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

Transcription

1 Proceedngs of the th WSEAS Internatonal onference on OUNIAIONS, Agos Nolaos, rete Island, Greece, July 6-8, 7 35 A method of mprovng SR for mllmeter wave F-W radar wthout nowledge of target and clutter statstcs FUIO NISHIAA and HIDEO URAKAI Department of nformaton and computer scence Kanazawa Insttute of echnology 7- Ohggaoa Nonoch, Ishawa 9-85 JAPAN Abstract: - hs paper proposes a new method for mprovng Sgnal-to-lutter Rato (SR) for mllmeter wave Frequency-odulated-ontnuous-Wave (F-W) radar. Receved echoes of F-W radar can be categorzed nto two types due to ether a target or clutter. Generally, the target receved data have a stronger correlaton wth respect to dfferent carrer frequences than that of the clutter receved data. hs dfference s exploted for estmatng the statstcs of target data from receved data only, and a matched flter used for mprovng SR s then desgned usng the nowledge of the statstcs. he performance of the method s analyzed and evaluated expermentally for 6GHz band F-W radar. he smulaton shows that the proposed method mproves SR better than competng wth other methods. Key-Words: - atched flter, Stochastc process, Sgnal-to-clutter rato, llmeter wave, F-W radar, Ground clutter, Automotve radar Introducton llmeter wave Frequency-odulated-ontnuous- Wave (F-W) radar s studed as an automotve sensor system of the ntellgent transportaton system, and mounted n several cars. F-W radar transmts a waveform whose frequency changes lnearly n tme. Such F-W 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 automotve radar [,3]. Automotve radar, beng placed at a poston near the ground, nevtably receves clutter echoes from varous objects such as road asphalt, sdewal lnes, and objects on the sdewals. he clutter thus conssts of objects wth varous szes and surfaces, whereas a target such as an automoble s modeled as a relatvely large plane wth a smooth surface. lutter s a major factor that causes a false alarm n target detecton. When a target s movng wth respect to ground clutter, dscrmnatng the target from clutter s relatvely easy by explotng the Doppler-effect. However, when a target s at rest, dstngushng t from the clutter s dffcult. For such cases, mprovng Sgnal-to-lutter Rato (SR) s vtally mportant. arget sgnals correspondng to dfferent carrer frequences generally have a stronger correlaton than that of clutter cases [4]. Usng ths dfference n correlaton, we propose a method of mprovng SR whch does not requre pre-nowledge of the correlaton for a target and clutter. In ths method, an autocorrelaton functon s frst computed from receved data for dfferent carrer frequences. Next, a power spectrum of receved data s computed by tang DF from the autocorrelaton functon of receved data. And then, a target power spectrum s estmated from the power spectrum of receved data. Fnally, usng the estmate, a matched flter s desgned to mprove SR [5]. hs paper s organzed as follows. In hap., the F-W radar system s brefly explaned and receved sgnal models are formulated as a stochastc process. In hap. 3, the proposed methods of estmatng the power spectrum of a target, and of a procedure of explotng the estmated power spectrum for ncreasng SR are descrbed. In hap. 4, performance of the proposed method s analyzed by usng data measured by 6GHz band F-W radar. oreover, n hap. 5, the performance s analyzed n detal usng a ovng Average (A) model for a target and clutter. F-W radar

2 Proceedngs of the th WSEAS Internatonal onference on OUNIAIONS, Agos Nolaos, rete Island, Greece, July 6-8, Stochastc process for receved data A bloc dagram of a double antenna F-W 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 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 targets or clutter, are receved va a recevng antenna. he receved carrer frequency waveform s converted nto a baseband frequency waveform by a demodulator and then sampled. he sampled dscrete sgnal s multpled by a wndow functon dvdng t nto blocs and then dscrete Fourer-transform (DF) of each bloc of samples s computed. Fgure (a) shows frequency varaton of the transmtted waveform for the F-W radar employng the saw-tooth modulaton [6]. 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 baseband waveform wth a faster rate than the dfference f max -f mn. Fgure (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 l ( n) r( ln + n), n N-, () where r(ln+n) s the sampled sgnal before wndow multplcaton. he N 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 ransmttng Antenna odulator Demodulator Recevng Antenna Sgnal Generator Sampler Wndow N-DF r l (n) Fg.. A bloc dagram of F-W radar. R l ( frequency fmax f fmn + m, m -. () f m mn hese DF values are arranged n the -dmensonal vector as [ xl ( ) xl () xl ( ) ] [ ) R ( ) R ( )] x R. (3) l l ( l l 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. Snce only these vectors x l are gong to be used for mprovng SR, they are smply called receved sgnals n followngs. Usng DF s partcularly sutable because the transmttng waveform s perodc wth the tme nterval, and the correlatonal dfference wth respect to dfference carrer frequences of targets and clutter s easly treated. oreover, a delay of the receved waveform due to the dstance between the antennas and the object does not change the absolute values of DF, and thus they are ndependent of the dstance. We want to treat each vector as an outcome taen from a stochastc process. o do ths, the numeral average of these L vectors s ntroduced as Frequency f max f mn L y x. (4) [ ] y() y() y( ) L l l me (a) Frequency varaton of a transmtted waveform wndow l (b) Wndow wndow l me Fg.. ransmtted sgnal and wndow functon for the F-W radar system.

3 Proceedngs of the th WSEAS Internatonal onference on OUNIAIONS, Agos Nolaos, rete Island, Greece, July 6-8, 7 37 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. he process can be vewed as the sum of two types of stochastc processes gven by yp y +P y, (5) where y and y are the stochastc processes correspondng to receved sampled sgnals due to targets and clutter respectvely. P and P are the probabltes of occurrence targets and clutter.. Power spectrum of target data he autocorrelaton functon of y s defned as φ (τ)e{y(m)y(m+τ)}-/ τ /-, (6) where E{. } denotes the expectaton operaton [7]. 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 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 / τ / φ ( τ ) exp( jπτ / ), -, (7) he stochastc process y s composed of the target stochastc process y and the clutter stochastc process y as seen by (5). he autocorrelaton functons of y and y are denoted as φ and φ ; the power spectrums of y and y are denoted as Φ and Φ. As stated before, target sgnals correspondng to dfferent carrer frequences generally are assumed to have a stronger correlaton than that of clutter cases. he proposed method assumes the followngs. Assumpton: he two processes y and y are statcally ndependent wth zero mean, Assumpton: he target process y has a much stronger correlaton than the clutter process y. By (5) and Assumpton, an autocorrelaton functon of receved data s obtaned as φ (τ)p φ (τ)+p φ (τ), (8) ang -pont DF of the autocorrelaton functon, a power spectrum of the process y s gven by Φ P Φ + P Φ, (9) he problem s to estmate Φ ( from Φ ( for desgnng a matched flter to mprove SR. 3 Processng at the recever 3. Estmaton of target power spectrum In order to proceed wth estmatng the target power spectrum, the receved sgnal autocorrelaton functon φ (τ) s frst approxmated from receved sgnals. o do ths, we compute the matrx B from the receved sgnals by x x B L xl * x x xl, () where the superscrpt * denotes the complex conjugate transpose operaton. he (m,n)th entry of ths matrx s gven by L * m, n xl ( m) xl ( n) L l b. () he autocorrelaton functon s approxmated from B as follows. he /-dmensonal vector v s computed accordng to [ v( ) v() v( / ) ] / [ b + / 4, b+ / 4, + b + / 4, + / ] v. () hen the approxmaton of the autocorrelaton functon of the receved sgnals s obtaned as ( / 4 + ) ˆ φ ( τ ) v τ. (3) Once ˆ φ ( τ ) s estmated, the receved sgnal power spectrum Φ ( s estmated by tang -pont DF of ˆ φ ( τ ). Next, gven the receved sgnal power spectrum Φ (, we need to estmate the target power spectrum Φ ( from the receved sgnal power spectrum Φ (, whch s the weghted sum of Φ ( and Φ ( as seen by (9). Assumpton says the bandwdth of Φ ( s much narrower than the bandwdth of Φ (, and thus the target autocorrelaton functon φ (τ) s recovered from the receved sgnal autocorrelaton functon φ (τ) by usng a lowpass flter smlar to the method of

4 Proceedngs of the th WSEAS Internatonal onference on OUNIAIONS, Agos Nolaos, rete Island, Greece, July 6-8, 7 38 recoverng a sgnal contamnated wth a wde band addtve nose. In order to desgn the lowpass flter, t s necessary to estmate the bandwdth of 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 ( would exhbt peas at p and p. For obtanng p, we use the second order numercal dervatve, { Φ ( + )} Φ ( ) + Φ ( )} { ( )} Δ Φ, (4) A constant p s estmated from peas of Δ {Φ ( p )}, and thus the bandwdth s obtaned accordngly. Knowng p, one may estmate the target power spectrum Φ ˆ drectly from Φ ( by the deal lowpass flter whch has the transton regon p ; namely, Φ ˆ s obtaned from each value of Φ ( as Φˆ Φ, p p,. (5) Φˆ, / < p, p < / An alternatve method s to pass the receved sgnal autocorrelaton functon through a lowpass flter wth the bandwdth of p, and then tae the DF of the flter output. 3. Receved sgnal norm Gven the target power spectrum, t s now ready to process receved sgnals to mprove SR. We prepare a matched flter G( gven as G Φˆ m ( m) Φˆ. (6) 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 x l (m) -DF calculated by X l ( P l Zl. (8) hs norm P l taes a large value when there s a 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 φ of receved data s approxmated from the matrx B usng the numercal average. () he power spectrum of receved data Φ ( s obtaned by tang DF of the autocorrelaton functon φ. (3) he bandwdth of the target power spectrum s estmated from Φ ( usng the second order numercal dervatve. he target power spectrum Φ ( s estmated by flterng from Φ ( wth the lowpass flter whch has the same bandwdth as the target power spectrum. (4) Fnally the matched flter s desgned gven by (6). he receved sgnal norm s computed by followng the procedure n Fg Analyss on SR 4. Improvement rato of SR he receved sgnal x l (m) becomes ether the random varable y (m) or y (m) dependng on whether there s a target or clutter at the tme of wndow l. Based on ths observaton, we assgn, n the place of P l, two random varables G( Z l ( ompute Norm Fg. 3. Steps for computng the receved sgnal norm. Q G(,,, (9) where ( and ( are the -pont DFs of y (m) and y (m), respectvely. herefore, Q and Q are the norm of the matched flter output when a target or clutter s receved. Evdently, phase components of the P l

5 Proceedngs of the th WSEAS Internatonal onference on OUNIAIONS, Agos Nolaos, rete Island, Greece, July 6-8, 7 39 matched flter do not affect to the computaton of the norm. From the relatons of Φ ((/)E[ ( ], the mean of the norm s gven by { } Q E G( Φ,,. () For evaluatng the method, t s necessary to compare SRs for the cases when the matched flter s used and not used. SR when the matched flter s used s gven as SR E { Q } { Q } E G( G( Φ Φ. () Substtutng G( nto (), SR when the matched flter s not used s gven by SR Φ Φ. () herefore, the mprovement rato of SR by usng the matched flter s defned by R Φ G( Φ SR SR SR Φ G( Φ. (3) We evaluate the performance of the method by the mprovement rato R SR. hs equaton means that when the power spectra of target and clutter are the same, SR s equal to one, and cannot be mproved by usng the matched flter. 4. A comparson wth conventonal methods he clutter process y generally conssts of echoes from varous objects, on the other hand, the target process conssts of echoes from large plane-le, smooth-surfaced objects. onsequently, the clutter process y tends to have a much weaer correlaton than the target process [8,9]. As a demonstraton for measurng the mprovement rato, we have used a 6GHz band F-W radar system. Branches wth leaves of a broadleaf tree are used as clutter, and a flat board of alumnum as a target wth ts surface facng to the antenna. able shows specfcatons for the demonstraton. Fg. 4 shows DFs of the data from the target and the clutter. he target sgnal has a narrower bandwdth than the clutter able. Specfcaton of the F-W radar system. enter 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. 4. DFs of the sgnals. sgnal; the target sgnal has a stronger correlaton than clutter data. he target power spectrum s estmated by the method descrbed n Sec. 3.. 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, and the method approaches the expected performance. However, when the number s small, the performance degrades accordngly. he mprovement rato R SR of SR s plotted as a functon of the number of targets n Fg. 5. he mprovement rato s compared wth two conventonal method: the ntegraton processng method [6] and the dscrete wavelet transform method [,]. For the ntegraton processng, the mprovement rato of SR 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 does not have capablty of learnng, and thus ther performances are ndependent of the number of targets.

6 Proceedngs of the th WSEAS Internatonal onference on OUNIAIONS, Agos Nolaos, rete Island, Greece, July 6-8, : a : a.65 RSR (db) 4 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 SR as a functon of the number of targets. As seen n the fgure, the mprovement rato ncreases as the 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. 5 Smulaton 5. arget and clutter models For smulaton, we employ the A models for both targets and clutter. hat s, the target sgnal y (n) and the clutter sgnal y (n) are created by K u y ( n) h ( u) w( n u),, (4) where h (u) denotes A parameter, and w(n) s a zero mean whte Gaussan. K wll be refered to as the order of the model. he power spectra are gven by Φ (σ w H (,, (5) where σ w s the varance of w(n), and H ( s DF of h (n) [7]. For the A parameters, we consder the form gven by h (n) exp(-a n ),,, (6) where the value a s a postve constant. DF of h (n) s obtaned as -3 3 Fg. 6. DF H ( of the A parameters h (n). N H h ( n)exp( πn / N) n. (7) ( exp( a ))( ( ) exp( an / )) exp( a )cos(π / N) + exp( a ) 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. 4. omparng Fg. 4 and Fg. 6, one can see that the alumnum board target and the branch clutter are modeled by selectng a.5, and a.65, respectvely. 5. Improvement rato R SR By substtutng Φ ( of R SR n (3) for Φ ( n (5) and Φ ( for Φ (σ w H (, the mprovement rato of SR by usng the matched flter s gven as R H SR H G( G( H. (8) H Assumng that the estmaton s accurate, Fg. 7 shows the mprovement rato R SR as a functon of a when a.65, and also the rato as a functon of a when a.5. he rato ncreases as a decreases or a ncreases. In other words, the rato ncreases as the target spectrum bandwdth decreases or the clutter spectrum bandwdth ncreases.

7 Proceedngs of the th WSEAS Internatonal onference on OUNIAIONS, Agos Nolaos, rete Island, Greece, July 6-8, 7 4 RSR (db) able. Smulaton parameters. he value a of target A parameter :.5 he value a of clutter A parameter :.65 and.9 Receved data, L : 64 matrces arget data vectors : 64 dmensons lutter data vectors : 64 dmensons he number of target data vector : - he number of clutter data vector : -8 7 a or a : a s vared between and.65, when a : a s vared between.5 and when a.5 Fg. 7. R SR as functons of a and a. RSR (db) Learnng speeds for the A models 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 (4). Smulaton parameters used n the computer smulaton are lsted n able. Fgure 8 shows the mprovement rato R SR as a 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 SR mproves by ncreasng the value a as expected from Fg. 7. As explaned at the end of Sec. 5., the alumnum board target and the branch clutter are sutably modeled as the A models wth a.5, and a.65, respectvely. he plots for a.5 and a.65 n Fg. 8 ndeed exhbt the smlar tendency to the plots n Fg oncluson hs paper has ntroduced the method for mprovng SR for mllmeter wave F-W radar. Under the assumpton that receved sgnals from a target wth dfferent carrer frequences have a stronger correlaton than receved sgnals from clutter, the method estmates frst the autocorrelaton functon of receved sgnals by accumulatng enough number of 5 5 he number of target vectors : he mean value of R SR when a c : he mean value of R SR when a c.9 : ypcal sngle value of R SR when Fg. 8. R SR as a functon of the number of targets when a.5. 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 target and 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 target sgnals than clutter sgnals s verfed from the data measured by 6GHz band F-W radar. hen the matched flter desgned from the measured sgnals was analyzed n terms of SR. oreover, performance of the proposed method s analyzed usng A models for target and clutter sgnals. Smulatons verfed that the proposed method s ndeed useful for mprovng SR for the F-W radar systems.

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