High resolution adaptative arrays based on random processing techniques: frequency hopping modulation

HIGH RESOLUTION ADAPTIVE ARRAYS BASED ON RANDOM PROCESSING TECHNIQUES: FREQUENCY HOPPPING MODULATION Mon se Niija , Miguel A. Lagunas. Depa men o Signal Theo y and Communica ions Uni e si a Poli knica de Ca alunya 08071 BARCELONA, SPAIN Phone:34-3-4017051. Fax: 34-3-4016447. ABSTRACT A new a chi ec u e o adap i e a ays using F equency Hopping modula ion is add essed in his pape . The esolu ion o he a ay and he in e e ence ejec ion inc ease subs an ially applying andom p ocessing o he ca ie equency o he signals. The p oposed amewo k is composed o wo di e en s ages. The an icipa i e s age, de o ed o minimize he noise and ixed in e e ences con ibu ion and he GSLC s age which p o ides cancella ion o ollowe jamme s and sol es he mul iuse collision p oblem. The de eloped sys em equi es nei he empo al no spa ial e e ence o i s implemen a ion, only he equency sequence mus be known. An adap i e app oach has been implemen ed, allowing a as con e gence o he op imal beha io . 1. INTRODUCTION The esolu ion o an a ay can be inc eased in wo di e en ways: swelling he numbe o senso s o augmen ing he dis ances be ween hem. Bo h o hese op ions ha e p oblems. The i s one aises he cos o he a ay and he second one has a well-known limi : i he in e elemen dis ance exceeds hal o any impinging signal wa e-leng h, g a ing lobes will appea in he a ay ac o . A possible solu ion o his p oblem can be ound in he nonpe iodic a ays (a ays wi h nonequidis an elemen s), in his case he elemen s can be dis ibu ed in a de e minis ic o a andom way. The p oblem o g a ing lobes does no appea in his kind o a ays, so he mean dis ance be ween senso s can exceed he limi o hal wa e-leng h. I is o his eason ha he nonpe iodic a ays allow g ea e esolu ion wi hou inc emen ing he numbe o senso s. Some p e ious wo ks dedica ed o his subjec a e e e ed [l]. An impo an d awback o hese a ays is ha he le el o he sidelobes can augmen signi ican ly i he numbe o senso s is low. Recen ly, Random Sampling echniques ha e been de eloped [2]. These echniques allow o use a sampling equency exceeding he Nyquis limi wi hou aliasing whene e he sum o he p obabili y densi y unc ions o all he sampling poin s is a cons an . In his case he es ima ed spec um o he andomly sampled signal will be equal o he o iginal spec um o he con inuous signal. The ou pu signal o an a ay is ob ained as a combina ion o all he ou pu senso s loca ed a di e en posi ions, ha is o say ha an a ay sys em spa ially samples he signals. The e o e, i seems o be This wo k was suppo ed by he Na ional Resea ch Plan o Spain, CICYT, G an numbe TIC92-0800-CO505 and by he Cope nicus P ojec CORELAR C8254. possible o apply some o he heo e ical esul s ob ained in he ime sampling domain o he space domain in o de o de elop andom p ocessing me hods, which pe mi o elimina e he g a ing lobes (spa ial aliasing) o an a ay sys em. The ou pu a ay signal consis s o a ec o o senso samples (snapsho ), which is aken a di e en ins an s o ime. The i s case o conside in Random A ay P ocessing lies in a andomiza ion o he senso posi ions, changing hem om one snapsho o ano he . I he p obabili y o he senso posi ioning a each poin o he ape u e is he same, hen he mean a ay ac o will co espond o he adia ion pa e n o a con inuos ape u e, which does no ha e g a ing lobes. Thus, he spa ial aliasing has disappea ed as in he empo al case, applying andom echniques. The in e es o his case, whe e he senso posi ion has been andomized, is mo e heo e ical han p ac ical, because i is un ealis ic o assume ha he e may be mechanical shi ing o he a ay senso s be ween epea ing snapsho s. None heless, he same e ec can be achie ed o he wise, o ins ance, cons uc ing an a ay wi h a high numbe o closely and equidis an ly spaced elemen s and ac i a ing only a ew o hem o each snapsho . The beha io o his sys em, in mean, will be as i he whole a ay was ac i a ed, howe e , he cos will be lowe . Some echniques ha e been u he s udied in o de o ob ain a mo e easible implemen a ion, in o he wo ds, he goal is o andomize he a ay a oiding a mechanical displacemen o he senso s. I seems ha he only possibili y is o andomize he equency o he ansmi ed signals and his e ec can be achie ed using F equency Hopping (FH) modula ion. In his case, i ual senso s will appea in he ape u e a andom posi ions. Simila ly o he p eceding case, in o de o ob ain a con inuous ape u e, he p obabili y o he i ual senso posi ioning a each poin o he ape u e mus be he same. FH is a me hod o spec um sp eading widely used o make a communica ion sys em less ulne able in on o in e e ences [3]. I consis o a sys em in which he ca ie equency is pseudo andomly hopped o e a wide band, Wss, unde he con ol o a pseudonoise sequence. The signal bandwid h on each hop is much smalle han Wss, howe e , a e aged o e many hops, he FH signal spec um occupies he en i e sp ead spec um bandwid h. Cu en echnology pe mi s FH bandwid hs o he o de o se e al GHz and a es g ea e han 1 Mhophec. The applica ion o FH modula ion in an an enna a ay will imp o e subs an ially he SINR (Signal o In e e ence plus Noise Ra io) as a consequence o he inc ease o he esolu ion and he in e e ence ejec ion. Ne e heless, li le in o ma ion is a ailable on pe o mance o a ays wi h FH signals: Comp on [4] s udied he ad e se e ec s o FH modula ion in an adap i e a ay based on he LMS (Leas Mean Squa ed) algo i hm. Bakh u [4] p oposed a speci ic me hod o 1737 0-7803-2431-5/95 $4.00 O 1995 IEEE adap i e a ays using FH signals, he Maximin algo i hm, which is based on he spec al cha ac e is ics o hese signals, equi ing nei he a e e ence signal no s ee ing ec o s o i s implemen a ion. None heless any adap i e algo i hm p esen s some discon inui ies when used wi h FH modula ed signals. The eason is ha he changes in he signal equency due o FH a e seen by he algo i hm as changes in he di ec ion o a i al. To ie i [6] sugges ed h ee di e en echniques o equency compensa ion o he Maximin algo i hm o sol e his p oblem: Pa ame e -dependen p ocessing is he mos complica ed o implemen and he one which p esen s la ge con e gence. Spec al p ocessing is he simples o implemen , bu he achie ed imp o emen is no signi ican . And, inally, he An icipa i e p ocessing p o ides he as es con e gence bu exhibi s he wo s beha io . This pape deals wi h a new a chi ec u e o FH in A ay P ocessing, composed o wo di e en s ages. Fi s o all he heo e ical sys em is desc ibed, nex , an adap i e app oach is p oposed: inally, some simula ion esul s and conclusions will be shown. 2. TWO STAGE RECEIVER FOR FREQUENCY HOPPING MODULATION I is well known ha he maximum SINR c i e ion in A ay P ocessing yields he op imal complex weigh ec o (l), bo h in empo al and in spa ial e e ence sys ems. being R, he in e e ence plus noise co ela ion ma ix and sd he s ee ing ec o o he desi ed signal. An app oach o his op imum solu ion is cons i u ed o wo di e en s ages. Bl cking 4 Ma ix:B I An icipa i e S age GSLC S age Figu e 1. F equency Hopping Recei e I The i s s age, named he An icipa i e s age, is de o ed o cancel in e e ences a ixed equencies ha a e al eady p esen o ac i e a he equency o in e es a he hop ime. The second s age is conside ed o comba ing in e e ences ha a e no p esen a he equency o in e es a he ime o he equency hop, bu may ge ac i a e some ime a e he hop occu s. This is he case o adap i e jamme s known as epea - back o equency- ollowe jamme s in mili a y scena ios. Mo eo e , his p oblem migh appea in mul iuse sys ems, o ins ance, in mobile communica ion sys ems using FH modula ion. Al hough use s in he same cell no mally use di e en hopping sequences, hey may in e e e among hem when he ca ie equencies coincide in some hops. This second s age consis o a GSLC. Y - 2.1. An icipa i e S age The An icipa i e s age is o med by wo dehopping p ocesso s: he an icipa i e, which gi es he name o his s age, and he on-line dehopping p ocesso s. (Figu e 1). The dehopping sys em (Figu e 2) ollows he low noise ampli ie o each senso because o bandwid h easons in he down-con e sion sequence, allowing he supp ession o he noise and in e e ences ou side he signal band. FREQUENCY I SYNTHESIZER I Figu e 2. Dehopping sys em (a each senso ) The idea o he an icipa i e dehopping is o ob ain a p e ious image o he scena io in o de o p edic a sys em ha maximizes he SINR a he ou pu o he on-line dehopping as as as possible. Thus, his dehopping is done wi h a ca ie equency be o e i s ansmission, h(i+l). The esul an snapsho xa(n) con ains he noise and in!e e ences ha will appea in he on-line p ocesso in he nex hopping, he desi ed signal a he hop equency h(i) is ejec ed by he dehopping wi h h(i+l). Hence, he equi ed Rn ma ix is calcula ed be o ehand om he an icipa i e dehopping ou pu . A e he hop ime, he in e se o his ma ix is ans e ed o he on-line p ocesso mul iplying he snapsho xol( n). ob ained by he on-line dehopping (done wi h he ca ie equency ansmi ed a each momen ). This ma ix blocks he scena io: noise and ixed equency in e e ences, in a simila way as he blocking ma ix in he GSLC s age blocks he desi ed signal, as i will be shown in he nex sec ion. 2.2. Gene alized Sidelobe Cancelle S age A weigh ec o equal o he s ee ing o he desi ed signal (sd) mus be implemen ed o achie e he op imal beam ec o (1). The noise and ixed in e e ences con ibu ion in y,(n) (Figu e 1) a e minimized. Ne e heless, new in e e ences ha may u n up du ing he hop ime a e no canceled a his poin . The second s age should maximize he SINR minimizing any di ec ional componen appea ing in he a ay snapsho ec o x(n), om angles o a i al di e en om he desi ed look di ec ion. In conclusion, we a e in on o a p oblem o cons ained minimiza ion powe . The solu ion o his p oblem can be implemen ed by he so-called GSLC (Gene alized Sidelobe Cancelle [7]), consis ing o wo di e en pa hs. On he one hand, he uppe pa h, e med he quiescen beam o me , p o ides he op imal solu ion when he inpu x(n) con ains only whi e noise and he desi ed signal. On he o he hand, he lowe pa h a ends o maximize he SINR in y(n) when in e e ences appea in he scena io. As i is well- known his lowe pa h con ains a blocking ma ix B a oiding he p esence o he desi ed signal be o e he uncons ained beam o me w, which is ob ained imposing a c i e ion o minimum mean squa ed e o a he inal ou pu y(n). 1738 3. ADAPTIVE APPROACH The an icipa i e s age does no need an adap i e implemen a ion. The in e se co ela ion ma ix R n-l is calcula ed du ing he whole hop ime in he an icipa i e p ocesso , be o e o be ans e ed o he on-line p ocesso , whe e i is kep un il nex hop succeed. I he desi ed di ec ion o a i al is known, he quiescen beam ec o sd will be also known. Consequen ly, he only pa o he ecei e ha would ha e o be adap i e is he uncons ained beam o me (Figu e 1). The weigh ec o w can be easily go by any o he adap i e algo i hms ha minimize he mean squa ed e o : LMS, NLMS, RLS, ... In a g ea numbe o applica ions he di ec ion o a i al o he desi ed signal is unknown. In his case, he quiescen beam o me should be ob ained om he snapsho x( n). Whene e he An icipa i e s age has canceled all he in e e ences p esen in he scena io, he snapsho x(n) will con ain only in o ma ion abou he desi ed signal. Thus, a simple adap i e es ima ion o he eigen ec o co esponding o he maximum eigen alue o he signal co ela ion ma ix p o ides he quiescen weigh ec o sd. Ri (n+l) = p Ri (n) + (p-1) x(n+l) xH(n+l) (n+l) = sd(n) + I.( Ri (n+l) sd(n) (2) (3) (n+l) sd(n+l) = V1 (n+ 1) (4) being (4) a no maliza ion by he i s componen o he es ima ed eigen ec o o ha e he s ee ing ec o . The co ela ion ma ix subindex i indica es he hop numbe . The desi ed signal is always p esen a e he on-line dehopping, wha e e equency is ansmi ed. Fo his eason, i is con enien o es ima e he co ela ion ma ix om he snapsho s acqui ed du ing he whole p ocessing ime, no only du ing he hop ime. Since he snapsho x(n) depends on he hop equency (s ee ing ec o ), he co ela ion ma ix es ima ion mus be done in a cohe en way. The co ela ion ma ix a he An icipa i e s age ou pu , in he i- h hop, can be exp essed as: When a new hop occu s he es ima ed co ela ion ma ix has o be modi ied by a ans o ma ion ma ix in o de o be cohe en wi h he incoming snapsho s: The eby, he co ela ion ma ix can be adap ed con inuously, imp o ing he eigen ec o es ima ion and inc easing he con e gence. Ob iously he quiescen weigh ec o sd( h(i)) es ima ed a he end o each hop mus also be modi icd o he new one. Because i coincides wi h a s ee ing ec o , he equency dependence is on he phases o i s componen s and i is linea , as i is ep esen ed in (8). Q is he numbe o a ay elemen s. So, he modi ica ion consis in a simple phase mul iplica ion by he equency a io: h(i+l)/ h(i). F om now on, i is easy o ob ain he exp ession o he ans o ma ion ma ix Ti [8]: Since he con e gence o his es ima ion p ocedu e is conside ably as , a e ew i e a ions he quiescen beam ec o and he blocking ma ix may be ozen. Thus, he uncons ained beam ec o allows he cancella ion o incoming in e e ences du ing he hop ime. 4. SIMULATION RESULTS The p esen ed simula ions ha e been made wi h a linea equally spaced a ay o 8 senso s, in which he in e elemen sepa a ion was hal wa eleng h. The desi ed sou ce, loca ed a 20 deg ees om he b oadside di ec ion, was a BPSK signal (4 sampleskymbol) cen e ed a 900 MHz, wi h 0 dB o SNR. This signal has been sp ead uni o mly o e a ela i e bandwi h equal o he SO pe cen , which is he a io o he o al hopping bandwi h o he cen e equency. The dwell ime o du a ion o he hop in e al was se equal o he du a ion o 9 symbols (36 samples). The e o e, Slow FH modula ion is conside ed. A andom sequence o 450 symbols has been gene a ed. So, SO equency hops occu ed. In he i s simula ion only a mul i one jamming is p esen in he scena io a 60 deg ees. This in e e ence is dis ibu ed o e he sp ead-spec um bandwid h, consis ing o ones o e hal he equency channels. The in e e ence o noise a io in each channel was 20 dB. In Figu e 3 he mean a ay ac o a e he SO hops is shown wi h solid line. One o he a ay ac o , pa icilla ly he co esponden o he 10- h hop is ep esen ed wi h dashdo line. Because in his case he e is only ixed in e e ences, he cancella ion is achie ed a he ou pu o he quiescen beam o me , being he uncons ained beam ec o app oxima ely equal o ze o. In Figu e 4 he e olu ion o he SINR is plo ed o e he whole ime, also he SNR o each hop is calcula ed sepa a ely and ep esen ed in he same igu e. I can be obse ed ha hey luc ua es by app oxima ely 3 dB. 1739 P .y oh...- Hm- Figu e 4. SINR E olu ion In he second simula ion a ollowe jamme , adia ing a -30 deg ees, is added o he scena io. This in e e ence hops wi h he same sequence as he desi ed signal wi h a delay o 12 samples. This signal mus be canceled by he GSLC s age. The quiescen beam ec o is adap ed only du ing he h ee i s symbols a each equency, ixing i be o e he ollowe jamme appea s a he hop equency. Since he con e gence o he algo i hm is e y as , a ew numbe o i e a ions a e su icien o assu e he quiescen adap a ion o he s ee ing ec o , and a e ha , he minimiza ion o he jamme con ibu ion by he uncons ained beam o me . The mean (solid line) and an ins an aneous a ay ac o (dashdo line) a e shown in Figu e 5. The e olu ion o he coe icien s is depic ed in Figu e 6: a) The quiescen Beam ec o (in dashdo line is plo ed he heo e ical s ee ing ec o ), b) The uncons ained beam ec o . e/. aiescen Beam ilo E dulm I I lb abm Numbe 00 200 400 600 800 loOD 1zw 1400 1600 lsoo bl Unccns emed Bea mecia E dubm '5, ' , I lb a icm Numbe Figu e 6. Coe icien s E olu ion Finally, a las simula ion has been done wi h he same a ay bu spacing he senso s he wa eleng h in o de o inc ease he esolu ion. I no FH modula ion was applied he a ay ac o would p esen a g a ing lobe a -40 deg ees (Figu e 7: dashdo line),being impossible o cancel an in e e ence a i ing om his di ec ion. Using he sys em de eloped in his pape , g a ing lobes a e educed conside ably. In Figu e 7 wi h solid line is ep esen ed he mean a ay ac o when an in e e ence wi h a SNR o 30 dB, a -40 deg ees, is impinging he a ay. 5. CONCLUSIONS A new adap i e ecei e o FH signals in A ay P ocessing, has been epo ed in o de o inc ease he a ay esolu ion and o imp o e he in e e ence ejec ion. The p oposed amewo k is composed o wo di e en s ages: The an icipa i e s age, de o ed o cancel ixed jame s, and he GSLC s age, which minimizes he e ec o he es o in e e ences. An app op ia e ans o ma ion o he co ela ion ma ix ensu es apid con e gence o he algo i hm. 6. REFERENCES Ills einbe g B. , "P inciples o Ape u e and A ay Sys em Design including Random Adap i e A ays", John Wiley & Sons, 1976. [2]Bilinskis I. , Lagunas M. 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