Fne Tme Adng n Unsynchronsed Cellular Systems: the Benefts for GPS Integraton n Moble Phones Peter Duffett-Smth, Cambrdge Postonng Systems Ltd. Tony Pratt, Orbstar Consultants BIOGRAPHIES Peter Duffett-Smth s the foundng drector of Cambrdge Postonng Systems Lmted and s ts Chef Scentfc Offcer. He s also Reader n Expermental Rado Physcs at the Cavendsh Laboratory, Unversty of Cambrdge. Hs PhD s n Rado Astronomy and, wth others, he s the nventor of the Matrx postonng method and E-GPS technologes mentoned here. Dr Tony Pratt graduated wth a B.Sc. and Ph.D. n Electrcal and Electronc Engneerng from Brmngham Unversty, UK. He was on the teachng staff at Loughborough Unversty, UK from 967 to 980. He held vstng professorshps at Yale Unversty; IIT, New Delh and Unversty of Copenhagen. In 980, he joned Navstar Ltd, as Techncal Drector. In 995, wth Peek plc, he was nvolved n the formaton of Tollstar Ltd, a 5 company consortum developng of Electronc Road Tollng. He left Peek n 997 and joned Navstar Systems Ltd as Techncal Consultant. Subsequently he was Techncal Drector (GPS) wth Parthus. He s also Specal Professor at the IESSG at the Unversty of Nottngham, UK. He s a Consultant to the UK Government n the development of Galleo Satellte System. He s a Member of the EC Sgnal Task Force and sub-groups and was closely nvolved wth the EU-US Agreement on GPS Galleo Cooperaton. He s Senor Consultant wth the GPS Telematcs Group at QnetQ Ltd, UK. ABSTRACT GPS wll play a central role n the provson of locaton based servces usng moble cellular telephones. Many commercally-avalable handsets (termnals) already nclude ntegrated GPS components, mostly for use on CDMA and CDMA 000 networks n whch the transmtted sgnals are synchronsed to GPS tme. Ths synchronsaton brngs advantage n that t s relatvely straghtforward to provde the GPS recever n the moble termnal wth assstance n the form of GPS tme accurate to wthn approxmately 0 s. By a somewhat complex route, the tme adng extends the usablty of the GPS servce nto buldngs and other shelded envronments. However, on GSM and W-CDMA networks, whch domnate globally, the provson of tme adng s more dffcult because the network transmtters are asynchronous by desgn. There s no concept of 'network tme', and the transmtted sgnals have no pre-determned relatonshp wth each other or wth GPS tme. Duffett-Smth et al. [,] have proposed and demonstrated a method of provdng fne tme adng (FTA) n GSM and W-CDMA networks, called Enhanced GPS (E-GPS), whch uses the Matrx method [3-6] of locatng a moble termnal from the network sgnals receved by the termnal. In E-GPS, the network sgnals are used as a receptacle for GPS tme after calbraton. In ref. [], they reported the frst measurements made on GSM networks showng that FTA accuraces of sec or better were sustanable even over several hours. Ths concluson s further supported n a companon paper to ths one [7] whch demonstrates that, n some crcumstances, FTA at the sub s level s possble over elapsed tme perods exceedng one day. In ths paper, we examne and quantfy the benefts whch FTA brngs n terms of the reducton n the complexty of a GPS mplementaton. We show how FTA combned wth a precse knowledge of the local oscllator offset render t unnecessary to use massve parallel correlator hardware desgns. On the contrary, we show that excellent n-buldng performance may be acheved usng as few as two complex correlators per GPS satellte channel. These benefts come manly from three factors: (a) a reducton n the code phase search wndow by a factor of more than 500; (b) frequency stablsaton of the local oscllator usng the network sgnals; and
(c) the use of a stronger statstcal test n the sgnal detecton algorthm for a gven false-alarm rate. The changes n the statstcal tests requrements n (c) provde an effectve gan n recever senstvty of up to 6 db whatever number of correlators s used. The further benefts of FTA can be traded off between cost savng (smpler GPS mplementatons), tme savng (tme to frst acquston), and senstvty ncrease (penetraton nto nbuldng envronments etc.). FTA at s accuracy provdes the smplest and lowest-cost GPS recever wth an overall performance gan approachng 3 db, gvng t a performance n speed and senstvty smlar to that acheved usng much more expensve parallel correlator desgns. INTRODUCTION The prncple of provdng assstance to a moble GPS recever s well known and examples may be seen datng before 986 (e.g. ICD GPS-50, frst verson). The assstance comes n several forms: satellte nformaton (almanac and ephemers), poston nformaton, and tme nformaton. We are concerned here wth the provson of tme nformaton, n partcular Fne Tme Adng (FTA) by whch the GPS tme at the termnal can be extracted from network sgnals wthn an accuracy of s. The standardsed method of provdng ths nformaton s by means of a message, sent from a GPS server n the network to the moble termnal, ndcatng that a partcular sgnature n a network sgnal recevable n the near future by the termnal corresponds precsely to a partcular GPS tme. There are several problems wth ths approach. The frst s that messages take a relatvely long tme to set up and send. Typcally, the termnal sends a message to the server (several seconds delay) requestng the GPS tme assstance. The server responds wth the requested nformaton (several more seconds), and only then can the GPS recever begn ts satellte acquston phase. It wll be apprecated that such assstance s only needed when the satellte sgnals are weak e.g. nsde buldngs and other shelded spaces, so that a long acquston perod s antcpated. Several more seconds of ntegraton may be requred. The overall effect can therefore be to nsert a long delay between poston request and poston response whch may be too much for the applcaton. A second problem wth ths approach s that the server n the network does not know the precse poston of the moble termnal. A coarse correcton may be made usng Tmng Advance (TA) nformaton, f avalable, or Cell Identfcaton (Cell-ID) nformaton. In ether case, there can be several mcroseconds of uncertanty n the GPS tme provded. A thrd problem s that expensve network-based GPS equpment s requred to provde ths FTA servce. Few, f any, GSM networks can have been so equpped so far. For these, and other, reasons, Duffett-Smth et al. [,] have proposed an alternatve method of provdng FTA to a moble termnal. The method s based around the Matrx postonng system whch s able to locate the moble termnal usng the measured relatve receve tme offsets of the sgnals from surroundng base statons of the network. The calculaton provdes not only termnal postons, but also a lst of relatve transmsson tme offsets of the base statons. When coupled wth the calculated poston of the handset and suffcent stablty of the network tmng sgnals, an ntal calbraton of the recept of the sgnals from one base-staton aganst GPS tme can be carred around wthn the termnal and used, at a later tme, to nfer GPS tme from the recept of the sgnals from the same or another base staton. Ths method, n effect, uses the unsynchronsed, but stable, network sgnals as a remote repostory of accurate GPS tme. Duffett-Smth and Tarlow [] have demonstrated FTA accuraces of about s. Pratt et al. [7] have provded addtonal support n the form of Allan standard devaton curves of GSM sgnals receved by a termnal whch show that s accuracy s avalable over elapsed tmes of many hours or more than a day. That the calbraton of the network sgnals s carred around nsde the termnal ensures that FTA s avalable wthout delay when needed, and ths method does not requre the support of a network-based GPS server. GPS EQUIPMENT DESIGN TRADE-OFF What performance and desgn advantages does the avalablty of FTA accurate to s brng? The answer, of course s mult-dmensonal, and depends n partcular on what GPS recever confguraton s beng consdered. The smplest useable confguraton s probably one n whch there are just two complex correlators per satellte channel, bearng n mnd the probable need to track a satellte once acqured. Such a confguraton wll have the lowest cost, lowest slcon real-estate footprnt (the baseband processng could also be mplemented n software), and may have the lowest power consumpton, but t wll be practcal wthout FTA only n strong sgnal condtons. On the other hand, confguratons wth thousands of correlators can do parallel searchng over all possble code-phase offsets, so need not be suppled wth FTA. However, these are expensve, power-hungry, and have larger slcon footprnts. Wth any complexty of GPS confguraton, whether there are just two or two thousand correlators per satellte
channel, FTA wll always provde up to 6 db of real senstvty gan. Ths s because the satellte detecton strategy can be made more aggressve for any gven falsealarm rate as the search wndow n whch a crosscorrelaton peak mght be attrbuted to a satellte sgnal s much narrower. The statstcal lkelhood of a nose peak crossng a detecton threshold wthn the wndow s therefore smaller. We quantfy ths below. The other benefts of FTA nclude, for a gven GPS recever complexty, ncreasng the sgnal ntegraton tme and reducng the re-acquston tme. These are also examned below. PERFORMANCE GAIN One of the key attrbutes for understandng the performance gan from fne tme adng s the reacquston budget. The GPS re-acquston mode can be entered when a GPS locaton soluton (or fx ) has prevously been determned wth a current ephemers, or at least wth one whch s nearly current. The defnton can be made precse: n the context of FTA, a fx wll have been obtaned wthn the prevous few hours. As explaned above, the FTA nformaton s obtaned from prevously-calbrated modulaton sgnatures (such as synchronsaton bursts) n the base-staton sgnals. The calbraton n relatve tme offset and tme offset rate s used to provde future calbrated GPS tme to an accuracy of not worse than s, and can be reled upon for many hours even though the moble termnal may have moved and changed servng base staton n the ntervenng perod. The code search budget durng reacquston s gven n Table. code uncertanty rms value unt recever clock error (FTA).0 s horzontal locaton error (Matrx) 00 m satellte clock error < 4 ns satellte poston error < 0. m HDOP.6 Requred code search space.0 chps Table : the code search budget for a GPS recever n reacquston mode. The major contrbutor s the recever clock uncertanty (.e. the accuracy of the FTA). The locaton accuracy nferred usng Matrx would only become a major contrbutor f the locaton accuracy degraded to approxmately 0.5 km. Table ndcates the crucal role whch FTA can play n contanng the reacquston search envelope for the correct code phase. There are several other mportant sde-effects ncludng: (a) (b) (c) a reducton n the search space leadng to a sgnfcant reducton n the complexty of the GPS base-band processor; for a gven GPS base-band complexty and fxed observaton nterval, a proportonal ncrease n the coherent or ncoherent sgnal ntegraton tme, mprovng GPS senstvty; for gven base-band complexty, a reducton n the re-acquston tme (observaton nterval); and an mprovement n the test statstcs, so that there s a lower probablty of false alarm or hgher probablty of detecton, or both. The proporton of each one of these s a performance cost trade-off establshed when the GPS recever desgn s frozen. We provde ndcatve gans for case (b) snce the reducton n re-acquston tme or base-band complexty s smply proportonal to the reducton n code search space. By nspecton of Table, ths s evdently about 500: n comparson wth an un-aded GPS recever, performng a blnd search (wth an accumulated ms tme or locaton uncertanty). Ths s an approprate response f no poston adng s avalable and the recever has been moved to a new, unknown, locaton. Partal tme or locaton adng would reduce the mprovement rato, but t s usually the recever clock whch then contrbutes the largest uncertanty (wth an undscplned quartz oscllator). Fne tme adng solves ths problem. SENSITIVITY IMPROVEMENT We now examne the senstvty mprovement whch can be attached to GPS recepton usng fne tme adng of the recever clock. In order to make vald comparsons, a number of recever varables have been fxed n what follows. In practce, the performance gan may be taken n varous ways and ths makes comparson more dffcult. The case studed here s somewhat artfcal but s representatve of what s possble. The features of the GPS recever, fxed for the comparson are:. the base-band complexty (.e. the number of complex correlators avalable to each satellte channel);. the observaton tme nterval (.e. the allowed reacquston tme); and 3. the detecton statstcs (.e. the probablty of detecton, P d, and probablty of false alarm, P f ).
As mentoned prevously, one consequence of the reducton n the search wndow n code phase s a smlar reducton n the overall false alarm probablty, or a change n the detecton threshold to mantan a gven P f. We ntroduce the statstcal prelmnares n the next secton whch permt the computaton of both P f and P d. STATISTICAL PRELIMINARIES We consder the output of a complex flter matched to the wanted GPS sgnal (.e. one whch uses a replca of the code sequence for the chosen satellte, a replca of the receved carrer sgnal, matched n frequency and phase wthn certan lmts, and ntegrated coherently for a tme, T ). Most of the statstcal expressons can be derved from standard forms (see for example: ref. [8]). PROBABILITY OF FALSE ALARM When there s no satellte sgnal present, the outputs (x, y) of the n-phase and quadrature-phase channels of a typcal correlaton recever, are random nose wth Gaussan probablty densty functons (PDF), havng means of zero and varances of n each channel. The varance s a result of thermal and recever nose, and ts value s affected by the band-lmtng acton of the correlaton recever, the gan of the RF processor and the ntegraton tme. The jont PDF, P(x, y) for x and y s therefore gven by: P( x, y) exp ( x y ), () where we have assumed that x and y are statstcally ndependent. In common wth many recever desgns, we take t that the recever computes the test statstc z = (x + y ) to determne the presence or absence of a sgnal by comparson wth a threshold. The PDF for z s computed by a reversble Cartesan to polar transformaton ( x, y) ( z, ), where z ( x y ) and θ tan ( y x). () The dstrbuton of z follows after ntegraton over the doman: z P ( z) exp, wth z and. (3) z Attempts to mprove GPS recever senstvty are lmted by the duraton of coherent ntegraton because of the data modulaton. A number of dfferent strateges have been proposed but ths s not the subject of ths paper. For now we wll take t that, because of FTA, the tmes of the databt transtons are known accurately n recever tme for the constellaton whch was vsble at the tme of the orgnal calbraton (the clock bas and clock rate of each satellte s requred). Ths mples that coherent ntegraton for T = 0 ms s allowed, though ths mght be lengthened wth some clever algorthms. In order to mprove senstvty, ncoherent ntegraton for a number, N, of T ntervals s used wth a test statstc, u, whch s the accumulated sum of the energy from each coherent ntegraton, z, weghted by the varance,, of each contrbuton: N z u. (4) In practce, each z contrbuton s usually gven the same weght. We can assume that each of the z random varables s statstcally ndependent of the others. The PDF for u s therefore gven by N u u P( u) exp, (5) N ( N) where (N) s the Gamma functon for N. It s not the purpose of the paper to dscuss the multple alternatve strateges for GPS recever processng (for example to mprove senstvty). The paper does, nevertheless, use a reasonable methodology for a sutable processng model. The results are therefore ndcatve of the performance whch can be attaned n general. A false sgnal detecton (false alarm) occurs when the test statstc, u, exceeds a threshold value, t. The probablty, P(u t), of ths event s: P( u t) P( u) du P. (6) t t There s a closed form nfnte seres expresson for P t (see for example n ref. [9]) but ths does not assst the process of determnng the values of t for a requred value of P f. Equaton (6) establshes the probablty wth whch the threshold s exceeded n any searched cell. In a typcal search arrangement, a number, k, of cells wll be searched. The probablty that the threshold has been reached or exceeded n one or more cells, correspondng to one or more false detectons, s therefore gven by the Bnomal dstrbuton: f P t k P ( ). (7)
In the case where P t s much less than (as s the usual case), equaton (7) can be approxmated by usng just the frst two terms of the bnomal expanson, gvng Pf kp t (8) Plots of P t vs t are shown n Fgure for varous values of N..0 0. 0 P t 0 0.0 P 0 0 3 j 3 0 0 4 4 0 5 0 5 0.00000 0 6 4 6 3 64 8 0 40 80 0 60 00 40 t / 0 0 40 60 80 00 0 40 60 80 00 0 40 0 nc j Fgure : the probablty, P t, of the nose crossng a threshold, t (n unts of ), n a sngle cell for varous accumulatons, N, of coherent ntegratons of 0 ms. (In Fgure, N has been selected as a power of snce the performance changes for smaller ncrements are not sgnfcant.) The curves n Fgure show how a hgher threshold, t, can be used for a gven false alarm probablty, P f. For example, FTA wth an accuracy of s provdes for a search wndow whch s about 500 tmes narrower than one whch encompasses the entre code-phase space. If we select, say, a probablty of false-alarm of 0, then the curve for N = n Fgure mples that a threshold value of about 0 s requred wth FTA (.e. for k = 4 n Equaton 7). The correspondng P f wthout FTA (k = 500) s 5.0 6, mplyng that the threshold value must be set to about 5. The correspondng thresholds n the case of N = 64 are about 75 and 0 respectvely. In each case, of course, the lower threshold mples a hgher probablty of detecton of a sgnal. If the deflecton n a channel s smply proportonal to the sgnal power, s (n unts of ), then the examples just gven for N = and N = 64 mply ncreased probabltes of detecton of about 5/0 (about 4 db) and 0/75 (about 0.8 db) respectvely. However, more precse calculatons are requred (especally for N > ) as follows. PROBABILITY OF DETECTION When a sgnal s present, the sgnal energy s splt between the I and Q channels of the code-phase algned correlator, the splt dependng upon the phase of the carrer replca wth respect to the sgnal. The frequency 40 dfference () between replca and receved sgnal may be non-zero, provdng t satsfes the condton that the phase-change over the coherent ntegraton perod s small,.e. T << /. The maxmum lkelhood (ML) detecton of the sgnal requres the formaton of a test statstc z = ( I + Q ), whereby the sgnal energy s concentrated n the measurement z. After the th perod of coherent ntegraton, each of the correlator outputs, (x, y ), s assumed to hold the same sgnal energy. We then apply the same non-coherent accumulaton process as we appled above to the nose-only case. The PDF of the output s an ndependent, jontly-normal dstrbuton wth a non-zero mean,. As before, we add together N values of z to form the accumulated output. Ths has a chsquared dstrbuton whch s non-central wth N degrees of freedom. There s a unque rotaton on the varables n N-space whch algns the vector to the dstrbuton mean wth just one of the co-ordnate axes: zˆ z. (9) The mean,, along ths chosen axs (say the N th axs) s then gven by, (0) where each s the mean of each z. Ths s precsely the process of measurng the accumulated energy from each coherent ntegraton nterval, weghtng n accordance wth the assocated nose energy, and formng the ncoherent sum. Ths s the processng requred by the ML optmum processor. After some manpulaton (see ref. [8] page 38), we obtan the PDF, P(us), for u (equaton (4)) gven a sgnal level s (n unts of ): u P( u s) ( N ) N ( u) ( r 0.5) exp ( u ) r (r)! ( N r) () The probablty of detecton for ths known sgnal s the cumulatve dstrbuton of P(u s) from a threshold, t (just as n equaton (6)). The value of t s chosen to provde the requred P f : P P( u s) du. () d t It s assumed n ths analyss that the sgnal s only present n one known cell (a specfc code algnment). Examples of curves of P d versus sgnal-to-nose rato are gven n Fgure. These and are known as Recever Operatng r
Characterstcs (ROC) curves. Fgure s for an llustratve sngle coherent ntegraton of 0 ms and no ncoherent ntegraton (.e. N = )..0 ta m 0 P d ta m ta m.53 0 5 0.9 0.8 0.7 0.6 ta m 3 ta 0.5 m 4 0.5 ta m 5 ta m 6 ta m 7 ta m 8 0.4 0.3 0. 0. 0 0 3 0 4 0 5 0 6 0.0 0 5 0 5 5 6 7 8 9 0 3 4 5 6 log 5 6 0 s m sgnal/nose rato (db) Fgure : the probablty of detecton, P d, plotted aganst the sgnal-to-nose rato (s/ ) for varous probabltes of false alarm, P f, from 0 to 0 6 n steps of a factor of 0.36, for a sngle 0-ms ntegraton (N = ). From Fgure, t s now possble to estmate more accurately the performance gan whch FTA affords because of the reducton n code-phase search range. As before, we assume that the code search wthout FTA has to cover the entre code phase space n ½ chp ncrements (k = 046 cells), and that wth FTA only k = 4 cells ( chps) have to be searched. Ths s a reducton of a factor of about 500 n k, so that for the same overall false alarm probablty, P f, the threshold, t, can be lowered, thereby mprovng the probablty of detecton, P d. Returnng agan to our prevous example for N =, an overall P f of 0 mples a sgnal-to-nose rato of about 0.3 db wth FTA (k = 4) for a probablty of detecton, P d, of 0.5 (Fgure ). Wthout FTA, the correspondng P f must be 5.0 6, mplyng a sgnal-to-nose rato of about 3.6 db. Hence the mprovement n senstvty brought about by FTA s about 3.3 db, consstent wth out prevous estmate of 4 db. The correspondng fgures for the case where N = 64 (from Fgure 3) are. and. db, mplyng an mprovement n senstvty brought about by FTA of about.4 db, consderably more than our prevous estmate of 0.8 db. In order to ntegrate coherently for ths perod, t s normally requred to have the ntegraton nterval algned wth the satellte data stream at recepton. Fne tme adng can enable ths. Wthout FTA, an approprate recever search strategy s to form coherent ntegratons over 0 ms (some other ntervals gve slghtly better results) and form the ncoherent sum of such results (coverng an nterval of 0 ms for comparson purposes). Ths technque results n a loss of sgnal-to-nose rato after processng. To determne the sze of ths effect, we consder each of the 0 ms coherent ntegratons to have a loss of sgnal-to-nose rato of 3 db n comparson wth a 0-ms coherent ntegraton. Of the 0 ms ntegratons, on average three quarters of them do not contan a data bt transton whlst one quarter do. Of these that do contan data bt transtons, the worst case effectve sgnal s zero (f the data bt transton s n the centre of the ntegraton nterval). The ncoherent addton of the two 0 ms coherent ntegratons recovers some of the lost sgnal power, but there s stll a resdual loss of approxmately.4 db. Ths s made up partly of the loss n sgnal energy (n the nterval contanng the data-bt transton) and partly n the change from a sngle 0-ms coherent ntegraton to havng two 0-ms coherent ntegratons beng added together ncoherently. The foregong llustrates that the use of FTA asssts n extendng the perod of coherent ntegraton, and also n reducng the search code space thereby allowng reduced detecton thresholds. Smaller sgnal powers then provde the same probablty of detecton. The overall mprovement n detecton senstvty from these two factors s about 6.4 db for the case where N = and about 5. db for the case where N = 64. INCOHERENT INTEGRATION OPPORTUNITIES A second beneft may be taken from FTA when consderng a GPS recever fxed n complexty (.e. havng a defned number of complex correlators) and wth a fxed observaton nterval. Ths s the bass for makng a far comparson between the performance of a recever wth and wthout FTA. The concept nvolved s that the channel slots released by the lmted code search space can be used to ncrease the perod of sgnal accumulaton pror to detecton. Ths does not apply to a recever havng an arbtrarly large number of correlators so that any task can have any number of correlators assgned to t. However, such a recever s expensve. For the sake of comparson, we wll consder the smplest case n whch the recever has just two complex correlators per satellte channel. Wthout FTA, these two correlators must be assgned to search over 500 code-phase offsets serally. Only one fve hundredth of the tme avalable can then be spent n an ntegraton at each offset. Wth FTA, the two correlators can be postoned at the correct code-phase offset, and can spend all the tme ntegratng the sgnal at that poston, achevng a hgher senstvty. As an llustraton of ths effect, we consder the cumulatve probablty dstrbuton for the probablty of detecton from equaton () above wth N = 64. Ths corresponds to an observaton nterval of.8 s. The ROC curves correspondng to ths number of ncoherent ntegratons are shown n Fgure 3.
8 7 6 5 4 3 0 3.0 0.999 0.9 0.8 ta P M 0 d 0.7 tam ta M 0.6 ta M 3 ta 0.5 M 4 0.5 ta ( M 5 ) ta M 6 0.4 ta M 7 ta M 8 0.3 0 0 3 0 4 0 5 0 6 almost always domnated by mult-path. Ths gves rse to large sgnal level varatons, wth a Raylegh magntude dstrbuton, and a coherence tme dependent upon the recever moton dynamcs (propagaton channel delay spread). In most cases, the coherence tme wll be much less than the ntegraton tme used n the above example. Nevertheless, the proposed calculaton methodology wll provde a near optmum use of the avalable sgnal energy. 0.0 5.758 0 6 0. 0. 0 8 8 7 6 5 5 4 3 0log 0 3 3 s M sgnal -to -nose rato / db Fgure 3: the probablty of detecton, P d, plotted aganst the sgnal-to-nose rato (s/ ) for varous probabltes of false alarm, P f, from 0 to 0 6 n steps of a factor of 0.36, for a 64 ncoherent addtons of 0-ms coherent ntegratons (N = 64). (Note that the curve for 3.0 5 s mssng from the plot.) As can be seen from Fgure 3, at an overall P f of approxmately 0 (over 4 cells), the nput sgnal to nose rato for P d = 0.5 s approxmately. db whereas the same result n Fgure s +0. db. Ths s a performance mprovement of.4 db, and t corresponds to an ncrease n the total tme of ntegraton of a factor of 64. However, we stll have a further factor of about 8 n tme to devote to the ntegraton wth FTA snce no seral searchng over dfferent code-phase offsets s requred. Snce we have not computed the curves beyond N = 64, we must extrapolate as follows. The rate of nput sgnal to nose rato depresson over the 64 ncoherent ntegratons s about.9 db per doublng n N, the number of ncoherent ntegratons. Usng ths fgure to extrapolate to N = 5 leads to a further performance enhancement of approxmately 3.9 = 5.7 db. The total mprovement wth FTA s then.4 + 5.7 = 7. db. Ths ncrease n senstvty s n addton to 3.3 db from the reducton n search space and.4 db from data bt transton synchronsaton an overall gan of nearly 3 db. The above fgures suggest that a sgnal acquston threshold of 9 dbw can be acheved n practce, a fgure below most manufacturers clams. Ths fgure s derved usng a standard GPS recever model wth sgnal threshold at 69 dbw and usng the addtonal gan of approxmately 3 db n 0 s of observng tme calculated above to depress the threshold to 9 dbw. These gans rely on assumptons concernng the sgnal model, n whch t has been assumed that the sgnal has constant magntude over the perod of ntegraton. In practce, there wll be few stuatons n whch the sgnal level s not random. Sgnal propagaton n low sgnal level cases s FINE TIME AIDING TRADE-OFF The prevous calculatons mply that a performance beneft of about 3 db s avalable wth FTA for tradng off between complexty of desgn (and hence cost), tme to sgnal acquston, and senstvty. Ths s llustrated n the somewhat naïve but llustratve Table below where we have made the assumpton that the cost of the GPS desgn s just proportonal to the number of correlators such that the 048 correlator desgn costs $4 for the correlators plus $ for the slcon support, plus $ for the front-end, makng a total of $6. The correlator desgn costs just $ as t has been assumed that the base-band processng has been mplemented n software. The fgures correspond to a total tme avalable of 0.4 s. correlators cost/$ Senstvty/dBW wth FTA no FTA (s/w).0 9 69 3 (h/w).0 9 74 56 (h/w).5 9 80 048 (h/w) 6.0 9 86 Table, llustratng how the performance benefts of FTA may be traded off between the complexty of the GPS recever mplementaton and senstvty whch may be acheved wth and wthout FTA CONCLUSIONS The avalablty of FTA accurate to s brngs wth t a performance beneft equvalent to about 3 db n senstvty. Ths may be traded, when the recever desgn s frozen, between the complexty (number of correlators), the senstvty, and the tme to sgnal acquston. Even for desgns wth 048 correlators per satellte channel, FTA stll brngs a senstvty ncrease of about 6 db. The smplest desgn, havng just complex correlators per channel and therefore one whch may be mplemented n software, can acheve a senstvty of 9 dbw wth FTA n about 0 s.
REFERENCES [] P. J. Duffett-Smth and B. Tarlow E-GPS - ndoor moble phone postonng on GSM and W-CDMA, Proc. ION GNSS 005 Meetng, Long Beach, September 3-6. [] P. J. Duffett-Smth and P. Hansen. Precse Tme Transfer n a Moble Rado Termnal, Proc. ION NTM 005 Meetng, San Dego, January 4-6. [3] C. Drane, P. J. Duffett-Smth, S. Hern and J. Brce. Moble Postonng usng E-OTD wthout LMUs, proceedngs of AeroSense 003, SPIE's 7th Annual Internatonal Symposum on Aerospace/Defence Sensng, Smulaton, and Controls, (003) [4] P. J. Duffett-Smth, P. Hansen, J. Brce. Improvements n Rado Postonng Systems, WO 00/7383, (00). [5] P. J. Duffett-Smth, P. Hansen, J. Brce, Improvements n Rado Postonng Systems, WO 00/7384, (00). [6] P. J. Duffett-Smth, M. Macnaughtan. Precse UE Postonng n UMTS usng Cumulatve Vrtual Blankng, proceedngs of IEE 3G 00 conference, (00). [7] A. R. Pratt, R. M. Faragher, and P. J. Duffett-Smth. Fne Tme Adng and Pseudo-Synchronsaton of GSM Networks, Proc. ION NTM 006 Meetng, Monterey, January 8-0. [8] M. Kendal and A. Stuart. Advanced Theory of Statstcs, Vol, 3rd Ed., 973, Hafner Publshng, New York. [9] I. S. Gradshteyn and I. M. Ryzhk. Tables of Integrals, Seres and Products, 980, Academc Press, ISBN 0-- 94760-6 page 30.