A Synthsis-fr Dirctional Modulation Transmittr using Rtrodirctiv Array Ding, Y., & Fusco, V. (06. A Synthsis-fr Dirctional Modulation Transmittr using Rtrodirctiv Array. IEEE Journal of Slctd Topics in Signal rocssing, (, 48-44. DOI: 0.09/JSTS.06.605066 ublishd in: IEEE Journal of Slctd Topics in Signal rocssing Documnt Vrsion: r rviwd vrsion Qun's Univrsity Blfast - Rsarch ortal: Link to publication rcord in Qun's Univrsity Blfast Rsarch ortal ublishr rights 06 IEEE. rsonal us of this matrial is prmittd. rmission from IEEE must b obtaind for all othr usrs, including rprinting/ rpublishing this matrial for advrtising or promotional purposs, crating nw collctiv works for rsal or rdistribution to srvrs or lists, or rus of any copyrightd componnts of this work in othr works. Gnral rights Copyright for th publications mad accssibl via th Qun's Univrsity Blfast Rsarch ortal is rtaind by th author(s and / or othr copyright ownrs and it is a condition of accssing ths publications that usrs rcognis and abid by th lgal rquirmnts associatd with ths rights. Tak down policy Th Rsarch ortal is Qun's institutional rpository that provids accss to Qun's rsarch output. Evry ffort has bn mad to nsur that contnt in th Rsarch ortal dos not infring any prson's rights, or applicabl UK laws. If you discovr contnt in th Rsarch ortal that you bliv brachs copyright or violats any law, plas contact opnaccss@qub.ac.uk. Download dat:30. Oct. 08
A Synthsis-fr Dirctional Modulation Transmittr using Rtrodirctiv Array Yuan Ding, and Vincnt Fusco, Fllow, IEEE Abstract By modification of th classical rtrodirctiv arrays (RDAs architctur a dirctional modulation (DM transmittr can b ralizd without th nd for synthsis. Importantly, through analytical analysis and xmplar simulations, it is provd that, bsids th convntional DM application scnario, i.., scur transmission to on lgitimat rcivr locatd along on spatial dirction in fr spac, th proposd synthsis-fr DM transmittr should also prform wll for systms whr thr ar mor than on lgitimat rcivrs positiond along diffrnt dirctions in fr spac, and whr on or mor lgitimat rcivrs xist in a multipath nvironmnt. on of ths hav vr bn achivd bfor using synthsis-fr DM arrangmnts. Indx Trms Dirctional modulation (DM, rmation pattrn, intrfrnc pattrn, rtrodirctiv array (RDA, synthsis-fr. I. ITRODUCTIO IRECTIOAL modulation (DM is a promising Dtchnology, bing catgorizd as a kylss physical-layr wirlss scurity mans. It ndows transmittrs th ability to distort signal wavform signaturs projctd wirlssly along all spatial dirctions in fr spac othr than an a-priori slctd dirction along which a lgitimat rcivr locats []. In som arly rportd DM work th charactristic of th dirction-dpndnt signal modulation format transmission was achivd by dirctly rconfiguring th antnna radiating lmnts during data transmission. Hr r-configurability was ralizd by ithr altring th nar-fild lctromagntic boundaris [], [3], or by r-routing th xcitation currnts on radiating structurs [4], rsulting in changabl far-fild radiation pattrns that wr dirction-dpndnt. Th major problm associatd with ths DM architcturs is lack of ffctiv synthsis mthods bcaus thr ar no analytical mans to dscrib th complx intraction btwn th nar-fild boundaris or currnt distributions and thir far-fild radiation bhaviors. This problm was solvd by introducing xcitation-rconfigurabl antnna arrays, which hav ability to updat array xcitation wightings on a pr transmittd symbol basis. At first th xcitation wighting updats wr prformd using attnuators and phas shiftrs at radio frquncy (RF frontnds [5] [9], thn it was illustratd in [0] that xcitation Yuan Ding, and Vincnt Fusco ar with th Institut of Elctronics, Communications and Information Tchnology (ECIT, Qun's Univrsity of Blfast, Blfast, Unitd Kingdom, BT3 9DT (phon: +44(089097806; fax: +44(08909770; -mail: yding03@qub.ac.uk; v.fusco@cit.qub.ac.uk. could also b updatd in th digital basband, avoiding th us of mor xpnsiv yt lss prcis RF rconfigurabl componnts. Synthsis mthods for xcitation rconfigurabl DM transmittr arrays hav progrssd gratly in rcnt yars. Bit rror rat (BER drivn optimization algorithm assistd approachs wr prsntd in [5], [6], [], []. A varity of DM synthsis mthods by constraining diffrnt proprtis of array far-fild radiation pattrns wr dscribd in [3] [7]. An orthogonal vctor approach was firstly proposd in [] and furthr rfind in [8], which synthsizs DM transmittr arrays by gnrating orthogonal vctors/intrfrnc in th null spac of th channl vctors btwn th DM transmittrs and th lgitimat rcivrs. This approach is rlativly univrsal as it is compatibl with both static and dynamic DM systms [9], and can b radily dployd into modrn digital wirlss transmittrs [0]. Furthrmor, th orthogonal vctor approach can b radily xtntd to ndow DM transmittrs with th ability for multipl indpndnt scur bam transmissions [] [3] and to mak th DM tchnology applicabl in multipath nvironmnt [4], [5]. Using th orthogonal vctor concpt th DM synthsis can b considrd as a procss of injcting artificial intrfrnc that is orthogonal to th transmittd rmation signals along slctd dirction(s in fr spac or at dsird location(s within a multipath nvironmnt. In othr words it is th procss of gnrating far-fild pattrns, in fr spac, or far-fild distributions, in multipath nvironmnts, which hav powr null(s at location(s whr intndd rcivr(s is/ar placd. Sinc artificial intrfrnc is injctd into DM systms through ths pattrns, w shall rfr to thm as intrfrnc pattrns hraftr. Similarly th far-fild pattrns through which rmation signals ar convyd ar lablld as rmation pattrns in this papr. For mor dtaild rmation on DM tchnology, intrstd radrs ar suggstd to rad th ovrviw paprs [6], [7]. Som practical issus with all of th abov mntiond DM synthsis approachs includ th acquisition of th dsird scur communication dirction along which th lgitimat rcivr locats, and th dmand of havy computation, spcially for dynamic DM systms, as wll as applications in th multipath nvironmnt. Ths hindr th ral-tim rspons of implmntd DM transmittrs. For xampl, th BER-drivn mthods in [5], [] and th far-fild radiation pattrn synthsis approachs in [4], [5] rquir a numbr of itrations in optimization procsss; th far-fild pattrn sparation mthod
[6], [7] and th orthogonal vctor approach or th MIMO-inspird approach [], [] [5] involvs matrix invrsion. In addition whn th slctd scur communication dirction/location or th multipath nvironmnt changs all of th DM synthsis procsss nd to b r-run. Two rcntly proposd DM transmittr architcturs allviat th rquirmnt of havy computation in som application scnarios. Thy ar trmd synthsis-fr DM transmittrs. On achivs DM functionality by activating a random subst of antnna lmnts for ach symbol transmission along th dsird dirction, to which th ntir phasd array is bam strd. This concpt was namd antnna subst modulation (ASM in [8], [9] or four-dimnsional (4-D arrays in [30], [3]. Howvr, this typ of DM transmittrs gratly rducs availabl bam-forming gain, and also, is not applicabl for multi-bam scur transmission scnarios and multipath channl nvironmnt usag. Th othr synthsis-fr DM structur xploits th bam orthogonality proprty of th Fourir bam-forming ntworks to gnrat th artificial intrfrnc that is orthogonal to gnuin rmation signals, i.., has a far-fild powr null, along th prscribd scur communication dirction [3] [34]. Howvr, this typ of DM arrangmnt suffrs high insrtion loss and low spatial pointing rsolution, and again it is not suitabl for us in multipath nvironmnts. In this papr w propos a nw typ of DM transmittr which builds upon a classical rtrodirctiv array (RDA. This novl DM solution has a sris of advantags that ar summarizd as blow; o xtra targt dirction dtction stimation facilitis ar rquird sinc automatic targt tracking is th inhrnt functionality that an RDA posssss. Th rtrodirction ability can b achivd using low powr purly analogu phas conjugation circuitry that nabls ral-tim rspons, [35], [36]; It is DM synthsis-fr. Th gnration of orthogonal intrfrnc that is usd to achiv DM functionality [], i.., signal wavform distortion along all spatial dirctions othr than th scur communication dirction, is indpndnt of th slctd scur dirction, and, importantly, can b prformd using low-cost low-complxity analogu solutions for ral-tim bhaviour; 3 Th proposd DM architctur can oprat in th scnario whr multipl lgitimat rcivrs locatd along diffrnt dirctions in fr spac acquir th sam rmation that is rquird to b convyd scurly. This is compltly un-rlatd to th dual-bam DM in [37], which utilizs two bams transmittd along th sam dirction to construct a singl-bam DM transmittr, and is also diffrnt to th multi-bam DM in [] [3], whr multipl DM bams for indpndnt rmation transmissions ar formd; 4 Th proposd DM architctur can oprat in a multipath nvironmnt. It should b notd that th RDA and th DM tchnologis wr prviously linkd togthr in [4], [5]. Howvr, unlik th synthsis-fr RDA DM architctur proposd in this papr, th orthogonal intrfrnc gnration in all prvious work is dirction-dpndnt, and dmands havy computation. This papr is organizd as follows. In Sction II th proposd synthsis-fr RDA DM transmittr architctur is dscribd. This is followd by validation undr thr diffrnt application scnarios in Sctions III, IV, and V, rspctivly. For ach cas both analytical analysis and simulation xampls ar prsntd. A brif discussion on its hardwar implmntation is providd in Sction VI. Conclusions on th work ar prsntd in Sction VII. Throughout this papr, th following notations will b usd: Boldfac capital lttr dnots a complx numbr; Boldfac capital lttr with an arrow on top rprsnts a vctor, whos lmnts ar complx numbrs, and whos subscript rprsnts T th numbr of its lmnts,.g., U = [ U U U ] ; Capital lttr with a bar on top mans th complmnt of th dsignatd st; ( T dnots vctor transpos oprator; rfrs to modulus of a complx numbr; Oprator is th Hadamard product of two vctors; Th sign in th txt mans b convrgnt to. II. ROOSED SYTHESIS-FREE RDA DM TRASMITTER θ = π El. El. El. λ/ Duplxr Duplxr Duplxr Tx Rx Tx Rx Tx Rx S C C S S C U U U V G V has Cntr G V G θ = 0 Fig.. roposd synthsis-fr RDA DM transmittr architctur. Th proposd synthsis-fr RDA DM transmittr architctur comprising antnna lmnts is illustratd in Fig.. Hr for clarity th frquncy down-convrsion and up-convrsion componnts normally involvd in th phas conjugators (Cs in th rciv (Rx chains and th signal modulation in th r-transmit (Tx chains ar omittd. In th Rx mod th pilot ton signal(s from lgitimat rcivr(s impingd on th antnna array is/ar phas conjugatd as occurs in classical RDAs. Bfor up-convrsion for r-transmission, th phas conjugatd signal vctor U is combind with a vctor V, which is drivd from U by wighting a ntwork G. W dnot th combind r-transmission signal vctor as S, i.., S = U + V. It will b shown in Sctions III, IV, and V for diffrnt application scnarios that th r-transmittd signal bams ar capabl of bing automatically strd towards th lgitimat rcivr(s, liminating additional targt dirction dtction hardwar, and th signal wavform signaturs transmittd lswhr ar
randomly distortd. Mor importantly th DM nabling ntwork G is indpndnt of th dirction(s or position(s whr lgitimat rcivr(s locats, i.., DM is synthsis-fr. In this papr it is assumd that all of th co-frquncy pilot tons ar radiatd only by lgitimat rcivrs. For th cas whn a malicious third party radiats a co-frquncy pilot ton, th RDA r-transmittd rmation could b rcivd by th third party. This issu can b solvd using sub-array concpt, using which a powr null is formd along th undsird rcivr, as dscribd in [38], or using som spcial-cas pilot-ton spctral signaturs prsntd in [39]. Anothr solution is to us modulatd pilot signals within which th idntifications of th lgitimat rcivrs can b ncodd for authntication purpos at RDA sid. It should b pointd out that th Cs can oprat with phas modulatd pilot signals [40] which could b usd for this purpos. In ordr to facilitat analysis in th following sctions, it is assumd that th RDA DM transmittr considrd in this papr consists of a uniformly spacd -by- antnna array with ach lmnt having an idntical isotropic radiation pattrn, λ/ sparatd, whr λ rfrs to th wavlngth corrsponding to th systm s oprating frquncy. III. VALIDATIO WITH OE LEGITIMATE RECEIVER I FREE SACE Whn on lgitimat rcivr is locatd along th spatial dirction α in fr spac and mits a pilot ton signal, th rcivd pilot ton signal on th n th array lmnt is jπ[n (+/]cosα. Hr α ϵ θ = [0, π]. Throughout w assum that th path loss is normalizd out, and th phas rfrnc is chosn as th array s gomtric cntr. Thus th phas conjugatd signal vctor U can b writtn as U = j ( + πcosα j ( + πcosα T j ( + πcosα Th r-transmittd radiation pattrn as a function of spatial dirction θ, s illustration in Fig., is θ = S F = U + V F = U + G U F ( ( ( ( Hr F is th array factor (AF vctor, taking th form in (3, F = j ( + πcosθ j ( + πcosθ Substituting ( and (3 into (, w gt T j ( + πcosθ ( (3 ( θ = U F + ( G U F intr j n ( + π( cosθ cosα j n ( + π( cosθ cosα n { } = + G (4 If w dsign a ntwork G whrin thn r-visiting (4, w can obtain intr G n = 0 (5 ( θ α = + G = (6 n intr = 0 which indicats th powr projctd along dirction α is constant, whil along othr dirctions (θ θ α is dpndnt on G. G can b randomly slctd as long as (5 is satisfid. Th far-fild pattrn (θ is sparatd into th rmation pattrn, and th intrfrnc pattrn intr, which is usd to distort signal modulation formats along all dirctions othr than th dsird scur communication dirction α. Fig. shows th calculatd powr normalizd (θ and 0 randomly gnratd intr(θ whn, for xampl, = 9 and α = 60. It is obsrvd that all intr(θ pattrns hav prfct powr nulls along th dirction α. As a consqunc, whn th modulatd r-transmission signals ar suprimposd onto th (θ, th undistortd signal constllation diagram in IQ spac can b dtctd only along this slctd dirction α. For illustration purpos, Fig. 3 dpicts th far-fild radiation pattrns for 50 random QSK symbols transmittd. For ach symbol th ntwork G is arbitrarily slctd undr th constraints (5 and (7. + G n = (7 Th powr fficincy of a DM systm, E DM, dfind in [], dscribs th prcntag of th total radiatd nrgy that is utilizd for usful rmation transmission. Thus with th condition in (7 th E DM of th xampl DM systm in Fig. 3 is 50%, s (8. E π n 0 dθ U θ = DM = = π 0 + intr dθ θ = Un + GU n n = = 00% = 50% + G n (8
E DM, th BER simulation rsults prsntd hr show th sam conclusion, i.., th smallr E DM th narrowr th BER main bams bcom and th gratr th BER sidlobs ar supprssd, as is vidnt in Fig. 4 undr diffrnt signal to nois ratios (SRs. Th dtaild BER calculation procdurs can b found in [9]. Fig.. Simulation xampl of powr normalizd rmation pattrns (θ and 0 randomly gnratd orthogonal intrfrnc pattrns intr(θ. = 9, α = 60, and E DM = 50%. In fr spac th far-fild pattrns can b intrprtd as constllation pattrns in IQ spac. Thus from Fig. 3 it can b obsrvd that th standard QSK constllation diagram, i.., four symbols with idntical amplitud and 90 phas intrvals, can b dtctd only along th slctd communication dirction, 60 in this xampl. IV. VALIDATIO WITH MULTILE LEGITIMATE RECEIVERS I FREE SACE Whn multipl dvics intrrogat a classical RDA using idntical frquncy pilot tons, th RDA r-transmittd far-fild pattrns will form multipl main bams in fr spac whos magnituds ar proportionat to th strngths of th incoming pilot signals [4], [4]. Firstly in this sction th scnario of two lgitimat rcivrs locatd along dirctions α and β (α β, rspctivly, in fr spac is takn as an xampl. It is also assumd that th dtctd signal strngths of two pilot tons from α and β by th RDA DM transmittr ar idntical. Scnarios with mor than two intndd rcivrs in fr spac ar thn discussd at th nd of this sction. (a (a (b Fig. 3. Simulatd far-fild (a magnitud and (b phas pattrns for 50 random QSK symbols transmittd via th xampl RDA DM systm. = 9, α = 60º, and E DM = 50%. As it has bn pointd out prviously in [] and [] that th achivabl scrcy prformanc is dtrmind by th chosn (b Fig. 4. Simulatd BER spatial distributions for diffrnt E DMs in th xampl RDA DM systm modulatd for Gray-codd QSK signal transmission. 0 +7 random symbols ar usd in simulation. Th E DM of 00% rfrs to th non-dm or classical RDA systm. = 9, α = 60, and (a SR = db; (b SR = 3 db. For th two-lgitimat-rcivr cas, th phas conjugatd signal vctor U can b writtn as
{ } { } j ( + πcosα j ( + πcos β+ ϕ + j ( + πcosα j ( + πcos β+ ϕ + U = (9 { } j ( + πcosα j ( + πcos β+ ϕ + Hr φ is th phas advanc of th pilot signal from β than that of th pilot signal from α. Using th sam RDA DM transmittr structur shown in Fig., and substituting (3 and (9 into (, w gt ( θ = U F + ( G U F intr j n ( + π( cosθ cosα j{ n ( + π( cosθ cos β ϕ} ( = + j n ( + π( cosθ cosα j{ n ( + π( cosθ cos β ϕ} n ( = + G + and intr (0 j{ n ( + π( cosα cos β ϕ} intr ( θ α= Gn ( + j n ( + µ Gn ( Gn ( = + ( µ j C sin n ifaaisaodd = j C sin ( nµ sin ( nµ ifaaisavn cos( µ cos( µ j C ifaaisaodd sin ( µ = cos( µ j C ifaaisavn sin ( µ (4 In ordr to gain mor insights into th rlationship btwn (α and intr(α, th ratio (α/ intr(α is plottd as a function of µ and φ in db scal in Fig. 5. Both odd and vn, 9 and 8 usd as xampls, ar considrd. Sinc paramtr C only scals th intr(α in a linar fashion, s (4, it is hld at unity in th xampls shown in Fig. 5. Whn θ = β, similar xprssions to ( and (4 can b obtaind. ( θ α j n ( + π( cosα cos β = + ( ( µ ( µ ( µ + + cos n ifaaisaodd = + cos( nµ cos( nµ ifaaisavn sin = + sin ( Hr (a ( cos cos, { 0, } µ = π α β µ ± π ( If w dsign a ntwork G satisfying G T C [ aa a0a aa] ifaaisaodd ( aitms ( aitms = T C [ aa a aa] ifaaisavn aitms aitms (3 whr C can b any arbitrary complx numbr, th following can b drivd; (b Fig. 5. Calculatd xampl (α/ intr(α as a function of µ and φ in db scal. (a = 9; (b = 8.
In ordr to achiv DM functionality it is rquird that no, or at last vry littl, artificial intrfrnc nrgy is projctd along slctd communication dirction(s. This thn guarants th prsrvation of th rmation signal wavform signaturs dtctd by th lgitimat rcivr(s. Thus in Fig. 5 four critical points, A, B, C, and D, nd to b idntifid, sinc whn (,C ( B,A ( D, µ Q = π π (5 x x x x th φ has grat impact on th (α/ intr(α. Bcaus th valu of φ, i.., th phas diffrnc btwn two pilot tons, can b arbitrary in practic, rgion Q in (5 should b avoidd in ordr to obtain larg (α/ intr(α. In ordr to facilitat discussion, lttrs, A, B, C, and D, with subscripts x and y rfr to th abscissa and th ordinat valus of thir corrsponding points in Fig. 5. It is intrsting to not that whn φ = 0º and µ 0 th (α/ intr(α +, indicating intr(α 0. This scnario is actually th on intrrogating dvic cas prsntd in Sction III. Th four critical points can b calculatd from (6 (9 It is worth noting that sinc 4π/ is th first null bamwidth (FBW in cosin domain in a classical bam string array, solutions in (9 actually indicat that th two lgitimat rcivrs nd to b sparatd at last half FBW in angl spac. lotting ( in Fig. 6, it can b sn that µ is a continuous and monotonic surfac. Thus by stting µ of A x, B x, C x, and D x, th domain in which th (α, β pairs satisfying µ Q can b slctd is shown as lying in th shadd aras in Fig. 7. Whn a (α/ intr(α valu of a DM systm gratr than A y is rquird, th allowabl µ rgion can b idntifid with th hlp of th (α/ intr(α curvs in Fig. 5. Th projction of th allowabl µ rgion in α-β plan st th ara whr (α, β pairs could b chosn. ( α intr ( α d ( µ d = 0 (6 Substituting ( and (4 into (6, w gt ( ( ( ( ( ( sin µ sin µ = 0 if ϕ = 0, aaisaodd tan µ 4 tan µ 4 = if ϕ = 0, aaisavn cot µ 4 tan µ 4 = if ϕ = π, aaisavn (7 Fig. 6. µ as a function of α and β. Upon considring µ ( π,0 ( 0, π ar, th solutions of (7 iπ µ =± ( i =,,, if ϕ = 0, aaisaodd π + 4iπ µ ± i = 0,,, if ϕ = 0, aaisavn π + 4iπ µ ± i =,,, if ϕ = π, aaisavn (8 By linking th solutions in (8 to th (α/ intr(α curvs in Fig. 5 four critical points can b idntifid, Fig. 7. Domain of accptabl (α, β pairs for (α/ intr(α gratr than A y (or B y, C y, D y. Rvisiting (4, th prfct DM condition, i.., intr(α = 0, can b mt whn π π ( π ( π A x =,B x =,C x =,Dx = ifaaisaodd π π ( π ( π A x,b x,c x,dx ifaaisavn
( µ = ( µ cos( µ = cos cos ifaaisaodd ifaaisavn 4iπ 3 µ = ± i =,, ifaaisaodd 4iπ µ =± i =,, + 4iπ µ =± i =,, ifaaisavn (0 Each valu of µ rprsnts a curv in (α-β plan. Thrfor thr ar infinit (α, β pairs satisfying th prfct DM condition. For xampl, whn = 9, th prfct DM condition can b mt by choosing (α, β as (60º, 90º, (45º, 78º, or (60º, 84.º, which corrspond to µ of π/, π/, or π/5, rspctivly. Fig. 8 dpicts th calculatd magnitud pattrns of (θ and intr(θ for diffrnt φ whn = 9 and (α, β = (60º, 90º. As xpctd intr has two prfct powr nulls along th slctd α and β, irrspctiv of th valus of φ. Whn φ = 90º thr ar no bam pointing rrors of th two main bams in, as highlightd in Fig. 8. It has to b mphasizd that vn whn φ is fixd th summd pattrns = + intr along dirctions othr than α and β can still b diffrnt sinc th phas of th complx numbr C in (3 can b arbitrarily slctd. This is th ky to scrambling signal wavforms along othr dirctions. In Fig. 9 th calculatd far-fild pattrns for 30 random QSK symbols transmittd ar shown. Hr = 9, (α, β = (60º, 90º, and φ = 90º. For ach symbol C is kpt as unity and its phas is randomly chosn. (a (b Fig. 9. Simulatd far-fild (a magnitud and (b phas pattrns for 30 random QSK symbols transmittd via th xampl RDA DM systm. = 9, (α, β = (60º, 90º, φ = 90º, and C =. BER simulation rsults of th xampl RDA DM systm modulatd for Gray-codd QSK ar obtaind undr diffrnt SR scnarios, and ar dpictd in Fig. 0. Undr th two-lgitimat-rcivr scnario, th systm E DM is a function of α, β, φ, and C, s ( to (5. E θ = 0 DM = π θ = 0 π + dθ intr dθ ( Fig. 8. Calculatd magnitud pattrns of (θ and intr(θ for diffrnt φ whn = 9, (α, β = (60º, 90º, and C =. In Fig. 9 it can b obsrvd that bsids th rquird 60º and 90º dirctions, standard QSK constllation pattrns ar also formd along 0º, 0º, and 80º, which is th consqunc of additional prfct powr nulls in intr along ths thr dirctions, s Fig. 8. Howvr, as noticd in Fig. 9, th powr along ths dirctions is 6 db lss than that along th two lgitimat rcivr dirctions. intr ( ξ ( ξ ( ξ ( ξ sin sin j = + ϕ ( sin sin ( ξ ( ξ sin ( ξ cos cos jc cos( ξ cos( ξ = + sin ( ξ cos cos ( ξ ( ξ ( ξ ( ξ ifaaisaodd jc + ifaaisavn sin sin (3
( cos cos, { 0, } ξ = π θ α ξ ± π (4 ( cos cos, { 0, } ξ = π θ β ξ ± π (5 Whn α, β, and φ ar fixd, th choic of C dtrmins th systm E DM. Again as prdictd, sn in Fig. 0, th gratr th valu of C, i.., th lowr th E DM, th narrowr th two BER main bams bcom and th highr th BER sidlobs ar, xcpt along th thr dirctions, i.., 0º, 0º, and 80º, as discussd in th last paragraph. Th C = 0 cas rfrs to th classical RDA opration, i.., E DM = 00%. (a liminats th powr nulls in intr(θ for most φ valus along othr dirctions, which always xist for prfct orthogonality DM systms such as th on in Fig. 8. Thrfor thr is a trad-off btwn th signal quality along th slctd communication dirctions and th amount of rmation lakag along othr dirctions. Fig. illustrats simulatd far-fild pattrns whn 30 random QSK symbols ar transmittd via th xampl RDA DM array. Again φ is st to 90º and C as unity. It can b sn in Fig. that th dtctd QSK signal formats ar slightly distortd along th dsird communication dirctions α and β. This minut disturbanc acts as intrfrnc, as a consqunc, rquiring a small amount of xtra rmation signal powr for th dtction of th sam lvls of BER in th corrsponding non-dm systms, i.., C = 0. For xampl, whn C =.44, an xtra 0.8 db signal powr is ndd to compnsat th introducd intrfrnc along α and β, rsulting in an quivalnt signal to intrfrnc plus nois ratio (SIR of db. S th xampl in Fig. 3(a. This, howvr, provids an opportunity of supprssing BER sidlobs along all othr dirctions, which can b obsrvd undr th highr SR scnario shown in Fig. 3(b. Ths obsrvations provid a guidlin on th choic of C whn a practical systm dsign is considrd. For th xampl in Fig. 3, if th systm rquirs at last 3.4 0 5 BER at lgitimat rcivr sids (corrsponding to SR of db in th non-dm systm and an allowabl maximum 0.8 db incras in rmation signal powr compard with that in th non-dm systm, thn th uppr limit of th choic of C is.44. It is worth noting that th sam valu of C for diffrnt rcivrs sttings normally rsults in diffrnt systm E DMs, s Fig. 0, Fig. 3, and Fig. 7. (b Fig. 0. Simulatd BER spatial distributions for diffrnt C in th xampl RDA DM systm modulatd for Gray-codd QSK signal transmission. 0 +7 random symbols ar usd in simulation. Th C of 0 rfrs to th non-dm or classical RDA systm. = 9, (α, β = (60º, 90º, φ = 90º, and (a SR = db; (b SR = 3 db. Anothr xampl of (θ and intr(θ for th RDA DM systm with = 9 and (α, β = (60º, 99.6º is shown in Fig.. Hr µ = π(cosα cosβ = π/3, corrsponding to on of th lowst (α/ intr(α sidlobs, i.., point E in Fig. 5(a. Unlik th charactristic of prfct orthogonality btwn and intr along α and β shown in Fig. 8, intr(α and intr(β ar no longr zro in Fig.. In this xampl thy ar 4.3 db lowr than (α and (β, s both Fig. 5(a and Fig.. This non-prfct orthogonality proprty, on th othr hand, Fig.. Calculatd magnitud pattrns of (θ and intr(θ for diffrnt φ whn = 9, (α, β = (60º, 99.6º, and C =. Th abov analysis in this sction can b xtndd for th scnarios whr mor than two, but lss than, lgitimat rcivrs intrrogating th proposd RDA DM transmittrs. Th limit of coms from th fact that an -lmnt linar array can form a maximum numbr of radiation main bams in half spac. Assum that thr ar M lgitimat rcivrs locatd along diffrnt spatial dirctions, M, and th ntwork G in th synthsis-fr RDA DM transmittr is still dsignd as in
(a (a (b Fig.. Simulatd far-fild (a magnitud and (b phas pattrns for 30 random QSK symbols transmittd via th xampl RDA DM systm. = 9, (α, β = (60º, 99.6º, φ = 90º, and C =. (3. Following th similar drivation procdurs as for th two-rcivr cas, th gnralizd (θ, as wll as sparatd θ θ, can b obtaind as in (6 to (8. ( and ( θi intr θ = θ i Hr θ i or θ m dnots th incidnt angl of th pilot ton from th i th or m th lgitimat rcivr, ( i, m ϵ (,, M. ( θ = U F + ( G U F ( θ M intr j{ n ( + π( cosθ cosθm ϕm} = m= M j{ n ( + π( cosθ cosθm ϕm} = + G n (6 m= i θ = + i intr M j{ n ( + π( cosθi cosθm ϕm} m= m i m= m i ( µ ( µ M sin i m im = + sin im (7 (b Fig. 3. Simulatd BER spatial distributions for diffrnt C in th xampl RDA DM systm modulatd for Gray-codd QSK signal transmission. 0 +7 random symbols ar usd in simulation. Th C of 0 rfrs to th non-dm or classical RDA systm. = 9, (α, β = (60º, 99.6º, φ = 90º, and (a SR = db and.8 db; (b SR = 3 db. intr ( θ θi = ( µ ( µ sin ( µ M cos cos m im im jc ifaaisaodd m= im m i M cos( µ m im jc ifaaisavn m= sin ( µ im m i (8 ( cos cos, { 0, } µ = π θ θ µ ± π (9 im i m im Th φ i or φ m ar th phas diffrncs of th i th or m th pilot ton signals rlativ to th phas of th first on, thus φ = 0. Similarly th (θ i/ intr(θ i can b calculatd, which is a function of µ im and φ m. By stting a minimum thrshold of th (θ i/ intr(θ i, th accptabl µ im, and hnc th slctabl (θ, θ,, θ M, with th hlp of th functions or surfacs dscribd in (9, can thn b idntifid. Sinc ths procdurs hav rcours to multi-dimnsional graphs which ar difficult to b prsntd in th papr, th associatd contnts ar omittd hr. In Fig. 4 two typical rsults of th calculatd far-fild magnitud pattrns, both rmation pattrns and
intrfrnc pattrns intr, gnratd by th proposd 9-lmnt RDA DM transmittrs for thr-lgitimat-rcivr cas ar prsntd. Whn (θ, θ, θ 3 = (60º, 90º, 0º, corrsponding to (µ, µ 3, µ 3 = (π/, π, π/, th and intr ar prfctly orthogonal along th thr slctd dirctions, s Fig. 4(a, which can b furthr validatd by substituting th valus of (µ, µ 3, µ 3 into (3 that rturns 0. Whil in Fig. 4(b th choic of (θ, θ, θ 3 = (60º, 90º, 50º rsults in non-prfctly orthogonal and intr. BER simulation rsults for multi-rcivr RDA DM systms, undr various choics of C that links to E DMs, xhibit th sam charactristics as thos for th two-rcivr cas, thus thy ar omittd hr. compatibility of th proposd synthsis-fr RDA DM transmittr. Th DM nabling ntwork G is dsignd as in (3. Th two-ray modl is illustratd in Fig. 5. In this xampl an intndd rcivr is locatd along borsight of a 9-lmnt half wavlngth (λ/ spacd linar RDA DM transmittr array at a lin-of-sight distanc of 00λ. By placing an infinit-sizd prfct rflctor prpndicular to th array, ach point in th two-dimnsional (-D ring-lik simulation ara, from a radius of 90λ to 00λ, can rciv two rays. On is rcivd dirctly from lin-of-sight, and th othr is routd through rflction. Th path loss diffrncs of ach ray ar considrd. (a Fig. 5. Simplifid two-ray multipath modl. Whn a pilot ton signal is isotropically mittd by th intndd rcivr, two rays from th paths Ray and Ray, sn in Fig. 5, in rvrs dirctions imping upon th RDA DM transmittr array, xciting r-transmittd rmation and intrfrnc pattrns, and intr. Thir magnituds for C = ar dpictd in Fig. 6. From th curv it can b obsrvd that th rflction bam around 50º is 6 db lowr than th borsight bam. This is bcaus Ray path lngth is twic as long as Ray. Th two pilot rays dtctd at th transmittr sid ar in-phas, which rsults in bam pointing rrors of th r-transmittd two bams, s discussions on φ for two-rcivr cas in Sction IV. (b Fig. 4. Calculatd magnitud pattrns of (θ and intr(θ for diffrnt φ whn = 9, φ 3 = 90º, C =, and (a (θ, θ, θ 3 = (60º, 90º, 0º; (b (θ, θ, θ 3 = (60º, 90º, 50º. V. VALIDATIO I MULTIATH EVIROMET Th applicability of th proposd RDA DM architctur in th fr spac multipl-lgitimat-rcivr scnarios givs us a hint that it should oprat in a multipath nvironmnt. Th only diffrnc for th multipath cas is that th r-transmittd signals along diffrnt propagation paths ar rquird to b constructivly combind at lgitimat rcivr location(s. Fortunatly, this is automatically guarantd bcaus it is th inhrnt proprty that an RDA posssss [43]. Firstly in this sction a simplifid two-ray multipath modl, usd prviously in [4], is adoptd to dmonstrat th multipath Fig. 6. Calculatd magnituds of r-transmittd rmation and intrfrnc pattrns, and intr, by th RDA DM transmittr in Fig. 5. = 9 and C =.
BER simulations for Gray-codd QSK transmission wr conductd undr th SR of 3 db for diffrnt valus of C, from which th systm E DMs can b calculatd using ( to (3 with a cofficint 0.5 bing addd bfor jφ, accounting for th path loss diffrnc btwn two rays in this xampl systm. Th rsults ar shown in Fig. 7. Th 3 db SR at intndd rcivr location was chosn to facilitat clar illustrations of -D BER distributions in gry-scal. Th AWG contribution is assumd to b idntical ovr th ntir simulation ara. From th obtaind BER rsults in Fig. 7, it can b sn that th proposd RDA DM transmittr is abl to scurly convy rmation signals to th intndd rcivr, with signals dtctd at most othr locations bing sriously distortd, rsulting in high BERs. Th gratr th slctd C, i.., th smallr th systm E DM, th smallr th rror-fr zon bcoms. It is intrsting to point out that th rror-fr zon around 50º cannot b liminatd by incrasing th valu of C, sinc no intrfrnc can b projctd into this ara, s th powr null around 50º in intr in Fig. 6. This is diffrnt to th DM systms synthsizd by th orthogonal vctor approach in [], whrin usful signals ar choppd into pics and ach pic is transmittd along diffrnt propagation paths with constructiv combination occurring only at th lgitimat rcivr location. Whil in th synthsis-fr RDA DM systms proposd in this papr, instad of rmation signal pics, th wightd copis of usful rmation signals ar projctd along diffrnt propagation paths with in-phas combination nabld only at th lgitimat rcivr location. As a consqunc, whn no intrfrnc nrgy can b dlivrd into th routs through which th copis of rmation signals travl btwn th transmittr and th intndd rcivr from othr propagation paths, th unscrambld rmation signal wavforms can b dtctd within ths aras,.g., th ara around 50º in Fig. 7. (a (b (c Fig. 7. Simulatd -D BER distributions for diffrnt C in th xampl RDA DM systm in th two-ray multipath nvironmnt. Th array is modulatd for Gray-codd QSK signal transmission. 0 +7 random symbols ar usd in simulation. on simulation zon is th ara blockd by th infinit prfct rflctor. Th C of 0 rfrs to th non-dm or classical RDA systm. = 9, SR = 3 db, and (a C = 0, E DM = 00%; (b C =, E DM = 56%; (c C = 3, E DM = %. In ordr to furthr invstigat th prformanc of th proposd RDA DM systm in multipath-rich nvironmnt, a mtal shildd cub of.5.5.5 m 3, in which a 7-lmnt RDA DM array with λ/ spacing, oprating at f =.4 GHz, is placd, is considrd. A squar mtal sht with a siz of.5.5 m is insrtd btwn th transmittr and th intrstd -D simulation ara to block lin-of-sight rays. Th dtaild modl paramtrs ar lablld in Fig. 8. Th wav propagation softwar Winrop vrsion.06 [44] was usd to gnrat th transmission cofficints btwn ach transmit antnna lmnt and ach point in th -D.5 m simulation ara. All of th mtallic plats hav thir rflction loss st to b 0.05 db and th diffraction loss is constraind to li btwn 8 and 5 db. In th simulation up to 00 rays with largst nrgy btwn ach transmit antnna and ach point in th simulation ara ar obtaind, and thn summd to gt th transmission cofficints.
Fig. 8. Mtal shildd cub modl for multipath-rich wirlss transmission. With th computd transmission cofficints btwn ach of th svn antnna lmnts and ach point on th -D simulation ara, BER simulations can b prformd undr various transmittr, i.., diffrnt C valus, and rcivr sttings. Again it is assumd that th ntwork G in th RDA DM transmittr taks th form in (3 and th r-transmittd signals ar modulatd for Gray-codd QSK. Thr diffrnt scnarios, with rgard to th numbr of intndd rcivrs and its or thir location(s, ar invstigatd. Undr th first scnario only on intndd rcivr locatd at th gomtric cntr of th -D simulation ara is considrd, i.., th point of (x, y, z = (0.5m,.5m,.5m. In th scond and th third scnarios two intndd rcivrs, bing placd, rspctivly, in a symmtrical and an asymmtrical fashion, ar considrd. Th pilot signals radiatd by th two lgitimat rcivrs ar assumd to b isotropic and hav idntical powr. Th phas diffrnc btwn thm can b arbitrarily slctd, and is st to 0 for th xampls illustratd blow. Simulatd BER distributions undr th singl rcivr scnario ar shown in Fig. 9 for various choics of C. Sinc a larg numbr of rays xist in this xampl systm, th calculation of systm E DMs is complicatd, thus thy ar not prsntd. Howvr, whn th choic of rcivrs is mad, thn largr valus of C always rsult in lowr E DMs. Th SRs dtctd by th dsird rcivr ar st to b 0 db. It can b sn that th proposd synthsis-fr RDA DM array has considrabl ability to distort th lakd rmation signals at othr locations, rsulting in high BER valus. Whil at th position whr th intndd rcivr locats, th artificial intrfrnc gnratd by th synthsis-fr ntwork G stays largly orthogonal to th rmation signal, sinc only whn C is as larg as 3 th impact of th intrfrnc on BER can b visibl. Th sam conclusion can b drawn for th scond scnario, i.., two lgitimat rcivrs locat at (0.5m, 0.65m,.5m and (0.5m,.875m,.5m, s BER simulation rsults in Fig. 0. Th involvmnt of mor numbr of dsird rcivrs, as xpctd, dgrads th orthogonality btwn rmation and artificial intrfrnc. In this xampl, whn C incrass to 8, bit rrors can b dtctd by th two intndd rcivrs undr SR of 0 db. Th third scnario is slightly diffrnt sinc th two dsird rcivrs ar asymmtrically placd at (0.5m,.5m,.5m and (0.5m, 0.469m,.5m. Thy ar lablld as R and R, rspctivly. It is notd hr that th valu of 0.469 corrsponds to th 30 th pixl out of total 60 pixls, into which th simulation ara is dividd along y axis, i.., 0.469 =.5/60 30. Sinc R and R ar asymmtrically placd, th powr of rmation signals dlivrd to thm is diffrnt. In this xampl th dtctd rmation powr, hnc th SR, by R is 3.7 db highr than that dtctd by R. Thus bit rrors appar first at R along with th incras of th paramtr C, s Fig. for SR of 0 db at R. VI. DISCUSSIO O HARDWARE IMLEMETATIO As w prsntd from Sction II to V, it is th ntwork G augmntd onto a classical RDA that nabls th synthsis-fr DM functionality in a numbr of application scnarios. Its mathmatical form in (3 for multi-rcivr applications satisfis th on in (5 for singl rcivr cas, thus (3 is th prfrrd choic in trms for ralization. From a hardwar implmntation prspctiv, (3 can b ralizd using an or -channl fixd phas dlay ntwork, corrsponding to th vctor [ ] T, and on gain- and phas-rconfigurabl componnt, corrsponding to th variabl C. It is worth noting that th variabl componnt can hav vry poor prcision sinc it dos not affct th orthogonality btwn th rmation and th gnratd artificial intrfrnc. Th practical ralization and oprating charactristics of th RDA DM architctur will b rportd sparatly. VII. COCLUSIO A practical DM transmittr architctur was proposd in this papr. Built upon classical RDA tchnology, it rquirs only a fw low-complx hardwar augmnts. Th proposd RDA DM transmittr has th uniqu capability that it can oprat without any prior knowldg of how many and whr th dsird rcivrs li vn in havily multipath-rich nvironmnts. Th ffctivnss of th proposd RDA DM systm was validatd through simulation undr various application scnarios, among which th multi-rcivr multipath opration pavs a way for futur fild us of DM tchnology in aras whr physical-layr wirlss scurity offrs additional, or scurity augmntation, bnfits ovr convntionally scurd systms.
(a (b (c (d ( Fig. 9. Simulatd -D BER distributions for diffrnt C in th xampl RDA DM systm in th multipath-rich cub nvironmnt. Th array is modulatd for Gray-codd QSK signal transmission. 0 +7 random symbols ar usd in simulation. Only on intndd rcivr locats at (0.5m,.5m,.5m. Th C of 0 rfrs to th non-dm or classical RDA systm. = 7, f =.4 GHz, SR = 0 db, and (a C = 0; (b C = ; (c C = 3; (d C = ; ( C = 3. (a (b (c (d ( Fig. 0. Simulatd -D BER distributions for diffrnt C in th xampl RDA DM systm in th multipath-rich cub nvironmnt. Th array is modulatd for Gray-codd QSK signal transmission. 0 +7 random symbols ar usd in simulation. Two intndd rcivrs locat at (0.5m, 0.65m,.5m and (0.5m,.875m,.5m. Th C of 0 rfrs to th non-dm or classical RDA systm. = 7, f =.4 GHz, φ = 0, SR = 0 db, and (a C = 0; (b C = ; (c C = 3; (d C = 7; ( C = 8. (a (b (c (d ( Fig.. Simulatd -D BER distributions for diffrnt C in th xampl RDA DM systm in th multipath-rich cub nvironmnt. Th array is modulatd for Gray-codd QSK signal transmission. 0 +7 random symbols ar usd in simulation. Two intndd rcivrs R and R locat at (0.5m,.5m,.5m and (0.5m, 0.469m,.5m. Th C of 0 rfrs to th non-dm or classical RDA systm. = 7, f =.4 GHz, φ = 0, SR = 0 db at R, and (a C = 0; (b C = ; (c C = ; (d C = 3; ( C = 4.
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