshed wth smple sht-add operaton or a desred rotatonal angle θ. It an be represented or M teratons o an nput vetor (x,y T settng ntal ondtons: x =x, y =y, and M M z =θ as z θ δα. I z = holds, then θ δ α,.e. the total aumulated rotaton angle s equal to θ. δ, M, denote a sequene o ±s that determne the dreton o eah elementary rotaton. When M s the total number o elementary rotaton angles, -th angle α s gven by: s(, s( m, s(, m, tan [ m ] tan ( m (, tanh s where m=, and orrespond to the rotaton operaton n lnear, rular, and hyperbol oordnate system respetvely. For a gven value o θ, the CORIC teraton s gven by: x y and z δ z δ α δ x y where α tan. To brng a unt vetor to desred angle θ, the CORIC algorthm gves known reursve rotatons to the vetor. The known rotatonal values are shown n Table. I as a Pre-Computed angle. One the vetor s at desred angle, the outome o the X and Y oordnates o the vetor are equal to Cosθ and Snθ respetvely. Let a unt vetor n teraton s rotated by some angle θ, then the reursvely updated equatons are generated n the ollowng orm: x x osδ α y snδα y y osδα x snδα (3 The above equaton an be smpled and wrtten as x osδα(x y tan δα y osδα (y x tan δα (4 Here, tan s restrted to. So multplaton s onverted n an arthmet rght sht. Sne osne s an even unton, thereore os os. The teratve equaton an be redued to- ( K (x y δ x y K (y x δ (5 Where os artan ( s known as gan K ator or eah teraton. I M teratons are perormed, then sale ator, K, s dened as the multplaton o every K. M M K K (. (6 The elementary untons sne and osne an be omputed usng the rotaton mode o the CORIC algorthm the ntal vetor starts at ( K, wth unt length. The nal outputs o the CORIC or the gven nput values x, y and z are as ollows: x K os, y K sn and z. Sne the sale ator s onstant or a gven number o rotatons, x / K an be set to get purely sn and os values. Table I Pre-Computed Angles or Ppelned CORIC artan( tan α n radan 45 o o o o o o o o III. CORIC ARCHITECTURE In ths CORIC arhteture, a number o dental rotatonal modules have been norporated and eah module s responsble or one elementary rotaton. Beause o dental CORIC teratons, t s onvenent to map them nto ppelned arhteture [9]. The purpose o ppelned mplementaton s to deve a mnmum rtal path. Thereore, ths knd o arhteture provdes better throughput and lesser lateny ompared to other desgns. It s assoated wth a number o stages o CORIC Unts where eah o the ppelned stages onssts o a bas CORIC engne. The CORIC engnes are asaded through ntermedate lathes as shown n Fg.. The sht operatons are hardwred usng permanent oblque bus onnetons to perorm multplatons by redung a large slon area as requred by barrel shters.the rtal-path o the ppelned CORIC s the tme requred by the Add/Substrat operatons n eah o the stages. Every stage ontrbutes rtal path delay amounts to T Path =T Add + T MUX + T C, where T Add, T MUX and T C are the tme requred or addton, : Multplexng and s Complement operatons, respetvely. The pre-omputed angles (Table

3 o -th teraton angle requred at eah CORIC engne an be stored at a ROM memory loaton, are known. Thereore, the need o multplexng and sgn deteton s avoded to redue rtal path. The lateny o omputaton s thus depends prmarly on the adder used. Sne no sgn deteton s needed to ore z, the arry save adders are well suted n ths arhteture. The use o these adders redues the stage delay sgnantly. The delay an be adjusted by usng proper bt-length n the sht regster. Wth the ppelnng arhteture, the propagaton delay o the multpler s the total delay o a sngle adder. So ultmately the throughput o the arhteture s nreased to a many old as the throughput s gven by: /delay due to a sngle adder. It mples that speed up ator beomes more than M and lateny o the desgn s M tmes o the delay o a sngle adder. It s obvous that we nrease the number o teratons then the lateny o the desgn also wll nrease sgnantly. I an teratve mplementaton o the CORIC were used, the proessor would take several lok yles to gve output or a gven nput. But n the ppelned arhteture, t onverts teratons nto ppelne phases. Thereore, an output s x x n y y z z P R E C O M P U T E A N G L E S n Fg.. Ppelned CORIC Arhteture Fg.. Smulaton Result o CORIC obtaned at every lok yle ater ppelne stage propagaton. Eah ppelne stage takes exatly one lok yle to pass one output (Smulated output shown n Fg.. The most reurrent problems or a CORIC mplementaton are overlow. Sne the rst tangent value s, then rotaton range wll be,. The derene n bnary representaton between these two angles s one bt. Overlow arses when a rotatonal angle rosses a postve rght angle to a negatve one. To avod overlow, an overlow ontrol s added. It heks or the sgn o the operands nvolve n addton or subtraton and the result o the operaton. I overlow s produed, the result keeps ts last sgn wthout aetng the nal result. In the overlow ontrol, the sgn o z determnes whether addton or subtraton s to be perormed. IV. NUMERICAL ERROR ANALYSIS Theoretally, CORIC realzaton has nnte number o teratons and that leads to aurate result. But pratally CORIC realzaton uses nte number o teratons resultng n approxmaton error. Ths knd o error arses due to approxmatons n angle as well as nte word length [8]. To get total approxmaton error, the error due to the angle approxmaton proess wll be derved and ollowed by the error due to the trunaton o word length wll be derved. The total error s taken as the summaton o the two. In the angle approxmaton proess the angle s approxmated as the algebra sum o predened elementary angles. M (7 = Angle yet to be rotated ater ompleton o the CORIC teratons. ue to onvergene relatonshp o the CORIC algorthm ( max tan M (8 * Let v be the deal result obtaned by the rotaton o the vetor v( [ x( y ( ] t by an angle o. Let v ( M be the output o the CORIC blok ater salng operaton and assumng that there s nnte preson n the CORIC operaton module. Then, * os sn v. v ( M (9 sn os

4 Let os sn sn os The error n the output due to the proess o angle approxmaton s * v v ( M. * = v v( M [ I]* v( M ( It an be easly shown that I (os (sn = *sn / I = *sn / * / = ( From equaton 9, I tan ( ( M < M ( we an get a onsoldated trunaton error due to nte wordlength usng sale ator K and number o nte teratons (M. K * M M b * ( ( ( j j (3 The salng operaton also ntrodues some error whh b amounts to maxmum o. So the nal expresson or the total quantzaton error s addton o all prevously mentoned errors. Total error M M * b b * v K * * ( M ( j j (4 Let the output o the CORIC blok has bts n ts ratonal part. Thereore, the upper lmt o the total quantzaton error an be taken as. Total error M M * b b v K * * * ( M ( j j (5 The above nequalty s smulated n MATLAB to nd out ratonal bts o the nternal word length o the CORIC. Number o Bts When Error Upper Lmt Number o Iteratons Fg. 3. The requred Bts Vs. Iteratons or CORIC Internal esgn V. BASICS OF I/Q EMOULATION As per the Euler s theorem, vetor sum o osne omponent s ompletely real whereas the spetrum o sne omponent s totally magnary. I the osne and sne omponents are ombned, the resultant spetrum beomes one sded wth dreton o rotaton (postve or negatve requeny and wth known real (osne and magnary (sne omponents []. os t j sn t e jt (6 The proess o reoverng both real and magnary sgnal omponent s known as I/Q demodulaton. I stand or n-phase hannel whh proesses osne (real omponents. Q stands or n-quadrature hannel whh proesses sne (magnary omponent. The nput o I/Q hannel s Intermedate Frequeny (IF as shown n Fg. 4. I the arrer requeny o IF s wth a tme varyng ampltude a(t and tme varyng phase (t, then nput sgnal s(t wll be: S( t a( t os[( t (. (7 In I hannel, the IF sgnal s multpled by reerene arrer requeny produed by rystal osllator at zero phase reerene. The output o the I hannel mxer s, I(t, gven by : I( t a( t os[( t (.os( t a( t os[ ( a( t os[4 t ( (8 The rst term s the average value (C o the produt and represents osne o the sgnal phase and ampltude. The seond term wth hgh requeny omponent s suppressed by Low Pass Flter (LPF. So the output o the I hannel s I( t a( t os[ (. (9 Smlarly, the Q hannel output an be derved. The LPF output at Q hannel s: Q( t a( t sn[ (. ( Thus, I and Q hannel together provde the ampltude and phase modulaton. VI. PHASE ETECTION TECHNIQUE IN FMCW RAAR The down onverted and ltered baseband sgnal has two omponents: real and magnary parts. Thereore, the baseband sgnal an hold both the ampltude and phase o the snusodal sgnal at the same tme. It does not hold any mage requeny. So only loop lter s suent or the dgtal demodulaton usng gtal PLL []. Usng the vetor rotaton operator T [ x, y], the omplex rst-order PLL demodulator equatons or a gven nput sgnal an be stated as: a. The real part o the output n phase omparator equaton : v( n } n { n b. The loop lter equaton: n K l n,where K l s the loop lter oeent. The loop lter oeent K l depends on the samplng requeny and number o

5 LPF AC IN-PHASE CHANNEL IF INPUT 3dB IVIER PHASE SHIFTER COHERENT OSCILLATOR CORIC EMOULATOR emodulated Output 9 QUARATURE CHANNEL LPF AC Fg. 4. CORIC Based PLL n I/Q Channel { s( n} CORIC { r( n} n BOXCAR d n { s( n} { r( n} Syn. Clok - z PHASE ACCUMULATOR + K LOOP FILTER Fg. 5. Complex PLL usng CORIC teratons o CORIC algorthm. For M number o teratons, the loop lter oeent K an be gven by: K K l CORIC ( M. The phase aumulator equaton: n ( n K l n mod, ( where s the enter requeny. The CORIC based PLL (as shown n Fg. 5 tres to adjust the ontnuous phase rotaton n suh a way that the omplex omponent o the rotated vetor wll always be zero. The post deteton lter ater the PLL an be a Boxar lter nstead o low-pass lter. It rejets the unwanted nose Low-pass lter averages the sgnal and produes an output rom the demodulated sgnal eently. BOXCAR lter has added advantage over the LPF as ar as normaton reovery rom narrow samples wth lttle energy sgnal s onerned. l Low-pass lter averages the sgnal and produes an output wth weak ampltude sgnals. To avod ths problem, the samples an be strethed or entre nter sample perod by nreasng ther sample ampltude at the lter output. The VLSI mplementaton o Boxar generator s very easy as t perorms only addton operaton. The smulaton study has been arred out n MATLAB smulator. The down onverted IF (wth oppler sht s taken as nput sgnal or the demodulator. The oherent osllator requeny has been taken as a reerene requeny to the demodulator. Any phase and ampltude varaton (as shown n equatons 8 and 9 n radar eho an be retreved n the phase detetor stage. Intal phase sht o 3 s ntrodued or the smulaton. Smulated radar deteted sgnal wth reerene to oherent reerene sgnal and the nal phaseampltude varaton at the demodulator output have been shown n Fg. 6, Fg. 7 and Fg. 8 respetvely. VII. HARWARE SYNTHESIS RESULT The man part o VLSI desgn s optmzaton o desgn n terms o speed, power, resoure utlzaton and delay et. The

6 Fg. 6. Phase varaton n In-phase Channel Radar Reever Fg. 7. Phase varaton n Quadrature Channel Radar reever Fg. 8. Phase eteted Output at Radar Reever

7 5 5 Fg. 9. Resoure Utlzaton proposed arhteture desgn was syntheszed on Spartan-3 based x3s5pq8-5 FPGA deve usng XILINX ISE. and smulated on ModelSm. The area utlzaton o proposed desgn s mplemented on above sad FPGA kt n terms o Regster, LUT and IOs. The area onsumed by regster, LUTs and IOs are 3%, % and 35% respetvely o avalable resoures as shown n Fg. 9.The result o power measurement or proposed arhteture also has been measured usng Cadene ustom IC desgn tool and shown n Table II. Cells Leakage Power (nw Table II. Power Measurement ynam Power (µw VIII. CONCLUSION The paper presents the demodulaton tehnque n a hgh speed FMCW Radar reever usng omplex gtal Phase Loked Loop. To mantan hgh degree o auray durng radar sgnal proessng, quantzaton error s needed to be mnmzed n desgn level tsel. For that purpose, numeral error analyss has been done to mnmze angle approxmaton as well as trunaton errors. Wth usng redued number o mrorotaton and adequate optmzed onvergene property o CORIC desgn, mplementaton o ths knd o demodulator beomes easer. Inherent ssue o overlow s qute approprately resolved n the proposed desgn. Numbers o mro-rotatons have been adjusted so as to aheve better loop perormane and speed o operaton whle mnmzng quantzaton error. The phase and ampltude varatons n the reeved eho sgnal are aptly demodulated. The BOXCAR lter gves addtonal alty n reonstrutng output sgnal eently. REFERENCES Avalable Used Total Power (µw [] W. Xu, C. Gu, C. L, M. Sarrazadeh, Robust doppler radar demodulaton va ompressed sensng, Eletrons Letters, vol. 48, no., pp , Ot. [] N. a alt, Lnearzed Analyss o a gtal Bang-Bang PLL and ts Valdty Lmts Appled to Jtter Transer and Jtter Generaton, IEEE Transatons on Cruts and Systems I:Regular paper, vol. 55, no., pp , e. 8. [3] J. E. Volder, "The CORIC Trgonometr Computng Tehnque", IRE Transatons on Eletron Computng, vol. EC-8, pp , Sept, 959. [4] Y. H. Hu, "CORIC-Based VLSI Arhtetures or gtal Sgnal Proessng", IEEE Sgnal Proessng Magazne, vol. 9, no. 3, pp. 6-35, 99. [5] S. Ugazo, esgn o real tme adaptve PLLs or gener and varable oppler requeny, In pro. O Internatonal Conerene on Loalzaton and GNNS (ICL-GNSS, pp , Tampere, Jun. [6] K. Kota and J.R. Cavallaro, Numeral auray and hardware tradeos or CORIC arthmet or speal-purpose proessors, IEEE Trans. Comput., vol.4, no.7, pp , Jul 93. [7] Y. H. Hu, "The Quantzaton Eets o the CORIC Algorthm", IEEE Transatons on sgnal proessng, vol. 4, no. 4, pp , Apr 99. [8] S.Y. Park and N.I. Cho, Fxed-pont error analyss o CORIC proessor based on the varane propagaton ormula, IEEE Trans. Cruts Syst. I, vol.5, no.3, pp , Marh 4. [9] T. Y. SUNG, H. C. HSIN, "Fxed-Pont Error Analyss o CORIC Arthmet or Speal-Purpose Sgnal Proessors", IEICE Trans. Fundamentals, vol. E9-A, no. 9, Sept 7. [] J. Vuor, "Implementaton o a gtal Phase-Loked Loop Usng CORIC Algorthm", IEEE Internatonal Symposum on Cruts and Systems, vol. 4, pp , Atlanta, 996. [] B. R. Mahaza, A. Elsherben, "MATLAB Smulatons or Radar Systems esgn", CRC, Florda, USA, 3. Amrtakar Mandal reeved hs Bahelor o Engneerng egree n Eletrons and Communaton Engneerng rom The Insttuton o Engneers (Inda n 6. He ompleted M.Teh wth spealzaton n VLSI rom Shobht Unversty, Inda n 9. He s urrently workng toward the Ph. egree n Eletrons and Communaton Engneerng n the epartment o Inormaton and Communaton Tehnology, Gautam Buddha Unversty, Inda. He has vast experene n Eletron Warare and Survellane Radar systems. Hs researh nterests nlude Radar Sgnal Proessng and Hgh Speed VLSI esgn or Communaton Systems. Rajesh Mshra s urrently workng as Assstant Proessor n Shool o Inormaton and Communaton Tehnology, Gautam Buddha Unversty Greater Noda, elh NCR (Inda. He reeved hs BE (Eletrons Eng., M. Teh and Ph.. degree (Relablty Eng. rom Relablty Engneerng Centre, IIT Kharagpur (Inda n year, 4, and 9 respetvely. He has researh nterest n the area o relablty engneerng, layout desgn or apatated networks, and network optmzaton. He has publshed papers n several nternatonal journals suh as IJPE, IEEE, RESS, QTQM et.