Research ArticleA New Acquisition Algorithm with Elimination SidePeak for All BOC Signals
Fang Liu and Yongxin Feng
School of Information Science and Engineering Shenyang Ligong University Shenyang 110159 China
Correspondence should be addressed to Yongxin Feng onceowned 1019163com
Received 21 January 2015 Accepted 15 March 2015
Academic Editor Francesco Tornabene
Copyright copy 2015 F Liu and Y Feng This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
A new inhibition side peak acquisition (ISPA) algorithm is proposed for binary offset carrier (BOC) modulated signals whichwill be utilized in global navigation satellite systems (GNSS) We eliminate all side peaks of the BOC correlation function (CF) bystructuring special sequences composed of PRN code and cycle rectangular sequences The new algorithm can be applied to bothgeneric sine- and cosine-phased BOC signals as well as to all modulation orders Theoretical and simulation results demonstratethat the new algorithm can completely eliminate the ambiguity threat in the acquisition process and it can adapt to lower SNR Inaddition this algorithm is better than the traditional algorithms in acquisition performance and inhibition side peak ability
1 Introduction
With the development and application of global navigationsatellite systems (GNSS) [1] GNSS signal receiving methodshave become highly valued Because the acquisition tech-nology is the core of receiving therefore it also becomesa focus problem Thus mass acquisition algorithms [2 3]are proposed for GNSS signals to improve receiving perfor-mance However modern GNSS has provided new signalswith longer PRN (pseudo random noise) codes and newermodulation methods which aim to improve the positioningperformance Binary offset carrier (BOC) [4] modulatedsignals are the most widely used signal families in GNSSand their side peak characteristics also require the highesttechnique complexity from GNSS receivers
BOC modulation signal acquisition techniques focus onrecovering the main correlation peak or eliminating ambigu-ities in the form of side peaks At present various techniquesare proposed for side peak cancellation and are built on thebasis of the correlation function (CF) of the BOC signalsThus the side band processing method originated fromBPSK-like method [5 6] and then some improved methods[7ndash9] are proposed The partial band is obtained by filteringor frequency domain processing in these kind methodsand then the main peak was estimated using similar BPSKcharacteristic These kind methods can reduce the influence
of subcarrier but the energy and the necessary informationare lostThus the auxiliary signal methods [10 11] are mainlythrough the local auxiliary signal establishment to reachthe purpose of removing side peaks These kind methodscan remove the side peak but they lack universality Thussome effective methods [12ndash14] are proposed to improve theprocessing performance However these techniques applyonly to sine-phased BOC signals Thus in [15] a mitigatingambiguity acquisition method is proposed This techniquecan counterbalance the undesired side peaks but it appliesonly to cosine-phased BOC signals
In this paper considering filter restriction and genericdeficiency problems in traditional algorithms we propose aninhibition side peak acquisition algorithm which is applica-ble to all orders and to both generic sine- and cosine-phasedBOC signals
2 BOC Modulation Signal andAcquisition Analysis
21 BOC Modulation Signal BOC modulation signal isobtained by the product of PRN code and the square waveThe complex form of the BOC signal is expressed as
119878 (119905) = 119890minus119894120579
sum
119896
119886119896
120583120576119879
119904
(119905 minus 119896 sdot 120576119879119904
minus 1199050
) 119862119879
119904
(119905 minus 1199050
) (1)
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 140345 9 pageshttpdxdoiorg1011552015140345
2 Mathematical Problems in Engineering
Beforehand processing
Signal
Multiplication
Carrier generator
Square wave generator Modulation
PRN code generator
Correlation Judgment
OutputYes
No
Frequency
Phase
Figure 1 The full band acquisition algorithm principle
Beforehandprocessing
Signal
Multiplication
Carrier generator
PRN code generator Modulation
Square wave generator
CorrelationJudgment
OutputYes
No
Correlation Peakoptimization
Frequency
Phase
Figure 2 The peak optimization acquisition algorithm principle
where 119886119896
is the modulated PRN code 119862119879
119904
(119905) is the subcarrier2119879119904
is the subcarrier cycle 120583119899119879
119904
(119905) is the spread spectrumsymbol 120576 is the modulation order and 120579 and 119905
0
respectivelyexpress the phase and time offset
The BOC signal is usually expressed as BOC(119891119904
119891119888
)the frequency of the subcarrier is 119891
119904
times the benchmarkfrequency and the frequency of the PRN code is 119891
119888
timesthe benchmark frequency The benchmark frequency is1023MHz The autocorrelation function of the BOC signalhas multiple peaks and passes through zero many times Itsautocorrelation function consists of the positive peaks andthe negative peaks and the number of peaks is 2120576 minus 1 Thedistance between peaks is119879
119904
and each peak height is (minus1)119897(120576minus|119897|)120576 where 119897 is the serial number of the peaks
22 The Acquisition Analysis From the perspective of algo-rithm generality the acquisition algorithm for BOC modu-lation signal is usually divided into three categories namelythe full band acquisition (FBA) algorithm [16] the peakoptimization acquisition (POA) algorithm [17] and thesingle peak recovery acquisition (SPRA) algorithm [18]Theirprinciples are shown in Figures 1 2 and 3 respectively
Beforehand processing
Signal
Multiplication
Carrier generator
PRN code generator
Frequency domain transformation
Frequency domainmoving
Judgment
OutputYes
NoPeaks processing
Frequency domain transformation
Frequency band extraction
Frequency band extraction
Time domain transformation
Frequency
Phase
Figure 3 The single peak recovery acquisition algorithm principle
FBA is a class of traditional algorithms in which thecorrelation arithmetic is executed between the received signaland the original PRN code modulated by a square wavePOA is a class of improved algorithms in which multiplecorrelations are executed to improve the main peak SPRA isa class of new methods in which a partial signal is separatedfrom the received signal by the corresponding operations toinhibit the square wave
3 ISPA Algorithm Structure
Let 119891119905
be the sampling frequency of the BOC signal and thefrequency of the subcarrier and PRN code are 119891
119904
times and119891119888
times the benchmark frequency respectively Consideringsquare wave modulation characteristics the product modelof the spread spectrum sequence and a series of rectan-gular sequences is structured which can be approximatelyexpressed as the BOC base-band signal model Hence thebase-band signal may be represented by the following equa-tion
where 119889(119899) is the message 119862(119899) is the PRN code 1205820
(119899) is themixed noise function caused by the discarded samples 119878
Δ
(119899)
is the frequency error function cause by the front processing119899 is the sequence position 119872 is the number of chips inaccumulation time and 120576 is both the modulation order and
Figure 4The structured process of the rectangular sequencemodel
the number of rectangular sequences in one chip which isexpressed as (3) 119873 is both the number of sampling pointsand the rectangular sequencewidthwhich is expressed as (4)119877119873
(119899 + 119873 minus 119895119873) is a shifting rectangular sequence which isexpressed in (5) where 119906(119899) is the step sequence
120576 =2119891119904
119891119888
(3)
119873 =119891119905
2119891119904
(4)
119877119873
(119899 + 119873 minus 119895119873) = 119906 (119899 + 119873 minus 119895119873) minus 119906 (119899 minus 119895119873) (5)
Considering the represented model of the BOC base-band signal the local rectangular sequence model is struc-tured to inhibit the acquisition of side peaks The structuredprocess is shown in Figure 4 in which 120576 is an odd numberThe square wave sequence is shown in Figure 4(a) andthe two structured cycle rectangular sequences are shownin Figures 4(b) and 4(c) The cycle rectangular sequencescan also be structured for an even number 120576 using thesame principle Further the 119894th cycle of two local channelrectangular sequences can be expressed as
119877119873
(119899 + 120576119873 minus 119894120576119873) = 119906 (119899 + 120576119873 minus 119894120576119873)
minus 119906 (119899 + 120576119873 minus 119873 minus 119894120576119873)
119877119873
(119899 + 119873 minus 119894120576119873) = 119906 (119899 + 119873 minus 119894120576119873) minus 119906 (119899 minus 119894120576119873)
(6)
The original PRN code is respectively multiplied by thetwo-channel cycle rectangular sequences to structure the twonew local channel sequences which are expressed as
1198671
(119899) = 119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus120576
119877119873
(119899 + 120576119873 minus 119894120576119873))
1198672
(119899) = 119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus1
119877119873
(119899 + 119873 minus 119894120576119873))
(7)
where 119862(119899 + 120591) is the delay PRN code and 120591 is the time delay
The beforehand processing received signal is executedby the correlation circumferential arithmetic with119883
1
(119899) and1198832
(119899) respectively which are expressed as
1198831
(119899)
= 119878BOC (119899) otimes 1198671 (119899)
=[
[
119889 (119899) 119862 (119899)
120576119872
sum
119895=1
((minus1)119895+1
119877119873
(119899 + 119873 minus 119895119873)) 119878Δ
(119899)+1205820
(119899)]
]
otimes [119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus120576
119877119873
(119899 + 120576119873 minus 119894120576119873))]
asymp and119879
119904
(119899) 119878Δ
(119899) minus and119879
119904
(119899 + 119879119904
) 119878Δ
(119899)
+ and119879
119904
(119899 + 2119879119904
) 119878Δ
(119899) minus sdot sdot sdot + 1205820
(119899)
=
120576
sum
119894=0
(minus1)120576
and119879
119904
(119899 + 119894119879119904
) 119878Δ
(119899) + 1205820
(119899)
1198832
(119899)
= 119878BOC (119899) otimes 1198672(119899)
=[
[
119889 (119899) 119862 (119899)
120576119872
sum
119895=1
((minus1)119895+1
119877119873
(119899 + 119873 minus 119895119873)) 119878Δ
(119899)+1205820
(119899)]
]
otimes [119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus1
119877119873
(119899 + 119873 minus 119894120576119873))]
asymp and119879
119904
(119899) 119878Δ
(119899) minus and119879
119904
(119899 minus 119879119904
) 119878Δ
(119899)
+ and119879
119904
(119899 minus 2119879119904
) 119878Δ
(119899) minus sdot sdot sdot + 1205820
(119899)
=
120576
sum
119894=0
(minus1)120576
and119879
119904
(119899 minus 119894119879119904
) 119878Δ
(119899) + 1205820
(119899)
(8)
where and119879
119904
(119899) is the trigonometry sequence of width 119879119904
and isexpressed as
and119879
119904
(119899) =
2
119879119904
119899 + 1 minus119879119904
2le 119899 lt 0
minus2
119879119904
119899 + 1 0 le 119899 le119879119904
2
0 other
(9)
When 120576 is five the autocorrelation result of the BOCbase-band signal is shown in Figure 5(a) and the two struc-tured correlation results are shown in Figures 5(b) and 5(c)respectively The results show that the positions of the twochannel main peaks exactly coincide with the position of theautocorrelation main peak and the numbers of peaks are thesame in both channels In addition the positions of the twochannel peaks are symmetrical about the main peak positionof the autocorrelation function
4 Mathematical Problems in Engineering
minus8 minus6 minus4 minus2 0 2 4 6 8minus1
0
1
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(a)
minus8 minus6 minus4 minus2 0 2 4 6 8minus02
0
02
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(b)
minus8 minus6 minus4 minus2 0 2 4 6 8minus02
0
02
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(c)
Figure 5 The correlation result of BOC
In view of these characteristics and combining (8) and(9) the addition and subtraction operations are performedby using the two structured correlation results expressed as
Δ1198831
(119899) = 1198831
(119899) + 1198832
(119899)
Δ1198832
(119899) = 1198831
(119899) minus 1198832
(119899)
(10)
Thus the new correlation function is structured to elimi-nate side peaks and the processing is expressed as
51 Side Peak InhibitionAnalysis Equations (9) and (13) showthat the final correlation result has a single peak whose mainwaveform is a triangular peak Thus the ISPA algorithm canachieve the goal of side peak inhibition The new algorithmis then simulated using the following parameters 1023MHzPRN code frequency 15345MHz square wave frequency and12276MHz sampling frequency modulation order of 3 andthe sine-phased BOC signal for these parameters is expressedas sinBOC(15 10)
The ISPA result for sinBOC(15 10) is shown in Figure 6The ISPA results for sinBOC(10 2) cosBOC(10 5) andcosBOC(6 1) are shown in Figures 7 8 and 9 respectivelyThe simulation results show that the ISPA algorithm can
6 Mathematical Problems in Engineering
minus20 minus10 0 10 20
minus05
0
05
1
15
2
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 8 The ISPA result for cosBOC(10 5)
minus50 0 50minus08
minus06
minus04
minus02
0
02
04
06
08
1
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 9 The ISPA result for cosBOC(6 1)
clearly recover the main peak whose position is the sameas the main peak position of the autocorrelation functionIn particular the ISPA algorithm can effectively inhibit sidepeaks
52 Adaptability Analysis The new algorithm result is influ-enced by the frequency error and the mixed noise accordingto (13) The algorithm result approximately conforms to thecycle equation because of the frequency error function cyclecharacteristics When the relationship of the frequency errorand accumulation time 119905 satisfies (21) the algorithm resulterror reaches its maximum We also find that the ISPA
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
Carrier error (Hz)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 10 The relationship between the relative main peak andfrequency error
algorithm result decreases gradually along with the increaseof mixed noise according to
119878Δ
(119899) =119896
2119905 (21)
where 119896 is the positive integerFurthermore the ISPA algorithmrsquos adaptability is simu-
lated with the following parameters 15345MHz square wavefrequency and 12276MHz sampling frequency modulationmode is sinemode andmodulation orders are 15 10 6 and 3respectively
The relationship between the relative main peak andfrequency error is shown in Figure 10 which shows that theresults satisfy (21)The relationship between the relativemainpeak and SNR is shown in Figure 11 revealing that the relativemain peak decreases gradually with decreasing SNR And theISPA algorithmrsquos adaptability to the SNR environment ismorethan minus25 dB according to (13) and Figure 11
53 Superiority Analysis To verify the superiority of the ISPAalgorithm this ISPA algorithm is compared with otheralgorithms namely the FBA algorithm POA algorithm andSPRA algorithm The simulation parameters are as follows2046MHz PRN code frequency and the modulation modeis sine mode
With changing modulation order the main peak widthchanges and the main peak relative changes are shown inFigures 12 and 13 The results show that the ISPA algorithmrsquosmain peak width is the smallest and its main peak relativeresult is the greatest demonstrating that this algorithmrsquosacquisition and tracking performance is the best
The side peak relative changes and the mainside peakratio changes with changing modulation order are shown inFigures 14 and 15 The results show that the ISPA algorithmside peak relative result is the smallest and the mainside
Mathematical Problems in Engineering 7
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
160
180
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 11The relationship between the relativemain peak and SNR
0 5 10 15 200
02
04
06
08
1
12
Modulation order
Mai
n pe
ak w
idth
(s)
FBA resultPOA result
SPRA resultISPA result
times10minus6
Figure 12 The relationship between the main peak width and themodulation order
peak ratio is the greatest demonstrating that this algorithmrsquosside peak inhibition ability is best
The main peak relative changes with changing SNR areshown in Figure 16 The results show that the adaptability ofthe ISPA algorithm is better than the FBA algorithm and POAalgorithm but there are no significant differences between theISPA algorithm and the SPRA algorithm
0 5 10 15 200
50
100
150
200
250
300
Modulation order
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 13 The relationship between the relative main peak and themodulation order
0 5 10 15 200
20
40
60
80
100
120
140
Modulation order
Side
pea
k re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 14 The relationship between the relative side peak and themodulation order
6 Conclusions
In this paper the principle and characteristics of BOC mod-ulation signals have been studied To implement the BOCmodulated signal acquisition effective algorithms have beenstudied including the full band acquisition (FBA) algorithmthe peak optimization acquisition (POA) algorithm and thesingle peak recovery acquisition (SPRA) algorithm Consid-ering the filter restriction and generic deficiency problemsin traditional algorithms we propose the ISPA algorithmWe eliminate all side peaks of the BOC correlation function(CF) by structuring special sequences composed of PRN codeand cycle rectangular sequences The ISPA algorithm can be
8 Mathematical Problems in Engineering
0 5 10 15 200
2
4
6
8
10
12
Modulation order
Mai
nsid
e pea
k ra
tio
times1017
FBA resultPOA result
SPRA resultISPA result
Figure 15 The relationship between the mainside peak ratio andthe modulation order
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 16The relationship between the relative main peak changesand SNR
applied to both generic sine- and cosine-phased BOC signalsand to all modulation orders In addition it outperforms thetraditional algorithms in acquisition inhibition side peakability and adaptability to lower SNR
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the Program for Liaoning Inno-vative Research Team in University (no LT2011005) NewCentury Program for Excellent Talents of Ministry of Edu-cation of China (no NCET-11-1013) Project of Science andTechnologyDepartment of Liaoning Province (no 20121038)Project of Education Department of Liaoning Province (noL2013085) and the Open Foundation of Key Laboratory ofShenyang Ligong University
References
[1] K Subburaj S Bhatara J Tangudu J R Samuel R Ganesanand K Ramasubramanian ldquoSpur mitigation in high-sensitivityGNSS receiversrdquo IEEE Transactions on Circuits and Systems IIExpress Briefs vol 61 no 2 pp 100ndash104 2014
[2] R R Rick and L B Milstein ldquoOptimal decision strategies foracquisition of spread-spectrum signals in frequency-selectivefading channelsrdquo IEEE Transactions on Communications vol46 no 5 pp 686ndash694 1998
[3] X Li and W Guo ldquoEfficient differential coherent accumulationalgorithm for weak GPS signal bit synchronizationrdquo IEEECommunications Letters vol 17 no 5 pp 936ndash939 2013
[4] T H Ta N C Shivaramaiah A G Dempster and L L PrestildquoSignificance of cell-correlation phenomenon inGNSSmatchedfilter acquisition enginesrdquo IEEE Transactions on Aerospace andElectronic Systems vol 48 no 2 pp 1264ndash1286 2012
[5] P Fishman and J W Betz ldquoPredicting performance of directacquisition for theM-code signalrdquo in Proceedings of the Interna-tional Technical Meeting of the Institute of Navigation (IONNTMrsquo00) pp 574ndash582 2000
[6] J Betz and P Capozza ldquoSystem for direct acquisition of receivedsignalsrdquo US patent no 20040071200 A1 2004
[7] N Martin V Leblond G Guillotel and V Heiries ldquoBOC(xy)signal acquisition techniques and performancesrdquo in Proceedingsof the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPSGNSS rsquo03) pp188ndash198 2003
[8] A Burian E S Lohan andM Renfors ldquoBPSK-likemethods forhybrid-search acquisition of galileo signalsrdquo in Proceedings ofthe IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 July 2006
[9] W-L Mao C-S Hwang C-W Hung J Sheen and P-H ChenldquoUnambiguous BPSK-like CSCmethod for Galileo acquisitionrdquoin Proceedings of the 18th International Conference on Methodsand Models in Automation and Robotics (MMAR rsquo13) pp 627ndash632 Międzyzdroje Poland August 2013
[10] B Kim and S-H Kong ldquoTwo-dimensional compressed correla-tor for fast acquisition of BOC(m n) signalsrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2662ndash2672 2014
[11] F Benedetto G Giunta E S Lohan and M Renfors ldquoAfast unambiguous acquisition algorithm for BOC-modulatedsignalsrdquo IEEE Transactions on Vehicular Technology vol 62 no3 pp 1350ndash1355 2013
[12] Z Yao M Lu and Z Feng ldquoUnambiguous sine-phased binaryoffset carrier modulated signal acquisition techniquerdquo IEEETransactions onWireless Communications vol 9 no 2 pp 577ndash580 2010
[13] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontracking
Mathematical Problems in Engineering 9
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
Figure 1 The full band acquisition algorithm principle
Beforehandprocessing
Signal
Multiplication
Carrier generator
PRN code generator Modulation
Square wave generator
CorrelationJudgment
OutputYes
No
Correlation Peakoptimization
Frequency
Phase
Figure 2 The peak optimization acquisition algorithm principle
where 119886119896
is the modulated PRN code 119862119879
119904
(119905) is the subcarrier2119879119904
is the subcarrier cycle 120583119899119879
119904
(119905) is the spread spectrumsymbol 120576 is the modulation order and 120579 and 119905
0
respectivelyexpress the phase and time offset
The BOC signal is usually expressed as BOC(119891119904
119891119888
)the frequency of the subcarrier is 119891
119904
times the benchmarkfrequency and the frequency of the PRN code is 119891
119888
timesthe benchmark frequency The benchmark frequency is1023MHz The autocorrelation function of the BOC signalhas multiple peaks and passes through zero many times Itsautocorrelation function consists of the positive peaks andthe negative peaks and the number of peaks is 2120576 minus 1 Thedistance between peaks is119879
119904
and each peak height is (minus1)119897(120576minus|119897|)120576 where 119897 is the serial number of the peaks
22 The Acquisition Analysis From the perspective of algo-rithm generality the acquisition algorithm for BOC modu-lation signal is usually divided into three categories namelythe full band acquisition (FBA) algorithm [16] the peakoptimization acquisition (POA) algorithm [17] and thesingle peak recovery acquisition (SPRA) algorithm [18]Theirprinciples are shown in Figures 1 2 and 3 respectively
Beforehand processing
Signal
Multiplication
Carrier generator
PRN code generator
Frequency domain transformation
Frequency domainmoving
Judgment
OutputYes
NoPeaks processing
Frequency domain transformation
Frequency band extraction
Frequency band extraction
Time domain transformation
Frequency
Phase
Figure 3 The single peak recovery acquisition algorithm principle
FBA is a class of traditional algorithms in which thecorrelation arithmetic is executed between the received signaland the original PRN code modulated by a square wavePOA is a class of improved algorithms in which multiplecorrelations are executed to improve the main peak SPRA isa class of new methods in which a partial signal is separatedfrom the received signal by the corresponding operations toinhibit the square wave
3 ISPA Algorithm Structure
Let 119891119905
be the sampling frequency of the BOC signal and thefrequency of the subcarrier and PRN code are 119891
119904
times and119891119888
times the benchmark frequency respectively Consideringsquare wave modulation characteristics the product modelof the spread spectrum sequence and a series of rectan-gular sequences is structured which can be approximatelyexpressed as the BOC base-band signal model Hence thebase-band signal may be represented by the following equa-tion
where 119889(119899) is the message 119862(119899) is the PRN code 1205820
(119899) is themixed noise function caused by the discarded samples 119878
Δ
(119899)
is the frequency error function cause by the front processing119899 is the sequence position 119872 is the number of chips inaccumulation time and 120576 is both the modulation order and
Figure 4The structured process of the rectangular sequencemodel
the number of rectangular sequences in one chip which isexpressed as (3) 119873 is both the number of sampling pointsand the rectangular sequencewidthwhich is expressed as (4)119877119873
(119899 + 119873 minus 119895119873) is a shifting rectangular sequence which isexpressed in (5) where 119906(119899) is the step sequence
120576 =2119891119904
119891119888
(3)
119873 =119891119905
2119891119904
(4)
119877119873
(119899 + 119873 minus 119895119873) = 119906 (119899 + 119873 minus 119895119873) minus 119906 (119899 minus 119895119873) (5)
Considering the represented model of the BOC base-band signal the local rectangular sequence model is struc-tured to inhibit the acquisition of side peaks The structuredprocess is shown in Figure 4 in which 120576 is an odd numberThe square wave sequence is shown in Figure 4(a) andthe two structured cycle rectangular sequences are shownin Figures 4(b) and 4(c) The cycle rectangular sequencescan also be structured for an even number 120576 using thesame principle Further the 119894th cycle of two local channelrectangular sequences can be expressed as
119877119873
(119899 + 120576119873 minus 119894120576119873) = 119906 (119899 + 120576119873 minus 119894120576119873)
minus 119906 (119899 + 120576119873 minus 119873 minus 119894120576119873)
119877119873
(119899 + 119873 minus 119894120576119873) = 119906 (119899 + 119873 minus 119894120576119873) minus 119906 (119899 minus 119894120576119873)
(6)
The original PRN code is respectively multiplied by thetwo-channel cycle rectangular sequences to structure the twonew local channel sequences which are expressed as
1198671
(119899) = 119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus120576
119877119873
(119899 + 120576119873 minus 119894120576119873))
1198672
(119899) = 119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus1
119877119873
(119899 + 119873 minus 119894120576119873))
(7)
where 119862(119899 + 120591) is the delay PRN code and 120591 is the time delay
The beforehand processing received signal is executedby the correlation circumferential arithmetic with119883
1
(119899) and1198832
(119899) respectively which are expressed as
1198831
(119899)
= 119878BOC (119899) otimes 1198671 (119899)
=[
[
119889 (119899) 119862 (119899)
120576119872
sum
119895=1
((minus1)119895+1
119877119873
(119899 + 119873 minus 119895119873)) 119878Δ
(119899)+1205820
(119899)]
]
otimes [119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus120576
119877119873
(119899 + 120576119873 minus 119894120576119873))]
asymp and119879
119904
(119899) 119878Δ
(119899) minus and119879
119904
(119899 + 119879119904
) 119878Δ
(119899)
+ and119879
119904
(119899 + 2119879119904
) 119878Δ
(119899) minus sdot sdot sdot + 1205820
(119899)
=
120576
sum
119894=0
(minus1)120576
and119879
119904
(119899 + 119894119879119904
) 119878Δ
(119899) + 1205820
(119899)
1198832
(119899)
= 119878BOC (119899) otimes 1198672(119899)
=[
[
119889 (119899) 119862 (119899)
120576119872
sum
119895=1
((minus1)119895+1
119877119873
(119899 + 119873 minus 119895119873)) 119878Δ
(119899)+1205820
(119899)]
]
otimes [119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus1
119877119873
(119899 + 119873 minus 119894120576119873))]
asymp and119879
119904
(119899) 119878Δ
(119899) minus and119879
119904
(119899 minus 119879119904
) 119878Δ
(119899)
+ and119879
119904
(119899 minus 2119879119904
) 119878Δ
(119899) minus sdot sdot sdot + 1205820
(119899)
=
120576
sum
119894=0
(minus1)120576
and119879
119904
(119899 minus 119894119879119904
) 119878Δ
(119899) + 1205820
(119899)
(8)
where and119879
119904
(119899) is the trigonometry sequence of width 119879119904
and isexpressed as
and119879
119904
(119899) =
2
119879119904
119899 + 1 minus119879119904
2le 119899 lt 0
minus2
119879119904
119899 + 1 0 le 119899 le119879119904
2
0 other
(9)
When 120576 is five the autocorrelation result of the BOCbase-band signal is shown in Figure 5(a) and the two struc-tured correlation results are shown in Figures 5(b) and 5(c)respectively The results show that the positions of the twochannel main peaks exactly coincide with the position of theautocorrelation main peak and the numbers of peaks are thesame in both channels In addition the positions of the twochannel peaks are symmetrical about the main peak positionof the autocorrelation function
4 Mathematical Problems in Engineering
minus8 minus6 minus4 minus2 0 2 4 6 8minus1
0
1
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(a)
minus8 minus6 minus4 minus2 0 2 4 6 8minus02
0
02
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(b)
minus8 minus6 minus4 minus2 0 2 4 6 8minus02
0
02
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(c)
Figure 5 The correlation result of BOC
In view of these characteristics and combining (8) and(9) the addition and subtraction operations are performedby using the two structured correlation results expressed as
Δ1198831
(119899) = 1198831
(119899) + 1198832
(119899)
Δ1198832
(119899) = 1198831
(119899) minus 1198832
(119899)
(10)
Thus the new correlation function is structured to elimi-nate side peaks and the processing is expressed as
51 Side Peak InhibitionAnalysis Equations (9) and (13) showthat the final correlation result has a single peak whose mainwaveform is a triangular peak Thus the ISPA algorithm canachieve the goal of side peak inhibition The new algorithmis then simulated using the following parameters 1023MHzPRN code frequency 15345MHz square wave frequency and12276MHz sampling frequency modulation order of 3 andthe sine-phased BOC signal for these parameters is expressedas sinBOC(15 10)
The ISPA result for sinBOC(15 10) is shown in Figure 6The ISPA results for sinBOC(10 2) cosBOC(10 5) andcosBOC(6 1) are shown in Figures 7 8 and 9 respectivelyThe simulation results show that the ISPA algorithm can
6 Mathematical Problems in Engineering
minus20 minus10 0 10 20
minus05
0
05
1
15
2
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 8 The ISPA result for cosBOC(10 5)
minus50 0 50minus08
minus06
minus04
minus02
0
02
04
06
08
1
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 9 The ISPA result for cosBOC(6 1)
clearly recover the main peak whose position is the sameas the main peak position of the autocorrelation functionIn particular the ISPA algorithm can effectively inhibit sidepeaks
52 Adaptability Analysis The new algorithm result is influ-enced by the frequency error and the mixed noise accordingto (13) The algorithm result approximately conforms to thecycle equation because of the frequency error function cyclecharacteristics When the relationship of the frequency errorand accumulation time 119905 satisfies (21) the algorithm resulterror reaches its maximum We also find that the ISPA
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
Carrier error (Hz)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 10 The relationship between the relative main peak andfrequency error
algorithm result decreases gradually along with the increaseof mixed noise according to
119878Δ
(119899) =119896
2119905 (21)
where 119896 is the positive integerFurthermore the ISPA algorithmrsquos adaptability is simu-
lated with the following parameters 15345MHz square wavefrequency and 12276MHz sampling frequency modulationmode is sinemode andmodulation orders are 15 10 6 and 3respectively
The relationship between the relative main peak andfrequency error is shown in Figure 10 which shows that theresults satisfy (21)The relationship between the relativemainpeak and SNR is shown in Figure 11 revealing that the relativemain peak decreases gradually with decreasing SNR And theISPA algorithmrsquos adaptability to the SNR environment ismorethan minus25 dB according to (13) and Figure 11
53 Superiority Analysis To verify the superiority of the ISPAalgorithm this ISPA algorithm is compared with otheralgorithms namely the FBA algorithm POA algorithm andSPRA algorithm The simulation parameters are as follows2046MHz PRN code frequency and the modulation modeis sine mode
With changing modulation order the main peak widthchanges and the main peak relative changes are shown inFigures 12 and 13 The results show that the ISPA algorithmrsquosmain peak width is the smallest and its main peak relativeresult is the greatest demonstrating that this algorithmrsquosacquisition and tracking performance is the best
The side peak relative changes and the mainside peakratio changes with changing modulation order are shown inFigures 14 and 15 The results show that the ISPA algorithmside peak relative result is the smallest and the mainside
Mathematical Problems in Engineering 7
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
160
180
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 11The relationship between the relativemain peak and SNR
0 5 10 15 200
02
04
06
08
1
12
Modulation order
Mai
n pe
ak w
idth
(s)
FBA resultPOA result
SPRA resultISPA result
times10minus6
Figure 12 The relationship between the main peak width and themodulation order
peak ratio is the greatest demonstrating that this algorithmrsquosside peak inhibition ability is best
The main peak relative changes with changing SNR areshown in Figure 16 The results show that the adaptability ofthe ISPA algorithm is better than the FBA algorithm and POAalgorithm but there are no significant differences between theISPA algorithm and the SPRA algorithm
0 5 10 15 200
50
100
150
200
250
300
Modulation order
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 13 The relationship between the relative main peak and themodulation order
0 5 10 15 200
20
40
60
80
100
120
140
Modulation order
Side
pea
k re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 14 The relationship between the relative side peak and themodulation order
6 Conclusions
In this paper the principle and characteristics of BOC mod-ulation signals have been studied To implement the BOCmodulated signal acquisition effective algorithms have beenstudied including the full band acquisition (FBA) algorithmthe peak optimization acquisition (POA) algorithm and thesingle peak recovery acquisition (SPRA) algorithm Consid-ering the filter restriction and generic deficiency problemsin traditional algorithms we propose the ISPA algorithmWe eliminate all side peaks of the BOC correlation function(CF) by structuring special sequences composed of PRN codeand cycle rectangular sequences The ISPA algorithm can be
8 Mathematical Problems in Engineering
0 5 10 15 200
2
4
6
8
10
12
Modulation order
Mai
nsid
e pea
k ra
tio
times1017
FBA resultPOA result
SPRA resultISPA result
Figure 15 The relationship between the mainside peak ratio andthe modulation order
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 16The relationship between the relative main peak changesand SNR
applied to both generic sine- and cosine-phased BOC signalsand to all modulation orders In addition it outperforms thetraditional algorithms in acquisition inhibition side peakability and adaptability to lower SNR
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the Program for Liaoning Inno-vative Research Team in University (no LT2011005) NewCentury Program for Excellent Talents of Ministry of Edu-cation of China (no NCET-11-1013) Project of Science andTechnologyDepartment of Liaoning Province (no 20121038)Project of Education Department of Liaoning Province (noL2013085) and the Open Foundation of Key Laboratory ofShenyang Ligong University
References
[1] K Subburaj S Bhatara J Tangudu J R Samuel R Ganesanand K Ramasubramanian ldquoSpur mitigation in high-sensitivityGNSS receiversrdquo IEEE Transactions on Circuits and Systems IIExpress Briefs vol 61 no 2 pp 100ndash104 2014
[2] R R Rick and L B Milstein ldquoOptimal decision strategies foracquisition of spread-spectrum signals in frequency-selectivefading channelsrdquo IEEE Transactions on Communications vol46 no 5 pp 686ndash694 1998
[3] X Li and W Guo ldquoEfficient differential coherent accumulationalgorithm for weak GPS signal bit synchronizationrdquo IEEECommunications Letters vol 17 no 5 pp 936ndash939 2013
[4] T H Ta N C Shivaramaiah A G Dempster and L L PrestildquoSignificance of cell-correlation phenomenon inGNSSmatchedfilter acquisition enginesrdquo IEEE Transactions on Aerospace andElectronic Systems vol 48 no 2 pp 1264ndash1286 2012
[5] P Fishman and J W Betz ldquoPredicting performance of directacquisition for theM-code signalrdquo in Proceedings of the Interna-tional Technical Meeting of the Institute of Navigation (IONNTMrsquo00) pp 574ndash582 2000
[6] J Betz and P Capozza ldquoSystem for direct acquisition of receivedsignalsrdquo US patent no 20040071200 A1 2004
[7] N Martin V Leblond G Guillotel and V Heiries ldquoBOC(xy)signal acquisition techniques and performancesrdquo in Proceedingsof the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPSGNSS rsquo03) pp188ndash198 2003
[8] A Burian E S Lohan andM Renfors ldquoBPSK-likemethods forhybrid-search acquisition of galileo signalsrdquo in Proceedings ofthe IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 July 2006
[9] W-L Mao C-S Hwang C-W Hung J Sheen and P-H ChenldquoUnambiguous BPSK-like CSCmethod for Galileo acquisitionrdquoin Proceedings of the 18th International Conference on Methodsand Models in Automation and Robotics (MMAR rsquo13) pp 627ndash632 Międzyzdroje Poland August 2013
[10] B Kim and S-H Kong ldquoTwo-dimensional compressed correla-tor for fast acquisition of BOC(m n) signalsrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2662ndash2672 2014
[11] F Benedetto G Giunta E S Lohan and M Renfors ldquoAfast unambiguous acquisition algorithm for BOC-modulatedsignalsrdquo IEEE Transactions on Vehicular Technology vol 62 no3 pp 1350ndash1355 2013
[12] Z Yao M Lu and Z Feng ldquoUnambiguous sine-phased binaryoffset carrier modulated signal acquisition techniquerdquo IEEETransactions onWireless Communications vol 9 no 2 pp 577ndash580 2010
[13] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontracking
Mathematical Problems in Engineering 9
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
Figure 4The structured process of the rectangular sequencemodel
the number of rectangular sequences in one chip which isexpressed as (3) 119873 is both the number of sampling pointsand the rectangular sequencewidthwhich is expressed as (4)119877119873
(119899 + 119873 minus 119895119873) is a shifting rectangular sequence which isexpressed in (5) where 119906(119899) is the step sequence
120576 =2119891119904
119891119888
(3)
119873 =119891119905
2119891119904
(4)
119877119873
(119899 + 119873 minus 119895119873) = 119906 (119899 + 119873 minus 119895119873) minus 119906 (119899 minus 119895119873) (5)
Considering the represented model of the BOC base-band signal the local rectangular sequence model is struc-tured to inhibit the acquisition of side peaks The structuredprocess is shown in Figure 4 in which 120576 is an odd numberThe square wave sequence is shown in Figure 4(a) andthe two structured cycle rectangular sequences are shownin Figures 4(b) and 4(c) The cycle rectangular sequencescan also be structured for an even number 120576 using thesame principle Further the 119894th cycle of two local channelrectangular sequences can be expressed as
119877119873
(119899 + 120576119873 minus 119894120576119873) = 119906 (119899 + 120576119873 minus 119894120576119873)
minus 119906 (119899 + 120576119873 minus 119873 minus 119894120576119873)
119877119873
(119899 + 119873 minus 119894120576119873) = 119906 (119899 + 119873 minus 119894120576119873) minus 119906 (119899 minus 119894120576119873)
(6)
The original PRN code is respectively multiplied by thetwo-channel cycle rectangular sequences to structure the twonew local channel sequences which are expressed as
1198671
(119899) = 119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus120576
119877119873
(119899 + 120576119873 minus 119894120576119873))
1198672
(119899) = 119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus1
119877119873
(119899 + 119873 minus 119894120576119873))
(7)
where 119862(119899 + 120591) is the delay PRN code and 120591 is the time delay
The beforehand processing received signal is executedby the correlation circumferential arithmetic with119883
1
(119899) and1198832
(119899) respectively which are expressed as
1198831
(119899)
= 119878BOC (119899) otimes 1198671 (119899)
=[
[
119889 (119899) 119862 (119899)
120576119872
sum
119895=1
((minus1)119895+1
119877119873
(119899 + 119873 minus 119895119873)) 119878Δ
(119899)+1205820
(119899)]
]
otimes [119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus120576
119877119873
(119899 + 120576119873 minus 119894120576119873))]
asymp and119879
119904
(119899) 119878Δ
(119899) minus and119879
119904
(119899 + 119879119904
) 119878Δ
(119899)
+ and119879
119904
(119899 + 2119879119904
) 119878Δ
(119899) minus sdot sdot sdot + 1205820
(119899)
=
120576
sum
119894=0
(minus1)120576
and119879
119904
(119899 + 119894119879119904
) 119878Δ
(119899) + 1205820
(119899)
1198832
(119899)
= 119878BOC (119899) otimes 1198672(119899)
=[
[
119889 (119899) 119862 (119899)
120576119872
sum
119895=1
((minus1)119895+1
119877119873
(119899 + 119873 minus 119895119873)) 119878Δ
(119899)+1205820
(119899)]
]
otimes [119862 (119899 + 120591)
119872
sum
119894=1
((minus1)119894120576minus1
119877119873
(119899 + 119873 minus 119894120576119873))]
asymp and119879
119904
(119899) 119878Δ
(119899) minus and119879
119904
(119899 minus 119879119904
) 119878Δ
(119899)
+ and119879
119904
(119899 minus 2119879119904
) 119878Δ
(119899) minus sdot sdot sdot + 1205820
(119899)
=
120576
sum
119894=0
(minus1)120576
and119879
119904
(119899 minus 119894119879119904
) 119878Δ
(119899) + 1205820
(119899)
(8)
where and119879
119904
(119899) is the trigonometry sequence of width 119879119904
and isexpressed as
and119879
119904
(119899) =
2
119879119904
119899 + 1 minus119879119904
2le 119899 lt 0
minus2
119879119904
119899 + 1 0 le 119899 le119879119904
2
0 other
(9)
When 120576 is five the autocorrelation result of the BOCbase-band signal is shown in Figure 5(a) and the two struc-tured correlation results are shown in Figures 5(b) and 5(c)respectively The results show that the positions of the twochannel main peaks exactly coincide with the position of theautocorrelation main peak and the numbers of peaks are thesame in both channels In addition the positions of the twochannel peaks are symmetrical about the main peak positionof the autocorrelation function
4 Mathematical Problems in Engineering
minus8 minus6 minus4 minus2 0 2 4 6 8minus1
0
1
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(a)
minus8 minus6 minus4 minus2 0 2 4 6 8minus02
0
02
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(b)
minus8 minus6 minus4 minus2 0 2 4 6 8minus02
0
02
Time (s)
Cor
relat
ion
resu
lt
times10minus7
(c)
Figure 5 The correlation result of BOC
In view of these characteristics and combining (8) and(9) the addition and subtraction operations are performedby using the two structured correlation results expressed as
Δ1198831
(119899) = 1198831
(119899) + 1198832
(119899)
Δ1198832
(119899) = 1198831
(119899) minus 1198832
(119899)
(10)
Thus the new correlation function is structured to elimi-nate side peaks and the processing is expressed as
51 Side Peak InhibitionAnalysis Equations (9) and (13) showthat the final correlation result has a single peak whose mainwaveform is a triangular peak Thus the ISPA algorithm canachieve the goal of side peak inhibition The new algorithmis then simulated using the following parameters 1023MHzPRN code frequency 15345MHz square wave frequency and12276MHz sampling frequency modulation order of 3 andthe sine-phased BOC signal for these parameters is expressedas sinBOC(15 10)
The ISPA result for sinBOC(15 10) is shown in Figure 6The ISPA results for sinBOC(10 2) cosBOC(10 5) andcosBOC(6 1) are shown in Figures 7 8 and 9 respectivelyThe simulation results show that the ISPA algorithm can
6 Mathematical Problems in Engineering
minus20 minus10 0 10 20
minus05
0
05
1
15
2
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 8 The ISPA result for cosBOC(10 5)
minus50 0 50minus08
minus06
minus04
minus02
0
02
04
06
08
1
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 9 The ISPA result for cosBOC(6 1)
clearly recover the main peak whose position is the sameas the main peak position of the autocorrelation functionIn particular the ISPA algorithm can effectively inhibit sidepeaks
52 Adaptability Analysis The new algorithm result is influ-enced by the frequency error and the mixed noise accordingto (13) The algorithm result approximately conforms to thecycle equation because of the frequency error function cyclecharacteristics When the relationship of the frequency errorand accumulation time 119905 satisfies (21) the algorithm resulterror reaches its maximum We also find that the ISPA
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
Carrier error (Hz)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 10 The relationship between the relative main peak andfrequency error
algorithm result decreases gradually along with the increaseof mixed noise according to
119878Δ
(119899) =119896
2119905 (21)
where 119896 is the positive integerFurthermore the ISPA algorithmrsquos adaptability is simu-
lated with the following parameters 15345MHz square wavefrequency and 12276MHz sampling frequency modulationmode is sinemode andmodulation orders are 15 10 6 and 3respectively
The relationship between the relative main peak andfrequency error is shown in Figure 10 which shows that theresults satisfy (21)The relationship between the relativemainpeak and SNR is shown in Figure 11 revealing that the relativemain peak decreases gradually with decreasing SNR And theISPA algorithmrsquos adaptability to the SNR environment ismorethan minus25 dB according to (13) and Figure 11
53 Superiority Analysis To verify the superiority of the ISPAalgorithm this ISPA algorithm is compared with otheralgorithms namely the FBA algorithm POA algorithm andSPRA algorithm The simulation parameters are as follows2046MHz PRN code frequency and the modulation modeis sine mode
With changing modulation order the main peak widthchanges and the main peak relative changes are shown inFigures 12 and 13 The results show that the ISPA algorithmrsquosmain peak width is the smallest and its main peak relativeresult is the greatest demonstrating that this algorithmrsquosacquisition and tracking performance is the best
The side peak relative changes and the mainside peakratio changes with changing modulation order are shown inFigures 14 and 15 The results show that the ISPA algorithmside peak relative result is the smallest and the mainside
Mathematical Problems in Engineering 7
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
160
180
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 11The relationship between the relativemain peak and SNR
0 5 10 15 200
02
04
06
08
1
12
Modulation order
Mai
n pe
ak w
idth
(s)
FBA resultPOA result
SPRA resultISPA result
times10minus6
Figure 12 The relationship between the main peak width and themodulation order
peak ratio is the greatest demonstrating that this algorithmrsquosside peak inhibition ability is best
The main peak relative changes with changing SNR areshown in Figure 16 The results show that the adaptability ofthe ISPA algorithm is better than the FBA algorithm and POAalgorithm but there are no significant differences between theISPA algorithm and the SPRA algorithm
0 5 10 15 200
50
100
150
200
250
300
Modulation order
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 13 The relationship between the relative main peak and themodulation order
0 5 10 15 200
20
40
60
80
100
120
140
Modulation order
Side
pea
k re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 14 The relationship between the relative side peak and themodulation order
6 Conclusions
In this paper the principle and characteristics of BOC mod-ulation signals have been studied To implement the BOCmodulated signal acquisition effective algorithms have beenstudied including the full band acquisition (FBA) algorithmthe peak optimization acquisition (POA) algorithm and thesingle peak recovery acquisition (SPRA) algorithm Consid-ering the filter restriction and generic deficiency problemsin traditional algorithms we propose the ISPA algorithmWe eliminate all side peaks of the BOC correlation function(CF) by structuring special sequences composed of PRN codeand cycle rectangular sequences The ISPA algorithm can be
8 Mathematical Problems in Engineering
0 5 10 15 200
2
4
6
8
10
12
Modulation order
Mai
nsid
e pea
k ra
tio
times1017
FBA resultPOA result
SPRA resultISPA result
Figure 15 The relationship between the mainside peak ratio andthe modulation order
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 16The relationship between the relative main peak changesand SNR
applied to both generic sine- and cosine-phased BOC signalsand to all modulation orders In addition it outperforms thetraditional algorithms in acquisition inhibition side peakability and adaptability to lower SNR
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the Program for Liaoning Inno-vative Research Team in University (no LT2011005) NewCentury Program for Excellent Talents of Ministry of Edu-cation of China (no NCET-11-1013) Project of Science andTechnologyDepartment of Liaoning Province (no 20121038)Project of Education Department of Liaoning Province (noL2013085) and the Open Foundation of Key Laboratory ofShenyang Ligong University
References
[1] K Subburaj S Bhatara J Tangudu J R Samuel R Ganesanand K Ramasubramanian ldquoSpur mitigation in high-sensitivityGNSS receiversrdquo IEEE Transactions on Circuits and Systems IIExpress Briefs vol 61 no 2 pp 100ndash104 2014
[2] R R Rick and L B Milstein ldquoOptimal decision strategies foracquisition of spread-spectrum signals in frequency-selectivefading channelsrdquo IEEE Transactions on Communications vol46 no 5 pp 686ndash694 1998
[3] X Li and W Guo ldquoEfficient differential coherent accumulationalgorithm for weak GPS signal bit synchronizationrdquo IEEECommunications Letters vol 17 no 5 pp 936ndash939 2013
[4] T H Ta N C Shivaramaiah A G Dempster and L L PrestildquoSignificance of cell-correlation phenomenon inGNSSmatchedfilter acquisition enginesrdquo IEEE Transactions on Aerospace andElectronic Systems vol 48 no 2 pp 1264ndash1286 2012
[5] P Fishman and J W Betz ldquoPredicting performance of directacquisition for theM-code signalrdquo in Proceedings of the Interna-tional Technical Meeting of the Institute of Navigation (IONNTMrsquo00) pp 574ndash582 2000
[6] J Betz and P Capozza ldquoSystem for direct acquisition of receivedsignalsrdquo US patent no 20040071200 A1 2004
[7] N Martin V Leblond G Guillotel and V Heiries ldquoBOC(xy)signal acquisition techniques and performancesrdquo in Proceedingsof the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPSGNSS rsquo03) pp188ndash198 2003
[8] A Burian E S Lohan andM Renfors ldquoBPSK-likemethods forhybrid-search acquisition of galileo signalsrdquo in Proceedings ofthe IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 July 2006
[9] W-L Mao C-S Hwang C-W Hung J Sheen and P-H ChenldquoUnambiguous BPSK-like CSCmethod for Galileo acquisitionrdquoin Proceedings of the 18th International Conference on Methodsand Models in Automation and Robotics (MMAR rsquo13) pp 627ndash632 Międzyzdroje Poland August 2013
[10] B Kim and S-H Kong ldquoTwo-dimensional compressed correla-tor for fast acquisition of BOC(m n) signalsrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2662ndash2672 2014
[11] F Benedetto G Giunta E S Lohan and M Renfors ldquoAfast unambiguous acquisition algorithm for BOC-modulatedsignalsrdquo IEEE Transactions on Vehicular Technology vol 62 no3 pp 1350ndash1355 2013
[12] Z Yao M Lu and Z Feng ldquoUnambiguous sine-phased binaryoffset carrier modulated signal acquisition techniquerdquo IEEETransactions onWireless Communications vol 9 no 2 pp 577ndash580 2010
[13] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontracking
Mathematical Problems in Engineering 9
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
In view of these characteristics and combining (8) and(9) the addition and subtraction operations are performedby using the two structured correlation results expressed as
Δ1198831
(119899) = 1198831
(119899) + 1198832
(119899)
Δ1198832
(119899) = 1198831
(119899) minus 1198832
(119899)
(10)
Thus the new correlation function is structured to elimi-nate side peaks and the processing is expressed as
51 Side Peak InhibitionAnalysis Equations (9) and (13) showthat the final correlation result has a single peak whose mainwaveform is a triangular peak Thus the ISPA algorithm canachieve the goal of side peak inhibition The new algorithmis then simulated using the following parameters 1023MHzPRN code frequency 15345MHz square wave frequency and12276MHz sampling frequency modulation order of 3 andthe sine-phased BOC signal for these parameters is expressedas sinBOC(15 10)
The ISPA result for sinBOC(15 10) is shown in Figure 6The ISPA results for sinBOC(10 2) cosBOC(10 5) andcosBOC(6 1) are shown in Figures 7 8 and 9 respectivelyThe simulation results show that the ISPA algorithm can
6 Mathematical Problems in Engineering
minus20 minus10 0 10 20
minus05
0
05
1
15
2
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 8 The ISPA result for cosBOC(10 5)
minus50 0 50minus08
minus06
minus04
minus02
0
02
04
06
08
1
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 9 The ISPA result for cosBOC(6 1)
clearly recover the main peak whose position is the sameas the main peak position of the autocorrelation functionIn particular the ISPA algorithm can effectively inhibit sidepeaks
52 Adaptability Analysis The new algorithm result is influ-enced by the frequency error and the mixed noise accordingto (13) The algorithm result approximately conforms to thecycle equation because of the frequency error function cyclecharacteristics When the relationship of the frequency errorand accumulation time 119905 satisfies (21) the algorithm resulterror reaches its maximum We also find that the ISPA
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
Carrier error (Hz)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 10 The relationship between the relative main peak andfrequency error
algorithm result decreases gradually along with the increaseof mixed noise according to
119878Δ
(119899) =119896
2119905 (21)
where 119896 is the positive integerFurthermore the ISPA algorithmrsquos adaptability is simu-
lated with the following parameters 15345MHz square wavefrequency and 12276MHz sampling frequency modulationmode is sinemode andmodulation orders are 15 10 6 and 3respectively
The relationship between the relative main peak andfrequency error is shown in Figure 10 which shows that theresults satisfy (21)The relationship between the relativemainpeak and SNR is shown in Figure 11 revealing that the relativemain peak decreases gradually with decreasing SNR And theISPA algorithmrsquos adaptability to the SNR environment ismorethan minus25 dB according to (13) and Figure 11
53 Superiority Analysis To verify the superiority of the ISPAalgorithm this ISPA algorithm is compared with otheralgorithms namely the FBA algorithm POA algorithm andSPRA algorithm The simulation parameters are as follows2046MHz PRN code frequency and the modulation modeis sine mode
With changing modulation order the main peak widthchanges and the main peak relative changes are shown inFigures 12 and 13 The results show that the ISPA algorithmrsquosmain peak width is the smallest and its main peak relativeresult is the greatest demonstrating that this algorithmrsquosacquisition and tracking performance is the best
The side peak relative changes and the mainside peakratio changes with changing modulation order are shown inFigures 14 and 15 The results show that the ISPA algorithmside peak relative result is the smallest and the mainside
Mathematical Problems in Engineering 7
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
160
180
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 11The relationship between the relativemain peak and SNR
0 5 10 15 200
02
04
06
08
1
12
Modulation order
Mai
n pe
ak w
idth
(s)
FBA resultPOA result
SPRA resultISPA result
times10minus6
Figure 12 The relationship between the main peak width and themodulation order
peak ratio is the greatest demonstrating that this algorithmrsquosside peak inhibition ability is best
The main peak relative changes with changing SNR areshown in Figure 16 The results show that the adaptability ofthe ISPA algorithm is better than the FBA algorithm and POAalgorithm but there are no significant differences between theISPA algorithm and the SPRA algorithm
0 5 10 15 200
50
100
150
200
250
300
Modulation order
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 13 The relationship between the relative main peak and themodulation order
0 5 10 15 200
20
40
60
80
100
120
140
Modulation order
Side
pea
k re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 14 The relationship between the relative side peak and themodulation order
6 Conclusions
In this paper the principle and characteristics of BOC mod-ulation signals have been studied To implement the BOCmodulated signal acquisition effective algorithms have beenstudied including the full band acquisition (FBA) algorithmthe peak optimization acquisition (POA) algorithm and thesingle peak recovery acquisition (SPRA) algorithm Consid-ering the filter restriction and generic deficiency problemsin traditional algorithms we propose the ISPA algorithmWe eliminate all side peaks of the BOC correlation function(CF) by structuring special sequences composed of PRN codeand cycle rectangular sequences The ISPA algorithm can be
8 Mathematical Problems in Engineering
0 5 10 15 200
2
4
6
8
10
12
Modulation order
Mai
nsid
e pea
k ra
tio
times1017
FBA resultPOA result
SPRA resultISPA result
Figure 15 The relationship between the mainside peak ratio andthe modulation order
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 16The relationship between the relative main peak changesand SNR
applied to both generic sine- and cosine-phased BOC signalsand to all modulation orders In addition it outperforms thetraditional algorithms in acquisition inhibition side peakability and adaptability to lower SNR
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the Program for Liaoning Inno-vative Research Team in University (no LT2011005) NewCentury Program for Excellent Talents of Ministry of Edu-cation of China (no NCET-11-1013) Project of Science andTechnologyDepartment of Liaoning Province (no 20121038)Project of Education Department of Liaoning Province (noL2013085) and the Open Foundation of Key Laboratory ofShenyang Ligong University
References
[1] K Subburaj S Bhatara J Tangudu J R Samuel R Ganesanand K Ramasubramanian ldquoSpur mitigation in high-sensitivityGNSS receiversrdquo IEEE Transactions on Circuits and Systems IIExpress Briefs vol 61 no 2 pp 100ndash104 2014
[2] R R Rick and L B Milstein ldquoOptimal decision strategies foracquisition of spread-spectrum signals in frequency-selectivefading channelsrdquo IEEE Transactions on Communications vol46 no 5 pp 686ndash694 1998
[3] X Li and W Guo ldquoEfficient differential coherent accumulationalgorithm for weak GPS signal bit synchronizationrdquo IEEECommunications Letters vol 17 no 5 pp 936ndash939 2013
[4] T H Ta N C Shivaramaiah A G Dempster and L L PrestildquoSignificance of cell-correlation phenomenon inGNSSmatchedfilter acquisition enginesrdquo IEEE Transactions on Aerospace andElectronic Systems vol 48 no 2 pp 1264ndash1286 2012
[5] P Fishman and J W Betz ldquoPredicting performance of directacquisition for theM-code signalrdquo in Proceedings of the Interna-tional Technical Meeting of the Institute of Navigation (IONNTMrsquo00) pp 574ndash582 2000
[6] J Betz and P Capozza ldquoSystem for direct acquisition of receivedsignalsrdquo US patent no 20040071200 A1 2004
[7] N Martin V Leblond G Guillotel and V Heiries ldquoBOC(xy)signal acquisition techniques and performancesrdquo in Proceedingsof the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPSGNSS rsquo03) pp188ndash198 2003
[8] A Burian E S Lohan andM Renfors ldquoBPSK-likemethods forhybrid-search acquisition of galileo signalsrdquo in Proceedings ofthe IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 July 2006
[9] W-L Mao C-S Hwang C-W Hung J Sheen and P-H ChenldquoUnambiguous BPSK-like CSCmethod for Galileo acquisitionrdquoin Proceedings of the 18th International Conference on Methodsand Models in Automation and Robotics (MMAR rsquo13) pp 627ndash632 Międzyzdroje Poland August 2013
[10] B Kim and S-H Kong ldquoTwo-dimensional compressed correla-tor for fast acquisition of BOC(m n) signalsrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2662ndash2672 2014
[11] F Benedetto G Giunta E S Lohan and M Renfors ldquoAfast unambiguous acquisition algorithm for BOC-modulatedsignalsrdquo IEEE Transactions on Vehicular Technology vol 62 no3 pp 1350ndash1355 2013
[12] Z Yao M Lu and Z Feng ldquoUnambiguous sine-phased binaryoffset carrier modulated signal acquisition techniquerdquo IEEETransactions onWireless Communications vol 9 no 2 pp 577ndash580 2010
[13] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontracking
Mathematical Problems in Engineering 9
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
51 Side Peak InhibitionAnalysis Equations (9) and (13) showthat the final correlation result has a single peak whose mainwaveform is a triangular peak Thus the ISPA algorithm canachieve the goal of side peak inhibition The new algorithmis then simulated using the following parameters 1023MHzPRN code frequency 15345MHz square wave frequency and12276MHz sampling frequency modulation order of 3 andthe sine-phased BOC signal for these parameters is expressedas sinBOC(15 10)
The ISPA result for sinBOC(15 10) is shown in Figure 6The ISPA results for sinBOC(10 2) cosBOC(10 5) andcosBOC(6 1) are shown in Figures 7 8 and 9 respectivelyThe simulation results show that the ISPA algorithm can
6 Mathematical Problems in Engineering
minus20 minus10 0 10 20
minus05
0
05
1
15
2
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 8 The ISPA result for cosBOC(10 5)
minus50 0 50minus08
minus06
minus04
minus02
0
02
04
06
08
1
Time (s)
Cor
relat
ion
resu
lt
Autocorrelation resultISPA result
Figure 9 The ISPA result for cosBOC(6 1)
clearly recover the main peak whose position is the sameas the main peak position of the autocorrelation functionIn particular the ISPA algorithm can effectively inhibit sidepeaks
52 Adaptability Analysis The new algorithm result is influ-enced by the frequency error and the mixed noise accordingto (13) The algorithm result approximately conforms to thecycle equation because of the frequency error function cyclecharacteristics When the relationship of the frequency errorand accumulation time 119905 satisfies (21) the algorithm resulterror reaches its maximum We also find that the ISPA
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
Carrier error (Hz)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 10 The relationship between the relative main peak andfrequency error
algorithm result decreases gradually along with the increaseof mixed noise according to
119878Δ
(119899) =119896
2119905 (21)
where 119896 is the positive integerFurthermore the ISPA algorithmrsquos adaptability is simu-
lated with the following parameters 15345MHz square wavefrequency and 12276MHz sampling frequency modulationmode is sinemode andmodulation orders are 15 10 6 and 3respectively
The relationship between the relative main peak andfrequency error is shown in Figure 10 which shows that theresults satisfy (21)The relationship between the relativemainpeak and SNR is shown in Figure 11 revealing that the relativemain peak decreases gradually with decreasing SNR And theISPA algorithmrsquos adaptability to the SNR environment ismorethan minus25 dB according to (13) and Figure 11
53 Superiority Analysis To verify the superiority of the ISPAalgorithm this ISPA algorithm is compared with otheralgorithms namely the FBA algorithm POA algorithm andSPRA algorithm The simulation parameters are as follows2046MHz PRN code frequency and the modulation modeis sine mode
With changing modulation order the main peak widthchanges and the main peak relative changes are shown inFigures 12 and 13 The results show that the ISPA algorithmrsquosmain peak width is the smallest and its main peak relativeresult is the greatest demonstrating that this algorithmrsquosacquisition and tracking performance is the best
The side peak relative changes and the mainside peakratio changes with changing modulation order are shown inFigures 14 and 15 The results show that the ISPA algorithmside peak relative result is the smallest and the mainside
Mathematical Problems in Engineering 7
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
160
180
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 11The relationship between the relativemain peak and SNR
0 5 10 15 200
02
04
06
08
1
12
Modulation order
Mai
n pe
ak w
idth
(s)
FBA resultPOA result
SPRA resultISPA result
times10minus6
Figure 12 The relationship between the main peak width and themodulation order
peak ratio is the greatest demonstrating that this algorithmrsquosside peak inhibition ability is best
The main peak relative changes with changing SNR areshown in Figure 16 The results show that the adaptability ofthe ISPA algorithm is better than the FBA algorithm and POAalgorithm but there are no significant differences between theISPA algorithm and the SPRA algorithm
0 5 10 15 200
50
100
150
200
250
300
Modulation order
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 13 The relationship between the relative main peak and themodulation order
0 5 10 15 200
20
40
60
80
100
120
140
Modulation order
Side
pea
k re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 14 The relationship between the relative side peak and themodulation order
6 Conclusions
In this paper the principle and characteristics of BOC mod-ulation signals have been studied To implement the BOCmodulated signal acquisition effective algorithms have beenstudied including the full band acquisition (FBA) algorithmthe peak optimization acquisition (POA) algorithm and thesingle peak recovery acquisition (SPRA) algorithm Consid-ering the filter restriction and generic deficiency problemsin traditional algorithms we propose the ISPA algorithmWe eliminate all side peaks of the BOC correlation function(CF) by structuring special sequences composed of PRN codeand cycle rectangular sequences The ISPA algorithm can be
8 Mathematical Problems in Engineering
0 5 10 15 200
2
4
6
8
10
12
Modulation order
Mai
nsid
e pea
k ra
tio
times1017
FBA resultPOA result
SPRA resultISPA result
Figure 15 The relationship between the mainside peak ratio andthe modulation order
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 16The relationship between the relative main peak changesand SNR
applied to both generic sine- and cosine-phased BOC signalsand to all modulation orders In addition it outperforms thetraditional algorithms in acquisition inhibition side peakability and adaptability to lower SNR
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the Program for Liaoning Inno-vative Research Team in University (no LT2011005) NewCentury Program for Excellent Talents of Ministry of Edu-cation of China (no NCET-11-1013) Project of Science andTechnologyDepartment of Liaoning Province (no 20121038)Project of Education Department of Liaoning Province (noL2013085) and the Open Foundation of Key Laboratory ofShenyang Ligong University
References
[1] K Subburaj S Bhatara J Tangudu J R Samuel R Ganesanand K Ramasubramanian ldquoSpur mitigation in high-sensitivityGNSS receiversrdquo IEEE Transactions on Circuits and Systems IIExpress Briefs vol 61 no 2 pp 100ndash104 2014
[2] R R Rick and L B Milstein ldquoOptimal decision strategies foracquisition of spread-spectrum signals in frequency-selectivefading channelsrdquo IEEE Transactions on Communications vol46 no 5 pp 686ndash694 1998
[3] X Li and W Guo ldquoEfficient differential coherent accumulationalgorithm for weak GPS signal bit synchronizationrdquo IEEECommunications Letters vol 17 no 5 pp 936ndash939 2013
[4] T H Ta N C Shivaramaiah A G Dempster and L L PrestildquoSignificance of cell-correlation phenomenon inGNSSmatchedfilter acquisition enginesrdquo IEEE Transactions on Aerospace andElectronic Systems vol 48 no 2 pp 1264ndash1286 2012
[5] P Fishman and J W Betz ldquoPredicting performance of directacquisition for theM-code signalrdquo in Proceedings of the Interna-tional Technical Meeting of the Institute of Navigation (IONNTMrsquo00) pp 574ndash582 2000
[6] J Betz and P Capozza ldquoSystem for direct acquisition of receivedsignalsrdquo US patent no 20040071200 A1 2004
[7] N Martin V Leblond G Guillotel and V Heiries ldquoBOC(xy)signal acquisition techniques and performancesrdquo in Proceedingsof the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPSGNSS rsquo03) pp188ndash198 2003
[8] A Burian E S Lohan andM Renfors ldquoBPSK-likemethods forhybrid-search acquisition of galileo signalsrdquo in Proceedings ofthe IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 July 2006
[9] W-L Mao C-S Hwang C-W Hung J Sheen and P-H ChenldquoUnambiguous BPSK-like CSCmethod for Galileo acquisitionrdquoin Proceedings of the 18th International Conference on Methodsand Models in Automation and Robotics (MMAR rsquo13) pp 627ndash632 Międzyzdroje Poland August 2013
[10] B Kim and S-H Kong ldquoTwo-dimensional compressed correla-tor for fast acquisition of BOC(m n) signalsrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2662ndash2672 2014
[11] F Benedetto G Giunta E S Lohan and M Renfors ldquoAfast unambiguous acquisition algorithm for BOC-modulatedsignalsrdquo IEEE Transactions on Vehicular Technology vol 62 no3 pp 1350ndash1355 2013
[12] Z Yao M Lu and Z Feng ldquoUnambiguous sine-phased binaryoffset carrier modulated signal acquisition techniquerdquo IEEETransactions onWireless Communications vol 9 no 2 pp 577ndash580 2010
[13] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontracking
Mathematical Problems in Engineering 9
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
clearly recover the main peak whose position is the sameas the main peak position of the autocorrelation functionIn particular the ISPA algorithm can effectively inhibit sidepeaks
52 Adaptability Analysis The new algorithm result is influ-enced by the frequency error and the mixed noise accordingto (13) The algorithm result approximately conforms to thecycle equation because of the frequency error function cyclecharacteristics When the relationship of the frequency errorand accumulation time 119905 satisfies (21) the algorithm resulterror reaches its maximum We also find that the ISPA
0 1000 2000 3000 4000 5000 60000
50
100
150
200
250
Carrier error (Hz)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 10 The relationship between the relative main peak andfrequency error
algorithm result decreases gradually along with the increaseof mixed noise according to
119878Δ
(119899) =119896
2119905 (21)
where 119896 is the positive integerFurthermore the ISPA algorithmrsquos adaptability is simu-
lated with the following parameters 15345MHz square wavefrequency and 12276MHz sampling frequency modulationmode is sinemode andmodulation orders are 15 10 6 and 3respectively
The relationship between the relative main peak andfrequency error is shown in Figure 10 which shows that theresults satisfy (21)The relationship between the relativemainpeak and SNR is shown in Figure 11 revealing that the relativemain peak decreases gradually with decreasing SNR And theISPA algorithmrsquos adaptability to the SNR environment ismorethan minus25 dB according to (13) and Figure 11
53 Superiority Analysis To verify the superiority of the ISPAalgorithm this ISPA algorithm is compared with otheralgorithms namely the FBA algorithm POA algorithm andSPRA algorithm The simulation parameters are as follows2046MHz PRN code frequency and the modulation modeis sine mode
With changing modulation order the main peak widthchanges and the main peak relative changes are shown inFigures 12 and 13 The results show that the ISPA algorithmrsquosmain peak width is the smallest and its main peak relativeresult is the greatest demonstrating that this algorithmrsquosacquisition and tracking performance is the best
The side peak relative changes and the mainside peakratio changes with changing modulation order are shown inFigures 14 and 15 The results show that the ISPA algorithmside peak relative result is the smallest and the mainside
Mathematical Problems in Engineering 7
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
160
180
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
Modulation order is 15Modulation order is 10
Modulation order is 6Modulation order is 3
Figure 11The relationship between the relativemain peak and SNR
0 5 10 15 200
02
04
06
08
1
12
Modulation order
Mai
n pe
ak w
idth
(s)
FBA resultPOA result
SPRA resultISPA result
times10minus6
Figure 12 The relationship between the main peak width and themodulation order
peak ratio is the greatest demonstrating that this algorithmrsquosside peak inhibition ability is best
The main peak relative changes with changing SNR areshown in Figure 16 The results show that the adaptability ofthe ISPA algorithm is better than the FBA algorithm and POAalgorithm but there are no significant differences between theISPA algorithm and the SPRA algorithm
0 5 10 15 200
50
100
150
200
250
300
Modulation order
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 13 The relationship between the relative main peak and themodulation order
0 5 10 15 200
20
40
60
80
100
120
140
Modulation order
Side
pea
k re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 14 The relationship between the relative side peak and themodulation order
6 Conclusions
In this paper the principle and characteristics of BOC mod-ulation signals have been studied To implement the BOCmodulated signal acquisition effective algorithms have beenstudied including the full band acquisition (FBA) algorithmthe peak optimization acquisition (POA) algorithm and thesingle peak recovery acquisition (SPRA) algorithm Consid-ering the filter restriction and generic deficiency problemsin traditional algorithms we propose the ISPA algorithmWe eliminate all side peaks of the BOC correlation function(CF) by structuring special sequences composed of PRN codeand cycle rectangular sequences The ISPA algorithm can be
8 Mathematical Problems in Engineering
0 5 10 15 200
2
4
6
8
10
12
Modulation order
Mai
nsid
e pea
k ra
tio
times1017
FBA resultPOA result
SPRA resultISPA result
Figure 15 The relationship between the mainside peak ratio andthe modulation order
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 16The relationship between the relative main peak changesand SNR
applied to both generic sine- and cosine-phased BOC signalsand to all modulation orders In addition it outperforms thetraditional algorithms in acquisition inhibition side peakability and adaptability to lower SNR
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the Program for Liaoning Inno-vative Research Team in University (no LT2011005) NewCentury Program for Excellent Talents of Ministry of Edu-cation of China (no NCET-11-1013) Project of Science andTechnologyDepartment of Liaoning Province (no 20121038)Project of Education Department of Liaoning Province (noL2013085) and the Open Foundation of Key Laboratory ofShenyang Ligong University
References
[1] K Subburaj S Bhatara J Tangudu J R Samuel R Ganesanand K Ramasubramanian ldquoSpur mitigation in high-sensitivityGNSS receiversrdquo IEEE Transactions on Circuits and Systems IIExpress Briefs vol 61 no 2 pp 100ndash104 2014
[2] R R Rick and L B Milstein ldquoOptimal decision strategies foracquisition of spread-spectrum signals in frequency-selectivefading channelsrdquo IEEE Transactions on Communications vol46 no 5 pp 686ndash694 1998
[3] X Li and W Guo ldquoEfficient differential coherent accumulationalgorithm for weak GPS signal bit synchronizationrdquo IEEECommunications Letters vol 17 no 5 pp 936ndash939 2013
[4] T H Ta N C Shivaramaiah A G Dempster and L L PrestildquoSignificance of cell-correlation phenomenon inGNSSmatchedfilter acquisition enginesrdquo IEEE Transactions on Aerospace andElectronic Systems vol 48 no 2 pp 1264ndash1286 2012
[5] P Fishman and J W Betz ldquoPredicting performance of directacquisition for theM-code signalrdquo in Proceedings of the Interna-tional Technical Meeting of the Institute of Navigation (IONNTMrsquo00) pp 574ndash582 2000
[6] J Betz and P Capozza ldquoSystem for direct acquisition of receivedsignalsrdquo US patent no 20040071200 A1 2004
[7] N Martin V Leblond G Guillotel and V Heiries ldquoBOC(xy)signal acquisition techniques and performancesrdquo in Proceedingsof the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPSGNSS rsquo03) pp188ndash198 2003
[8] A Burian E S Lohan andM Renfors ldquoBPSK-likemethods forhybrid-search acquisition of galileo signalsrdquo in Proceedings ofthe IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 July 2006
[9] W-L Mao C-S Hwang C-W Hung J Sheen and P-H ChenldquoUnambiguous BPSK-like CSCmethod for Galileo acquisitionrdquoin Proceedings of the 18th International Conference on Methodsand Models in Automation and Robotics (MMAR rsquo13) pp 627ndash632 Międzyzdroje Poland August 2013
[10] B Kim and S-H Kong ldquoTwo-dimensional compressed correla-tor for fast acquisition of BOC(m n) signalsrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2662ndash2672 2014
[11] F Benedetto G Giunta E S Lohan and M Renfors ldquoAfast unambiguous acquisition algorithm for BOC-modulatedsignalsrdquo IEEE Transactions on Vehicular Technology vol 62 no3 pp 1350ndash1355 2013
[12] Z Yao M Lu and Z Feng ldquoUnambiguous sine-phased binaryoffset carrier modulated signal acquisition techniquerdquo IEEETransactions onWireless Communications vol 9 no 2 pp 577ndash580 2010
[13] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontracking
Mathematical Problems in Engineering 9
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
Figure 11The relationship between the relativemain peak and SNR
0 5 10 15 200
02
04
06
08
1
12
Modulation order
Mai
n pe
ak w
idth
(s)
FBA resultPOA result
SPRA resultISPA result
times10minus6
Figure 12 The relationship between the main peak width and themodulation order
peak ratio is the greatest demonstrating that this algorithmrsquosside peak inhibition ability is best
The main peak relative changes with changing SNR areshown in Figure 16 The results show that the adaptability ofthe ISPA algorithm is better than the FBA algorithm and POAalgorithm but there are no significant differences between theISPA algorithm and the SPRA algorithm
0 5 10 15 200
50
100
150
200
250
300
Modulation order
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 13 The relationship between the relative main peak and themodulation order
0 5 10 15 200
20
40
60
80
100
120
140
Modulation order
Side
pea
k re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 14 The relationship between the relative side peak and themodulation order
6 Conclusions
In this paper the principle and characteristics of BOC mod-ulation signals have been studied To implement the BOCmodulated signal acquisition effective algorithms have beenstudied including the full band acquisition (FBA) algorithmthe peak optimization acquisition (POA) algorithm and thesingle peak recovery acquisition (SPRA) algorithm Consid-ering the filter restriction and generic deficiency problemsin traditional algorithms we propose the ISPA algorithmWe eliminate all side peaks of the BOC correlation function(CF) by structuring special sequences composed of PRN codeand cycle rectangular sequences The ISPA algorithm can be
8 Mathematical Problems in Engineering
0 5 10 15 200
2
4
6
8
10
12
Modulation order
Mai
nsid
e pea
k ra
tio
times1017
FBA resultPOA result
SPRA resultISPA result
Figure 15 The relationship between the mainside peak ratio andthe modulation order
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 16The relationship between the relative main peak changesand SNR
applied to both generic sine- and cosine-phased BOC signalsand to all modulation orders In addition it outperforms thetraditional algorithms in acquisition inhibition side peakability and adaptability to lower SNR
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the Program for Liaoning Inno-vative Research Team in University (no LT2011005) NewCentury Program for Excellent Talents of Ministry of Edu-cation of China (no NCET-11-1013) Project of Science andTechnologyDepartment of Liaoning Province (no 20121038)Project of Education Department of Liaoning Province (noL2013085) and the Open Foundation of Key Laboratory ofShenyang Ligong University
References
[1] K Subburaj S Bhatara J Tangudu J R Samuel R Ganesanand K Ramasubramanian ldquoSpur mitigation in high-sensitivityGNSS receiversrdquo IEEE Transactions on Circuits and Systems IIExpress Briefs vol 61 no 2 pp 100ndash104 2014
[2] R R Rick and L B Milstein ldquoOptimal decision strategies foracquisition of spread-spectrum signals in frequency-selectivefading channelsrdquo IEEE Transactions on Communications vol46 no 5 pp 686ndash694 1998
[3] X Li and W Guo ldquoEfficient differential coherent accumulationalgorithm for weak GPS signal bit synchronizationrdquo IEEECommunications Letters vol 17 no 5 pp 936ndash939 2013
[4] T H Ta N C Shivaramaiah A G Dempster and L L PrestildquoSignificance of cell-correlation phenomenon inGNSSmatchedfilter acquisition enginesrdquo IEEE Transactions on Aerospace andElectronic Systems vol 48 no 2 pp 1264ndash1286 2012
[5] P Fishman and J W Betz ldquoPredicting performance of directacquisition for theM-code signalrdquo in Proceedings of the Interna-tional Technical Meeting of the Institute of Navigation (IONNTMrsquo00) pp 574ndash582 2000
[6] J Betz and P Capozza ldquoSystem for direct acquisition of receivedsignalsrdquo US patent no 20040071200 A1 2004
[7] N Martin V Leblond G Guillotel and V Heiries ldquoBOC(xy)signal acquisition techniques and performancesrdquo in Proceedingsof the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPSGNSS rsquo03) pp188ndash198 2003
[8] A Burian E S Lohan andM Renfors ldquoBPSK-likemethods forhybrid-search acquisition of galileo signalsrdquo in Proceedings ofthe IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 July 2006
[9] W-L Mao C-S Hwang C-W Hung J Sheen and P-H ChenldquoUnambiguous BPSK-like CSCmethod for Galileo acquisitionrdquoin Proceedings of the 18th International Conference on Methodsand Models in Automation and Robotics (MMAR rsquo13) pp 627ndash632 Międzyzdroje Poland August 2013
[10] B Kim and S-H Kong ldquoTwo-dimensional compressed correla-tor for fast acquisition of BOC(m n) signalsrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2662ndash2672 2014
[11] F Benedetto G Giunta E S Lohan and M Renfors ldquoAfast unambiguous acquisition algorithm for BOC-modulatedsignalsrdquo IEEE Transactions on Vehicular Technology vol 62 no3 pp 1350ndash1355 2013
[12] Z Yao M Lu and Z Feng ldquoUnambiguous sine-phased binaryoffset carrier modulated signal acquisition techniquerdquo IEEETransactions onWireless Communications vol 9 no 2 pp 577ndash580 2010
[13] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontracking
Mathematical Problems in Engineering 9
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
Figure 15 The relationship between the mainside peak ratio andthe modulation order
minus30 minus25 minus20 minus15 minus10 minus5 00
20
40
60
80
100
120
140
SNR (dB)
Mai
n pe
ak re
lativ
e res
ult
FBA resultPOA result
SPRA resultISPA result
Figure 16The relationship between the relative main peak changesand SNR
applied to both generic sine- and cosine-phased BOC signalsand to all modulation orders In addition it outperforms thetraditional algorithms in acquisition inhibition side peakability and adaptability to lower SNR
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by the Program for Liaoning Inno-vative Research Team in University (no LT2011005) NewCentury Program for Excellent Talents of Ministry of Edu-cation of China (no NCET-11-1013) Project of Science andTechnologyDepartment of Liaoning Province (no 20121038)Project of Education Department of Liaoning Province (noL2013085) and the Open Foundation of Key Laboratory ofShenyang Ligong University
References
[1] K Subburaj S Bhatara J Tangudu J R Samuel R Ganesanand K Ramasubramanian ldquoSpur mitigation in high-sensitivityGNSS receiversrdquo IEEE Transactions on Circuits and Systems IIExpress Briefs vol 61 no 2 pp 100ndash104 2014
[2] R R Rick and L B Milstein ldquoOptimal decision strategies foracquisition of spread-spectrum signals in frequency-selectivefading channelsrdquo IEEE Transactions on Communications vol46 no 5 pp 686ndash694 1998
[3] X Li and W Guo ldquoEfficient differential coherent accumulationalgorithm for weak GPS signal bit synchronizationrdquo IEEECommunications Letters vol 17 no 5 pp 936ndash939 2013
[4] T H Ta N C Shivaramaiah A G Dempster and L L PrestildquoSignificance of cell-correlation phenomenon inGNSSmatchedfilter acquisition enginesrdquo IEEE Transactions on Aerospace andElectronic Systems vol 48 no 2 pp 1264ndash1286 2012
[5] P Fishman and J W Betz ldquoPredicting performance of directacquisition for theM-code signalrdquo in Proceedings of the Interna-tional Technical Meeting of the Institute of Navigation (IONNTMrsquo00) pp 574ndash582 2000
[6] J Betz and P Capozza ldquoSystem for direct acquisition of receivedsignalsrdquo US patent no 20040071200 A1 2004
[7] N Martin V Leblond G Guillotel and V Heiries ldquoBOC(xy)signal acquisition techniques and performancesrdquo in Proceedingsof the 16th International Technical Meeting of the SatelliteDivision of the Institute of Navigation (ION GPSGNSS rsquo03) pp188ndash198 2003
[8] A Burian E S Lohan andM Renfors ldquoBPSK-likemethods forhybrid-search acquisition of galileo signalsrdquo in Proceedings ofthe IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 July 2006
[9] W-L Mao C-S Hwang C-W Hung J Sheen and P-H ChenldquoUnambiguous BPSK-like CSCmethod for Galileo acquisitionrdquoin Proceedings of the 18th International Conference on Methodsand Models in Automation and Robotics (MMAR rsquo13) pp 627ndash632 Międzyzdroje Poland August 2013
[10] B Kim and S-H Kong ldquoTwo-dimensional compressed correla-tor for fast acquisition of BOC(m n) signalsrdquo IEEE Transactionson Vehicular Technology vol 63 no 6 pp 2662ndash2672 2014
[11] F Benedetto G Giunta E S Lohan and M Renfors ldquoAfast unambiguous acquisition algorithm for BOC-modulatedsignalsrdquo IEEE Transactions on Vehicular Technology vol 62 no3 pp 1350ndash1355 2013
[12] Z Yao M Lu and Z Feng ldquoUnambiguous sine-phased binaryoffset carrier modulated signal acquisition techniquerdquo IEEETransactions onWireless Communications vol 9 no 2 pp 577ndash580 2010
[13] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontracking
Mathematical Problems in Engineering 9
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
technique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007
[14] Z Yao X CuiM Lu Z Feng and J Yang ldquoPseudo-correlation-function-based unambiguous tracking technique for sine-BOCsignalsrdquo IEEE Transactions on Aerospace and Electronic Systemsvol 46 no 4 pp 1782ndash1796 2010
[15] Y Zhou X Hu T Ke and Z Tang ldquoAmbiguity mitigating tech-nique for cosine-phased binary offset carrier signalrdquo IEEETransactions on Wireless Communications vol 11 no 6 pp1981ndash1984 2012
[16] S Fischer A Guerin and S Berberich ldquoAcquisition conceptsfor galileo BOC(22) signals in consideration of hardware lim-itationsrdquo in Proceedings of the IEEE 59th Vehicular TechnologyConference (VTC-Spring rsquo04) pp 2852ndash2856 May 2004
[17] Y Feng M Xu X Liu and F Liu ldquoMain lobe overlappedacquisition algorithm of frequency domain based on BOCmodulation signalrdquo Journal of Data Acquisition amp Processingvol 27 no 1 pp 27ndash31 2012
[18] L Yang Y Feng C Pan and Y Bo ldquoThe research of side-bandacquisition for BOC-modulated signalrdquo in Proceedings of theInternational Conference on Wireless Communications Net-working and Mobile Computing pp 645ndash648 September 2007
