GPS L5 Receiver Implementation Issues

Transcription

1 GS L5 Receiver Imlemetatio Issues Christohe MACABIAU, EAC Lioel RIES, CES Frédéric BASTIDE, EAC/TéSA Jea-Luc ISSLER, CES BIOGRAHY Christohe Macabiau graduated as a electroics egieer i 99 from EAC (Ecole atioale de l Aviatio Civile i Toulouse, Frace. Sice 994, he has bee workig o the alicatio of satellite avigatio techiques to civil aviatio. He received his h.d. i 997 ad has bee i charge of the sigal rocessig lab of the EAC sice. Lioel Ries is a avigatio Egieer i the Radioavigatio Deartemet at CES (Frech Sace Agecy, sice Jue. He studies GSS sigal icludig BOC ad GSIIF-L5. I additio, he is ivolved i exerimets o a GSS avigatio ayload demostrator (develoed by CES. He formely worked for Altra, as cosultat (Astrium, Toulouse ad Allgo Stockholm, Swede. He graduated i 997 from the "Ecole olytechique de Bruxelles, at Brussels Free Uiversity (Brussels, Belgium, i 997, ad received a M.S. degree from the "Ecole atioale Suerieure de l'aeroautique et de l'esace" (Suaero, Toulouse, Frace. Frederic Bastide graduated as a electroics egieers at the EAC, the Frech uiversity of civil aviatio, i, Toulouse. He is ow a h.d studet at the EAC. His researches focus o the study of dual frequecies receivers for civil aviatio use. Curretly he is workig o DME/TACA sigals imact o GSS receivers. He also set 6 moths at the Staford GS Lab earlier this year as a exchage researcher. Jea-Luc Issler is head of the Radio avigatio Deartmet at CES, whose mai task are sigal rocessig ad radio-avigatio equimets. He is ivolved i the develomet of several GSS sacebore receivers i Euroe, as well as studies o the future Euroea Radioavigatio rograms, like Galileo ad the seudolite etwork. ABSTRACT The ew L5 sigal is QSK modulated, with a omial carrier frequecy of MHz ad a badwidth of 4 MHz. Its two comoets have each a differet sreadig code clocked at.3 MHz. The i-hase comoet, also called the data chael, carries the avigatio message at symbols er secod (5 bits er secod with a covolutioal ecoder while the quadrature comoet, called the ilot chael, carries o message at all. The data ad ilot L5 sreadig codes are each modulated with a distict euma-hoffma code clocked at khz. The secified ower is such that the received levels o the groud should be 54.9 dbw (i.e dbw for each comoet. Such a ew sigal structure imlies ew receiver structures for acquisitio, trackig ad data demodulatio. I articular, differet strategies ca be evisioed for L5 codes ad euma-hoffma acquisitio, ad several correlator oututs usig data ad ilot sigals ca be combied to form the trackig loos discrimiatio fuctios. The aim of the roosed aer is to show results of a aalysis of the ossible structures for acquisitio of the L5 codes ad of the euma-hoffma codes, as well as structures used for L5 sigal trackig, ad evaluated erformace of these acquisitio ad trackig structures. I. ITRODUCTIO The US declared i 999 their itetio to rovide a ew GS sigal called L5 [Silker ad Va Dieredock, 999] cetred i MHz, targeted for civil aviatio uses. That ew sigal civil should be radiated by the first Block IIF satellites lauched i 5. It will make GS rovide a avigatio service more robust for multile alicatios, ad esecially for civil aviatio alicatios. Ideed, this additio will icrease Sigal-I-Sace accuracy, availability, itegrity ad cotiuity of service. This ew L5 sigal is QSK modulated, with a omial carrier frequecy of MHz ad a badwidth reseted at IO GS 3, ortlad

2 of 4 MHz. Its two comoets have each a differet sreadig code clocked at.3 MHz. The i-hase comoet, also called the data chael, carries the avigatio message at symbols er secod (5 bits er secod with a covolutioal ecoder while the quadrature comoet, called the ilot chael, carries o message at all. The data ad ilot L5 sreadig codes are each modulated with a distict euma-hoffma code clocked at khz. The secified ower is such that the received levels o the groud should be 54.9 dbw (i.e dbw for each comoet. Such a ew sigal structure imlies ew receiver structures for acquisitio, trackig ad data demodulatio. I articular, differet strategies ca be evisioed for L5 codes ad euma-hoffma acquisitio, ad several correlator oututs usig data ad ilot sigals ca be combied to form the trackig loos discrimiatio fuctios. This aer reorts the aalysis of several questios raised durig the desig ad the imlemetatio of a L5 geerator/receiver simulator carried out by M3SYSTEMS ad TéSA (EAC, SuAéro for the CES. Those questios are related to the erformace of the acquisitio of the L5 ad euma-hoffma codes, ad to the erformace of the differet trackig strategies that ca be evisioed. The aer starts by recallig the GS L5 sigal structure ad roosed geeric receiver architecture. This is followed by two distict sectios, oe dealig about acquisitio, the secod oe dealig about trackig. The classical structure for L5 code acquisitio usig ilot oly or ilot+data chaels is described, ad acquisitio erformace is recalled. ext, we describe a roosed techique to acquire the euma-hoffma codes after the L5 codes were acquired, which cosists i ruig a FLL to reduce residual Doler, the erformig a euma-hoffma code search. It is also show that a FLL ca be ru after the L5 code acquisitio as its loss of lock threshold is below the L5 code acquisitio threshold. Fially, we aalyze the erformace of a roosed structure for direct ad combied L5 code ad euma-hoffma code acquisitio, ad we show that its erformace is highly degraded whe the residual Doler is larger tha Hz. Idicatio of ossible erformace imrovemet usig other or bit code will be give i the aer. We the aalyze several ossible techiques for code ad carrier hase trackig usig ilot ad data correlator oututs. I articular, cocerig carrier hase trackig, we show the aalysis of a roosed techique combiig data arctaget discrimiator ad ilot exteded arctaget, which requires carrier hase jums detectio ad reair, ad we show that its erformace is o better tha the erformace of ilot exteded arctaget oly. A selectio of the most aroriate code ad hase trackig techiques is fially roosed. II. GS L5 SIGAL STRUCTURE The L5 sigal radiated by satellite i is a QSK modulatio of the L5 carrier with a data ad a ilot chael that ca be modeled as: S i L5 ( t + i d ( t i ( t XI ( tcos i ( t XQ ( tsi ( f 5t ( f t where is such that the miimum total ower of the received L5 sigal is 54.9 dbw, or 57.9 dbw for each oe of the data ad ilot comoet [RTCA, ]. d is the /RZ/L materializatio of the L5 avigatio message ecoded with a covolutioal FEC (rate ½. The origial L5 avigatio message has a 5 bs rate, while d has a fial ss rate after ecodig. Thus the duratio of oe fial symbol i d is ms. ad are resectively the /RZ/L materializatio of a bit ad bit euma- Hoffma code. These codes are clocked at a rate of khz, thus the duratio of oe bit is ms. XI ad XQ are resectively the /RZ/L materializatio of the data ad ilot comoet R codes. Those codes are clocked at a rate of.3 MHz ad have a eriod of ms. roerties of the L5 codes were aalyzed i [Macabiau et al., ]. III. RECEIVER ARCHITECTURE The roosed L5 geeric receiver trackig loos architecture is show i figure at the ed of this aer. I each chael, the hase ad code trackig loos ca otetially use correlator oututs from the data ad ilot chaels. As a cosequece from this, the chael may track the data or the ilot sigal or both. IV. ACQUISITIO STRUCTURE /ERFORMACE GS L5 sigal acquisitio is uderstood here as the rough sychroizatio of the sigals geerated locally by the receiver with the icomig sigals. This cocers the local carrier ad the local codes. The local codes ca be the L5 codes oly, or the L5 codes ad the euma-hoffma codes. I this sectio, we first reset a roosed structure for L5 codes acquisitio ad discuss the erformace of this acquisitio. The, we reort the strategies for a comlete acquisitio of the L5 sigal, i.e. the acquisitio of the carrier, L5 codes ad euma-hoffma codes. IV. L5 CODES ACQUISITIO 5 reseted at IO GS 3, ortlad

3 The L5 codes acquisitio is accomlished usig both the data ad ilot comoets to use the maximum sigal ower, as show i figure. I I I Q Q Q Q I ( ( ( ( Figure : L5 acquisitio structure. It has bee show i [Bastide et al., ] that a accetable acquisitio threshold with a simle sigle dwell rocedure is aroud 33.7 db Hz. This has bee obtaied through a coheret itegratio time T of ms to reduce the Doler ucertaity bi to a width of [-5 Hz; + 5 Hz] ad 5 o-coheret itegratios, iducig a worst case loss of -.5 db ad a mea sequetial acquisitio time aroud 64 s whe searchig oly oe Doler bi with a code search ste of.5 chi. I the case of FFT acquisitio, the 33.7 db acquisitio is still valid with T ms ad 5 ocoheret itegratios. ote that this threshold is db higher tha i the case where oly oe sigle data or ilot comoet is used [Bastide et al., ]. The L5 mea code acquisitio time is times larger tha that the GS L C/A code acquisitio time because the L5 codes are times loger tha L C/A codes ad ca oly be comesated by augmeted hardware. The L5 acquisitio erformace is also reduced comared to L acquisitio erformace because of the resece of euma-hoffma codes both o the data ad ilot sigal comoets. Ideed, these euma-hoffma codes are viewed as data modulatio durig the acquisitio rocedure where bit sychroizatio is ot achieved yet. As the legth of oe euma-hoffma bit is ms, the coheret itegratio time is therefore limited to ms with L5 to limit ower losses due to data bit trasitios, while the coheret itegratio time is limited to ms with L. Although icreasig the coheret itegratio time has the drawback to icrease the umber of searched Doler bis by the same amout, there is a iterest to icrease that time whe oly oe Doler bi eeds to be searched [Bastide et al., ] or whe the available hardware has a icreased erformace. But ufortuately there is o otetial imrovemet of the coheret itegratio time with L5 from the classical ms, which is ot the case for L C/A. IV.. L5 CODES + EUMA-HOFFMA CODES ACQUISITIO Before usig correlator samles that have bee itegrated over a iterval larger tha ms, it is ecessary to erform the euma-hoffma codes sychroisatio. M T That oeratio ca be doe usig the ms samles through a search rocess similar to the L5 code search rocess: the ms samles are correlated with a local code geeratio ad the eak is searched. The roblem here is that the search rocess is affected by the resece of a residual Doler shift o the ms oututs. Therefore, the autocorrelatio roerties are highly degraded because the codes are short codes. As a examle, figure 3 shows the sigal rocessig techique roosed i [Hegarty, Tra ad Va Dieredock, ] for direct combied ad L5 code acquisitio of the ilot comoet. The curret aer focuses o the degradatio of the acquisitio criterio used i resece of residual Doler shift. The roosed acquisitio techique ca be alied either o the data or o the ilot sigal comoet. The iut sigal (data or ilot comoet is exressed as ( f t ( s ( t d( t τ c( t τ ( t τ cos θ + t here is the L5 sigal ower (data lus ilot d is the L5 data waveform if the cosidered L5 comoet is the data comoet c is the L5 code waveform of the cosidered sigal comoet XI or XQ is the euma-hoffma waveform ( if data comoet, if ilot comoet f is the last itermediate frequecy τ is the grou roagatio delay, θ is the received carrier hase shift (both vary over time is the additive oise c ( t τˆ ( f t ˆ θ cos ( f t ˆ θ si ms ms ms ms I( ( Q( Figure 3: acquisitio structure. ( w T M k ( reseted at IO GS 3, ortlad 3

4 I the geeral case, the I ad Q correlator oututs ca be exressed as: ( ft si I( ft + I ( si Q( ft + Q ( where ( ft d( ( K d( ( K c ( ε cos( ε c τ ( ε si( ε K c is the L5 code auto-correlatio fuctio T is the coheret itegratio time (T ms i our case f is the residual relative Doler shift (differece betwee icomig carrier frequecy ad local carrier frequecy θ ˆ θ is the hase trackig error ε θ τ ˆ τ is the code trackig error ε τ I ad Q are the correlator outut oise samles If we deote θ 5 T ( t + θ sigal, ( t f the hase of the icomig T beig the liear ortio of the grou roagatio delay dθ f d i the icomig sigal Doler dt shift d ˆ θ f d l the local sigal Doler shift dt f f d f the residual relative Doler shift i d l It ca be show that i resece of residual Doler, the correlator oututs ca be exressed as: I( Q( si ( ft si ft cos ( ft + εθ si( ft ft ( ft + ε τ d( ( K + ( d( ( K + ( θ I Q c ( ε c τ ( ε τ θ θ where T is the coheret itegratio time (T ms i our case. ε θ θ θˆ As we ca see from this exressio, the correlator oututs are multilied by cos ad si weights whose hase is varyig ms after ms. The frequecy of this variatio is recisely the relative Doler residual f. Whe a classical acquisitio structure is used, these correlator oututs are squared ad summed, removig these cos ad si weights. I the structure roosed i [Hegarty, Tra ad Va Dieredock, ], these correlator oututs are multilied by a local relica, the or samles are accumulated deedig o the sigal comoet cosidered. Therefore, i resece of a residual Doler, as these weights will have chaged from samle to samle, the squared sums will ot remove these weights ad the resultig squared correlatio fuctio will be distorted. Cosiderig, the samles resultig from this ew accumulatio ca be exressed as: I Q ( m ( m I( Q( ( m ( m ote that the code correlatio fuctio i resece of Doler is differet from the code correlatio with zero Doler. To take this effect ito accout, a ew code / Doler search ca be erformed. I this case, the I ad Q correlator samles eed ot oly to be multilied by a local code relica, but also by a local carrier. I that case, due to the sic weight affectig the correlator oututs, a Doler search must be carried out usig Doler cells. A evaluatio of the umerical imact of the Doler residual o the acquisitio criterio is roosed first. We roose here to evaluate the effect of the Doler residual o the direct ad combied L5 code ad acquisitio criterio. I the first ste, the direct ad combied L5 code ad acquisitio criterio roosed i [Hegarty, Tra ad Va Dieredock, ] is evaluated i resece of Doler residual. I the secod ste, this acquisitio criterio is evaluated for a comlete code / Doler search. This reseted at IO GS 3, ortlad 4

5 search is carried out for all bits of the code, ad i the comlete -9 khz + 9 khz search iterval. The size of the Doler bis is imlied by the ms itegratio time iducig a sic weight havig its first zero i 5 Hz. I the evaluatio roosed, the comlete search widow is [-5 Hz; 5 Hz]. I both stes, we assume that the L5 code aligmet is correct withi ms ( τ ˆ τ modulo ms ad o additioal costat hase shift is affectig the carriers θ θˆ. ( We aalyze the evolutio of the combied L5 code acquisitio test criterio as a fuctio of the local lag with differet values of the residual relative Doler shift ACQUISITIO TEST CRITERIO T(Σ I* +(Σ Q* FOR Fd Hz (LOSS O MAX EAK db, ISOLATIO4 db Figure 4 shows the correlatio fuctio of the code i the absece of Doler residual. We ote the 4 db isolatio betwee the mai eak ad the secodary eaks. Figure 5 shows the correlatio fuctio of the code with a Doler residual of 5 Hz. ote that the isolatio betwee the mai eak ad the secodary eaks is ow oly 6.6 db. Therefore, this direct ad combied L5 code ad acquisitio criterio degrades quickly ad does ot reset ay useful eak whe the Doler residual is larger tha 3 Hz. We recall that i this case, we assume that the L5 code aligmet is correct withi ms ( τ ˆ τ modulo ms ad o additioal costat hase shift is affectig the carriers ( θ θˆ. We aalyze the evolutio of the combied L5 code acquisitio test criterio as a fuctio of the local lag. First of all, this test criterio is evaluated i all the Doler bis withi [-5 Hz; +5 Hz], each Doler bi havig a size of Hz LAG Figure 4: Cross-correlatio betwee ms correlator oututs ad local (residual Doler Hz..45 ACQUISITIO TEST CRITERIO T(Σ I* +(Σ Q* FOR Fd5 Hz (LOSS O MAX EAK -3.9 db, ISOLATIO6.6 db Figure 6: 3D lot of the test acquisitio criterio evolutio as a fuctio of code ad Doler offsets (residual Doler Hz. Figure 6 shows the evolutio of that criterio i resece of residual Doler of Hz. As we ca see, may secodary lobes aear that could hide the mai eak i resece of erturbatios LAG Figure 5: Cross-correlatio betwee ms correlator oututs ad local (residual Doler5 Hz. reseted at IO GS 3, ortlad 5

6 Figure 7: 3D lot of the test acquisitio criterio evolutio as a fuctio of code ad Doler offsets (residual Doler Hz. Figure 7 shows the evolutio of that criterio i resece of residual Doler of Hz. As we ca see, agai, may secodary lobes aear that could hide the mai eak i resece of erturbatios. As we ca see, the acquisitio criterio is agai very distorted ad the isolatio betwee the mai eak i the good Doler bi ad the secodary eaks i the other bis is oly 4.8 db. ote that this margi does ot imrove whe the received L5 sigal ower icreases. We the searched for aother bit sequece that would offer good cross-correlatio roerties i absece ad i resece of residual Doler. We tried the sequece roosed i [Mertes, 996]. The resultig correlatio fuctio i absece of residual Doler exhibits the same isolatio as the sequece (4 db. The suerositio of all values of the acquisitio criterio for all Doler bis is show i figure 9. As we ca see, the isolatio of the mai eak i resece of Doler is 6.8 db DOLER UCERTAITY: Hz bit MERTES SEQUECE ACQUISITIO CRITERIO I RESECE OF DOLER The, the test criterio is evaluated i all the Doler bis withi [-5 Hz; +5 Hz], each Doler bi havig a size of 5 Hz. This search is erformed so that the Doler shift i the correct frequecy bi is Hz leadig to the worst atteuatio of the correlatio eak. We the lot the suerositio of that curve for all Doler bis i figure ISOLATIO: 6.8 db euma-hoffma (h Acquisitio Criterio i resece of Doler Doler ucertaity : Hz Figure 9: Suerositio of the test acquisitio criterio (Mertes code for various Doler offsets as a fuctio of code lag (residual Doler Hz Margi : 5 db As a coclusio, accordig to the evaluatio reseted here, the direct ad combied L5 code / euma-hoffma acquisitio criterio roosed i [Hegarty, Tra ad Va Dieredock, ] is highly degraded by relative Doler residual Figure 8: Suerositio of the test acquisitio criterio for various Doler offsets as a fuctio of code lag (residual Doler Hz. Ideed, this criterio o loger exhibits a clear eak i the roer search cell as secodary lobes of the correlatio fuctio ca show to be isolated oly by 4.8 db with resect to the mai eak. However, to coclude o this acquisitio erformace, it remais to be evaluated the exact effect of oise o this acquisitio criterio i order to assess the real emergece of the eak. IV.3. EUMA-HOFFMA CODES ACQUISITIO reseted at IO GS 3, ortlad 6

7 Because of these degradatios, it is ecessary to determie whether it is ossible to reduce the frequecy ucertaity usig a FLL, the erform the sychroizatio oce the residual frequecy error is low. At the ed of the acquisitio rocess, oe ca assume a Doler ucertaity of [-5 Hz; + 5 Hz] ad a code delay ucertaity of [-.5 T c ; +.5 T c ]. As a cosequece, it is required that the FLL used right after the acquisitio rocess has a ull-i rage of [-5 Hz; + 5 Hz]. The imlemeted FLL ca be used easily with a redetectio itegratio time T of ms, but use of a larger itegratio time requires the sychroizatio of the euma-hoffma codes either o the data or o the ilot chael. The erformace of the FLL will be drive by the ature of correlator oututs used (data, ilot, the ature of the discrimiator used, ad the discrimiator combiatio techique i case of the use of data ad ilot correlator oututs. I the case of the use of data ad ilot romt correlator oututs I I, Q I, I Q ad Q Q, the several discrimiators ad combiatio techiques ca be used to build the FLL. Examles of ossible FLL discrimiators for the data or the ilot chael are give here: ( Q ( Q ( V arcta arcta ad I ( I ( V ( V ( if V ( > V ( V ( + if V ( < I V( arcta I ( Q ( I ( I ( + Q ( Q ( Q ( ( where arcta(r is the commo arctaget fuctio returig a agle lyig i ;. Exteded arcta discrimiators are ot cosidered here because of the resece of the euma-hoffma code. If we model the correlator oututs o the data comoet as si f I( D( ( R( ετ cosεθ + I ( f si f Q( D( ( R( ετ siεθ + Q ( f the the outut of these discrimiators is V ( ε ( + k( ε ( k( + V ( whatever the value of ad data bits V ( ε ( ε ( + k ( + ( whatever V the value of ad data bits where k is such that k is such that < ε ( + k( < < ε ( ε ( + k( < v is the oise affectig the discrimiator tesio If we model ε ( ft, the the limit for a accetable variatio of the trackig error ε with time is give by < ft < or ad V < f < 4T 4 for V T Therefore, at the startu of the FLL, the Doler differece betwee the local ad the icomig carrier should be limited to +/- 4T for V ad V. I the case where T ms, the the admissible Doler rage at the startu of the loo is [-5 Hz; +5 Hz]. We ca see here that i the case of the first discrimiator, jums of ca occur i the discrimiator fuctio. I the case of the secod discrimiator, jums of may occur, ad jums of or may also occur if the estimated data bit is wrog. ote that these jums do ot systematically lead to the divergece of the loos. If these jums are rare, the the loo will be able to coverge ayway. oe: θ (z I each case, the liear loo model is the followig θ ˆ( z Kz z z F(z Figure : FLL liear model. It is imortat to ote that this model is oly valid whe the loo oise badwidth is at least times smaller reseted at IO GS 3, ortlad 7

8 tha the redetectio badwidth. I our case where the redetectio itegratio time is ms, this meas that this model is oly valid whe the FLL loo oise badwidth is lower tha Hz. From the liear model, we see that if this is true, the usig a d order FLL filter F(z ( d order FLL is eough to guaratee o trackig error i resece of a jerk of ay magitude. Thus i that case the ull-i rage is as wide as the accetable rage give earlier. The oise resistace is drive here by the loss of lock threshold, determied by the liear rage of the discrimiator. Here, the limit is give by the arcta discrimiator liear rage. That rage is ; for the arcta. As exlaied i [Kala, 996], the stadard deviatio of the frequecy estimatio error is 8B σ + FLL Hz. T C C T for a FLL. The loss of lock threshold is such that 3 σ < Th LL which is equivalet to 36 B C T Th + + Th 8 B T T where Th is such that [-Th;Th] is the liear rage i Hz of the discrimiator. I the case of the arcta discrimiator, that rage is ;, therefore Th. As a cosequece, 4T 4T 4T the loss of lock threshold is exressed as: C 9B + + 9BT The evolutio of the loss of lock threshold as a fuctio of the FLL oise badwidth is lotted i figure. C/ i db Hz FLL LOSS OF LOCK THRESHOLD OISE LOO BADWIDTH I Hz Tms Tms Tms Figure : FLL loss of lock threshold o a sigle data or ilot sigal comoet. As we ca see, for a FLL with a oise loo badwidth of Hz, the comosite L5 sigal loss of lock threshold is 4.6 db Hz whe T ms ad the comosite L5 sigal loss of lock threshold is. db Hz whe T ms. The FLL loss of lock threshold for T ms ad B Hz is thus aroud 5 db Hz for the comosite L5 sigal, which is well uder the acquisitio threshold (33.7 db Hz. Therefore, that simle FLL ca be used right after the acquisitio rocess. If the FLL is to be used at a C/ lower tha 5 db Hz, the either the oise badwidth must be reduced or the itegratio time must be icreased. V. TRACKIG ERFORMACE ATA AD EXTEDED ATA DISCRIMIATORS COMBIATIO The ossible LL discrimiators are the followig oes: Q ( V( arcta I ( V ( arcta Q (, I ( ( where arcta(r is the commo arctaget fuctio returig a agle lyig i ; arcta(y,x is the exteded arctaget fuctio returig a. agle lyig i [ ; ] reseted at IO GS 3, ortlad 8

9 After sychroizatio, ay of these discrimiators ca be alied with the ilot chael correlator oututs. The use of the exteded arcta discrimiator o the data chael would require the estimatio of the data bit from the correlator oututs, the a correctio of the correlator oututs before they ca be used to form a discrimiator fuctio. If we model the correlator oututs as si f I( D( ( R( ετ cosεθ + I ( f si f Q( D( ( R( ετ siεθ + Q ( f the the outut of these discrimiators is V ( ε ( + k ( + ( whatever the resece V ad the value of data bits V ( ε ( + k ( + ( if the data bits are ot V reset or roerly estimated where ε k is such that < ( + k( < k is such that < ε( + k ( < v is the oise affectig the discrimiator tesio Each of these idividual discrimiator fuctios i the data ad i the ilot chael ca be combied to form a comosite discrimiator fuctio used to drive the carrier CO [Hegarty, 999], [Tra ad Hegarty, ]. The combiatio ca be a simle average or a more comlex weighted sum deedig o the rior kowledge of the oise ower affectig each discrimiator outut such as modelled here: α data α ilot V ( V ( + V ( α + α α + α Whe imlemetig this tye of combiatio, oe must take care to the jums i V( that may arise from a steady-state trackig error due to rage dyamics iducig a wraig of oe idividual discrimiator. For examle, we ca build a comosite discrimiator fuctio by combiig a classical arcta discrimiator o the data chael with a classical arcta discrimiator o the ilot chael. I this case, i the resece of large dyamics, a bias will be reset at the outut of each discrimiator ad jums of may arise from each idividual discrimiator due to the limited rage of the classical arcta, resultig i o bias for the comosite discrimiator. I resece of oise oly, the trackig threshold will be drive by the accetable oise ower i the oeratig rage of the classical arcta fuctio. I order to take beefit from the absece of data o the ilot chael, oe may desire to form a comosite discrimiator fuctio by combiig a classical arcta o the data chael with a exteded arcta o the ilot chael. I that case, to beefit from the full oeratig rage of the exteded arcta, it is ecessary to detect ad correct the ossible jums of that may arise from the classical arcta discrimiator i the resece of large dyamics. A ossible techique to do this is to ru a ste detectio rocedure o the differece of the data discrimiator ad ilot discrimiator. The roosed test criterio is thus data V ( V ( V ilot ( The average value of the test criterio is zero whe the arcta discrimiator is ot affected by a ste. We ca assume that each discrimiator is affected by ideedet oise as it origiates from the correlatio of the icomig sigal with differet R codes. Therefore, the variace of the test criterio is the sum of the variace of each discrimiator which is take here to be B σ LL + C C T A examle ste detectio rocedure is a CUSUM test [Basseville ad ikiforov, 993]. That CUSUM test could be desiged to test chages i the average value of the test criterio, modellig the test criterio as a white Gaussia oise with stadard deviatio σ such that B σ V + C C T Imortat desig arameters of this CUSUM test are the false alarm rate fa, the missed detectio rate md, ad the time to alert T A. Whe the desig false alarm rate teds to, it ca be show that the smallest detectable bias is equal to b σ ε ( h + α h D D where hd is the T A test threshold h D l ad fa α ERFIV ( md. The followig figure shows the lowest C/ required to guaratee the erformace of the CUSUM rocedure as a fuctio of the V reseted at IO GS 3, ortlad 9

10 loo oise badwidth whe the redetectio time is set equal to ms: 9 8 LOWEST ACCETABLE C/ FOR A CUSUM TEST OF I JUMS (Ta famd. famd. It is also iterestig to determie the trackig threshold of a exteded arcta loo trackig oly the ilot sigal comoet. That trackig threshold is lotted i figure 3. 6 EXTEDED ARCTA LL LOSS OF LOCK THRESHOLD (Tms 7 C/ i db Hz C/ i db Hz B i Hz 4 Figure : Lowest accetable data or ilot chael C/ as a fuctio of loo oise badwidth to test for i jums i the classical arcta discrimiator whe T ms. That lowest C/ for efficiet detectio ca be comared to the trackig threshold of a loo usig a comosite discrimiator formed usig classical arcta discrimiators o the data ad ilot chaels. The stadard deviatio of a arcta LL is σ LL C / i db Hz B C + C T ARCTA LL LOSS OF LOCK THRESHOLD (Tms B i Hz Figure 3: Arcta LL loss of lock threshold (comosite data+ilot L5 sigal C/ as a fuctio of LL equivalet oise badwidth B i Hz Figure 4: Exteded arcta LL loss of lock threshold (ilot L5 sigal C/ as a fuctio of LL equivalet oise badwidth. As we ca see from the comariso of figures ad, whe T ms, the comosite data+ilot L5 sigal C/ threshold for detectio of the i jums is larger tha the loo trackig threshold for a classical arcta discrimiator. I additio, from figure 4, the comosite data+ilot L5 sigal C/ loss of lock threshold of a exteded arcta LL usig oly the ilot comoet is lower tha the above two thresholds. Therefore, the utility of the imlemetatio of hybrid discrimiator fuctios is questioable ad does ot seem to brig a ossible gai with resect to the imlemetatio of a simle exteded arcta LL o the ilot L5 comoet. It must also be oted here that each idividual discrimiator fuctio could be combied at the outut of differet loo filters. The data discrimiator could be take at the outut of a much tighter loo filter tha the ilot discrimiator. I that way, the data loo filter could comesate for the larger oise affectig the data discrimiator. Other ossibilities iclude the comutatio of roducts of I ad Q samles of the data correlator oututs before further accumulatio ad combiatio with ilot discrimiator. Fially, the combiatio of data ad ilot correlator oututs to drive the DLL is ot affected by jums due to the ature of DLL discrimiators, ad therefore reresets a real iterest to reduce the code trackig threshold. COCLUSIO reseted at IO GS 3, ortlad

11 There is a db beefit i the acquisitio of L5 codes by usig correlator oututs joitly from data ad ilot comoets. There is a limitatio to ms i the duratio of the coheret itegratio due to the euma-hoffma codes which is small comared to the ms limitatio i the L GS C/A sigal. Direct ad combied L5 codes ad euma- Hoffma codes acquisitio criterio is highly degraded i resece of residual Doler (eak isolatio 5 db for, eak isolatio 7 db for bit Mertes code. The real erformace of this acquisitio remais to be assessed. euma-hoffma codes ca be acquired after reductio of the residual frequecy error usig a FLL that was show to have a trackig threshold lower tha the L5 codes acquisitio threshold. Combiatio of ata ad exteded ata discrimiators i the L5 LL is affected by jums ad does ot rovide the exected gai i the hase trackig threshold comared to a ure LL usig oly ilot correlator oututs. [Mertes, 996], S. MERTES «Exhaustive Search for Low Autocorrelatio biary Sequeces, Istitute Autovo-guericke-uiversitat, Magdeburg, Letter to the Editor. [RTCA, ], RTCA SC-59 «AVSTAR GS L5 Sigal Secificatios [Silker ad Va Dieredock., 999], J. SILKER, A.J. VA DIEREDOCK, «roosed ew Civil GS Sigal at MHz, IO GS 999 [Tra ad Hegarty., ], M. TRA, C. HEGARTY, «Receiver Algorithms for the ew Civil GS Sigals, IO TM ACKOWLEDGMETS The authors would like to ackowledge the assistace of eila Kraiem ad icolas Sacco who searched for other short R sequeces, as well as Ae-Laure Morisseau ad Fatou Gueye for the aalysis of the L5 sigal. REFERECES [Basseville ad ikiforov, 993], M. BASSEVILLE, I. IKIFOROV, «Detectio of Abrut Chages: Theory ad Alicatio, retice Hall, 993 [Bastide et al., ], F. BASTIDE, O. JULIE, C. MACABIAU, B. ROTURIER, «Aalysis of E5/L5 acquisitio, trackig ad data demodulatio thresholds, IO GS [Hegarty., 999], C. HEGARTY, «Evaluatio of the roosed Sigal Structure for the ew Civil GS Sigal at MHz, The MITRE Cororatio, Workig ote W99W34, Jue 999 [Hegarty, Tra ad Va Dieredock, ], C. HEGARTY, M. TRA ad A.J. VA DIEREDOCK, Acquisitio Algorithms for the GS L5 sigal [Kala., 996], E. KALA, «GS riciles ad Alicatios, Artech House [Macabiau et al., ], C. MACABIAU, V. CALMETTES, W. VIGEAU, L. RIES, J-L. ISSLER «L5 Codes roerties, GSS [RTCA, ], RTCA SC-59 «AVSTAR GS L5 Sigal Secificatios reseted at IO GS 3, ortlad

12 Figure : roosed L5 trackig loos structure. reseted at IO GS 3, ortlad