A LFM Interference Suppression Scheme Based on FRFT and Subspace Projection

Transcription

1 teratoal Joural of Emergg Egeerg esearch ad Techology Volume 3, ssue 6, Jue 15, PP SS (Prt) & SS (Ole) A LF terferece Suppresso Scheme Based o FFT ad Subspace Projecto Xg ZOU 1 1 Shagha sttute of satellte egeerg, Shagha 4, Cha ABSTACT The lear frequecy modulated (LF) terferece s becomg more ad more serous radar, GPS ad other commucato felds. Cosder the good tme-frequecy aggregatveess of Fractoal Fourer Trasform (FFT) ad favourable at-jammg performace of subspace projecto terferece suppresso (SPS), ths paper proposes a LF terferece Suppresso Scheme Based o FFT ad Subspace Projecto. The smulato result proves the proposed scheme ca acheve good LF terferece suppressg performace. Keywords: lear frequecy modulated sgal, SPS, FFT TODUCTO owadays, GPS s extremely useful may mltary ad cvl areas. owever, real applcatos, GPS sgals are ofte dsturbed by varous kds of terfereces. The mmum power for GPS sgals s -163dBW whe reachg the groud whch made GPS sgals vulerable [1]. Thus, the ma challege recevg GPS sgals s the suppresso of terfereces. recet years, the effect caused by ostatoary terfereces o GPS has become a hotspot. As a typcal ostatoary terferece, lear frequecy modulated (LF) sgals have the characterstc of tme-varyg frequecy []. ormally, the jammg effect caused by LF terferece s serous tha that caused by statoary terferece []. owever, Fourer Trasform (FT) ca hardly deal wth ostatoary terferece, especally LF terferece. order to fx ths problem, umbers of tme-frequecy aalyss methods are uder study, for stace Wer-Vlle dstrbuto [3] (WVD), Short-Tme Fourer Trasform [4] (STFT) ad Fractoal Fourer Trasform (FFT). Due to the exstece of cross-term WVD ad the selecto of wdow fucto STFT [5], both tmefrequecy aalyss methods have ecoutered ther dsadvatages. cotrast, FFT has lower complexty as well as takg fully advatage of the tme-frequecy aggregatveess. O the other had, space-tme adaptve processg (STAP) s also a mportat at-jammg method [6]. STAP ca be acheved may ways ad subspace projecto terferece suppresso (SPS) s oe of them [7]. Ths paper proposes a LF terferece suppresso scheme based o FFT ad a mproved SPS algorthm. The scheme ca take advatage of both tme-frequecy sythess ad space-tme sythess. The smulato result proves the proposed scheme ca acheve good LF terferece suppressg performace. TE PCPLE OF FFT w v u t Fgure1. The prcple of FFT *Address for correspodece: zouxgs@16.com teratoal Joural of Emergg Egeerg esearch ad Techology V3 6 Jue

2 Xg ZOU A LF terferece Suppresso Scheme Based o FFT ad Subspace Projecto 198, amas proposed a dsparate Fourer trasform form, amely FFT [8]. The FFT of a sgal ca be cosdered as a atclockwse rotato from the tme axs to the axs wth a rotato agle. ormally, the axs s called the fractoal Fourer doma. The prcple ca be clearly expressed Fg.1. The FFT of a sgal xt () ca be defed as X p( u) x( t) K p( u, t) dt (1) j [( t ) cot ut csc ] 1 cot, j e K ( u, t) ( t u), p ( t u), ( 1) () K u t s the core fucto. p s the order of the trasform ad p /. ote that f p 1, where p (, ) amely / expressed as j() t e t j ( ft ), the FFT reduces to covetoal Fourer trasform. A typcal LF sgal ca be where f s the tal frequecy ad s the sweep rate. The most mportat factor for FFT to elmate the LF terferece s to estmate f ad. Wheever f ad s estmated, the LF terferece ca be recostructed. SUBSPACE POJECTO The Basc Prcple of Subspace Projecto Cosder the case of GPS sgal corrupted by LF terferece ad ose. The receved sgal ca be wrtte as X ( ) S( ) ( ) ( ) S, ( ) ad ( ) ( ) stads for GPS sgal, terferece ad ose, respectvely. ormally, GPS sgal, terferece ad ose are depedet from each other. Thus, the covarace matrx of the receved sgal s E X ( ) X ( ) X S Where S,, stads for the covarace matrx of GPS sgal, terferece ad ose. The deftos of these three parameters are as follows: E ( ) ( ) S S S E ( ) ( ) E ( ) ( ) (6) (3) (4) (5) eawhle,, s the varace of the ose, s a ut matrx wth the order of. Because X s a postve defte matrx, the egevalue of r r1 X ca be wrtte as: The subspace of the terferece ad sgal s Q q, q,..., q S 1 s Q q, q,..., q 1 formula. The orthogoal complemetary space 158 teratoal Joural of Emergg Egeerg esearch ad Techology V3 6 Jue 15 (7) ad the subspace of the terferece Q ca be deduced by the followg

3 Xg ZOU A LF terferece Suppresso Scheme Based o FFT ad Subspace Projecto Q Q Q The the receved sgal s projected to Q. Thus the output ca be wrtte as (8) Y( ) Q X ( ) Q ( X ( ) ( )) S Theoretcally, accordg to the formula (9), the terferece s absolutely elmated. Weghtg Processg Due to the vast terfereces, the fully elmato of the terferece ca't be realzed. We propose a weghtg operato to dspose the output Y. ( ) Suppose the weght coeffcet s wrtte as: W 1 C Z W Y ( ) W Q X ( ) W Q ( X ( ) ( )) S The choose of W W ca be gaed accordg to S crtero. S ( ) ( ) E W Q X E W Q Y arg max arg max E W Q ( ) ( ) E W Q (9). After weghtg operato, the output sgal ca be Let sk ad S stad for GPS sgal ad ts space-tme drecto vector. The Spread spectrum sequece cycle L 13. Defe q [ s(1), s(),..., s( L)] T S, after dspreadg, (1) (11) Z q Y ( ) z z The S ca be defed as s (1) P L 1 E ( z ) s 1 S Ez ( ) ad stad for the correlato coeffcet of the space-tme doma for the ferece. eawhle, a seres GPS data cludes Spread spectrum cycle, thus (13) Ez ( ) z 1 Thus, Substtutg (14) to (13), we obta formula as follows (14) L S L P 1 1 P L / Where L / stads for the S uder deal codto, 1 1 stads for the data loss durg the processg. After weghtg processg, the output S turs to be: S W L L 1 1 P Compare formula (16) to formula (15), the weghtg processg helps to mprove 1logW db. eawhle the tradtoal subspace projecto oly mproves 1log db. teratoal Joural of Emergg Egeerg esearch ad Techology V3 6 Jue (15) (16)

4 Xg ZOU A LF terferece Suppresso Scheme Based o FFT ad Subspace Projecto Jot terferece Suppresso Accordg to the FFT ad weghtg subspace projecto, we propose a jot terferece suppresso method. Because FFT has good eergy aggregato performace for LF terferece ad weghtg subspace projecto method ca spread the array elemets, the proposed method takes advatage of both ways. The schematc dagram of jot terferece suppresso method s show Fg. () Sgal FFT terferece ebuldg terferece subspace of space-tme doma Orthogoal projecto matrx of terferece subspace Orthogoal projecto of spacetme subspace Despre adg eceved Space-tme sgal Fgure. Schematc dagram of jot terferece suppresso Thus, the proposed jot terferece suppresso method s summarzed as follows Step1: Take as the depedet varable, ad use t to coduct Cotuous fractoal Fourer trasform so that,u based two-dmesoal surface ca be formed. The, use least mea square crtero to lock the pot that makes the terferece eergy fltered out possble. Step: Accordg to the specfc pot, u, estmate the lth orgal frequecy ad frequecy modulato dex, ad the recostruct the lth sgal. Step3: Costruct the Space-tme terferece steerg vector of the lth sgal based o step. Step4: epeat step ad step3 utl the Space-tme terferece subspace s obtaed. Step5: Buld the Orthogoal projecto matrx, ad project the space-tme receved sgal to the orthogoal subspace of the terferece subspace to obta the terferece suppresso sgal. Step6: Dspread the terferece suppresso sgal, ad after judgmet the desred GPS sgal s obtaed free of terferes. DGTAL SULATO To cofrm the aalyss ad ga more sght to the achevable performace, we provde umercal smulato results ths secto. our smulato, a uform le atea (ULA) wth =5 elemets spaced a half wavelegth s cosdered. The LF terferg source s assumed to have a DOA of -6, wth correspodg terferece-to-ose rato () s 5dB. The presumed desred GPS sgal mpges o the array from drecto =. the examples, the sample covarace matrx s computed based o 51data sapshots, ad all of the followg results are calculated based o 3 ote Carlo expermets. Fgure3. The GPS sgal capture result before processg 16 teratoal Joural of Emergg Egeerg esearch ad Techology V3 6 Jue 15

5 Xg ZOU A LF terferece Suppresso Scheme Based o FFT ad Subspace Projecto Fgure4. The GPS sgal capture result after processg Fgure5. The beam patter comparsos the example, the S s set to be a costat of -db. Fg.3 s the capture result of the receved sgal before the process. Ad Fg.4 s the correspodg capture result after terferece suppresso. t ca be see that obvous peaks occur Fg.3. Ths s because the LF terferes are preset the recever. Whle the sgal ampltude dstrbuto s relatvely flat Fg.4 due to the LF terferece suppressed. Fg.5 shows that the proposed FFT based method ad the jot subspace projecto algorthm form deeper ulls the terferece drecto of -6 tha that of the orgal method. oreover, wth the two proposed methods, the ma lobe of the beam patter becomes arrower ad the sde lobe s much lower. Thus, the proposed methods have much better beam drectvty. addto, the proposed FFT based method s slghtly better tha the jot subspace projecto algorthm. Ufortuately, the orgal method has a poor performace. addto to the beam patter aalyss above, we coduct quattatve aalyss maly from the perspectve of mathematcal statstcs. the smulato, the S vares form -15dB to 5dB. COCLUSO ths work, a LF terferece Suppresso Scheme Based o FFT ad Subspace Projecto s developed. the proposed method, the mproved subspace s combed wth FFT to derve the jot LF terferece suppresso algorthm. Dgtal smulato results prove the proposed scheme ca acheve good LF terferece suppressg performace ad outperforms the other LF terferece suppressg methods. teratoal Joural of Emergg Egeerg esearch ad Techology V3 6 Jue

6 Xg ZOU A LF terferece Suppresso Scheme Based o FFT ad Subspace Projecto EFEECES [1] Zhag Y D, Am G. At-jammg GPS recever wth reduced phase dstortos [J]. Sgal Processg Letters, EEE, 1, 19(1): [] Zhao X, Tao, Deg B, et al. ew methods for fast computato of fractoal Fourer trasform [J]. Daz Xuebao(Acta Electroca Sca), 7, 35(6): [3] Lach S, Am G, Ldsey A, Broadbad terferece excso for software-rado spread-spectrum commucatos usg tme-frequecy dstrbuto sythess, EEE Joural o Selected Areas Commucatos, 1999, 17(4): 74~714 [4] Ouyag X, Am G, Short-tme Fourer trasform recever for ostatoary terferece excso drect sequece spread spectrum commucatos, EEE Trasactos o Sgal Processg, 1, 49(4): 851~863 [5] Q-hu Z Y W, J-log W. LF terferece Suppresso Usg Tme-Frequecy Wdowed Short-Tme Fourer Trasform [J]. Joural of Electrocs & formato Techology, 7, 6: 19. [6]cDoald K F, Costa P J, Fate L, sghts to jammer mtgato va spacetme adaptve processg, Proceedgs of Posto Locato ad avgato Symposum, 6, 13~17 [6] amas V, The fractoal order Fourer trasform ad ts applcato to Quatum mechacs, A Joural of Appled athematcs, 198, 5(3): 41~65 [7] cdoald K F, Costa P J, Fate L, sghts to jammer mtgato va space-tme adaptve processg, Proceedgs of Posto Locato adavgato Symposum, 6, 13~17 [8] uag W, Lu D, Wu, et al. A ovel bld GPS at-jammg algorthm based o subspace techque[c]//sgal Processg, 6 8th teratoal Coferece o. EEE, 6, teratoal Joural of Emergg Egeerg esearch ad Techology V3 6 Jue 15