An Acquisition Algorithm with NCCFR for BOC Modulated...

Research ArticleAn Acquisition Algorithm with NCCFR forBOC Modulated Signals

Yongxin Feng1 Fang Liu2 Xudong Yao2 and Xiaoyu Zhang2

1Communication and Network Institute Shenyang Ligong University Shenyang Liaoning China2School of Information Science and Engineering Shenyang Ligong University Shenyang Liaoning China

Correspondence should be addressed to Yongxin Feng fengyongxin263net

Received 3 May 2017 Revised 24 June 2017 Accepted 2 July 2017 Published 3 August 2017

Academic Editor Iickho Song

Copyright copy 2017 Yongxin Feng et al 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

With the development of satellite navigation technology BOC (BinaryOffsetCarrier) signals are proposed and applied in navigationsystem However in the advantages of enhancing the utilized rating of the band resource some new problems are also emerging inthe acquisition processing On the basis of analyzing the limitations of the existing methods in suppressing side peaks a NCCFR(New Cross-Correlation Function Reconstruction) algorithm is proposed in which different modulation coefficients are used toconstruct correlation function with a shifter phaseThe simulation results show that the new algorithm can suppress first side peaksand restrain other side peaks

1 Introduction

With the continuous development of satellite communi-cation technology the limited frequency band resourcesbecome increasingly scarcity so BOC modulation signalis proposed and used in satellite navigation to solve theseproblems On the basis of traditional PSK signal BOC sig-nal owns superior spectrum splitting characteristics whichcan solve the frequency resource shortage problem mean-while it has better acquisition precision However the BOCsignal also brings some problems such as the acquisi-tion ambiguity problem caused by multipeak characteristics[1]

Many effective acquisition methods [2 3] have been pro-posed to solve some acquisition problems and some trackingtechnology [4] is proposed for BOC signals In additionsome methods are proposed to remove side peaks such asthe BPSK-like method [5] ASPeCT method and RQCC(Remove Quadratic BOC Cross-Correlation) reconstructionalgorithm In BPSK-like method the frequency domain ofBOC signals is regarded as the two BPSK signals On the basisof filtering and frequency transform to the side-lobe of BOCsignal the acquisition processing is accomplished by usingconventional BPSK acquisition method [6 7] In ASPeCTmethod the cross-correlation function of the signal and PRN

code is applied which is constructed by pseudorandom codeto restrain the side peaks [8] Using appropriate phase shift ofthe cross-correlation function and nonrelated accumulationabout the shifted correlation function the filtered methodcan enhance the main peak and restrain the side peaks[9] In RQCC method the new QBOC (Quadratic BinaryOffset Carrier) auxiliary signal is reconstructed by usingthe characteristics of same autocorrelation function peakwidth between the auxiliary signal and BOC signals to solvethe problem that the side peaks restrained weakly which iscaused by different correlation function peak width betweenthe PRNauxiliary signal andBOC signals [10] On the basis ofthe shifted correlation function phase by introducing QBOCauxiliary signal and adding the shifted results to eliminatethe side peaks these methods can solve some multipeakproblems but they cannot restrain the multipeak problem indifferent modulation coefficient and meanwhile ensure mainpeak sharply

Therefore considering the acquisition ambiguity prob-lems and the shortage of the existing methods a NCCFR(New Cross-Correlation Function Reconstruction) acqui-sition algorithm is proposed Using different modulationcoefficient to make a different fixed phase shifter correlationfunction the algorithm can efficiently restrain the first sidepeaks and improve the main peak

HindawiJournal of Electrical and Computer EngineeringVolume 2017 Article ID 4241297 9 pageshttpsdoiorg10115520174241297

2 Journal of Electrical and Computer Engineering

2 NCCFR Acquisition Algorithm

Firstly an QBOC auxiliary signal [11 12] can be got by 1205872shifting the phase of local BOC signals and then the BOCsignal and the QBOC signal are defined in formulas (1) and(2) Then the autocorrelation function of receiving signal119877119883(120591) will be got through correlation processing and thecross-correlation function 119877119883119876(120591) will be got by correlationprocessing between the auxiliary signal and received signalwhich is shown in formulas (3) and (4) respectively where119862(119899) is the baseband code SN(119899) is the square wave andtri119909(120591) is the correlation peak whose position is 119909

BOC (119898 119899) = 119862 (119899) SN (2120587120596119899 + 120579) (1)

QBOC (119898 119899) = 119862 (119899) SN(2120587120596119899 + 1205872 + 120579) (2)

119877119883 (120591) =119899minus1

sum119894=1

([(minus1)119894 triminus119894119899 (120591) + (minus1)119894 tri119894119899 (120591)]

times 119899 minus 119894119899 ) + tri0 (120591) =119899minus1

sum119894=minus(119899minus1)

(minus1)|119894| triminus119894119899 (120591) 119899 minus |119894|119899(3)

119877119883119876 (120591) =119899

sum119894=1

([(minus1)119894 triminus(2119894minus1)2119899 (120591)

+ (minus1)119894+1 tri(2119894minus1)2119899 (120591)] times 2119899 minus (2119894 minus 1)2119899 ) (4)

Due to the difference of correlation peak phase between119877119883119876(120591) and 119877119883(120591) the main peak and some side peakswhich is similar to 119877119883(120591) can be reconstructed Thereforethe nonconstant phase shift of119877119883119876(120591) is taken both early andlate ((119899minus1)119879119888)2119899 where 119899 is themodulation coefficient119879119888 isthe period of one chip and 120591 is the chip delay As formulas (5)and (6) show the superfluous side peaks will be eliminated asmuch as possible by taking addition and subtraction whichis shown in formula (7) as follows

119877119883119876 (120591 minus (119899 minus 1) 1198791198882119899 ) =119899

sum119894=1

([(minus1)119894 triminus(2119894+119899minus2)2119899 (120591)

+ (minus1)119894+1 tri(2119894minus119899)2119899 (120591)] times 2119899 minus (2119894 minus 1)2119899 )(5)

119877119883119876 (120591 + (119899 minus 1) 1198791198882119899 ) =119899

sum119894=1


+ (minus1)119894+1 tri(2119894+119899minus2)2119899 (120591)] times 2119899 minus (2119894 minus 1)2119899 )(6)

119872 = 10038161003816100381610038161003816100381610038161003816119877119883119876(120591 minus(119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816 +10038161003816100381610038161003816100381610038161003816119877119883119876 (120591

+ (119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816 minus10038161003816100381610038161003816100381610038161003816119877119883119876(120591 minus

(119899 minus 1) 1198791198882119899 )

+ 119877119883119876(120591 + (119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816 =1119899 (triminus12 (120591)

+ tri12 (120591)) +1198992minus1

sum119894=minus1198992+1

triminus119894119899 (120591) (119899 + 1119899 minus|2119894|119899 )

(7)

where triplusmn119894119899(120591) represents the correlation peak in locationplusmn119894119899

There are many correlation peaks similar to 119877119883(120591) informula (7) especially themain peak and the correlation peakbefore 1198992 Therefore the reconstructed signal can improvemain peak and restrain the side peaks of the correlationfunction and then can obtain formula (8) as follows

119877119883 (120591) + 119872

=119899minus1


(minus1)|119894| triminus119894119899 (120591) 119899 minus |119894|119899+ 1119899 (triminus12 (120591) + tri12 (120591))

+1198992minus1

sum119894=minus1198992+1

triminus119894119899 (120591) (119899 + 1119899 minus|2119894|119899 )

=1198992minus1

sum119894=minus1198992+1

triminus119894119899 (120591) [(minus1)|119894| 119899 minus |119894|119899 +119899 + 1119899 minus|2119894|119899 ]

+ (1119899 +12) (triminus12 (120591) + tri12 (120591))

+119899minus1

sum119894=1198992+1

(minus1)|119894| 119899 minus |119894|119899 (triminus119894119899 (120591) + tri119894119899 (120591))

(8)

According to formula (8) when 119894 = 0 tri0(120591) represents themain correlation peak of the signal and the main peak willpromote (119899 + 1)119899 Not only will the signal synchronizationacquisition rate of receiver be greatly improved but also theacquisition ambiguity of the signal will be reduced effectivelywhen 119894 = 1 and the results of both tri1119899(120591) and triminus1119899(120591)are 0 indicating that the first side peak is eliminated In theodd condition the absolute value of (minus1)|119894|((119899 minus |119894|)119899) +(119899 + 1)119899 minus |2119894|119899 is less than (minus1)|119894|((119899 minus |119894|)119899)(minus1)|119894|((119899 minus|119894|)119899) Therefore the odd correlation peak before 1198992 afterthe reconstruction can be restrained and the even correlationpeak can be enhanced

Because there are no high rate subcarrier signals mixedmaking the peak width 119877119883119875(120591) of both auxiliary signalPRN and the received BOC signals wider than 119877119883(120591) whichcan restrain the side peaks in some extent auxiliary signalPRN can be introduced to restrain the even peak and thecorrelation peak after 1198992 The cross-correlation function isshown in formula (9)

119877119883119875 (120591) =1198992

sum119894=1

([minustriminus(2119894minus1)119899 (120591) + tri(2119894minus1)119899 (120591)] times 1119899) (9)

Journal of Electrical and Computer Engineering 3

FFT

IFFT

IFFT

PRNCode

BOC

FFT Conjugate

FFT Conjugate

Receivesignal

Carrier

IFFT

Square

Square

QBOC FFT Conjugate

Coefficient Judgment

Phasecontroller

Yes

No

Output+

+

+

+

+

++

++minus

minus

minusTc

n

RXP()

+Tc

n

RX()

|∙|

minus(n minus 1)Tc

2n

|∙|

|∙|

RXQ()

+(n minus 1)Tc

2n

Figure 1 The principle of NCCFR

In order to get the reconstructed signal which only consists ofthe even peak by phase shift of the cross-correlation function(CCF) we can get formula (10)

10038161003816100381610038161003816100381610038161003816119877119883119875 (120591 +119879119888119899 ) + 119877119883119875 (120591 minus

119879119888119899 )10038161003816100381610038161003816100381610038161003816

=1198992minus1

sum119894=1

([triminus2119894119899 (120591) + tri2119894119899 (120591)] times 2119899) +1119899

times (tri1 (120591) + triminus1 (120591))

(10)

According to the characteristics that there is only even peakappearance in formulas (8) and (10) the constant coefficientcoef can adjust the correlation peak value in formula (10)moreover the acquisition results of the correlation side peakswill be restrained Therefore the final formula of NCCFR canbe expressed as follows by the similar processing as formula(11) between formulas (8) and (10)

[119877119883 (120591) + (10038161003816100381610038161003816100381610038161003816119877119883119876(120591 minus

(119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816

+ 10038161003816100381610038161003816100381610038161003816119877119883119876(120591 +(119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816

minus 10038161003816100381610038161003816100381610038161003816119877119883119876(120591 minus(119899 minus 1) 1198791198882119899 )

+ 119877119883119876(120591 + (119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816)]2

minus [coef times 10038161003816100381610038161003816100381610038161003816119877119883119875 (120591

minus 119879119888119899 ) + 119877119883119875 (120591 minus119879119888119899 )10038161003816100381610038161003816100381610038161003816]2

(11)

Combined with the principle of NCCFR the principle basedon FFT (Fast Fourier Transform) is shown in Figure 1

3 Algorithm Simulation and Test

31 Comparison Analysis of the Reconstruction AlgorithmIn order to verify the performance of the new algorithmin restraining side peaks according to the design modelof Figure 1 reconstruction comparison analysis of differentalgorithm is fulfilled based on several typical BOC signalsThe simulation parameters are as follows

A BOC (2 2) signal pseudorandom code rate is 2 times10231198906 and subcarrier rate is 2 times 10231198906

B BOC (8 4) signal pseudorandom code rate is 4 times10231198906 and subcarrier rate is 8 times 10231198906

C BOC (6 1) signal pseudorandom code rate is 1 times10231198906 and subcarrier rate is 6 times 10231198906


Reconstruction comparison diagram of BOC (22)

0

1

2

3

4

5

6

Nor

mal

ized

ampl

itude

0604020 08 1minus04minus06minus08 minus02minus1Time delay of the code

BPSK-likeASPeCTFiltered

RQCCNCCRF

Figure 2 The reconstruction comparison of BOC (2 2)


0604020 08 1minus04minus06minus08 minus02minus1Time delay fo the code

0

1

2

3

4

5

6

Nor

mal

ized

ampl

itude


RQCCNCCRF


The carrier rate and sampling rate are 30 times 10231198906 and480 times 10231198906 respectively the simulation results are shownin Figures 2ndash4

They show the side peaks restrained performance pro-moted in NCCFR correlation reconstruction for BOC (2 2)signal from Figure 2 in which the side peaks have almostbeen eliminated It can be seen fromFigure 3 that the first sidepeak has been eliminated in NCCFR for BOC (8 4) signalalthough new side peaks are produced whose ratio is smallerthan the promotion of the main peak From Figure 4 it can beseen that the first side peak has been eliminated in NCCFRfor BOC (6 1) signal but it also produces new larger side


0

1

2

3

4

5

6

Nor

mal

ized

ampl

itude

0604020 08 1minus04minus06minus08 minus02minus1

Time delay of the code


RQCCNCCRF


peaks In conclusion NCCFR has very good performance inside peaks restrained for low order modulation coefficient ofBOC signals and weaker peaks restrained performance forhigh order modulation coefficient

32 Comparison Analysis of the Correlation Value Moreoverin order to validate the adaptability of the algorithm innoisy environment comparison analysis should be doneAndMPMR is defined which is the ratio between the main peakand the mean peak MSPR is defined which is the ratiobetween the main peak and the side peak and MFSPR isdefined which is the ration between the main peak and thefirst side peak where the first side peaks represent the secondhigh degree of the peak [13]

First of all the main peak enhanced performance isanalyzed from MPMR [14ndash16] The simulation results areshown in Figures 5ndash7

It shows that the main peak enhanced performance pro-moted in NCCFR correlation reconstruction for both BOC(2 2) and the BOC (8 4) fromFigures 5 and 6 combinedwiththe formula analysis andNCCFRalgorithmenhance (119899+1)119899of the main peak so main peak enhanced performance willbe shown for low order BOC signal But it is weaker thanRQCC in high order modulation coefficient that is becausethe algorithm will produce new correlation side peaks byusing ASPeCT acquisition algorithm which will restrain thecorrelation peak after 1198992

Secondly the correlation peak enhanced performancealso contains the restrain performance of the side peaksTherefore acquisition performance can be analyzed fromMSPR which is shown in Figures 8ndash10

The results show that all MSPR for different BOC signalsin NCCFR is the biggest indicating that the algorithmhas good performance in restraining the side peaks andenhancing the main peak for different order modulationcoefficient BOC signals combined with the formula analysis


Main peak mean ratio value comparison diagram of BOC (22)

0

1000

2000

3000

4000

5000

6000

Mea

n ra

tio o

f the

mai

n pe

ak

1050 15 20minus10minus15 minus5minus20SNR (dB)


RQCCNCCRF

Figure 5 The MPMR comparison of BOC (2 2)




RQCCNCCRF

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Mea

n ra

tio o

f the

mai

n pe

ak


the new algorithm has better side peaks restrained abilitythat is NCCFR has the best enhanced performance onMSPR

Finally the first side peaks restrain performance is ana-lyzed forMFSPR in different conditions of SNR Consideringthat there are no other side peaks in NCCFR reconstructionfor low order BOC (2 2) the MFSPR is analyzed for bothBOC (8 4) and BOC (6 1) which is shown in Figures 11 and12

The results show that MFSPR for BOC (8 4) in NCCFRis the biggest indicating that the algorithm has good per-formance in restraining the first side peaks At the same


0

500

1000

1500

2000

2500

3000

3500

Mea

n ra

tio o

f the

mai

n pe

ak

1050 15 20minus10 minus5minus15SNR (dB)


RQCCNCCRF


Main to side peak ratio value comparison diagram of BOC (22)

4

6

8

10

12

14

16

18

20

Mai

n to

side

pea

k ra

tio (d

B)



RQCCNCCRF

Figure 8 The MSPR comparison of BOC (2 2)

time performance in restraining the first side peaks ofNCCFR is weaker than RQCC for BOC (6 1) but in generalthe new algorithm has a better first side peaks restrainedperformance

33 Comparison Analysis of the Detection Probability Signalacquisition probability is another important capability forsignal acquisition including the detection probability andfalse alarm probability [17 18] Noise will exist to the receivedsignal during the transmission which probability usuallyobeys the noncentral chi square distribution however pure



0

5

10

15

20

25

Mai

n to

side

pea

k ra

tio (d

B)



RQCCNCCRF



0

2

4

6

8

10

12

14

16

18

Mai

n to

side

pea

k ra

tio (d

B)



RQCCNCCRF


noise or nonsynchronized signal usually obeys the noncen-tral chi square distribution [19] Furthermore in order tovalidate the acquisition performance of NCCFR setting theparameter of false alarm probability pfa = 001 which is aconstant value comparison analysis has been done from thecorrelation peak detection probability according to severaltypical signals in different SNR conditions which mainlyfocuses on the main peak detection probability (MPDR) theside peaks detection probability (SPDR) and the first sidepeaks detection probability (FSPDR)

Firstly the MPDR has been analyzed in different SNRconditions which are shown in Figures 13ndash15

Main to first side peak ratio value comparison diagram of BOC (84)

4

5

6

7

8

9

10

11

12

13

14

Mai

n to

firs

t sid

e pea

k ra

tio (d

B)



RQCCNCCRF

Figure 11 The MFSPR comparison of BOC (8 4)


05

1

15

2

25

3

35

4

45

Mai

n to

firs

t sid

e pea

k ra

tio (d

B)



RQCCNCCRF


The results show that MPDR performance for both (2 2)and BOC (8 4) in NCCFR is better than others and MPDRperformance of NCCFR is weaker than RQCC for BOC(6 1) but in general the new algorithm has a better MPDRperformance

Secondly according to the ambiguity problem of theside peaks the SPDR has been analyzed in different SNRconditions which are shown in Figures 16ndash18

The results show that SPDR for NCCFR in different SNRconditions is the smallest one indicating that the algorithm


Main peak detection probability comparison diagram of BOC (22)

0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty



RQCCNCCRF

Figure 13 The MPDR comparison of BOC (2 2)



0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty


RQCCNCCRF


has good performance in restraining the side peaks for BOCsignals

Finally according to the problem of producing newside peaks in reconstruction algorithm the acquisition per-formance has been analyzed in different SNR conditionsfocusing on FSPDR which are shown in Figures 19-20

The results show that algorithm has good performance inrestraining the first side peaks for BOC (8 4) signal FromFigure 20 it can be seen that the performance in restrainingthe first side peaks of NCCFR is better than others whenthe SNR is low but weaker than RQCC when the SNR is


0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty



RQCCNCCRF


Side peak detection probability comparison diagram of BOC (22)

0

005

01

015

02

025

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF

Figure 16 The SPDR comparison of BOC (2 2)

high In general the new algorithm has better first side peaksrestrained performance in different modulation coefficientfor all BOC signals

4 Conclusions

On the basis of analyzing the limitations for the existingcorrelation reconstruction methods a method of NCCFR isbeen proposed In order to verify the acquisition performancefor the new algorithm the simulation comparison has beenanalyzed by using different acquisition methods in different



0

01

02

03

04

05

06

07

08

09

1

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



0

01

02

03

04

05

06

07

08

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF


SNR conditions based on BOC (2 2) BOC (8 4) and BOC(6 1) The simulation results show that the proposed algo-rithm is better than all of the other algorithms in enhancingthe main peak and restraining the side peaks when themodulation coefficients are of low order And the resultsshow that the new algorithm has better performance thanother algorithms when the modulation coefficients are ofhigh order

Conflicts of Interest

The authors declare that they have no conflicts of interest

First side peak detection probability comparison diagram of BOC (84)

0

01

02

03

04

05

06

07

08

09

1

Firs

t sid

e pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF

Figure 19 The FSPDR comparison of BOC (8 4)


0

01

02

03

04

05

06

07

08

Firs

t sid

e pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF

Figure 20 The FblackSPDR comparison of BOC (6 1)

Acknowledgments

This work was supported by the National Natural Sci-ence Foundation of China (no 61501309) the Programfor Liaoning Innovative Research Team in University (noLT2011005) New Century Program for Excellent Talents ofMinistry of Education of China (no NCET-11-1013) and theChina Postdoctoral Science Foundation (no 2015M580231no 2017T100185)


References

[1] P Li F Gao and Q Li ldquoAn improved unambiguous acquisitionscheme for BOC (nn) signalsrdquo in Proceedings of the Interna-tional Conference onWireless Communications Signal ProcessingWCSP rsquo15 pp 1ndash6 2015

[2] S Yoon S C Kim J Heo I Song and S Y Kim ldquoTwin-celldetection (TCD) a code acquisition scheme in the presenceof fractional doppler frequency offsetrdquo IEEE Transactions onVehicular Technology vol 58 no 4 pp 1797ndash1803 2009

[3] D Chong Y Lee I Song and S Yoon ldquoA two-stage acquisitioncheme based on multiple correlator outputs for UWB signalsrdquoIEICE Electronics Express vol 8 no 7 pp 436ndash442 2011

[4] Y Lee D Chong I Song S Y Kim G-I Jee and S YoonldquoCancellation of correlation side-peaks for unambiguous BOCsignal trackingrdquo IEEE Communications Letters vol 16 no 5 pp569ndash572 2012

[5] H Chen W Jia and M Yao ldquoCross-correlation functionbased multipath mitigation technique for cosine-BOC signalsrdquoJournal of Systems Engineering and Electronics vol 24 no 5Article ID 00087 pp 742ndash748 2013

[6] 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 IEEE Międzyzdroje Poland August 2013

[7] A Burian E S Lohan and M Renfors ldquoBPSK-like methodsfor hybrid-search acquisition of galileo signalsrdquo in Proceedingsof the IEEE International Conference on Communications (ICCrsquo06) pp 5211ndash5216 IEEE Istanbul Turkey July 2006

[8] O Julien C Macabiau M E Cannon and G LachapelleldquoASPeCT unambiguous sine-BOC(nn) acquisitiontrackingtechnique for navigation applicationsrdquo IEEE Transactions onAerospace and Electronic Systems vol 43 no 1 pp 150ndash1622007

[9] E F Brickell D M Gordon K S Mccurley et al ldquoFastexponentiation with precomputationrdquo in Proceedings of theEurocrypt on Advances in Cryptology vol 658 pp 200ndash207Springer-Verlag New York NY USA 1993

[10] L Yanzan The Fast Acquisition Technology of Multi-ModeNavigation Signals Based onTheBOCSignals DalianUniversityDalian China 2013

[11] W Cui D Zhao J Liu S Wu and J Ding ldquoA novel unambigu-ous acquisition algorithm for BOC(mn) signalsrdquo in Proceedingsof the 5th IEEE International Conference on Signal ProcessingCommunications and Computing ICSPCC rsquo15 IEEE NingboChina September 2015

[12] Y ZhangW Luy andD Yu ldquoA fast acquisition algorithm basedon FFT for BOC modulated signalsrdquo in Proceedings of the 35thIEEE Region 10 Conference TENCON rsquo15 IEEE Macao ChinaNovember 2015

[13] Z Yang Z Huang and S Geng ldquoUnambiguous acquisitionperformance analysis of BOC(mn) signalrdquo in Proceedings ofthe International Conference on Information Engineering andComputer Science ICIECS rsquo09 IEEEWuhan China December2009

[14] F Liu Y-X Feng and M-H Tian ldquoThe main peak estimatealgorithm based on BOC(2nn) signalrdquo in Proceedings of the 3rdIEEE International Conference on Advanced Computer ControlICACC rsquo11 pp 165ndash168 IEEE Harbin China January 2011

[15] O M Mubarak ldquoPerformance comparison of multipath detec-tion using early late phase in BPSK and BOC modulated

signalsrdquo in Proceedings of the 7th International Conference onSignal Processing and Communication Systems ICSPCS rsquo13IEEE Carrara VIC Australia December 2013

[16] L Yang C-S Pan Y-X Feng and Y-M Bo ldquoA new algorithmfor synchronous main lobe detection for BOC modulatednavigation signalsrdquo Journal of Astronautics vol 31 no 8 pp2008ndash2014 2010

[17] A Wang J Wang and B Xue ldquoAcquisition of BOC(n n) withlargeDopplerrdquo inProceedings of the 7th International Conferenceon Wireless Communications Networking and Mobile Comput-ing WiCOM rsquo11 IEEE Wuhan China September 2011

[18] F Shen G Xu and D Xu ldquoUnambiguous acquisition techniquefor cosine-phased binary offset carrier signalrdquo IEEE Communi-cations Letters vol 18 no 10 pp 1751ndash1754 2014

[19] Y Chuanxi Performance Analysis of Ranging Codes And Studyon Acquisition Algorithm of BOC Signal Chinese Academy ofScience (National Time Service Center) Beijing China 2013

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DistributedSensor Networks



2 NCCFR Acquisition Algorithm

Firstly an QBOC auxiliary signal [11 12] can be got by 1205872shifting the phase of local BOC signals and then the BOCsignal and the QBOC signal are defined in formulas (1) and(2) Then the autocorrelation function of receiving signal119877119883(120591) will be got through correlation processing and thecross-correlation function 119877119883119876(120591) will be got by correlationprocessing between the auxiliary signal and received signalwhich is shown in formulas (3) and (4) respectively where119862(119899) is the baseband code SN(119899) is the square wave andtri119909(120591) is the correlation peak whose position is 119909

BOC (119898 119899) = 119862 (119899) SN (2120587120596119899 + 120579) (1)

QBOC (119898 119899) = 119862 (119899) SN(2120587120596119899 + 1205872 + 120579) (2)

119877119883 (120591) =119899minus1

sum119894=1

([(minus1)119894 triminus119894119899 (120591) + (minus1)119894 tri119894119899 (120591)]

times 119899 minus 119894119899 ) + tri0 (120591) =119899minus1


(minus1)|119894| triminus119894119899 (120591) 119899 minus |119894|119899(3)

119877119883119876 (120591) =119899

sum119894=1


+ (minus1)119894+1 tri(2119894minus1)2119899 (120591)] times 2119899 minus (2119894 minus 1)2119899 ) (4)

Due to the difference of correlation peak phase between119877119883119876(120591) and 119877119883(120591) the main peak and some side peakswhich is similar to 119877119883(120591) can be reconstructed Thereforethe nonconstant phase shift of119877119883119876(120591) is taken both early andlate ((119899minus1)119879119888)2119899 where 119899 is themodulation coefficient119879119888 isthe period of one chip and 120591 is the chip delay As formulas (5)and (6) show the superfluous side peaks will be eliminated asmuch as possible by taking addition and subtraction whichis shown in formula (7) as follows

119877119883119876 (120591 minus (119899 minus 1) 1198791198882119899 ) =119899

sum119894=1

([(minus1)119894 triminus(2119894+119899minus2)2119899 (120591)

+ (minus1)119894+1 tri(2119894minus119899)2119899 (120591)] times 2119899 minus (2119894 minus 1)2119899 )(5)

119877119883119876 (120591 + (119899 minus 1) 1198791198882119899 ) =119899

sum119894=1


+ (minus1)119894+1 tri(2119894+119899minus2)2119899 (120591)] times 2119899 minus (2119894 minus 1)2119899 )(6)

119872 = 10038161003816100381610038161003816100381610038161003816119877119883119876(120591 minus(119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816 +10038161003816100381610038161003816100381610038161003816119877119883119876 (120591

+ (119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816 minus10038161003816100381610038161003816100381610038161003816119877119883119876(120591 minus

(119899 minus 1) 1198791198882119899 )

+ 119877119883119876(120591 + (119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816 =1119899 (triminus12 (120591)

+ tri12 (120591)) +1198992minus1

sum119894=minus1198992+1

triminus119894119899 (120591) (119899 + 1119899 minus|2119894|119899 )

(7)

where triplusmn119894119899(120591) represents the correlation peak in locationplusmn119894119899

There are many correlation peaks similar to 119877119883(120591) informula (7) especially themain peak and the correlation peakbefore 1198992 Therefore the reconstructed signal can improvemain peak and restrain the side peaks of the correlationfunction and then can obtain formula (8) as follows

119877119883 (120591) + 119872

=119899minus1


(minus1)|119894| triminus119894119899 (120591) 119899 minus |119894|119899+ 1119899 (triminus12 (120591) + tri12 (120591))

+1198992minus1

sum119894=minus1198992+1

triminus119894119899 (120591) (119899 + 1119899 minus|2119894|119899 )

=1198992minus1

sum119894=minus1198992+1

triminus119894119899 (120591) [(minus1)|119894| 119899 minus |119894|119899 +119899 + 1119899 minus|2119894|119899 ]

+ (1119899 +12) (triminus12 (120591) + tri12 (120591))

+119899minus1

sum119894=1198992+1

(minus1)|119894| 119899 minus |119894|119899 (triminus119894119899 (120591) + tri119894119899 (120591))

(8)

According to formula (8) when 119894 = 0 tri0(120591) represents themain correlation peak of the signal and the main peak willpromote (119899 + 1)119899 Not only will the signal synchronizationacquisition rate of receiver be greatly improved but also theacquisition ambiguity of the signal will be reduced effectivelywhen 119894 = 1 and the results of both tri1119899(120591) and triminus1119899(120591)are 0 indicating that the first side peak is eliminated In theodd condition the absolute value of (minus1)|119894|((119899 minus |119894|)119899) +(119899 + 1)119899 minus |2119894|119899 is less than (minus1)|119894|((119899 minus |119894|)119899)(minus1)|119894|((119899 minus|119894|)119899) Therefore the odd correlation peak before 1198992 afterthe reconstruction can be restrained and the even correlationpeak can be enhanced

Because there are no high rate subcarrier signals mixedmaking the peak width 119877119883119875(120591) of both auxiliary signalPRN and the received BOC signals wider than 119877119883(120591) whichcan restrain the side peaks in some extent auxiliary signalPRN can be introduced to restrain the even peak and thecorrelation peak after 1198992 The cross-correlation function isshown in formula (9)

119877119883119875 (120591) =1198992

sum119894=1

([minustriminus(2119894minus1)119899 (120591) + tri(2119894minus1)119899 (120591)] times 1119899) (9)


FFT

IFFT

IFFT

PRNCode

BOC

FFT Conjugate

FFT Conjugate

Receivesignal

Carrier

IFFT

Square

Square

QBOC FFT Conjugate


Phasecontroller

Yes

No

Output+

+

+

+

+

++

++minus

minus

minusTc

n

RXP()

+Tc

n

RX()

|∙|

minus(n minus 1)Tc

2n

|∙|

|∙|

RXQ()

+(n minus 1)Tc

2n



10038161003816100381610038161003816100381610038161003816119877119883119875 (120591 +119879119888119899 ) + 119877119883119875 (120591 minus

119879119888119899 )10038161003816100381610038161003816100381610038161003816

=1198992minus1

sum119894=1



(10)


[119877119883 (120591) + (10038161003816100381610038161003816100381610038161003816119877119883119876(120591 minus

(119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816

+ 10038161003816100381610038161003816100381610038161003816119877119883119876(120591 +(119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816


+ 119877119883119876(120591 + (119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816)]2

minus [coef times 10038161003816100381610038161003816100381610038161003816119877119883119875 (120591

minus 119879119888119899 ) + 119877119883119875 (120591 minus119879119888119899 )10038161003816100381610038161003816100381610038161003816]2

(11)









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4 Conclusions




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Acknowledgments



References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










FFT

IFFT

IFFT

PRNCode

BOC

FFT Conjugate

FFT Conjugate

Receivesignal

Carrier

IFFT

Square

Square

QBOC FFT Conjugate


Phasecontroller

Yes

No

Output+

+

+

+

+

++

++minus

minus

minusTc

n

RXP()

+Tc

n

RX()

|∙|

minus(n minus 1)Tc

2n

|∙|

|∙|

RXQ()

+(n minus 1)Tc

2n



10038161003816100381610038161003816100381610038161003816119877119883119875 (120591 +119879119888119899 ) + 119877119883119875 (120591 minus

119879119888119899 )10038161003816100381610038161003816100381610038161003816

=1198992minus1

sum119894=1



(10)


[119877119883 (120591) + (10038161003816100381610038161003816100381610038161003816119877119883119876(120591 minus

(119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816

+ 10038161003816100381610038161003816100381610038161003816119877119883119876(120591 +(119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816


+ 119877119883119876(120591 + (119899 minus 1) 1198791198882119899 )10038161003816100381610038161003816100381610038161003816)]2

minus [coef times 10038161003816100381610038161003816100381610038161003816119877119883119875 (120591

minus 119879119888119899 ) + 119877119883119875 (120591 minus119879119888119899 )10038161003816100381610038161003816100381610038161003816]2

(11)









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4 Conclusions




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Acknowledgments



References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











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4 Conclusions




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Acknowledgments



References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

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4 Conclusions




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Acknowledgments



References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











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5

6

7

8

9

10

11

12

13

14

Mai

n to

firs

t sid

e pea

k ra

tio (d

B)



RQCCNCCRF



05

1

15

2

25

3

35

4

45

Mai

n to

firs

t sid

e pea

k ra

tio (d

B)



RQCCNCCRF







0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty



RQCCNCCRF




0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty


RQCCNCCRF






0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty



RQCCNCCRF



0

005

01

015

02

025

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



4 Conclusions




0

01

02

03

04

05

06

07

08

09

1

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



0

01

02

03

04

05

06

07

08

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF






0

01

02

03

04

05

06

07

08

09

1

Firs

t sid

e pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



0

01

02

03

04

05

06

07

08

Firs

t sid

e pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF


Acknowledgments



References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty



RQCCNCCRF




0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty


RQCCNCCRF






0

01

02

03

04

05

06

07

08

09

1

Mai

n pe

ak d

etec

tion

prob

abili

ty



RQCCNCCRF



0

005

01

015

02

025

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



4 Conclusions




0

01

02

03

04

05

06

07

08

09

1

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



0

01

02

03

04

05

06

07

08

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF






0

01

02

03

04

05

06

07

08

09

1

Firs

t sid

e pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



0

01

02

03

04

05

06

07

08

Firs

t sid

e pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF


Acknowledgments



References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

01

02

03

04

05

06

07

08

09

1

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



0

01

02

03

04

05

06

07

08

Side

pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF






0

01

02

03

04

05

06

07

08

09

1

Firs

t sid

e pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF



0

01

02

03

04

05

06

07

08

Firs

t sid

e pea

k de

tect

ion

prob

abili

ty



RQCCNCCRF


Acknowledgments



References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










References





















RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









RoboticsJournal of





Journal of



RotatingMachinery



Journal of

Volume 201


VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









An Acquisition Algorithm with NCCFR for BOC Modulated...

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