IEEE TRANSACTIONS ON COMMUNICATIONS, MARCH 1977 3 74

(111

Commun. Syst. Lab., Sylvania Electron. Syst., Tech Rep. 15, Oct. 1968. P. A. Bello and B. D. Nelin, “The influence of fading spectrum on the binary error probabilities,” IRE Trans. Commun. Syst., vol. CS-10, pp. 160-168, June 1962.

Tracking Loops for Carrier Reconstruction in Vestigial Sideband (VSB) Suppressed-Carrier Data Transmission

R. DOGLICITTI AND u. MENGALI, MEMBER, IEEE

Abstract-This paper deals with a tracking-loop-type approximation to the maximum likelihood (ML) estimator of the carrier phase in a suppressed-carrier vestigial sideband (VSB) data-transmission system. Two different tracking loops are considered, the one resembling a Costas loop, the other a data-aided receiver (DAR). The performance of these circuits is analyzed in the presence of thermal noise and intersym- bo1 interference, and the results are compared with those relevant to a conventional scheme wherein a pilot tone is used to reconstruct the carrier at the receiver.

I. INTRODUCTION

To make efficient use of channel bandwidth many high- speed data-transmission systems employ pulse amplitude modulation, either in the form of vestigial sideband (VSB) or of single sideband (SSB) modulation. One of the drawbacks of these systems is that a very accurate knowledge of the phase e of the received carrier is necessary t o assure satis- factory demodulation operations; slight errors on e affect the probability of error considerably [ 1 1 - [ 3 1 .

The recovery of 0 is usually accomplished by transmitting auxiliary pilot tones which can be extracted from the received waveform using more or less conventional techniques [41- [ 71. Difficulties in the use of some of these techniques have been pointed out by various authors [ 81 -[ 91. In particular it has been observed that, when the pilot tone is transmitted at the carrier frequency, the data components in the vicinity generate errors in the estimation of 8 . On the other hand, extra bandwidth is required to transmit pilot tones in a fre- quency zone where no signal energy is present. This appears to be a particularly high price for channels with rapid phase jitter [ 91. Furthermore, since the phase characteristics of the channel are often highly nonlinear, the amount of the phase- shift affecting the pilot tone is different from that affecting the signal components. Adjustments are then required which can be difficult to implement, expecially if they are time varying, as happens in the presence of phase jitter.

For these reasons the idea of recovering 0 directly from the data signal itself was suggested [ 81-[ 141. Several strategies have been proposed to accomplish this task. For example, Chang [ 131 analyzes a gradient method to minimize the

Paper approved by the Editor for European Contributions of the IEEE Communications Society for publication without oral presenta- tion. Manuscript received May 20, 1975; revised May 17, 1976.

zioni (CSELT), Turin, Italy. R. Dogliotti is with the Centro Studi e Laboratori Telecomunica-

U. Mengali is with the Dipartimento di Elettrotecnica ed Elettroni- ca, Pisa, Italy.

equalization mean-square error, whereas Kobayashi [ 8 ] , [ 101 finds the maximum likelihood (ML) estimator of e and dis- cusses some practical modifications of it.

In this paper we start from Kobayashi’s results but we propose an approximation of the phase-locked loop (PLL) type to the estimator of 8. As we shall see, this approach leads to tracking schemes very similar to some popular circuits, well known in literature for various applications [ 121, [ 151 - [181.

11. COMMUNICATION SYSTEM MODEL

The synchronous transmission system to be considered is shown in Fig. 1. The data sequence {ci} modulates a basic signaling waveform m(t ) , producing1

where T is the symbol spacing. This voltage is multiplied by a carrier cos (act + 8 ) and sent t o a bandpass VSB or SSB filter h f ( t ) which partially or totally filters out one of the signal sidebands and gives

Here, % ( t ) can be thought of as obtained from m ( t ) with the filter [ 5 I

where fo(a) is an arbitrary odd function such that fo (a0 ) = 1. For 00 = 0, s f ( t ) becomes SSB modulated whereas, when %(t) is identically zero, s f ( t ) becomes double-sideband (DSB) modulated.

The output of h f ( t ) passes through a linear dispersive channel h c ( t ) which adds white Gaussian noise w ( t ) with one- sided spectral height N o . The waveform arriving at the receiver is then x ( t ) = s f ( t ) @ h c ( t ) 4- w ( t ) , where @ denotes convolu- tion operation.

The receiver’s object is to deduce the transmitted data sequence {ci} from the observation of x ( t ) during a certain interval (0, M T ) . To accomplish this task the receiver needs information on the carrier phase 8. Assuming this information must be extracted from the data signal itself, the actual re- ceiver problem is t o jointly estimate {ci} and 8 . In the next section we shall consider optimum and suboptimum estima- tors of these parameters.

111. OPTIMUM AND SUBOPTIMUM ESTIMATORS

The optimum ML estimator of {ci}and e has been treated by Kobayashi [ 81 , [ l o ] , who found the structure illustrated

Unless otherwise noted here and in the sequel the sums are for i = O,+ 1 ,+ 2, etc.

CONCISE PAPERS 375

‘q m ( t )

cos(0c t+ 9)

Fig. 1. Communication system model.

in Fig. 2. Here, the incoming waveform x ( r ) is first bandpass filtered in h f c ( - t ) , a bandpass filter matched t o h f c ( r ) 4 h f ( t ) (8 h c ( t ) . Then it is demodulated and sent to the low-pass filter m(- t ) , matched to the signaling waveform m(t ) . Next, it is sampled. The samples{yi} are used in two ways. On one hand they feed a suitable equalizer which gives {Fi}, the ML esti- mates of {ci}. On the other hand, they are correlated with {c} to form

The ML es t ica te of 8 is such that it maximizes J(8). Thus, for each 8, J ( e ) is computed and compared with the previous results. Eventually, when a maximum is reached, the output of the voltage-controlled oscillator (VCO) gives a sinusoid whose phase is O M L , the estimate wanted.

As observed in [ 81 , [ 101, this recursive method is often impractical since it requires storing the waveform x ( t ) received during the full observation interval (which can be quite long). Furthermore, it does not enable “on-line” processing of the received data stream. For these reasons other (perhaps subop- timal) schemes are of interest. For example, Kobayashi suggests an algorithm based on the Robbins-Monro stochastic approxi- mation method.

Here we shall consider a different approach which relies on the PLL principle [ 191. TO explain thz matter let us refer t o Fig. 2. Since J ( 8 ) has a maximum in 8,= e M L , its deriva- tive

will be a monotonically decreasing function of g i n t h e vicinity z f 8 M L ; in particular it will be 2 0 according to whether 8 5 g M ~ . This suggests using the following trykingfrocedure. At tl = T we start with a tentative value of 8, say 81, and we compute ciy1’(81). Then we change €J1 by increasing or de- creasing it according to the sign of Zlyl’(61). In this way_we get 8 2 , the new estimate of 8, and we compute Z2iy2‘(82) which is added to i?lyl@l) to correct and so on.

It should be observed that, since the output of m(-t) is

A t ) = { [ x ( t ) CZI h f c ( t ) ] cos (cpct + 8)) CZI m(-t)

one has

Hence, the samples y i ’ (8) required to accomplish the search procedure outlined above can simply be obtained by multi- plying the output of h f c ( - t ) by - sin (q,t + e) . In this way we arrive at the scheme in Fig. 3.

vco SEARCH MAX. J

J ( f )

Fig. 2. Maximum likelihood estimator of {ci} and e.

TO EOdALlZER AND [ “ , I DECISION CIRCUIT

c

vco

Fig. 3. Phase-carrier tracking loop.

Here x ( t ) is first bandpass filtered in z fe ( - t ) . In general L f c ( - t ) does not coincide with h f c ( - t ) since, in practical situations, we don’t know the channel characteristics exactly. The output of &,(-t) is used to form the samples{yi} in the upper branch and the samples {yi’} in the lower branch. According t o (3), the former should be equalized and corre- lated with the latter to produce a control signal. However, putting an equalizer in the loop creates a number of problems. For example, since the channel characteristics are often slowly changing with time, an adaptive equalizer would be appro- priate. Unfortunately in this case the analysis of the loop appears mathematically untractable. On the other hand it has been found that with a fixed equalizer instability of the loop may result, especially in the presence of high distortion in the group delay of the channel. Thus, for simplicity, the samples { y i } are directly multiplied by bi‘} and sent to the loop filter, whereas the equalizer is shifted out of the loop.

By adjusting the memory of the loop filter we can drive the VCO with the sum of the products y i y f . Actually, since the carrier phase 8 will not remain constant in time, a weighed sum of the products, which accentuates the recent ones and attenuates the others, seems more appropriate.

Finally, the output sequence {ei} of the loop filter is used to update the phase 8i of the VCO according to the rule

A

= ei + K~~~ ei. (4)

In the next sections we shall analyze the tracking system in Fig. 3 . Before proceeding, however, let us emphasize that this is not really a new structure in the field of synchroni- zation systems. Indeed, it is very similar to the popular Costas loop [ 121 , [ 151 , [ 171 with the sole difference being that here the control voltage is obtained from sampled sequen- ces rather than from continuous waveforms.

IV. BASEBAND MODEL

In this section our task is to determine a baseband equiva- lent model for the system in Fig. 3. We shall rest the discussion on the following practical assumptions:

W L T Q 1 and W L < 8, (5)

376 IEEE TRANSACTIONS ON COMMUNICATIONS, MARCH 1977

where W, is the two-sided noise bandwidth of the loop and @fc is the bandwidth of Efc(- t ) . Essentially, these assump- tions entail that the phase process (gi}varies much more slowly than the signal or the noise process.

Under hypotheses ( 5 ) it can be shown that the outputs y ( t ) and y’ ( t ) of the filters m(-t) can be written

. - w ) $ ’ W f -’

dw

271

Here M(w), Hfc(w), and f i f , (w) are the Fourier transforms of m ( t ) , h f c ( t ) , and h f c ( t ) , respectively, whereas v ’ ( t ) and ~ “ ( t ) are sample functions from zero-mean stationary Caussian random processes, independent of each other, of {ei}, and having equal two-sided spectral density

4

+ I f i f c (W, - W ) 1 2 ) . (9)

It is worthwhile considering the physical meaning of gl(t) and g2( t ) . From (6) and (7) we see that they represent the responses at the sampler inputs which are due to an impulse applied t o m ( t ) in Fig. 1 , in the case of perfect phase carrier synchronization. It should be observed further that in the case of lower-sideband SSB modulation Hfc(w) is zero for 1 0 1 > a,. Correspondingly, from (8) it. can be shown that gz(t) equals the Hilbert transform g;(t) of gl(t). Likewise, for upper-sideband SSB molulation, one finds g2(t) = -gl(t). In the general case of VSB modulation, g l ( t ) andg2(t) are not related to each other in a simple way. However, if the channel and the bandpass filter transfer functions have conjugate symmetry 1201 around the carrier frequency a,, then one finds that g2(t) and g l ( t ) are input and output functions to the filter in ( 2 ) . Finally, in the case of DSB modulation and under the same hypotheses for h,(t) and h”f,(-t), one finds g 2 ( t ) identically zero.

Next we concentrate our attention on the input to the loop filter. From (6) and (7) we have

and g 2 ( i - k ) assume significant values only for not too large values of Ii - k l , and that, as a consequence of (s), y k does not vary appreciably over many symbol periods. Putting these facts together, we conclude that 9 k in (10) and (1 1) can be replaced by vi. Thus,

At this point, by multiplying y i by yi’ we obtain the filter input. For convenience, let us introduce the following time- discrete process:

where E{. I vi} denotes conditional expectation on both {ci} and the input noise process. Assuming zero-mean uncorrelated and stationary symbols, i.e.,

for h = k

for I1 # k ,

the following expression of E{ygi ’ 1 Vi} is found:

A

2 ~ { y ~ y ~ ‘ I cp} = - sin 2(q - 3)

where

Therefore, collecting (4), (1 2) , ( 1 3) and denoting with F d ( z ) the discrete-time transfer function of the loop filter, we arrive at the block diagram in Fig. 4 which represents, in the z-transform domain, the equivalent baseband model of the tracking loop in Fig. 3.

Next, we, replace this discrete-time model by a continuous- time’model such that; for each point in the former where a sequence {zk} is observed, there is a corresponding point in the latter where the voltage

where, t o avoid notational complexity, we have written is present. As a consequence of (5), the continuous model is gl(i) in place of g l ( i T ) , etc. It should be observed thatgl(i - k ) simply drawn by substituting exp ( S T ) = 1 i- ST for z through-

CONCISE PAPERS 377

Fig. 4. Baseband model for the tracking loop.

out Fig. 4. Thus, letting F(s) 4 Fd(1 -I S T ) and K g I ( , , ~ ~ / T , we arrive at the scheme in Fig. 5, which i s the standard model for an analog PLL.

There are some comments with regard to the static phase error Cp, to the gain A of the amplifier in the loop, and to the shape 2-1 sin 29 of the phase-detector characteristic. Let us begin with the last topic. We realize that the loop exhibits a 180-degree phase ambiguity since its stable points are separa- ted by only 180 degrees. To resolve this ambiguity, some redundancy may be introduced in the data sequence {ci}. As far as' (p and A are concerned, we see from (14) that they depend on g l ( t ) and gz(t). To get better insight into this point, let us express the right-hand sides of (1 5) by means of G ~ ( o ) ( i = 1,2), which is the discrete Fourier transform of {gi(kT)} . As is known, Gi(w) is related to the continuous Fourier transform Gi(w) by

It can be shown that [211

For instance, let us consider SSB modulation and assume g l ( t ) is restricted to the Nyquist band, as would be the case in partial-response systems. As previously stated, g z ( t ) = kz l l t ) , so G 2 ( o ) = Tj sgn (o)Gl(w). Furthermore, from (1 7) we deduce G(w) = Gl(o) and G2(o) = G ~ ( w ) (because G , ( o ) and G2(w) are zero for I o I > n / T ) . Hence, (18) and (19) give C , = C2 = 0, which entails zero loop gain. Of course, under these hypotheses the method of carrier recovery fails. In the next section we shall see a modified version of this scheme which works also for SSB partial-response signaling.

A second case which leads t o simple results occurs when the channel characteristics are known so that the impulse response %,,(-t) of the bandpass filter can be made to coin- cide with h f c ( - r ) . Equation (8) gives

g1(t) = g1I-t) and gz(t) = -g2(-r) (20)

so that from (14) and (1 5) we have (p = 0. In general, for unknown channel characteristic, (20) does

not hold true. However, numerical evidence indicates that a suitable choice of the sampling times always exists, which produces a zero static phase error.

V. AN ALTERNATIVE SCHEME

In the previous section we considered a tracking-loop-type approximation to the ML estimator of the carrier phase. According to this approximation the samples { y i } of the in-phase 'demodulated waveform are used to form a control signal which corrects the local estimate of the carrier phase. Meanwhile, the same samples are sent to an equalizer, followed b) a decision circuit, to produce gn estimate' {ci'} of the transmitted data sequence {ci}. Now, it is fairly intuitive that better tracking operations would result from replacing {yi} with {ci} in the control signal. In practice this would be possible if some known pattern of the sequence were used in a training period or if, assuming an almost perfect setting of the carrier phase and a reasonably low noise level, the data sequence were detected with small probability of ermr so that {ci} would almost always coincide with {ci'}.

All this leads to the structure of Fig. 6 where the delay element is required to compensate the delay N T of the equal- izer. It is worthwhile noticing the similarity of this structure to that of a data-aided receiver (DAR) [ 161, [ 171. Again 'we observe that the main difference here is due to the presence of intersymbol interference which suggests building the con- trol signal by sampled waveforms rather than by continuous waveforms. In this area it is interesting to consider also [ 181, wherein a sample-data control loqp is studied for carrier reconstruction of DSB modulated signals.

Henceforth we shall refer to the scheme in Fig. 6 as the data-aided' tracking loop (DATL) t o distinguish it from that in Fig. 3, which we shall call Costal-like. tracking loop (CLTL). Unfortunately, a general analysis of the DATL seems mathe- matically untractable. The problem is greatly simplified by assuming operating conditions with low error probability so that ci' = ci, almost always. Under these hypotheses the base- band model of the DATL can be drawn following*-the same steps used for the CLTL. The result is again like that in Fig.' 5, but with differences in the statistics of the noise and in the expressions of G, A , and of the phase-error characteristic. In particular, (1 2 ) becomes

and (1 3)

It should be noted that, as opposed to the DATL , the CLTL does not fail for SSB modulation with Nyquist restricted g l ( t ) .

378 IEEE TRANSACTIONS ON COMMUNICATIONS, MARCH 1977

Fig. 6. Decision-aided tracking loop.

VI. NOISE SPECTRAL DENSITIES

In this section we shall characterize the noise n ( t ) in the baseband model of Fig. 5. .From (16) we have

form of (27) and (28) say that, in situations where the signal- to-noise ratio is large enough, virtually exact carrier-phase recovery can be obtained with both systems. In fact, if D l and Dl ' are negligible, both N C L T L and N D A T L are zero for cp = 0. Physically this means that no noise is injected into the loop in Fig. 5. On the other hand, since (p is found to be zero, the output of the phase detector is zero too. Thus, no correction acts on the VCO and therefore, as long as 0 remains constant, cp will remain zero.

As a second example, let us assume upper-sideband SSB binary modulation with ci = +1. In this case g 2 ( t ) = -i l( t) . Furthermore, let g l ( t ) be modeled .as follows; Disregarding the effect of the channel, C l ( w ) would be of the raised- cosine type, say R,(w,a), with a rolloff parameter 01: The channel transfer function is taken flat in amplitude but quad- ratic in its group delay:

where {nk(cpk) } are given in (12) or (22) according to whether we are referring to DATL or CLTL. In both cases, since n k depends on q k , strictly speaking n ( t ) depends on all samples {qk} of cp(t). However, as a consequence o f ' t he shape of the function cp(t), n( iT) depends essentially on few values o f q k : only those with an index k not too different from i. On the other hand, because of (5), cp(t) remains essentially constant over many symbol periods. All this leads to the conclusion that in computing the right of (25) we can replace $ok by cp = cp(t). To emphasize this, henceforth we shall denote n ( t ) by nkcp).

In this light it makes sense to speak about N(w,cp), the power spectral density of n(t,cp), conditioned on cp. Of course, the actual spectrum of the noise could be obtained from N(o,cp) by averaging on the probability 'density. function (pdf) of 9. The spectral density N(w,cp) is given by

N(o,cp) = I

where 0T represents the group-delay at a frequency n/T apart from the carrier wc/2n. As a result

Gl (w) = R,(o,a) exp [-j0T303/3n2]

Finally, the thermal noise is negligible and the sampling times are chosen so as to make (p = 0.2

In Fig. 7 the normalized power spectral densities S(cp) 4 N(O;cp)/TA2 for DATL and CLTL are drawn versus cp for a = 0.5 and some values of (3. The curves SDATL (cp) are limited to a small interval around cp = 0 since, in getting the expression of N D A T L ( O , ~ ) , we assumed a small error prob- ability and hence, implicitly, a limitation on the range of values of cp around zero. As we can see, for a given 0, SDATL (0) and S C L T L (0) assume comparable values and hence com- parable performances of DATL and CLTL are expected under operating conditions characterized by small fluctuations of cp(t). It should be observed in fact that in this case the variance ofcpisgivenby [17], [19]

0, otherwise. where W,, the two-sided noise bandwidth of the loop, is given bY

We now observe that since n(t,cp> is injected into a loop with a very narrow band, we are interested in the.spectrum of n(t,cp) only in the region l oT l 4 1 where N(w,cp) can be replaced by

(30)

This quantity is evaluated in I21 I both for the CLTL and for the DATL.

A comparison between the two expressions of N(0,cp) is interesting. For example, let us suppose that the channel is known so that (20) holds true. Then, one finds

N c L T L ( O . ~ ) = D l -k 0 2 sin2 2cp (27)

N D A T L ( O , ~ P ) = D ~ ' -I D2' sin2 cp (28)

For instance, if 0 = 1 and W,T = 0.1, one finds UDATL' = 8.3 X lou3 and (SCLTL' = 4.8 X lom3.

It is worthwhile to compare these results with those one could obtain in a conventional SSB system wherein a pilot carrier p ( t ) = sin ( a c t -k 6) were added to the signal s p ( t ) in (1). TO be definite, let US consider the same channel as before and a binary partial-response class IV signaling scheme. Following Zegers [ 221 it can be shown that a well designed PLL will track p ( t ) with a phase-error variance

where Di and Di' are all positive constants and Dl and Dl' *The search of these sampling times requires a cut-and-try pro- vanish in the absence of thermal noise. This fact and the very cedure.

CONCISE PAPERS

l------ T

Fig. 7. Normalized spectral density S ( 9 ) versus phase error 9.

where P, is the power of s,(t>. Thus, for example, for W L T = 0.1 and 0 = 1, (31) gives the same variance of a DATL for Ps/Pp 2.2 dB. Equation (29) gives a measure of the per- formance of the loops operating in the linear region. For a nonlinear analysis of the CLTL, see [ 2 1 I .

VII. CONCLUSIONS

Two tracking loops have been considered for the recon- struction of the carrier phase in VSB data transmission systems. The topologies of these loops are very similar to those of the popular Costas loop and the DAR. The difference lies in the fact that the Costas loop and the DAR operate on continuous waveforms, whereas the schemes in this paper operate on sampled data. The reason is recognized as due to the presence, here, of intersymbol interference. In this light our results extend those of Lindsey-Simon [ 171.

Further work on this subject involves the following. We observe that both CLTL and DATL require symbol timing. Now, it is natural to think of extracting symbol timing from the same samples used to obtain 8. In doing so, however, we will have a timing whose accuracy depends on the accuracy of the reconstructed carrier, and vice versa. In summary, we have to consider two coupled tracking loops, whose analysis looks rather complicated. Work is in progress in this direction.

REFERENCES [ l ] E. Y. Ho and D. A. Spaulding, “Data transmission performance

in the presence of carrier phase jitter and Gaussian noise,” Bell Syst. Tech. J., pp. 1927-1931, Oct. 1972.

[2] G. Schollmeier, “The effect of carrier phase and timing on a single-sideband data signal,” ZEEE Trans. Commun., vol. COM- 21, pp. 262-264, Mar. 1973.

[3] G. Schollmeier, “A fast start up procedure for carrier phase and timing recovery in SSB-AM data transmissions,” in Proc. Int. Conj: Commun., pp. 2-18-2-22, 1973.

[4] W. R. Bennet and J. R. Davey, Data Transmission. New York: McGraw-Hill, 1965.

[5] R. W. Lucky, J. Salz, and E. J. Weldon, Principles ofData Com- munications. New York: McGraw-Hill, 1968.

(61 E. Y . Ho, “A new carrier recovery technique for vestigial- sideband (VSB) data systems,’’ ZEEE Trans. Commun., vol. COM-22, pp. 1866-1870, NOV. 1974.

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Y. Fang, “Carrier phase-jitter extraction method for VSB and SSB data transmission systems,” IEEE Trans. Commun., vol. COM-20, pp. 1169-1175, Dec. 1972. H. Kobayashi, “Simultaneous adaptive estimation and decision for carrier modulated data transmission systems,” ZEEE Trans. Commun. Technol., vol. COM-19, pp. 268-280, June 1971. E. D. Gibson and M. A. Caloyannides, “Coherent SSBSC re- ception using no carrier or pilot tone,” inProc. Znt. Con$ Com- mun., pp. 2-31-2-38, 1973. H. Kobayashi, “Iterative and sequential methods for recovering sample-timing and carrier phase in data transmission systems,” IBM res. rep. RC.2491, May 1969. E. D. Gibson, “High-performance MOS/LSI modems,” in Proc. Znt. Con$ Commun., pp. 29-18-29-23, 1974. P. M. Ebert and E. Y. Ho, “Application of a Costas loop to car: rier recovery for VSB communication systems,” in Proc. Int. Con$ Commun., pp. 33-20-33-24, 1973. R. W. Chang, “Joint equalization, carrier acquisition, and timing recovery for data communication,” in Proc. Znt. Con$ Com- mun., pp. 28-34-2843, 1970. G. Schollmeier and N. Schatz, “The design of nonlinear phase- tracking loops by simulation,” ZEEE Trans. Commun., vol. COM-23, pp. 296-299, Feb. 1975. J. P. Costas, “Synchronous communications,” Proc. IRE, pp. 1713-1718, Dec. 1956. M. K. Simon and J. C. Springett, “The theory, design, and operation of the suppressed carrier data-aided tracking receiver,” Jet Propulsion Laboratory, Pasadena, CA, tech. rep. 32-1583, June 1973. W. C. Lindsey and M. K. Simon, Telecommunication Systems Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1973. R. Matyas and P. J. McLane, “Decision aided tracking loop for channels with phase jitter and intersymbol interference,” ZEEE Trans. Commun., pp. 1014-1023, Aug. 1974. W. C. Lindsey, Synchronization Systems in Communication and Control. Englewood Cliffs, NJ: Prentice-Hall, 1972. A. Papoulis, The Fourier Integral and its Applications. New York: McCraw-Hill, 1962. R. Dogliotti and U. Mengali, “Carrier recovery methods for VSB data transmission,” CSMDRT, int. rep., Oct. 1975. L. E. Zegers, “Common bandwidth transmission of data signals and wide-band pseudonoise synchronization waveforms,” Philips Res. Rep., suppl. 1972, no. 4.

Some Observations on the Statistics of Beyond-the-Horizon Transionospheric Propagation from a Satellite

P. F. PELLEGRINI AND P. BEN1

Ahtrucr-The HF signals radiated (from heights above Fzh,,,) by the first satellite orbited by the Peoples Republic of China (1970-34A) were monitored at a ground site in Florence, Italy. Beyond-the-horizon reception with distances up to antipodality were repeatedly observed. Path loss improvement with respect to free space was typically 4 dB for distances of 12 000 km and 8 dB for distances of 20 000 km (anti- podal focusing). A cross correlation receiver, designed to detect the most frequent tone (784 Hz) contained in the musical theme (“The East is Red”) emitted by the satellite, provided a processing gain of 27 dB and made possible reliable reception for input SNR as low as -13 dB.

Paper approved by the Editor for Space Communication of the IEEE Communications Society for publication without oral presenta- tion. Manuscript received November 28, 1975; revised September 20, 1976.

The authors are with the Istituto di Ricerca sulle Onde Elettro- magnetiche (IROE), Italian National Research Council (CNR), Florence, Italy.