research article a novel demodulation system...

Research ArticleA Novel Demodulation System Based on ContinuousWavelet Transform

Lanting Fang1 Lenan Wu1 and Yudong Zhang2

1 School of Information Science and Engineering Southeast University Nanjing 210096 China2 School of Computer Science and Technology Nanjing Normal University Nanjing 210023 China

Correspondence should be addressed to Lanting Fang 230139356seueducn

Received 28 May 2014 Accepted 15 September 2014

Academic Editor Jyh-Hong Chou

Copyright copy 2015 Lanting Fang 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

Considering the problem of EBPSK signal demodulation a new approach based on the wavelet scalogram using continuous wavelettransform is proposed Our system is twofold an adaptive wavelet construction method that replaces manual selection existingwavelets method and on the other hand a nonlinear demodulation system based on image processing and pattern classificationis proposed To evaluate the performance of the adaptive wavelet and compare the performance of the proposed system with theexisting systems a series of comprehensive simulation experiments is conducted under the environment of uniform white noisecolored noise and additive white Gaussian noise channel respectively Simulation results of different wavelets show that the systemusing adaptive wavelet has lower bit error rate (BER) Moreover simulation results of several systems show that the BER of theproposed system is the lowest among all systems such as amplitude detection integral detection and some continuous wavelettransform systems (specific scales and times and maximum lines) In a word the adaptive wavelet construction proposed in thispaper yields superior performances compared with the manual selection and the proposed system has better performances thanthe existing systems Index terms are signal demodulation adaptive wavelet continuous wavelet transform and BER

1 Introduction

Spectrum shortage has been a focus of concern in the fieldof communications Due to the rapid development in mul-timedia services such as high definition (HD) video ultra-HD video and lossless music radio spectrum is increas-ingly needed In order to meet the increasing demand forcommunication systems the research on bandwidth efficientmodulations is extremely urgent Recently many advancedtechnologies have been proposed in the field of high efficientmodulations which own very high data rates and very highspectra efficiency Consequently many researchers begin topay more attention to this breakthrough [1ndash3] The extendedbinary phase shift keying (EBPSK) modulation as one kindof high efficient modulation has very high energy efficiency[4] A special impacting filter (SIF) which can produce highimpact at the phase jumping point constrict bandwidthand extend channel capacity is applied in the demodula-tor [5] Performance can be elevated by using nonlineardemodulation method [6] Introducing wavelet transform

in demodulation system can achieve great results Wavelettransform is a mathematical process that is closely linkedwith the world of graphics [7ndash9] Image processing methodsare always introduced to deal with CWT scalogram such asfeature selection and background subtraction which can beseen in [10ndash12] Meanwhile wavelet transform is a commonmethod for image processing [13 14] Furthermore wavelettheory has been widely used to analyze evaluate pick anddetect signals [15ndash18]

This paper has provided a new EBPSK demodulationsystem based on the continuous wavelet transform (CWT)and the simulation results show that this system has betterperformance than the existing demodulation systems Ourdemodulation system has to be fulfilled by four modulesof SIF CWT image processing system (IPS) and patternclassification (PC) In this paper an adaptive wavelet insteadof manual selection existing wavelets has been developedWe construct an adaptive wavelet based on the modulationsignal without noise and perform image processing on thewavelet scalogram which is the output of CWT A feature

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 513849 9 pageshttpdxdoiorg1011552015513849

2 Mathematical Problems in Engineering

template is generated according to the characteristics of thesignal under noise free condition and the feature templateis then used for IPS Only the information retained afterimage processing can be used to reveal the signal featuresAfter that we perform the signal detection by using a patternrecognition method Section 21 shows the system modelSection 22 shows the modulation signal model The CWTand the adaptive wavelet construction method are shown inSection 23 while in Section 24 we will give a brief presenta-tion of image processing and pattern classification Section 3presents the simulation results under the conditions of whitenoise with uniform distribution colored noise and additivewhite Gaussian noise (AWGN) With the proposed systemthe performance of adaptive wavelet construction methodand manual selection method is compared Furthermore theproposed system using the adaptive wavelet is compared withthe existing linear and nonlinear systems respectively

2 Theoretical and Mathematical Preliminaries

21 SystemModel The system is composed of threemodulesthat is modulation channel and demodulation The modu-lation system creates the modulated signals and the channeladds noise to it the demodulation system is fulfilled by fourprocesses of SIF CWT IPS and PCThe detailed descriptionof the method is illustrated in Figure 1 in which the dashedrectangle shows the demodulation system

The signal of the channel output can be expressed as119908(119896) = 119911(119896) + 119899(119896) and the SIF output signal 119910(119896) canbe expressed as 119910(119896) = 119908(119896) lowast ℎ(119896) where ℎ(119896) is theimpulse response of SIF ldquolowastrdquo represents convolution opera-tionM(119886 119887) shows the wavelet scalogram and C(119886 119887) is theIPS output

22 Mathematical Modulation Model of the EBPSK SignalEBPSK is a kind of modulation system with high spectrumefficiency its modulate signal is defined as follows

1198920 (

119905) = 119860 sin 2120587119891119888119905 0 le 119905 lt 119879

1198921 (t) =

119861 sin (2120587119891119888119905 + 120579) 0 le 119905 lt 120591 0 le 120579 le 120587

119860 sin 2120587119891119888119905 0 lt 120591 le 119905 lt 119879

(1)

where 1198920(119905) and 119892

1(119905) respectively indicate the modulated

signals of bits ldquo0rdquo and ldquo1rdquo 120579 is the modulating angle 119879 =

119873119891119888indicates the temporal length of a code and parameter

119891119888represents the carrier frequency and 119873 the number of

carriers The phase modulation temporal length 120591 = 119870119891119888

in the bit ldquo1rdquo lasted 119870 le 119873 cycles of carrier The amplitudeof 1198921(119905) after jumping is equal to that of 119892

0(119905) which is

represented by 119860 119861 represents the amplitude of 1198921(119905) before

jumping

23 CWT The CWT of a signal 119891(119905) is given by

W119891 (119886 119887) = ⟨119891 Ψ

119886119887⟩

= |119886|minus12

int

R

119891 (119905) Ψ (

119905 minus 119887

119886

)d119905

(2)

SIF

CWT

IPS

PC

Modulation

Channel

Demodulation

y(k)

M(a b)

w(k)

C(a b)

Figure 1 The block diagram of system model

where ldquo119886rdquo represents the scale factor and ldquo119887rdquo is the shift factorandΨ

119886119887(119905) = Ψ((119905minus119887)119886) is awavelet functionwith zeromean

as follows

int

infin

minusinfin

Ψ (119905) d119905 = 0 (3)

CWT is the calculation of the cross covariance betweenthe signal and the wavelet function which is shifted in timeand stretched in scale The coefficient W

119891(119886 119887) indicates

the similarity between the wavelet function and the signalA larger value of W

119891(119886 119887) indicates a better waveforms

match Wavelet coefficient depends on the wavelet functionConsequently in order to detect certain signal the waveformof the wavelet function similar to the signal should bechosenThe advantage of the CWTover the classical templatematching methods arises from the special properties of thewavelet template allowing optimal scale separation of thesignal [19]

It is essential to choose the mother wavelet to makethe easiest identification of the wavelet scalogram featureThe existing wavelet functions are divided into five maintypes finite impulse response (FIR) filter wavelet such asHaar Daubechies (db) Coiflets (coif) and Symlets (sym)biorthogonal wavelet with a FIR filter such as Bior Splines(bior) filter without FIR but with a scale equation such asMeyer (meyr) wavelet wavelet without FIR filter or scaleequation such as Morlet (morl) and Mexican hat (mexh)complex wavelet with a finite impulse and a scale equationsuch as complex Gaussian and Shannon

The selection of a particular wavelet function depends onthe scalogram features to be extracted [20 21] As the adaptivewavelet waveform can be adjusted as requested using theadaptive wavelet can achieve superior results than manualselection existing wavelets We transform bit ldquo1rdquo signal underthe noiseless condition though SIF and then we customizethe SIF output to function ΨEBPSK by orthogonal projectionfor constants As most of the information is concentrated atthe beginning of a bit we cut out 12 temporal length of abit in order to fit custom wavelet which starts from 31198794 ofthe prior code The adaptive wavelet waveform is shown inFigure 2

Mathematical Problems in Engineering 3

Am

plitu

de

Time (s)

0

0 02 04 06 08 1

2

1

3

4

minus1

Figure 2 Adaptive wavelet

24 IPS and PC The wavelet scalogram of coefficients Mgenerated by the signal 119910(119896) is given by the followingequation

M (119886 119887) = ⟨119910 ΨEBPSK⟩

= |119886|minus12

int

R

119910 (119896) ΨEBPSK (

119896 minus 119887

119886

)d119896

(4)

where ΨEBPSK is the custom wavelet functionThewavelet scalogramof coefficientsM includes the char-

acteristic information as well as the redundant informationAs scalogram features are focused in fixed region a waveletscalogram windowing was also proposed for extracting fea-ture information Matrix C transformed by the IPS can beexpressed as follows

C (119886 119887) = M (119886 119887) times I (119886 119887) (5)

where matrix I is the window matrix and it uses ldquo1rdquo and ldquo0rdquoto indicate the highlight regions and the background regionsof bit ldquo1rdquo

We transform a bit ldquo1rdquo signal without noise through SIFand CWT whileM1015840 represents the CWT outputMatrix I canbe expressed as follows

I (119886 119887) =

1

10038161003816100381610038161003816M1015840 (119886 119887)

10038161003816100381610038161003816

gt Th0

10038161003816100381610038161003816M1015840 (119886 119887)

10038161003816100381610038161003816

le Th

(6)

Th is a threshold used to distinguish the highlight regionsand the background regions and it is determined by thesignal and the environment In Section 3 we use Th = 0which indicates that all nonzero sections are highlight sec-tions

Figure 3(a) shows the output of a noise-free signalthrough SIF While Figure 3(b) shows the wavelet scalogramit is displayed with ldquopinkrdquo colormap using the maximumabsolute value in all scales The coefficients line for scale 119886 =

40 is demonstrated in Figure 3(c)Pattern classification is the kernel of image classification

and we utilized the methods of this field in signal classifica-tion to achieve the desired results

The Euclidean distance between transformed matrix Cwhich is the output of IPS and the wavelet scalogramtemplateW

119870(119870 = 1 2) is given by the following equation

119863119870

=1003817100381710038171003817CminusW

119870

1003817100381710038171003817119865

(7)

whereW1represents the scalogram template of bit ldquo1rdquo signal

andW0represents that of bit ldquo0rdquo signal

M10158401015840 represents the CWT output of noiseless bit ldquo0rdquoCoefficient templatesW

1andW

0are respectively defined by

the following equations

W1

(119886 119887) = M1015840 (119886 119887) times I (119886 119887)

W0 (

119886 119887) = M10158401015840 (119886 119887) times I (119886 119887)

(8)

Since the distribution of data for component of eachdimension is not the same we have improved formula (7) bystandardizing each component to equal mean and variance

X(119886 119887) is the mean value of each sample set (C(119886 119887)W1(119886 119887) W

2(119886 119887)) and the standard deviation of each

sample set S(119886 119887) can be expressed as follows

S2 (119886 119887) =

(C (119886 119887) minus X (119886 119887))

2

3

+

(W1

(119886 119887) minus X (119886 119887))

2

3

+

(W0 (

119886 119887) minus X (119886 119887))

2

3

(9)

After improving we can define the Euclidean distanceldquo1198631rdquo as follows

1198631

=

10038171003817100381710038171003817100381710038171003817

CminusW1

S

10038171003817100381710038171003817100381710038171003817119865

(10)

The improved Euclidean distance ldquo1198630rdquo is defined as

follows

1198630

=

10038171003817100381710038171003817100381710038171003817

CminusW0

S

10038171003817100381710038171003817100381710038171003817119865

(11)

The signal characteristics can be detected by Euclideandistance andwe determine that the signal is bit ldquo1rdquo if119863

0gt 1198631

otherwise we will consider the signal as bit ldquo0rdquoThe simulation under the AWGN condition is shown in

Figure 4 Figure 4(a) shows the SIF output of signal mixedwith noise The wavelet scalogram M and the processedmatrix C are shown in Figures 4(b) and 4(c) respectivelywhere we identified the figures with ldquopinkrdquo colormap usingthe maximum absolute value in all scales

3 Experiments and Results

In order to validate the proposed methodology of the CWTbased demodulation system introduced in Section 2 wecompared it with several existing methods (ID AD ML SSTand the proposed system adoptingmanual selectionwavelet)


500 1000 1500 2000 2500

40

60

80

Am

plitu

de

Time (s)

(a)

Scal

es

Time (s)

3032343638404244464850

500 1000 1500 2000 2500

(b)

500 1000 1500 2000 2500

0

Time (s)

50Sc

ales

minus50

(c)

Figure 3 Simulation under noise free condition (a) SIF output (b) wavelet scalogram and (c) coefficients line for scale 119886 = 40

0 500 1000 1500 2000 25000

50

100

150

Am

plitu

de

Time (s)

(a)

500 1000 1500 2000 2500

5

10

15

20

Time (s)

Scal

es

(b)

500 1000 1500 2000 2500

5

10

15

20

Time (s)

Scal

es

(c)

Figure 4 Simulation under AWGN condition (a) SIF output (b) wavelet scalogram and (c) IPS output

The simulations assumed that the system has 1000 sym-bols for training and the reported bit error rate (BER) iscomputed using 15 times 10

5 symbols 119870 = 2 8 16 indicatethat the simulation model is binary octal and hexadecimalThe carrier frequency 119891

119888and parameter 119873 can impact the

power spectral density of the EBPSK signal Amplitude 119860

determines the signal strength of bit ldquo0rdquo and jumped bit ldquo1rdquoand 119861 the signal strength of bit ldquo1rdquo before jumping

In this paper we only discuss the case of 119870 = 2 and wechoose the carrier frequency 119891

119888= 30MHZ and parameters

119873 = 50 119860 = 119861 = 1 and 120579 = 120587 The experiments are sampledat the rate of 119891

119904= 300MHZ

31 Performance Comparisons of the System Proposed andSeveralWell-Known Systems We compared the performanceof the proposed system adopting adaptive wavelet with thenonlinear systems (ID and AD) under different kinds ofenvironments such as white noise with uniform distributionAWGN and colored noise

Figure 5(a) depicts the simulation result under the condi-tion of white noise with uniform distribution It can be seenin Figure 5(a) that while SNR lt minus3 dB BER of the proposedsystem is similar to that of AD and ID While using SNR gt

minus3 dB our method has a lower BER compared to the well-known AD and ID


minus1minus2minus3minus4minus5 0 1 2

10minus4

10minus5

10minus3

10minus2

10minus1BE

R

SNR (dB)

Proposed methodIDAD

(a)

0 05 1 15SNR (dB)

Proposed methodIDAD

10minus4

10minus3

10minus5

10minus2

BER

minus25 minus2 minus15 minus1 minus05

(b)

minus1minus2minus3minus4minus5 0 1 210minus4

10minus3

10minus2

10minus1

BER

SNR (dB)

Proposed methodIDAD

(c)

Figure 5 ID AD and the proposed method under different kinds of environments (a) white noise with uniform distribution (b) AWGNand (c) colored noise

Figure 5(b) shows the simulation results under the envi-ronment of additive white Gaussian noise (AWGN) WhileSNR lt minus1 dB BER of the proposed system has no advantagehowever when the SNR gt minus1 dB our system has a betterresult

Figure 5(c) demonstrates the excellent performance ofthe proposed method under the environment of colorednoise Actually in communications the real channel isalways bandwidth limited which results in colored noise orband-limited noise We have generated the colored noise by

low-pass filtering theGaussianwhite noiseTheparameters ofthis low-pass filter are pass-band corner frequency 119882

119901= 06

stop-band corner frequency 119882119904

= 1 pass-band ripple in dec-ibels 119877

119901= 05 and stop-band attenuation 119877

119904= 40 dB

32 Experimental Results of Systems Based on CWT To showthe competitive performance of our system some experimentresults of other CWT demodulation systems such as specificscales and times (SST) and maximum lines (ML) are shownin Figure 6 All CWT demodulation systems were performed


SNR (dB)

Proposed methodMLSST


10minus4

10minus5

10minus3

10minus2

10minus1

BER

(a)

SNR (dB)

10minus4

10minus5

10minus3

10minus2

BER

0 05 1 15minus25 minus2 minus15 minus1 minus05


(b)

SNR (dB)



10minus3

10minus2

10minus1

BER

(c)

Figure 6 ML SST and the proposed method under different kinds of environments (a) white noise with uniform distribution (b) AWGNand (c) colored noise

using adaptive wavelet As Figure 6 revealsML algorithmhasthe highest BER under the environment of AWGN ML andSST have a similar performance under the condition of whitenoise with uniform distribution and colored noise While theproposed method yields the lowest BER under all studiedenvironments

33 Simulation Results of DifferentWavelets In order to dem-onstrate the superiority of the adaptive wavelet we simulated

the proposed system adopting manual selection existingwavelets which include db2 morl Meyer mexh and sym2The demodulation performances are presented in Figure 7for all the studied noise types

Figure 7(a) shows the simulation results of the adaptivewavelet and several existing wavelets under the condition ofwhite noise with uniform distribution Experiments underthe condition of AWGN are shown in Figure 7(b) Figure 7(c)shows the simulation results under the condition of colored


Proposed methodmexhdb2

meyrmorletsym2

10minus4

10minus5

10minus3

10minus2

10minus1

100BE

R

SNR (dB)minus1minus2minus3minus4minus5 0 1 2

(a)BE

R


meyrmorletsym2


10minus4

10minus5

10minus3

10minus2

10minus1

100

(b)


meyrmorletsym2

10minus4

10minus3

10minus2

10minus1

100

BER


(c)

Figure 7 Proposed system adopting different wavelets under studied environments (a) white noise with uniform distribution (b) AWGNand (c) colored noise

noise It can be realized from Figure 7 that mexh anddb2 are more suitable to EBPSK compared with the otherexisting wavelets however the adaptive wavelet yields thebest performance in all wavelets

The computational complexity of all studied systems isshown in Table 1 119899 is the length of code from which wesee that ID and ADrsquos asymptotical complexity is proportionalwith the parameter 119899 and the complexity of ML SST andthe proposed system using manual selection wavelets is thesame as the complexity of the proposed systemusing adaptivewavelet They are all quadratic-time complexity AlthoughID and AD have lower complexity the proposed system has

better demodulation performance than them and their BERare higher than the proposed method which can be seen inFigure 5ML SST and the proposed system adoptingmanualselection wavelets have the same complexity as the proposedmethod while their BER are higher than the proposedmethod which can be seen in Figures 6 and 7

4 Discussion

Thispaper presents an adaptivewavelet constructionmethodUnlike manual wavelet selection methods this algorithm


Table 1 Computational complexity

Methods ComplexityID 119874 (119899)

AD 119874 (119899)

ML 119874 (1198992)

SST 119874 (1198992)

Our systemAdaptive wavelet 119874 (119899

2)

Manual selection 119874 (1198992)

does not need to select wavelet in the light of experimentsThe wavelet is constructed based on the transformed signalwaveform Therefore the adaptive construction method hasbetter real-time capability and higher accuracy

SIF CWT IPS and PC are introduced into the demodula-tion system CWT transforms the signal to the wavelet scalo-gram IPS highlights the signal information and enhancesthe distinction between the signal and the noise PC fulfillsthe signal detection and the detection results show thatthe proposed system obtains lower BER than the existingsystems

The proposed approach can be combined with any signalclassification and detection system The wavelet scalogramclassification integratedwith the image processing system canbe used in fault detection medical signal processing andparticular signal picking systems

Our demodulation system has no advantage in terms ofcomplexity and the system may reflect the limited advantageat extremely low SNR probably because image process-ing procedure enhances the noise in a manner similar tothe signal information at extremely low SNR For furtherimprovement in the demodulation performance and morereduction in the complexity of the algorithm future workwillfocus on the feature extraction and the system optimization

5 Conclusion

A novel EBPSK demodulation system based on CWT isproposed in this study An adaptive wavelet is proposed totransform the SIF output signal IPS is utilized to enhancethe distinction between the signal and the noise The sys-tem is detected by PC The performance of the proposedsystem is checked under the condition of white noise withuniform distribution AWGN and colored noise The resultsare compared with AD ID ML and SST techniques Ourresults show that the proposed system has lower BER Theproposed system adopting adaptive wavelet is compared withthe proposed system adopting traditional manual selectionwavelets and the results show that the adaptive wavelet ismore suitable to the transformed signal

Conflict of Interests

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

Acknowledgments

Thework is supported by the National Key Technology RampDProgram under the Grant 2012BAH15B00 and the NationalNatural Science Foundation of China (nos 61271204 and610011024)

References

[1] J Zhang W Bai L Cai Y Xu G Song and Q Gan ldquoObserva-tion of ultra-narrow band plasmon induced transparency basedon large-area hybrid plasmon-waveguide systemsrdquo AppliedPhysics Letters vol 99 no 18 Article ID 181120 pp 1ndash3 2011

[2] X Liu ldquoA novel ultra-narrow transmission-band fiber Bragggrating and its application in a single-longitudinal-mode fiberlaser with improved efficiencyrdquo Optics Communications vol280 no 1 pp 147ndash152 2007

[3] C Moser and F Havermeyer ldquoUltra-narrow-band tunablelaserline notch filterrdquo Applied Physics B vol 95 no 3 pp 597ndash601 2009

[4] LWu andM Feng ldquoOn BER performance of EBPSK-MODEMin AWGN channelrdquo Sensors vol 10 no 4 pp 3824ndash3834 2010

[5] M Feng L Wu J Ding and C Qi ldquoBER analysis and verifica-tion of EBPSK system in AWGN channerdquo IEICE Transactionson Communications vol E94-B no 3 pp 806ndash809 2011

[6] X Chen and L Wu ldquoNonlinear demodulation and channelcoding in EBPSK schemerdquo The Scientific World Journal vol2012 Article ID 180469 7 pages 2012

[7] Y Zhang S Wang Y Huo L Wu and A Liu ldquoFeatureextraction of brain MRI by stationary wavelet transform and itsapplicationsrdquo Journal of Biological Systems vol 18 no 1 pp 115ndash132 2010

[8] T Cheng B Rivard A G Sanchez-Azofeifa J-B Feret SJacquemoud and S L Ustin ldquoPredicting leaf gravimetric watercontent from foliar reflectance across a range of plant speciesusing continuous wavelet analysisrdquo Journal of Plant Physiologyvol 169 no 12 pp 1134ndash1142 2012

[9] Y Zhang S Wang G Ji and Z Dong ldquoGenetic pattern searchand its application to brain image classificationrdquo MathematicalProblems in Engineering vol 2013 Article ID 580876 8 pages2013

[10] T-P Le and P Paultre ldquoModal identification based on continu-ous wavelet transform and ambient excitation testsrdquo Journal ofSound and Vibration vol 331 no 9 pp 2023ndash2037 2012

[11] X Jiang Z J Ma and W-X Ren ldquoCrack detection from theslope of the mode shape using complex continuous wavelettransformrdquo Computer-Aided Civil and Infrastructure Engineer-ing vol 27 no 3 pp 187ndash201 2012

[12] A Lazaro A Ramos D Girbau and R Villarino ldquoChiplessUWB RFID tag detection using continuous wavelet transformrdquoIEEE Antennas and Wireless Propagation Letters vol 10 pp520ndash523 2011

[13] Y Zhang S Wang and G Ji ldquoA rule-based model forbankruptcy prediction based on an improved genetic ant colonyalgorithmrdquo Mathematical Problems in Engineering vol 2013Article ID 753251 10 pages 2013

[14] Y Zhang S Wang G Ji and Z Dong ldquoAn MR brain imagesclassifier system via particle swarm optimization and kernelsupport vector machinerdquoThe ScientificWorld Journal vol 2013Article ID 130134 9 pages 2013


[15] J T Bialasiewicz D Gonzalez J Balcells and J Gago ldquoWavelet-based approach to evaluation of signal integrityrdquo IEEE Transac-tions on Industrial Electronics vol 60 no 10 pp 4590ndash45982013

[16] S Banerjee and M Mitra ldquoApplication of cross wavelet trans-form for ECG pattern analysis and classicationrdquo IEEE Trans-actions on Instrumentation and Measurement vol 63 no 2 pp326ndash333 2014

[17] N Karamzadeh G J Doloei and AM Reza ldquoAutomatic earth-quake signal onset picking based on the continuous wavelettransformrdquo IEEE Transactions on Geoscience and Remote Sens-ing vol 51 no 5 pp 2666ndash2674 2013

[18] F B Costa ldquoFault-induced transient detection based on real-time analysis of the wavelet coefficient energyrdquo IEEE Transac-tions on Power Delivery vol 29 no 1 pp 140ndash153 2014

[19] V Bostanov ldquoBCI competition 2003mdashdata sets Ib and IIbfeature extraction from event-related brain potentials with thecontinuous wavelet transform and the t-value scalogramrdquo IEEETransactions on Biomedical Engineering vol 51 no 6 pp 1057ndash1061 2004

[20] L Smital M Vitek J Kozumplik and I Provaznik ldquoAdaptivewavelet wiener filtering of ECG signalsrdquo IEEE Transactions onBiomedical Engineering vol 60 no 2 pp 437ndash445 2013

[21] J Gilles ldquoEmpirical wavelet transformrdquo IEEE Transactions onSignal Processing vol 61 no 16 pp 3999ndash4010 2013

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template is generated according to the characteristics of thesignal under noise free condition and the feature templateis then used for IPS Only the information retained afterimage processing can be used to reveal the signal featuresAfter that we perform the signal detection by using a patternrecognition method Section 21 shows the system modelSection 22 shows the modulation signal model The CWTand the adaptive wavelet construction method are shown inSection 23 while in Section 24 we will give a brief presenta-tion of image processing and pattern classification Section 3presents the simulation results under the conditions of whitenoise with uniform distribution colored noise and additivewhite Gaussian noise (AWGN) With the proposed systemthe performance of adaptive wavelet construction methodand manual selection method is compared Furthermore theproposed system using the adaptive wavelet is compared withthe existing linear and nonlinear systems respectively

2 Theoretical and Mathematical Preliminaries

21 SystemModel The system is composed of threemodulesthat is modulation channel and demodulation The modu-lation system creates the modulated signals and the channeladds noise to it the demodulation system is fulfilled by fourprocesses of SIF CWT IPS and PCThe detailed descriptionof the method is illustrated in Figure 1 in which the dashedrectangle shows the demodulation system

The signal of the channel output can be expressed as119908(119896) = 119911(119896) + 119899(119896) and the SIF output signal 119910(119896) canbe expressed as 119910(119896) = 119908(119896) lowast ℎ(119896) where ℎ(119896) is theimpulse response of SIF ldquolowastrdquo represents convolution opera-tionM(119886 119887) shows the wavelet scalogram and C(119886 119887) is theIPS output

22 Mathematical Modulation Model of the EBPSK SignalEBPSK is a kind of modulation system with high spectrumefficiency its modulate signal is defined as follows

1198920 (

119905) = 119860 sin 2120587119891119888119905 0 le 119905 lt 119879

1198921 (t) =

119861 sin (2120587119891119888119905 + 120579) 0 le 119905 lt 120591 0 le 120579 le 120587

119860 sin 2120587119891119888119905 0 lt 120591 le 119905 lt 119879

(1)

where 1198920(119905) and 119892

1(119905) respectively indicate the modulated

signals of bits ldquo0rdquo and ldquo1rdquo 120579 is the modulating angle 119879 =

119873119891119888indicates the temporal length of a code and parameter

119891119888represents the carrier frequency and 119873 the number of

carriers The phase modulation temporal length 120591 = 119870119891119888

in the bit ldquo1rdquo lasted 119870 le 119873 cycles of carrier The amplitudeof 1198921(119905) after jumping is equal to that of 119892

0(119905) which is

represented by 119860 119861 represents the amplitude of 1198921(119905) before

jumping

23 CWT The CWT of a signal 119891(119905) is given by

W119891 (119886 119887) = ⟨119891 Ψ

119886119887⟩

= |119886|minus12

int

R

119891 (119905) Ψ (

119905 minus 119887

119886

)d119905

(2)

SIF

CWT

IPS

PC

Modulation

Channel

Demodulation

y(k)

M(a b)

w(k)

C(a b)

Figure 1 The block diagram of system model

where ldquo119886rdquo represents the scale factor and ldquo119887rdquo is the shift factorandΨ

119886119887(119905) = Ψ((119905minus119887)119886) is awavelet functionwith zeromean

as follows

int

infin

minusinfin

Ψ (119905) d119905 = 0 (3)

CWT is the calculation of the cross covariance betweenthe signal and the wavelet function which is shifted in timeand stretched in scale The coefficient W

119891(119886 119887) indicates

the similarity between the wavelet function and the signalA larger value of W

119891(119886 119887) indicates a better waveforms

match Wavelet coefficient depends on the wavelet functionConsequently in order to detect certain signal the waveformof the wavelet function similar to the signal should bechosenThe advantage of the CWTover the classical templatematching methods arises from the special properties of thewavelet template allowing optimal scale separation of thesignal [19]

It is essential to choose the mother wavelet to makethe easiest identification of the wavelet scalogram featureThe existing wavelet functions are divided into five maintypes finite impulse response (FIR) filter wavelet such asHaar Daubechies (db) Coiflets (coif) and Symlets (sym)biorthogonal wavelet with a FIR filter such as Bior Splines(bior) filter without FIR but with a scale equation such asMeyer (meyr) wavelet wavelet without FIR filter or scaleequation such as Morlet (morl) and Mexican hat (mexh)complex wavelet with a finite impulse and a scale equationsuch as complex Gaussian and Shannon

The selection of a particular wavelet function depends onthe scalogram features to be extracted [20 21] As the adaptivewavelet waveform can be adjusted as requested using theadaptive wavelet can achieve superior results than manualselection existing wavelets We transform bit ldquo1rdquo signal underthe noiseless condition though SIF and then we customizethe SIF output to function ΨEBPSK by orthogonal projectionfor constants As most of the information is concentrated atthe beginning of a bit we cut out 12 temporal length of abit in order to fit custom wavelet which starts from 31198794 ofthe prior code The adaptive wavelet waveform is shown inFigure 2


Am

plitu

de

Time (s)

0

0 02 04 06 08 1

2

1

3

4

minus1



M (119886 119887) = ⟨119910 ΨEBPSK⟩

= |119886|minus12

int

R

119910 (119896) ΨEBPSK (

119896 minus 119887

119886

)d119896

(4)



C (119886 119887) = M (119886 119887) times I (119886 119887) (5)



I (119886 119887) =

1

10038161003816100381610038161003816M1015840 (119886 119887)

10038161003816100381610038161003816

gt Th0

10038161003816100381610038161003816M1015840 (119886 119887)

10038161003816100381610038161003816

le Th

(6)







119863119870

=1003817100381710038171003817CminusW

119870

1003817100381710038171003817119865

(7)




1andW



W1

(119886 119887) = M1015840 (119886 119887) times I (119886 119887)

W0 (

119886 119887) = M10158401015840 (119886 119887) times I (119886 119887)

(8)





S2 (119886 119887) =

(C (119886 119887) minus X (119886 119887))

2

3

+

(W1

(119886 119887) minus X (119886 119887))

2

3

+

(W0 (

119886 119887) minus X (119886 119887))

2

3

(9)


1198631

=

10038171003817100381710038171003817100381710038171003817

CminusW1

S

10038171003817100381710038171003817100381710038171003817119865

(10)


follows

1198630

=

10038171003817100381710038171003817100381710038171003817

CminusW0

S

10038171003817100381710038171003817100381710038171003817119865

(11)


0gt 1198631






500 1000 1500 2000 2500

40

60

80

Am

plitu

de

Time (s)

(a)

Scal

es

Time (s)

3032343638404244464850

500 1000 1500 2000 2500

(b)

500 1000 1500 2000 2500

0

Time (s)

50Sc

ales

minus50

(c)


0 500 1000 1500 2000 25000

50

100

150

Am

plitu

de

Time (s)

(a)

500 1000 1500 2000 2500

5

10

15

20

Time (s)

Scal

es

(b)

500 1000 1500 2000 2500

5

10

15

20

Time (s)

Scal

es

(c)










119904= 300MHZ






10minus4

10minus5

10minus3

10minus2

10minus1BE

R

SNR (dB)

Proposed methodIDAD

(a)

0 05 1 15SNR (dB)

Proposed methodIDAD

10minus4

10minus3

10minus5

10minus2

BER


(b)


10minus3

10minus2

10minus1

BER

SNR (dB)

Proposed methodIDAD

(c)





119901= 06




119904= 40 dB



SNR (dB)



10minus4

10minus5

10minus3

10minus2

10minus1

BER

(a)

SNR (dB)

10minus4

10minus5

10minus3

10minus2

BER



(b)

SNR (dB)



10minus3

10minus2

10minus1

BER

(c)








meyrmorletsym2

10minus4

10minus5

10minus3

10minus2

10minus1

100BE

R


(a)BE

R


meyrmorletsym2


10minus4

10minus5

10minus3

10minus2

10minus1

100

(b)


meyrmorletsym2

10minus4

10minus3

10minus2

10minus1

100

BER


(c)





4 Discussion





AD 119874 (119899)

ML 119874 (1198992)

SST 119874 (1198992)


2)






5 Conclusion




Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Am

plitu

de

Time (s)

0

0 02 04 06 08 1

2

1

3

4

minus1



M (119886 119887) = ⟨119910 ΨEBPSK⟩

= |119886|minus12

int

R

119910 (119896) ΨEBPSK (

119896 minus 119887

119886

)d119896

(4)



C (119886 119887) = M (119886 119887) times I (119886 119887) (5)



I (119886 119887) =

1

10038161003816100381610038161003816M1015840 (119886 119887)

10038161003816100381610038161003816

gt Th0

10038161003816100381610038161003816M1015840 (119886 119887)

10038161003816100381610038161003816

le Th

(6)







119863119870

=1003817100381710038171003817CminusW

119870

1003817100381710038171003817119865

(7)




1andW



W1

(119886 119887) = M1015840 (119886 119887) times I (119886 119887)

W0 (

119886 119887) = M10158401015840 (119886 119887) times I (119886 119887)

(8)





S2 (119886 119887) =

(C (119886 119887) minus X (119886 119887))

2

3

+

(W1

(119886 119887) minus X (119886 119887))

2

3

+

(W0 (

119886 119887) minus X (119886 119887))

2

3

(9)


1198631

=

10038171003817100381710038171003817100381710038171003817

CminusW1

S

10038171003817100381710038171003817100381710038171003817119865

(10)


follows

1198630

=

10038171003817100381710038171003817100381710038171003817

CminusW0

S

10038171003817100381710038171003817100381710038171003817119865

(11)


0gt 1198631






500 1000 1500 2000 2500

40

60

80

Am

plitu

de

Time (s)

(a)

Scal

es

Time (s)

3032343638404244464850

500 1000 1500 2000 2500

(b)

500 1000 1500 2000 2500

0

Time (s)

50Sc

ales

minus50

(c)


0 500 1000 1500 2000 25000

50

100

150

Am

plitu

de

Time (s)

(a)

500 1000 1500 2000 2500

5

10

15

20

Time (s)

Scal

es

(b)

500 1000 1500 2000 2500

5

10

15

20

Time (s)

Scal

es

(c)










119904= 300MHZ






10minus4

10minus5

10minus3

10minus2

10minus1BE

R

SNR (dB)

Proposed methodIDAD

(a)

0 05 1 15SNR (dB)

Proposed methodIDAD

10minus4

10minus3

10minus5

10minus2

BER


(b)


10minus3

10minus2

10minus1

BER

SNR (dB)

Proposed methodIDAD

(c)





119901= 06




119904= 40 dB



SNR (dB)



10minus4

10minus5

10minus3

10minus2

10minus1

BER

(a)

SNR (dB)

10minus4

10minus5

10minus3

10minus2

BER



(b)

SNR (dB)



10minus3

10minus2

10minus1

BER

(c)








meyrmorletsym2

10minus4

10minus5

10minus3

10minus2

10minus1

100BE

R


(a)BE

R


meyrmorletsym2


10minus4

10minus5

10minus3

10minus2

10minus1

100

(b)


meyrmorletsym2

10minus4

10minus3

10minus2

10minus1

100

BER


(c)





4 Discussion





AD 119874 (119899)

ML 119874 (1198992)

SST 119874 (1198992)


2)






5 Conclusion




Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










500 1000 1500 2000 2500

40

60

80

Am

plitu

de

Time (s)

(a)

Scal

es

Time (s)

3032343638404244464850

500 1000 1500 2000 2500

(b)

500 1000 1500 2000 2500

0

Time (s)

50Sc

ales

minus50

(c)


0 500 1000 1500 2000 25000

50

100

150

Am

plitu

de

Time (s)

(a)

500 1000 1500 2000 2500

5

10

15

20

Time (s)

Scal

es

(b)

500 1000 1500 2000 2500

5

10

15

20

Time (s)

Scal

es

(c)










119904= 300MHZ






10minus4

10minus5

10minus3

10minus2

10minus1BE

R

SNR (dB)

Proposed methodIDAD

(a)

0 05 1 15SNR (dB)

Proposed methodIDAD

10minus4

10minus3

10minus5

10minus2

BER


(b)


10minus3

10minus2

10minus1

BER

SNR (dB)

Proposed methodIDAD

(c)





119901= 06




119904= 40 dB



SNR (dB)



10minus4

10minus5

10minus3

10minus2

10minus1

BER

(a)

SNR (dB)

10minus4

10minus5

10minus3

10minus2

BER



(b)

SNR (dB)



10minus3

10minus2

10minus1

BER

(c)








meyrmorletsym2

10minus4

10minus5

10minus3

10minus2

10minus1

100BE

R


(a)BE

R


meyrmorletsym2


10minus4

10minus5

10minus3

10minus2

10minus1

100

(b)


meyrmorletsym2

10minus4

10minus3

10minus2

10minus1

100

BER


(c)





4 Discussion





AD 119874 (119899)

ML 119874 (1198992)

SST 119874 (1198992)


2)






5 Conclusion




Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











10minus4

10minus5

10minus3

10minus2

10minus1BE

R

SNR (dB)

Proposed methodIDAD

(a)

0 05 1 15SNR (dB)

Proposed methodIDAD

10minus4

10minus3

10minus5

10minus2

BER


(b)


10minus3

10minus2

10minus1

BER

SNR (dB)

Proposed methodIDAD

(c)





119901= 06




119904= 40 dB



SNR (dB)



10minus4

10minus5

10minus3

10minus2

10minus1

BER

(a)

SNR (dB)

10minus4

10minus5

10minus3

10minus2

BER



(b)

SNR (dB)



10minus3

10minus2

10minus1

BER

(c)








meyrmorletsym2

10minus4

10minus5

10minus3

10minus2

10minus1

100BE

R


(a)BE

R


meyrmorletsym2


10minus4

10minus5

10minus3

10minus2

10minus1

100

(b)


meyrmorletsym2

10minus4

10minus3

10minus2

10minus1

100

BER


(c)





4 Discussion





AD 119874 (119899)

ML 119874 (1198992)

SST 119874 (1198992)


2)






5 Conclusion




Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










SNR (dB)



10minus4

10minus5

10minus3

10minus2

10minus1

BER

(a)

SNR (dB)

10minus4

10minus5

10minus3

10minus2

BER



(b)

SNR (dB)



10minus3

10minus2

10minus1

BER

(c)








meyrmorletsym2

10minus4

10minus5

10minus3

10minus2

10minus1

100BE

R


(a)BE

R


meyrmorletsym2


10minus4

10minus5

10minus3

10minus2

10minus1

100

(b)


meyrmorletsym2

10minus4

10minus3

10minus2

10minus1

100

BER


(c)





4 Discussion





AD 119874 (119899)

ML 119874 (1198992)

SST 119874 (1198992)


2)






5 Conclusion




Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











meyrmorletsym2

10minus4

10minus5

10minus3

10minus2

10minus1

100BE

R


(a)BE

R


meyrmorletsym2


10minus4

10minus5

10minus3

10minus2

10minus1

100

(b)


meyrmorletsym2

10minus4

10minus3

10minus2

10minus1

100

BER


(c)





4 Discussion





AD 119874 (119899)

ML 119874 (1198992)

SST 119874 (1198992)


2)






5 Conclusion




Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra












AD 119874 (119899)

ML 119874 (1198992)

SST 119874 (1198992)


2)






5 Conclusion




Acknowledgments


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article a novel demodulation system...

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