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

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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 results are derived from

No pp Oct

realizations for each mo dulation typ es of interest The

p erformance of these metho ds is measured at two esti

S Mallat and W L Hwang Singularity detection

mation errors values and For the metho d

and pro cessing with wavelets IEEE Trans Infor

I levelcrossing it is clear that at SNR dB the

mation TheoryVol No pp March

probability of correct estimation of the baud duration is

except PSK if the accuracy of estima

Y Xu and J B Weaver DMHealy JrLu and

tion is within of the true value Meanwhileifthe

Jian Lu Wavelet transform domain lters A

accuracy of baud duration estimation is the prob

spatially selective noise ltration technique IEEE

ability of correct estimation is For the metho d I I

Trans Image Pro cessing Vol No pp

derivative and at SNR dB the probabilityofcor

Nov

rect estimation is if the accuracy of estimation

is within of the true value Furthermore if the

K S Shanmugam Digital and analogue commu

accuracy of baud duration estimation is the prob

nication systems John wiley and sons Inc

ability of correct estimation is For the metho d

III Wavelet and at SNR dB the probabilityof

correct estimation is except PSK when

Metho d I Metho d I I Metho d I I I

the accuracy of estimation is within of the true

SNR

value If the accuracy of baud duration estimation is

the probability of correct estimation is for

ASK and FSK but for PSK is

Conclusions

Table Baud duration estimation accuracy ASK

In this pap er fast and reliable baud duration estima

tors have b een intro duced Three metho ds the level

crossing metho d the spikes determination metho d and

the wavelet transform principles Sample results have

b een presented at the SNR of dB and dB

Metho d I Metho d I I Metho d I I I

SNR

only It is found that the threshold SNR for successful

baud duration estimation at a success rate greater than

is ab out dB The most interesting observation

is that these metho ds can b e extended to larger number

of levels M Currentlythework is under way

in implementing and testing these metho ds for M

as well as in radar applications such as pulse width and

Table Baud duration estimation accuracy PSK

pulse rep etition p erio d estimations

References

A W Wegener Practical techniques for baud

Metho d I Metho d I I Metho d I I I

SNR

rate estimation IEEE pp IV

L W Couch I I Digital and analogue communica

tion systems fourth edition Maxwell Macmillan

Canda Inc

G Gaby and W McMillan Automatic bit pat

Table Baud duration estimation accuracy FSK

tern analysis of communication signals Pro ceed ings ICASSP pp April Noisy instant. amplitude Scale (4) 1.5 1.5 Received Signal 1 1 0.5

0 0.5 Instantaneous amplitude −0.5

Pre-processing & 0 −1 Instantaneous phase 0 1000 2000 3000 0 1000 2000 Scale (1) Scale (5) Modulation recognition 0.1 1.5 Instantaneous frequency 1 0.05 0.5 0 0 −0.05 1) Level-crossing method −0.5

Symbols transitions −0.1 −1 2) Derivative method 0 1000 2000 0 1000 2000 Scale (2) Scale (6) sequence extraction 0.4 2 3) Wavelet transform method 0.2 1

0 0

−0.2 −1

−0.4 −2 0 1000 2000 0 1000 2000 Greatest common divisor Baud duration estimation Scale (3) (GCD) 1

0.5 SNR = 20 dB

Figure Blo ck diagram for the prop osed metho ds 0 Number of samples is 2048

−0.5

0 1000 2000

Figure First six scales of the instant amplitude for ASK Number of samples is 2048 SNR = 20 dB

Noisy instant. amplitude 1.1 First correlation Fourth correlation 1 1 1 0.8 0.9 0.5

0.8 0.6 0 0.7 0.4 0.6 −0.5 0.5 0.2

0.4 0 −1 0 1000 2000 0 1000 2000 0.3

0.2 Second correlation Fifth correlation 1 1 0.1 0 500 1000 1500 2000 0.8

0.5 0.6

0.4 Derivative of Instant. Ampli. 10 0 0.2

0 5 −0.5 −0.2 0 1000 2000 0 1000 2000

0 Third correlation 1

0.8 −5 SNR = 20 dB

0.6 Number of Samples is 2048 −10 0.4

0.2 −15 0 500 1000 1500 2000 0

−0.2

0 1000 2000

Figure Instant amplitude and its derivative

Figure First ve correlation sequences