doi: / Lognormal Distribution Clutter Modeling Based on ZMNL Principle

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1 Re. Téc. Ing. Un. Zula. Vol. 39, Nº 8, - 6, 6 do:.3/ Lognormal Dstrbuton Clutter Modelng Based on ZMNL Prncple Bn Wang*, Xn Song, Fengmng Xn School of Computer and Communcaton Engneerng, Northeastern Unersty at Qnhuangdao, Qnhuangdao 66, Hebe, Chna *Correspondng author(e-mal: wangbnneu@qq.com) Abstract Wth electromagnetc workng enronment becomng more and more complex, how to model and analyze clutter exactly s ery mportant n the radar research. Especally for cognte radar whch combats wth complex enronment, the modelng and generaton of clutter plays a basc role n echo analyss. In ths paper, based on the prncple of zero memory nonlnear (ZMNL) and the characterstcs of Lognormal dstrbuton, we use lnear flter and nonlnear mappng transformaton functon to generate Lognormal dstrbuton clutter. In smulatons, we change samplng frequency and length of the random sequence. The results show that n both clutter ampltude and clutter spectrum, the estmated alue approaches the theoretcal alue. Fnally, a summary of the full paper s presented. Key words: Clutter Modelng, Zero Memory Nonlnear, Cognte Radar.. INTRODUCTION Wth the adancement of modern technology, radar deelops rapdly wth arous needs of people. Howeer, more extense use of electromagnetc spectrum and hgh speed of target wll make electromagnetc enronment become more and more complex. Wth the deelopment of modern radar technology, there s a great demand for nnoate sensors and sensng confguratons based on cuttng-edge technologes, such as waeform dersty, robotcs, and supportng software languages. Present-day systems are ery sophstcated and adanced. More and more modern radar systems are proposed, for example, cognte radar(haykn, 6), MIMO radar(daum and Huang, 9), etc. Modelng clutter accurately can mproe radar detecton performance and prode a realstc smulaton enronment of radar clutter. So t s becomng a hot topc n the research and engneerng feld. A research n the area of bstatc radar clutter modelng s presented. After the bstatc clutter scenaro s defned two land-clutter models, based on a common general geometry are descrbed(pola, Bezousek and Pdanc, 3). Unlke tradtonal sgnal-dependent stochastc models, a new "stochastc transfer functon" approach s presented that results from a fundamental physcs scatterng model(guerc, Bergn, Guerc, Khann and Rangaswamy, 6). An mproed emprcal model for radar sea clutter reflectty s proposed(hansen and Mtal, ). Measurements of urban ground clutter made from the CSIR campus n Pretora, South-Afrca s descrbed. The measurements were made usng a wdeband X-band radar(strydom, Wtt and Cllers,). A model s proposed for generatng low-frequency synthetc aperture radar (SAR) clutter that relates model parameters to physcal characterstcs of the scene(jackson and Moses, 9). A new method of modelng and smulaton of temporal-spatal-correlated (TPC) clutter s proposed, based on the weghted norm n dscrete complex lnear space and a smple matrx transformaton(teng and Dan,). Two-dmensonal exponental correlaton rough surfaces characterzed by textures are combned wth the small-slope approxmaton (SSA) method to comparately study electromagnetc (EM) scatterng features of textured surfaces(we, Zhang, Sun and Yuan, ). Artfcal neural network s used to classfy four common radar clutter models. Clutter models s smulated and ther mportant features lke skewness and kurtoss are extracted(darzkolae, Ebrahmzade and Gholam, 5). In the oboe methods, ether clutter ampltude performance s better or clutter spectrum performance s better. Two performances cannot be acheed at the same tme. In ths paper, based on the prncple of ZMNL and the characterstcs of Lognormal dstrbuton, we uselnear flter and nonlnear mappng transformaton functonto generate Lognormal dstrbuton clutter. Fnally, we compare the generated clutter wth the theoretcal alue n smulatons n both clutter ampltude and clutter spectrum.. COGNITIVE RADARAND ZMNL PRINCIPLE Cognte radar can work n sea leel and ground plane, and the accurate clutter modelng s a ery mportant part n cognte radar. Lofnormal dstrbuton s sutable for the sea clutter wth hgh resoluton and low grazng angle, and ground clutter wth low grazng angle.we make a bref ntroducton to cognte radar.

2 Re. Téc. Ing. Un. Zula. Vol. 39, Nº 8, - 6, 6 Enronment Control Scene Analyzer Feedback Channel Fgure.Basc sgnal-processng cycle n cognte radar. Cognte radar s the next generaton radar system. Fgure s a basc sgnal-processng cycle n cognte radar. Cognte radar has the capablty to obsere and learn from the enronment through radar echo. After analyzng and computng releant nformaton, t operates closed loop and the transmtted waeform wll be adapte. Form fgure, we can conclude that echo analyss s crucal to cognte radar, the bass of whch s accurate modelng and smulaton of clutter. In order to achee objectes more effcently, the waeforms should be adapted n response to pror measurements.especally for cognte radar whch combats wth complex enronment, accurate modelng and smulaton of clutter s more mportant. To smulate radar clutter, we can take computer numercal smulaton based on the physcal model of electromagnetc scatterng theory consderng seeral knds of radar workng enronment, or use radar equaton accordng to specfc radar enronment and parameters. Howeer, the two methods are not often used as a result of the lmtatons. Monte Carlo methods are a broad class of computatonal algorthms that rely on repeated random samplng to obtan numercal results. Ther essental dea s usng randomness to sole problems that mght be determnstc n prncple. They are often used n physcal and mathematcal problems and are most useful when t s dffcult or mpossble to use other approaches. Accordng to statstcal mathematcal model proded by the theoretcal and actual data, the methods of producng correlated random sequence whch has a certan probablty are under nestgaton. At present, the method of SIRP, the method of ZMNL, and the method of SDE are extremely common. SDE method s complex and ts applcaton range s lmted. Ths paper manly researches on the method based on ZMNL prncple. The basc method of ZMNL s to transfer the correlated Gaussan random sequence process to the requred correlated random process by a sort of nonlnear transformaton, whch can be realzed by nonlnear mappng transformaton functon. After selected nonlnear transformaton form through the relatonshp of clutter dstrbuton functon, the correlated characterstcs of Gaussan process before the transformaton can not be optonally desgnated, we should fnd out the transformaton relatonshp between the correlaton functon before and after the transformaton accordng to the concrete transformaton method. The key to ths method s to dere correlaton functon of Gaussan process before the transformaton by the gen non-gaussan process correlated functon. Fgure s prncple dagram of clutter modelng wth ZMNL. wk ( ) s whte Gaussan random process, and zk ( ) has unt arance. H() z s lnear flter, such as Bessel flter. wk ( ) yk ( ) Lnear Flter H(z) Nonlnear Mappng Transformaton Functon zk () Fgure. Prncple dagram of clutter modelng wth ZMNL The step wth the prncple of ZMNL s as follows: () Generate whte Gaussan nose sequence wk ( ). () Make whte Gaussan nose sequence wk ( ) get through a lnear flter H() z, and correlated Gaussan sequence yk ( ) can be obtaned. (3) Choose a type of nonlnear mappng transformaton functon, and correlated sequence ( ) zk wth certan probablty dstrbuton can be obtaned after functon mappng.

3 probablty dstrbuton Re. Téc. Ing. Un. Zula. Vol. 39, Nº 8, - 6, 6 3.GENERATIONOF LOGNORMAL DISTRIBUTION CLUTTER Wth the ncrease of radar resoluton, t s found that the actual clutter has longer tal than Gaussan model. Usng Gaussan model wll makefalse alarm probablty of radar produce large deaton. So Lognormal model s ntroduced. For the sea clutter wth hgh resoluton and low grazng angle, and ground clutter wth low grazng angle, Lognormal model s applcable. When the sea s at the peak of a wae, Lognormal dstrbuton can well smulate clutter data at that tme. When the ground has large reflectors, these reflectors produce many brght peaks and shadows accordng to dfferent angles of obseraton, thus a large range of clutter s generated. Probablty densty dstrbuton functon of Lognormal s ln ( x / c ) x exp[ ] () x Fgure 3 shows the correspondng probablty densty dstrbuton cure. Correspondng dstrbuton functon s ln x c Fln ( x) erfc ( ) () where c s scale parameter, s shape parameter, and erfc() s Cosne error functon..5 σ= σ=..5 σ=.7 σ= σ=.5 σ= clutter ampltude Fgure 3. Probablty densty dstrbuton of Lognormal As s known, random arables n N (,) can be used to generate random arables w whch obey normal dstrbuton N (ln c, ) through lnear transformaton. After w gettng through nonlnear transformaton x exp( w ) (a type of nonlnear mappng transformaton functon), Lognormal dstrbuton wth double parameters can be obtaned. So Lognormal dstrbuton clutter can be generated. n H( z) y w exp x ln c Fgure. Generaton prncple dagram Fgure s generaton prncple dagram of Lognormal dstrbuton clutter. n s a whte Gaussan sequence wth dstrbuton of N (,). y s a correlated Gaussan sequence wth dstrbuton of N (,). j s correlaton coeffcent. x s the ncoherent Lognormal dstrbuton clutter wth correlaton coeffcent S j. We can get the relatonshp between j and S j after derng

4 Re. Téc. Ing. Un. Zula. Vol. 39, Nº 8, - 6, 6 From the formula aboe we can obtan Defne normalzaton transfer functon S j e e j ln[ Sj ( e )] j (3) () H( w) S ( w) / () FT ( ) / () (5) where S u s Fourer transformaton of j.. Accordng to the analyss aboe, the steps of generatng Lognormal dstrbuton clutter are as follows: () Choose the needed PSD Sw ( ) and approprate samplng rate w, and sequence { S } can be obtanedafter samplng from Sw. ( ) () Do IFFT to the sequence { S n }, and the requred correlaton coeffcent sequence Sj can be obtaned. (3) Compute correlaton coeffcent sequence j and generate correlated Gaussan sequence { y n }. () Make nonlnear transformaton exp( ) (a type of nonlnear mappng transformaton functon) n y through the parameters ln c and, and correlated Lognormal dstrbuton sequence { x } can be obtaned..simulations In ths secton, n order to erfy the performance of the proposed algorthm, we wll compare the estmated alue from the genarated clutter wth the theoretcal alue. Smulaton condtons are set as follows. The length of the random sequence s 89 ponts. Samplng frequency fs Hz, shape parameter.8, scale parameter c.5. Smulaton results are n fgure 5 to fgure 8. u n Fgure 5. Independent non-correlated Gaussan random sequence Fgure 6. Lognormal dstrbuton clutter 3

5 power spectrum densty probablty densty Re. Téc. Ing. Un. Zula. Vol. 39, Nº 8, - 6, 6 Fgure 5 s ndependent non-correlated Gaussan random sequence, and fgure 6 s Lognormal dstrbuton clutter obtaned n smulaton. The changes of sequences before and after the smulaton can be seen through fgure 5 and fgure estmated alue theoretcal alue clutter ampltude Fgure 7. Dstrbuton of clutter ampltude.9 estmated alue theoretcal alue frequency/hz Fgure 8. Clutter spectrum Fgure 7 shows the ampltude dstrbuton comparson between the estmated alue from the generated clutter and the theoretcalalue. We can see that both are bascally consstent wth each other. Fgure 8 shows that n the aspect of clutter spectrum, the estmated alue approaches the theoretcal alue. From the aspect of approach degree, the second-order characterstcs of generated clutter are better than frst-order characterstcsof generated clutter. In order to make a comparson between dfferent parameters, we smulate another experment. The length of the random sequence s 638 ponts. Samplng frequency fs Hz. Shape parameter and scale parameter hae no changes. Fgure 9 to fgure shows the smulaton results of the second experment Fgure 9. Independent non-correlated Gaussan random sequence n the second experment

6 power spectrum densty probablty densty Re. Téc. Ing. Un. Zula. Vol. 39, Nº 8, - 6, Fgure. Lognormal dstrbuton cluttern the second experment.7.6 estmated alue theoretcal alue clutter ampltude Fgure. Dstrbuton of clutter ampltuden the second experment.9 estmated alue theoretcal alue frequency/hz Fgure. Clutter spectrumn the second experment In the second experment,we can get a smlar concluson as n the frst experment. Wth the ncrease of samplng frequency and length of the random sequence,estmated alue n clutter ampltude and clutter spectrum approaches the theoretcal alue. Contrast fgure 7 wth fgure and fgure 8 wth fgure, t can be concluded that wth the ncrease of samplng frequency and length of the random sequence, the estmated alue n the second experment s further away from the theoretcal alue than the estmated alue n the frst experment. 5.CONCLUSIONS In ths paper, based on the prncple of ZMNL and the characterstcs of Lognormal dstrbuton, weuse lnear flter and nonlnear mappng transformaton functonto generatelognormal dstrbuton clutter.smulaton results show that n both clutter ampltude and clutter spectrum, the estmated alue approaches the theoretcal alue. Moreoer, from the aspect ofapproach degree, the second-order characterstcs of generated clutter are 5

7 Re. Téc. Ing. Un. Zula. Vol. 39, Nº 8, - 6, 6 better than frst-order characterstcs. The estmated alue s more closer to the theoretcal alue wth the decrease of samplng frequency and length of the random sequence.so n better to obtan better performance, samplng frequency and length of the random sequence should be chosen as small as possble. Acknowledgements Ths work was supported by the Natonal Natural Scence Foundaton of Chna(No. 6367). REFERENCES Darzkolae,M. A., Ebrahmzade,A. A., GholamE. (5) Classfcaton of radar clutters wth Artfcal Neural Network,Proc. Conf. on Knowledge-Based Engneerng and Innoaton,pp Daum,F., Huang,J. (9) MIMO radar: Snake ol or good dea?,ieee Aerospace and Electronc Systems Magazne, (5), pp. 8-. Guerc,J. R., Bergn,J. S., Guerc,R. J., KhannM.,RangaswamyM. (6) A new MIMO clutter model for cognte radar, Proc.Conf. onieee Radar, pp. -6. Hansen, V. G., Mtal,R. () An mproed emprcal model for radar sea clutter reflectty, IEEE Aerospace and Electronc Systems, 8(), pp Haykn,S. (6) Cognte radar: a way of the future, IEEE Sgnal Processng Magazne, 3(), pp. 3-. Jackson, J. A., Moses,R. L. (9) A model for generatng synthetc VHF SAR forest clutter mages, IEEE Aerospace and Electronc Systems, 5(3), pp Pola, M., Bezousek,P., Pdanc, J. (3) Model comparson of bstatc radar clutter,proc. Conf. on Mcrowae Technques, pp Strydom,J. J., Wtt, J. J., Cllers,J. E. () Hgh range resoluton X-band urban radar clutter model for a DRFM-based hardware n the loop radar enronment smulator,proc.conf. oninternatonal Radar, pp Teng, L., Dan, H. () Model for spatal-correlated clutter and ts applcaton to temporal-spatal correlated clutter, IET Mcrowaes, Antennas & Propagaton, 5(3), pp We,P. B., Zhang,M., Sun,R. Q., Yuan,X. F. () Scatterng Studes for Two-Dmensonal Exponental Correlaton Textured Rough Surfaces Usng Small-Slope Approxmaton Method,IEEE Transactons on Geoscence and Remote Sensng, 5(9), pp