Performance Analyss of the Weghted Wndow CFAR Algorthms eng Xangwe Guan Jan He You Department of Electronc Engneerng, Naval Aeronautcal Engneerng Academy, Er a road 88, Yanta Cty 6400, Shandong Provnce, Chna E-mal: mengxw63@sohu.com Abstract Wth the deteroraton of radar operaton envronment and the enhancement of menace to radar, the task of radar targets detecton becomes more complcated. Such as the detecton of arplane, shp or cruse mssle n over the horzon radar (OTHR), and the detecton of the movng targets n synthetc aperture radar (SAR). Therefore, t s necessary to make further study on CFAR algorthms. The performance of conventonal cell averagng (CA) algorthm s the best n homogeneous background snce t uses the maxmum lkelhood estmate of the nose power to set the adaptve threshold. But f the nterferng target s present n the reference wndow wth a target return n the test cell, sever maskng of targets appears due to ncreased threshold. In order to overcome ths problem, the ordered statstc (OS) and the trmmed mean (T) algorthms usng trmmed technque are proposed. If the reference sample number s not too bg, the CFAR loss of OS and T ncrease greatly. Ths case can usually be encountered n complcated envronment and lower SNR stuaton. In ths paper, weghted wndow technques such as rectangle, steps and trapezum wndows are dscussed. The analyss results show that weghted wndow technque can mprove greatly n homogeneous background and obtans an mmune ablty to nterferng targets to some extent. I. INTRODUCTION Wth the deteroraton of radar operaton envronment and the enhancement of menace to radar, the task of radar targets detecton becomes more complcated. Such as the detecton of arplane, shp or cruse mssle n over the horzon radar (OTHR), and the detecton of the movng targets n synthetc aperture radar (SAR). Therefore, t s necessary to make further study on CFAR algorthms. The performance of conventonal cell averagng (CA) algorthm s the best n homogeneous background snce t uses the maxmum lkelhood estmate of the nose power to set the adaptve threshold. But f the nterferng target s present n the reference wndow wth a target return n the test cell, sever maskng of targets appears due to ncreased threshold. In order to overcome ths problem, the ordered statstc [] (OS) and the trmmed mean [] (T) algorthms usng trmmed technque are proposed. In practcal applcatons, the nformaton about the number of nterferng targets s not known n advance, the bggest samples of reference wndow are always trmmed wth OS or T method not only n multple targets stuaton but also n homogeneous background, ths wll results addtonal CFAR loss. Especally n the case of the short reference wndow, ths CFAR loss wll becomes unacceptable, and ths can usually be encountered n complcated envronment and lower SNR stuaton. In ths paper, the weghted wndow technques such as rectangle, steps and trapezum wndows are dscussed. The analyss results show that the weghted wndow technque can mprove greatly n homogeneous background and obtans an mmune ablty to nterferng targets. II. GENERAL DETECTION PRINCIPLE In ths paper we assume that the background nose envelope s Raylegh dstrbuted, the test cell and the reference cell varables are ndependent, we only consder the sngle pulse square-law detecton. In homogeneous background, the reference samples are IID wth common probablty densty functon (pdf) and cumulatve dstrbuton functon (cdf) x f ( x) exp( ) x F( x) exp( ) ( x 0) () represents nose power. The detector n ths paper forms a fnte reference wndow of sze surroundng the cell under test and uses the reference samples that fall wthn the wndow to estmate the total nose power. The returns n the reference cells X, X -,, X 3, X, X are sorted accordng to ther ampltudes, the ordered samples are obtaned as x( ) x( ) x( 3 ) x( ) x( ) () The weghted sum of ordered samples s used as a nose power estmaton X k h k x ( k ) There, the mean of the kth ordered sample s [3] (3)
Report Documentaton Page Form Approved OB No. 0704-088 Publc reportng burden for the collecton of nformaton s estmated to average hour per response, ncludng the tme for revewng nstructons, searchng exstng data sources, gatherng and mantanng the data needed, and completng and revewng the collecton of nformaton. Send comments regardng ths burden estmate or any other aspect of ths collecton of nformaton, ncludng suggestons for reducng ths burden, to Washngton Headquarters Servces, Drectorate for Informaton Operatons and Reports, 5 Jefferson Davs Hghway, Sute 04, Arlngton VA 0-430. Respondents should be aware that notwthstandng any other provson of law, no person shall be subject to a penalty for falng to comply wth a collecton of nformaton f t does not dsplay a currently vald OB control number.. REPORT DATE 4 APR 005. REPORT TYPE N/A 3. DATES COVERED - 4. TITLE AND SUBTITLE Performance Analyss of the Weghted Wndow CFAR Algorthms 5a. CONTRACT NUBER 5b. GRANT NUBER 5c. PROGRA ELEENT NUBER 6. AUTHOR(S) 5d. PROJECT NUBER 5e. TASK NUBER 5f. WORK UNIT NUBER 7. PERFORING ORGANIZATION NAE(S) AND ADDRESS(ES) Department of Electronc Engneerng, Naval Aeronautcal Engneerng Academy, Er a road 88, Yanta Cty 6400, Shandong Provnce, Chna 8. PERFORING ORGANIZATION REPORT NUBER 9. SPONSORING/ONITORING AGENCY NAE(S) AND ADDRESS(ES) 0. SPONSOR/ONITOR S ACRONY(S). DISTRIBUTION/AVAILABILITY STATEENT Approved for publc release, dstrbuton unlmted. SPONSOR/ONITOR S REPORT NUBER(S) 3. SUPPLEENTARY NOTES See also AD00798, Proceedngs of the Internatonal Conference on Radar (RADAR 003) Held n Adelade, Australa on 3-5 September 003. 4. ABSTRACT 5. SUBJECT TERS 6. SECURITY CLASSIFICATION OF: 7. LIITATION OF ABSTRACT UU a. REPORT unclassfed b. ABSTRACT unclassfed c. THIS PAGE unclassfed 8. NUBER OF PAGES 4 9a. NAE OF RESPONSIBLE PERSON Standard Form 98 (Rev. 8-98) Prescrbed by ANSI Std Z39-8
x( k ) K N and the estmaton varance of usng x (k) s obtaned as k ( N ) Dˆ E( ˆ ) (5) k j( N j ) When the number of the reference sample s 4, Fg. depcts the mean curve of X (k) versus k, t s shown that the mean of hgher ordered sample s bgger and that of the lower ordered sample s smaller. Fg. depcts the estmaton varance curve of usng X (k) versus k, t s shown that the varance of hgher ordered sample s smaller than that of lower ordered sample, but the varance of the bggest ordered sample s not the smallest. mean Fg. The curve of the mean value of X (k) versus k. Fg. The estmaton varance curve usng X (k) versus k. Fnally, the moment generaton functon (mgf) of X n (3) can be obtaned as c X ( u) ( c ) (6) u c h k The nose power estmaton X s multpled by a threshold k (4) constant and then compared wth the test cell return. If the test cell return exceeds ths threshold, a detecton s declared. The nose power estmaton X whch sets threshold s a random varable, thus the detector performance s determned by average detecton and false alarm probablty, average detecton probablty and false alarm probablty s respectvely P fa X ( u) T u P d X u) T u b ( (7) x (u) s mgf of X, b=+, s the per pulse average SNR. The analytc expressons of average detecton threshold (ADT) s obtaned as T d X ( u ) ADT T 8 du c III. PERFORANCE ANALYSIS OF THE WEIGHTED WINDOW ALGORITHS In order to enhance the ablty of the detector to combat the nterferng targets, OS, C, T, the best lnear unbased [4] (BLU) and the quas best weghted [5] (QBW) algorthms use trmmng method to trm the bgger or smaller ordered samples. But f the length of the reference wndow s not too bg, ths trmmng method wll results the more addtonal CFAR loss wth respect to CA that averages all reference samples. Furthermore, ths short reference wndow whch s confned by the practcal stuaton s usually encountered n complcated radar detecton envronment and low SNR case. In order to mprove the detecton performance and enable the detector to have an mmune ablty to nterferng targets, the weghted wndow technques such as rectangle, steps and trapezum wndows are presented n ths paper, and we gve some analytc results wth comparson to other schemes. Some CFAR methods such as CA, C, OS, T, BLU and QBW can be obtaned by some specal cases of (3). If the weghted coeffcents h selects as h / (,, ), that s CA method. If h selects as h /( )(,, ), others are zero, that s C method. If h selects as /( )(,, ), others are zero, h h ( that s T method. If h select as k), others are zero, that s OS method. If h selects as j0 h j0 (,, ( j ) j )
( ( j ) ) j0 ( ) (9) ( j ) j the mathematcal model of BLU can be obtaned. If h of expresson (3) selects as,, h (0) 0 else the method of QBW can be obtaned. Now we consder the weghted wndows technque, n the frst case, the rectangle wndow h 0 or () In fact, CA, OS, C and T are the specal cases of rectangle wndow. The second case, steps wndow h () Because the nterferng targets usually occupy the hgher order statstcs and the null sample wll occupy the lower order statstcs, the weghted coeffcent and of hgher and lower order satstcs take smaller, rather than take zero n the case of T. The thrd case also from the vew pont of the smaller coeffcent of hgher and lower order statstcs, the coeffcents of trapezum wndow s w h (3) w j j where ( j ) j w j j ( j ) j ( 0, 0 ) (4) ( 0 TABLE I. The performance comparson of detecton schemes n homogenous background. Schemes (the sample number) 6(the sample number) CFAR loss ADT CFAR loss ADT CA.737 5.9473.9957.940 OS (k=9)3.99 34.470 (k=3).748 6.36 C(=3) 3.8560 33.96.5973 5.668 T(=3, =3) 3.849 33.63.586 5.7 BLU(=3, =3) 3.785 3.8405.495 4.6404 QBW(=3, =3) 3.76 3.90.4954 4.6575 Rectangle wndow (=3, =3) 3.849 33.63.586 5.7 Steps wndow (=3, 3.360 8.703.899 3.58 =3, =/8,=/8) Trapezum wndow (=3, =3=/8,=/8).9569 7.4985.599.805 TABLE II. The ADT and CFAR loss of steps wndow versus and. 6, 3, 3 =/0,=/0 =/8,=/8 =/4,=/4 =/,=/ ADT 3.746 3.58.7805.76 CFAR loss.3305.899.536.0393 TABLE III. The ADT and CFAR loss of trapezum wndow versus and. 6, 3, 3 =/0,=/0 =/8,=/8 =/4,=/4 =/,=/ ADT.9050.805.459.058 CFAR loss.776.599.0938.069
The performance analyss of the weghted wndow technques and other schemes are carred out by ther CFAR loss and ADT values. Table I shows the performance of the weghted wndow technque and other schemes n homogeneous background. It s can be seen that an evdent mprovement s obtaned through weghted wndow technques n homogeneous background, and the nfluence of nterferng targets can be counteracted due to the smaller coeffcents of hgher ordered sample. For example, the number of reference samples s, the CFAR loss of CA s.737, the CFAR loss of OS at k=9 s 3.99, the CFAR loss of steps wndow and trapezum wndow at ==/8 s 3.360 and.9569 respectvely. Table II and table III gve the CFAR loss and ADT values of steps wndow and trapezum wndow versus and respectvely. It can be shown that wth the ncrease of and, the CFAR loss and ADT decrease, f ==, the scheme becomes CA. Because of the smplcty of CA n ther mplementaton, t s commonly used n radar systems. But n the cases of multple targets, the maskng effect of CA wll appears. OS and T methods can resolve the multple targets well, they also brng some addtonal CFAR loss, especally n the case of the short reference wndow. The weghted wndow technque dscussed here can be consdered as a compromse between CA and T. REFERENCES [] H.Rohlng. Radar CFAR thresholdng n clutter and multple-target stuatons. IEEE Trans.on AES, 983, 9(4):608~6. [] P.P.Gandh, S.A.Kassam. Analyss of CFAR processors n nonhomogeneous background. IEEE Trans.on AES, 988,4(4):47~445. [3] eng Xangwe.Statstcal analyss of negatve exponental dstrbuton and ts applcaton for CFAR. Sgnal Processng (Chnese),00:99-30 [4] D.T. Nagle, J.Sane. Performance analyss of lnearly combned order statstc CFAR detectors. IEEE Trans. on AES, 995, 3():5-533. [5] eng Xangwe, He You. A greatest of selecton CFAR algorthm based on quas-best weghted order statstcs. ACTA ELECTRONICA SINICA (Chnese), 997, 5(): 74-78. IV. CONCLUSION In order to mprove the detecton performance of OS and T n the case of the short reference wndow, the weghted wndow technques are proposed n ths paper. The weghted wndow technque can be consdered as a compromse between CA and T. In the cases of the low SNR stuaton and the short reference wndow, applyng weghted wndow technques are of practcal nterest. It s shown that an evdent mprovement s obtaned through the weghted wndow technques n homogeneous background, and the nfluence of nterferng targets can be counteracted due to the smaller coeffcents of hgher ordered samples. Wth the ncrease of and, the CFAR loss and ADT decrease, f ==, the scheme becomes CA. The smaller and are, the stronger ablty to combat the nterferng targets. It s shown from Fg. that the varance of hgher ordered sample s smaller than that of lower ordered sample, but the varance of the bggest ordered sample s not the smallest. Therefore n practcal applcatons, the upper-medum parts of weghted coeffcents should be bgger, whereas the two ends of ordered samples should be smaller.