Automatic Target Recognition wi Unknown Orientation and Adaptive Waveform Junhyeong Bae Department of Electrical and Computer Engineering Univerity of Arizona 13 E. Speedway Blvd, Tucon, Arizona 8571 dolbit@email.arizona.edu Naan A. Goodman Department of Electrical and Computer Engineering Univerity of Arizona 13 E. Speedway Blvd, Tucon, Arizona 8571 goodman@ece.arizona.edu Abtract In previou work, we have demontrated e utility of a feedback loop for enabling optimized tranmit pule haping in radar target recognition. Thi previou work wa baed on low-fidelity target model, but in i paper, we demontrate e cloed-loop, adaptive-waveform approach applied to highfidelity target model ignature generated by commercial electromagnetic FDTD oftware. We alo incorporate e radar equation into our model for u in e waveform deign procedure. Becaue SNR varie wi range, o do our optimized waveform for target recognition. Contant-modulu waveform contraint are enforced, and a template-baed claification trategy i ued. I. INTRODUCTION Cognitive radar [1] ue an adaptive tranmitter to tranmit cutomized waveform. At each tranmiion, e adaptive tranmitter update it waveform baed on e radar objective, a probability model for previou meaurement, and oer prior information. Waveform cutomization can refer to bo e temporal tructure of e waveform a well a e tranmit beampattern. Becaue e adaptive tranmitter exploit previou meaurement, we can view cognitive radar a having a feedback loop between e radar receiver and tranmitter. Thi feedback loop deliver analyzed information from previou radar meaurement to e radar tranmitter in e form of updated prior information. In i paper we focu on e cutomization of a waveform temporal tructure in order to perform automatic target recognition (ATR) wi reduced tranmit power and/or at longer range. The goal of ATR i to identify an object at i oberved by e radar ytem. In our earlier work [], an adaptively haped temporal waveform wa applied to a target identification cenario. Thi work howed at a radar performing ATR according to cognitive radar principle ue fewer radar reource (i.e., reduced power or energy) and make a fat deciion wi low error rate. Cognitive radar can alo be applied to make better ue of e radar timeline in detection and tracking cenario. In [3], a cognitive-radarbaed technique for adaptive beamteering wa implemented. Thi cloed-loop approach to beamteering ha been demontrated to improve detection time. In [4], cognitive tracking radar wa implemented. The tranmit waveform wa elected from a precribed library according to information collected by e receiver, and e cognitive tracking radar wa hown to outperform conventional radar. In [5], cognitive radar wi knowledge-aided (KA) proceing wa propoed. We extend our previou work in e area of ATR wi two contribution in i paper. Firt, we ue new high-fidelity target ignature. In previou work, our target ignature were generated from imple arbitrary target outline and handplaced catterer, which allowed e ignature to vary wi rotation of e target. In i paper, we ue commercial EM oftware (XFdtd, by Remcom) and publicly available target CAD model to calculate target ignature veru angle. Second, e radar equation i incorporated directly into e target ignature to model propagation lo. Therefore, e radar equation affect e target ignature pectral treng. Becaue optimized waveform deign i SNR-dependent, uing e radar equation in e target ignature model affect our waveform deign procedure. The performance of cloed-loop radar can en be conidered a a function of target range. Thi paper i organized a follow. In Section II, we preent e problem tatement and ignal model. In Section III, we decribe e target ignature model. In Section IV-A, we how e waveform deign technique and incorporation of e radar equation to e deign technique. In Section IV-B, we ummarize contant-modulu waveform contraint. In Section V, we decribe e deciion-making procedure and probability update baed on Baye Theorem. In Section VI, we how imulation reult, and in Section VII, we make our concluion. II. PROBLEM STATEMENT AND SIGNAL MODEL A monotatic radar ytem wi a matched illumination waveform i applied to e target recognition cenario in e preence of additive white Gauian noie (AWGN). The baic problem formulation i imilar to our previou work [6] 978-1-444-89-/11/$6. 11 IEEE 1
and ummarized below. It i aumed at a target ha already been detected and i known to be one of M poible target type. The target ha a continuum of target ignature a a function of azimu and elevation angle. For implicity, here we hold e elevation angle fixed and conider only azimu rotation. Conider a linear target model a follow. When e radar waveform ( i tranmitted, e radar received ignal y ( i denoted a y ( = g( * + n( (1) where g ( i e azimu-varying target ignature of e unknown target, * i e convolution operator, and n ( i AWGN wi power σ n. A dicrete-time verion of e ignal model i neceary to implement a a computer imulation. In dicrete-time notation, e target ignature i repreented by a leng- L g vector g, e waveform i denoted a a leng- L vector, e noie i defined a a leng-l n vector n, and e received ignal i repreented by a leng-l y vector y. To implement e convolution between waveform and target impule repone in e dicrete-time model, a ignal matrix S i defined a [7] 1) ) S = L ) L 1) 1) L ) L 1) L ) 1). () 1) ) L ) Uing e ignal matrix and above definition, e dicretetime ignal model i y = Sg + n. (3) To handle target ignature at vary wi azimu angle, e azimu angle i divided into N g uniformly ized angular ector. Multiple target ignature are generated for angle wiin each ector, and e ignature are averaged to acquire a mean template for at ector. The mean template of all M target type are defined a g i ( t ), i = 1,..., N g,..., MN g. When e number of ector N g i large, e ize of each ector i mall, and e mean-template for each ector i a good repreentation of e target ignature acro e ector. However, computational complexity increae when we mut conider many ector, epecially in cognitive radar where probabilitie aociated wi each ector will be updated after each tranmiion. Thu, e ector ize hould be baed on bo required accuracy and ytem complexity. To employ prior information about e target orientation (derived, for example, from target bearing information), e target orientation at e beginning of e recognition phae i aumed known to wiin a few angular ector. To et up e target recognition problem in term of hypoei teting, we define a ingle hypoei a correponding to a ingle angular ection wiin a ingle target type. Thu, for e ake of feeding information back to e tranmitter and optimizing e waveform deign, each angular ector i treated a a different hypoei. A meaurement are received, e probabilitie aociated wi each target/ector combination are updated to reflect what ha been learned. But to do i, we need to define a probability denity function (pdf) of e radar received ignal for each target/ector hypoei. One potential ditribution i Gauian, which might be able to capture bo e mean template for a ector a well a e variation of e ignature around e mean for at ector. Unfortunately, a multivariate normality tet applied to e XFdtd target ignature [8] over a ector howed at Gauian wa not repreentative, even a an approximate ditribution. Thu, intead of making a Gauian aumption for e target ignature, e ignature are treated a contant acro a ector, reulting in a determinitic model wi e mean-template g i for each ector. Since e waveform and target template (given a particular target and ector) are determinitic, and e noie n i AWGN, e received ignal y i Gauian. The pdf of e complex received ignal given e i target/ector hypoei i defined a 1 1 H p( y H i ) = exp( ( y μ, ) (, )) N y i y μ y i (4) ( πσ ) σ n where μ y, i = Sgi i e mean of e received ignal under e i target/ector hypoei and tranpoe operator. The mean ignal n H ( ) i e conjugate μ y, i i waveformdependent and mut be updated a e tranmit waveform change. III. TARGET MODEL In prior work [6], our target model conited of arbitrary target outline wi cattering center placed at variou location along e outline. Thi model allowed e rotation of e target to affect e reulting target ignature. However, e model were admittedly low-fidelity. Here, we ue a 3D commercial electromagnetic (EM) imulator, XFdtd, to calculate high-fidelity target ignature. The XFdtd oftware wa provided by Remcom. The etup for generating e ignature i a follow. We ued caled 3D target CAD model in e XFdtd imulation. A monotatic radar wa located in far-field. A broadband waveform wa tranmitted to e target and e reflected ignal wa tored. The procedure wa repeated at many different apect angle to create a received ignal library. Wi each reflected ignal, we calculated frequency-domain target tranfer function according to G ( f ) = Y ( f ) / S( f ) (5) 978-1-444-89-/11/$6. 11 IEEE 11
Figure 1. Head-on target ignature of F-16 aircraft. where G ( f ), Y ( f ), and S ( f ) are e Fourier tranform of target ignature, e radar received ignal, and e wideband tranmitted waveform, repectively. The bandwid of e tranmitted pule in i ignature generation phae wa ignificantly larger an e maximum waveform bandwid for any of e ATR imulation at ued e ignature. For e cognitive-radar ATR imulation, a ection of e target tranfer function correponding to e radar tranmiion band wa extracted from e wideband function in (5). The timedomain target ignature wa en generated from e invere Fourier tranform of e reulting bandlimited target tranfer function. Two example of target ignature generated by XFdtd are hown in Figure 1 and. A monotatic radar i located lightly above e target horizontal plane at elevation. A wideband pule wi 5 GHz bandwid wa imulated via XFdtd. Figure 1 how e head-on target ignature for an F- 16. The leng of F-16 CAD model i 1.445 m (approximately a 1:1 cale model). The peak of e target ignature correpond to e location of catterer in e CAD model. The firt peak correpond to e tip of e noe and e econd peak correpond to e canopy of aircraft. The two larget peak correpond to e larget under-wing miile. The lat peak i from e tail of e aircraft. The leng of target ignature between e firt peak and e lat peak i lightly maller an e CAD leng, becaue e radar i above e target and e reflection from e tail happen at e leading edge of e tail. Figure how e target ignature of an A-1 CAD model at 3 azimu. The leng of A-1 CAD model i.817 m. The firt and e lat mall peak correpond to e noe and tail of e A-1, repectively. The four big peak are generated by e two Figure. Azimu angle 3 target ignature of A-1 aircraft. under-wing landing-gear houing and two engine. In XFdtd, e propagation of e EM wave in pace i calculated according to Maxwell equation, which provide much more repreentative target ignature an we have ued previouly. IV. RADAR WAVEFORM DESIGN A. Waveform deign and e radar equation The waveform deign technique at we ue here i baed on maximization of mutual-information. The technique i adapted from e analyi in [9] and ummarized below. We aume at an enemble of target impule repone exit. We alo aume at e radar waveform ha everal contraint (energy, time, and frequency). For a Gauian target enemble, e waveform at maximize e mutual information between e radar received ignal and e (Gauian) enemble of target impule repone can be found according to [9] 1 σnt y f max, A T S( f ) = G( f ) 1 σ (6) f > T where e enemble pectral function i defined a σ ( f ) = E{ G( f ) E{ G( f )} }, G ( f ) i e Gauian target G tranfer function, and T i e ampling interval of e ignal. The total energy in e waveform i controlled by e calar value A, uch at 978-1-444-89-/11/$6. 11 IEEE 1
E = 1 TS 1 TS σ nty max, A df. (7) σ G ( f ) A mentioned, e above deign technique i baed on a Gauian enemble, which we do not have. Fortunately, e pectral variance function can be extended for a finite number of dicrete target hypoee according to [] G MN g MN g Pi Gi ( f ) i= 1 i= 1 σ ( f ) = P G ( f ) (8) where G i ( f ) i e Fourier tranform of e i mean target template. Thi pectral variance can be ubtituted in (6), and e waveform pectrum i found according to e waterfilling technique [9]. In i technique, e deired waveform energy pectrum i acquired by inverting e function A σ n Ty / σ G ( f ) and pouring energy into e lowet part of e inverted function until e allowable energy i gone. The amount of energy at i poured into each pectral component determine e waveform magnitude pectrum. The phae of e waveform i an additional deign variable at may be ued to meet oer deign contraint, uch a a contant modulu contraint. A een in (6), e optimum waveform depend on e noie power a well a e treng of e target enemble (rough e pectral variance). When SNR i low, e waveform defined by (6) will tend to have energy in only a couple narrow pectral band. When SNR i high, e waveform become diverified and pread it energy over e allowable band. Becaue e waveform deign i SNRdependent, it i important to factor e radar equation into e ignal model. The power, P r, of e return ignal from e target at e radar receiver can be calculated by e radar equation according to [1] PG T aλσ Pr = = P 3 4 TσC = PTσeff (9) (4 π ) R where P T i e radar tranmit power, G a i e antenna gain, λ i e operating waveleng, σ i radar cro ection, and R i e range between radar and target. The variable C can be incorporated into σ to repreent an effective radar cro ection at varie wi range, and i effective radar cro ection can be ued to properly cale e target ignature library. Therefore, propagation lo i factored into e pectral variance function above, which en affect e waveform deign. In i work, we cale e target template librarie uch at e average level of e magnitude of all target tranfer function for a particular target i equal to e average quare root of RCS for at target. In oer word, uppoe at a target ha an RCS of σ, en we et e target tranfer function caling uch at ( ) = E G f C σ. (1) i i Thi normalization enure at for a narrowband waveform centered around frequency f, we have a contant-valued tranfer function over e waveform bandwid wi average magnitude equal to ( ) E = The received waveform will en be () G f CE σ. (11) G a λ ( 4π ) ( ) ( ) y t = E σ t R c + n t 3 4 R. (1) Wi e caling of e radar range equation incorporated into e target ignature, e ignal model now fit e form of (1) a required by e mutual information waveform deign meod. B. Waveform contraint Any practical radar ytem ha a peak power limitation, o e temporal radar waveform hould be deigned and operated under i limitation. Thu, a contant modulu [11] contraint on e radar waveform i neceary to operate e radar ytem efficiently. The technique ued here to contruct a contant-modulu ignal wi a precribed Fourier tranform magnitude i baed on iterative magnitude and amplitude projection. The technique i preented in [11] and ummarized below. The et of function { v ( } wi equal Fourier tranform magnitude F(w) over e frequency et Ψ i denoted a D M. Then, we can define a magnitude projection operator P M at project an arbitrary function x ( to nearet point on D M. Auming jω( w) e Fourier tranform of x ( i X ( w) = X ( w) e, e magnitude projection procedure i repreented by jω( w) F( w) e, w Ψ PM x( =. (13) X ( w), w Ψ' The et of function { v ( over e temporal duration T i repreented by } wi poitive contant value B D A. Then, P at we can alo define an amplitude projection operator A project an arbitrary function x ( to cloet point on D A. Auming x ( i equal to a( e i defined a j B e PA x( = x(, φ ( jφ(, e amplitude projection, t T. (14) oerwie The above magnitude and amplitude projection i performed iteratively according to xk + 1( = PA PM xk ( (15) where x k ( i e arbitrary function after k projection. After many iteration, e function x ( maintain exact contant modulu amplitude, but ha a Fourier tranform magnitude at approximate e deired Fourier magnitude. 978-1-444-89-/11/$6. 11 IEEE 13
V. FIXED NUMBER OF ITERATIONS AND BAYES THEOREM We adopt a procedure whereby a claification deciion i made after tranmitting a fixed number of optimized waveform. Therefore, e number of tranmiion i fixed in advance. At each tranmiion, e likelihood are formed and e probabilitie aociated wi each target/ector combination are updated. The expreion of e i hypoei likelihood after e k tranmiion depend on joint pdf of e received ignal on all tranmiion. However, ince e radar waveform and target ignature are modeled a determinitic, and e white Gauian noie ample are uncorrelated and independent, e meaurement data are tatitically independent. Then, e joint pdf of e data on all tranmiion can be accumulated to update e likelihood of e i hypoei according to p ) P (16) ( Hi yk ) pi1( y1) pi( y) pik ( yk where p y ) i e pdf of e k received ignal for e ik ( k i hypoei, y k i e received ignal due to tranmiion, and P i i e probability of e i k i hypoei prior to any tranmiion. The final deciion i made after e number of tranmiion reache e pre-defined iteration limit. The hypoei H i correponding to e highet likelihood i e final deciion. In e cloed-loop radar ytem, e waveform are updated at each tranmiion. To update e waveform, e hypoei probabilitie are update by Baye eorem according to (16) (except for a caling factor at enure e probabilitie um to unity). The updated probabilitie are ubtituted into (8) to update e radar waveform. VI. RESULTS We performed a computer imulation of a radar target recognition cenario baed on e technique above. We have two plane target (F-16 and A-1). We aume at e elevation angle between e horizontal plane of e target and e radar line of ight i, uch at e monotatic radar i a little above e target. We conider azimu angle over a 9 range from head-on to broadide of each target. We generated target ignature at every.1 interval. Since we know e actual ize of ee target from e literature, we ue a caling factor to adjut e ampling interval and bandwid of e original CAD-baed XFdtd target ignature to e actual target ize, approximately. Table I how e leng and caling factor. The target ignature are grouped into 1 ector. The target ignature wiin each uniform angular ector are averaged to generate a mean-template. We aume at we have prior knowledge about e velocity and bearing information of a target. Thu, for a given trial of e ATR imulation, we can narrow down e poible target angular ector to two adjacent mean-template for each target. We treat each ector a a hypoei, o we have four hypoee in total for a given trail. For randomly elected Error rate Error rate TABLE I. TARGET LENGTHS AND SCALING FACTORS Target Actual leng(m) CAD leng(m) Scaling factor 1 1 1 1 1 3 1 4 F-16 15.6 1.445 1 A-1 16.6.817 Waterfilling(R=km) Waterfilling(R=3km) Impule(R=km) Impule(R=3km) 1 5 5 1 15 5 3 Tranmit power (db) Figure 3. Error rate veru tranmit power for fixed number of tranmiion. 1 1 1 1 1 3 1 4 Waterfilling Impule 1 5 5 45 4 35 3 5 Range (Km) Figure 4. Error rate veru range for fixed number of tranmiion. target angle at do not fall on e.1 increment, we generate e true target ignature by a weighted average of e two adjacent target ignature. We compare e performance of two waveform: e information-baed waveform realized via e pectral variance trategy over a 5-MHz bandwid, and a 5-MHz wideband impule. We ue e radar equation to compare e performance of e waveform baed on e range between radar and target. The radar parameter ued were an antenna gain of 3dB at S band, a noie temperature of 9 K, and an average total RCS for each target of 1 m. Five waveform were tranmitted before making a deciion. We ran, Monte Carlo trial (over noie realization and orientation angle), and counted e number of incorrect deciion to compute error rate. 978-1-444-89-/11/$6. 11 IEEE 14
Figure 3 how e error rate veru tranmit power. The information-baed waveform perform better an e wideband waveform for e ame range becaue e information-baed waveform put energy into e frequency band where pectral dicrimination i trong. The radar return ignal from farer range ha lower ignal-to-noie (SNR), o e error rate are higher. The two waterfilling waveform (for R = km and 3 km) at error rate.1 are hift by approximately 7 db. Becaue e ratio between ee ditance i 3/ = 1.5, and e received power ha a 1/R 4 4 relationhip to target range, 1*log1 (1/(1.5) ) = -7.437dB, and e 7 db hift i expected. The information-baed waveform require about 5 db le power an e wideband waveform at e ame range. Figure 4 how e error rate veru range when e tranmit power i 6 db. In i cae, e information-baed waveform can achieve e ame error rate a e wideband waveform, but at an approximately 3% increae in range. VII. CONCLUSIONS We have imulated a cloed-loop radar ytem for target recognition uing high-fidelity target model calculated via commercial EM oftware and publicly available target CAD model. We alo incorporated e radar equation into e target ignature a part of e waveform deign proce. The information-baed waveform wi a contant modulu contraint wa compared to a flat-pectrum wideband waveform in a target recognition cenario. The two target being claified were an F-16 and an A-1. The reult how at e information-baed waveform provide approximately 5 db improvement in tranmitted power for e ame error rate, which tranlated to a more an 3% increae in recognition range. ACKNOWLEDGMENT The auor acknowledge upport from e ONR via grant #N1491338. We are alo very grateful to Remcom for providing eir XFdtd oftware. REFERENCES [1] S. Haykin, Cognitive radar: a way of e future, IEEE Sig. Proc. Mag., vol. 3, no. 1, pp. 3-4, Jan. 6. [] N.A. Goodman, P.R. Venkata, and M.A. Neifeld, Adaptive waveform deign and equential hypoei teting for target recognition wi active enor, IEEE J. Selected Topic in Signal Proceing, vol. 1, no. 1, pp. 15-113, June, 7. [3] P. Nielen and N.A. Goodman, Integrated detection and tracking via cloed-loop radar wi patial-domain matched illumination, in Proc. 8 International Conference on Radar, Adelaide, Autralia, pp. 546-551, Sept. 8. [4] S. Haykin, A. Zia, I. Araaratnam, and Y. Xue, Cognitive tracking radar, 1 IEEE Radar Conference, pp 1467-147, Wahington DC., May 1. [5] J.R. Guerci, Cognitive radar: a knowledge-aided fully adaptive approach, 1 IEEE Radar Conference, pp 1365-137, Waington DC., May 1. [6] J. Bae, N. A. Goodman, Evaluation of modulu-contrained matched illumination waveform for target identification, 1 IEEE Radar Conference, pp 871-876, Wahington DC., May 1. [7] D.A. Garren, M. K. Oborn, A. C. Odom, J. S. Goldtein, S. U. Pillai, and J. R. Guerci, Enhanced target detection and identification via optimized radar tranmiion pule hape, Proc. IEEE, vol. 148, no. 3, pp. 13 138, Jun. 1. [8] S.P. Smi and A. K. Jain, A tet to determine e multivariate normality of a dataet,. IEEE Tranaction on Pattern Analyi and Machine Intelligence, vol. 1, no. 5, pp 757 761, Sep. 1988. [9] M.R. Bell, Information eory and radar waveform deign, IEEE Tran. Info. Theory, vol. 39, no. 5, pp. 1578-1597, Sept. 1993. [1] D.R. Wehner, High-reolution radar, Artech Houe Publiher, Boton, 1995. [11] S.U. Pillai, K.Y. Li, and H. Beyer, Contruction of contant envelope ignal wi given Fourier Tranform magnitude, 9 IEEE Radar Conference, Paadena, California, USA, May 4-8, 9. 978-1-444-89-/11/$6. 11 IEEE 15