PHOTOIC SESORS/ Vol. 5, o. 3, 05: 84 88 A Two-Level Detecton Algorthm for Optcal Fber Vbraton Fukun BI, uecong RE *, Hongquan QU, and Ruqng JIAG College of Informaton Engneerng, orth Chna Unversty of Technology, Bejng, 0044, Chna * Correspondng author: uecong RE E-mal: 03300@mal.ncut.edu.cn Abstract: Optcal fber vbraton s detected by the coherent optcal tme doman reflecton technque. In addton to the vbraton sgnals, the reflected sgnals nclude clutters and noses, whch lead to a hgh lse alarm rate. The cell averagng constant lse alarm rate algorthm has a hgh computng speed, but ts detecton performance wll be declned n nonhomogeneous envronments such as multple targets. The order statstcs constant lse alarm rate algorthm has a dstnct advantage n multple target envronments, but t has a lower computng speed. An ntellgent two-level detecton algorthm s presented based on cell averagng constant lse alarm rate and order statstcs constant lse alarm rate whch work n seral way, and the detecton speed of cell averagng constant lse alarm rate and performance of order statstcs constant lse alarm rate are conserved, respectvely. Through the adaptve selecton, the cell averagng s appled n homogeneous envronments, and the two-level detecton algorthm s employed n nonhomogeneous envronments. Our Monte Carlo smulaton results demonstrate that consderng dfferent sgnal nose ratos, the proposed algorthm gves better detecton probablty than that of order statstcs. Keywords: Optcal fber vbraton, the adaptve selecton, Monte Carlo smulaton, two-level detecton Ctaton: Fukun BI, uecong RE, Hongquan QU, and Ruqng JIAG, A Two-Level Detecton Algorthm for Optcal Fber Vbraton, Photonc Sensors, 05, 5(3): 84 88.. Introducton Optcal fber vbraton can be detected by the coherent optcal tme doman reflecton technque whch employs coherent detecton [], and the weak backscatterng sgnal can be extracted effectvely. Besdes vbraton, the reflected sgnals nclude clutters and noses, whch lead to a hgh lse alarm rate. Constant lse alarm rate (CFAR) detecton nvolves the estmaton of the parameters of the local clutter and the settng of a threshold for decson so that a constant lse alarm probablty (P ) s guaranteed for all values of unknown clutter parameters. A large number of CFAR detectors have been proposed wth dfferent local statstcs of the background clutter [ 4]. The cell averagng (CA) [5] CFAR s the optmum CFAR algorthm n a homogeneous background, compared wth CA-CFAR, the order statstcs (OS) [6] CFAR processor has some detecton wastage n homogenous envronments, but has a dstnct advantage n multple target envronments. However, the real-tme performance cannot be guaranteed, because of takng a long tme to rank. Consderng the development of the CFAR detector, there are plenty of researches tryng to combne them so as to utlze the advantages of dfferent methods and balance the detecton algorthm performance n the homogeneous backgrounds and nonhomogeneous envronments. Receved: 5 May 05 / Revsed verson: 9 June 05 The Author(s) 05. Ths artcle s publshed wth open access at Sprngerlnk.com DOI: 0.007/s330-05-063-y Artcle type: Regular
Fukun BI et al.: A Two-Level Detecton Algorthm for Optcal Fber Vbraton 85 Mean of order statstcs and cell averagng (MOSCA) has been proposed n [7], ordered statstcs (OS)-cell-averagng (CA)-greatest-of selecton (GO) formed OSCAGO was presented n [8, 9], and ordered statstcs (OS)-cell-averagng (CA)-smallest-of selecton (SO) formed OSCASO was proposed n [9]. The key of these methods s that they use OS parametrc estmaton n the left sldng wndow and CA estmaton separately n the rght sldng wndow, then use the sum of estmaton of the leadng and laggng sldng wndow as the estmate of the total power level. By usng the combned algorthm, the tme for sortng samples s only the half of OS. Based on varablty ndex () CFAR [0], the modfed algorthm was proposed n [ 3]. These methods utlze a background estmaton algorthm whch s a composte of the CA-CFAR, SO-CFAR, and GO-CFAR approaches, and take advantage of the excellent homogeneous envronment performance. However, these algorthms are complex and have a low effcency. The above detecton algorthms need to be detected only once, whch cannot balance multple problems. For these problems that CA-CFAR exhbts severe performance degradaton n the presence of multple targets and the OS-CFAR costs long tme for sortng, an adaptve CFAR s frstly proposed n ths paper. In ths algorthm, the homogenety of background s estmated before detecton. When the background s judged as homogeneous, CA-CFAR s appled. On the other hand, CA-OS-CFAR s used. For the CA-OS, the frst level detecton s CA-CFAR wth a two-dmensonal column wndow to mprove the detectng speed and reduce the data to the next level detecton. The second level detecton, OS-CFAR, should be used to detect the outcome. In ths method, the detecton speed of CA-CFAR and performance of OS-CFAR are conserved, respectvely. Fnally, the performance s analyzed by Monte Carlo smulaton, so that the feasblty and the avalablty can be proved.. Prncple of adaptve selecton detecton The CA-CFAR processor sets the threshold by usng reference wndows (also called as sldng wndows n [4]) to estmate local statstcs of the background. In ths paper, a two-dmensonal column wndow proposed n [5] s employed. The OS-CAFR processor sets the threshold by the kth ordered value after rankng accordng to the ncreasng magntude. The detecton schematc s shown n Fg.. Square Law Detector Input Samples L L Ln UP UP D UP UP R R Rn u Z=x(k) Background Estmaton Selecton Logc K CA-CFAR Detecton Result CA-CFAR Sort and Select k-th cell TOS / reference cells Detecton cell Protect cells Calculate &Sum OS-CFAR K u CA-CFAR Fnal Detecton Result Fnal Detecton Result / reference cells Fg. Schematcs of adaptve detecton. For the background estmaton selecton logc, the -CFAR s [0] method s employed. For mplementaton purposes, the smplfed statstc s employed as follows: ( ) () ( ) ( ) where μ s the estmated populaton mean, s the estmated populaton varance, and s the
86 Photonc Sensors arthmetc mean of the cells n a reference wndow. The s compared wth a threshold K to decde f the cells wth whch the s computed are from a homogeneous envronment or from a nonhomogeneous envronment usng the followng hypothess test: K Homogeneous K onhomogeneous. For the hypothess test, α 0, gven n (), s defned as the probablty of error such that a homogeneous envronment s classfed as varable 0 P[ K Homogeneous Env.]. () By analyzng the detected sgnals, the n-phase and quadrature sgnals are ndependent, dentcally dstrbuted (IID), Gaussan random processes. Consequently, the envelope ampltude at the output of a square-law detector s an exponentally dstrbuted random varable. Based on the formula (), through Monte Carlo smulaton, f the α 0 and are gven, then K can be calculated as shown n Table. Table K for background estmaton selecton logc. α 0 =0 =0 =30 =40 0..5.440.3864.3497 0.05.896.6750.5796.545 0.0 3.5768 3.608 3.050.954 0.005 3.9389 3.5340 3.70 3.097 0.00 4.769 4.05 3.88 3.5765 0.0005 5.0994 4.56 4.0887 3.7754 0.000 5.950 5.3367 4.6973 4.3595 For CA-CFAR, accordng to [6], t can be known that P T (3) where P s the probablty of lse alarm, s the length of the reference wndow, and T s the scale ctor. Whle detectng by CA-CFAR, the number of reference cells s = c d, that s the product of the length of reference cells c and the length of tme dmenson d wth usng the D column wndow. The threshold coeffcent of the frst level detecton s shown as follows: cd u cd P. (4) For OS-CFAR, the probablty of lse alarm s gven by [5] k! u k P = = k u! (5) k+ u + k. k u + Accordng to the ncreasng magntude, the ampltude values taken from the reference wndow are rank-ordered, and the kth ordered value s selected as the mean level statstc estmaton. For a P, the threshold coeffcent can be computed teratvely from (5) whle the reference wndow sze and the order number k already have been gven. By CA-CFAR detecton, the probablty densty functon of the data s as follows: y f y y exp( ) dy uy (6) y ( ) y exp( ). ( ) For the resultant probablty of lse alarm, t can be calculated by the followng equaton: P fz ( z) fy y dydz 0 uz (7) where, based on [6], f Z (z) s defned as follows: k k z/ z/ k f Z z e e k. (8) Therefore, the resultant probablty of lse alarm s as follows: P fz ( z) fy y dydz 0 uz (9) u ( ) f ( z) y exp( y) dydz. ( )! Z 0 u z Because t s dffcult to analyze the relatonshp between two thresholds and the resultant probablty of lse alarm, so the numercal approxmaton by the Monte-Carlo experment s employed. Only the data crossed both the frst level detecton threshold gven by CA-CFAR and the
Fukun BI et al.: A Two-Level Detecton Algorthm for Optcal Fber Vbraton 87 second level detecton threshold gven by OS-CFAR can be detected by usng the two-level CFAR detecton algorthm. Therefore, the practcal lse alarm rate s lower than the set lse alarm rate n ths way. Because the analytcal method s dffcult to mplement, so Monte-Carlo smulaton s employed, and the frst threshold coeffcents u and the second threshold coeffcents u should be multpled by coeffcents α and α so as to acheve the set lse alarm rate, respectvely. In ths paper, the CA-CFAR, OS-CFAR, and CA-OS-CFAR are proposed to detect the same data fle, respectvely. The lse alarm tme s gven that T =5 mn, based on the gven relatonshp between the lse alarm rate and tme by (0): P. (0) T In our system, the pulse wdth s τ = 6 ms, and a gven P s 6/(5 60 000) = 5.33 0 5. The Monte-Carlo trals need to be mplemented by 0000 tmes to choose the value of α and α. From the trals, when α =0.9 and α =0.9, the three lse alarm rates are shown n Table, respectvely. Table P comparson for three knds of CFAR n homogeneous envronments. CFAR P CA 5.356*0 5 OS 5.305*0 5 CA-OS 5.359*0 5 From Table, the actual lse alarm rate s close to the set value, therefore, the two coeffcents are both chosen as 0.9. For the frst level detecton, the arthmetc speed ncreases by usng a D slp wndow, then the least amount of data s detected by the second level detecton. After two-level detecton, the nterference of the nterferng targets decreases, and the detecton speed of CA-CFAR and performance of OS-CFAR are conserved, respectvely. As shown n Table, the same data are carred out by OS-CFAR, CA-CFAR, and CA-OS-CFAR, respectvely, and the tme taken by the experments s shown n Table 3. Table 3 Executon tme comparson for three knds of CFAR detecton algorthm. CFAR 0 0 30 40 50 CA 4.5786 4.048 4.4747 4.604 4.380 CA-OS 4.54096 4.404 4.4973 4.50570 4.47693 OS.8978.599.689.9536.8496 From Table 3, t can be known that the speed of CA-CFAR wth the two-dmensonal column wndow s the stest, and the speed of OS-CFAR s the slowest. Compared wth OS-CFAR, the speed s st about three tmes, and t s ster than that of the algorthm of combned by CA and OS proposed n [7 9]. 3. Analyss of performance The detecton performance of the presented detecton algorthm and OS-CFAR algorthm are analyzed by usng Monte-Carlo smulaton. The length of reference cell s =40, and the gven lse alarm rate s P = 5.33*0 5, For the OS-CFAR, CA-OS-CFAR, and the presented algorthm, the order number k=30. The performance curves are gven n Fg. whle only one target exsts n the reference wndow. Detecton probablty-pd.0 0.8 0.6 0.4 0. Presented algorthm CA-OS-CFAR OS-CFAR 0 4 6 8 0 SR (db) Fg. Detecton probablty comparson of OS-CFAR and CA-OS-CFAR n dfferent sgnal nose ratos (SRs). From the performance curves shown n Fg., the performance of the presented detecton algorthm s much better than that of CA-OS and OS-CFAR whle one target exsts n the reference wndow.
88 Photonc Sensors 4. Conclusons For sgnals detected by the COTDR technque, a research by usng the CFAR detecton algorthm to decrease the lse alarm rate of detecton sgnals s presented. The CA-CFAR algorthm exhbts severe performance degradaton n the presence of multple targets, and the OS-CFAR algorthm costs long tme for sortng. To overcome these problems, an adaptve CFAR algorthm based on ordered data varablty has been proposed. It does not requre any pror nformaton about the envronments, whch s a choce between CA-CFAR and the two-level CFAR detecton algorthm ncludng CA-CFAR and OS-CFAR whch work n seral way, and the detecton speed of CA-CFAR and performance of OS-CFAR are conserved, respectvely. In ths algorthm, the relatonshp of two threshold coeffcents s determned by Monte-Carlo smulaton, and the relatve formulas haven t been derved. Further research wll be needed to derve the detaled formulas for calculatng threshold coeffcents. Acknowledgment Ths work s supported by Scentfc pre-research foundaton of orth Chna Unversty of Technology and General project of scence and technology program of Bejng Educaton Commsson. Open Access Ths artcle s dstrbuted under the terms of the Creatve Commons Attrbuton Lcense whch permts any use, dstrbuton, and reproducton n any medum, provded the orgnal author(s) and source are credted. References []. L, H. Lang, W. u, and. Zhang, Comparson of characterstcs of commonly-used dstrbuted optcal fber sensors, Optcal Communcaton Technology, 007, 3(5): 4 8. [] D. J. Crsp, The state-of-the-art n shp detecton n synthetc aperture radar magery. Australa: Defence Scence and Technology Organsaton, 004. [3] A. Pourmottagh, M. R. Taban, and S. A. Gazor, CFAR detector n a nonhomogenous Webull clutter, IEEE Transactons on Aerospace and Electronc Systems, 0, 48(): 747 758. [4] J. Lu, Z. Zhang, Y. Yang, and H. Lu, A CFAR adaptve subspace detector for frst-order or second-order Gaussan sgnals based on a sngle observaton, IEEE Transactons on Sgnal Processng, 0, 59(): 56 540. [5] H. M. Fnn and R. S. Johnson, Adaptve detecton mode wth threshold control as a functon of spatally sampled clutter level estmates, RCA Revew, 968, 9(3): 44 464. [6] H. Rohlng, Radar CFAR thresholdng n clutter and multple target stuatons, IEEE Transactons on Aerospace and Electronc Systems, 983, 9(3): 608 6. [7] Y. He, J. Guan, Y. Peng, and D. Lu, A new CFAR detector based on order statstc and cell averagng, n Conference on CIE 996 Internatonal Radar, Bejng, pp. 06 08, 996. [8] Y. He and J. Guan, A new CFAR detector wth greatest of selecton, n Conference on Radar IEEE 995 Internatonal, Alexandra, USA, pp. 589 59, 995. [9] Y. He and J. Guan, Two new CFAR detectors based on greatest of and smallest of selecton, Systems Engneerng and Electroncs, 995, 7(7): 6 6. [0] M. E. Smth and P. K. Varshney, Intellgent CFAR processor based on data varablty, IEEE Transactons on Aerospace and Electronc Systems, 000, 36(3): 837 847. [] C. Hao, C. Hou, and W. Wang, Dstrbuted CFAR detecton based on modfed -CFAR algorthm, Journal of System Smulaton, 007, 9(4): 830 83. [] C. u, T. Jan, Y. He, and. Gu, An mproved -CFAR detector, Sgnal Processng, 0, 7(6): 96 93. [3] H. Yu, J. Tao, and L. An, -CFAR detector based on censored mean level, Modern Defence Technology, 03, 4(4): 35 40. [4] G. Gao, L. Lu, L. Zhao, G. Sh, and G. Kuang, An adaptve and st CFAR algorthm based on automatc censorng for target detecton n hgh-resoluton SAR mages, IEEE Transactons on Geoscence and Remote Sensng, 009, 47(6): 685 697. [5] Q. Pan and F. L, Fast algorthm of target detecton for termnal gudance radar, Gudance & Fuze, 007, 8(): 6 9. [6] P. P. Gandh and S. A. Kassam, Analyss of CFAR processors n nonhomogeneous background, IEEE Transactons on Aerospace and Electronc Systems, 988, 4(4): 47 445.