research article an accurate modulation recognition method

Research ArticleAn Accurate Modulation Recognition Method of QPSK Signal

Yongxin Feng Zhenyu Teng Fanwei Meng and Bo Qian

School of Information Science and Engineering Shenyang Ligong University Shenyang 110159 China

Correspondence should be addressed to Yongxin Feng fengyongxin263net

Received 5 November 2014 Revised 21 April 2015 Accepted 19 May 2015

Academic Editor Chih-Cheng Hung

Copyright copy 2015 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

Quadrature phase shift keying (QPSK) modulation has been widely applied in communication systems With the increasingdevelopment of QPSK modulation recognition it is meaningful for ensuring validity and accuracy of recognition methodTherefore themethod of signal recognition has been presented based on the features ofQPSKmodulated signal inwhich the featureparameters of QPSK signal are extracted Besides signal classification is fulfilled through thresholds and modulation recognitionis completed with quartic spectrum The simulation results show that the method can recognize QPSK modulation effectively inless sample space condition and can be more accurate

1 Introduction

Modulation recognition is the technology which can deter-mine the modulation by analyzing the received signal inthe premise of unknown signal modulation (or only a littleknown priori information)Modulation recognition technol-ogy has been widely used in the communication field [1ndash5] such as software radio platform and electronic warfaretechnology

The QPSK modulated signal has the features of low errorrate strong antijamming ability and low complexity [6] soit is widely used in the intersatellite communications suchas GPS navigation systems BeiDou navigation systems [7]and common data links (CDL) [8] Recognition methods forQPSK modulated signal can be categorized into two kindsthe time-domain feature parameter methods and the high-order cumulants methods [9ndash11] However the performancesof both methods are constrained by the number of samplespace and neither of them considers how to distinguish theQPSK modulated signals from the MPSK modulated ones

In this paper we focus on the need for recognizing theQPSKmodulation and present a method based on extractingthe feature parameter of the signal which can distinguish theQPSK modulated signals from the MPSK modulated onesDetails on analyzing the quartic spectrumofQPSK signal andvalidating the feasibility of the method are discussed in thelater sections

2 QPSK Signal and Feature Parameters

21 QPSK Signal Model A QPSK signal can be expressed as

119904 (119905) = 119860 cos (1205960119905 + 120579119896) 119896 = 1 2 3 4 (1)

where 119860 is the signal amplitude 1205960 is the carrier frequency120579119896 119896 = 1 2 3 4 are set as 0 1205872 120587 and 31205872 respectivelyand the selection of 120579119896 is determined by the value of the base-band code

Table 1 shows the relationship between the base-bandcode and 120579119896 Each QPSK base-band code contains 2-bitinformation which is represented by the symbol 119886119887 Thereare four statuses in the symbol 119886119887 namely 00 01 11 and 10Each status is represented by one of 120579119896 119896 = 1 2 3 4 Thevarious relationships between the phase values are designedaccording to the Gray code [12]

22 Feature Parameters Since the phase value of QPSKis controlled by the base-band code the change of theamplitude information can be indicated by the change ofphase values The nonamplitude modulated signal such as2FSK MFSK and MSK signals can be distinguished fromQPSK signal through this feature The QPSK signal containsthe information of the absolute phase so the BPSK and ASKmodulation without the information of the absolute phasecan be distinguished from QPSK signal through this featureThe instantaneous envelopersquos mean of the QPSK signal is

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 516081 7 pageshttpdxdoiorg1011552015516081

2 Mathematical Problems in Engineering

Table 1 The relationship between the base-band code and 120579119896

119886119887 00 01 11 10Phase values 120579

1198960 1205872 120587 31205872

close to 1 while the instantaneous envelopersquos mean of theQAM signal changes in a relatively large range so QAMcan be distinguished from QPSK signal through this featureAbove all three feature parameters are needed to recognizethe QPSK modulations [13 14]

(1) The maximum value of the spectral power density ofthe normalized-centered instantaneous amplitude119877max of thesignal is given by

119877max =MAX (

1003816100381610038161003816FFT (119886cn (119894))

1003816100381610038161003816

2)

119873119904

(2)

where 119886cn(119894) is the normalized-centered instantaneous ampli-tude and119873119904 is the number of samples per block

(2) The standard deviation of the absolute value of thecentered nonlinear component of the instantaneous phaseevaluated over the nonweak intervals120575119886119901 of the signal is givenby

120575119886119901 =radic1119888

[

[

sum

119886119899(119894)gt119886119905

1205932NL (119894)

]

]

minus[

[

1119888

sum

119886119899(119894)gt119886119905

1003816100381610038161003816120593NL (119894)

1003816100381610038161003816]

]

2

(3)

where 119886119905 = 1 is a threshold which determinates thenonweak signal 119888 is the number of samples in 120593NL for which119886119899(119894) gt 119886119905 and 120593NL is the centered-nonlinear components ofinstantaneous phase

(3) The average value of the instantaneous amplitude 119864119886is given by

119864119886 =

1119873119904

119873119904

sum

119899=1119886 (119899) (4)

where 119886(119899) is the instantaneous amplitude and 119873119904 is thenumber of samples per block

3 Quartic Spectrum and ModulationRecognition Process

31 Quartic Spectrum Analysis of QPSK Signal In thissection quartic spectrum of QPSK signal is analyzed todetermine the modulation Since four-phase values exist inthe QPSKmodulation discrete spectral lines will appear nearthe quadruple frequency [15] after the signal is processed byquartic spectrum and FFT processing which is significantlydifferent from otherMPSK (119872 ge 8) signalsTheQPSK signalin (1) is squared which can be expressed as

1198782(119905) =

1198602

2

+

1198602

2cos (21205960119905 + 2120579119896) 119896 = 1 2 3 4 (5)

In order to remove the DC component a high-passfilter is used after square processing After another square

Table 2The relationship between the base-band code and phase of8PSK

Code0 0 0 0 1 1 1 10 0 1 1 1 1 0 00 1 1 0 0 1 1 0

Phase values 120579119896 0 1205874 1205872 31205874 120587 51205874 31205872 71205874

operation the quartic spectrum of QPSK modulated signalis got which can be expressed as follows

1198784(119905) =

1198604

8

+

1198604

8cos (41205960119905 + 4120579119896) 119896 = 1 2 3 4 (6)

where the phase values 4120579119896 will be 0 2120587 4120587 and 6120587respectively

Then (6) can be written simply as

1198784(119905) =

1198604

8

+

1198604

8cos (41205960119905) 119896 = 1 2 3 4 (7)

From (7) we can conclude that the discrete spectral linesof QPSK signals will appear at quadruple frequency 41205960 afterthe quartic spectrumandFFTprocessing ForMPSK (119872 ge 8)

modulation signal119872 phase values are used For example thephase values of 8PSK signal are shown in Table 2

For 8PSK after the quartic spectrum and FFT processingthe value of 4120579119896 modulo 2120587 is 0 or 120587 so the discrete spectrallines at the quadruple frequency will not appear Accordingto this the QPSK modulation can be distinguished from the8PSK (MPSK119872 ge 8) one

32 Modulation Recognition Process The modulation recog-nition process of QPSK signal is shown in Figure 1

Step 1 Three feature parameters of the signal being rec-ognized are extracted successively including the maximumvalue of the spectral power density of the normalized-centered instantaneous amplitude 119877max the standard devia-tion of the absolute value of the centered nonlinear compo-nent of the instantaneous phase evaluated over the nonweakintervals 120575119886119901 and the average value of the instantaneousamplitude 119864119886

Step 2 The feature parameters are compared with the thresh-old value set before If the conditions 119877max gt 119905(119877max) 120575119886119901 gt119905(120575119886119901) and119864119886 gt 119905(119864119886) cannot bemet it can be concluded thatthe signal being recognized is not a QPSKmodulated one andthe recognition process will end

Step 3 The quartic spectrum of the received signal is calcu-lated If the discrete spectral lines at the quadruple frequencydo exist the modulation of the received signal will bedetermined as QPSK

4 Simulation

Simulation is performed to verify the correctness and effec-tiveness of the modulation recognition method The simula-tion parameters are set as follows the carrier wave frequency

Mathematical Problems in Engineering 3

Received signal

Square HPF

SquareSpectrum

Spectrum scatter

QPSK signal

Others

Yes

Yes

Yes

No

No

No

Yes

No

Extract feature parameters

Quartic spectrumanalyze

Rmax

gt t(Rmax

)

120575ap gt t(120575ap)

Ea lt t(Ea)

Figure 1 Modulation recognition process of QPSK signal

is 1023MHz the code frequency is 1023MHz the samplingfrequency is 9207MHz and the number of sampling pointsis 18000 Because the reasonable threshold values are closelyrelated to the simulation parameters above a large numberof simulations and tests are performed to get the priorknowledge and the threshold values are set as 119905(119877max) = 30119905(120575119886119901) = 06 and 119905(119864119886) = 12

According to the first step of the recognition processthree feature parameters are calculated Firstly themaximumvalue of the spectral power density of the normalized-centered instantaneous amplitude119877max is calculated Figure 2shows a plot of 119877max versus SNR It can be clearly found thatthe calculated feature parameter 119877max of QPSK signal canmeet the condition of 119877max gt 119905(119877max) Meanwhile 119877max ofMSK and QPSK signals is calculated under the same SNRcondition and the results are shown in Figure 3 It can beclearly found that119877max ofQPSK signal canmeet the conditionof 119877max gt 119905(119877max) while the 119877max of MSK cannot whichprove the rationality of the threshold 119905(119877max) Therefore theQPSKmodulation can be distinguished from theMSK one byusing the parameter 119877max

Secondly the standard deviation of the absolute valueof the centered nonlinear component of the instantaneousphase evaluated over the nonweak intervals 120575119886119901 is calculatedFigure 4 shows a plot of 120575119886119901 versus SNR It can be clearlyfound that he calculated feature parameter 120575119886119901 can meet the

8 10 12 14 16 18 200

1

2

3

4

5

6

7

Signal to noise ratio

Valu

e of f

eatu

re p

aram

eter

QPSK signalThreshold value

Figure 2 The 119877max of QPSK signal

conditions of 120575119886119901 gt 119905(120575119886119901) Meanwhile the same featureparameter 120575119886119901 of BPSK and QPSK signals is calculated underthe same SNR condition and the results are shown in


8 10 12 14 16 18 200

1

2

3

4

5

6

7


Valu

e of f

eatu

re p

aram

eter

MSK signalQPSK signal

Figure 3 The 119877max of QPSK and MSK signals

8 10 12 14 16 18 200

1

2

3

4

5

6


Valu

e of f

eatu

re p

aram

eter


Figure 4 The 120575119886119901of QPSK signal

Figure 5 It can be found that the 120575119886119901 of QPSK signal canmeetthe condition of 120575119886119901 gt 119905(120575119886119901) while the 120575119886119901 of BPSK cannotwhich prove the rationality of the threshold 119905(120575119886119901)Thereforethe QPSK modulation can be distinguished from the BPSKone by using the parameter 120575119886119901

Thirdly the average value of the instantaneous amplitude119864119886 is calculated Figure 6 shows a plot of 119905(119864119886) versus SNRIt can be clearly found that he calculated feature parameter119864119886 can meet the conditions of 119864119886 gt 119905(119864119886) Meanwhile thesame feature parameter 119864119886 of 16QAM and QPSK signals iscalculated under the same SNR condition and the results areshown in Figure 7 It can be found that the 119864119886 of QPSK signalcan meet the condition of 119864119886 gt 119905(119864119886) while the 119864119886 of 16QAMcannot which prove the rationality of the threshold 119905(119864119886)

8 10 12 14 16 18 200

1

2

3

4

5

6


Valu

e of f

eatu

re p

aram

eter

BPSK signalQPSK signal

Figure 5 The 120575119886119901 of QPSK and BPSK signals

8 10 12 14 16 18 20Signal to noise ratio

Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3


Figure 6 The 119864119886 of QPSK signal

Therefore the QPSK modulation can be distinguished fromthe 16QAM one by using the parameter 119864119886

According to the second step of the recognition processthe modulation of signals can be determined Due to thehigh similarity between QPSK and MPSK signals (119872 ge 8)the quartic spectrum of the signals is analyzed to distinguishthem Take the 8PSKmodulation as an example of the MPSKsignals Figures 8 and 9 show the quartic spectrum of QPSKand 8PSK signals respectively on condition that the SNR is8 dB

Figure 8 indicates that a discrete spectrum line doesexist at the quadruple frequency of the QPSK signal whileFigure 9 indicates that no discrete spectrum lines exist atthe quadruple frequency of the 8PSK signal By calculating



Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3

QPSK signal16QAM signal

Figure 7 The 119864119886 of QPSK and 16QAM signals

Frequency (GHz)

Pow

erfr

eque

ncy

(dB

Hz)

Power spectral density estimate via periodogram

minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

0 005 01 015 02 025 03 035 04 045

Figure 8 Quartic spectrum of QPSK signal

the ratio of themaximum peak value to themean value in thequartic spectrum and comparing it with the threshold valuesit can be determined whether the signal is QPSK modulatedor not

Another simulation is performed to test the performanceof the proposed method which is influenced by the numberof phase sample space As a comparison a simulation ofthe method based on fourth-order cumulants under thesame conditions is also performedThe simulation results areshown in Figures 10 and 11 in which the SNR is 10 dB

Figure 10 indicates that for the method based on fourth-order cumulants when the number of the phase sample spaceis more than 200 QPSK signal can be recognized effectivelywhile when the number of the phase sample space is less than200 it is difficult to distinguish between QPSK modulation


Pow

erfr

eque

ncy

(dB

Hz)

minus150

minus160

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Frequency (GHz)0 005 01 015 02 025 03 035 04 045

Figure 9 Quartic spectrum of 8PSK signal

0 200 400 600 800 1000 1200The number of the phase sample space

QPSK signal8PSK signal

minus04

minus02

0

02

04

06

08

1Va

lue o

f fou

rth-

orde

r cum

ulan

ts

Figure 10 The fourth-order cumulants of QPSK and 8PSK signals

and 8PSK modulation This is because the method based onfourth-order cumulants can work well only when the samplevalues of phase space appear with a similar probability whichcannot be guaranteed when the number of phase sample isinsufficient

Figure 11 indicates that for the proposed method theQPSK signal can be distinguished easily form the 8PSK signalas long as the number of phase sample space is greater than 30So the proposedmethod can still work well when the numberof the phase sample space is less than 200 (as long as it islarger than 30) which cannot be done by the method basedon fourth-order cumulants This is because in the proposedmethod the quartic spectrum peak proportion is calculatedby energy integration which does not need a large number ofphase samples


0 200 400 600 800 1000 12000

200

400

600

800

1000

1200

1400

The number of the phase sample space

The q

uart

ic sp

ectr

um p

eak

prop

ortio

n


Figure 11Thequartic spectrumpeak proportion ofQPSKand 8PSKsignals

0 5 10 15 20Signal to noise ratio

Method based on this paperMethod based on feature parameters

0

01

02

03

04

05

06

07

08

09

1

The c

orre

ct re

cogn

ition

rate

Figure 12 The correct recognition rate of methods

Simulations are also performed to test the correct recog-nition rate of the proposed method and the traditionalmethod based on feature parameters The result is shown inFigure 12 It can be found that the correct recognition rate ofthe proposed method is greater than that of the traditionalmethod based on feature parameters especially for the SNRrange between 8 dB and 10 dB

5 Conclusion

Wepresented amodulation recognitionmethod ofQPSK sig-nal which is based on the combination of feature parametersand the quartic spectrum analysis Firstly three vital feature

parameters of signal which are the maximum value of thespectral power density of the normalized-centered instanta-neous amplitude 119877max the standard deviation of the absolutevalue of the centered nonlinear component of the instanta-neous phase evaluated over the nonweak intervals 120575119886119901 andthe average value of the instantaneous amplitude 119864119886 areextracted Secondly the extracted parameters are comparedwith the thresholds Lastly by analyzing the quartic spectrumpeak proportion the recognition of QPSK modulation canbe realized The simulation results show that the proposedmethod can recognize QPSK modulation effectively in lessphase space samples and it is much more accurate than thetraditional method based on feature parameters

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The research is supported by New Century Program forExcellent Talents of Ministry of Education of China (NCET-11-1013) the State Key Laboratory of Rail Traffic Controland Safety (Contract no RCS2012K012) Beijing JiaotongUniversity and Open Fund of Information Network andInformation Countermeasure Technology Key Laboratory ofLiaoning Province Shenyang Ligong University

References

[1] L Stankovic I Djurovic S Stankovic M Simeunovic SDjukanovic and M Dakovic ldquoInstantaneous frequency intime-frequency analysis enhanced concepts and performanceof estimation algorithmsrdquo Digital Signal Processing vol 35 pp1ndash13 2014

[2] A I R Fontes A D M Martins L F Q Silveira and J CPrincipe ldquoPerformance evaluation of the correntropy coeffi-cient in automatic modulation classificationrdquo Expert Systemswith Applications vol 42 no 1 pp 1ndash8 2015

[3] A K Nandi and E E Azzouz Automatic Modulation Recog-nition of Communication Signals Kluwer Academic PublishersAmsterdam The Netherlands 1996

[4] L Que and Q Feng ldquoStudy on phase unwrapping threshold ofdigital signal identificationrdquo Signal Processing vol 26 no 1 pp56ndash59 2010

[5] H-D Liu H-X Zhang and P-F He ldquoStudy on hybrid patternrecognition algorithm for modulated signalsrdquo The Journal ofChina Universities of Posts and Telecommunications vol 21 pp106ndash109 2014

[6] E Kabalci Y Kabalci and I Develi ldquoModelling and analysisof a power line communication system with QPSK modem forrenewable smart gridsrdquo International Journal of Electrical Powerand Energy Systems vol 34 no 1 pp 19ndash28 2012

[7] J Huang R Li Y Wang and C Wu ldquoHigh-sensitivityacquisition algorithm of QPSK-modulate BeiDou B1 signalrdquoAeronautical Computing Technique vol 42 no 5 pp 38ndash422012


[8] G Luo B Yang Z Qiu and Y Li Data Link-Connectionof Information System and Weapon System National DefenseIndustry 2010

[9] J Chen H Liu and S Chen ldquoA method for channel estimationand digital modulation identification based on higher-ordercumulantsrdquo Computer System Application no 11 pp 172ndash1752009

[10] S Cao Z Ye N Hu and X Xu ldquoDOA estimation based onfourth-order cumulants in the presence of sensor gain-phaseerrorsrdquo Signal Processing vol 93 no 9 pp 2581ndash2585 2013

[11] N Madhavan A P Vinod A S Madhukumar and A KKrishna ldquoSpectrum sensing and modulation classification forcognitive radios using cumulants based on fractional lowerorder statisticsrdquo International Journal of Electronics and Com-munications vol 67 no 6 pp 479ndash490 2013

[12] P W J Van Eetvelt S J Shepherd and S K Barton ldquoThedistribution of peak factor in QPSK multi-carrier modulationrdquoWireless Personal Communications vol 2 no 1-2 pp 87ndash961995

[13] A E Sherme ldquoA novel method for automatic modulationrecognitionrdquo Applied Soft Computing vol 12 no 1 pp 453ndash4612012

[14] Y Li G-T Li and G-Q Yang ldquoAutomatic digital modulationrecognition algorithm of communication signalsrdquo Journal ofElectronics amp Information Technology vol 27 no 2 pp 197ndash2012005

[15] H Fan Z Yang and Z Cao ldquoAutomatic recognition forcommonusedmodulations in satellite communicationrdquo Journalof China Institute of Communications vol 25 no 1 pp 140ndash1492004

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Mathematical Problems in Engineering

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Algebra

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Stochastic AnalysisInternational Journal of


Table 1 The relationship between the base-band code and 120579119896

119886119887 00 01 11 10Phase values 120579

1198960 1205872 120587 31205872

close to 1 while the instantaneous envelopersquos mean of theQAM signal changes in a relatively large range so QAMcan be distinguished from QPSK signal through this featureAbove all three feature parameters are needed to recognizethe QPSK modulations [13 14]

(1) The maximum value of the spectral power density ofthe normalized-centered instantaneous amplitude119877max of thesignal is given by

119877max =MAX (

1003816100381610038161003816FFT (119886cn (119894))

1003816100381610038161003816

2)

119873119904

(2)

where 119886cn(119894) is the normalized-centered instantaneous ampli-tude and119873119904 is the number of samples per block

(2) The standard deviation of the absolute value of thecentered nonlinear component of the instantaneous phaseevaluated over the nonweak intervals120575119886119901 of the signal is givenby

120575119886119901 =radic1119888

[

[

sum

119886119899(119894)gt119886119905

1205932NL (119894)

]

]

minus[

[

1119888

sum

119886119899(119894)gt119886119905

1003816100381610038161003816120593NL (119894)

1003816100381610038161003816]

]

2

(3)

where 119886119905 = 1 is a threshold which determinates thenonweak signal 119888 is the number of samples in 120593NL for which119886119899(119894) gt 119886119905 and 120593NL is the centered-nonlinear components ofinstantaneous phase

(3) The average value of the instantaneous amplitude 119864119886is given by

119864119886 =

1119873119904

119873119904

sum

119899=1119886 (119899) (4)

where 119886(119899) is the instantaneous amplitude and 119873119904 is thenumber of samples per block

3 Quartic Spectrum and ModulationRecognition Process

31 Quartic Spectrum Analysis of QPSK Signal In thissection quartic spectrum of QPSK signal is analyzed todetermine the modulation Since four-phase values exist inthe QPSKmodulation discrete spectral lines will appear nearthe quadruple frequency [15] after the signal is processed byquartic spectrum and FFT processing which is significantlydifferent from otherMPSK (119872 ge 8) signalsTheQPSK signalin (1) is squared which can be expressed as

1198782(119905) =

1198602

2

+

1198602

2cos (21205960119905 + 2120579119896) 119896 = 1 2 3 4 (5)

In order to remove the DC component a high-passfilter is used after square processing After another square

Table 2The relationship between the base-band code and phase of8PSK

Code0 0 0 0 1 1 1 10 0 1 1 1 1 0 00 1 1 0 0 1 1 0

Phase values 120579119896 0 1205874 1205872 31205874 120587 51205874 31205872 71205874

operation the quartic spectrum of QPSK modulated signalis got which can be expressed as follows

1198784(119905) =

1198604

8

+

1198604

8cos (41205960119905 + 4120579119896) 119896 = 1 2 3 4 (6)

where the phase values 4120579119896 will be 0 2120587 4120587 and 6120587respectively

Then (6) can be written simply as

1198784(119905) =

1198604

8

+

1198604

8cos (41205960119905) 119896 = 1 2 3 4 (7)

From (7) we can conclude that the discrete spectral linesof QPSK signals will appear at quadruple frequency 41205960 afterthe quartic spectrumandFFTprocessing ForMPSK (119872 ge 8)

modulation signal119872 phase values are used For example thephase values of 8PSK signal are shown in Table 2

For 8PSK after the quartic spectrum and FFT processingthe value of 4120579119896 modulo 2120587 is 0 or 120587 so the discrete spectrallines at the quadruple frequency will not appear Accordingto this the QPSK modulation can be distinguished from the8PSK (MPSK119872 ge 8) one

32 Modulation Recognition Process The modulation recog-nition process of QPSK signal is shown in Figure 1

Step 1 Three feature parameters of the signal being rec-ognized are extracted successively including the maximumvalue of the spectral power density of the normalized-centered instantaneous amplitude 119877max the standard devia-tion of the absolute value of the centered nonlinear compo-nent of the instantaneous phase evaluated over the nonweakintervals 120575119886119901 and the average value of the instantaneousamplitude 119864119886

Step 2 The feature parameters are compared with the thresh-old value set before If the conditions 119877max gt 119905(119877max) 120575119886119901 gt119905(120575119886119901) and119864119886 gt 119905(119864119886) cannot bemet it can be concluded thatthe signal being recognized is not a QPSKmodulated one andthe recognition process will end

Step 3 The quartic spectrum of the received signal is calcu-lated If the discrete spectral lines at the quadruple frequencydo exist the modulation of the received signal will bedetermined as QPSK

4 Simulation

Simulation is performed to verify the correctness and effec-tiveness of the modulation recognition method The simula-tion parameters are set as follows the carrier wave frequency


Received signal

Square HPF

SquareSpectrum

Spectrum scatter

QPSK signal

Others

Yes

Yes

Yes

No

No

No

Yes

No



Rmax

gt t(Rmax

)

120575ap gt t(120575ap)

Ea lt t(Ea)





8 10 12 14 16 18 200

1

2

3

4

5

6

7


Valu

e of f

eatu

re p

aram

eter





8 10 12 14 16 18 200

1

2

3

4

5

6

7


Valu

e of f

eatu

re p

aram

eter



8 10 12 14 16 18 200

1

2

3

4

5

6


Valu

e of f

eatu

re p

aram

eter





8 10 12 14 16 18 200

1

2

3

4

5

6


Valu

e of f

eatu

re p

aram

eter




Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3








Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3



Frequency (GHz)

Pow

erfr

eque

ncy

(dB

Hz)


minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

0 005 01 015 02 025 03 035 04 045






Pow

erfr

eque

ncy

(dB

Hz)

minus150

minus160

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Frequency (GHz)0 005 01 015 02 025 03 035 04 045




minus04

minus02

0

02

04

06

08

1Va

lue o

f fou

rth-

orde

r cum

ulan

ts





0 200 400 600 800 1000 12000

200

400

600

800

1000

1200

1400


The q

uart

ic sp

ectr

um p

eak

prop

ortio

n





0

01

02

03

04

05

06

07

08

09

1

The c

orre

ct re

cogn

ition

rate



5 Conclusion





Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Received signal

Square HPF

SquareSpectrum

Spectrum scatter

QPSK signal

Others

Yes

Yes

Yes

No

No

No

Yes

No



Rmax

gt t(Rmax

)

120575ap gt t(120575ap)

Ea lt t(Ea)





8 10 12 14 16 18 200

1

2

3

4

5

6

7


Valu

e of f

eatu

re p

aram

eter





8 10 12 14 16 18 200

1

2

3

4

5

6

7


Valu

e of f

eatu

re p

aram

eter



8 10 12 14 16 18 200

1

2

3

4

5

6


Valu

e of f

eatu

re p

aram

eter





8 10 12 14 16 18 200

1

2

3

4

5

6


Valu

e of f

eatu

re p

aram

eter




Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3








Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3



Frequency (GHz)

Pow

erfr

eque

ncy

(dB

Hz)


minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

0 005 01 015 02 025 03 035 04 045






Pow

erfr

eque

ncy

(dB

Hz)

minus150

minus160

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Frequency (GHz)0 005 01 015 02 025 03 035 04 045




minus04

minus02

0

02

04

06

08

1Va

lue o

f fou

rth-

orde

r cum

ulan

ts





0 200 400 600 800 1000 12000

200

400

600

800

1000

1200

1400


The q

uart

ic sp

ectr

um p

eak

prop

ortio

n





0

01

02

03

04

05

06

07

08

09

1

The c

orre

ct re

cogn

ition

rate



5 Conclusion





Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










8 10 12 14 16 18 200

1

2

3

4

5

6

7


Valu

e of f

eatu

re p

aram

eter



8 10 12 14 16 18 200

1

2

3

4

5

6


Valu

e of f

eatu

re p

aram

eter





8 10 12 14 16 18 200

1

2

3

4

5

6


Valu

e of f

eatu

re p

aram

eter




Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3








Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3



Frequency (GHz)

Pow

erfr

eque

ncy

(dB

Hz)


minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

0 005 01 015 02 025 03 035 04 045






Pow

erfr

eque

ncy

(dB

Hz)

minus150

minus160

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Frequency (GHz)0 005 01 015 02 025 03 035 04 045




minus04

minus02

0

02

04

06

08

1Va

lue o

f fou

rth-

orde

r cum

ulan

ts





0 200 400 600 800 1000 12000

200

400

600

800

1000

1200

1400


The q

uart

ic sp

ectr

um p

eak

prop

ortio

n





0

01

02

03

04

05

06

07

08

09

1

The c

orre

ct re

cogn

ition

rate



5 Conclusion





Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Valu

e of f

eatu

re p

aram

eter

05

1

15

2

25

3



Frequency (GHz)

Pow

erfr

eque

ncy

(dB

Hz)


minus150

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

0 005 01 015 02 025 03 035 04 045






Pow

erfr

eque

ncy

(dB

Hz)

minus150

minus160

minus140

minus130

minus120

minus110

minus100

minus90

minus80

minus70

minus60

Frequency (GHz)0 005 01 015 02 025 03 035 04 045




minus04

minus02

0

02

04

06

08

1Va

lue o

f fou

rth-

orde

r cum

ulan

ts





0 200 400 600 800 1000 12000

200

400

600

800

1000

1200

1400


The q

uart

ic sp

ectr

um p

eak

prop

ortio

n





0

01

02

03

04

05

06

07

08

09

1

The c

orre

ct re

cogn

ition

rate



5 Conclusion





Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 200 400 600 800 1000 12000

200

400

600

800

1000

1200

1400


The q

uart

ic sp

ectr

um p

eak

prop

ortio

n





0

01

02

03

04

05

06

07

08

09

1

The c

orre

ct re

cogn

ition

rate



5 Conclusion





Acknowledgments


References
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra

























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article an accurate modulation recognition method

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