A method of improving SCR for millimeter wave FM-CW radar without knowledge of target and clutter statistics

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1 INERNAIONAL JOURNAL OF COUNICAIONS A method of mprovng SCR for mllmeter wave F-CW radar wthout nowledge of target and clutter statstcs Fumo Nshyama, and Hdeo uraam Abstract Frequency-modulated-contnuous-wave (F-CW) radars transmt a waveform whose frequency changes lnearly n tme. Receved echoes of these radars can be categorzed nto two types due to ether targets or clutter. Generally, the receved target sgnals have a stronger correlaton wth respect to dfferent carrer frequences than that of the receved clutter sgnals. hs paper dscusses a method of mprovng sgnal-to-clutter rato (SCR) for mllmeter wave F-CW radar based on ths statstcal dfference between the target and the clutter. he method frst approxmates an autocorrelaton functon from receved sgnals usng a numercal averagng. A power spectrum of receved sgnals s obtaned by tang dscrete Fourer-transform of ths autocorrelaton. A target power spectrum s estmated from the power spectrum of receved sgnals explotng the statstcal dfference, and a matched flter s then desgned from ths target power spectrum. he matched flter s used to mprove SCR. Performance of the method s analyzed and evaluated expermentally for 6GHz band F-CW radar. he smulaton shows that the proposed method mproves SCR better than competng wth other methods. Keywords F-CW radar, Ground clutter, atched flter, llmeter wave. I. INRODUCION ILLIEER wave frequency-modulated-contnuouswave (F-CW) radars are studed for used as an automotve sensor of the ntellgent transportaton system, and n fact mounted n several cars. F-CW radar transmts a waveform whose frequency changes lnearly n tme. Such F-CW radar can ncrease transmsson energy wthout ncreasng pea power by employng contnuous waves nstead of pulses used n usual radar systems []. hs property s partcularly advantageous for the automotve radar [], [3]. he automotve radar, beng placed at a poston near the ground, nevtably receves clutters from varous objects such as road asphalt, sdewal lnes, and objects on the sdewals. Whereas, the target such as an automoble s modeled as a relatvely large plane wth a smooth surface. he clutter s a major factor that causes a false alarm n target detecton. When the target s movng wth respect to the ground clutter, dscrmnatng the target from the clutter s relatvely anuscrpt receved arch 5, 7; June, 7. Fumo Nshyama and Hdeo uraam are wth the nformaton and computer engneerng, Kanazawa Insttute of echnology, Nonoch, Ishawa, Japan (phone: ; e-mal: crcus@venus.anazawa-t.ac.jp, muraam@nfor.anazawa-t.ac.jp). Issue, Volume, 7 68 easy by explotng the Doppler-effect. However, when the target s at rest, dstngushng t from the clutter s dffcult. For such cases, mprovng sgnal-to-clutter rato (SCR) s vtally mportant. For pulse radar system, a method usng wavelet-transform explots the statstcal dfference between the target and the clutter to mprove SCR [], and also ntegraton processng s used [5]. When the clutter wth respect to dfferent carrer frequences s assumed to be statstcally whte [6]-[8], the method of mprovng SCR explotng the statstcal dfference has been proposed for F-CW radar [9], []. However, n many practcal cases, the clutter statstcs s not whte. herefore, assumng that target sgnals wth dfferent carrer frequences have a stronger correlaton than that of clutter [7]-[], we propose a method of mprovng SCR whch does not requre pre-nowledge of the correlaton for the target and the clutter []. In ths method, an autocorrelaton functon s frst computed from receved sgnals wth dfferent carrer frequences. A power spectrum of receved sgnals s then computed by tang dscrete Fourer-transform (DF) of the receved sgnal autocorrelaton functon. A target power spectrum s estmated from the power spectrum of receved sgnals usng the statstcal dfference between the target and the clutter. Fnally, a matched flter s desgned from ths target power spectrum [9]-[]. hs paper s organzed as follows. In Chap., the F-CW radar system s brefly explaned and receved sgnal models are formulated as stochastc processes. In Chap. 3, the proposed methods of estmatng the target power spectrum, and of a procedure of explotng the estmated power spectrum for ncreasng SCR are descrbed. In Chap., performance of the proposed method s analyzed by usng the data measured by 6GHz band F-CW radar. In Chap. 5, the performance s analyzed n detal usng a movng average (A) model for the target and the clutter. II. F-CW RADAR A. Stochastc Process for Receved Sgnals A bloc dagram of a double antenna F-CW radar system studed n ths paper s shown n Fg.. A sgnal generator generates a tran of trangular pulses le a saw-tooth shape, and a modulator converts the tran of pulses nto a carrer frequency

2 waveform sweepng ts frequency accordng to the pulse tran. hen the waveforms are radated nto space through a transmttng antenna. Echoes reflected from objects, ether the targets or the clutter, are receved va a recevng antenna. he receved carrer frequency waveform s converted nto a base-band frequency waveform by a demodulator and then sampled. he sampled dscrete sgnal s multpled by a wndow functon dvdng t nto blocs and then DF of each bloc of samples s computed. Fg. (a) shows frequency varaton of the transmtted waveform for the F-CW radar employng the saw-tooth modulaton [5]. he carrer frequency lnearly vares from f mn to f max, and repeats ths cycle as shown n the fgure. A tme nterval for the frequency change cycle s denoted as. At the recever, the sampler samples the base-band waveform wth a faster rate than the dfference f max -f mn. Fg. (b) shows a seres of wndows to be multpled to the sampled sgnals. he duraton of each wndow s the same as the tme nterval for the frequency change cycle. he wndow multplcaton dvdes the receved samples nto blocs of N samples, and then the N-pont DF of each bloc s computed. he lth bloc samples are wrtten as r( n) = r( ln+ n), n N-, () l INERNAIONAL JOURNAL OF COUNICAIONS ransmttng Antenna odulator Demodulator Recevng Antenna where r(ln+n) s the sampled sgnal before the wndow multplcaton. he N-pont DF of lth bloc samples s denoted as R l (), N-. he samplng rate beng chosen to be faster than the dfference between f mn and f max, there exst DF values R l ( m ) n such a way that m corresponds to the frequency fmax fmn fm = fmn + m, m -. () hese DF values are arranged n the -dmensonal vector as xl = xl() xl() xl( ) Sgnal Generator Sampler Wndow N-DF r l (n) Fg. A bloc dagram of F-CW radar R l () = Rl( ) Rl( ) Rl( ). (3) he mth entry x l (m) of the vector s the DF value correspondng to the frequency f m. he small letters are used, because the vectors wll be treated as a stochastc process wth respect to m although the ndex m stands for the frequency f m. Frequency f max f mn Snce only these vectors x l are gong to be used for mprovng SCR, they are smply called receved sgnals n followngs. Usng DF s partcularly sutable because the transmttng waveform s perodc wth the tme nterval, and a delay of the receved waveform due to the dstance between the antennas and the object does not change the absolute values of DF. Let y and y C be stochastc processes correspondng to receved sampled sgnals due to targets and clutter respectvely. he numercal average of these L vectors s ntroduced as L y = l = [ y() y() y( ) ] L x. () l= When L s large enough, y can be regarded as a stochastc process. It should be emphaszed that the mth entry of y corresponds to the carrer frequency f m, and does not ndcate tme as n a usual stochastc process. Under ths nterpretaton, y s wrtten as y=p y +P C y C, (5) where P and P C are probabltes of occurrence of the targets and the clutter. B. Power Spectrum of arget Sgnals he autocorrelaton functon of y s defned as me (a) Frequency varaton of a transmtted waveform wndow l= (b) Wndow wndow l= me Fg. ransmtted sgnal and wndow functon for F-CW radar system φ Y (τ)=e{y(m)y(m+τ)}, -/ τ /-, (6) where E{ } denotes the expectaton operaton []. Because the length of the vectors s fnte, the autocorrelaton functon depends on the varable m. However, to avod complexty n the followng analyss, we concede that y s statonary, and that the Issue, Volume, 7 69

3 autocorrelaton functon gven by (6) s well-defned. he power spectrum of the process s defned as the -pont DF of the autocorrelaton functon, / Φ Y( ) = φ ( τ)exp( j πτ/ ), -. (7) Y τ = / he stochastc process y s composed of the target stochastc process y and the clutter stochastc process y C as seen by (5). he autocorrelaton functons of y and y C are denoted as φ and φ C ; the power spectra of y and y C are denoted as Φ and Φ C. As a wavelength of carrer changes, the reflecton from the ground clutter havng a rough surface scatters more than that of the target havng a smooth surface. herefore, the target sgnals correspondng to dfferent carrer frequences tend to have a stronger correlaton than that of clutter cases [7]-[]. Based on these observatons, the proposed method assumes the followngs. Assumpton : he two processes y and y C are statcally ndependent wth zero mean. Assumpton : he target process y has a much stronger correlaton than the clutter process y C. By (5) and the assumpton, an autocorrelaton functon of receved sgnals s obtaned as φ Y (τ)=p φ (τ)+p C φ C (τ). (8) ang -pont DF of the autocorrelaton functon, a power spectrum of the process y s gven by Y C C Φ ( ) = P Φ ( ) + P Φ ( ). (9) he problem s to estmate Φ () from Φ Y () for desgnng the matched flter to mprove SCR. III. PROCESSING A HE RECEIVER A. Estmaton of arget Power Spectrum In order to proceed wth estmatng the target power spectrum, we compute matrx B from the receved sgnals by B INERNAIONAL JOURNAL OF COUNICAIONS * x x x x =, () L x x L L where the superscrpt * denotes the complex conjugate transpose operaton. he (m,n)th entry of ths matrx s gven by L * mn, l l L l= b = x ( m) x ( n). () he autocorrelaton functon s approxmated from B as follows. he /-dmensonal vector v s computed accordng to [ v() v() v( / ) ] v= = / b+ /, b+ /, + b+ /, + / =. () he approxmaton of the autocorrelaton functon of the receved sgnals s obtaned as ( ) ˆ φ ( τ ) = v / + τ. (3) Y Once ˆ φy ( τ ) s estmated, the receved sgnal power spectrum Φ Y () s estmated by tang -pont DF of ˆ φy ( τ ). Next, gven the receved sgnal power spectrum Φ Y (), we need to estmate the target power spectrum Φ () from the receved sgnal power spectrum Φ Y (), whch s the weghted sum of Φ () and Φ C () as seen by (9). he assumpton says the bandwdth of Φ () s much narrower than the bandwdth of Φ C (), and thus the target autocorrelaton functon φ (τ) s recovered from the receved sgnal autocorrelaton functon φ Y (τ) by usng a low-pass flter smlar to the method of recoverng a sgnal contamnated wth a wde band addtve nose. In order to desgn the low-pass flter, t s necessary to estmate the bandwdth of the target autocorrelaton functon from the receved sgnal autocorrelaton functon. Suppose that the bandwdth s p, that s, Φ ()<ε for <- p or > p, where ε s a small postve real number. hen the second order dervatve of the receved sgnal power spectrum Φ Y () would exhbt peas at p and p. For obtanng p, we use the second order numercal dervatve, { Φ Y( + )} Φ Y( ) +ΦY( )} Δ { Φ Y ( )} =, 6. () A constant p s estmated from peas of Δ {Φ Y ( p )}, and thus the bandwdth s obtaned accordngly. Knowng p, one may estmate the target power spectrum Φ ˆ ( ) drectly from Φ Y () by the deal low-pass flter whch has the transton regon p ; namely, Φ ˆ ( ) s obtaned from each value of Φ Y () as Φ ˆ ( ) =ΦY( ), p p, Φ ˆ ( ) =, / <, < /. (5) p p Issue, Volume, 7 7

4 INERNAIONAL JOURNAL OF COUNICAIONS An alternatve method s to pass the receved sgnal autocorrelaton functon through a low-pass flter wth the bandwdth of p, and then tae the DF of the flter output. B. Receved Sgnal Norm Gven the target power spectrum, t s now ready to process receved sgnals to mprove SCR. We prepare the matched flter G() gven as G ( ) = Φˆ ( ). (6) ˆ Φ ( m) m= he matched flter G() s normalzed so that the sum of G(), -, becomes. Usng the matched flter G(), we perform the steps descrbed n Fg. 3. he nput x l (m), m -, s assumed to be computed accordng to (3) n advance. he -pont DF X l () of ths nput s computed, and then each DF value s multpled by the matched flter to obtan ts output Z l () as Z l ()= G()X l (), -. (7) Fnally, the norm of ths matched flter output Z l () s calculated by Pl = Zl( ). (8) hs norm P l taes a large value when there s the target at the tme of wndow l. he proposed method that has been explaned so far s summarzed as follows: ) he matrx B s computed from receved sgnals n accordance wth (). he autocorrelaton functon of receved sgnals φ Y s approxmated from the matrx B usng the numercal average. ) he power spectrum of receved sgnals Φ Y () s obtaned by tang DF of the autocorrelaton functon φ Y. 3) he bandwdth of the target power spectrum s estmated from Φ Y () usng the second order numercal dervatve. he target power spectrum Φ () s estmated by flterng from Φ Y () wth the low-pass flter whch has the same bandwdth as the target power spectrum. ) Fnally the matched flter s desgned gven by (6). he receved sgnal norm s computed by followng the procedure n Fg. 3. IV. ANALYSIS ON SCR A. Improvement Rato of SCR he receved sgnal x l (m) becomes ether the random varable y (m) or y C (m) dependng on whether there s the target or the clutter at the tme of wndow l. Based on ths observaton, we assgn, n the place of P l, two random varables Q= G( ) Y( ), =,C, (9) where Y () and Y C () are the -pont DFs of y (m) and y C (m), respectvely. herefore, Q and Q C are the norm of the matched flter output when the target or the clutter s receved. Evdently, phase components of the matched flter do not affect to the computaton of the norm. From the relatons of Φ ()=(/)E[ Y () ], the mean of the norm s gven by { } ( ) ( ), =,C. () EQ = G Φ For evaluatng the method, t s necessary to compare SCRs for the cases when the matched flter s used and not used. When the matched flter s used, SCR s gven as { } G Φ EQ SCR= = EQ { C} G ΦC ( ) ( ). () ( ) ( ) Substtutng G()= nto (), when the matched flter s not used, SCR s gven by SCR x l (m) = -DF Φ ( ). () Φ ( ) C X l () G() Z l () Compute Norm Fg. 3 Steps for computng the receved sgnal norm herefore, the mprovement rato of SCR by usng the matched flter s defned by P l Issue, Volume, 7 7

5 R INERNAIONAL JOURNAL OF COUNICAIONS Φ C SCR SCR = = SCR Φ ( ) G( ) Φ ( ) ( ) G( ) Φ ( ) C. (3) We evaluate the performance of the method by the mprovement rato R SCR. hs equaton means that when the power spectra of the target and the clutter are the same, SCR s equal to one, and cannot be mproved by usng the matched flter. B. Comparson wth Conventonal ethods As a demonstraton for measurng the mprovement rato, we have used a 6GHz band F-CW radar system. Branches wth leaves of a broadleaf tree are used as the clutter, and a flat board of alumnum as the target wth ts surface facng to the antenna. able I shows specfcatons for the demonstraton. Fg. shows DFs of the sgnals from the target and the clutter. he target sgnal has a narrower bandwdth than the clutter sgnal; the target sgnal has a stronger correlaton than the clutter sgnal. he target power spectrum s estmated by the method descrbed n Sec. III. A. As the number of target sgnals n the ensemble of the receved sgnals x l, l L-, contaned n the matrx B gven by () ncreases, the accuracy of the estmate of target power spectrum mproves. he method approaches the expected performance. However, when the number s small, the performance degrades accordngly. he mprovement rato R SCR s plotted as a functon of the number of targets n Fg. 5. he mprovement rato s compared wth two conventonal methods: the ntegraton processng method [5] and the dscrete wavelet-transform method [], [3]. For the ntegraton processng, the mprovement rato of SCR at 5 wndows s computed. For the dscrete wavelet-transform method, the scalng functon of orders of the Daubeches wavelet s employed. he mprovement ratos of the conventonal methods are also exhbted n Fg. 5. he conventonal methods do not have capablty of learnng, and thus ther performances are ndependent of the number of targets. As seen n the fgure, the mprovement rato ncreases as the ABLE I SPECIFICAION OF HE F-CW RADAR SYSE Center frequency 6GHz Frequency bandwdth 7Hz ransmttng power dbm Frequency nterval of receved sgnals Hz H() -3 3 : DF of the target sgnal (Alumnum flat board) : DF of the clutter sgnal (Branches wth leaves) Fg. DFs of the sgnals number of targets ncreases, and then saturates after the number reaches fve. he mprovement rato of the proposed method after the saturaton s better than the conventonal methods. V. SIULAION A. arget and Clutter odels For smulaton, we employ the A models for both the targets and the clutter. hat s, the target sgnal y (n) and the clutter sgnal y C (n) are created by K y( n) = h( u) w( n u), =,C, () u= where h (u) denotes A parameter, and w(n) s a zero mean whte Gaussan. K wll be referred to as the order of the model. he power spectra are gven by Φ ()=σ w H (), =,C, (5) where σ w s the varance of w(n), and H () s DF of h (n) []. For the A parameters, we consder the form gven by h (n)= exp(-a n ), =,C, (6) where the value a s a postve constant. DF of h (n) s obtaned as N H ( ) = h ( n)exp( π n/ N) n= ( exp( a))( ( ) exp( an / )) =. (7) exp( a )cos( π / N) + exp( a ) Issue, Volume, 7 7

6 INERNAIONAL JOURNAL OF COUNICAIONS : a = : a =.65 R SCR (db) 3 H () 5 5 he number of target data vectors : he proposed method : he ntegraton processng method : he dscrete wavelet-transform method Fg. 5 R SCR as a functon of the number of targets hese DFs are shown n Fg. 6 when a =.5 and a =.65. As the constant a ncreases, the bandwdth of H () and thus the bandwdth of the power spectrum ncrease. hese constants are delberately chosen to fnd sutable A models for the alumnum board target and the branch clutter shown n Fg.. Comparng Fg. and Fg. 6, one can see that the alumnum board target and the branch clutter are modeled by selectng a =.5, and a C =.65, respectvely. R SCR (db) Fg. 6 DF H () of the A parameters h (n) B. Improvement Rato R SCR By substtutng Φ () of R SCR n (3) for Φ () n (5) and Φ C () for Φ C ()=σ w H C (), the mprovement rato of SCR by usng the matched flter s gven as R HC( ) G( ) H( ) SCR = H( ) G( ) HC( ). (8) a or a C : a s vared between and.65, when a C = : a C s vared between.5 and when a =.5. Fg. 7 R SCR as functons of a and a C Assumng that the estmaton s accurate, Fg. 7 shows the mprovement rato R SCR as the functon of a when a C =.65, and also the rato as the functon of a C when a =.5. he rato ncreases as a decreases or a C ncreases. In other words, the rato ncreases as the target spectrum bandwdth decreases or the clutter spectrum bandwdth ncreases. C. Learnng Speeds for the A odels Smulatons are performed to see how many targets are needed to acqure a desrable performance. he target and the clutter sgnals are created as the A models accordng to (). Smulaton parameters used n the computer smulaton are lsted n able II. Fg. 8 shows the mprovement rato R SCR as the functon of the number of targets used n the learnng. When the number of target vectors s not large enough, the rato does not reach ts value gven by (8) because the target power spectrum s not accurately estmated. he rato R SCR mproves by ncreasng the value a C as expected from Fg. 7. As explaned at the end of Sec. V. A, the alumnum board target and the branch clutter are sutably modeled as the A models wth a =.5, and a C =.65, Issue, Volume, 7 73

7 respectvely. he plots for a =.5 and a C =.65 n Fg. 8 ndeed exhbt the smlar tendency to the plots n Fg. 5. VI. CONCLUSION hs paper has ntroduced the method for mprovng SCR for R SCR (db) INERNAIONAL JOURNAL OF COUNICAIONS ABLE II SIULAION PARAEERS he value a of target A parameter.5 he value a C of clutter A parameter.65 and.9 Receved data, L 6 matrces arget data vectors 6 dmensons Clutter data vectors 6 dmensons he number of target data vector - he number of clutter data vector he number of target vectors : he mean value of R SCR when a C = : he mean value of R SCR when a C =.9. : ypcal sngle value of R SCR when a C =.65. Fg. 8 R SCR as a functon of the number of targets when a =.5 mllmeter wave F-CW radar. Under the assumpton that receved sgnals from the target wth dfferent carrer frequences have a stronger correlaton than receved sgnals from the clutter, the method estmates frst the autocorrelaton functon of receved sgnals by accumulatng enough number of receved sgnals. he power spectrum of receved sgnals s obtaned by tang DF of ts autocorrelaton functon. And then the target power spectrum s extracted by explotng the dfference between the statstcs of the target and the clutter. he matched flter s desgned from the nowledge of the target power spectrum. hen the steps descrbed n Fg. 3 are performed to obtan the norm of receved sgnals gven by (8). he stronger correlaton for the target sgnals than the clutter sgnals s verfed from the data measured by the 6GHz band F-CW radar. hen the matched flter desgned from the measured sgnals was analyzed n terms of SCR. oreover, the performance of the proposed method s analyzed usng the A models for the target and the clutter sgnals. he smulatons verfed that the proposed method s ndeed useful for mprovng SCR for the F-CW radar systems. REFERENCES []. I. Soln, Introducton to Radar Systems, thrd edton. New Yor: cgraw-hll Boo Company,, pp []. Hormatsu and. Htotsuya, llmeter-wave radar n practcal use, he journal of IEICE, vol.87, no.9, pp ,. [3] H. Kondoh, H. Nagash, H. Shnoda, N. Kurta,. Nagasau and K. aano, llmeter-wave automotve radar sensors for IS applcatons, rans. of IEICE(C), vol.j88-c, no.8, pp.63-6, 5. [] A. Satou, S, Kouya, S. wa and N. Kau, Radar SCR mprovement usng a wavelet transform, rans. of IEICE(B), vol.j8-b, no.5, pp.93-93,. [5]. I. Soln, Radar Handboo, second edton. New Yor: cgraw-hll Boo Company, 99, pp..7-.8, -7. [6] F.. Ulaby and. C. Dobson, Handboo of Radar Scatterng Statstcs for erran. Boston: Artech House, 989, pp [7] H. Yamaguch, A. Kajwara, S. Hayash, R. Saga, F. Nshyama and K. Serzawa, arget detecton n ground clutter wth mllmeter-wave stepped frequency radar, IEICE echncal Report, SANE-6, pp.3-36,. [8] A. Kajwara and H. Yamaguch, Clutter suppresson characterstcs of stepped-f radar wth USIC algorthm, rans. of IEICE(B), vol.j8-b, no., pp ,. [9] F. Nshyama and H. uraam, Blnd matched flter method for F-CW radar, Proc. IASED SIP6 Conf., proceedng 53, 53-8, 6. [] F. Nshyama and H. uraam, A method of mprovng SCR for F-CW radar, rans. of SICE, vol.3, no.9, pp , 7. [] F. Nshyama and H. uraam, A method of mprovng SCR for mllmeter wave F-CW radar wthout nowledge of target and clutter statstcs, Proc. th WSEAS Conf. Communcatons, vol.3, pp.35-, 7. [] A. Papouls and S. U. Plla, Probablty, Random Varables, and Stochastc Processes, forth edton, New Yor: cgraw-hll Boo company,, pp.-, 58,. [3] H. Naano, S. Yamamoto and Y. Yoshda, Sgnal Processng and Image Processng by usng Wavelet ransform, oyo: Kyortsu Publcaton, 999, pp.7-9. Fumo Nshyama receved the B.E. degree n electrcal engneerng from oyo Unversty of Scence, oyo, n 995, and the.e. degree n nformaton engneerng from Kanazawa Insttute of echnology, Kanazawa, n 5. He has been n echncal Research and Development Insttute, nstry of Defense, snce 99. He s also currently wth Kanazawa Insttute of echnology as a doctorate student. Hs research nterests nclude dgtal sgnal processng and mllmeter-wave radar systems. Hdeo uraam receved the B.S. degree n electrcal engneerng from Kanazawa Unversty, Kanazawa, n 968, and the.s. and Ph.D. degrees n electrcal engneerng from the Unversty of Southern Calforna, Los Angeles, U.S.A., n 973 and 977, respectvely. From , he was employed at tsubs Electrc Corporaton, Hyogo. Snce 977, he has been wth Kanazawa Insttute of echnology, Kanazawa, where he was an Assocate Professor, and s currently a Professor there. Hs research nterests nclude dgtal sgnal processng and codng theory. Issue, Volume, 7 7