PROCEEDINGS OF THE IRE

Bandwidth Considerations in a JANET System*L. L. CAMPBELL, t MEMBER IRE, AND C. 0. HINES t

Summary-Some of the considerations which influence thechoice of transmission bandwidth in a JANET system are discussedin this paper. It is shown that the mean rate of transfer of informa-tion increases with bandwidth, for bandwidths in the range currentlycontemplated, in spite of the consequent decrease in the duty cycle.A system designed to maintain a constant snr by varying the band-width with received signal power is discussed, and its advantageover a fixed bandwidth system is calculated.

I. INTRODUCTION

N CONVENTIONAL communication systems, anincrease in transmitter power can be employedeither to reduce the error rate through increased

snr in a fixed bandwidth or to increase the signaling ratethrough the use of a wider bandwidth. In the JANETsystem, described by Forsyth et al.,' ain inicrease intransmitter power can be used in either of these waysor it can be used to increase the duty cycle (fractionof time that communication is possible). In general,an increased duty cycle causes a decrease in the meandelay of a message in the system and an increase inthe mean rate of information transfer, even withoutan increase in bandwidth. These advantages are offsetto some extent by the increased possibility of multipathpropagation. The dependence of duty cycle on sensi-tivity is discussed more fully in Section II.An alternative approach is to consider the trans-

mitter power fixed while the bandwidth and signalingrate are increased. In a conventional system this wouldinormally lead to an increase in the error rate because ofthe increased noise accepted by the receiver in thebroadened band. However, with a JANET system thebandwidth may be increased without an increase in er-ror rate if, at the same time, the received signal levelwhich is required to start transmission is increasedproportionately, thereby maintaining the same thresh-old snr during transmission. The increased bandwidthallows an increased instantaneous signaling rate duringtransmission, but the increased signal level required fortransmission reduces the duty cycle. Thus, in designinga system, it becomes important to decide whether to usea high instantaneous rate for a small fraction of time ora lower instantaneous rate for a larger fraction of time.This question will be discussed in Section III.The approach adopted in the preceding paragraph

may be extended. It is evident that a further advantagemight be gained by the use of a variable bandwidth

* Original manuscript received by the IRE, March 22, 1957. Thiswork was performed under project PCC No. D48-28-30-05.

t Radio Physics Lab., Defence Research Board, Ottawa, Canada.I P. A. Forsyth, E. L. Vogan, D. R. Hansen, and C. 0. Hines,

"The principles of JANET a meteor-burst communication system,"PROW. IRE, this issue, p. 1642.

system capable of following the rapidly changingstrength of useful signals. The object of such a systemwould be to vary the bandwidth in proportion to thesignal power, keeping the snr constant, and so to makethe most effective use of both strong and weak signals.The transmission rate could vary continuously orthrough several discrete steps. The improvement whichmay be expected from such a variable rate system anidone possible method of achieving it will be indicated inSection IV.

II. DUTY CYCLE AND SYSTEM SENSITIVITYThe effect of the operating threshold level on the

duty cycle can be derived simply, if it is assumed thatall signals are of the underdense type.' The variation ofsignal amplitude is then given by

A =0

A = Ap exp (-I/r)for I < 0

for t > 0, (1)

where AP is the peak signal amplitude, r gives a measureof the signal duration, and t measures time from theformation of the trail. For simplicity it will be assumedthat a single value of r is applicable to all signals, al-though the actual distribution could be taken into ac-count by an appropriate integration. The variation ofAp from one signal to another is, however, of direct in-terest here, and a specific distribution of peak ampli-tudes must be adopted. It will be assumed that thenumber of signals per unit time, No with peak ampli-tudes greater than some value Ao is given by

No = CA0-2n, (2)

where n is some positive number.The JANET system transmits information only when

the received snr exceeds a suitable value. If this valuecorresponds to the amplitude level Ao, then the usefulduration of a signal of the form (1) is given by

To= r ln (A,/Ao) (3)

forA p > A o. If A,, <A0, the duration is zero and the signalis of no use. Thus the probability that the useful dura-tion of the signal exceeds a value T is the same asthe probability that the peak amplitude exceedsAo exp (T/r). From (2), the number of signals per unittime whose durations exceed T is CA 0-2n exp (- 2n T/r).The total number of useful signals per unit time isCAo2n and hence, the probability that the duration ofa useful signal will exceed T is exp (- 2n T/r). Thus theprobability distribution of the durations, and hence themean duration, is independent of Ao. Now the duty

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Campbell and Hines: Bandwidth Considerations in a JA NET System

cycle, or fraction of time that the received signal ampli-tude exceeds Ao, is given by

F = CA0-2nTm, (4)

where Tm is the mean duration of an individual signal.Eq. (4) is valid only when F is so small that the possi-bility of two suitable reflecting trails existing simultane-ously may be neglected. Since C and Tm are independentof Ao, (4) may be written

F = KPo-n, (5)

where Po is the threshold power corresponding to A0 andK is independent of Po.

McKinley2 has proposed an empirical relation of theform (5), and has estimated the value of n to be 0.56.Some records have also been analyzed at this laboratoryand they confirm that the relationship between F andPo is approximated well by an equation of this form, al-though the values of n which were obtained here rangefrom 0.57 to 0.96. Forsyth and Vogani, in an earlieranalysis based on (2), obtained a value 0.72. The distri-bution of meteor masses which was indicated in thecompanion paper,' combined with the assumption ofunderdense trails, would have given as a theoreticalestimate the value n = 0.5. The larger values found inpractice can be attributed to the occurrence of over-dense trails. In view of the simplifying assumptionswhich were necessary to derive (5) it seems best to re-gard this equation as a simple approximation to a muchmore complicated one.The relation between duty cycle and mean rate of

information transfer is a complex one which is discussedelsewhere.4 In an important limiting case, however, itmay be written

mean rate = instantaneous rate X duty cycle. (6)

The duty cycle, in turn, is directly proportional to thenth power of the transmitted signal power, as may beinferred from (5). Consequently, for a given bandwidth,the mean rate of transfer of information is proportionalto the nth power of the transmitter power.

It should be emphasized that (5) must not be expectedto hold for very large or very small values of Po. WhenPo is small, considerable overlapping of signals must beexpected and thus F will be smaller than (5) predicts.On the other hand, the transmitted power imposes anupper bound on Po, above which the duty cycle must beidentically zero. However, (5) does seem to be a goodapproximation for vaues of F between 0.005 and 0.1.

2 D. W. R. McKinley, "Dependence of integrated durations ofmeteor echoes on wavelength and sensitivity," Can. J. Phys., vol. 32,pp. 450-467; July, 1954.

3 P. A. Forsyth and E. L. Vogan, "Forward-scattering of radiowaves by meteor trails," Can. J. Phys., vol. 33, pp. 176-188; May,1955.

4 L. L. Campbell, 'Storage capacity in burst-type communicationsystems," PROC. IRE, this issue, p. 1661.

III. FixED BANDWIDTH SYSTEMSIn the preceding section, the relation between mean

rate of information transfer and transmitter power wasdiscussed. In the present section, the relation betweenmean rate and receiver bandwidth will be examined onthe assumption that the transmitter power is fixed. Itwill be assumed that the bandwidth is proportional tothe instantaneous rate, that (5) and (6) hold, that thesnr required for satisfactory operation is independentof the instantaneous rate and that the received noisepower is proportional to the bandwidth. As a conse-quence of the last two assumptions, the required thresh-old power level, P0, is seen to be directly proportionalto the bandwidth and hence, (5) may be rewritten as

F =KB-n, (7)

where K, is independent of B. The mean rate of infor-mation transfer, Rf, is then given by

Rf = K2BF = KIK2B'-n, (8)where K2 is another constant. Since n is normally lessthan unity it appears from (8) that the bandwidth andsignaling rate should be chosen as large as possible if itis desired to make the mean rate large.

Operation of the system with a large bandwidth andsmall duty cycle may have one further advantage andat least one disadvantage. The favorable feature is thatthe number of characters per burst is increased as thesignaling rate goes up. This reduces the number of errorswhich may be caused by start and stop procedures atthe beginning and end of each burst. The unfavorablefeature is the large delay of a message in the systemwhen the duty cycle is small.

It is more difficult to estimate the effect on multipatherrors of increasing the signaling rate and reducing theduty cycle. On the one hand, the higher signaling ratemay mean more errors when multipath propagation oc-curs. On the other hand, a reduced duty cycle will meanthat multipath propagation occurs less often. Multipathpropagation occurs when two or more suitably orientedand suitably ionized meteor trails exist simultaneouslyin the antenna beams. In general, if communication ispossible for a fraction F of the time, there will be multi-path propagation for approximately a fraction F2 of thetime. However, much of this multipath propagation willbe quite harmless, either because one reflected signal ismuch stronger than the other or because the path dif-ferences are such that the signals arrive in phase at thereceiver. Experience indicates that multipath propaga-tion does not cause serious difficulties for duty cycles upto 5 per cent.

IV. VARIABLE RATE SYSTEMSIt has been suggested by Forsyth' that the perform-

ance of a JANET system could be improved by making

P. A. Forsyth, unpublished report.

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the l)andwidth and signaling rate vary in direct propor-tion to the received signal power throughout each indi-v7idual burst in order to use most efficiently all availablesignals. Such a variable rate system will be comparedwith a fixed rate system on the same assumptions asbefore.

It will be assumed that the bandwidth may be variedcontinuously between some lower limit, Bo, and someupper limit, Bi. When the received signal is so small thatthe snr in the bandwidth Bo is below the threshold notransmission takes place; and when the snr in the band-width B1 is above the threshold, the bandwidth remainsfixed at the value B1. Between these limits, the band-width varies so as to maintain the snr at the thresholdvalue. The limits Bo and B1 would probably be deter-mined by practical design considerations and for thepresent development must lie within the limits forwhich (7) is valid.Now the fraction of time that communication is possi-

ble in a bandwidth B or greater is F(B), where F(B) isgiven by (7). Thus, if Bo<B <B1, the fraction of timethat the variable rate system would operate with abandwidth B to B+dB is F(B) -F(B+dB), or approxi-mately - F'(B)dB. Hence, in the mode of operation de-scribed, the mean rate of transfer of information isgiven by

rBiRv -K2 J BF'(B)dB + K2B1F(B1). (9)

When the value of F(B) given by (7) is substituted inthis, the result is

1-n L \B~j1/iR KB,''[ (B,- ( 10)

The best fixed bandwidth system with a bandwidthin the range Bo to B1 is the system with bandwidth Bi.The mean rate with this system is given by

Rfl KjK2B1 -. (I11)

Thus, if an improvement factor, I, is defined by

I = R,/Rf , (12)

thenI = (1 - n)-1[1 - n(Bo/BI)'-nl] (13)

If the bandwidth is varied in discrete steps, rather thancontinuously, the improvement will be somewhat lessthan that predicted by (13). If the typical value 0.75 ischosen for n, then for Bo/B1=I/10, I=2.31. If Bo/B,=1/100, then -=3.05.Hansen6 has proposed a technique which would pro-

vide a variable rate system and which might be feasibleif the ratio B1/Bo is not great. Briefly, the technique isto convert digital information to modulation waveformat a fixed low rate and then store the modulation wave-form. The modulation waveform would be dischargedto the transmitter at a variable rate which is controlledby a signal from the receiving station. At the receiverthe signal is demodulated and the modulation waveformis entered in the receiver store at the same rate as it isdischarged from the transmitter store. Finally, themodulation waveform is discharged from the receiverstore at a fixed low rate and is then converted to digitalinformation. Now, if the snr is high enough that pre-detection filtering and post-detection filtering may beconsidered equivalent, a fixed audio frequency filter atthe output of the receiver store is equivalent to a varia-ble band-pass filter at the receiver input. Clearly thistechnique involves several problems of synchronizationand the operation of servomechanisms which will con-trol the speed of the storage units. It is not known yetwhether the cost of surmounting these problems is lowenough to make this a practical system.

In conclusion, it should be emphasized that the cri-terion used in this paper for comparing systems has beenthe mean rate of transfer of information. It is conceiva-ble that other factors, for example the possible delay ofa meassage, may be more important. In this case, onemight wish to compare the variable rate system with afixed rate system which has a lower mean rate than Rf,but which has other desirable features. If the variablerate system retains these desirable features, as it wouldin the case of delays, the improvement factor over thegiven fixed bandwidth system might easily be muchgreater than that given by (13).

6 D. R. Hansen, unpublished report.

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