N PTIVE SIGNL SERH LGORITHM IN GPS REEIVER Item Type text; Proceeding uthor Li, Sun; Yinfeng, Wang; Qihan, Zhang Publiher International Foundation for Telemetering Journal International Telemetering onference Proceeding Right opyright International Foundation for Telemetering ownload date 1/7/18 4:9: Link to Item http://hdl.handle.net/115/67349
N PTIVE SIGNL SERH LGORITHM IN GPS REEIVER Sun Li Wang Yinfeng Zhang Qihan eijing Univerity of eronautic and tronautic, P. R.hina STRT GPS ignal fixed dwell and variable dwell time equential earch algorithm are compared with probability of fale alarm and detection and earching rate. n adaptive earch algorithm i propoed according to different work mode and interference or jam circumtance, which ha effectively improved ignal acquiring peed and reliability. Mathematical imulation how it correction and feaible. KEY WOR GPS, fale alarm probability, detection probability, earch rate, algorithm INTROUTION Sequential earch technique are by far the mot commonly ued to achieve the initial coare ynchronization for low input carrier-to-noie denity ratio environment, which GPS ignal ha undergone. ecaue of uncertainly of PRN code phae delay and oppler frequency hift, GPS receiver mut perform a two-dimenional equential earch proce for GPS ignal. The mean acquiition time i crucial for determining code loop parameter and earch algorithm. Thi paper compare the performance of fixed dwell time and variable dwell time earch algorithm by analyzing ignal detection probability, fale alarm probability and earch rate. ccording to different work mode and interference an adaptive ignal earch algorithm i propoed to effectively improve ignal acquiring peed and reliability. It i implemented in GPS digital acquire ytem bae on GPS correlator. GPS SIGNL SERH SHEME In GPS receiver, ignal acquiition digital ytem i compoite of correlator, envelopee detector and earch control cheme. The correlator include PRN code generator, carrier O, mixer and integrate-and-dump filter. The receiver adjut local PRN code phae (range dimenion, aociated with the replica code) and oppler hift etimation (line-ofight velocity dimenion, aociated with the replica carrier) to produce matching in-phae
and quadra-phae ignal to correlate with the incoming ignal. the ample rate of correlator i a fat a enough, auming that the code delay and oppler hift are contant over the k th correlation interval, the output of the integrate-and-dump filter I ( k ), Q( k ) are function of time-variable carrier phae, code correlation error and oppler hift etimation error. The input of the envelope detector can be expreed a ( ) ( ) ( ) S k = I k + Q k. all each range earch increment a a code bin (d code chip) and each velocity earch increment a a oppler bin ( F Hz), the each code bin and oppler bin make up a earch cell. uming the maximum oppler hift i F max (a time of oppler bin), and the code length i (GPS / code ha 13 chip), then the number of earch cell Y can be given by: F Y = max η. (1) d F Whereη i oppler hift earch reliability coefficient. oppler hift can be poitive or negative, o the earch cope doubled. Without precie etimation of F max, oppler hift variance i ued to ubtituted for F max, η take a 1~3 (aη =3, the reliability i cloe to 1). Set ignal detection threhold a V t, compare S( k ) with V t in algorithm, then ignal detection can be accepted or denied. Signal earch proce can be expreed that local ignal generator adjut code phae and oppler hift etimation and make the replica ignal aligned to a certain earch cell. If ignal i uccefully detected out, then earch proce top and code tracking tart; otherwie, if ignal i denied, earch proce make code phae advance a code bin and continue until all code cope are earched. If ignal i till not detected out, it make oppler hift etimation advance to the next oppler bin, the above proce repeat until the ignal earch ucceed. onidering the direction of oppler hift, ignal earch marche on the two ide of the initial cell alternately. PERFORMNE OF SERH LGORITHMS Search algorithm i the heart of earch trategy. Two powerful equential earch detector are analyzed and compared in thi paper: the fixed dwell algorithm (ignal dwell, M out of N dwell and 1+M/N dwell) and the variable dwell algorithm (with different initial count value). The algorithm have been explained in [1] [][3], Here jut get ome ideal over them. Single dwell algorithm compare envelope of earch cell S( k ) with threhold V t, if S( k ) V t, ignal acquiition ucceed, otherwie the ignal i denied and earch advance to the next cell.
It i known that I ( k ), Q( k ) can be aumed a Gauian random ditribution, the envelope S( k ) i a Ricean ditribution [4]. uming probability denity function (PF) for noie with no ignal preent i p ( z) n and PF for noie with ignal preent i p ( z), which i defined by: z z + z exp I for z p ( z) = σ σ σ () otherwie Where z = random variable, σ =RMS noie power, =RMS ignal amplitude and z I = modified eel function of zero order. When ignal i not preent =, p ( ) z σ become to p ( z) n. Equation () can be expreed in term of the predetection ignal-tonoie, n (dimenionle), then get: z z n p ( z) = n I exp σ σ (3) σ Where n =predetection ignal-to-noie ratio = σ 1 T (power ratio), S N = 1lg n (predetection ignal-to-noie in d) = N + lg, T =predetection integration time in econd and N =carrier-to-noie power ratio in d. Signal detection probability and fale alarm probability are determined a follow: P d = V t p ( z) dz ( ) exp( ) P = p z dz = V fa Vt n t (4) σ (5) Rearrange equation (5) yield the threhold in term of the deired ingle trial probability of fale alarm and meaured 1-igma noie power: V t = σ ln P (6) fa Take σ = 1 (normalized), threhold V t can be determined by deired P fa. Uing thi reult, the ingle trial probability of detection P d i computed for the expected N and dwell time T. M N Search lgorithm take N envelope and compare them to the threhold for each cell. If M or more of them exceed the threhold, the ignal i declared preent. If not, the ignal i declared abent and the proce advance to the next earch cell. Thee are treated a ernoulli trial and the number of envelope, n, which exceed the threhold ha a inomial ditribution. The overall probability of fale alarm and detection in N trial i: N ( fa) N n n n PF1= N Pfa 1 P (7) n= M
N N n N d ( d ) 1 1 (8) n= M n n P = P P 1+ M N Search algorithm i combination of the above two. Firt, make a ingle trial, if S( k ) < V t ignal abent i declared and the earch advance to the next earch cell; if S( k ) V t, the M N earch algorithm i adopted for further trial. In thi time, probability of fale alarm and detection are: PF = Pfa PF1 (9) P = P P (1) d 1 If ingle trial fale alarm probability i deired a P fa =16%, σ = 1(normalized), then V t = 1914.. From equation (4)(5)(7)(8)(9)(1), probabilitie of fale alarm and detection can be calculated out. Figure 1 how the reult correpond to different n (predetection ignal-to-noie ratio). i for ingle trial algorithm, i for M N algorithm ( M = 7, N = 8 ), i for 1+ M N algorithm. i for a kind of variable time dwell, which i explained later. P r o b. o f f a l e a l a r m 1 1-1 1-1 -3 1-4 1-5 P r o b. o f d e t e c t i o n 1.9.8.7.6.5.4.3..1 1-6 5 1 5 1 Fig.1 performance of fixed time dwell algorithm When code earch bin and predetection integration time i determined, earch rate R i inverely proportional to mean dwell time N E of each earch cell, that i R = d NE T. In ingle dwell algorithm, N E = 1 while in M N algorithm, N E = N. The cot of it maller fale alarm probability i decreaing earch rate, which i not good for mean acquiition time. to 1+ M N algorithm, becaue mot cell include only noie, and average time of dimiing thoe cell i cloe to 1, o the total mean dwell time i a little greater than 1, and it earch rate ha been improved a fale alarm decreed. However, thi alo decreae ignal detection probability, which ha little effect in high ignal-to-noie ratio circumtance but deteriorate ignal detection performance in low ignal-to-noie ratio circumtance. Tong, P.S ha propoed variable time dwell earch algorithm [5]. It Firtly, it initialize up/down counter L to and compare ignal envelope with threhold. If S( k ) V t, the L counter increae 1, otherwie the L counter decreae 1, when L get to zero, the ignal
abent i declared, and when L get to (which i et a certain value), the ignal preent i declared. Tong ha give it fale alarm probability and detection probability a following: P P = [( Pfa ) Pfa ] ( Pfa ) Pfa 1 1 [ ] F3 1 = 1 1 [( Pd ) Pd ] ( P ) P 1 1 [ d d ] 3 1 + (11) + (1) 1 1 Where Pfa, Pd are fale alarm probability and detection probability of ingle trial, alo take P fa = 16. a example to compare performance of the algorithm when, have different value. Their probabilitie are hown in figure,3. P r o b. o f f a l e a l a r m 1 1-1 1-1 -3 1-4 P r o b. o f d e t e c t i o n 1.9.8.7.6.5.4.3 1-5..1 1-6 5 1 5 1 Fig. performance of variable time dwell algorithm ( = 1) 1 1 P r o b. o f fa l e a l a r m 1-1 1-1 -3 1-4 P r o b. o f d e t e c t i o n.9.8.7.6.5.4.3 1-5..1 1-6 5 1 5 1 Fig.3 performance of variable time dwell algorithm ( = )
In figure, i for = 1, = ; are ituation for = 1, = 4, 6, 8. ecaue mot earch cell contain only noie, mean dwell time of dimiing thoe cell i cloe to 1, their earch rate i imilar to 1+ M N algorithm. From figure 1, when = 8, fale alarm probabilitie of 1+ M N and = 1, = 8 have 1 6 magnitude, but the latter ha better detection performance when ignal-to-noie ratio i low. In figure, with increae, fale alarm performance improved while detection performance improve a little but earch rate decreae. When ignal- to-noie ratio i high, = 8 can get nice performance. In figure 3, i for = 1, = ; i for = 1, = 8; and are for = = It i een the latter two have nearly ame probability curve. all have 1 6 magnitude fale alarm probability, when ignal-to-noie ratio i low, variable time dwell algorithm with = get better detection performance. It i known from algorithm cheme that the improvement i obtained with cot of decreaing earch rate. 1, 4, 8. N PTIVE SERH LGORITHM N ITS IMPLEMENTTION aed on above analyi and comparion, it i known that fixed time dwell algorithm and variable time dwell algorithm have different performance, even variable time dwell technique, thing alo change with different initial value (, ). In fact, the three indexe of fale alarm probability, detection probability and earch rate are contradictory, algorithm hould trade off between them. However, the ignal power reaching receiver antenna i definite. When external interference (multipath effect, intentional/non-intentional in/out band interference) are not taken into conideration, channel noie, circuit implementation lo and pread pectrum gain can be counted out, therefore the depreaded ignal-to-noie ratio hould be expected in a reaonable range. In other world, from the depreaded ignal-to-noie ratio input ignal-to-noe can be derived and information about external interference i obtained. When ome atellite ignal wa acquired and tracked, ambient noie and interference can be etimated by calculating equivalent carrier-to-noie ratio [6]: 1 1 = + c n [ c n ] 1 Where [ c n ] eq 1 preent (in d), [ N ] eq [ N ] eq =, c n eq j P f N 1 c (13) = 1, N = carrier-to-noie ratio with no interference = equivalent carrier-to-noie ratio with interference or jam preent (in d), j = interference-to-ignal ratio, P = adjut coefficient which i 1 for narrow band and for wide band interference, f c = code rate. c n i defined in I- GPS-, and [ ] c n eq can be counted out by tracked atellite, then from equation (13), j i etimated.
From above, an adaptive ignal earch algorithm i propoed according to different work mode and interference condition. It mean when receiver work in initial acquiring and no atellite or interference information get (blind earching), ( 1+ M N ) algorithm i adopted for fat earching. oon a a atellite i acquired and tracked, external interference information i derived from depreaded ignal-to-noie ratio of the tracked atellite. lgorithm ( 1+ M N ) or variable dwell algorithm ( = 1, = 8) i adopted for high ignal-to-noie ratio condition (with low fale alarm probability, high detection probability and fat earch rate), while variable algorithm ( =, = 4) i adopted for low ignal-to-noie ratio condition which ha lower earch rate for enure ignal detection performance. In experiment, function of PRN code generation, carrier O, and integrate-and-dump filtering are implemented by 1 channel parallel correlator upported by microcomputer, while envelope and earch control cheme are implemented by oftware. The input ignal of correlator i down-converted digital IF GPS ignal, PRN code length = 13, code rate i 1.3 MHz, earch code bin i d = 5. chip, and correlation interval i T = 1 m. oppler hift bin i F = 5 Hz. ode O and carrier O can be preciely et by oftware, and make ignal earch march on time and frequency domain at ame time. oppler hift cope i determined by maximum velocity of receiver V 1 (when i in direction of atellite-to-receiver, the wort), atellite oppler hift (V, relative to tationary uer) and crytal ocillator frequency bia F c : f F = L V + max V + 1 Fc (14) Where f c = 15754 L GHz ( ). ( L 1 carrier), c = peed of light. The output ignal amplitude of integrate-and-dump filter decreae a code phae error and oppler hift etimation error increae. ode phae error i linear and carrier error i function of in( x) x. When acquiring ignal, code phae increment and oppler hift increment tep amount hould be taken into conideration in order to avoid lip over the real ignal. Noie variance i determined by G in RF front and correlator performance. Signal threhold i determined by requirement of fale alarm probability, detection probability and earch rate a well a tep error caued by code bin and oppler bin.
ONLUSION From above analyi and comparion, the adaptive algorithm can chooe appropriate algorithm according to receiver work mode and interference or jam circumtance information fed back by ome tracked atellite, and therefore improve mean ignal earch peed and reliability. Mathematically imulation how it correction and feaible. REFERENE 1. icarlo,.m, Weber, L. Multiple dwell erial earch: Performance and application to direct equence code acquiition. IEEE Tran OM.1983, 31(5):65-659. Sun Li, Zhang Qihan. Signal earch algorithm and it implementation in GPS / code receiver. Journal of eijing Univerity of tro. and ero.1998 3. Phillip W. Ward. GPS Receiver Search Technique. In: IEEE Poition, Location and Navigation Sytem Proceeding, 1996:64-611 4. Zhou Yingqin. Introduction of Random Proce. eijing: eijing Univerity of tro. & ero. Pre.1987 5. Tong P.S. Sub-optimum Synchronization Procedure for Peudo Noie ommunication Sytem. In: Proc. National Telecommunication onference, 1973.61-65. 6. ian Zhongzhong. ommunication ytem Signal and Noie. Xi an: Xi an Jiao Tong Univerity pre.199