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New Techniques for the Baud Duration Estimation NEW TECHNIQUES FOR THE BAUD DURATION ESTIMATION E E Azzouz and A K Nandi Department of Electronic and Electrical Engineering University of Strathclyde Glasgow G XW U K Tel Fax Email asokeeeestrathacuk ABSTRACT baud durations This work is concerned with the sec ond category range of baud durations The aim of this pap er is to intro duce fast and reli In Wegener intro duced a review ab out the dier able baud duration estimators This work is concerned ent metho ds used for baud duration estimations He with the symb ols transitions sequence extraction and mentioned that the most simple baud duration estima the baud duration estimation The symb ols transitions tion metho d assumes that there is at least one duration sequence is extracted using one of three metho ds the baud was received in the observed sequence which levelcrossing metho d the derivative metho d and the requires long signal duration to achieveandsortthe wavelet metho d Subsequently the baud duration is es sequence of transitions dierence in an ascending or timated by applying the greatest common divisor prin der Then consider the rst element as the baud du ciples on the symb ols transitions dierence sequence ration and compare the rest of the transition dierence sequence with that element However this metho d re Intro duction quires a priori information ab out the lower limit of the Automatic estimation of baud duration is very essen baud rate estimation In it is mentioned that Gaby tial for automatic digital mo dulation recognition and and McMillan intro duced an metho d for baud dura digital symb ol sequence extraction By integrating the tion estimation based on the pattern analysis but this automatic baud duration estimator into an electronic metho d requires long signal duration There are some supp ort measurement receiver including an energy de other metho ds based on baud features extraction In tector a directional nder and a digital mo dulation it is mentioned that all these metho ds are mainly used identier will increase the ability of information extrac in the oline analysis tion Several techniques used for baud duration estima In the following section three new and fast metho ds tion are intro duced in for baud duration estimations is intro duced In section There are many practical techniques for baud du computer simulations for test signals used in p erfor ration estimations One of these techniques utilizes the mance evaluations are presentedInsectionacompar averaged sp ectrum of the digitally mo dulated signals It ison b etween the develop ed metho ds is intro duced The is well known that all digitally mo dulated signals have pap er is concluded in section fsin xxg sp ectrum shap e with main lob e width equal to twice the baud rate recipro cal of the baud duration Baud duration estimation metho ds except the binary FSK signal sp ectrum consists of two fsin xxg centered at the mark and space frequencies In this pap er three metho ds for the online baud dura Thus by observing the averaged sp ectrum one can tion estimation are intro duced The functional owchart measure the baud duration This metho d requires long for these is shown in Fig Once the correct mo dula signal duration Hence this metho d is used in the o tion typ e of digitally mo dulated signals is determined line analysis the baud duration estimation can b e achieved easily In automatic signal classication systems no priori If the input signal is ASK the interested sequence is information ab out the exact signal parameters as well the instantaneous amplitude at If the input signal is as the signal nature is available Sometimes ranges for PSK the interested sequence is the instantaneous phase some parameters such as carrier frequencies and baud t Finally if the input signal is FSK the interested durations are sp ecied Indeed there are three system sequence is the instantaneous frequency f t For the mathematical expressions of the instantaneous ampli categories according to the amount of the available priori tude phase and frequency see baud duration information These are systems with The only dierence b etween the develop ed metho ds no priori information systems with dened range of is in the way for extracting the transition sequence In baud durations and systems with dened a list of one of these two metho ds the durations b etween suc the rst metho d the transition sequence extraction is cessive transitions are obtained To the list of these based on the levelcrossing of the input sequence Note estimated durations the greatest common divisor prin that in binary mo dulations the levelcrossing is equiv ciple GCD is applied to measure the common baud alent to the zerocrossings In the second metho d the duration of the received signal extraction of the transition sequence is based on the the determination of the spikes in the derivative of the input sequence The dierentiation of the input sequence may Computer Simulations be achieved in one of twoways in time domain using The carrier frequency f the sampling rate f and c s the numerical dierence and in frequency domain using the symbol rate r were assigned the values kHz s the Fourier transform prop erty as follows kHz and kHz resp ectively The generation of the mo dulating symb ol sequence comprised the follow Y f j f X f ing steps where Xf is the Fourier transform of the input se The average value x of a simulated sp eechsignal av quence xt and Yf is the Fourier transform of the sequence fxig was calculated derivativeofxt Thus y t can b e obtained through the second use of the Fourier transform as The numb er of samples p er symb ol duration N b was determined from the assumed symb ol and y tIF T fY f g sampling rates Due to the numerical problems asso ciated with the The simulated sp eech signal sequence fxig was di numerical dierence the authors use the frequency do vided into adjacent sets of N samples Then b main metho d which gives more smo othing in the deriva in every set if the numb er of samples exceeding tive sequence In this metho d the symb ol transitions x was larger than samples the set was rep av sequence is identied as the set of spikes in the deriva resented by binary bit otherwise the set was tive sequence Fig shows a bandlimited binary se represented by a binary quence and its derivative using and The third metho d is based on the use of the wavelet transform ASK PSK and FSK signals were derived from as a metho d for edge detection In wavelet transform signals are decomp osed into multiscale details As f i s ia cos N i signals are decomp osed into elementary frequencies the s f s wavelet transform can measure the lo cal regularityofa signal such as the p erio dicity in digitally mo dulated sig The selection of the parameters a f and were nals In this metho d the symb ol transitions sequence made as shown in Table to simulate the ab ove is identied as a set of the spikes that o ccurs at the mentioned digitally mo dulated signals same p osition at several adjacent scales Direct correla Every communication transmitter has a nite trans tion of the wavelet transform at dierent scales are used mission bandwidth Consequently the transmitted sig to identify the symb ol transitions sequence In wavelet nal is bandlimited Therefore the simulated mo du transform there are manytyp es of lter for the dierent lated signals were bandlimited to make them represent signal pro cessing applications In this work we use the more realistic test signals The bandlimitation of dig lter intro duced by Mal lat for spikes detection The itally mo dulated signals was exercised after generation rst six scales are computed using Mal lat lter then the Note that digital mo dulation systems are usually im direct spatial correlations b etween the rst six scales of plemented in practice as shiftkeying systems and hence the wavelet transform are calculated as cannot b e regarded as versions of analogue mo dulation systems In this case the simulated digitally mo du Y lated signals were bandlimited to bandwidth containing CorrL W i LL N of the total average p ower according to i Z Z f B c where W i are the scales of wavelet transform us G f df G f df s s ing Mal lat lter i is the scale number of the wavelet f B c transform and N is numb er of samples of a signal under consideration Fig demonstrates the rst six scales where G f isthepower sp ectral density of the mo d s of the wavelet transform for a noisy bandlimited bi ulated signal s t For the analytic expressions of the nary sequence instantaneous amplitude for an ASK bandwidth for dierenttyp es of digital mo dula signal Also the rst ve direct correlation dened by tion see App endix C In our simulations the band b etween the extracted scales are shown in Fig width for ASK PSK and FSK are chosen to b e After determining the symb ols transitions sequence by r r and r resp ectively s s s Performance Evaluations E E Azzouz and A K Nandi Automatic identi cation of digital mo dulations Signal Pro cessing Simulations of three bandlimited binary digitally Vol No Novemb er pp mo dulated signals ASK PSK and FSK corrupted H Urkowitz Signal theory and random pro with a bandlimited Gaussian noise have b een carried cesses Artech House Inc out at dierent SNR to evaluate the p erformance of the prop osed metho ds Sample results are presented in the O Rioul and M Vetterli Wavelets and signal following tables at the SNR of and dB It is pro cessing IEEE Signal pro cessing Magazine Vol worth noting that all these
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