Downloaded from eee.ust.ac.r at 7:59 IRDT on Sunday July 1st 18 [ DOI: 1.68/IJEEE.14..116 ] Null Steerng PS Array n the Presence of Mutual Couplng. Sedghy* (C.A.) 1 Introducton1 Abstract: A null steerng PS antenna array s desgned n ths paper. In the proposed method, the exact full wave antenna radaton propertes wth the effect of mutual couplngs and nearby scatterers are consdered to calculate the array steerng vector, precsely. Although the proposed method s not constraned by the array geometry and the antenna element specfcatons, a fve patch antenna elements wth planar array geometry s desgned and smulated as an ant am PS antenna example. The smulaton results show the mportance of the mutual couplng effects. Moreover, the results verfy the proposed method ablty to encounter wth the multple PS ammer sources. Fnally, the effect of ammer power s nvestgated whch shown that the antenna performance s ncreased by ammer power enhancement. Keywords: Null Steerng, Jammng, Mutual Couplng, PS, Antenna Array. PS satellte navgaton system performance s strongly depended on the sgnal qualty, whch s affected by the nose, nterference and ammng sgnals. In the nomnal condtons, these undesred sgnals are absent and the PS satellte sgnals are receved wth enough lnk budget margn. Therefore, the PS recevers are able to perform the necessary processng for navgaton nformaton achevement. Snce the antenna s sotropc, the strong undesred sgnals are receved n the same way as the desred PS satellte sgnals n a ammng condton. Therefore, even f the recever LNA s not saturated n ths condton and the sgnal s receved, the carrer to nose rato s decreased and the PS performance s degraded, consequently. The temporal flterng cannot be used to suppress the ammng sgnals whch are n the PS frequency bandwdth. Snce the ammer and PS sgnals usually orgnate from dfferent spatal locatons, spatal flterng can be employed to mprove the receved sgnal qualty. Ths flterng can be performed by adaptve sgnal processng of the spatal separated antenna outputs. In terms of antenna radaton patterns, ths Iranan Journal of Electrcal & Electronc Engneerng, 18. Paper frst receved 14 August 17 and accepted January 18. * The author s wth the School of New Technologes, Iran Unversty of Scence and Technology (IUST), Tehran, Iran. E-mals: sedghy@ust.ac.r. Correspondng Author:. Sedghy. flterng steers the antenna pattern nulls n the drecton of ammer sources arrval by optmum determnaton of the antenna weght n the array confguraton. Moreover, ths flterng can mprove the PS sgnal recepton by ncreasng the array gan n the drecton of PS satelltes whch needs some pror knowledge about them [1-4]. The correspondng algorthms of these optmum weght determnatons have been dscussed n the lteratures where the antenna array elements have usually been consdered as sotropc sources. The null steerng pattern synthess technques have been dscussed n [5,6] whch need the pror knowledge about the desred pattern and drecton of the ammers. The radaton patterns of the antenna elements can sgnfcantly degrade the algorthm results. Moreover, the nteracton of the antenna array elements where placed close to each other known as mutual couplng can affect the system performances, hghly. In [7], a PS antenna array has been desgned by usng polarzaton dversty to acheve more flexblty n the null steerng. In ths antenna, a smplfed model of a patch antenna was used n the desgn approach. An adaptve array processng for PS nterference reecton was proposed n [8] wth deal antenna patterns model. A compact controlled recepton pattern antenna has been proposed n [9] formed by 7 pnwheel antenna elements. Snce the mutual couplng between the array antenna elements has been low, ts effect was not consdered n ths null steerng process. Mnaturzed PS antenna arrays wth 4 smple PS antennas have been desgned n [1,11] where the mutual couplng Iranan Journal of Electrcal & Electronc Engneerng, Vol. 14, No., June 18 116
Null Steerng PS Array n the Presence of Mutual Couplng. Sedghy Downloaded from eee.ust.ac.r at 7:59 IRDT on Sunday July 1st 18 [ DOI: 1.68/IJEEE.14..116 ] effects have been gnored n the array analyss. The effect of mutual couplng n the PS ant ammng antenna has been studed n [1-13]. In these papers, frst the mutual couplng effect n the antenna array gan, beam wdth and sde lob levels has been dscussed, deeply. Then, the error between the output and a locally generated reference sgnal has been mnmzed by mean squared error algorthm. A PS recever that utlzes an adaptve drectonal antenna array whch ponts electroncally to PS satelltes and suppressng ammers by some pror knowledge about them has been proposed n [14]. The applcatons of antenna arrays n NSS nterference and multpath envronments have been consdered n [15] wth two stage beamformer wthout consderng the mutual couplng effects. A controlled recepton pattern antenna for PS system has been ntroduced n [16] whch studed the characterzaton of the code and carrer phase bases ntroduced by CRPA antenna hardware. A software-based NSS recever archtecture wth a blnd null steerng beamformer known as the power mnmzaton beamformer has been mplemented n [17] by commercal NSS antennas wthout consderng the mutual couplng effect. Moreover, a fve elements ant-ammng antenna array has been desgned and fabrcated n [18] to mtgate the nterference wthn a compact footprnt. Although, ths antenna acheve a good polarzaton, phase and gan dversty wthn a compact footprnt, but the mutual couplng effect has been not studed n the paper. A sngle feed dual band antenna backed by a hybrd artfcal magnetc conductor cavty was ntroduced for ant ammng applcatons wthout dscussng about the algorthm. Recently, a robust method has been proposed n [3] to suppress ammng for satellte navgaton by reconstructng sample matrx covarance wthout man lobe nullng. owever, the antenna radaton patterns and mutual couplng effect have not been consdered. In ths paper, a new method s proposed to extract the optmal complex weghts for suppresson of the ammng sgnals n a PS antenna array n presence of mutual couplng. As t depcted n Fg. 1, the optmal element weghts are adaptvely updated wthout need to any pror knowledge about the drecton of ammer nterferences. In more detals, the exact actve radaton pattern of the array elements are used to acheve the proper complex weght of the antennas. The actve radaton pattern of an element s taken wth ts feedng n the array confguraton, where all other array elements are termnated wth matched loads. Ths pattern s generally dfferent from the solated element pattern, because ts adacent elements radate some power due to the mutual couplng wth the fed element [19]. Moreover, ths pattern ncludes the antenna nearby scatterers such as antenna holders. Usng actve element pattern n beam formng has been ntroduced n [] and developed n [1-3]. ere we use ths method for precse desgn of an ant am null steerng PS antenna whch not consdered, prevously. Fg. 1 Null Steerng PS antenna array. To the best of author knowledge, these specfcatons have been not consdered n the related references all wth each other. The presented smulaton results clarfy the mportant rule of the mutual effects n the antenna performance. The outlne of ths paper s as follow. In Secton, PS antenna array geometry s consdered that s able to form four nulls n ts radaton pattern. The full wave smulaton results verfy the sgnfcant effects of mutual couplng n the antenna radaton patterns. Notce that although we consder a 5-elements PS array, but the proposed method s unversal and can be used n all D and 3D array confguraton, easly. In the proposed algorthm dscussed n Secton 3, the array output power s mnmzed to suppress the effect of ammng sources. The man pont n ths process s the correct determnaton of array manfold n the presence of mutual couplng. The smulaton results are depcted n Secton 4 that clarfy the sgnfcant effect of mutual couplng n the overall performance of the array. Fnally, the antenna performance s evaluated by changng the ammer to sgnal rato, SJR and number of ammer sources. Antenna Array eometry The proposed antenna array geometry s shown n Fg.. In ths array, four smple lnear polarzed PS patch antenna elements are prnted unformly along of a crcle wth radus of a = 6 cm and the ffth antenna elements s placed at the array center whch s the coordnate orgn. Ths element s used as the reference element for the complex weght calculaton dscussed n Secton 3. All patch antennas are prnted on a square RO43 substrate wth length of L = cm, 3 ml thckness and relatve permttvty of ε r = 3.55. The PS patch antenna element s shown n Fg. n more detals, also. The sde length of ths proposed patch antenna s w = 4.96 mm to acheve a resonance at PS L1 band, 1.575 z. Also, the feed connecton pont s located on x axs of the antenna structure by h =.8 mm Iranan Journal of Electrcal & Electronc Engneerng, Vol. 14, No., June 18 117
Null Steerng PS Array n the Presence of Mutual Couplng. Sedghy Downloaded from eee.ust.ac.r at 7:59 IRDT on Sunday July 1st 18 [ DOI: 1.68/IJEEE.14..116 ] L L ll w w Feedng Pont l Fg. Antenna array geometry formed by fve dentcal patch antennas. y y 5 5 L h 45 45 a a x x 1 1 3 4 movement from the orgn, as shown n Fg.. Moreover, the substrate length of the stand alone patch antenna element s consdered as l = 8 cm. All patch antennas are orented dentcally n the array confguraton, also. The full wave smulaton patterns of the stand alone PS antenna element and the reference actve element patterns n the array (ffth elements) are compared here. Fgs. 3(a) and (b) show the normalzed antenna radaton patterns comparson at φ =, 9 planes where the antenna gan s 5.4 and 3.94 db for the stand alone and reference antennas, respectvely. Notce that these antennas are dentcal and only the mutual couplng changes ther attrbutes. Also, the S 11 responses of these two antennas are plotted n Fg. 3(c). As t shown n ths fgure, the antenna element has 1 Mz bandwdth ( S 11 <-1dB) around the L1 PS center frequency whch covers the bandwdth requred for commercal PS. Theses smulaton results clarfy the mportance of mutual couplng n the antenna specfcatons. 3 Null Steerng Algorthm In ths secton, we descrbe the null steerng method. Notce that n ths algorthm, there are nether lmtatons mposed on the array geometry, nor t s necessary to assume dentcal antenna element radaton patterns. A purely blnd null steerng beamformer whch doesn't need any pror nformaton about the ammer drecton of arrval s used to mtgate the ammng sgnal. Snce the PS sgnals are well below the nose floor, ther contrbuton n the array covarance matrx S 11, db -5-1 -15 - -5 9 o 6 o 1 o 9 o 6 o 1 o 3 o 15 o 3 o 15 o o 18 o (a) o 18 o (b) 3 o 15 o 6 o -3 - -1 9 o db 3 o 15 o 1 o 6 o -3 - -1 9 o db 1 o -3 Wthout Mutual Wth Mutual -35 1.55 1.56 1.57 1.58 1.59 1.6 Frequency, z (c) Fg. 3 The desgned patch antenna specfcatons wthout (black and sold lne) and wth mutual couplng (red and dashed lne) for the ffth element a) radaton pattern at φ = b) radaton pattern at φ = 9 c) s11. can be gnored. Therefore, the array output mnmzaton leads to steer the nulls n the drecton of nterferences [18, 4]. Notce that ths smple method can only mtgate the nterferences and the multpath sgnals cannot be reected by ths approach. Consder N-elements antenna array where a narrowband beamformer output for ths array can be expressed as Y( t) w X( t) (1) where X( t ) [ x 1( t ), x ( t ),..., x N ( t )] s the complex Iranan Journal of Electrcal & Electronc Engneerng, Vol. 14, No., June 18 118
Null Steerng PS Array n the Presence of Mutual Couplng. Sedghy Downloaded from eee.ust.ac.r at 7:59 IRDT on Sunday July 1st 18 [ DOI: 1.68/IJEEE.14..116 ] vector of array observatons versus tme and w [ w 1, w,..., w N ] s the null steerng weghts vector. Regardng the notaton of ths paper, subscrpt stands for the complex conugate transpose and the boldface letters are used for matrces. The array observaton vector n a ammng envronment can be expressed as (.) M () PS X( t ) S ( t ) J ( t ) N( t ) where S ( ) PS t s the observaton desred sgnal vector receved from the -th PS satellte, J ( t ) s the -th observaton ammer sgnal and N( t ) s a vector specfyng the spectral addtve whte aussan nose (AWN) presented n each antenna channel. The total observed array vector, X( t ) can be expressed wth more detals as M t s t J t X a, a, N t (3) where a(, ) s the array manfold vector n (, ) drecton, s () t and J () t are the PS and ammer sgnal, respectvely. Assumng zero mean sgnals wth random processes and uncorrelated attrbute, the total covarance matrx s defned as the expectaton of the outer product of the observed array vector as R E X t X t a, a, M M a, a, I n N n N R R I. (4) where the correlaton matrx for PS and ammng sgnals are R a (, )a (, ), R a (, )a (, ), respectvely. Also, (1,,..., ), (1,,..., M ) and n are the powers of uncorrelated mpngng sgnals s(k), (k), and n(t), respectvely. Moreover, I N s N N dentty matrx. Snce the PS sgnals pror to dspreadng/correlaton are below the nose floor, the PS sgnal power s very week. In other words, the total covarance matrx, R s manly related to the ammer sgnals and nose. Therefore, the total output power should be mnmzed by proper complex weght selectons to encounter wth the ammng sgnal powers. Also, to avod the trval soluton (null weght vector), the problem should be modfed wth a proper constrant. Ths constrant can be defned so that only one element (e.g. the reference one) s used n the absence of ammer sgnals as w c 1, c [,,...,, 1]. (5) 1N Notce that that other constrans whch need the pror knowledge about the PS drecton of arrval can be used, also to mprove the PS sgnal recepton whch leads to complexty and cost enhancement. In other hand, the total array output power can be wrtten as Y( )Y ( ) w X( ).X( ) w E t t P E t t E t t w X( ).X( ) w=w Rw. (6) Therefore, ths power mnmzaton problem can be formulated as [5-8] mn P w Rw, subect to w c 1. (7) out The soluton of ths mnmzaton problem can be found by usng a Lagrange multpler method leads to, w Rw w c 1 L w (8) where λ s the Lagrange multpler and Lw (, ) s the cost functon. The soluton of ths quadratc functon can be calculated by [18, 4] 1 w R c c R 1 c (9) Now, the man problem s R calculaton whch s related to the array manfold vectors n the ammer and desred PS sgnal drectons, a(, ) as expressed n (4). ere we defne two dfferent cases, deal and real, to acheve the array manfold vectors n dfferent drectons,. 3.1 Ideal Case Wthout Mutual Couplng Effect (, ) The frst case where named the deal case, consders the array antenna elements as sotropc sources wthout mutual couplng effects from the adacent antenna elements. Therefore the array manfold for ths case can be calculated as ka 1 ka sn cos,..., ka a, exp sn cos, cos sn N 1,. (1) where the n s the angular locaton of each antenna as shown n Fg. 4. Snce the last element, N, s consdered n the orgn as a reference elements, t's receved sgnal s not related to the angle of arrval rather than the other elements. Therefore the last matrx entry s set zero Iranan Journal of Electrcal & Electronc Engneerng, Vol. 14, No., June 18 119
Null Steerng PS Array n the Presence of Mutual Couplng. Sedghy Downloaded from eee.ust.ac.r at 7:59 IRDT on Sunday July 1st 18 [ DOI: 1.68/IJEEE.14..116 ] n (1). 3. Real Case Wth Mutual Couplng Effect ere we focus on the real case wth the mutual couplng effects between the array elements. For ths purpose, the actve radaton pattern of the antenna elements are extracted from the FSS full wave smulaton software as 1 re, re, re,..., re N (11) where ˆ,,, re re re ˆ (1) It s clear that the radaton patterns of the array antenna elements are dfferent due to the mutual effects of the other array elements and scatterer nearby the antenna such as radome, feed lne and antenna holders. Now, the array covarance matrx can be expressed as [1] 1 R re(, ).[ re(, )] Z c * (13) ere * (.) denotes the complex conugate,. s the scalar product and Z c s the characterstc mpedance of the transmsson medum. As t mentoned n the ntroducton, the actve element pattern of an antenna n the array structure s obtaned by exctng the antenna and termnatng the other antenna elements by a match load. The electrcal feld radaton pattern dentfed as re (, ) n the abovementoned relatons s the electrc feld radated feld, whch s multpled by the radal dstance. In more detals, snce the r dependence s nherent characterstc of a sphercal TEM wave and a key feature of far felds, the dstance dependence s removed by ths multplcaton for more smplfcatons n the relatons. 4 Smulaton Results 4.1 Mutual Effects As t depcted n Fg. 3, the antenna patterns are changed sgnfcantly due to the mutual couplng effects. ere we am to evaluate the effect of mutual couplng n the null steerng process. For ths purpose, we consder the smple 5-elemnts PS array desgned n Secton. The ammer s assumed to be located at 45 and 45 wth ammer to sgnal rato (JSR) of 3 db. Notce that snce the PS sgnal s below the nose floor, the JSR can be consdered as the ammer to nose rato, also. Moreover, we consder the whte aussan nose wth n.1 n the smulatons. The complex weght vector of the proposed null steerng are calculated for two deal and real cases dscussed n Secton 3. Whle the antenna radaton patterns are consdered as sotropc n the deal case, they are extracted n the real case (wth mutual) from FSS software n 5 degree steps n both θ and φ drectons. In more detals, the electrcal farfeld vectors of each antenna element whch ncludes and E (, ) E (, ) components are computed by the FSS to use n (13). It should be mentoned that the FSS software acheves the electrc radated farfeld multpled by the radal dstance, r whch s the one needed n the relatons provded n the prevous secton. The requred complex weght vectors are calculated by usng (8) for these two cases. The results of usng these two complex weght vectors are depcted n φ- plane wth θ = 45 (Fg. 5(a)) and θ-plane wth φ = 45 (Fg. 5(b)). It can be seen clearly that mutual couplng affects the antenna performance, sgnfcantly. In the real case where the mutual couplngs are consdered, the ammer sgnal s encountered wth more than 5 db null depth, whle t s low n the deal case and maybe not acceptable. These results clarfy the mportance of the mutual couplng n extracton of the complex weght vector. 4. Mult s After showng the mportance of the mutual couplng effect n the proposed method, we am to nvestgate the method ablty to deal wth mult ammer sources. As t s well know, an array wth N elements can reects N-1 ammer sources. Therefore we evaluate the method wth, 3 and 4 ammer sources whch have the same JSR as 3 db. The ammer sources locatons n these three scenaros are tabulated n Table 1 and the correspondng smulaton results are shown n Fg. 6. It can be seen that the proposed method can create proper null n the drecton of ammer sources to reect ther power. Moreover, t can be seen that the null depth s hghly related wth the number of ammer sources. In other words, the results show that although the null depth s x 4 n 1 z 3 5 Antenna Pattern Antenna Element Fg. 4 Antenna array wth deal (pont source) and real radaton pattern. y Iranan Journal of Electrcal & Electronc Engneerng, Vol. 14, No., June 18 1
Null Steerng PS Array n the Presence of Mutual Couplng. Sedghy Downloaded from eee.ust.ac.r at 7:59 IRDT on Sunday July 1st 18 [ DOI: 1.68/IJEEE.14..116 ] good enough n all scenaros, but the null depth n the - ammer source scenaros s much hgher than the 3 and 4-ammer source. To acheve more null depth wth constant ammer sources, we can ncrease the number of array elements, also. 4.3 to Sgnal Effects Snce the proposed method works based on the array power mnmzaton, t s expected that JSR enhancement can help more the algorthm to recognze the ammer sgnals from the nose. To show ths fact, we consder one ammer source n and 45 45 wth three dfferent JSR as 3, and 1 db. The smulaton results are shown n φ-plane for θ = 45 (Fg. 7(a)) and θ-plane for φ = 45 (Fg. 7(b)). As t can be seen, the null depth s related hghly to the JSR. For example, we have about 6 db null depth for JSR = 3 db, whle t s about 4 db for JSR = and only about 5 db for JSR = 1 db. 5 Concluson An ant ammng PS antenna was desgned n ths paper. The desgned antenna array was formed by fve mcrostrp patch antenna n planar array geometry. The null steerng method was performed by usng the exact Normalzed E, db Normalzed E, db -1 - -3-4 -5 Real, WthMutual Ideal, Wthout Mutual -6 45 9 135 18 5 7 315 36, deg (a) -1 - -3-4 -5-6 Real, WthMutual Ideal, Wthout Mutual 3 6 9 1 15 18, deg (b) Fg. 5 PS Antenna array wth pont sources and real radaton patterns for SJR=3 db, SNR=- db and σ =.1. The ammer s placed at φ = 9 and θ = 3. a) φ plane wth θ = 3 b) θ-plane wth φ = 9. actve element patterns of the array antenna. These patterns nclude the mutual couplng effect and the antenna nearby scatterer such as holder whch ncrease the antenna performance to deal wth the ammer sources whch was not consdered n the lterature based on the author knowledge. Moreover, the proposed method can be easly used n conformal array structures due to usng actve antenna pattern n the method. The smulaton results clarfed the antenna ablty to reect the ammer sources effects. Table 1 The Source Locatons n Three Dfferent Scenaros. Sources Scenaros Source Locatons a) - (, ), (,3 ), b) 3- (, ), (,3 ), (6, 15 ) c) 4-, deg, deg, deg 18 15 1 18 15 1 9 6 3 (, ), (3,9 ), (6, 15 ), (,3 ) -75dB -66dB 45 9 135 18 5 7 315 36, deg (a) 9 6-31dB 3 45 9 135 18 5 7 315 36, deg (b) 18 15 1 9 6-13dB -3dB 3-6dB -8dB -9 db -15 db 45 9 135 18 5 7 315 36, deg (c) Fg. 6 Array patterns after null steerng wth SJR = 5dB for dfferent ammer locatons reported n Table 1. a) - ammers b) 3- ammers c) 4-ammers. - -4-6 - -4-6 -5-1 -15 - -5-3 Iranan Journal of Electrcal & Electronc Engneerng, Vol. 14, No., June 18 11
Null Steerng PS Array n the Presence of Mutual Couplng. Sedghy Downloaded from eee.ust.ac.r at 7:59 IRDT on Sunday July 1st 18 [ DOI: 1.68/IJEEE.14..116 ] Normalzed E, db Normalzed E, db -1 - -3-4 -5 JSR= 3 db -6 JSR= db JSR= 1 db 3 6 9 1 15 18, deg (a) -1 - -3-4 -5 JSR= 3 db -6 JSR= db JSR= 1 db -7 45 9 135 18 5 7 315 36, deg (b) Fg. 7 PS Antenna wth dfferent sgnal to ammer rato for SNR = - db and σ =.1. The ammer s placed at φ = 45 and θ = 45. a) φ plane wth θ = 45 b) θ plane wth φ = 45 References [1] Z. Fu, A. ornbostel, J. ammesfahr and A. Konovaltsev, Suppresson of multpath and ammng sgnals by dgtal beamformng for PS/alleo applcatons, PS Solutons, Vol. 6, No. 4, pp. 57 64, 3. [] M. Cuntz, A. Konovaltsev, A. Dreher and M. Meurer, Jammng and spoofng n PS/NSS based applcatons and servces threats and countermeasures, Communcatons n Computer and Informaton Scence, Vol. 318, pp 196 199, 1. [3] J. R. Lambert, A. Z. Tempe, C. A. Balans and D. DeCarlo, Sphercal cap adaptve antennas for PS antennas and propagaton, IEEE Transactons on Antennas and Propagaton, Vol. 57, No., pp. 46 413, 9. [4] M. M. Casabona and M. W. Rosen, Dscusson of PS ant-am technology, PS solutons, Vol., No. 3, pp.18 3, 1999. [5] V. Tree and L. arry, Detecton, estmaton and modulaton theory, Massachussets nsttute of technology, Jhon Wley and Sons, 1968. [6] R. T. Compton Jr, The power-nverson adaptve array: Concept and performance, IEEE Transactons on Aerospace and Electronc Systems, Vol. 6, pp. 83 814, 1979. [7] M. Trnkle and W. C Cheuk, Null-steerng PS dual-polarsed antenna arrays, n The 6 th Internatonal Symposum on Satellte Navgaton Technology Includng Moble Postonng & Locaton Servces Melbourne, Australa, pp. 5, 3. [8] D. S. De Lorenzo, J. auter, J. Rfe, P. Enge and D. Akos, Adaptve array processng for PS nterference reecton, n Proceedngs of the 18th Internatonal Techncal Meetng of the Satellte Dvson of the Insttute of Navgaton, pp. 618 67, 5. [9] W. Kunysz, Advanced pnwheelä compact controlled recepton pattern antenna (AP-CRPA) desgned for nterference and multpath mtgaton, Proceedngs of the ION PS, pp. 3 36, 1. [1] D. Reynolds, A. Brown and A. Reynolds, Mnaturzed PS antenna array technology and predcted ant-am performance, Proceedngs of the 1 th Internatonal Techncal meetng of the Satellte Dvson of the Insttute of Navgaton, PS-99, Nashvlle, pp. 777 785, 1999. [11] D. Wllams, S. Clark, J. Cook, P. Corcoran and S. Spauldng, Four-element adaptve array evaluaton for unted states navy arborne applcatons, n Proceedngs of the 13 th Internatonal Techncal Meetng of the Satellte Dvson of The Insttute of Navgaton, pp. 53 53,. [1] K. A. rffth and I. J. upta, Effect of mutual couplng on the performance of PS AJ antennas. Navgaton, Navgaton, Vol. 56, No. 3, pp. 161 173, 9. [13] A. S. C. Svendsen and I. J. upta, The effect of mutual couplng on the nullng performance of adaptve antennas, IEEE Antennas and Propagaton Magazne, Vol. 54, No. 3, pp. 17 38, 1. [14] D. De Lorenzo, Navgaton Accuracy and Interference Reecton for PS Adaptve Antenna Arrays, Stanford Unversty, 7. [15] S. Daneshmand, NSS Interference Mtgaton Usng Antenna Array Processng, Doctoral dssertaton, Unversty of Calgary, 13. [16] U. S. Km, Mtgaton of Sgnal Bases Introduced by Controlled Recepton Pattern Antennas n a gh Integrty Carrer Phase Dfferental PS System, Dss. Stanford Unversty, 7. Iranan Journal of Electrcal & Electronc Engneerng, Vol. 14, No., June 18 1
Null Steerng PS Array n the Presence of Mutual Couplng. Sedghy Downloaded from eee.ust.ac.r at 7:59 IRDT on Sunday July 1st 18 [ DOI: 1.68/IJEEE.14..116 ] [17] J. Arrbas, P. Closas and C. Fernandez-Prades, Interference mtgaton n NSS recevers by array sgnal processng: A software rado approach, n Sensor Array and Multchannel Sgnal Processng Workshop (SAM), 14 IEEE 8 th, pp. 11 14, 14. [18] W. Alshraf, U. Engel and T. Bertuch, Compact controlled recepton pattern antenna for nterference mtgaton tasks of global navgaton satellte system recevers, IET Mcrowaves, Antennas & Propagaton, Vol. 9, No. 6, pp. 593 61, 14. [19] D. M. Pozar, The actve element pattern, IEEE Transactons on Antennas and Propagaton, Vol. 4, No. 8, pp. 1176-1178, 1994. []. Roger and D. D. Zutter, Beamformng strateges for compact arrays n moble termnals usng the exact actve element pattern method, Mcrowave and Optcal Technology Letters, Vol. 35, No. 3, pp. 1 3,. [1] P. Demarcke,. Roger, R. oossens and P. D. Jaeger, Beamformng n the presence of mutual couplng based on constraned partcle swarm optmzaton, IEEE Transactons on Antennas and Propagaton, Vol. 57, No. 6, pp. 1655 1666, 9. []. Roger and D. D. Zutter, Predcton of nose and nterference cancellaton wth a movng compact recever array n an ndoor envronment, IEEE transactons on vehcular technology, Vol. 54, No. 1, pp. 191-197, 5. [3] R. oossens, I. Bogaert and. Roger, Phasemode processng for sphercal antenna arrays wth a fnte number of antenna elements and ncludng mutual couplng, IEEE Transactons on Antennas and Propagaton, Vol. 57, No. 1, pp. 3783 379, 9. [4] F. Le Chevaler, D. Lesseler and R. Stara, Ant ammng for satellte navgaton, Non-standard Antennas, pp. 343 383. [5] S. A. Vorobyov, Prncples of mnmum varance robust adaptve beamformng desgn, Sgnal Processng, Vol. 93, No. 1, pp. 364 377, 13. [6] B.. Frank, Smart Antennas for Wreless Communcatons wth MATLAB, Mcraw-ll. New York, 5. [7] J. Ltva and T. K. Lo, Dgtal Beam Formng n Wreless Communcatons, Artech house, 1996. [8] Van Trees, arry L. Detecton, Estmaton, and modulaton theory, optmum array processng, John Wley & Sons, 4. [9] S. X. Ta and I. Park, A sngle-feed dual-band antenna for an ant-am PS array, n Internatonal Workshop on Antenna Technology (WAT), pp. 37 39, 15. [3] Y. ong L. Wang, R. Yao, and Z. Zhang, A robust method to suppress ammng for NSS array antenna based on reconstructon of sample covarance matrx, Internatonal Journal of Antennas and Propagaton, pp.1 1, 17.. Sedghy was born n Qaen, South Khorasan, Iran n 1983. e receved B.Sc., M.Sc. and Ph.D. degrees n Electrcal Engneerng from Iran Unversty of Scence and Technology (IUST) n 6, 8 and 13 respectvely. From December 11 to July 1, he was wth the Unversty of Calforna, Irvne as a Vstng Scholar. e s currently an Assstant Professor n School of New Technologes of IUST. Iranan Journal of Electrcal & Electronc Engneerng, Vol. 14, No., June 18 13