Efficient Methods of Doppler Processing for Coexisting Land and Weather Clutter

Transcription

1 Efficient Method of Doppler Proceing for Coexiting Land and Weather Clutter Ça gatay Candan and A Özgür Yılmaz Middle Eat Technical Univerity METU) Ankara, Turkey ccandan@metuedutr, aoyilmaz@metuedutr Abtract The joint uppreion of return from land and weather clutter i required in many radar application Although the optimal method of land-weather clutter uppreion i known, the olution i uually not practical to implement In thi paper, we propoe a method that employ rank-1 and rank- approximation on the weather clutter correlation matrix to obtain uboptimal but impler detector which are eaier to implement The performance of the propoed detector i compared with the optimal detector and ome other detector commonly ued for clutter uppreion Index Term MTI, Doppler Proceing, Weather Clutter I INTRODUCTION We conider the problem of clutter cancellation for pule Doppler radar ytem when the received ignal contain clutter return due to reflection from both land and weather ytem The problem tudied frequently occur in air urveillance radar ytem For uch ytem, the echo received may have component due to target ignal, land clutter and return from dene cloud with non-zero velocity Epecially urveillance operation in rain or fog can be everely compromied by the weather clutter if it effect i not properly cancelled The tationary clutter land clutter) cancellation problem i a well tudied in the literature [1] Moving target indicator MTI) and Doppler proceing technique with DFT bank or optimized filterbank have been tudied in depth along with the optimal method baed on clutter correlation Cancellation of weather clutter ha been le elaborated In [1], a imple MTI operation, whoe null i at the Doppler frequency of weather clutter, i uggeted In [], the performance of MTI for weather clutter cancellation i tudied and it performance i compared with the optimal method under variou condition It ha been noted that the uppreion performance of MTI i ufficient under ome cenario, but in ome other it fall behind the moving target detector MTD) filterbank with optimized filter, [3] In thi paper, we re-examine the problem tudied in [] and propoe a novel method approximating the optimal operation With the propoed method, an approximate yet cloe to the optimal olution i achieved with realizable computational requirement The paper i organized a follow In Section, we decribe the problem, the clutter model and the optimal olution In Section 3, we decribe the MTI approach, whitening approach, and the propoed approximation to the optimal method In Section 4, we preent numerical comparion of the method under variou operational cenario and finally we preent the concluion II PROBLEM DESCRIPTION A train of N pule are ued to decide the preence of a target in a range cell The vector r i aumed to contain the I/Q ample of the ignal repreented with the complex baeband repreentation: r = α + E l c l + E w c w + w 1) In equation 1), the vector i the deired ignal denoting the return from the target, the vector c l and c w are clutter return vector due to land and weather ytem, repectively The vector w repreent thermal noie and the entrie of thi vector are independent identically ditributed circularly ymmetric complex Gauian random variable with zero mean and unit variance The parameter α, E l, E w, are calar to repreent the power of each term The vector i aumed to be a determinitic quantity in the form [1 W W W N 1 ] where W = e jw t The parameter w t correpond to the Doppler frequency of the target in radian) after modulo PRF pule repetition frequency) reduction The goal i to detect the determinitic ignal, which i the complex exponential vector, in the preence of random diturbance due to clutter and thermal noie The auto-correlation of land clutter and weather clutter vector c l, c w are aumed to be in the form r c k) = ρ k exp j πf wk PRF ) ) In ), f w i the Doppler frequency in Hertz) of the clutter object For land clutter, f w i equal to zero and for weather clutter it i proportional to the radial velocity of the cloud The correlation parameter ρ i frequently ued in radar with antenna canning modulation It i baed on the aumption that clutter motion i inignificant in comparion with the motion of the antenna during the coherent proceing interval The parameter ρ i related with the parameter of the radar ytem uch a angular peed of the rotating antenna, PRF etc Under thee condition, the input SNR for each received ample) become SNR in = α /E l + E c + ) The goal of MTI or Doppler proceing ytem i to increae the ample SNR by jointly proceing N ample of the vector r

2 A linear combination operation of the received ample can be expreed a w H r Here w i the linear combination vector which i a column vector of length N After linear combination, the SNR at the output become SNR out = α wh H w w H Rw 3) Here the matrix R denote the auto-correlation matrix of the clutter and thermal noie term More explicitly the ith row and kth column of matrix R i Ri, k) = E l r cl i k) + E w r cw i k) + δi k) 4) Here the term r cl and r cw refer to land and weather clutter auto-correlation whoe definition are given in ) When i a determinitic parameter, the component of SNR out in 3) are totally determinitic The vector w maximizing the ratio in 3) i the generalized eigenvector of matrix R and rank-1 matrix H The optimal vector i given by w opt = R 1 [1], [4] The optimal weight vector can be written a follow: w opt = R 1 = E l R cl + E w D fw R cl D H f }{{ w + I) } R w 1 = 1 R cl + E w D fw R cl D H f w + I 5) In 5), the matrix R cl denote the normalized auto-correlation matrix for land clutter The weather clutter matrix R w ) i repreented in term of R cl through prior and poterior multiplication by D fw The matrix D fw i a diagonal matrix with diagonal entrie [1, W, W, W N 1 ] W = e jπf w/p RF ) We note that the land clutter correlation matrix and weather clutter correlation matrix are imilarity tranformation of each other Therefore both matrice have the ame eigenvalue We denote the eigen decompoition of land clutter correlation matrix a R cl = EΛE H Here E i the matrix whoe column are the eigenvector of R cl and Λ i a diagonal matrix with aociated eigenvalue on the diagonal Uing the eigendecompoition in 5), we get w opt = 1 EΛE H + E w D fw E)ΛD fw E) H + I From the lat equation, it can be noted that when one of the clutter term i dominant, the proceor implifie When land clutter i dominant, the filter become w l opt = 1 EΛE H + I 7) Similarly when weather clutter i the dominant factor, we get wopt w = 1 Ew D fw EΛE H D H f N w + D fw D H f w o = D fw w l optd H f w 8) From equation 8), it can be noted the optimal filter to remove the weather clutter when land clutter i negligible, i formed by the frequency hifted verion of the land clutter filter In many practical ytem, the clutter power i etimated and tored in a clutter map The clutter power information i ued to fetch pre-calculated optimal combination weight w opt ) from a look-up table The torage requirement for the lookup table can be critical in many application The land clutter removal ytem whoe equation i given in 7) ha only one free parameter E l / Therefore a look-up table with a ingle index dimenion) i ufficient to tore the coefficient A filter trictly removing weather clutter can be eaily adapted from the tored land clutter removal filter coefficient uing equation 8) But for a general ytem capable of removing land and weather clutter at the ame time, the dimenion of torage require change from 1 to 3, that i in addition to E l / one ha to tore E w / and f w Since the dimenion for the torage unit i tripled, the ytem may become infeaible to implement via pre-calculated look-up table In thi paper, we preent alternative method for the olution of the problem with feaible torage at the expene of ome additional calculation The additional calculation have little extra weight on the proceor III PROPOSED TECHNIQUES We preent three method for the clutter uppreion The implementation complexity of thee method are briefly dicued A Shifted MTI Followed By Land-Only Filter The proceing output can be defined a follow: r out = w opt) l H 1 1 Dfw DH f w r 9) 1 1 }{{} w 1) ) H With thi proceing, the receive vector r i firt proceed by a ingle order MTI filter whoe null frequency i hifted to f w and then the land removal filter calculated from 7) i ued to remove the effect of land clutter Thi proce can be 6) implemented by modulating the received ignal by frequency f w, then MTI filtering, and finally by modulating it back to the frequency f w a hown in 9) Thi method i imple to implement and ha minor extra computational load on the proceor The firt order MTI filter decribed here can be generalized to higher order, [1] B Land Filter Followed by Weather Filter Thi method implement a cacade of land and weather clutter removal filter For the propoed cheme, the land clutter i proceed by R 1/ l matrix where R l i the auto-correlation matrix of land clutter and thermal noie, R l = E l R cl + I Thi operation correpond to the whitening of the ignal if weather clutter component i ignored After thi tage, the

3 reultant vector i one more time proceed with R w 1/ which i the whitening matrix for r in the abence of land clutter Finally, the ignal i captured by matched filtering Thi method approximate the whitened matched filter olution which i known to be equivalent to the SNR maximizing olution given in 3) The approximate whitened matched filter vector become w ) = R l 1/ R w 1 R l 1/ 1) Thi proceor require torage of invere of R l and R w matrice Since the parameter pace for two matrice i decoupled the torage requirement double in ize but not in dimenion However, the increae in computational complexity i quite ignificant ince the computation involve multiple matrix multiplication Alternatively the vector w ) in 1) can be tored to reduce the number of operation In thi cae, the look-up table dimenion increae by 1 One hould decide on one of thee approache baed on the ytem pecification C Approximation to the Optimal Solution The equation 5) give the optimal olution for arbitrary clutter power and weather clutter Doppler frequency center An approximate yet computationally feaible approach i to approximate the weather clutter correlation matrix with lower rank matrice Since the clutter matrix i highly correlated, very few term can be ufficient to repreent the matrix accurately The eigen-decompoition of weather clutter i given a follow R w = N λ k u k u H k 11) k=1 In equation 11), the vector u k i the unit-norm eigenvector of R w correponding to the k th larget eigenvalue λ k A tated in 8), the vector u k are modulated frequency hifted) verion of the eigenvector of the land clutter matrix In thi paper we approximate R w with rank-1 and rank- matrice and apply matrix inverion lemma 1 to derive a Doppler proceor The generalization to higher order approximation i poible but not purued here The rank-1 and rank- approximation for R w i given a follow R 1) w = tracer w )u 1 u H 1 1) R ) λ1 w = tracer w ) u 1 u H 1 + λ ) u u H 13) λ 1 + λ λ 1 + λ The approximation are weighted according to energy in each eigenvector direction The total energy trace) of the original R w and it approximation are et to be the ame We alo note the fact that due to the normalization tracer w ) = N 1 A + UCV = A 1 A 1 UC 1 + VA 1 U VA 1 When the reduced rank approximation are ubtituted for R w in 5), we get the following ŵ 1) opt = 1 R cl + E w R1) w + I = 1 R l + E w Nu 1 u H 1 = 1 R 1 l 1 ) σc cc H 14) where c = R l 1 u 1 and σ c = /NE w ) + u H 1 R l 1 u 1 follow from the matrix inverion lemma The lat line of equation 14) contain two term The firt term i 1/ R l 1 and it tand for the cancellation of clutter in the abence of weather clutter The econd term i the correction on the firt term when the weather clutter of power E w coexit It can be noted that the effect of econd term vanihe a E w get maller When the ame proce i repeated for rank- approximation, we get ŵ ) opt = 1 Rl 1 Ccc H Ddd H + Erealdc H ) ) 15) The variable appearing in equation 15) are given a follow: c = R l 1 u 1 d = R 1 l u C = 1/σc + γ /σc 4 σd) D = 1/σd E = γ/σc σd) The parameter linking the clutter power to the parameter ued in 15) are γ = u H R l 1 u 1 σc = /NE w )λ 1 + λ )/λ 1 + u H 1 R 1 l u 1 σd = /NE w )λ 1 + λ )/λ + u H R 1 l u γ /σc We note that there i no additional torage requirement for the propoed olution if invere of R l matrice are tored in the look-up table The vector c and d can either be calculated on-line increaing computational complexity due to matrix multiplication; or if the online calculation i not feaible, the vector c, d and calar u H R 1 l u 1, u H 1 R 1 l u 1 and u H R 1 l u can be pre-calculated and tored in a look-up table All of the mentioned variable are function of f w and hence the torage dimenion increae only by one IV NUMERICAL COMPARISONS In thi ection, we compare the performance of the method preented in Section 3 In Figure 1, the improvement factor SNR out /SNR in ) of each ytem i given In thi figure, the number of proceing pule i 16, land and weather clutter both ha a power of 4 db above the thermal noie level, ρ = 999 and the weather clutter ha a Doppler frequency at 1/PRF In Figure 1, the improvement factor IF) for the optimal olution and

4 the propoed olution are given The approximation to the optimal olution i given for rank-, rank-1 and rank- cae The rank- cae correpond to the cae when weather clutter i completely ignored and the land clutter filter i applied a if the weather clutter doe not exit One can note from Figure 1 that there i a ignificant lo of performance if the weather clutter i ignored Shifted MTI reult in ome improvement and the approximate whitening method provide further improvement on MTI The approximate optimal olution provide cloe to the optimal olution for the rank- approximation IF db) Optimal Rank 6 5 Rank Optimal Fig N = 16, E l / = 4 db, E w / = 4 db, f w = PRF IF db) 1 6 Rank IF db) Fig 1 N = 16, E l / = 4 db, E w / = 4 db, f w = 5PRF In Figure, the performance of the method i compared when weather clutter Doppler frequency i changed to PRF all other parameter are the ame a of Figure 1) It can be noted that the hifted MTI and the ucceive whitening method have a imilar performance under thee condition The rank- approximation to the optimal olution i cloe to the optimal olution In Figure 3, the performance of the method i compared when weather clutter i at db over all other parameter are the ame a of Figure ) It can be noted that hifted MTI preent a poorer performance than rank- approximation A diadvantage of the hifted MTI method i that it can not adapt it attenuation to the power of weather clutter In ome cenario uch a the one preented in Figure 3, ignoring the weather clutter can be more beneficial than applying hifted MTI method The econd method which i the ucceive whitening method preent a performance cloe to optimal for thi cenario The rank- approximation i virtually identical to the optimal olution V CONCLUSIONS We have preented method to jointly uppre land and weather clutter ignal The optimal method for clutter cancellation i known, but i not practical to implement in many Fig 3 N = 16, E l / = 4dB, E w / = db, f w = PRF application In thi paper, we have ued rank-1 and rank- approximation to the weather clutter correlation matrix to define Doppler proceor which are more uitable for the implementation The propoed ytem can adapt it attenuation power baed on the central Doppler frequency of weather clutter and the relative power level of land - weather clutter ytem The improvement over the alternative olution ha been hown to be ignificant in many cenario ACKNOWLEDGMENT Author would like to acknowledge the upport provided by ASELSAN AŞ for thi work

5 REFERENCES [1] M A Richard, Fundamental of Radar Signal Proceing New York: McGraw-Hill, 5 [] EDAddio, A Farina, and F Studer, Performance comparion of optimum and conventional MTI and Doppler proceor, IEEE Tran on Aeropace and ectronic Sytem, vol, pp , 1984 [3] D Schleher, Performance comparion of MTI and coherent Doppler proceor, IEEE Radar Conference, pp , 198 [4] J Hiao, On the optimization of MTI clutter rejection, IEEE Tran on Aeropace and ectronic Sytem, vol, pp 6 69, 1974 [5] D Schleher, MTI and puled Doppler radar Artech Houe, 1991