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1 POLITECNICO DI TORINO Repoitory ISTITUZIONALE GNSS ignal acquiition in the preence of ign tranition Original GNSS ignal acquiition in the preence of ign tranition / KEWEN SUN; LO PRESTI L.; FANTINO M.. - STAMPA. - (9), pp. -8. ((Intervento preentato al convegno ENC - GNSS 9 tenutoi a Naple, Italy nel 3-6 May, 9. Availability: Thi verion i available at: 583/973 ince: Publiher: Helio Publihe DOI: Term of ue: openacce Thi article i mae available uner term an conition a pecifie in the correponing bibliographic Publiher copyright (Article begin on next page) 4 January 8

2 GNSS Signal Acquiition in the Preence of Sign Tranition Kewen Sun, Letizia Lo Preti, Politecnico i Torino, Dipartimento i Elettronica C.o Duca egli Abruzzi 4, 9 Torino, Italy name.urname@polito.it Maurizio Fantino, Itituto Superiore Mario Boella Via P.C. Boggio 6, 38 Torino, Italy name.urname@imb.it BIOGRAPHY Sun Kewen receive hi Bachelor Degree of Science in Material Science in July at Hefei Univerity of Technology, China an the Mater Degree of Science in Mechatronic Engineering in March 5 at Univerity of Science & Technology, Beijing, China, followe he receive the Mater Degree of Science in Electronic Engineering in March 7 at Univerity of Uine, Italy. At preent, he i a Ph.D tuent in Electronic an Communication Engineering at Politecnico i Torino, Italy. Since 7 he ha been with the NavSAS (Navigation Signal Analyi an Simulation) group, at the Navigation Laboratory in Itituto Superiore Mario Boella (ISMB). Currently hi reearch activitie are mainly focue on innovative GPS / Galileo ignal acquiition an tracking algorithm for GNSS receiver. Letizia Lo Preti i a full profeor of telecommunication in the Electronic Department of Politecnico i Torino, Italy. She got the egree in Electronic Engineering at Politecnico i Torino in 97. Her reearch activitie are focue on the fiel of igital ignal proceing, telecommunication ytem imulation, array proceing for aaptive antenna, an the technology of navigation an poitioning ytem. Her teaching activity i mainly focue on ignal proceing an igital communication. Currently, he i the coorinator of Mater Degree coure in Telecommunication Engineering (ince 3), an i a member of the Dean boar of the Engineering Faculty in the ICT fiel. She i the cientific coorinator of the mater on Navigation an Relate Application hel by Politecnico i Torino. Maurizio Fantino receive the egree in Communication Engineering in at Politecnico i Torino an a Ph.D egree in Electronic an Communication Engineering in May 6. At preent Maurizio Fantino i a reearcher at the Itituto Superiore Mario Boella (ISMB), member of the NavSAS (Navigation Signal Analyi an Simulation) group, at the Navigation Laboratory. Hi reearch interet cover the fiel of localization, navigation an communication. In particular, hi work i mainly focue on innovative architecture for high performance GPS an Galileo receiver. The main goal of thi activity i the eign an implementation of Software Define Raio Receiver for GPS an Galileo ignal in pace. Other important area of interet of hi reearch are the tuy of the optimization of GNSS ignal a well a the analyi of Signal Quality Monitoring trategie for example of Multipath affecte ignal. ABSTRACT The next generation of Global Navigation Satellite Sytem (GNSS), uch a Galileo [] an GPS moernization [], will ue ignal with equal coe an bit perio, which will introuce a potential ign tranition in each egment of the ignal procee in the acquiition block. If FFT i ue to perform the correlation a ign tranition occurring within the integration time may caue a plitting of the main peak of the Cro Ambiguity Function (CAF) into two maller lobe along the Doppler hift axi [3]. In thi paper a metho to overcome the poible impairment ue to the lobe plitting i propoe an valiate by imulation. I. INTRODUCTION The firt tage in the operation of a GNSS receiver i the acquiition of the atellite in view, which provie rough etimate of the parameter, uch a coe elay an Doppler hift of the Signal-In- Space (SIS) tranmitte by the atellite. Thi activity i performe by the o calle acquiition block an with the avent of the European Galileo ytem ome moification on it mut be

3 coniere. The main factor that lea to the ue of ifferent trategie for the Galileo SIS are the ue of the, [] ub-carrier, the preence of the econary coe in the pilot channel an the higher ata rate in the ata channel. Thee new feature have been eigne to guarantee the interoperability with the GPS ytem an better performance for inoor poitioning. The next generation of GNSS ytem, uch a Galileo [] an GPS moernization [], will ue ignal with equal coe an bit perio, which will introuce a potential ign tranition in each egment of the ignal procee in the acquiition block. If FFT i ue to perform the circular correlation a ign tranition occurring within the integration time may caue a plitting of the main peak of the Cro Ambiguity Function (CAF) into two maller lobe along the Doppler hift axi [3]. In general thi i a critical apect in all the acquiition metho where the ata are procee in block. It i very well known that increaing the coherent integration time improve the acquiition enitivity, but the bit ign tranition limit the achievable maximum performance. Similarly, the acquiition enitivity coul be increae by non-coherent integration, which i le enitive to bit tranition but preent the ie effect of quaring lo [4][5]. In orer to mitigate the CAF peak impairment an increae the acquiition enitivity, in thi paper a novel two tep acquiition metho i propoe aiming to overcome the problem of the CAF peak plitting. The CAF peak plitting along the Doppler hift axi i caue of error in the Doppler hift etimation, while, a far a the coe phae elay i concerne, thi plitting effect prouce only a correlation amplitue reuction, but it poition remain unchange along the coe elay axi. The main iea of thi propoe metho i to take avantage of thee two ijoint effect affecting the CAF along the coe elay an Doppler hift axe. The coe elay i recovere in the firt acquiition tep, o a to roughly remove the ign tranition, while in the econ acquiition tep the Doppler hift etimate i recovere. In orer to pee up both thee acquiition tep, the fat acquiition approach bae on Fat Fourier Tranformation (FFT) ha been aopte. In orer to analyze the performance of the propoe metho, imulation campaign have been aree. The ignal electe for conucting thi teting activity i the Galileo Open Service (OS) broacat on E, where the preaing coe i moulate by fake ata but with the correct rate. Hitogram plot of the etimate Doppler frequency hift an coe phae elay are carrie out to compare the propoe metho with the tate of the art acquiition technique. The acquiition performance comparion have alo been aree by mean of the o calle Receiver Operative Characteritic (ROC) curve. The analyi reult how how the two tep acquiition metho outperform the claical fat acquiition approach, which prove the avantage of the propoe technique when ealing with weak ignal an bit tranition an further prove it valiity an effectivene. II. SIGNAL MODEL The ignal at the input of the acquiition ytem of a GNSS receiver i generally an intermeiate frequency (IF) ignal, obtaine by own converting a Raio Frequency (RF) ignal. The SIS tranmitte by a certain given atellite an receive at the terminal antenna can be written a r( t) = A in ( t τ ) c( t τ ) co(π ( f IF + ( t τ ) f ) t + ϕ) b () where i the amplitue of the receive GNSS ignal, whoe power i given by = ; i the primary preaing coe elaye by with repect to a local coe replica. Denoting with the chip interval, can be expree a =, where i th chip of the Peuo Ranom Noie (PRN) equence with chip rate = an i the unitary rectangular pule with uration. i the ub-carrier ue for the Galileo OS on E. The navigation ata meage i inicate a, i the IF at the output of the front en (FE), i the unknown Doppler hift an i a ranom unknown initial phae. It i known that Galileo i mae by the concatenation of a primary an a econary coe for each pilot channel. The primary coe on E i a PRN with the chip rate of.3 MHz an a repetition perio of 4 m. The navigation ata meage i moulate with a ata rate of 5 Hz o with a bit uration of 4 m. Thi mean that there i a potential ata ign tranition each coe perio. In a igital receiver the IF ignal i ample through an Analog to Digital Converter (ADC). The ADC generate a ample equence, obtaine by ampling at the ampling frequency =. From now on the notation = will be aopte to inicate a generic equence to be procee in any igital platform.

4 The realitic moel of the receive ignal at the input of the acquiition tage can be written a y[ n] = r[ n] + η[ n] () where = i the ignal component an i AWGN with zero mean an variance equal to ( being the front en banwith). III. CAF EVALUATION BY FFT By applying the reult of the Maximum Likelihoo (ML) etimation theory, it i poible to how that the bet etimate of the propagation elay an the Doppler frequency hift, in the preence of aitional white Gauian noie (AWGN), are bae on the maximization of the Cro Ambiguity Function (CAF). In thi ection the CAF evaluation uing the FFT to perform circular correlation i ecribe [6]. Thi metho i extremely efficient becaue it work on vector in a parallel way. However thi metho i enitive to peak impairment becaue of bit ign tranition. In the FFT-bae cheme, a ignal vector =,,, of ample i extracte from the incoming SIS an multiplie by a complex tet ignal, o a to obtain the equence =. Thi ignal i FFT-tranforme an multiplie by the complex conjugate of the FFT tranform of the prouct of the local coe replica an the ub-carrier. Finally the invere FFT tranform i mae o a to obtain the circular correlation,,, which can be written a elay etimate an i the Doppler hift etimate in the acquiition tage. In fact when the local coe replica matche the receive ignal perfectly, the CAF envelope become S y, r ( τ, f ) = L n = f ( nt ) nt τ ) co(π ( f + ϕ ) e IF + j π ( f IF + f ) nt (4) where the term co + + can be written a b [ n] = p [ n] ( nt τ)co(π ( f + f ) nt ϕ) (5) τ L IF + with the preence of a rectangular winow function in the interval n [, L-] an with unitary amplitue. In cae of bit tranition the function = revere the ign being a two-pule ignal. Equation (4) can be regare a the Dicrete Time Fourier Tranform (DTFT) of a inuoial function moulate by, which behave a a ort of ubcarrier. The effect on the CAF peak i to plit it power into two ifferent maller lobe. To how thi effect in the acquiition earch pace we have imulate the Galileo Open Service E ata channel ignal (E-B) containing navigation ata meage with the ymbol rate of 5 ymbol/, which mean that there i a poible bit ign tranition at each PRN coe perio. R y, r ( τ, f ) = IDFT{ DFT[ q [ n]] [ DFT[ c( nt ) b l * ( nt )]] } (3) IV. BIT SIGN TRANSITIONS PROBLEM The fat acquiition metho bae on FFT i extremely efficient, but ince it intrinic nature of proceing block of ata, it may uffer from peak plitting impairment ue to the preence of bit ign tranition. In cae of the Galileo E ata channel, the bit ign tranition coul poibly occur in any time interval of 4 m (equivalent of a ingle coe perio). It i poible to how that the ign tranition o not etroy the poibility of etecting the atellite in view, but there might be an error in the election of the etimate pair =,, where i the coe Figure : CAF envelope of the Galileo OS ignal in the E ban when no bit tranition occur. The acquiition experiment have been performe with a Doppler hift of 35 Hz, a coe phae elay of m an a carrier to noie power enity ratio of 45 BHz. Thi value repreent a relatively optimitic ituation, which ha been coniere to how the CAF peak plitting effect

5 an then to motivate the moification to the tate of the art acquiition cheme. In Figure, the CAF envelope i evaluate bae on the fat acquiition cheme in cae of no preence of bit ign tranition. Figure : CAF envelope of the Galileo OS ignal in the E ban when a bit ign tranition i preent. Figure 3: Curve extracte from the CAF envelope in cae of no bit ign tranition Frequency bin Delay bin x Frequency bin Delay bin x 4 Figure 4: Curve extracte from the CAF envelope in cae of with bit ign tranition. When we introuce the bit ign tranition to the ignal, the plitting effect of the CAF main lobe can be clearly een in Figure. In thi cae the FFT bae fat acquiition cheme uffer much from the peak lo caue by the preence of the bit ign tranition. In Figure 3 an 4 two plot extracte from the CAF envelope of Figure an Figure are given repectively. The upper curve repreent the Cro Function (CCF) in the Doppler hift omain (which i a energy pectrum) at the correct coe elay bin. In Figure 3, it i known that the CAF peak locate it poition correctly along the coe elay an Doppler hift axe repectively when bit ign tranition i not preent. When ealing with the bit tranition, in the upper plot of Figure 4, it i clearly oberve that the CAF peak i ivie into two ifferent maller lobe along the Doppler hift axi. While from the lower plot of Figure 4 it i evient that the bit tranition oe not impair the CCF in the coe elay omain. V. TWO STEPS ACQUISITION METHOD In thi ection, a two tep acquiition cheme i propoe to overcome the problem of CAF peak plitting. The iea i to exploit the fact that the plitting occur only in the Doppler frequency omain, while in the coe elay omain the peak poition remain almot unchange. In the firt tep the coe elay i etimate o a to tentatively align the local coe equence with the ata ign tranition, while in the econ tep the Doppler hift i etimate. In other wor, the etimate pair =, i obtaine in two conecutive tep. The firt tep aim to get etimate coe elay value by uing the FFT-bae acquiition metho. The Doppler hift, i not etimate in thi tep becaue it coul be erroneou. Noie reuction technique, uch a coherent integration an non-coherent integration, can be ue in orer to increae the acquiition enitivity. The coherently integrate CAF envelope, evaluate in the firt tep can be written a S τ, f ) = Ri, y r ( τ, f ) (6) N (, i= N where,,, i the contribution in the coherent integration proce; i the number of the coe perio applie to the coherent integration proce in the firt tep. Non-coherent integration can be ue after the coherent integration operation

6 i mae. The non-coherently integrate CAF envelope, can be written a in the following or it can be ue to refine the elay etimation obtaine in the firt tep. K G ( τ, f ) = S, i( τ, f ) (7) K i= where,, i the coherently integrate CAF envelope in the non-coherent integration proce; i the number of the non-coherently integrate CAF envelope. In the firt acquiition tep the etimate pair, =,, p ˆ ˆ ML, = ( ˆ τ, f,) = argmaxg ( τ, f ) (8) i obtaine, but only the value i retaine a vali. The value, i icare, a poibly affecte by plitting error (a hown in Figure 4). In the econ tep the value i ue to extract a new ignal vector aligne with the local coe. In thi way the effect of the bit tranition practically iappear, even if the alignment i not perfect. Coherent an non-coherent integration can be again aopte in the econ acquiition tep. The coherently integrate CAF envelope, evaluate in the econ tep can be written a S p τ, f ) = Ri, y r ( τ, f ) (9) N (, i= N Similarly, the non-coherently integrate CAF envelope, in the econ tep can be written a i= K G ( τ, f ) = S, i( τ, f ) () K A new pair, =,, i now etimate a = ( ˆ τ, fˆ p ˆ ML,,) = argmax G ( τ, f p ) () an only the frequency value i retaine. The elay etimate houl give now a null value, ue to the coe alignment performe in the econ tep. Therefore the elay etimate can be now icare Figure 5: CAF envelope of the Galileo OS ignal evaluate by the two tep metho for a C/N o of 45 BHz with bit tranition Frequency bin Delay bin x 4 Figure 6: Curve extracte from the CAF envelope evaluate with the two tep acquiition metho with bit tranition. The CAF envelope in the earch pace evaluate in the econ tep ( = an =) i hown in Figure 5. Two peak appear now at the correct frequency value ( = 35 Hz). Thi i ue to the fact that the coe elay i zero in the econ tep, an then the typical correlation triangle appear now plit at the beginning an at the en of the bin. Thi reult i better highlighte in Figure 6: the upper curve how that the CAF peak appear at the correct Doppler hift poition ( = 35 Hz); the lower curve prove that the local coe replica align perfectly to the bit tranition poition in the econ tep becaue of the correct recovery of the coe phae elay in the firt tep. Since in the ieal cae the CAF envelope, in the econ tep houl concentrate it energy only in the correct bin without peak plitting, we can aume that the Doppler hift

7 etimate, obtaine in the econ tep houl be correctly recovere an i equal to the real Doppler hift value. We alo aume that the coe elay etimate in the econ tep i correctly locate at the beginning or ening poition along the coe elay axi, that i to ay i equal to or (Notice that i the number of the ample in a coe perio). In orer to achieve the correct coe elay etimate, the etimate coe elay value an obtaine from both acquiition tep houl be coniere. If, then (Notice that i the real coe elay in the ignal), therefore can be expree a = + ; if >, then >, therefore can be expree a = = +. Finally the algorithm to evaluate the etimation pair =, can be ummarize a in the following fˆ ˆ = f, L if ˆ τ then ˆ τ = ˆ τ + ˆ τ ele ˆ τ = ( ˆ τ + ˆ τ ) L en if ˆ τ [, L]then ˆ τ = ˆ τ en VI. SIMULATION RESULTS WITH GALILEO E SIGNAL In thi ection, the behavior of the propoe two tep acquiition trategy i given in term of hitogram of the etimate Doppler frequency hift an coe elay. In orer to ae the acquiition performance alo ROC curve have been aree o a to compare the propoe metho with the tate of the art acquiition approach. Simulation campaign have been performe imulating the Galileo, ignal. In particular, the Galileo E-B ignal with both PRN coe an navigation ata meage ha been generate for ifferent value of carrier to noie power enity ratio, Doppler frequency hift an location of the bit ign tranition along the ignal. The imulation cenario electe for the two tep acquiition aement in term of hitogram of the Doppler frequency hift an coe elay etimate coniere a Galileo E ignal with a coe elay of.5 m, a Doppler hift of 35 Hz an a carrier to noie power enity ratio of 3 BHz. Six coe perio have been coherently integrate =6, = for both the claical fat acquiition approach an the propoe two tep acquiition metho. The Monte Carlo imulation experiment have been repeate for time an the hitogram of the etimate of an are given repectively. 5 5 Fat acquiition metho -5 5 Etimate Doppler hift (Hz) 4 3 Two tep acquiition metho -5 5 Etimate Doppler hift (Hz) Figure 7: Hitogram of the etimate Doppler hift in two cae: the fat acquiition approach an the two tep acquiition metho for a C/N o of 3 BHz with bit ign tranition. 3 Fat acquiition metho Etimate coe elay () x Two tep acquiition metho Etimate coe elay () x -3 Figure 8: Hitogram of the etimate coe elay in two cae: the fat acquiition approach an the two tep acquiition metho for a C/N o of 3 BHz with bit ign tranition. Figure 7 how the hitogram of the Doppler hift etimate for the claical fat acquiition approach an the propoe two tep acquiition technique. The upper plot of Figure 7 i the hitogram evaluate by the claical approach which how that the Doppler hift etimate eviate much from the correct value ( = 35 Hz) becaue of the CAF peak plitting. The claical acquiition approach how inaequate performance when ealing with bit tranition problem. The lower plot of Figure 7 i the hitogram of the Doppler hift etimate obtaine by the propoe acquiition technique, a can be een that the achieve Doppler

8 hift etimate much more concentrate aroun the correct Doppler hift value. Thi propoe methoology i le affecte by the peak plitting effect an outperform the claical acquiition approach. Figure 8 how the comparion of the hitogram of the coe elay etimate for both ecribe acquiition technique. The upper hitogram of the coe elay etimate i evaluate by the claical approach an the lower hitogram i achieve by the propoe technique. It i eaily known from Figure 8 that the propoe acquiition technique provie much improve etection rate of the coe elay etimate over the claical fat acquiition approach. A more etaile analyi ha been performe by evaluating the ROC curve [7], which i the graph of the etection probability veru the fale alarm probability, or, equivalently, of the mie etection probability veru the fale alarm probability. The preence of bit tranition in the Galileo ignal reuce the benefit eriving by coherently extening the integration time, for uch a reaon in the firt acquiition tep a combination between the coherent an non-coherent integration technique over more coe perio i uggete. In the imulation experiment ifferent number of the coherent an non-coherent integration coe perio have been choen to compare the performance between ifferent acquiition cheme. Each imulate ROC curve report the comparion of the performance about ifferent acquiition cheme uing the ame number of coe perio, coherently or non-coherently integrate. Figure 9 epict the acquiition performance comparion among three cae repectively: the fat acquiition approach with an without ata tranition on the ignal, an the propoe two tep acquiition metho coniering ign reveral uring the correlation. The imulation ha been mae coniering the coherent integration of two Galileo, coe perio =, ten noncoherent integration operation =, a of 3 BHz an a ampling frequency of about 8. MHz. The reult of Figure 9 how that the two tep acquiition metho provie improve acquiition performance in term of etection probability over the claical fat acquiition approach, when the receive ignal preent the well known problem of the bit ign tranition. A the value of carrier to noie power enity ratio increae, le non-coherent integration are neceary to achieve a reaonable etimation rate for the coe elay in the firt acquiition tep, o to conequently recover the correct Doppler hift in the econ tep. An example of that i hown in Figure for a of 3 BHz an coherent integration coe perio = an 6 noncoherent integration operation =6. Similarly to the comparion of Figure 9, Figure highlight how better performance can be achieve by the two tep acquiition metho with repect to the claical fat acquiition cheme. P P fat acquiition approach,no tranition,n=,k= fat acquiition approach,with tranition,n=,k= two tep,with tranition,n =,K =,N =,K = P fa x -3 Figure 9: Comparion between the fat acquiition approach an the two tep acquiition metho for a cae of C/N o = 3 BHz, N = an K = fat acquiition approach,no tranition,n=,k=6 fat acquiition approach,with tranition,n=,k=6 two tep,with tranition,n =,K =6,N =,K = P fa x -3 Figure : Comparion between the fat acquiition approach an the two tep acquiition metho for a cae of C/N o = 3 BHz, N = an K = 6. Thi tren i clearly even more evient for high ratio a hown in the comparion of Figure for 38 BHz. For uch a high carrier to noie ratio the firt acquiition tep i generally able to recover the coe elay at which the bit ign tranition might occur an initialize the econ acquiition tep in a proper way. Figure clearly how like in thi cae, in real ituation, when the bit tranition occur the two tep acquiition metho coul ai the acquiition phae of a GNSS receiver.

9 P Figure : Comparion between the fat acquiition approach an the two tep acquiition metho for a cae of C/N o = 38BHz. VII. CONCLUSION fat acquiition approach,no tranition,n=,k= fat acquiition approach,with tranition,n=,k= two tep,with tranition,n =,K =,N =,K = fat acquiition approach,no tranition,n=,k=.55 fat acquiition approach,with tranition,n=,k= two tep,with tranition,n =,K =,N =,K = P fa x -3 coe an bit rate, IEEE/ION PLANS Conference, Monterey, California, USA, May 5-8, 8. [4] M. Fantino, Stuy of Architecture an algorithm for Software Galileo Receiver, Ph.D iertation, Politecnico i Torino, 6. [5] D. Borio, M. Fantino an L. Lo Preti, Acquiition Analyi for Galileo BOC Moulate Signal: Theory an Simulation, European Navigation Conference, Mancheter, UK, 7- May, 6. [6] D. J. R. Van Nee an A. J. R. M. Coenen, New Fat GPS Coe-Acquiition Technique Uing FFT, Electronic Letter, Vol. 7 No., 7th January 99. [7] J. I. Marcum, A Statitical Theory of Target Detection By Pule Raar, IEEE Tranaction on Information Theory, pp.59-67, t December 947. The preence of ata meage or a econary coe which moulate each primary coe perio reuce the poibility of increaing the integration time in a coherent way, ince ata or the econary coe may lea to ign reveral uring the correlation winow. In orer to overcome the peak plitting caue by uch a ign tranition on the CAF, an innovative two tep acquiition metho ha been propoe an preente in thi paper. A comparion between thi propoe two tep acquiition metho an the claical fat acquiition approach i carrie on by imulation campaign in term of hitogram of the coe phae elay an Doppler hift etimate a well a ROC curve. Thoe imulation have hown how the ign tranition may reuce the etection rate of the claical acquiition cheme in a ignificant way, while the propoe methoology i le affecte. The imulation reult alo how how the two tep acquiition metho can generally achieve better performance when the ignal moulation preent a potential ign tranition each PRN perio, which i exactly the ituation of the Galileo OS ignal broacat on the E carrier. REFERENCES [] European Space Agency / European GNSS Superviory Authority, Signal In Space Interface Control Document, OS SIS ICD, Draft, February 8. [] E. D. Kaplan, Unertaning GPS: Principle an Application, n eition, Norwoo, MA 6, Artech Houe, 6. [3] L. Lo Preti, M. Fantino, P. Mulaano an X. Zhu, Acquiition ytem for GNSS ignal with the ame