Impact of Multipath and Cross-Correlation on GPS acquisition in Indoor Environments

Transcription

1 mpat o Multpath an Cross-Correlaton on GS aquston n noor Envronments Hanaa A. EL-NAOUR, Eole Natonale e l Avaton Cvle/ esa Anne-Chrstne ESCHER, Eole Natonale e l Avaton Cvle Chrstophe MACABAU, Eole Natonale e l Avaton Cvle Mare-Laure BOUCHERE, Eole Natonale Supéreure e éléommunatons BOGRAHY Hanaa A. EL-NAOUR grauate rom the Lebanese Unversty o Berut n 00 (Engneerng egree n Networks an eleommunatons, an rom the ENSEEH n oulouse, Frane n 003 (masters o researh egree n Networks an eleommunatons. Currently, she s a hd stuent at the ENAC (Eole Natonale e l Avaton Cvle, n oulouse, Frane. She s nvestgatng erent sgnal proessng tehnques or noor GS postonng. Anne-Chrstne ESCHER grauate as an eletrons engneer n 999 rom the ENAC n oulouse, Frane. Sne 00, she has been workng as an assoate researher n the sgnal proessng lab o the ENAC. She reeve her h.d. n 003. Chrstophe MACABAU grauate as an eletrons engneer n 99 rom the ENAC n oulouse, Frane. Sne 994, he has been workng on the applaton o satellte navgaton tehnques to vl avaton. He reeve hs h.d. n 997 an has been n harge o the sgnal proessng lab o the ENAC sne 000. Mare-Laure BOUCHERE grauate rom the ENS Bretagne n 985 (Engneerng egree n Eletral Engneerng an rom eleom ars n 997 (hd egree. She worke as an engneer n Alatel Spae rom 986 to 99 then move to ENS as an Assoate roessor then a roessor. Her els o nterest are gtal ommunatons (moulaton/ong, gtal reevers, multarrer ommunatons, satellte onboar proessng (lter banks, DBFN an navgaton systems. ABSRAC he nee or noor loalzaton s expete to nrease ramatally wth the rsng Loaton-Base Serves (LBS an other loaton an navgaton applatons. But the hallengng noor envronment s one o the bggest obstales or noor loalzaton. he am o the propose paper s to analyze the perormane o the L GS sgnal aquston n noor envronments, n the presene o multpath an o ross-orrelaton eets.. NRODUCON n the past, n orer or GS to work aurately, the presene o an unobstrute Lne-O-Sght (LOS sgnal was neessary. Weak sgnals were not sutable or use beause they may have large assoate nose an other errors. he expanson o GS to Loaton-Base Serves an other navgaton applatons all over the worl, suh as the E-9 an the E- manates n the Unte States an Europe respetvely, s hangng the paragm. Consequently a ramat nrease n the number o requre noor wreless systems s expete. hese rsng noor loalzaton requrements pose a partularly ult hallenge or system esgners, sne an noor hannel s hghly omplate an path loss s very severe most o the tme. An noor rao ommunaton hannel s governe by multple ators lke multpath propagaton, shaowng eets, surrounng objets veloty, moble relatve veloty, an sgnal ntererene (ether wth other GS sgnals or wth other rao sgnals. he multpath onssts o erent replas o the orgnal sgnal ause by reletons, ratons or usons generate when the sgnal enounters an obstale. hese replas are attenuate versons o the orgnal sgnal; they have erent phases, an erent arrval tmes. At the reever they ombne an proue a storte verson o the transmtte sgnal. he shaowng eet manly attenuates the ret sgnal. hs attenuaton s very severe when the sgnal must pass through onrete walls, or ense olage. On the other han, the moble relatve veloty wth respet to the emttng satellte makes the hannel varable over tme. Furthermore, sgnal ntererene wth other rao sgnals an ross-orrelaton wth other GS sgnals also auses a sgnal storton. resente at ON NM 005, San Dego

2 n orer to esgn an noor rao ommunaton system wth optmal perormane, there must be a subtle stuy o the hannel haratersts. n ths paper we manly nvestgate the mpat o multpath an ross-orrelaton on GS L sgnal aquston n a smulate typal noor envronment. For that purpose we have ene a tme-varyng moble rao hannel moel, base on an noor hannel moel realze wthn an ESA (European Spae Ageny projet enttle Navgaton sgnal measurement ampagn or rtal envronments an presente at the ON-GS- 003 [F. érez-fontán et al., 003]. n ths projet, the ESA nvestgate a statstal non-tme-varyng moel whh proves the DF (robablty Densty Funton or eah o the our parameters use to haraterze the hannel: the number o paths, eah path s ampltue, elay, an phase. hese parameters were set to be onstant over tme. n our moel we generate an orgnal sgnal whh stans or a ret LOS sgnal, an many relete an rate replas o ths sgnal. he erene between ths moel an that o the ESA s that eah path elay an phase are assume to be tmevaryng. For the sake o smplty, the relatve ampltues an the number o paths are assume to be onstant urng the aquston pero. hese two parameters are hosen at the begnnng o the smulaton aorng to ther respetve strbutons presente n the ESA paper. hs moel s use to stuy the eet o ether multpath or GS sgnals ross-orrelaton on the aquston phase o the sgnal proessng n the reever. he paper s organze as ollows: rst we esrbe the noor hannel moel use, next, we present the aquston algorthm evelope uner Matlab. he two subsequent parts show smulaton results. he rst shows the mpat o multpath on the aquston perormane, whle the seon eals wth ntererene nue by another GS sgnal. Fnally, a onluson s rawn rom these results.. HE NDOOR CHANNEL MODEL he GS sgnal stue s onsere as the output o an noor tme-varyng hannel whh has the ollowng transer unton: h( t = Eq N = α δ ( t e j smulaton, an s hosen aorng to the strbuton o the number o rays reahng the reever gven n [F. érez-fontán et al., 003], α s the multpath replas relatve ampltue wth respet to the ampltue o the ret ray. hs parameter s onsere to be onstant over the uraton o the smulaton, an s also hosen aorng to the strbuton o the rays powers gven n [F. érez-fontán et al., 003], s the elay experene by the ret LOS ray an the relete rays respetvely. hs elay s essentally ue to the sgnal propagaton rom the satellte to the reever, π 0 0 = s the phase storton ntroue by the hannel. 0 s a ranom 0 ;π. ntal phase unormly strbute over [ ] Consequently, the GS sgnal that s suppose to reah the reever has the ollowng expresson: N = ( t ( t os( π t s = α Wth L the Coarse/Aquston (C/A GS oe arrer requeny, L = MHz, the C/A oe, an the ata bts. When proessng the GS sgnal we assume that the arrer requeny was alreay shte to an ntermeate Frequeny (F o.5 MHz. he stue sgnal s then: N = ( t ( t os( π t s = α Eq Note that the hannel phase storton only aets the arrer phase. he elay s assume to have lnear varatons wth respet to tme. ts value epens on two types o multpath replas: relete replas an rate ones. hese two ases are llustrate n Fg. 0 Where N s the number o rays that reah the reever. hs set o rays may ether ontan a ret LOS or not. N s onstant over the uraton o the resente at ON NM 005, San Dego

3 S the satellte elevaton angle. v s also onsere onstant over the uraton o the smulaton. Dratng obstale ' 0 R γ h Dreton o the th obstale plane th reletng obstale he elays experene by the multpath replas are ene wth respet to that o the ret LOS. n the ase o relete rays, ths s one usng a lassal moel o releton. he path ollowe by the relete ray ers rom that o the ret ray ( 0 by h sn, where s the angle between the ret ray an the obstale plane. t has a ranom value unormly strbute n [ 0 ;π ]. An, h s the stane between the reever an the obstale plane. h s also suppose to have lnear varatons wth respet to tme: h = h0 + vrt sn( γ, where h 0 s the ntal stane between the reever an the obstale; t takes a ranom value between [ 0 m; 5m], v r s the reever veloty. st reletng obstale h Reletng obstales Horzontal lne Hene, the elay experene by a relete ray s expresse as: 0 vt h = + + sn Eq 4 Fg relete an rate rays o a GS sgnal. Relete rays are n otte lnes an rate rays are n sol lnes. he ret LOS s n ashe lne. he reever s suppose to be at m above the groun level,.e. n the han o a user. We also suppose that t moves horzontally, an ts stane wth respet to obstales vares between 0 an 5m approxmately. he elay experene by the ret LOS ray s: Eq 3 = 0 Where + vt 0 s the ntal stane between the satellte an the reever. t s onstant throughout the smulaton, v s the Doppler veloty orresponng to the onsere satellte elevaton angle. t s gven vsre osγ by: v = [Kaplan, r + r r r sn γ e s 996], where v s s the satellte lnear veloty, r e s the earth s raus, r s s the stane between the earth s entre an the satellte, γ s e s Where s the lght veloty. For a rerate ray, the elay s gven by the rato o the length o the total path ollowe by the ray ve to the veloty o lght. n Fg, Al-Kash law gves: ' ( + v t + ( ( + v t ( = + Eq os Where ( + ( v t ( ( v t ( γ ' an also. =, 0 r 0 r os 0 s a ranom ntal stane that les n [ 0 m; 5m] Whle there are muh more rerate rays than relete rays, the ormer are muh more attenuate. hs s why 80% o the multpath replas generate wll be onsere as relete rays (the less attenuate ones, an the remanng rays are onsere to be rerate. Eah generate sgnal has a uraton o s. All o the results presente n ths paper eal wth a stat user sne we oun that the results obtane wth a ynam user (wth a veloty o m/s were smlar or the sgnal uraton o s. hs oul nee be explane by the at that the reever veloty s very neglgble wth respet to that o the satellte. resente at ON NM 005, San Dego 3

4 Ater generatng the sgnal, we a to t whte nose wth a known power. he resultng value o the sgnal power to nose ensty rato wll be reerre to by the nput C / N0. hen we quanty t usng a -bts quantaton proess. An attenuaton o approxmately B s urther nue ue to ths quantaton [Splker et al., 996]. Fnally, we aqure the sgnal. hroughout the aquston proess we estmate the arrer Doppler requeny, the oe elay an the C / N0 rato. he result s llustrate by a orrelaton matrx as t wll be explane n the next seton.. HE ACQUSON ALGORHM ALED Aquston s a oarse synhronzaton proess gvng estmates o the RN oe oset an the arrer Doppler. he oe oset s ue to the sgnal propagaton. he arrer Doppler s the result o the satelltes an the reever ynams, an o the requeny rt o the reever loal osllator. he estmate RN oe oset an arrer Doppler an be use to ntalze the trakng loops whh perorm a ner searh over the two parameters the C / N 0 s suently hgh. We assume the RN oe that must be use or espreang to be alreay known. hs GS sgnal two-mensonal searh proess s ene n an unertanty regon n whh oe an arrer phase are algne wth the reeve sgnal. he orret algnment s ente by the measurement o the output power o the orrelators (Fg. he result o ths two mensonal searh s an estmate o the oe Oset to wthn one hal hp, an o the arrer Doppler to wthn hal the Doppler searh bn sze (several hunre Hz. he aquston sheme apple to the quante GS sgnal s base on a Fast Fourer ransorm (FF algorthm as llustrate n the ollowng blok agram: FF s(t os( π k e ˆ ( k e sn( π k e ˆ FF nphase FF quarature Correlator onj Fg : Aquston proess blok agram FF ( Q FF ( M Averagng the nphase an the quarature omponents respetvely, n the orrelator, beore squarng them s alle oherent ntegraton. he oherent ntegraton s realze over p ms o sgnal. hs reues the mpat o nose on the sgnal. he whole proess an be repeate many tmes n orer to urther reue the mpat o nose. hs s alle non-oherent ntegraton. We ene M as the number o non-oherent ntegratons. he well tme s then ene as the prout o p an M. t gves the total uraton o the sgnal beng proesse n the aquston phase. he output sgnal an be expresse as [Splker et al., 996]: = Eq 6 M ( ( k + Q ( k k= Wth A sn( π p ( k = ( k R k π p ( ε ( k os( ε ( k + n ( A sn( π p Q( k = ( k. R Q k π p ( ε ( k sn( ε ( k + n ( Where, ε (k an ε (k are the Doppler requeny, the oe elay an the phase error respetvely. he mpat o the phase error on the useul sgnal s elmnate by squarng the two sgnal omponents an ang them. beomes: = = Eq 7 Wth M k= M k= n an Q n are the whte Gaussan orrelator output nose omponents, wth power N 0 p σ n = = σ nq 4 A A + A R 4 N = A + A ( k R( ε ( k R( ε ( ε ( π sn π ( k R ( ε ( k R ( ε ( π sn π ( π sn π os + ( π sn π ( ε + n ( k sn ( π sn π ( ε + n ( k Q [ n ( k + nq ( k ] os sn ( ε n ( k ( ε n ( k Q + N resente at ON NM 005, San Dego 4

5 he prevous expresson shows that the nal sgnal ( π ontans a sgnant term A sn R ( ε an 4 π two other nose terms that wll eventually ause sgnal attenuaton. One o these terms n ( k n ( k + Q s an atve nose ue to the sgnal propagaton rom the satellte to the user reever, an the other nose term s ue to the oe elay an the arrer Doppler estmaton errors. he next step s to n the rght peak o the eteton matrx. he one whh s lkely to orrespon to the rght Doppler requeny an oe elay o the GS sgnal stue. hs s one by applyng a hypothess test, alle the eteton rtera. n the presene o nose, a threshol s set an ompare to the value o the sgnal at the output o the reever (. Any ell envelope that s below the threshol s etete as nose, an any ell envelope that s at or above the threshol s etete as the presene o the sgnal. s maxmum when the repla an the reerene sgnal are algne. he requeny bns are a unton o the oherent ntegraton tme. n our ase they are equal to: =. p he avantage o the FF algorthm wth respet to the onventonal sequental tme oman tehnque s that t alulates, or a selete Doppler, the orrelaton or an entre elay range menson o uratonp n a sngle step. We assume n the ollowng that we nee to searh all oe elays over the whole pero o the C/A oe, thus usng an FF algorthm reues the mean aquston tme. Note that nreasng the oherent ntegraton tme p urng the aquston proess, mproves the SNR rato, beause the orrelator output nose power, n σ = N / 4 s nversely proportonal to 0 p / 4 = N0 p ths tme, an wll be lowere. However, ths nvolves more alulatons an hene, s tme onsumng. he tme onsumpton oes not nrease lnearly wth p. n at, a hgher p mples smultaneously an nrease number o ata ponts to be treate, an an nrease number o requeny ells to be searhe sne the aeptable requeny unertanty s nversely proportonal to p resultng n more requeny ells to be searhe. Another lmtng ator or p s an eventual ata bt transton, knowng that a ata bt has a uraton o 0ms. hs problem oul be avoe by settng p to ms, an nreasng the number o non-oherent ntegratons M. But, as a result, the nose s square. Generally, the nose ompensaton obtane when nreasng p s better than that obtane when nreasng M. n summary, a ompromse must be oun. As a onluson, the eteton o the sgnal s a statstal proess base on a hypothess test: Hypothess H 0 : he sgnal s not present, an the onsere ell ontans only nose. Hypothess H : he onsere ell ontans nose wth sgnal present. n the ase o H, when the rght Doppler requeny an oe elay are oun, the resultng attenuaton s suppose to be neglgble, an the value o the peak A etete s suppose to be: max + m b, where m b s 4 the mean nose level. hus the power o the useul sgnal A s C = = ( max m b. n other wors, one a peak s oun at the en o the aquston proess, the sgnal power an be estmate. Durng our smulatons, to nsure that the Doppler an the oe elay oun at the en o the aquston proess are aurate, these two parameters are alulate a pror or eah sgnal. he Doppler requeny an be eue rom the arrer nstantaneous phase whh s gven by: = t φ π π 0 Aorngly, the nstantaneous requeny s: nst Wth φ = = π t hs yels: 0 = t the Doppler requeny. v v 0 + sn( elev sn r = For a stat reever,.e. vr = 0 m/s, the Doppler requeny o the ret LOS s gven by: = 0 Eq 8 v Next the smulaton results wll be presente. Note that the global aquston tme was not stue. By global aquston tme we mean the tme neee to loa the sgnal an then proessng t. resente at ON NM 005, San Dego 5

6 V. MAC OF MULAH ON ACQUSON ERFORMANCE n orer to stuy the mpat o multpath on the aquston perormane, we wll ompare results obtane wth a sgnal wthout multpath (.e. just the LOS sgnal, wth a omposte sgnal ontanng a LOS an erent multpath replas, an wth a omposte sgnal wthout a LOS (Non-LOS. wo GS sgnals are teste: that o satellte number wth a onstant elevaton angle o 30, an that o satellte number wth a onstant elevaton angle o 45. he multpath replas have erent relatve ampltues, phases an angle o arrvals. hese parameters are not the same or the two sgnals. he stanes between the reever an the obstales are not nether the same or the two sgnals. However, all o these parameters wll be the same n the three ases esrbe above, namely the LOS only, the LOS wth multpath replas an the Non-LOS ase or a spe GS sgnal. he Doppler requeny an the oe elay or the GS sgnal o satellte number are alulate by applyng Eq 3 an Eq 8 whh gves F = 4666Hz an = hps respetvely. For the GS sgnal o satellte number, the Doppler requeny an the oe elay are expete to be at 4075Hz an hps respetvely. Detete peaks Fg 3: LOS wthout multpath replas; true values: Doppler requeny -4666Hz, oe elay hps, ntal C / N0 BHz; estmate values: Doppler requeny -4750Hz, oe elay hps, C / N BHz n the presene o a LOS wth multpath replas, the mnmal C / N 0 that oul be etete was also BHz (Fg 4. For eah o these omposte sgnals we wll try to aqure the orgnal sgnal usng the aquston algorthm esrbe n seton. We rst start by settng p to ms n orer to reue the tme onsumpton. hen we nrease the value o M up to 000 untl we got the rght values o Doppler requeny an the oe elay. a nonoherent ntegraton over 000 ms o sgnal,.e. seon, was not suent we nrease the value o p as long as the omputaton altes o the proessor allow ong t. he results below show the mnmum C / N0 value that oul be aqure. he rst value o the C / N0 s that o the nput C / N0. he nose ntroue pror to the quantaton stage represents the nose that aete the ret LOS. he seon one s the C / N0 estmate by the aquston algorthm at the en o the aquston. he real C / N0 value s obtane by ang to the estmate value the attenuaton ue to quantaton. As t s llustrate n Fg 3 below, or a LOS sgnal wthout multpath replas the mnmum C / N0 that oul be aqure s BHz. Fg 4: LOS sgnal wth multpath replas; true values: Doppler requeny -4666Hz, oe elay hps, ntal C / N 0 BHz; estmate values: Doppler requeny -4750Hz, oe elay hps, C / N BHz We note that the estmate C / N 0 n these two ases s very lose to the real one wth an estmaton error that s below 0.5BHz, an the values o the Doppler an the oe elay are aurate. Hene multpath replas not sturb the aquston proess. resente at ON NM 005, San Dego 6

7 As epte n Fg 5, n the ase o a Non-LOS omposte sgnal, the mnmum C / N 0 rato that oul be etete s rather 40BHz. n other wors, a ret LOS sgnal ha a C / N 0 rato lower than 40BHz an oul not reah the reever (beause o shaowng, or nstane, the multpath replas generate woul not allow or nng the esre sgnal. Fg 5: Non-LOS sgnal, multpath replas only; true values: Doppler requeny -4666Hz, oe elay hps, ntal C / N 0 40BHz ( C / N0 that aete the LOS that oul not reah the reever; estmate values: Doppler requeny -4750Hz, oe elay hps, C / N0.985BHz n ths ase we oun that the multpath replas were severely attenuate wth respet to the LOS. We repeate the prevous smulatons wth another sgnal, an we got smlar results as epte n Fg 6 an Fg 7 Fg 7: Non-LOS sgnal, multpath replas only; true values: Doppler requeny -4075Hz, oe elay hps, ntal C / N 0 5BHz ( C / N0 that aete the LOS that oul not reah the reever; estmate values: Doppler requeny -4000, oe elay hps, C / N0 0.9BHz n Fg 7, the multpath replas were not as attenuate as n the rst ase. But n both Fg 5 an 7 we oul aqure the sgnal, an we not have errors on the Doppler an the oe elay estmate. As a onluson, the multpath replas have mnor mpat on the aquston perormane, when a ret LOS s present. n aton, even a LOS s not avalable, the multpath replas oul be explore, but they are muh attenuate wth respet to the LOS sgnal. n all ases multpath replas not nue errors on the sgnal aquston. On the other han, n Non-LOS ases, the mnmum C/N0 o the ret (maske sgnal or suessul aquston epene on the noor envronment (5-40 BHz. V. MAC OF CROSS-ORRELAON ON ACQUSON ERFORMANCE Fg 6: LOS sgnal wth multpath replas; true values: Doppler requeny -4075Hz, oe elay hps, ntal C / N 0 BHz; estmate values: Doppler requeny -4000Hz, oe elay hps, C / N0.677BHz Ater havng stue the eet o multpath on sgnal ang n noor envronments, the next step wll be to stuy the mpat o ntererene between erent satellte sgnals. n at there are stuatons where a strong path may nterere wth another weak path. n ths ase, aqurng the weak sgnal s very ult, an may lea to a ross-orrelaton peak. hs ross-orrelaton peak s generally expete approxmately -3.9BHz apart rom the autoorrelaton peak [roaks, 995]. o llustrate ths stuaton, we use the same moel that was evelope or the multpath smulaton, an extene t to support resente at ON NM 005, San Dego 7

8 erent satellte sgnals. We tre two satellte sgnals ntererng wth eah other, wth erent powers. etete peak has the same (Doppler requeny, oe elay ouple as that o Fg 8 (n Fg 9. We starte by smulatng two GS sgnals (or satelltes number an an ther multpath versons, settng the C / N 0 rato to 50BHz or the rst one an 5BHz or the other one. Note that satellte has a null Doppler, whle satellte has a Doppler requeny o 4000Hz. We tre to aqure the satellte number. he result o aquston s epte n Fg 8. Fg 9: LOS sgnal o satellte number wthout multpath replas or nose, true Doppler 0Hz, true oe elay hps, sgnal aqure wth C/A oe o satellte number. Estmate values: Doppler requeny 0Hz, oe elay hps, C / N BHz Fg 8: Cross-orrelaton between GS sgnals: - LOS sgnal o satellte number wth multpath replas, true Doppler -4075Hz, true elay hps, ntal C / N0 5BHz - LOS sgnal o satellte number wthout multpath replas, true Doppler 0Hz, true elay hps, C / N0 50BHz. he sgnal aqure s the rst one (sat. Estmate values: Doppler requeny 0Hz, oe elay , C / N0.77BHz As we an see n ths gure, the peak orrespons to a null Doppler whh s the Doppler o satellte, the stronger sgnal. n aton, ths peak s oun at approxmately 7BHz less than the ntal C / N 0 apple to the sgnal o ths satellte, namely 50BHz. By ang the attenuaton ue to the quantaton, the estmate C / N0 orresponng to ths peak wll be very lose to the theoretal value o approxmately 5BHz. hs leas us to assume that the peak s very lkely to be a ross-orrelaton one. We note that there s a erene o 0. hps approxmately between the oe elay estmate n the ase o Fg 8, an that estmate n the ase o Fg 9. n at, the oe elay unertanty at the en o aquston s equal to the samplng pero e = Fe = 5*0, sne we use a samplng requeny o 5MHz. hs gves a samplng pero o 0. µ s, whh orrespons to 0.hp. hus the erene we observe between the two gures orrespons to one oe elay bn, wth a uraton o e. But n general, the oe elay unertanty neee at the en o the aquston proess s o 0.5 hp. hus the erene observe prevously s largely wthn ths lmt. However, n general, the ross-orrelaton matrx s not suppose to have peaks whh are stronger than others. But ths s not the ase n Fg 9. n other wors, we were not suppose to have many strong peaks n the Doppler bn o satellte. hs may be ue to the eet o the oe Doppler rt whh may anel some rossorrelaton peaks. Fg 0 llustrates another ase where a ross-orrelaton peak s etete. We also vere that the etete peak s a ross-orrelaton one by the same way as beore. 6 n orer to be sure that t s a ross-orrelaton peak, we aqure the sgnal o satellte alone wthout nose, but use the C/A oe o satellte n ths aquston. he resente at ON NM 005, San Dego 8

9 replas. he ross-orrelaton eet was stue by ang two o these sgnals together. Fg 0: Cross-orrelaton between GS sgnals: - Non LOS sgnal o satellte number 6 (just multpath replas, true Doppler Hz, true elay hps, ntal C / N0 5BHz - LOS sgnal o satellte number wth multpath replas, true Doppler 0Hz, true elay hps, ntal C / N 0 50BHz. Estmate values: Doppler requeny 0Hz, oe elay hps, C / N0.5877BHz Fg 8 an 0 show that the ross-orrelaton sturbs the aquston o a spe sgnal. he weakest sgnals presente the prevous gures, namely the sgnals o satelltes an wth 5 BHz eah, oul be aqure wthout ultes the ntererng sgnals were not present. n onluson, the man mpat o GS ross-orrelaton on the aquston perormane s a probable rossorrelaton peak, whh leas to naurate values o the Doppler requeny an the oe elay, an hene to nauraes n the user poston estmaton. Furthermore, the peak etete by the aquston algorthm s lkely to be a alse alarm one. hus t s generally ult to very that a peak s a rossorrelaton one or not, espeally when ealng wth real GS ata. V. CONCLUSON n ths paper we nvestgate the mpat o Multpath replas an ross-orrelaton on the GS sgnals aquston. Frst, we mplemente an noor tme varyng hannel moel base on a stat noor moel evelope by the ESA an presente n 003. hs moel was use to generate three types o noor GS sgnals: a ret LOS sgnal, a omposte LOS sgnal wth multpath replas, an a Non-LOS sgnal whh ontans only multpath Next, we nvestgate the mpat o multpath by testng the aquston o these generate sgnals or a total well tme o s, wth p= or ms, an M=000 or 500. he aquston s base on a lass FF algorthm. We ouse our work on the apaty o eteton o a orrelaton peak over the eteton threshol, an we not analyze the total tme neee or aquston. he multpath replas elays n ths moel are very neglgble wth respet to those o the ret LOS, thus we etet a multpath repla t has approxmately the same elay an Doppler as that o the LOS. he results show that n the LOS ases, multpath replas have mnor eets an o not sturb the sgnal aquston sne they muh attenuate wth respet to the ret LOS. n the Non-LOS ases, even though the multpath replas are muh attenuate, they oul be use to n the ntal sgnal. Stuyng the ross-orrelaton, we oun that aorng to ths moel, a ross-orrelaton sturbs the aquston perormane. But no subtle onlusons oul be rowne yet onernng the mpat o ross-orrelaton. Our uture works nlue a eeper analyss o the sgnature o ross-orrelaton eets. hs sgnature wll be use to try an evelop erent mtgaton tehnques or noor aquston. ACKNOWLEDGMENS We woul lke to thank Dr. Bernar SOUNY rom the ENAC, oulouse, Frane, an ng. Stephane CORRAZZA rom Alatel Spae, oulouse, Frane, or ther valuable remarks an suggestons. REFERENCES [F. érez-fontán et al., 003] - F. érez-fontán, B. Sanmartn, A. Stengass, A. Lehner, J. Selva, E. Kubsta, B. Arbesser-Ratsburg (003, Measurements an Moelng o the Satellte-to-noor Channel or Galleo, roeengs o the ON-GS-003 [Kaplan, 996] Elott D. Kaplan (996, Unerstanng GS: rnples an Applatons, Arteh House, Norwoo, MA [roaks, 995] - J. G. roaks (995, Dgtal Communatons, hr Eton, MGraw-Hll. [Splker et al., 996] - J.J Splker Jr. an B. W. arknson (996, Global ostonng System: heory an Applatons Volume, Ameran nsttute o Aeronauts an Astronauts, n, Washngton DC. resente at ON NM 005, San Dego 9