Beampattern Synthesis for Frequency Diverse Array Based on Time-Modulated Double Parameters Approach

Transcription

1 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: Beampatten Synthess fo Fequeny Dvese Aay Based on Tme-Modulated Double Paametes Appoah Tong Mu, Yaolang Song, Zhonghan Wang Shool of Eleton and Optal Engneeng, Nanjng Unvesty of Sene and Tehnology, Nanjng, Chna. Abstat The bas fequeny dvese aay (FDA) usng lnealy neasng fequeny nements geneates a ange-angle dependent beampatten. Howeve, t s oupled n ange and angle dmensons and s also peod n ange and tme, makng ts applatons lmted. In ths pape, a novel FDA beampatten synthess appoah s poposed utlzng the tme-modulated double paametes based on the haos sequene. The hp sgnal mehansm s used nstead of the sngle-fequeny sgnal mehansm. Meanwhle, the mult-ae ahtetue s used fo ange-angle deouplng. Satsfatoy tme-nvaant ange-angle beampatten an be syntheszed fo both sngle and multple tagets loatons. Smulaton esults show the effetveness of the poposed FDA sheme. Futhemoe, ompaatve study wth the exstng tehnology ndates that the poposed appoah an povde bette pefomane n spatal fousng and sde-lobe suppessng. Index Tems beampatten synthess, haos sequene, fequeny dvese aay, tme modulaton. I. INTRODUCTION Fst poposed n [1] and [2], fequeny dvese aay (FDA) tehnology geneates beampattens that depend on the ange, angle and tme by ntodung a tny fequeny offset among the aay elements. In a onventonal aay, the beampatten an be foused to the desed angle utlzng the pogessve phase shft (PPS) between the elements [3-4], but the beam steeng s fxed n an angle fo all ange ells. The FDA tansmts the beampatten ove the desed ange and angle thus t an suppess ange-dependent ntefeenes and luttes whh s desable n ada applatons. Besdes, the FDA povdes new degees of feedom n the ange, angle and tme fo desgnng the aay fato, whh enables the beam to san wthout the need of phase shftes o mehanal steeng [5]. Theefoe the FDA an offe muh apabltes suh as synthet apetue ada magng [6], auto sannng [7] and loalzaton of tagets [8], et. In the bas FDA, the lnealy neasng fequeny nements ae appled and esult n a beampatten oupled n ange and angle domans, whh has a S shape [5]. Ths haatest lmts FDA s applatons n unambguously loalzng tagets n ange-angle dmenson [9]. Moeove, the bas FDA beampatten s peod n ange and tme, deteoatng the esultng sgnal-to- Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

2 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: ntefeene-plus-nose ato (SINR) and taget detetablty. The ange and tme peodty of FDA beampatten s analyzed n [10], and the ange-angle oupled beamfomng has been nvestgated usng fequeny-dvese hps n [11]. A logathm fequeny offset sheme s poposed n [12] whh an deouple the beampatten and elmnate the ange peodty. Howeve, ts edued angeangle esoluton and enhaned sde-lobes may not be aeptable fo most applatons. A FDA system based on mult-ae fequenes wth logathm fequeny offset s poposed n [13], whh eques addtonal onvex optmzaton algothm fo syntheszng the omplex element weghts to geneate dot-shaped beampattens. Patulaly, the beampattens geneated by these appoahes ae tme-vaant, ausng the loss n SINR and seously affetng the taget detetablty beause of extemely shot duaton of the beam llumnaton at the taget poston. Tme-ndependent beampatten based on tme-modulated fequeny offset (TMFO) s poposed n [14], but the ange peodty s stll not elmnated. Then, tme-nvaant beampatten wth a sngle maxmum at the taget loaton s aheved n [15] usng the tme-modulated logathmally neasng fequeny offset (TMLFO). Also n [15], tme-modulated optmzed fequeny offset (TMOFO) s developed fo obtanng bette spatal fousng pefomane. Reently, mult-ae ahtetue ombned wth nonlnea dstbuted fequeny offset s poposed n [16] and penl-shaped tme-nvaant beampatten s aheved. The exstng eseah ae based on the sngle-fequeny sgnal mehansm and thus only sngle paamete modulaton s onsdeed, namely the fequeny offset modulaton. In ths pape, a novel FDA beampatten synthess appoah s poposed based on the hp sgnal mehansm whee fequeny offset as well as hp onstant modulaton ae both onsdeed. The Logst mappng haos sequene s appled fo the double paamete modulaton, and the mult-ae ahtetue s employed to deouple the beampatten n ange and angle dmensons. Tme-nvaant beampatten at the desed loaton an be aheved by the poposed appoah. Also, the tme wndow veson of the poposed FDA s used fo multple tagets senao. Smulaton expements ae aed out to evaluate the pefomane of the poposed appoah. The esults ae also ompaed wth the Mult- Cae-FDA (MC-FDA) eently poposed n [16] and t tuned out that the poposed FDA an povde mpoved spatal fousng pefomane wth moe effetve sde-lobe suppesson smultaneously. Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

3 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: II. TIME-MODULATED DOUBLE-PARAMETER FDA A. Sgnal model Consde an antenna aay of M dental tansmt elements wth unfom spang d. Fg. 1. Dagam of the poposed FDA. As shown n Fg. 1, P s an obsevaton pont n the fa feld, and m s the dstane fom P to the m th element. Mult-ae famewok s onsdeed n the system thus eah tansmt element emts a weghted summaton of a sees of bas sgnals. Unlke the pevous eseah, the hp sgnal nstead of the sngle-fequeny sgnal s used hee as the ae. Suppose the numbe of aes at eah element s N, then the sgnal tansmtted fom the m th element s N j2 ( fn, mt un, mt ) 2 n, m (1) n0 x ( t) a e, 0 t T, 0 m M 1 m whee a, f and u ae the omplex weght used fo steeng the maxmum of the beampatten at the taget loaton, adaton fequeny and hp onstant fo the n th ae at the m th element, espetvely. T s the duaton of the tansmtted pulse sgnal. The fequeny omponent f an be expessed as fn, m f0 f n, m, 0 n N 1, 0 m M 1 (2) whee f 0 s the efeene fequeny and f s the fequeny offset. Theefoe, the oveall sgnal obseved at an abtay fa feld pont P (, ) s M1N1 m0 n0 m 1 m 2 j2 [ fn, m ( t ) un, m ( t ) ] 2 X ( t,, ) a e (3) whee s the speed of lght n fee spae, and ae the ange and azmuth angle fom the pont to the fst element espetvely, and m s the dstane between the pont and the th Takng the fa feld appoxmaton nto onsdeaton yelds Substtutng (2) and (4) nto (3) yelds m element. md sn (4) m Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

4 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: M1N1 X ( t,, ) a e m0 n0 md sn 1 md sn 2 j2 [( f0 fn, m )( t ) un, m ( t ) ] 2 2( ) sn sn fnm, md sn t md 1 2 sn ( ) M N f md md j f t j2 { fn, m ( t ) un, m[( t ) ( ) ]} 2 m0 n0 e a e In patal FDA system, the fequeny offset satsfes (5) max{ f } f (6) 0 fnm, md sn thus the tem an be negleted fom (5). Besdes, the tem md sn ( ) 2 2( t ) md sn n (5) an also be gnoed beause 1 1 md sn unm, ( ) 2 Theefoe, (5) an be futhe appoxmated as f md sn 2 (7) u, f, 2 n m n m( t ) 2( t ) md sn (8) 0 sn ( ) M N f md j f t j2 [ fn, m ( t ) un, m ( t ) ] 2 m0 n0 X ( t,, ) e a e (9) Then the oespondng aay fato (AF) an be obtaned M1N1 m0 n0 f0md sn 1 2 j2 [ fn, m ( t ) un, m ( t ) ] 2 AF( t,, ) a e (10) B. Beampatten synthess based on the poposed FDA Lnea nemental fequeny offset makes the FDA beampatten peod n ange and tme, whle nonlnea dstbuted tme-modulated fequeny offset an esult n tme-nvaant spatal fousng beampatten. In ode to elmnate the tme-vaant and ange-peod haatests of the beampatten, and also mpove the pefomane of the FDA system n spatal fousng and sde-lobe suppessng, a new sheme based on the tme-dependent fequeny offset and hp onstant s desgned, namely the Tme-Modulated Double-Paamete FDA (TMDP-FDA). Suppose the taget poston s ( 0, 0), and fo the n th ae at the m th element, the fequeny offset and hp onstant ae defned as u f pnm, = f 0 t = u 2q 0 2 ( t ) (11) (12) Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

5 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: espetvely wth t [0, T] and T. f and u ae the fequeny offset and hp onstant ontollng oeffents espetvely. Fo eah element, p and q ae geneated by the haos sequene based on the Logst mappng and they ae gven by p p0, m, n 0 4 pn 1, m (1 pn 1, m ),1 n N 1 (13) q q0, m, n 0 4 qn 1, m (1 qn 1, m),1 n N 1 (14) whee p 0,m and q 0,m ae the ntal values fo the m th element and satsfy 0 < p0, m < 1 and 0<q 1 0, m<, espetvely. The tansmt beampatten an be deoupled as ange and angle pats by applyng the mult-ae ahtetue [16], theefoe the esultng aay fato an be expessed as M1N1 pn, m 1 2qn, m 2 j2 [ f ( t ) u ( t ) ] f0md sn j2 t ( t ) AF( t,, ) a e a e (15) m0 n0 wth an, m= a a. Obvously, the beampatten value of (15) s maxmum fo t 0, 0, 0. To stee the maxmum at the desed taget poston ( 0, 0), the oespondng omplex weghts ae desgned as f0md sn0 j2 a e (16) j2 ( fpn, m uqn, m ) a e (17) espetvely. Wthout loss of genealty, the tme vaable s set as t 0, and by substtutng (16) and (17) nto (15) the aay fato an be futhe dedued as 2 2, 0, 0 0 (sn sn 0) pn m ( ) qn m ( ) M 1N 1 f md j2 j2 [ f u ] AF(, ) e e (18) m0 n0 Theefoe, the beampatten maxmum s geneated at the desed loaton based on the desgned omplex weghts. C. Beampatten synthess fo multple tagets Fo multple tagets senao, the tme wndow veson of the poposed FDA an be used to geneate multple maxmums at the postons of dffeent tagets. Suppose thee ae I tagets n the spae loated at (, ) espetvely, 1,2,..., I. Then the duaton of sngle tansmt pulse an be unfomly dvded nto I tme wndows, as shown n Fg. 2. Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

6 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: Fg. 2. Dvson of sngle pulse duaton. Dung the th tme wndow, the fequeny offset and hp onstant fo the n th ae at the m th element ae defned as espetvely whee 0 () t s gven by f u pnm, = f 0 () t t = u 2qnm, () t 0 2 ( t ) (19) (20) and ( t) [ ( t t ) ( t t )], t [ t, t ) (21) , t 0 () t (22) 0, t<0 As a esult, by ombnng the tme wndow subdvson wth the hp sgnal mehansm, the soluton fo mult-tagets beampatten synthess s gven by pn, m 1 2qn, m 2 j2 [ f ( t ) u ( t ) ] M1N1 f0md sn 0 ( t) 2 0 ( t) 2 j2 t ( t ) 1 m0 n0 AF ( t,, ) a e a e, t [ t, t ) (23) Smla wth (16) and (17), the omplex weghts fo steeng the maxmum at the th desed taget poston (, ) ae desgned as f0md sn j2 a e (24) j2 ( fpn, m uqn, m ) a e (25) espetvely. It an be seen that the angle omplex weght needs to be hanged fo dffeent subpulses, whle the ange omplex weght emans unhanged dung the total pulse duaton. III. NUMERICAL SIMULATIONS A. Smulaton setup In ths seton, smulaton expements ae aed out to examne the effetveness of the poposed TMDP-FDA. The numeal data ae obtaned by MATLAB R2013b on the PC wth CPU fequeny beng 3.3GHz and RAM beng 8GHz, and the poessng tme fo the beampatten synthess ode of the TMDP-FDA s 5.27 seonds. The smulaton paametes ae set as follows: element numbe s Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

7 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: M 15, ae numbe s N 10, pulse duaton s T 1ms and efeene fequeny s f0 5 GHz. In ode to avod the gatng lobes n angle dmenson, the nteelement spang s set as d. The sope of ange and angle domans ae set as km and 2max{ f } espetvely, and the taget loaton s (500km, 30 ). The fequeny offset and hp onstant ontollng oeffents ae set as f 7 and u 5 espetvely. Two pseudo andom sequenes eah ontanng M values between 0 and 1 ae geneated and stoed to seve as the ntal values of p and q. () Fg. 3. Matx of p, q and () logathm funton. The matx P made up of p and Q made up of q ae depted n Fg. 3 and espetvely. The logathm funton used n MC-FDA fo ontollng the fequeny offset s also shown n Fg. 3 () fo ompason. It an be seen that fo P and Q, the sequene wth espet to eah element s nonlnea, non-monoton, egula and dffeent fom eah othe. As fo Fg. 3 (), the sequene wth espet to eah element s nonlnea, monoton neasng and the same wth eah othe. B. Results and dsussons If the tme s fxed, the beampatten n a 3-D plot n ange and angle domans an be llustated whh ontans the spatal nfomaton of the beampatten. Fg. 4 shows the nomalzed beampatten of the poposed TMDP-FDA when t 0. Fom Fg. 4 t an be seen that a sngle maxmum of the beampatten appeas ght at the desed taget loaton. The ange peodty s elmnated and good ange-angle deouplng s ealzed, ndatng the satsfatoy spatal fousng pefomane of the poposed appoah. Fo analyzng the sde-lobe level (SLL), the geneated beampatten s pojeted nto ange and angle dmensons, as shown n Fg. 4 and (), espetvely. It shows that the peak SLL n both ange and angle dmensons ae below 0.1, ndatng the effetve sde-lobe suppessng pefomane of the poposed method. The esults at t 0 obtaned by the MC-FDA ae depted n Fg. 5. It shows that the MC-FDA an also podue fne spatal fousng beampatten wth low SLL. Howeve, the man-lobe beam wdth n ange dmenson of the TMDP-FDA s naowe, whh means moe enegy an be tansmtted at the taget loaton and taget detetng wth hghe auay an be povded by the poposed FDA. Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

8 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: () Fg. 4. Nomalzed beampatten of the TMDP-FDA n ange-angle dmenson, ange dmenson and () angle dmenson at t 0. () Fg. 5. Nomalzed beampatten of the MC-FDA n ange-angle dmenson, ange dmenson and () angle dmenson at t 0. Next the tme s fxed at t 1ms and the esults of the TMDP-FDA and MC-FDA ae shown n Fg. Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

9 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: and Fg. 7, espetvely. It s obseved that the man-lobe beam wdth n ange dmenson of the two methods both get naowe, and meanwhle, the peak SLL of the TMDP-FDA s stll below 0.1. As fo the MC-FDA, seveal hgh sde-lobes appeas n the ange dmenson and the peak SLL s () Fg. 6. Nomalzed beampatten of the TMDP-FDA n ange-angle dmenson, ange dmenson and () angle dmenson at t 1ms. Fg. 7. Nomalzed beampatten of the MC-FDA n ange-angle dmenson, ange dmenson and () angle dmenson at t 1ms. Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN ()

10 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: In ode to vefy the tme-nvaant haatest of the TMDP-FDA, the beampatten s pojeted nto tme-ange and tme-angle dmensons, as shown n Fg. 8 and, espetvely. It s obseved that the loaton of the beampatten maxmum n both ange and angle dmensons emans unhanged as the tme neases n a pulse duaton. Coespondngly, Fg. 8 () and (d) show the esults of the MC-FDA. Fom Fg. 8 () t an be seen that the numbe and the level of sde-lobes n ange dmenson nease as the tme hanges, whh s not obseved n the TMDP-FDA. In addton, the man-lobe beam wdth n angle dmenson of the two methods ae the same and do not hange wth tme. It s beause the beampatten s totally deoupled as ange and angle by applyng the multae, and the tme modulaton ats only on the ange dmenson. Fo aqung naowe beam wdth n angle dmenson, one an nease the numbe of tansmt elements to enlage the aay apetue. () (d) Fg. 8. Beampatten pojeton on tme-ange dmenson fo TMDP-FDA, tme-angle dmenson fo TMDP-FDA, () tme-ange dmenson fo MC-FDA and (d) tme-angle dmenson fo MC-FDA. Compasons of the man-lobe wdth n ange dmenson fo thee dffeent shemes ae povded n Fg. 9,.e. the TMDP-FDA, the Tme-Modulated Sngle-Paamete FDA (TMSP-FDA) and the MC- FDA. Fg. 9 and show the esult at t 0 and ts amplfed detal, and Fg. 9 () and (d) show the esult at t 1ms and ts amplfed detal. Note that the only dffeene between the TMDP-FDA and TMSP-FDA defned hee s that the latte uses the sngle-fequeny sgnal mehansm thus t ontans only fequeny offset modulaton. The esults show that the use of hp sgnal ombned wth haos sequene modulaton has bette spatal fousng pefomane than the sngle-fequeny Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

11 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: sgnal ombned wth haos sequene modulaton, both of whh ae supeo to the logathm funton based sngle paamete modulaton. () (d) Fg. 9. Beam wdth ompasons n ange dmenson at t 0, amplfed detal of, () t 1ms and (d) amplfed detal of (). The tme wndow veson of the poposed TMDP-FDA s used fo multple tagets beampatten synthess. Fo smplty, t s supposed that thee ae two tagets loated at (450km, 20 ) and (700km, -30 ) espetvely. The pulse duaton s dvded nto two tme wndows, the length of eah s 0.5ms. By fxng the tme t 0 and t 0.5ms espetvely, the esultng nomalzed beampatten fo the two tagets s shown n Fg. 10. The beampatten pojeton on tme-ange and tme-angle dmensons ae depted n Fg. 10 and () espetvely. It s shown that tme-nvaant multple tagets beampatten wth good spatal fousng an be aheved by the TMDP-FDA as well. Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

12 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: () Fg. 10. Nomalzed ange-angle beampatten fo two tagets, pojeton on tme-ange dmenson and () pojeton on tme-angle dmenson. Futhemoe, the effet of hangng the value of fequeny offset and hp onstant ontollng oeffents to the pefomane of the TMDP-FDA s nvestgated. Fstly, the fequeny offset s kept as f 7 and u hanges fom 1 to 10 and the values of the -3dB man-lobe wdth n ange dmenson and the peak SLL fo eah u ae obtaned. Then, the hp onstant ontollng oeffent s kept as u 5 and f hanges fom 1 to 10 and the oespondng values fo eah ae obtaned. The esults ae depted n Fg. 11. On the one hand, when one of the ontollng oeffents s fxed and the othe one neases, the -3dB man-lobe wdth n ange dmenson deeases, whh means naowe beampatten an be obtaned. On the othe hand, the peak SLL mantans ts small value aound 0.1 when the oeffent hanges. Theefoe, based on the TMDP- FDA, one an flexbly ontol the beampatten fousng sope as needed by hoosng the appopate fequeny offset and hp onstant ontollng oeffents. f Fg. 11. Vaaton uves of the -3dB man-lobe wdth wth espet to f ( u ) and vaaton uves of the peak SLL wth espet to f ( u ). Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

13 Jounal of Mowaves, Optoeletons and Eletomagnet Applatons, Vol. 17, No. 3, Septembe 2018 DOI: At last, the ntal values p 0,m and q 0,m ae hanged by usng dffeent pas of pseudo andom sequenes, and t tuned out that the esultng beampatten s steady n both spatal fousng and SLL. It ndates that the TMDP-FDA s obust to the ntal values thus ntal value optmzaton s not neessay, whh edues the system desgn omplexty. IV. CONCLUSION In ths pape, a novel TMDP-FDA beampatten synthess appoah has been poposed. Tmenvaant ange-angle beampatten s aheved by usng the tme-modulated double paametes based on the hp sgnal mehansm. It s able to geneate fne spatal fousng beampatten at the desed loaton fo both sngle and multple tagets, and t also povdes good pefomane n sde-lobe suppessng. Numeal smulatons ae aed out to evaluate the pefomane of the poposed TMDP-FDA, and the man esults ae ompaed wth the MC-FDA. It tuned out that at a fxed tme the TMDP-FDA has naowe man-lobe beam wdth n ange dmenson, and also, t has satsfatoly lowe sde-lobes wth the tme hangng n a pulse duaton. In addton, the beampatten fousng sope of the TMDP-FDA an be flexbly ontolled by adjustng the oespondng oeffents and t also edues the system desgn omplexty. In futue eseah, the optmal FDA geomet onfguaton suh as the applaton of plana o dstbuted geomety and the eeve beamfomng fo the FDA ada need to be nvestgated. Futhemoe, fo the patal mplementaton of the poposed FDA sheme, many ssues need to be onsdeed suh as geneatng the wavefom, elmnatng the ntemodulaton poduts of the fequeny mxes and edung the stutue omplexty, et [10,17-18]. ACKNOWLEDGMENT Ths wok was suppoted by the Natonal Natual Sene Foundaton of Chna unde Gant and Gant REFERENCES [1] P. Antonk, M. C. Wks, H. D. Gffths and C. J. Bake, Fequeny dvese aay adas, n IEEE Rada Conf., Veona, NY, USA, 2006, pp [2] M. C. Wks and P. Antonk, Fequeny dvese aay wth ndependent modulaton of fequeny, ampltude, and phase, U.S. Patent , Jan. 15, [3] C. A. Balans, Antenna theoy: analyss and desgn, 3d ed. New Yok, NY, USA: John wley & sons, [4] Y. Konsh, Phased aay antennas, IEICE T. Commun., vol. E86B, no. 3, pp , Ma [5] W. Q. Wang, Fequeny dvese aay antenna: new oppotuntes, IEEE Antennas Popag. Mag., vol. 57, no. 2, pp , Ap [6] J. Faooq, M. A. Temple and M. A. Savlle, Applaton of fequeny dvese aays to synthet apetue ada magng, n ICEAA, Tono, Italy, 2007, pp [7] J. J. Huang, K. F. Tong and C. J. Bake, Fequeny dvese aay wth beam sannng featue, n IEEE Ap-S, San Dego, CA, USA, 2008, pp [8] W. Q. Wang and H. Z. Shao, Range-angle loalzaton of tagets by a double-pulse fequeny dvese aay ada, IEEE J. Sel. Tops Sgnal Poess., vol. 8, no. 1, pp , Feb [9] Y. B. Wang, W. Q. Wang and H. Z. Shao, Fequeny dvese aay ada Camé-Rao lowe bounds fo estmatng deton, ange, and veloty, Int. J. Antenn. Popag., vol. 2014, no. 12, pp. 1-15, [10] M. Semen, S. Dem, A. Hzal and T. Eke, Fequeny dvese aay antenna wth peod tme modulated patten n ange and angle, n IEEE Rada Conf., Boston, MA, USA, 2007, pp Bazlan Mowave and Optoeletons Soety-SBMO eeved 12 Feb 2018; fo evew 08 Ma 2018; aepted 01 Aug 2018 Bazlan Soety of Eletomagnetsm-SBMag 2018 SBMO/SBMag ISSN

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