BPSK-like Methods for Hybrid-Search Acquisition of Galileo Signals Adina Burian, Elena Simona Lohan, Markku Renfors Institute of Communications Engineering, Tampere University of Technology P.O.Box 553, FIN-33101, Finland,, Abstract— The Binary Offset Carrier (BOC) modulation which has been proposed for future Galileo and GPS M-code signals, provides a higher spectral separation from BPSK-modulated signals, such as GPS C/A code. Th
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  BPSK-like Methods for Hybrid-Search Acquisitionof Galileo Signals Adina Burian, Elena Simona Lohan, Markku RenforsInstitute of Communications Engineering, Tampere University of TechnologyP.O.Box 553, FIN-33101,,,  Abstract —The Binary Offset Carrier (BOC) modulation whichhas been proposed for future Galileo and GPS M-code signals,provides a higher spectral separation from BPSK-modulatedsignals, such as GPS C/A code. The absolute value of the auto-correlation function of a BOC signal has a narrower main lobe,which may increase the resolution of delay estimates, but alsopresents deep fades, which may lead to a higher number of timinghypotheses to acquire the signal. In order to get rid of theseambiguities, several approaches have been proposed in literature,which provide an unambiguous BPSK-like shape of correlationfunction. In this paper we analyze, compare and develop furthertwo BPSK-like methods which allow to acquire a BOC-signalunambiguously. The focus is on hybrid search, where severaltime-frequency bins are searched in parallel.We introduce here a modified version of a BPSK-like methodwhich decreases the receiver complexity and is valid for bothodd and even BOC orders. We analyze both single-side band(SSB) processing (i.e., only one band is used) and dual-side band(DSB) processing (i.e., upper and lower bands are combinednon-coherently). While eliminating the ambiguities in auto-correlation function, both SSB and DSB processing present someperformance degradation, induced by the band selection andnon-coherent processing. The analysis is done in the presenceof multipath fading channels. As a benchmark, we keep also theambiguous BOC processing. We consider parameters specified inthe proposals for Galileo system Open Service (OS), respectivelyPublicly Regulated Service (PRS). I. I NTRODUCTION The BOC modulation has been selected for both Galileoand modernized GPS signals [1]. The main target of BOCmodulation has been to provide a better spectral separationwith existing BPSK-modulated GPS signals, while allowingoptimal usage of the available bandwidth for different GNSSsignals [1], [2]. Also, BOC signals present a narrower mainlobe of the absolute value of their autocorrelation function(ACF), which enhances the tracking accuracy. On the otherhand, the additional fades which appear in ACF within thetwo-chip intervals may induce a missed detection due to azero (or very low) sampling point and may lead to a longeracquisition time. In consequence, the necessary step to searcha given time-uncertainty window, ∆ t bin , should be smallenough in order to find the main lobe of ACF. Therefore, thecomputational complexity in acquisition process is increased,the computational load being inversely proportional to thesquare of step time bin ∆ t bin , as reported in [3].A BOC ( m,n ) signal ( m and n are not necessarily integers)is created by a square sub-carrier modulation, where the signalis multiplied by a rectangular sub-carrier (e.g., with +1 and -1values) at sub-carrier frequency. The modulation parametersare equal to m = f  sc /f  ref  and n = f  c /f  ref  where f  sc isthe sub-carrier frequency, f  c is the code rate and f  ref  =1.023MHz is the reference frequency. Thus, the power spectrumis split into two symmetrical components around the carrierfrequency. The common baseline for OS structure (agreed byUS and European negotiation in June 2004) employs the sineBOC(1,1) modulation, which uses a 1.023 MHz square-wavesub-carrier modulated by spreading code chips at a chip rate f  c =1.023 MHz [8]. For PRS services, both sine and cosineBOC(15,2.5) have been proposed [8]. Other BOC modulationshave also been considered, such as BOC(15,10), BOC(10,5)or BOC(10,4) [5], [6].In order to eliminate the ambiguities of the ACF envelope,different methods have been approached in literature [3], [4],[5], [6], [7]. The main idea behind these ”BPSK-like” methods(generic name proposed in [5]) is that the BOC-modulatedsignal can be obtained as the sum of two BPSK-modulatedsignals, located at positive and negative sub-carrier frequen-cies. The effect of sub-carrier modulation can be removed byusing a pair of single-sideband correlators. We may have asingle-side band (SSB) receiver, where either the negative orthe positive of the sidebands correlators is used, or a dual-sideband (DSB) receiver, when both bands are combined non-coherently. Due to filtering and correlation losses, the BPSK-like methods bring some degradation in the signal level.In [3], [5] it is asserted that a SSB BPSK-like methodinduces at least 3 dB degradation in SNR. If DSB processingis used, this loss can be partially compensated, exceptinganyway the squaring losses in non-coherent integration [5].Compared to coherent processing of both sidebands, non-coherent processing looses about 0.5 dB of SNR.The ’BPSK-like’ methods proposed so far in the literaturefall in of the following two categories: either the main lobesof the signal and of the reference BOC-modulated PRN codeare selected (via filtering) and then correlated [3], [4], [7],or both the main lobes and secondary lobes between of thereceived signal are kept and the reference code is based onthe BPSK-modulated PRN code [5], [6]. We will refer tothe former method as Fishman & al. method [3], [4], [7],and to the later method as the Martin & al. method [5], [6](from the authors’ names). The Martin & al. method, if thereference code is properly selected, has the advantage of lower This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2006 proceedings. 1-4244-0355-3/06/$20.00 (c) 2006 IEEE 5211  Upper SideBand FilterUpper SideBand FilterRX signal(at samplelevel) ReferenceBOC-modulatedPRN sequence I & Don N c ms| . | 2 non-cohintegr. onN nc blocks + singleSBstatistic Right Sideband Processing singleSBstatisticdual SBstatistic Similar processing as in right sideband,but uses Lower Side Band FiltersPSDf f carrier Received BOC-modulated signalf carrier +f sc f carrier -f sc Fig. 1. Method 1 (Fishman & al.) . Selecting the main lobes of the BOC-modulated received signal and reference PRN sequence and correlate them. complexity, as we will discuss in our paper. On the otherhand, its performance is dependent on the BOC-modulationorder N  BOC  (defined here as N  BOC  = 2 f  sc /f  c ) and may beslightly lower than the performance of Fishman & al. method.The purpose of this paper is to analyze these non-ambiguousBPSK-like approaches, which differ through the manner thereceived signal and reference code are selected and processed:the first method is based on Fishman & al. approach, wheretwo filters are used and only the upper/lower main lobes areselected, both for the incoming signal and the reference code.The second method is a modified version of the Martin &al. method, where only one filter is used, which includesboth the main lobes and secondary lobes between them. Ourproposed method differs from the Martin & al. method in twoaspects: first, the reference sequence here is the pseudorandom(PRN) code kept at sub-sample level, and not the shifted PRNcode; second, our method is valid for both even and oddBOC modulation orders, not only for even BOC modulationorders which was the case in Martin & al. method. Ourproposed method has the advantage of a lower complexityimplementation than Fishman & al. method, as explained in[9].In order to evaluate the performance of our method, wehave selected for comparison the Fishman & al. approach(and not Martin & al.), because this method is patented andmay bring an improvement in results. Also, we have verifiedthrough simulations that Martin & al. technique provides verysimilar performance to our method. We compare both SSBand DSB cases of each method. As a benchmark, we keepalso the ambiguous BOC approach, where all spectrum (of signal and reference code) is used and the reference code isthe BOC-modulated PRN sequence.The performance of the studied methods is tested for a hy-brid search acquisition in multipath-fading channels. We willshow that, for a step of the time bin equal to half chip, thereis always an improvement in performance when DSB methodis used, but the SSB processing does not always improve theperformance compared to ambiguous-BOC processing. Also,as expected, for smaller time steps, the performances of BPSK-like methods may be worse than that of the ambiguous BOCapproach. Therefore, as suggested in [5], [6] the ’BPSK-like’methods can be used in initial energy search, while sweepingthe uncertainty time-domain with a higher time step ∆ t bin .Once the energy is found with enough confidence, the receivermay return to the BOC processing and use a finer time step.II. BPSK- LIKE METHODS  A. Method I (Fishman & al. method) In this method, the receiver selects only the main lobes of the BOC-modulated received signal and the reference code.The block diagram of this approach, illustrated in Fig. 1, ithas been proposed in [3] and [4], and later analyzed in [7].The main lobe of one of the sidebands (upper or lower) of BOC-modulated received signal is selected (via filtering) andit is correlated with a filtered PRN BOC-modulated referencecode, having the tentative delay  τ  and the tentative Dopplerfrequency  f  D . The BOC-modulated reference sequence isobtained in a similar manner with the received signal, filteringout the main lobe. Hence, the SSB Fishman & al. approachneeds three sideband selection filters (one for the real codeand two for the in-phase and quadrature components of thereceived signal). The Integrate & Dump (I&D) block performsthe coherent integration on N  c ms. Further non-coherentintegration on N  nc blocks may be employed to reduce thenoise.The correlation function between the received signal andreference code, on each sideband, will be unambiguous andwill resemble the ACF of a BPSK-modulated signal. However,the shape of resulting ACF is not exactly the one of a BPSK-modulated signal, since there are information losses due toselection of main lobes. This method has rather high complex-ity due to the fact that six complex filters are needed for DSBprocessing [4]. A less complex version of this implementationwill be to use just one of sidebands (SSB approach), but inorder to compensate for SNR degradation, a longer dwell timeis needed. This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2006 proceedings. 5212  RX signal(at samplelevel)BPSK ReferencePRN sequence(at chip level)I & Don N c ms| . | 2 non-cohintegr. onN nc blocks + singleSBstatisticSimilar processing as in right sideband, but shifted atthe center frequency of band with exp(+j . 2 . pi . f SC. a . t)Right Sideband ProcessingsingleSBstatisticdual SBstatisticholdN BOC N S exp(-j . 2 . pi . f SC. a . t) Filtered BOC-modulated signal (i.e. BOC(10,5))PSD f f carrier f carrier +f sc f carrier -f sc Interference from GPS C/A Fig. 2. Method 2 (proposed; modified Martin & al.) . Select the main lobes of received signal and the secondary lobes between them, shift them close tothe carrier frequency and correlate with a BPSK PRN reference code.  B. Method II (proposed method) A less complex implementation method is shown in Fig. 2.This method is a modified approach of Martin & al. techniquepresented in [5], [6]. Instead of using two filters (one for everymain lobe), only one filter is used, centered at middle of carrierfrequency band f  carrier . This filter has a bandwidth whichincludes the two main lobes and the secondary lobes betweenthem. After the band selection, the main lobes of receivedsignal (situated at f  carrier - f  sc , respectively at f  carrier + f  sc )are shifted towards the middle of frequency band (the shiftingfactor, af  sc , will be discussed later) and correlated with theBPSK reference signal, held at sub-sample level (in Fig. 2 N  s is the oversampling factor or the number of sub-samplesper BOC sample). The method originally proposed in [5]and [6] was shifting the reference code to f  carrier - f  sc and f  carrier + f  sc , respectively, thus changing the code sequencefrom a sequence of  +1 s and − 1 s to a complex signal. Also,shifting the signal (or the reference code) with ± f  sc is notworking properly for all modulation orders, as it was observedfrom simulations and as it will be explained in detail in thenext section.We note that the proposed method is less complex than theprevious one, first due to the fact that only one filter is used,and second, because the reference code is a sequence of  +1 sand − 1 s, and thus, the complex multiplication between thereceived signal and the reference code can be done via simpleadditions and sign inversions, as explained in [10].III. T HE SIGNAL MODEL IN THE PRESENCE OF BOC MODULATION AND OVERSAMPLING The simplified baseband block diagram of the transmitterand receiver for a BOC-modulated PRN signal is shown in Fig.3. After spreading and BOC modulation, the data sequenceis oversampled with an oversampling factor N  s , representingthe number of sub-samples per BOC sub-chip interval. Thisoversampling determines the desired delay accuracy in thedelay estimation process (e.g., minimum ∆ t bin is equal to SpreadingBOCmodulationNs ChannelDopplerCodeAcquisitionDatasymbolsb n PRNsequenceDespreading, datarecovery and positionestimation blocks Fig. 3. Main operations performed at transmitter and receiver 1 / ( N  s N  BOC  ) when no further interpolation is employed).Thus, one chip will consists of  N  BOC  N  s sub-samples. Forexample, BOC(1,1) signal has an even modulation order N  BOC  =2, while BOC(15,10) signal has an odd modulationorder N  BOC  =3.The baseband model of received signal r ( t ) via an L -pathfading channel can be written as (eq. 1): r ( t ) =   E  b e + j 2 πf  D tn =+ ∞  n = −∞ b nL  l =1 α n,l ( t ) s n ( t − τ  l )+ η ( t ) (1)Above, s n ( t ) is the PRN code sequence corresponding to n -th code bit, E  b the bit energy of signal, b n is the databit corresponding to the n -th code epoch (the same data bitis usually kept for 20 ms [8]), α n,l ( t ) is the time-varyingcomplex fading coefficient of the l -th path during the n -th codeepoch, τ  l is the corresponding path delay (rounded to integermultiples of the sampling interval T  s ), f  D is the Doppler shift,and η ( · ) is the additive white noise added by the channel.The BOC-modulated and spread code sequence, correspond-ing to n -th code bit is: s n ( t ) = S F   k =1 c k,nN  BOC − 1  m =0 ( − 1) m  p ( t − nS  F  N  BOC  N  s T  s − kN  BOC  N  s T  s − mN  s T  s ) (2) This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2006 proceedings. 5213  where c k,n is the k -th chip value corresponding to the n -thdata symbol, S  F  is the spreading factor or the code epochlength (e.g., for GPS C/A signal, S  F  = 1023 ), p ( · ) is a trainof rectangular pulses, and T  s is the sampling interval ( T  s =1 / ( N  s f  c ) ).Depending on the method, at the receiver part either onlythe main lobes of the incoming BOC signal are filtered (usingtwo complex filters per each band, upper or lower) or thewhole bandwidth of signal containing the main lobes and thesecondary lobes between them is selected (by using only onefilter per band, since the reference signal remains unfiltered).For the second method, after filtering, the signal is shifteddown or up around the center frequency by multiplicationwith exp ( −  j 2 πf  sc at ) and exp (+  j 2 πf  sc at ) , for upper andthe lower side-bands, respectively. The shifting parameter a depends on the order of BOC modulation used and has beenfound to be equal to: a =  1 if  N  BOC  even, Sin- and CosBOC N  BOC − 1 N  BOC if  N  BOC  odd, SinBOC N  BOC +1 N  BOC if  N  BOC  odd, CosBOC(3)We have remarked that, if we use a = 1 for odd BOCmodulation orders, we loose the peak after the correlation, andtherefore, the ’BPSK-like’ method becomes invalid. In [5] and[6] no discussion about the impact of odd BOC modulationorders on the algorithm performance was done.The signal is then correlated with a reference signal s ref  ( t,   τ,   f  D ,n 1 ) , which can include either the PRN codeand BOC modulation or only the PRN code. For example,in the ambiguous BOC case, the reference signal is the BOC-modulated PRN code: s ref,ambig. BOC  ( t,   τ,   f  D ,n 1 ) = e − j 2 π   f  D tS F   k =1 c k,n 1 N  BOC − 1  m =0 ( − 1) m × p ( t − n 1 S  F  N  BOC  N  s T  s − kN  BOC  N  s T  s − mN  s T  s −   τ  ) (4)For Method I, the reference code is the filtered BOC-modulated PRN code, as shown in Fig. 1. For Method II, thereference code is the PRN BPSK sequence, held at sub-samplelevel: s ref,proposed ( t,   τ,   f  D ,n 1 ) = e − j 2 π   f  D tS F   k =1 c k,n 1 N  BOC − 1  m =0  p ( t − n 1 S  F  N  BOC  N  s T  s − kN  BOC  N  s T  s − mN  s T  s −   τ  ) (5)The correlation output is coherently averaged over N  c ms(as seen in Figs. 1 and 2) and, next, it is non-coherently av-eraged over N  nc blocks. The maximum coherence integrationlength N  c is dictated by the coherence time of the channel andby the stability of the oscillator clock. The decision statisticis formed in a hybrid manner, by splitting the code-Dopplersearch space into several code-Doppler windows. Each correla-tor output corresponds to a time-frequency bin and several bins −1.5−1−0.500.51 1.500.,1), DSBDelay error [chips]        A       C       F −1.5−1 −0.5 0 0.5 1 1.500.,4), SSBDelay error [chips]        A       C       F Fig. 4. Shapes of ACF envelopes for even modulation order ( Upperplot : N  BOC = 2 ,e.g. BOC(1,1)) and odd modulation order ( Lower plot : N  BOC = 5 , SinBOC(10,4)); continuous black : ambiguous BOC, dashedred : Fishman & al. method, dash-point blue : proposed method .are grouped together in order to form a decision window. Thedecision variable is further compared to a variable threshold γ  , which is set such that we have a sufficiently small falsealarm probability P  fa . If the decision variable is greater thanthe threshold, the acquisition is declared, otherwise the searchprocess is continued.The normalized ACF envelopes after single and dual side-band processing, together with the ambiguous-BOC waveformare presented in Fig. 4, for SinBOC(1,1) ( N  BOC  = 2 ) and Sin-BOC(10,4) ( N  BOC  = 5 ) respectively, in the absence of noise.The signal before sideband processing was assumed to haveinfinite bandwidth, hence the sharp peaks in the ambiguous-BOC waveform. We remark that the proposed BPSK-likemethod does not eliminate completely the ambiguities of theACF for odd BOC modulation orders. We also remark thatthe ACF after DSB processing with Fishman & al. methodhas a wider main lobe than the DSB processing of proposedmethod, which helps the acquisition process.IV. S IMULATIONS RESULTS For the simulations from this paper we have selecteddifferent modulation types which have been proposed invarious papers as candidates for Galileo signals [1], [8] (i.e.SinBOC(1,1), SinBOC(10,5), SinBOC(15,2.5) for even ordersand SinBOC(15,10) for odd N  BOC  orders). As performancemeasures we have used the root mean square error (RMSE)and the detection probability P  d . The RMSE in chips was This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE ICC 2006 proceedings. 5214
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