Combined Scheme for Fast PN Code Acquisition
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1 13 th Iteratioal Coferece o AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT- 13, May 6 8, 009, asat@mtc.edu.eg Military Techical College, Kobry Elkobbah, Cairo, Egypt Tel : +(0) , Fax: +(0) Combied Scheme for Fast PN Code Acquisitio Salah Sayed Elagooz * Abstract: I direct-sequece widebad (DS-WB) systems, log spreadig sequeces are used to spa multiple symbol itervals i order to remove spectral lies ad to mitigate multiple access iterferece. The usage of log spreadig sequeces will result i a large search space durig acquisitio stage. As a result, the DS-WB systems will eed a lot of time to achieve acquisitio state. This paper proposes a combied acquisitio scheme, kow as Fast Serial Search Sequetial Estimatio (FSSSE), which could be applied to the direct sequece spread spectrum systems with log PN sequeces. The proposed scheme is a combiatio of two acquisitio schemes which are the serial search acquisitio scheme ad the rapid acquisitio by sequetial estimatio (RASE) scheme. The proposed scheme gets the advatages of both schemes while overcome their drawbacks. The mea acquisitio time of the proposed scheme is reduced 100 times compared to the covetioal serial search scheme for PN sequece with a period of Keywords: Direct-sequece widebad spread spectrum system - PN code acquisitio - Serial search acquisitio scheme - Fast Serial search sequetial estimatio acquisitio scheme - Rapid acquisitio by sequetial estimatio scheme. I- Itroductio: I Direct-Sequece Spread Spectrum (DSSS) systems, the goal of code acquisitio is to achieve a coarse time aligmet betwee the received PN code ad the locally geerated code to a accuracy of a fractio of oe PN sequece chip [1, ]. Serial search strategy [3] is the most popular approach to code acquisitio which correlates the received ad locally geerated code sequeces ad the tests the sychroizatio based o either the crossig of threshold or the maximum correlatio. A threshold value is determied depedig o the sigal to oise ratio at the matched filter output [] ad it may be adjusted to the partial correlatio [1]. A direct approach [4] for obtaiig statistics of the code acquisitio time for serial search spread-spectrum receivers is preseted. It combies algebraic characterizatio of the search with trasform-domai methods. This approach gives a very deep isight ito the ature of the acquisitio process. This fact permits the author to propose two alterate search strategies that outperform the covetioal oes whe the code rewidig time is small i compariso to the dwell times. The serial search scheme has a drawback of its relatively log acquisitio time for log periods PN codes. A double-dwell serial code acquisitio system employig a adaptive threshold estimator is described ad aalyzed ad a geeral expressio for the mea acquisitio time is derived [5]. * Egyptia Armed Forces 1/8
2 The performace of a ocoheret [6], serial acquisitio techique is evaluated for DSSS commuicatios. The output of a matched filter is sampled at twice the chip rate durig acquisitio with the advatages of fast acquisitio ad less hardware. acquisitio, ad each sample is compared with a fixed acquisitio threshold. The effect of sample-timig error o the acquisitio performace is examied. A ew scheme of PN code acquisitio usig FIR adaptive filter is preseted ad it provides better performace tha earlier desigs of the matched filter [7]. A acquisitio scheme [8], amed larger step ad serial acquisitio, of a PN code for DSSS is itroduced with a focus o the acquisitio problem of log sequeces buried deeply i oise. This method is similar to the hybrid Aother approach for PN code acquisitio is the recursio-aided rapid acquisitio by a sequetial estimatio (RARASE) [9]. This method is a outgrowth of the (RASE) method, rapid acquisitio by sequetial estimatio. I RARASE method, the kow recursio relatio of the PN sigal is used to determie if a short estimate of the state of the received PN sigal is probably correct ad if, cosequetly, a attempt should be made to track that estimate. The RARASE has the drawback of beig highly sesitive to oise ad iterferece sigals because the estimatio process is performed o a chip by chip basis ad as such makes o use of the iterferece rejectio capabilities of PN sigals. However, it has the advatages of simplicity ad fast code acquisitio. For log spreadig sequeces, as the case of direct-sequece ultra-widebad (DS-UWB) systems [10], a improved sigalig format i which the fial log spreadig sequece used is derived from the combiatio of two short sequeces. Accordig to the feature of the proposed sigalig format, a two-stage acquisitio scheme is proposed ad studied i detail. Results show that the acquisitio time ca be reduced greatly with the proposed scheme. This paper presets a ew acquisitio scheme to accout with log spreadig sequeces that are used i DS-WB systems. This scheme is a hybrid system that combied from a serial search scheme ad rapid acquisitio by sequetial estimatio scheme. This system ca be expressed as: fast serial search sequetial estimatio (FSSSE) scheme, which carries the state iformatio of log period PN code geerator over aother short period PN sequece. This scheme gets the advatages of both serial search ad sequetial estimatio schemes while overcomes their drawbacks. The paper is orgaized as follows: Sectio ІІ provides the basic priciple of the FSSSE acquisitio scheme. Sectio ІІІ describes the implemetatio ad operatio of the acquisitio scheme. Sectio IV drives its performace. Sectio V shows the results. Sectio VI gives the coclusio. II- Basic Priciple of the FSSSE Acquisitio Scheme Oe ca sychroize two liear feedback shift register geerators of the same structure by loadig the same iitial states i the two shift registers at early the same time. So, if we ca trasmit this iitial state ad estimate its values at the receiver side, the system ca acquire sychroizatio i a fast maer. I order to do that, oe should solve the problem of how to trasmit the iitial state of the code geerator i practical low sigal to oise ratio ad the, how to correctly estimate this iitial state at the receivig side. The proposed FSSSE system ca solve these problems. /8
3 Acquisitio strategy i FSSSE system is achieved i three steps. First, a short period PN sequece, kow as sychroizatio sequece, is sychroized i a very short time due to its short period. This sychroizatio sequece is used as a carrier for the iitial state of the mai log period PN sequece. Secod, the iitial state of the mai sequece is estimated out of the sychroizatio sequece. Third, the log period PN code sequece is fially sychroized by applyig the estimated iitial state to the log period shift register geerator at the receivig side. The operatio of each of the three steps takes a relatively very short time i a low SNR eviromet so that, the overall acquisitio time becomes very short comparig with either of the two idividually workig schemes. III- Implemetatio ad Operatio of FSSSE Acquisitio Scheme The data to be trasmitted is spreaded by a mai log period PN code sequece. The spreadig log period PN sequece it self is spreaded by aother fast short period PN sequece, which ca be cosidered as a carrier sigal for the log PN code sequece. The basic buildig blocks for the trasmitter module are show i Fig.1 At the receivig side show i Fig., the locally geerated short period PN sequece is firstly sychroized usig a serial search acquisitio scheme because it is more practical i a low SNR eviromet. Whe the system achieves sychroizatio for the short PN sequece, the state sigal is estimated ad loaded ito the log code geerator to perform sychroizatio of the log PN sequece usig the RASE scheme. As the two steps take very short times the, the overall system acquisitio is achieved i a relatively short time. Iput Data Log PN code geerator Short PN code geerator Mixer Mixer State sigal Data spreaded sigal State spreaded sigal Fig. 1 Trasmitter block diagram. 3/8
4 Received short period sequece (State Sigal) Mixer LPF ABS I&D D THR Comparator L Short PN geerator [Early, Late Geerator] E CLK Search lock uit Trackig uit CLK States Hard decisio Itegrator Modulo adder Received log period sequece Mixer Load Track Log PN geerator Examiatio period geerator I lock detector Load/ track logic Cotrol sigal CLK Fig. Receiver Block Diagram. From trackig uit 4/8
5 IV- Performace of FSSSE Acquisitio Scheme Because the FSSSE scheme is a combiatio of double dwell acquisitio scheme (serial search strategy) [3] ad RASE scheme [9] so, the average acquisitio time of the all system is obtaied by averagig the acquisitio times of the two schemes. Double dwell acquisitio scheme is oe of the fastest serial search strategies; it depeds o usig two differet dwell (itegratio) times. The first oe is the shortest time ad therefore it results i a high probability of detectio P D ad a high probability of false alarm P FA. So, this allows eglectig usychroized cells rapidly. The secod dwell time is loger with low P D ad low P FA, these results i a reductio i the overall acquisitio time. It ca be show that the performace i terms of the average acquisitio time T acq ad the acquisitio time variace σ acq for the double dwell acquisitio scheme is give by [1, 4]: T ( P ) qτ L d acq =, (1) P L σ = d + acq τ q, () 1 PL PL where P L = P D1 P D, q is the umber of cells to be tested q = N, N is the PN code legth N= -1, is the legth of the shift register, ad P D1, P D are the probabilities of detectio for the first ad the secod dwell times respectively. The average dwell time τ d is give by: τ d = τ d 1 + τ d PFA1 + TpPFA1PFA, (3) where τ d1 is the first dwell time, τ d is the secod dwell time of the scheme, ad P FA1,P FA are the probabilities of false alarm for the first ad secod dwell times respectively. The total pealty time is give by: T p = K τ d, (4) where K is the umber of pealty times. The mea acquisitio time for RASE scheme is evaluated as follow [9]. Let p deotes the probability of correctly estimatig a particular received symbol; this probability is a fuctio of received SNR. The probability of correctly loadig the shift register of legth i a sigle trial is p, ad the probability of a icorrect shift register load is l-p. The probability of obtaiig a correct load o the k th trial is give by: r k ( k ) = p ( 1 p ) 1 p (5) The average umber of trials required to achieve a correct load is: k= 1 ( k), k = kp (6) k = 1 r ( 1 p ) k 1 k = kp, (7) 5/8
6 Usig the substitutio q=l-p ad m = k-l alog with the idetity m a q ( a + m) q = +, (8) (1 q) ( 1 q) Fially, the average umber of trials required to achieve a correct load is: 1 k =. (9) p Each shift register requires T c secods plus T e (verificatio time) secods to evaluate the correctess of the load. Igorig the possibility that a correct load could be misidetified as a icorrect load, the time required for each trial is (T c +T e ) ad the mea acquisitio time for this system will be: Tc + Te Ts = k( Tc + Te ) =, (10) p Where T c is the chip period ad T e is the verificatio time or the examiatio period. Fially, the over all average acquisitio time of the FSSSE scheme is the summatio of the average acquisitio times of the double dwell acquisitio scheme ad the RASE acquisitio scheme. Tacq =[(-PL)q τ d /PL]+[(Tc+Te)/P]. (11) Oe should otice that i FSSSE acquisitio scheme, the first step of acquisitio, usig the double dwell acquisitio scheme, is doe usig a short period PN sequece (iitial state carrier sigal) istead of the log period sequece ad hece, the average acquisitio time is highly reduced specially i a low SNR eviromet. V- Results: The performace of the FSSSE acquisitio scheme is obtaied i terms of average time to sychroize as a fuctio of SNR, takig ito cosideratio the presece of AWGN. The obtaied result is compared separately with each of the double dwell serial search acquisitio scheme ad the RASE acquisitio scheme for the same code legth. Fig.3 provides the average acquisitio time of the double dwell acquisitio scheme, the RASE acquisitio scheme, ad the FSSSE scheme as a fuctio of SNR. From the figure oe ca otice the followig: 1- The average acquisitio time of FSSSE scheme has a comparable average acquisitio time with the RASE acquisitio scheme at moderate to high SNR. - The RASE acquisitio scheme has a low acquisitio time at moderate to high SNR. However, this system is ot workig at low values of SNR. 3- The average acquisitio time of FSSSE scheme is much less the average acquisitio time of the double dwell acquisitio scheme that works idividually. 4- The FSSSE acquisitio scheme provides the lowest average acquisitio time whe workig i a low SNR eviromet. 6/8
7 Fig. 3 The average acquisitio time of the double dwell scheme, the RASE scheme, ad the FSSSE scheme as a fuctio of SNR i [db]. VI- Coclusios: A proposed combied acquisitio scheme for direct sequece spread spectrum kow as fast serial search sequetial estimatio acquisitio scheme has bee proposed. This scheme gets the advatages of both serial search acquisitio scheme ad RASE acquisitio scheme, while overcomes their drawbacks. The FSSSE proposed scheme provides the lowest average acquisitio time, especially for log period PN codes uder a low sigal to oise ratio workig coditios, whe compared with each of the double dwell serial search acquisitio scheme ad the RASE acquisitio scheme that work idividually. 7/8
8 VII- Refereces 1- M. K. Simo, J. K. Omura, R. A. Scholtz, ad B. K. Levitt, spread spectrum commuicatio hadbook. New York: McGraw- Hill, S. S. Rappaport ad D. M. Grieco, Spread-spectrum sigal acquisitio Methods ad techology. IEEE Commu. Mag., vol., pp. 6-1, Jue A. Polydoros ad C. Weber, A uified approach to serial search spread-spectrum code acquisitio, IEEE Tras Commu. Vol. COM-3, pp , May Jovaovic ad Vlada M. Aalysis of strategies for serial-search spread-spectrum code acquisitio - Direct approach, Tras. Commu., vol. COM-36, , Nov Hyug-Rae Park ad Bub-Joo Kag, O serial search code acquisitio for directsequece spread spectrum system: a applicatio to IS-95 CDMA system, Vehicular Techology Coferece, IEEE 45th Volume 1, Issue, 5-8, pp , Jul Noeaker, D.L., The performace of serial, matched-filter acquisitio i direct-sequece packet radio commuicatios, Military Commuicatios Coferece, MILCOM 001. Vol., pp , Asoodeh, S.ad Maddahi, H., O PN code acquisitio i direct sequece code divisio multiple access, Iteratioal Coferece o Wireless Commuicatios, Networkig ad Mobile Computig, WiCom, pp , Sept Feg She, Digjie Xu ad Big Xue A approach to DS-SS sigal acquisitio usig larger step ad serial acquisitio algorithm, Iteratioal Coferece o Mechatroics ad Automatio, ICMA, pp , Aug R. B. Ward ad K. P. Yiu, Acquisitio of pseudooise sigals by recursio aided sequetial estimatio, IEEE Tras. Commu., vol. COM-5, pp Aug Peg Wag ad Deqiag Wag Acquisitio scheme for DS ultra-widebad with combied spreadig sequece, Iteratioal coferece o wireless commuicatios, etworkig ad mobile computig, WiCom, pp , Sept /8
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