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A Digital Approach to Clock Recovery inGeneralized Minimum Shift KeyingAbsh ret-A new method for clock recovery to be used with general-

ized minimum -shift-keying modulations is presented. Attractive featuresof the method are that it is suited for digital implemen tation and thatits performance is not affected by the camer phase recovery process.Clod reference is extracted by passing the sampled baseband waveformthrough the cascade of a nonlinearity, followed by a digital differentiatorwhose average output represents the error signal to be employed in atracking loop. The performance of this scheme is analyzed by means ofsimulation, both in the steady state and in transient conditions. Track-ing errors are comp ared with those attained by the well-known De Budasynchronizer and with the Cramer-Rao lower bound.

I. INTRODUCTIONENERALIZED minimum-shift-keying (MSK) modula-G ion has received considerable attention in the recent past

due to its attractive properties such as constant envelope,bandwidth efficiency, and simplicity of receiver implemen-tation [11-[3]. Receiver operation, however, requires knowl-edge of carrier phase and symbol timing, which, in order toavoid waste of power, must be extracted from the information-bearing w aveform by m eans of a self-synchronizin g algorithm .Global approaches, such as maximum-likelihood (ML) ormax imum -a-poste riori (MAP) based joint estimation of car-rier phase, symbol timing, and symbol sequence [4], [5], ar eof considerable theoretical interest but usually lead to mech-anizations of discouraging complexity. In many practical sit-uations, simplified or ad ho c techniques may be preferred,wherein carrier and symbol timing are reconstructed indepen-dent of one another or in a nonoptimal manner.This paper focuses on the clock recovery problem for gen-eralized MSK. O ne possible solution to this problem is bor-rowed from linear modulations and consists in passing thein-phase (or, alternatively, the quad rature) component of thesignal complex envelope through a nonlinearity such as asquaring device [6]. The output of the nonlinearity contains aclock-synchronous periodic com ponent that can be extracted

by means of a phase-locked loop (PL L) or a narrow-band filtercentered on the clock frequency. A drawback of this approachis that it requires that the carrier p hase be previously estimatedin order to effect a coherent demodulation. Thus errors ordelays in carrier-phase estimation may slow down the clockrecovery process.A different approach, proposed by de Buda [7] and ana-lyzed in [8], is to pass th e intermediate frequency (IF) wave-Manuscript received Novem ber 21, 1989; revised March 28 , 1990.The authors are with the Institute of Electronics and Telecommunications,IEEE Log Number 9036996.Via D iotisalvi-2, 56126 Pisa, I taly.

form through a second-order nonlinearity to generate peri-odic components whose frequencies are symmetrically dis-posed around twice the carrier frequency and spaced by clockrate apart. The nonlinearity is followed by a couple of phase-locked loops whose outputs are properly co mbined and scaledin frequency to allow simultaneous recovery of carrier andclock references. It has been shown in [8] that this methodpermits estimation of carrier and clock with errors close tothe Cramer-Rao lower bound (CRLB) [9]. Nevertheless, themethod has a number of shortcomings, such as possibility offalse lock of the P LLs, interdependence of noise bandwidthsof carrier and clock recovery processes, etc. An additionalmajor disadvantage of the method is that it does not easilylend itself to a digital implementation.To date, m any simple numeric clock synchronizers operat-ing at various sampling rates have been devised, essentiallyfor linear, non staggered modulations. To mention just a few,a decision-directed (DD ) approach, which is suited for PAM-like signals, is discussed in [lo ] while [ l I] presents a non-data-aided (NDA) algorithm for BPSK/QPSK. Another ap-proach, proposed in [12], eliminates the need for an analogVCO, and so forth. The search for new algorithms suited fornonlinear modulations appears most appealing in view of thegrowing demand for digitalization in all communication as-pects.This paper presents a new method for clock recovery ingeneralized MSK that is suited for digital implementation anddoes not rely on previous or simultaneous acquisition of car-rier phase. In view of its insensitivity to the cited phase, thealgorithm is especially useful in all those situations whereincarrier recovery is not required, e.g ., when differential or dis-criminator detection of the generalized MSK signal is used.Th e IF waveform is converted to baseband in a noncoherentfashion, then sampled and fed to a fourth-order nonlinearity.The output of the nonlinearity contains a clock-synchronousperiodic component that can be exploited in a data-sampledclosed loop to extract clock reference. This scheme was de-vised as a byproduct of a more general search for maximumlikelihood (M L) delay estimators for MSK-mo dulated signals

In the following, the m ethod is analyzed both in the steadystate (tracking behavior) and in transient conditions (acqui-sition behavior), taking the mean squared clock error asperformance measure. Simulation results are provided forMSK and Gaussian-filtered MSK [14]. The effect of a fre-quency offset at the demodulator stage (generated, for in-stance, by oscillator inaccuracies or Doppler phenomena) is

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2 2 8 IEEE TRANSACTIONSON VEHICULAR TECHNOLOGY, VOL. 39, NO. 3, AUGUST 1990also discussed. The tracking performance of the method iscompared with that exhibited by the De Buda synchronizerand with the CRLB.The paper is organized as follows. The next section intro-duces channel and signal models. Section 111 is devoted to thedescription of the new synchronization algorithm. Simulationresults follow in Section IV, where steady-state and transientanalysis is carried out and the effect of a frequency mismatchat the demodulator stage is discussed. Finally, conclusions aredrawn in Section V.

11. C HANNELN D SIGNAL ODELThe received waveform is converted to IF and then passedthrough the IF filter, which is supposed to limit noise band-width without altering the useful signal component. Usingcomplex-envelope notation, the noise-corrupted waveform atthe IF filter output can be written as

z ( t )= Re { i ( t ) e j ( 2 r r f a r + S ) (1 )where fo and 0 denote carrier frequency and phase, respec-tively, and i ( t ) s given by

i ( t ) = s ( t )+ q t ) . (2 )nc ( t ) + j n , ( t ) , where nc(t) and n s ( t )ar eindependent identically distributed Gaussian noise processeswith two-sided power spectral density No , and s( t ) is theuseful signal component, which is assumed to be a continuous-phase modulated (CPM ) signal. Nex t,

In (2), f i ( t )

s ( t )= e j $ ( t - 7 )9

$ ( t ) A 2 ~ ha i q ( t iT). (3 )In (3), 7 is the channel delay to be estimated by the clocksynchronizer, h denotes the modulation index, ai is the ith datasymbol drawn from the alphabet * , 4~3 , . ,*(M- l ) , T i s

the symbol spacing, and q ( t ) s the so-called phase responseof the CPM modulator, which is constrained as follows:

I

lim q ( t )= 0,t - - slim q ( t )= 1/2.

In the following, attention will be focused on a special sub-set of CPM signals; namely, those commonly referred to asgeneralized MSK signals, wherein M = 2 , h = 1/2, and thefrequency pulse is a filtered version of the MSK rectangu-lar pulse of length T and amplitude 1/2T. For instance, inthe Gaussian MSK modulation [141, the filter to be used hasfrequency response

I+%

where U and PT denote frequency and 3-dB bandwidth, re-spectively, both normalized to symbol rate.After IF filtering, the signal is fed to a synchronous de-modulator that operates in a noncoherent fashion; that is, it

employs a local free-running oscillator with fixed but randomphase. As shown in the next section, the reason for this choiceis that phase compensation is not required in the clock recov-ery process.

111. DESCFUPTIONF CLOCK YNCHRONIZERA . Operating Principle

As mentioned in the introduction, a motivation for thepresent paper arose [131 from a systematic search for ML es-timators of the delay parameter 7. t was observed that certainnonlinear combinations of delayed versions of the demodula-tor output contain periodic components that can be exploitedfor clock reference extraction. An examination of the variouscombinations led to the choice of the following fourth-ordernonlinear transformation:

q t ) = j 2 ( t ) z 2 ( r -T ) (6)where the asterisk denotes complex conjugate. From (6 ) , itis seen that Z ( t ) is not affected by a fixed or slowly varyingcarrier-phase error at the demodulator output, thus permittingthe clock recovery process to be carrier-phase-independent .The periodic part of q t ) can be extracted by taking theexpectation of the right side of (6 ) over data symbols andnoise. Details of the calculation can be found in Appendix I.As a result, the following real function is obtained:

33

E{i;(t))= n OS [2Tg(t - - ~ ) ]I = - %

33

+ 8 R , ( T ) n os [a g ( t - 7 - i T ) ] + 8 R ; ( T ) (7)1= - - 3=

where R , ( T )denotes the autocorrelation function of nc( t ) ndns(t), and g(t) is defined ass ( t )4 q ( t )- 4( t - T ) . (8 )

It is noted that the term R,(T ) in (7 ) is normally very small, asa consequence of the assumption that the IF bandwidth is largeenough to let the useful signal pass undistorted. T herefo re onlythe first term at the right side of (7) need be retained.From (7) it is seen that the expectation E{Z.(t)}s a periodicfunction of time with period T. In the special case of MS K, thefollowing closed-form expression of E {Z.( t ) } an be obtained(see App endix 11):

Dsn 0 ~ [ 2 n g ( ti T ) ] = 2;=-m \ I

The preceding considerations suggest that the real part ofthe sampled derivative of ? ( t ) e used as the error signal in adigital tracking loop wherein the value of T is estimated in arecursive fashion, according to the iteration formula

where the dot indicates derivative andf k

Ek = Tk -estimated clock delay at step kstep size,clock estimation error at step k.-

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NCO DECIMATION

DEMODULATOR

YFig. 1. Functional block diagram of synchronizer.

For a fixed estimation error E , the statistical expectationof Re {c(kT+ E) } does not depend on k and represents theso-called S-curve of the tracking loop:S ( E )4 E{Re {c(kT+ ) } ~ E } . (11)

Following (9), an ex act calculation of the S-cur ve is possiblefor MSK, yieldingT 2TET T( E )= - in --.

In a digital implementation, the derivative in (10) must becarried ou t numerically, using a finite-difference approxim a-tion on the samples of E(t). It was found that a reasonablygood solution can be obtained with as few as two samples persymbol (see next section).Performance of algorithm (10) is difficult to analyze undergeneral conditions due to its highly nonlinear nature. Underthe small-error assumption, i. e. , in steady-state conditions,the term Re {c,(kT + ~ k ) } at the right side of (10) can bereplaced by the sum

Re {C(kT + ~ k ) } & ( E ) + k (13)where A ( ; ) is the S-curve slope at E , the steady-state clockmean error, and T J ~ epresents a zero-mean disturbance term.After substitution of (13) in (l o ), the loop operation canbe studied using standard linear techniques. However, theo-retical analysis of the loop performance is still too complex,since it involves consideration of eighth-o rder moments of theprocess Z ( t ) , the latter function being hidden in the term q k in(13). Therefore the clock synchronizer performance has beenevaluated entirely by simulation.B. Functional Block Diagram

Fig. 1 shows the functional block diagram of the clock syn-chronizer. After demodu lation, the complex baseband signal issampled at twice the clock rate at th e instants t , = nT/2 .in.As previously mentioned, this sampling rate is required toimplement the derivative operation specified in (10). The se-quence of samples &, & Z(t , ) is fed to a nonlinear networkwhose output is @ n Z i Z * i - , . Then it is passed through adigital differentiator, which simply forms the difference be-tween @ and w, - l . The subsequent step, labeled decima-tion, is required because clock adjustment must operate atclock (or submultiple of clock) rate. The emerging erro r se-

quence finally drives a number-controlled oscillator (NCO) ofgain y , which modifies the sampling phase accordingly.The loop S-curve can be determined by fixing the sam-pling error E and calculating the expected value of the er-ror sequence. Fig. 2 shows the S-curves pertaining to MSKand Gaussian MSK (PT =0.3) modulations, respectively. Topoint out the deterioration introduced by numeric differentia-tion, also shown in the figure is the S-curve relative to MSKwith ideal differentiator. The slope of the S-curve at the sta-ble lock point (i.e ., the positive-slope zero crossing in Fig. 2)is an important parameter since, as far as the small-error as-sumption can be considered valid, it determines the equivalentnoise bandwidth of the linearized loop as well as the speed ofconvergence of the algorithm. From inspection of Fig. 2 , itcan be argued that the degrad ation induced by num eric differ-entiation ought to be small in the MSK case.IV. PRESENTATIONF RESULTS

A . Steady -State ErrorsIn this section, the tracking performance of the scheme de-picted in Fig. l is analyzed. Th e tracking erro r (jitter) varianceof the reconstructed symbo l timing is assumed as performancemeasure. The results presented hereafter have been obtainedby means of Monte Ca rlo simulation. The attention is focusedon MSK and Gaussian MSK. In the latter case, a normalized3-dB-bandwidth PT = 0.3 is assumed. T he normalized IF fil-

ter bandwidth is chosen as BpT = 2.0, a compromise valuewhich permits us to keep noise effect and signal distortionat reasonably low levels. The parameters allowed to vary inthe simulations are the energy-per-bit-to-noise-power-densityratio Eb / N O nd the loop-normalized noise equivalent band-width B,T. Assuming the small-error linearized model of theloop is valid, the latter parameter can be shown [15] to be

(14)with A denoting the S-curve slope at stable lock point.

Figs. 3 and 4 show clock-jitter variance as a function ofEb/No for the proposed scheme and for the de Buda syn-chronizer [8]. Also shown for comparison purposes is theCRLB , as derived from [9]. Both synchronizers have normal-ized equivalent noise bandwidth B,T = 5 . With MSKmodulation (Fig. 3) in the low-to-moderate range of signal-to-noise ratios, the synchronizer of Fig. 1 exhibits only a limiteddegradation with respect to the de Buda synchronizer, also tothe CRLB. A more pronounced departure from the de Budaand CRL B curves is observed with Gaussian MSK modulation(Fig. 4).B. Transient Analysis

Another important aspect for investigation is the synchro-nizer performance under the large-error assumption, i.e.,when the linearized model utilized in the previous section canno longer be considered valid. This situation may occur, forinstance, at transmission start-up (clock acquisition) or after acycle slip. The synchronizer behavior in the acquisition phasehas been an alyzed by sim ulation assuming different values ofE b No and different initial conditions.

7-4B,T =-

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4.003-4.00 I I I I-0.50 -0.30 -0.1 0 0.10 0.30 0.50

Normalized clock errorFig. 2 . Loop S-curve. a) MSK, ideal differentiator. b) M SK, hvo-point ditferentiator,T / 2 pacing. c) Gaussian MSK, pT =0 . 3 ,two-point differentiator,T / 2 spacing.

a,0C0.-I0>a,Lw.--7

10 20 30 40 50

Fig. 3 . Timing jitter variance versus Eh,"", MSK, B,T = 5 . op7. a) Proposed algorithm. b) De Buda synchron izer. c)Cramer-Rao lower bound.

From (9 ) it can be seen that the proposed synchronizer maysuffer from the hang-up phenomenon, which arises when thetiming erro r lies in the close vicinity of an unstable lock point.Hang-up is evident from Fig. 5 , which shows the normalizedmean squared cloc k error d uring acquisition. Initial clock er-Tors ar e 0.45T and 0.5T, respectively. The error curves are.moothed by means of a rectangular sliding window of lengthIOT. Both trials are carried out using Eb/No = 50 dB ,B,T = 5 . lop3. In the former case (initial error 0.457), thealgorithm shows a monotonic convergence towards the stableequilibrium point, while in the latter case the error exhibitsminimal fluctuations around the value 0.5T for a long timebefore being pulled down. It is observed that in the formerrial th e acquisition time is on the order of the inverse of B,T,i.e.. a few hundred symbols. It is also noted that the log-error

curve evolves in an almost rectilinear fashion for most of theacquisition (Fig. 5 , curve (a)), with slope approximately givenby (B,T)-' . In these conditions, the system behavior can infact be predicted to a good accuracy using a first-order linearmodel.Fig. 6shows the synchronizer behavior for MSK, startingfrom the error 0.45T, B,T = 5 . in the cases of low(10 B) and high (50 dB) value of Eb/No. The two curvesare almost superimposed in the first part of the acquisition,and ultimately diverge toward their resp ective steady-state val-ues. Fig. 7has been obtained for Gaussian MSK, using thesame parameters as in Fig. 6.While the acquisition time isapproximately the same as in the MS K case, fluctuations aremore pronounced. This effect could easily be anticipated fromobservation of the tracking error curves in Figs. 3 an d 4.

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lo- I I I

IO 110-9 1 I 1 I10 20 30 40 50

Fig. 4. Timing jitter variance versus E b / N o , Gaussian MSK, l = 0.3,B, T = 5 a) Proposed algorithm. b) De Budasynchronizer. c) Cramer-Rao lower bound.

1 I I 1 I

L

Y000-

I I I I0 200 400 600 800 loo0

Number of s y m b o l sb) Initial error = 0.5T.Fig. 5 . Mean squared timing error versus number of symbols, MSK, E b / N o = 50 dB , B,T = 5 . lop3 . a) Initial error =0.45T.

C .Eflect of a Frequency OflsetWhile the proposed scheme is immune from carrier-phaseerrors, the presence of a frequency offset Af at the demod-ulator output produces the net relative rotation 27rAfl radbetween the terms i ( t ) an d i ( t -T) appearing in (6). Recall-ing ( l l ) , t is seen that the effect on the S-curve is merely amultiplication by cos 47rAfT. In these conditions, if the step

size y is left unchanged, the acquisition time is multipliedapproximately by the inverse of cos 47rAjT, and thus maygrow over unreasonable limits. This effect is also present inother non data-aided digital timing recovery schem es operatingat baseband, such as the one proposed in [ l l] .Fig. 8showsthe S-curve, obtained by simulation, pertaining to MS K withA f T = 0.1, corresponding to a carrier-phase rotation of 36

per symbol. Also shown in the figure is the S-curve relativeto A f l = 0. The preceding considerations indicate that theproduct A f l should not exceed the value 0.1,V . CONCLUSION

A new method for timing recovery in generalized MSKmodulations has been presented. The method does not rely oncarrier-phase synchron ization and is suited for digital imple-mentation, with a sampling rate that is only twice the symbolrate.A sim ulation analysis of the proposed scheme has been car-ried out for two different modulations, MSK and GaussianMSK. The tracking performance has been analyzed and com-pared with that exhibited by the de Buda synchronizer and

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 39, NO. 3, AUGUST 1990

-: -- I I I I

1 I I I I i

lo->0 0 100 200 500 400 500

Number of symbolsFig. 6. Mean squared timing error versus number of symbols, MSK, initial error = 0.45T, B, T = 5 . a) Eb/No 50dB. b) Eb /No= 10 dB .

1 I I I I

Number of symbolsFig. 7. Mean squared timing error versus number of symbols, Gaussian MSK, pT = 0.3, initial error = 0.45T, B, T = 5 .a) Eb/No 50 dB. b) Eb/No 10 dB .

with the Cramer -Rao lower bound. The acquisition behaviorhas also been discussed, and it has been shown that, in nor-mal conditions, convergence times of the order of the inverseof the system equivalent noise bandwidth are to be expected.Finally, the effect of an uncomp ensated frequency offset at thedemodulator output has been considered. It has been shownthat proper synchronizer operation requires the frequency off-set to be very small with respect to symbol rate.APPENDIX

In this Appendix, the statistical expectation of the functionE(t) is calculated. Using (2 ) in (6) and ignoring zero-mean

terms leads toE{?( t )2 * 2 ( t - T ) } = E{?(t)i * 2 ( t - T ) }+E{i i2( t ) i i 2 ( t - T ) }

+4E{i(t)S'(t - T ) }E { i i ( t) i i ( t - T ) } . (15)Recalling the properties of n c ( t ) and n s ( t ) , t can be shown

thatE { i i 2 ( t ) i i * 2 ( t-T ) }= 8 R i ( T ) (16)

E{i i ( t ) i i ( t - T ) }= 2R, (T ) (17)

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-0.50 -0.x) -0.10 0.10 0.30 0.50Normalized clock error

. .. - -Fig. 8. Loop S-curve with frequency offset. a) MSK, A j T = 0.1. b) MSK, A j T = 0.

where R , ( T )the autocorrelation function of n c ( t )and n,( t ) .lated. Recalling ( 3 ) , one gets

E { n , ( t ) n , ( t + T ) } = E{n,(t)n,(t + T ) } isThe terms in ( 1 5 ) nvolving the signal j ( t ) are now Ca l CU -AP P E NDIX1

This appendix is concerned with the calculation of the firstterm at the right side of ( 7 ) under the assumption that thesignal is MSK modulated. The phase response of the MS K

where g ( t )Assuming that the symbols ai are independent and take onthe values f with equal probability permits us to manipulate( 1 8 ) as follows:

q ( t )- q(t - T ) .

= n o s 27rhg(t - T ) ] . ( 1 9 )I

( 1 / 2 , t > TTherefore the function g ( t ) defined by ( 8 ) can be expressedas

O < t < T

1 elsewhereIt is easily recognized that for nT < t < ( n + l ) T the firstterm at the right side of (7 ) simplifies to the product of twotermst

g ( t ) = 1 -&, T < t

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M. K. Simon, A generalization of minimum shift keying (M SK)-typesignalling based upon input data symbol pulse shaping, IEEE Trans.Commun.. vol. COM-24. pp. 845-856, Aug. 1976.A. Svensson and C.-E . Sundberg, Optimum M SK-type receivers forCPM on Gaussian and Rayleigh fading channels, IEE Proc., Pt. F,vol. 131, no. 5, pp. 480-490, 1984.G. Ascheid and H. Meyr, Synchronisation bei Bandbreiten-Effizientermodulation, in NTG-Fachtagung Conf. Record, Mar. 23-25, 1983,Garmisch-Partenkirchen. BRD. pp. 107-1 14.R. W. D. Booth. An illustration of the MAP estimation method forderiving closed-loop phase tracking topo logies: The MSK signal struc-ture, IEEE Trans. Commun., vol. COM-28 . pp. 1137-1 142, Aug.1980.L. E. Franks and J . P. Bubrousky, Statistical properties of timingjitter in a PAM timing recovery scheme. IEEE Trans. Commun.,R. de Buda, Coherent demodulation of frequency shift keying withlow deviation ratio. IEEE Trans. Commun.. vol . COM-20, pp.429-435, June 1972.N. A. DAndrea, U. Mengali. and R. Reggiannini, Carrier phase andclock recovery for continuous phase modulated signals, IEEE Trans.Commun., vol. COM-35, no. 10, pp. 1095-1101, Oct. 1987.M. Moeneclaey and 1. Bruyland, The joint carrier and symbol syn-chronizability of continuous phase modulated waveforms, in Proc.ICC 86, Toronto. Canada. paper no. 31.5.K. H. Mueller and M. Muller, Timing recovery in digital synchronousdata receivers, IEEE Trans. Commun., vol. COM-14, pp. 516-530,May 1976.F. M. Gardner. A BPSKQPSK timing error detector for sampledreceivers. IEEE Trans. Commun..vol. COM -34. pp. 423-429, May1986.M. Oerder and H. Meyr, Digital filter and square timing recovery,IEEE Trans. Commun.,vol. CO M-3 6, pp. 605-612, May 198 8.N. A. DAndrea. U. Mengali, and R. Reggiannini, Symbol timingrecovery in generalized minimum shift keying. tech. rep., Istituto diElettronica e Telecomunicazioni, Pisa (Italy ). Nov. 1989 (in Italian).K. Murota and K . Hirade, GM SK modulation for digital mobile radiotelephony. IEEE Trans. Commun.. vol. C OM-2 9, pp. 1044-1050.July 1981.W . C. Lindsey and M. K . Simon, Telecommunication Systems En-gineering. Englewood Cliffs, NJ : Prentice-Hall. 1973.

vol. COM- 22, pp. 913-920, July 1974.

Elettronica e Telecomudesign and analysis of

Aldo N. DAndrea received the Dr. Ing. degree inelectronic engineering from the University of P isa,Italy, in 1977.From 1977 to 1981 he was a Research Fellowengaged in research on digital phase-locked loopsat the Centro Studi per i Metodi e Dispositivi diRadiotrasmissione of the Con siglio Nazionale delleRicerche (CNR). Since 1978 he has been involvedin the development of the Italian Air Traffic Controlprogram (ATC). Currently, he is an Associate Pro-fessor of Communication Networks at the Istituto diinicazioni, University of Pisa. His interests include thedigital communication systems and synchronization.

Umberto Mengali (M69-SM85-F90) receivedthe Dr. Ing. Degree in electrical engineering fromthe University of Pisa, Italy, in 1961 and the Lib-era Docenza in Telecommunications from the ItalianEducation Ministry in 1971.Since 1963 he has been with the Istituto di Elet-tronica e Telecomunicazioni of the University ofPisa where he is currently Professor of Telecom-munications His research interests are in digitalcommunication theory, with emphasis on synchro-nization methods and modulation techniques.Dr Mengali is a former Editor for Synchronlzation Systems and Tech-niques of t he IEEE TRANSACTIONSw C O M M U N I C A T I O N Snd is now 11s Editorfor Transmission SystemsRuggero Reggiannini was born in Viareggio, Italy,on August 6, 1952. He received the Dr. Ing. de-gree in electronic engineering from the Universityof Pisa, Italy, in 1978.From 1978 to 1983 he was with USEA S .p. A. ,where he was engaged in the design and develop-ment of underwater acoustic systems. He is cur-rently a Researcher at the Istituto di Elettronica eTelecomunicazioni of the University of Pisa. His in-terests include the analysis of digital communicationsystems and synchronization.