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TECHNICAL CONSIDERATIONS LEADING

TO AN OPTIMUM ALLOCATION OF RADIO

FREQUENCIES IN THE BAND 25 TO 60 MC

BY KENNETH A. NORTON

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NATIONAL BUREAU OF STANDARDS

technical <Vtote

13

June, 1959

Technical Considerations Leading to an Optimum

Allocation of Radio Frequencies in the Band 25 to 60 Mc

by

Kenneth A. Norton

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

listed or referred to in the open literature. They are for sale by the Office of Technical Services, U. S. Department of Commerce, Washington 25, D. C.

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National Bureau of Standards OCT 3 19G0

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IMPORTANT FOREWARD

This Technical Note was originally printed as a restricted

NBS Report on March 1, 1955. Many of the technical details have

undergone extensive additional study since that time as discussed

briefly below, but nevertheless it is considered desirable to reprint

this report and make it generally available at this time since some

of the general considerations for optimizing the use of the spectrum

are as valid today as they were in 1955.

1. Noise predictions more recent than those in reference 7

are available in CCIR Report No. 65 "Report on Revision of Atmospheric Radio Noise Data" (Warsaw 1956, available as a separate

document from the International Telecommunication Union, Geneva,

or in Vol. I of the Documents of the Vlllth Plenary Assembly of the

CCIR, Warsaw, 1956). Data from the current world-wide atmospheric radio noise measurement program are to be published as

Technical Notes.

2. The material on tropospheric scatter in reference 23

has now been or will shortly be published:

Kenneth A. Norton, P. L. Rice, and L. E. Vogler,

"The Use of Angular Distance in Estimating Transmission Loss and Fading Range for Propagation

-2-

Through a Turbulent Atmosphere Over Irregular

Terrain, " Proc. IRE, 43, 1488, (1955).

Kenneth A. Norton, "System Loss in Radio Wave

Propagation, " J. Research NBS, 63-D, (Radio Propagation), 53-73, (1959).

P. L. Rice, A. G. JLongley, and K. A. Norton,

"Prediction of the Cumulative Distribution With

Time of Ground Wave and Tropospheric Wave Transmission Loss, " to be offered for publication shortly

in J. Research NBS, Part D.

3. On page 19> a prediction was made that the next sunspot

cycle would have an unusually low maximum. The actual maximum

exceeded all previous maxima on record. This points up somewhat

further the desirability of recommendation "c" on page 36. It appears

desirable that the McNish- Lincoln method should be used for longer

range predictions as well as for the shorter range predictions for

which it is now used. Further work should be done on prediction

at both long and shoit ranges of ionospheric indices of sunspot

activity as well.

-3-

4. Recommendation "a" on page 36 has since been acted

upon and appropriate maps are now available in Technical Note

No. 2, by Donald H. Zacharisen, "World Maps of F2 Critical

Frequencies and Maximum Usable Frequency Factors, " dated

April, 1959.

5. Appendix VII of the original NBS Report on Sporadic

E and Ionospheric Forward Scatter has been omitted since much

of this material has now been published elsewhere. Some pertinent references are:

R. M. Davis, Jr., E. K. Smith and C. P. Ellyett,

"Sporadic E at VHF in the U.S.A., " Proc. IRE, 47,

762-769, (1959) (this paper lists other recent important references).

R. C. Kirby, "VHF Propagation by Ionospheric

Scattering - A Survey of Experimental Results, "

IRE Trans. CS-4, 17-27, (1956).

R. C. Kirby, "1958 Critique of Ionospheric Scatter

Communications," IRE-G.W.U. Symposium on

Space and Extended Range Communication, Washington, Oct., 1958,

-4-

R. M. Davis, Jr. , "F2 Interference at VHF, "(to

be published).

James Blair, "Frequency Dependence of VHF Ionospheric Scattering, " to be published as a Technical

Note.

Kenneth A. Norton, "Transmission Loss in Radio

Propagation: II, " NBS Technical Note No. 12,

July, 1959.

TECHNICAL CONSIDERATIONS LEADING TO AN

OPTIMUM ALLOCATION OF RADIO FREQUENCIES

IN THE BAND 25 to 60 MC

by

Kenneth A. Norton

National Bureau of Standards

Boulder, Colorado

Table of Contents

Page

1. Introduction 1

2. Present Occupancy 2

3. Summary of Conclusions and Recommendations ...... 2

4. General Technical Principles for Radio

Frequency Allocation 5

5. The Allocation of High Power Fixed Services (RPIS)

Jointly with Medium Power Land Mobile Services 10

(a) F2 Propagation 15

(b) Sporadic E Propagation 23

(c) Ionospheric Forward Scatter 28

(d) Tropospheric Forward Scatter ............ 28

6. Technical Conclusions 30

7. Some Philosophy of Radio Frequency Allocation ..... 32

8. Recommended Allocation Procedures 35

9. Recommended Further Radio Propagation Research . 36

10, Recommended Further Frequency Allocation

Research 37
Table of Contents (cont'd)

Appendix I frequency Assignments in the Band 25-60 Mc

Appendix II Desired-Carrier to Noise, R, and DesiredCarrier to Undesired-Carrier, R , Ratios

Required for Satisfactory Reception of f-s-k

Teletype and FM Voice Communication Systems

by A. D. Watt

Appendix III Sporadic E Computations

by E. K. Smith

Appendix IV Long-Term Distribution of Instantaneous

Received Power

by Garner McCrossen

1. Introduction

2. The Cumulative Distribution Function

3. Method for Approximating the Cumulative

Distribution Function for Large Values

of °Z

Appendix V Accurate Equations foi Determining the Interference to be Expected Between Radio Services

Operating on the Same or Adjacent Channels

Appendix VI The Carrier Frequency Dependence of the Transmitter Power Required to Provide Various Types

of Service in the Presence of Noise
TECHNICAL CONSIDERATIONS LEADING TO AN

OPTIMUM ALLOCATION OF RADIO FREQUENCIES

IN THE BAND 25 TO 60 MC

by

Kenneth A. Norton

National Bureau of Standards

Boulder, Colorado

1. INTRODUCTION

The object of this study is to outline very briefly the technical

considerations leading to an optimum allocation of radio frequencies

in the band 25 to 60 Mc. This report will indicate what technical

information is now available and where it may be obtained, as well

as what additional information should be obtained in the future.

By optimum allocation I mean one which will best serve the

public interest. It is most important to recognize that technical

considerations alone will not lead to such an optimum allocation

since they do not allow for differences in the social and economic

importance of the various uses which may be made of this portion

of the radio spectrum. It is only after these social and economic

considerations have been superimposed upon the technical considerations that an optimum allocation can be achieved. This portion of the

spectrum is used extensively by both government and non- government

services. Although there is an agency, the Federal Communications

Commission, responsible for allocating frequencies to non- government

services in an optimum way, the comparable agency for all allocations

government and non-government - the Interdepartment Radio Advisory

Committee, is not organized in such a way as to make it feasible for

them to consider the relative social and economic importance of the

various uses of the spectrum. }_/ In view of the absence of any

zJ A good discussion of government organization in the telecommunications field is given in Chapter V of the report "Telecommunications, A Program for Progress," by the President's

Communications Policy Board, Washington, March 1951,

which is available from the Superintendent of Documents,

Government Printing Office, Washington 25, D. C.
- 2 -

regularly constituted government agency with direct responsibility

for optimum radio frequency allocations, it will perhaps not be

inappropriate if suggestions are made in the course of this report

as to how some of these social and economic conflicts should be

resolved. Obviously, any suggestions made in this area represent

only the personal opinions of the author. These statements may

assist in pointing up the problems involved, and it is only with this

in mind that these opinions are given.

2. PRESENT OCCUPANCY

First it is desirable to describe the nature of the uses to

which this part of the radio spectrum is at present allocated in the

United States:

a. Land Mobile

b. Maritime Mobile

c. Fixed Point-to-Point

d. International Broadcasting

e. Television Broadcasting

f. Amateur

The information presently available on the extent and nature of

these services is given in Appendix I. In particular an analysis

of the statistics in Appendix I indicates that mobile services of one

type or another are the principal occupants of this band; in fact

93. 26 percent of all transmitters assigned to this band are in the

mobile service. On the other hand, only a relatively small number - 4.57 percent - are at present assigned to fixed point-to-point services

The remaining 2. 17 percent of the transmitters are assigned to all

of the other types of service occupying this band.

3. SUMMARY OF CONCLUSIONS AND RECOMMENDATIONS

The vise of the concept of transmission loss is first explained

as it relates to the problem of determining the mutual interference

to be expected between services occupying the same or adjacent

portions of the frequency spectrum. It is then shown that services

operating on the same radio frequencies inthis particular band are

subject at times to severe mutual interference due to (a) transmission

by way of the regular F2 layer of the ionosphere or (b) transmission

by way of sporadic E ionization of the ionosphere.
It is shown that F2 layer interference is the most severe in

terms of its intensity. However, this kind of interference decreases

systematically in its duration of occurrence as the radio frequency

is increased, and also varies to a substantial degree geographically,

diurnally, seasonally, and with the sunspot cycle.

Sporadic E interference may also be quite intense, but the

probability of its occurrence (or the percentage of time that it exists) decreases rapidly with increasing intensity of the interfering

signals and with increasing frequency. The geographical, diurnal,

seasonal, and sunspot cycle variations of this mode of propagation

are not as well understood or as predictable as F2 interference.

Other modes of propagation of potential interference are

ionospheric and tropospheric forward scatter, but the interference

arising from these modes is usually much less intense and can often

be avoided by careful planning of the use of this portion of the

spectrum in terms of station separations and the use of directive

antennas.

It is shown in Appendix VI that the power required to provide

a given service may either increase or decrease with increasing

frequency, depending largely on the kind of antennas used. Thus,

mobile services which normally use non-directional antennas at

both ends of the circuit require more power for a given range the

higher the frequency. On the other hand, point-to-point services

may use large directional arrays at both ends of the circuit and,

for a given size, these arrays have an increased gain the higher

the radio frequency; thus the point-to-point services may often

operate more efficiently at the highest frequencies free from the

effects of atmospheric absorption, i. e. , above 2000 Mc and below,

say, 20, 000 Mc.

Based on the above conclusions, the following allocation

procedures are recommended:

a. Since the new High Power Fixed Service (RPIS) provides

a kind of communication facility which cannot readily be duplicated

elsewhere in the entire radio spectrum, it should be favored relative to other services occupying this particular portion of the spectrum,
b. Because of the ease of jamming by means of F2 propagation, all services likely to be jammed should use frequencies

sufficiently high so that F2 propagation will not occur during most,

if not all, of the time.

c. High Power Fixed Services likely to be jammed should be

allocated frequencies sufficiently high so that FZ propagation is not

feasible even at sunspot maximum and geographically separated

(by, say, 1500 miles or more) from other users of these same

frequencies so that other modes of propagation do not cause interference.

d. High Power Fixed Services unlikely to be jammed may

be allocated cleared channels anywhere within the 25 to 60 Mc

range. Such cleared channels would necessarily have to be negotiated and cleared internationally.

e. Since the Land Mobile Services are evidently able to operate

as at present under conditions of fairly severe sporadic interference

such as that caused by tropospheric and sporadic E propagation, it

seems likely that many more such stations can be allocated to individual channels in this band before the loss in service suffered by

those stations already on the channels becomes greater than the

additional service provided by the newly allocated stations. Only

when such a balance is struck can it truly be said that efficient use

is being made of this portion of the spectrum.

f. By the use of higher transmitter-carrier-frequency and

receiver-oscillator-frequency stabilities, narrower range modulation schemes and improved receivers, more channels may be made

available per megacycle of this valuable spectrum space,

g. Sufficiently high power should be used by all services so

that noise does not limit the communications at any time in the case

of point-to-point services or at any location within normal operational range in the case of mobile or broadcast services,,

h. Many land mobile services can operate satisfactorily in

higher frequency portions of the spectrum and, especially if reliable,
- 5 -

continuous service is essential, should seek channels in these

higher frequency bands.

4. GENERAL TECHNICAL PRINCIPLES FOR

RADIO FREQUENCY ALLOCATION

In a recent paper jV the author outlined the concept of transmission loss and showed how it could be used in radio frequency

allocation engineering. It will be convenient to recapitulate some

of that theory here. The transmission loss of a radio communication

circuit is defined to be the ratio of the power radiated from the

transmitting antenna to the resulting signal power available from

a loss -free receiving antenna. The transmission loss depends upon

the length and geographical location of the transmission path, the

time of day, the season of the year, the phase of the sunspot cycle,

the radio frequency, and the path antenna gain. The path antenna

gain, Gp, expressed in decibels, is approximately equal to, but

is in general somewhat less than, the sum of the free space gains

of the transmitting and receiving antennas, G| and Gr :

G

p < Gt + Gr

It is convenient to define a quantity, L^,* expressed in decibels,

—2/

' Kenneth A. Norton, "Transmission Loss in Radio Propagation, " NBS Report 2044, Oct. 31, 1952; also Proc. IRE, Vol. 41,

No. 1, p. 146, January 1953.

* In this report capital letters are used to denote the ratios,

expressed in decibels, of the corresponding quantities designated

with lower-case type. The symbol L^ was used to denote the

basic transmission loss in free space in reference 2, but is here

generalized to apply to the actual transmission path, i.e. , the

Lfo in this report corresponds to the (Lb + A) of reference 2.
- 6 -

which will be called the basic transmission loss, and which is equal

to the transmission loss expected for propagation between isotropic

transmitting and receiving antennas. If we let L denote the actual

measured or calculated transmission loss for the circuit, expressed

in decibels, then:

Lb = L + G

p

(2)

If we let Pr denote the power radiated from the transmitting antenna

and let Pa denote the power available from the receiving antenna,

both expressed in decibels above one watt, then we may write:

Pa = Pr

- L 1 Pr + Gt + Gr " H < 3 )

In the above the approximate expression on the right neglects the

difference between Gp and (Gj. + Gr ), this latter difference being

sometimes called the "loss in path antenna gain. "

Satisfactory communication over a particular transmission

path will be possible only when Pa > Pm where Pm denotes the

minimum signal power, available from the receiving antenna,

which will provide satisfactory reception in the presence of noise

and m other undesired signals. The maximum range of a system

is determined approximately by the relation Pa

= Pm.

I m

Pm = 10 log]; 10 I rfktb + E *u Pau

L u=1

«4)

In the above r denotes the minimum signal-to-noise power ratio

which will provide satisfactory reception in the absence of interference other than noise, f is the effective receiver noise figure^/
k is Boltzmann's constant and is equal to 1. 3802 x 10~" joules

per degree Kelvin, t is a reference absolute temperature taken

to be 288.44 degrees Kelvin so that 10 log^n^t is equal to 204

db below one watt per cycle bandwidth, b is the effective receiver

noise bandwidth expressed in cycles per second, r denotes the

minimum signal-to-interference power ratio which will provide

satisfactory reception in the presence of the available signal power

Pau from one of the undesired signals and in the absence of interference from noise or other undesired signals.

The radiated power, Pr r> required to just over-ride the

noise, in the absence of other forms of interference, may be determined from the relation:

P rr= 10 log 10 (rfktb) + L = R+F+B + L- 204 (5)

In general F and L. will vary with time; in order to ensure service

for, say, 99 percent of the time, it is necessary to use a value of

Prr which is exceeded only 1 percent of the time, i. e. , with a

probability, p = 0. 01. It is shown later in this section that it is

often desirable to use a radiated power Pr

= Prr + APr where

APr

is, say 10 db, in order to ensure that optimum use is made

of the spectrum. A further discussion of (5) is given in Appendix VI.

As pointed out in reference 2, it is often satisfactory in

solving (4) to neglect all except the dominant term in the square

brackets. With this approximation, the problem of radio allocation of frequencies is reduced to a consideration of the relative

magnitudes of the terms rfktb and ru p au ; thus a reasonably

interference -free allocation is achieved when:
rup au < rf ktb (u = 1 to m) (6)

or Pau < 10 logio(rfktb) - Ru

(decibels) (7)

The above criterion for a reasonably interference-free allocation

may be expressed as follows in terms of the transmission losses,

Lu , on the m paths between the various undesired service transmitters and the desired service receivers:

Lu = (Pru- pau) > Lmu = Pru+Ru-10 log10 (r f ktb) (u = 1 to m) (8)

The above criterion was developed on the assumption that

the desired station uses just the right amount of transmitter power

to provide a satisfactory noise -free service. If we let APr denote

the desired station power, expressed in decibels, in excess of

that required to provide a satisfactory service in the absence of

interference, other than noise, then the interference criterion,

Iu , expressed in decibels, may be written:

lu = < Lmu " Lu) <9)

(for APr < 0; i. e. , desired station power

less than that required to over-ride noise)

lu = (Lmu - Lu

- APr ) (10)

(for APr > 0; i.e. , desired station power

more than that required to over-ride noise)
- 9 -

The desired signals will be reasonably free of interference from

the u*h undesired transmitter when Iu < 0; when positive, Iu is a measure, expressed in decibels, of the degree of degradation of

the desired service by the uth interfering transmitter.

A necessary condition for the optimum use of the radio

spectrum is that APr be positive, i.e. , that somewhat more power

be used than is strictly necessary to over-ride the noise. It should

be noted that the use by all transmitters of, say 10 db, more power

than is strictly necessary (i.e. , APr= 10 db) will not increase the

interference from other stations since the desired -signal to undesired

signal ratio will not be modified at any receiving location by such a horizontal increase in power. The only effect of such a horizontal

increase in power would be an increase in the desired -signal to noise

ratio at all receiving locations and thus an improvement in the service

available.

Although the argument presented above contemplated a horizontal increase in transmitter power, studies 3,4, 5/ f individual

ZJ Kenneth A. Norton and Harry Fine, "A Study of Methods for the

Efficient Allocation of Radio Frequencies to Broadcasting Services Operating in the Range above 50 Mc, " CRPL Report 4-5,

Reference E to the Report of the FCC Ad Hoc Committee for the

Evaluation of the Radio Propagation Factors Concerning the

Television and Frequency Modulation Broadcasting Services

in the Frequency Range between 50 and 250 Mc, Federal Communications Commission Dockets Nos. 8736, 8975 and 9175,

August 1, 1949.

_/ Harold Staras, "The Effect on Television Service of Transmitting Antenna Height, Radiated Power, the Use of Off-Set or

Synchronized Co-Channel Carriers, and of Correlation among

the Radio Fields Received from Several Transmitters, " CRPL Report 6-1, Reference K to the Report of the FCC Ad Hoc

Committee for the Evaluation of the Radio Propagation Factors

Concerning the Television and Frequency Modulation Broadcasting Services in the Frequency Range between 50 and 250 Mc,

Federal Communications Commission Dockets Nos. 8736, 8975

and 9175, October 10, 1949.
- 10 -

cases in the television broadcast service have shown that an increase

in the power of one station on a channel while another interfering

station on the same or adjacent channels maintains the same power,

results in a net increase in the total service area provided by both

stations since the increase in the service area of the first station

is substantially greater than the reduction of the service area of

the other station. It seems likely that the advantages accruing from

a non-horizontal increase in transmitter power in the broadcast case

will apply to other types of service as well, but this question deserves

further study.

Unfortunately there are valid technical and economic reasons

in some cases why these increases in transmitter power are not

feasible. Otherwise it appears that higher transmitter powers should

be encouraged for the efficient use of the spectrum in all cases where

the power now used does not exceed that required to over-ride the

noise by, say 10 db. In this way it is possible to effectively eliminate the influence of the first term in the square brackets of (4).

Several approximations were purposely introduced into the

above development of general principles in order to simplify their

application. A more accurate treatment is given in Appendix V.

The application of these general principles will be illustrated

by an example in the next section.

5. THE ALLOCATION OF HIGH POWER FIXED SERVICES (RPIS)

JOINTLY WITH MEDIUM POWER LAND MOBILE SERVICES

This particular example has been chosen since the Land

Mobile Services are the principal present users of this portion of

the spectrum, while High Power Fixed Services employing ionospheric

forward scatter as the mode of propagation are strong new contenders

for a portion of this spectrum.

5/—' Kenneth A. Norton, "Addendum to Reference E, " Working Document of the FCC Ad Hoc Committee for the Evaluation of the

Radio Propagation Factors Concerning the Television and Frequency Modulation Broadcasting Services in the Frequency Range

between 50 and 250 Mc, November 16, 1950.
- 11 -

The following numerical values may be used to characterize the High Power Fixed Service: P =46 db above one watt;

Gt = Gr

= 22. 5 db; carrier frequency 35 Mc; bandwidth, b = 500

cycles per second, v/hile the following values are typical of the

.Land Mobile Service: Pr

= 30 db above one watt; G

p

= 4.3 db;*

carrier frequency 35 Mc; bandwidth, b = 20, 000 cycles per second.

Consider first whether the Land Mobile Service is likely to

interfere with the High Power Fixed Service. It is assumed that

the power used for the High Power Fixed Service will be just equal

to that required to over-ride the noise (APr = 0; for technical

reasons the use of higher power is probably impracticable at the

present time); thus we need only evaluate the maximum value of

rfktb in order to have an estimate of the value of the Fixed Service

Signal Power available at the receiver which should be protected

against interference. It is known, as a result of extensive studies

at CRPL, that radio noise of galactic origin determines the minimum signal suitable for reception throughout the band 25 to 60 Mc,

except near sunspot maximum when atmospheric noise may be more

important in the lower part of this band in some geographical locations. In particular, Cottony and Johler have reported W the levels

of galactic noise as received on a horizontal half-wave antenna in

the range 25 to 110 Mc, and these may easily be translated into

effective antenna noise figures, fa , H simply by dividing their

reported equivalent black body radiation temperatures by 288.44.

In this way we find that fa varies at 35 Mc between 28. 8 and 57. 2

Since receivers with low noise figures may be constructed readily

in this frequency range, and since antenna and transmission line

losses are low, we may assume that f c

f

t f r 2/ is equal to, say 4,

and thus we find that the effective receiver noise figure, f, for

the maximum galactic noise received on a half-wave horizontal

* Vertical half-wave dipoles at each end of the path.

-' H. V. Cottony and J. R. Johler, "Cosmic Radio Noise

Intensities in the VHF Band," Proc. IRE, 40, 1053-1060,

(1952). —
- 12 -

dipole near Sterling, Virginia-V should be equal to 60. 2.* The

receiving antenna used in the High Power Fixed Service is a highgain rhombic and, for this case, the received galactic noise level,

fa, will be of the order of 3 db higher** than the half-wave antenna

value whenever the rhombic is pointing towards the milky way.

Thus we may take the effective receiver noise figure, f, to be not

greater than 117*** at 35 Mc when reception is on a high-gain

rhombic antenna. Consider next the minimum signal-to-noise

power ratio, r. Since the desired signal is fading in accordance

with a Rayleigh distribution 8/ and since the galactic noise has

characteristics similar to random gaussian noise, we may use

the theoretical results obtained by Montgomery 9/ for a FrequencyShift modulation system to determine r. Assuming that one binary

error is one hundred may be tolerated during the small number of

]_' For translating these galactic radio noise levels to other geographical locations, reference may be made to NBS Circular

557 by W. Q. Crichlow, D. F. Smith, R. N. Morton, and

W. R. Corliss, entitled "World-Wide Radio Noise Levels

Expected in the Frequency Band from 10 Kilocycles to 100

Megacycles, " (to be published shortly). These geographical

differences are not large and will be neglected in the present

discussion. ( cf . Foreword, this report).

£/ D. K. Bailey, R. Bateman, and R. C. Kirby, Proc. IRE,

43, 1181, (1955).

jL' G. Franklin Montgomery, "A Comparison of Amplitude and

Angle Modulation for Narrow-Band Communication of BinaryCoded Messages in Fluctuation Noise, " Proc. IRE, _2, 447-

454, (1954).

* 60.2 = (57.2 - 1 -«-4)

** Verbally communicated to the author by Ross Bateman.

*** 117 = (2« 57.2-1 + 4)
- 13 -

hours that the signal-to-noise ratio is a minimum for the transmission circuit, we obtain R = 16.9 db from Equation (13) in reference 9. Combining the above information we find that average

values of the Rayleigh distributed desired signal power as small

as 139. 2 db* *£/ below one watt should be protected against interference from signals originating from the Land Mobile Service.

It is shown in Appendix II that Ru

= 1. 3 db for satisfactory reception

of the Frequency Shift telegraph signals in the presence of Land

Mobile FM interference, so we find that

Lmu = 30 + 1.3 + 139. 2 = 170. 5 db.

In a similar manner we may determine the criteria, Lmu, corresponding to the other three possible service-interference

combinations, and these are listed in Table I together with the

values of R, 10 logjo (rfktb), and Ru required for their determination. The methods used in estimating R and Ru are given

in Appendix II; in this connection it was assumed that both the

desired and undesired fixed service signals, as well as the undesired mobile service signals, fade in accordance with a Rayleigh

distribution, while the desired mobile service signal is assumed

to be constant in intensity. The values given for the other two

frequencies were obtained by assuming that the galactic noise

level, fa , varies in inverse proportion to the 2. 3 power of the

radio frequency. «/

* 10 log 10 (rfktb) = (16.9+ 10 log10 117 - 204 + 10 log10 500) = -139. 2db

zzj Still weaker signals should be protected from interference when

diversity reception is employed. The improvement to be expected

with a Rayleigh distiibuted desired signal is given in the paper

by G. Franklin Montgomery, "Message Error in Diversity Frequency-Shift Reception, " Proc. IRE, Vol. 42, No. 7, pp. 1184-

1187, July 1954.
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••H £ a CM

0) 45

(1)

<L>

rd

U)

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M-l o a •r-l ti >*

••-I T» fc rU o (L> rd * o a. U

rd rt <—i s a

4Ju r-l

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a)

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rd

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a) . o M M Tl <L> U) -»-> (> n h rJ i u

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1)M

(L> O

•i-i >u

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r-lrd>

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43

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r?oMh

rd z

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bO

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rd

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4-> rd 0)

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0)

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rd

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i—i

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to
- 15 -

Estimates may now be made of the circumstances under which

interference may be expected between these two services when they

use the same radio frequencies. There are a number of modes of

propagation possible in the frequency band 25 to 60 Mc. At short

distances the diffracted ground wave may cause interference, but

stations will presumably be separated by sufficiently large distances

that this source of interference will normally not be important. At

intermediate distances, say from 50 to 300 miles, tropospheric

forward scatter becomes important. At still greater distances

ionospheric modes of propagation are active, and a good summary

of the likely importance of the various possible ionospheric modes

is given by Morgan, jj/ In this report only four modes of propagation of the interference will be considered, namely, transmission

by way of the regular F2 layer of the ionosphere; transmission by

way of sporadic E ionization; transmission by way of ionospheric

forward scatter; and transmission by way of tropospheric forward

scatter. It seems likely that a consideration of only these four modes

of propagation of the interference will suffice for a very good first

approximation to this allocation problem.

(a) F2 Propagation

Under conditions IJLlJ-LlI-1/ such that the F2 layer will support

propagation, it is generally recognized 1°> \J_t JJV that the transmission loss in this frequency range (ff^c > 25 Mc) is approximately the

same as that expected in free space: JJ

12j

13,

M. G. Morgan, "A Review of VHF Ionospheric Propagation, ,f Proc. IRE, Vol. 41, No. 5, pp. 582-587, May 1953. See also

Report No. 7, "Long Distance Propagation of Waves of 30 to

300 Mc/s by Way of Ionization in the E and F Regions of the

Ionosphere, " Documents of the Vllth Plenary Assembly,

London, 1953, International Radio Consultative Committee,

International Telecommunication Union, Geneva, Switzerland.

NBS Circular 465, "Instructions for the Use of Basic Radio

Propagation Predictions, " 1947, Superintendent of Documents , Government Printing Office, Washington 25, D. C.
16 -

Lu

= 36. 58 + 20 log 10 f Mc + 20 log 10 D - Gpu (11)

The above has its maximum possible value for transmission between

any two points on the earth when D = 12, 500 miles, corresponding

to propagation half-way around the earth from a transmitter at the

antipode* of the receiver; values of Lu corresponding to this case

and for fjY| c

= 25, 35, and 60 Mc are given in the following table,

together with estimates of the path antenna gains, G„u , to be

expected on the undesired transmission paths:

14/

15/

16,

17/

This neglects the effects of focusing which might occur to some

extent near the antipode.

CRPLi Series D, "Basic Radio Propagation Predictions - Three Months in Advance, " Superintendent of Documents,

Government Printing Office, Washington 25, D. C.

Kenneth A. Norton, "Sunspots and Very High Frequency Radio

Transmission," CRPL Report 4-3, October 29, 1947; also

published in QST, Vol. XXXI, No. 12, pp. 13-17, December

1947.

Kenneth A. Norton, "The Nature of Very High Frequency Ionospheric Wave Propagation, " FCC Hearing on Allocation of Radio

Frequencies Between 10 kc and 30,000 Mc, Sept. 28, 1944.

E. W. Allen, Jr. , "Very-High-Frequency and Ultra-HighFrequency Signal Ranges as Limited by Noise and Co-Channel

Interference," Proc. IRE, Vol. 35, No. 2, pp. 128-152,

Feb. 1947.

JJr_/ Paul O. Laitinen anc

1 George W. Haydon, "Analysis and Prediction of Sky- Wave Field Intensities in the High Frequency Band,"

Technical Report No. 9, Radio Propagation Unit, Baltimore

Signal Depot, Baltimore 20, Maryland, August 1950.
17 -

<u —4

nl H o

•H

-t-> nl

bfl

ft} a.ou

Ph

fMMO

X»

<D

+-» O

a>aX! Wm

10O

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.•-i inw

en H oomQ

h- r~- r~

u

O o o ^ •tf r^ ^ •—4 —

i—t o • ^o o o o o M (-> * *J

II i—

* * *•

M-l o o o

CO o en

i—r——1

—

i—4 i—

m m in

•* * <tf —

f—

•—I

i—4 3J m o O o

CO -t-> -t-> * 8- u <* ^ i—i O

<+-i • m ^ in

(Nl o (M

i—

1—4 •—

fM rq rg aJ rsl rvj

u tf ^r ^ 2 i—

•—

rvj

i—4 o o O

m 4-1 +-> f\J fM

-8- •^ -KII IT) in .—

m ^ (M i-H (NJ f\3 O 00

i—i i—

—<

tf

m -* (M tf r\j 3 O o m O a +-> -l-> M a 00 CO •^ m * ^ •tf"

a)

m

O o c

0)

oj

M <u <u " 0)

1—1H T> >—

•r-l x>

H

m 3 M o o

a) o <v co -

1—4 2

•lH s • r-4 to

<uo <L> a> • r-< X) X) i—

• r-l —4

•r-4 >

CO

X• t-t •r-l

O2 O2 J
- 18 -

Using the values in the above table we may now compute the corresponding minimum value of the interference criterion, ImUi assuming

that APr = 0. At other distances Iu

= Imu + (81 .94-20 log10 D).

nt H

V**o

2 *

X > " 0) C o

O ©

•a*

U ^O

O •

« o • 2

««H rj

«S

O «4-J

- «»

r-l ^

fl» P,

1<n r< *»». T* P h

Q> o

o

«—

1

COo

r-l o

«M

• Oh 0) i V

t—

i

<tf

• r-l O* a r-i o co o *--» in +

(M 3

II »-* Q

88 03

0) u u

2 u

H o

* * *

nO CM .—

u

- • • s

m 00 t^ ^ O^ vO

o O O

<* O -*» -M «— M

II m

VI O^ in -* in t^ r-

(VI in -* * * *

O

r-i r- 00 2 in r- vO

B

in ^tf O^

«—

i

vO

co o O o

II * M t—

i

••-» ^ o CO 1—

I

U-t . . in r- t^ IM m ^F * * *

o 00 -* nO 2 -* r^ nO

•* O" vO m s CM o O o

-t-» *-» -r-> II o t—

1

r- m o^

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rq in ^

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<*-i V

o c

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Source .terfer

i—

-t-i O

2

T3X• r-l

t—

1

•rlO

2

u

X

G

i—

i

0)o

-a XJ «—

i

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•r4 > <U 0> ,D ,a

f-| X X O o

en

-«-• k 2 s

o u ft) * 2

o

si u

r-l ^2

«s»

Q.O 43 © u> o 2 o

f3

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' X
- 19 -

It is clear from the above table that a fixed service will be most

seriously degraded - in fact interrupted - during the entire time

that F2 propagation is possible between the fixed service receiving

location and any other mobile or fixed transmitting station in the

world. The mobile service will have its maximum reliable range

greatly reduced during periods of F2 propagation between its re- ceivers and any other mobile or fixed transmitting stations anywhere

in the world; the amount of the reduction in range during these

periods will be the same as if the desired mobile station reduced

its power by Iu decibels.

It will be useful now to consider in somewhat greater detail

the conditions under which the F2 layer will support propagation.

Reference 13, 14, 15/ has already been made to general methods

for solving this problem; in general F2 propagation is much less

prevalent at these high frequencies at high latitudes and at sunspot

minimum and, near Washington, D. C. , is much less prevalent in

the summer months.

There are regions within which a negligible amount of propagation via the F2 layer is to be expected. Fig. 1 illustrates how such

regions may be determined using the "NBS Basic Radio Propagation

Predictions. 11 13, 14/ Fig. 1 applies to stations within the geographical W Zone 13/ and corresponds to a wxnter month at sunspot number

130 (although 25 percent of the maxima of past sunspot cycles

exceeded 130, this sunspot number was exceeded for only 1. 7 percent

of the months during the period November 1833 to January 1944,

inclusive); thus Fig. 1 corresponds to conditions which are most

favorable to F2 propagation. Under these favorable conditions the

two solid contours on Fig. 1 enclose regions, defined in terms of

both time and geographical area, outside of which the 4000 kilometer

MUF is less than 35 Mc. If we now determine the locus of points

2000 kilometers outside of these contours, then the resulting dashed

contour encloses a region outside of which a station receiving on

frequencies above 35 Mc should be free from interference propagated

via the F2 layer from transmitters anywhere in the world for at

least 50 percent of the days of this worst month. Fig. 2 gives similar

information for other frequencies and sunspot numbers.

It is of interest to note that the present indications are that the

next sunspot cycle will have a comparatively low maximum. Thus,
- 20 -

in an unpublished paper the author has a method of making an estimate even at this early time as to the next maximum. According to

this method, which depends on an observed correlation between the

following maximum and preceding minimum, the next smoothed

maximum sunspot number will exceed 56 with a probability 0.9*

will exceed 92 with a probability 0. 5, and will exceed 129 with a

probability 0.1. The expected maximum value is thus 92, and the

expected time of the next maximum (obtained from other correlations) is July 1959. Using other results in the same paper it should

be possible, in about two years time, to make a somewhat better

estimate of the next maximum and its time of occurrence. If, in

fact, this next maximum of sunspot activity is lower than usual,

this will have the effect of alleviating the F2 interference in this

frequency band until the next following maximum which should not

occur for the next 10 to 20 years. Thus, if a chart similar to Fig. 2

were prepared for sunspot number 92 and for the month and geographical zone corresponding to the highest maximum usable frequencies,

it would be possible to determine a frequency above which F2 propagation would not be expected anywhere in the world for more than 50 per«

cent of the days of one month during the next 10 to 20 years; for

sunspot number 92 this frequency is 54 Mc.

Fig. 2 shows clearly that stations operating in the lower part

of this frequency band, say below 35 Mc, at all except extremely

high latitudes will be subject to F2 propagated interference during

several hours of the day near noon. If such interference can be

tolerated, allocations of such frequencies to more than one transmitter on a given channel will be practicable. In such a situation

it will be desirable to examine the extent of the expected interference

in greater detail. Examples of such studies for particular propagation paths between specific geographical locations are given in recent

reports by Klapper and Rieth jjy and by Gautier and Sargent. 20/

It would appear to be desirable, whenever a new service is allocated

a channel in this frequency band, to prepare a comprehensive

tZJ Eric Klapper and Edna Shultz Rieth, Private Communication,

May, 1953.

^£./T. N. Gautier, Jr. , and C. J. Sargent, "Prediction of the Likelihood of Interference at Frequencies of 30 to 42 Megacycles in

Alaska," Journal of Research of the National Bureau of Standards,

Vol. 52, No. 1, pp. 21-31, Jan. 1954.
NORTH LATITUDE SOUTH 5O

<r

Ul

LU

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NORTH LATITUDE SOUTH — O O O O O OO O ?j J, i. o o g o o

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oo

BASIC TRANSMISSION LOSS VERSUS DISTANCE AT 25 MC

The Labels on the Curves Refer to the Probability, p, During a Period of One Year that the Observed

Basic Transmission Loss will be Less than the Indicated Values

O

D

COD

O

I

120

130

140

150

170

210

220

230

240

1 1

1 \

1

r-. is-r/iie ^„„„,j„ »i ml-^

A

1 \

-- Sporadic E (Japan)

p= 0.001

/ —1

/

/

~-~^

^^

/

0.01 'Bas/c Transi77/55/0nLoss in Free Space

r

1

\\ /

1 /

\\

0.1 -^. /1 ••...'''• P= o.oi \\ \ '•(D.02

,^— P= O.OOOI

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1 IK

• O.OOI p=0.lx

1 \

-0.01

1 \ 0.5 v

> / i\y.1, N\

'• 3.05

-O.I

0.9 w

V

/ \\

0.5 \ \

\\

\ \ ,0.9

>

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099 \

&

¥ 200 400

Distance in Statute Miles

Figure 3 <NBS>
- 23 -

interference study of this kind showing the expected times of F2

interference from each of the transmitters presently assigned.

(b) Sporadic E Propagation

It has been known_Ll/ for many years that sporadic propagation

by way of the E layer of the ionosphere occurs for small percentages

of the time in the distance range 400 to 1500 miles throughout this

band of frequencies. In fact, it was largely because of the relatively

high incidence of this mode of propagation on frequencies below 50

Mc that the FCC decided to move the FM Broadcast Band from 42 to

50 Mc up to 88 to 108 Mc. Sporadic E propagation is well known as

a source of interference to the lower television channels; a good

review of this interference has been prepared by Smith. £*/

Figs. 3, 4, 5, and 6 show the hourly median levels of sporadic E basic transmission loss versus distance extrapolated to the

four frequencies: 25, 35, 45, and 55 Mc, respectively, from samples

of data obtained (a) in the United States, (b) in Japan, and (c) in

Alaska. The analysis of (a) and (b) leading to these estimates was

made by E. K. Smith and is given in Appendix III. The observed

values of sporadic E transmission loss are instantaneous values;

a method of adjusting these to correspond to hourly median values

is given in Appendix IV. This method was used in converting the

instantaneous values given in Appendix III to the hourly median values

shown on Figs. 3, 4, 5, and 6; these adjustments amount at most

to a few decibels, and are equal to about 1 db on the average.

Although the distance ranges do not quite overlap for the United

States and Japanese samples, it is quite clear that sporadic E is

much more prevalent in Japan than it is in the United States. This

indicates the necessity for making much more extensive experimental studies of this mode of propagation before attempting to draw

any precise estimates of its world-wide importance in radio frequency

allocation.

, / Ernest K. Smith, Jr. , "The Effect of Sporadic E on TV Reception, " Radio Electronics , Vol. XXIV, No. 6, pp. 54-56, June

1953. Also published in Trans. IRE, PGAP-2, pp. 54-61,

March 1952.
BASIC TRANSMISSION LOSS VERSUS DISTANCE AT 35 MC

The Labels on the Curves Refer to the Probability, p, During a Period of One Year that the Observed

Basic Transmission Loss will be Less than the Indicated Values

-QO

a

120

130

140

150

170

o

CDo

-3O

I

190

200

210

220

230

240

Sporadic E (U.S.. Canada. Alaska) h

Sporadic E (Japan)

Ionospheric Forward Scatter p

O.OOI

/

/ P ^V--"" / ^ — Basic Transmission Loss m Free Space

1 / /

i / \

\J

O.OI /

•

1 \

\v \

p

= O.OC 01 """'••

.m

> = QOC)l

- O.OOI

/

—- __^

'•••!..

(

1 \ \ y

o.i[ N-«v___

/ **—1_ Sjc.

'"'• O.OI

jXP ' \\Jr-O.OI

l\ 0.5

\

\ \ p=O.I \ t

/

0.9

0.5

0.9 \V7\

/

\

\ ^\ \ \W ^

/ \

VQ99 \

\

\ \

\

\\m

^% 200 400

Distance in Statute Miles

Figure 4 <NBS>
BASIC TRANSMISSION LOSS VERSUS DISTANCE AT 45 MC

The Labels on the Curves Refer to the Probability, p, During a Period of One Year that the Observed

Basic Transmission Loss will be Less than the Indicated Values

120

130

140

150 a

170

D

CO

oX

190

200

210

220

230

240

i i

i i Fropospheric Forward Scatter — Sporadic E (Japan) /^ u \

p =0.0001 ^ ir

-Basic Transmission Loss in Free Space --

1 1

1

1

1

/.._

0.001 \

/

/ \

O.OI _.-"

-—p= O.OOC)l 0.001 I—O.OOI "P =0.00 31

i VA

--- ^ .**N \

II

O.I

AC .5 \

I

,0.9 \

0.99 v|\ p

= O.I /

vt

0.5 \

\\\

0.9 \ / r

V V \

\

\

\V

\

m

m

xI

2 )0 4 )0 6 30 8()0 10 00 12 00 14 00 \i 00

Distance in Statute Miles

Figure 5 NBS.
BASIC TRANSMISSION LOSS VERSUS DISTANCE AT 55 MC

The Labels on the Curves Refer to the Probability, p, During a period of One Year that the Observed

Basic Transmission Loss will be Less than the Indicated Values

CDO

Q

ina

CD

oX

IIU i i

i i Tropospheric Forward Scatter

<n\

120 —— Sporadic E (Japan)

130

/ V.

p

= OOOI

/

/

140

1 »

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K8as/c Transmission Loss in Free Space

O.OOI y j

150

1 -^

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-0.00

-O.OI

160 Vr / j

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_Uo i \\\

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170

oTi

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\

"-C .001

180

\o b \

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190 V).99\

200 \w

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210 \\\

0.5 \

0.9 V

/ \\

220 \\ \

\

230 \VV

\

\\

\ iJ\

\

600 800 1000

Distance in Statute Miles

Figure 6 <NBS>
- 28 -

The Alaskan data and part of the United States data were

reported by Bailey, Bateman, and Kirby. 8/ These data are discussed in Appendix VII. The levels of sporadic E observed in

Canada and Alaska are more nearly comparable to those observed

in the U. S. than to those observed in Japan.

(c) Ionospheric Forward Scatter

This mode of propagation is, in some respects, difficult to

distinguish from sporadic E propagation. Over short periods of

time the instantaneous transmission loss is Rayleigh distributed,

while the hourly median values are approximately log normally

distributed, i.e. , hourly median values of L are normally distributed. Thus sporadic E may be casually identified simply with

those cases of ionospheric forward scatter for which the transmission loss and its probability of occurrence are both low. However,

if we identify the ionospheric forward scatter mode of propagation

with the larger transmission losses and correspondingly larger

percentages of occurrence, then this mode of propagation does have

this distinguishing characteristic - there is a considerable "loss in

path antenna gain" with high gain antennas as regards these larger

transmission loss levels.

The values of hourly median basic transmission loss shown on

Figs. 3, 4, 5, and 6 for the ionospheric forward scatter mode of

propagation were measured by Bailey, Bateman, and Kirby 8_/ and

the methods used for determining L^ from their data are discussed

in Appendix VII.

(d) Tropospheric Forward Scatter

Methods have recently become available rAiJlzJ for estimating

the basic transmission loss expected with tropospheric forward

scatter in this range of frequencies. These methods have been used

for obtaining the estimates shown on Figs. 3, 4, 5, and 6, which

are the values expected using transmitting and receiving antennas

22/

J. W. Herbstreit, K. A. Norton, P. L. Rice and G. E. Schafer,

"Radio Wave Scattering in Tropospheric Propagation," 1953

Convention Record of the IRE, Part 2, Antennas and Communications, pp. 85-93.
- 29 -

30 feet above an assumed smooth spherical earth with a standard

atmosphere. A detailed description of the particular assumptions

and approximations made in this method of calculation is given in

an unpublished report by Daniel, Mansfield, Rice, and Short. 24/

Up until recently it had been assumed that the transmission

losses associated with tropospheric forward scatter would be

roughly the same throughout the world. This assumption was

based on the fact that the levels observed in Colorado 25/ have

a remarkably small seasonal dependence and the fact that the

levels reported by many ether observers, 26/ over both land and

sea, were comparable to those observed in Colorado. Recently,

however, some measurements made in Canada (so far unpublished'

by the Defence Research Telecommunications Establishment have

indicated that the levels there are lower by an order of magnitude

than the levels reported elsewhere. For this reason the levels of

23/

24,

25/

26/

Kenneth A. Norton, "Dependence of the Transmission Loss in

Tropospheric Radio Wave Propagation on the Angular Distance. ,! This paper was originally presented with the title "The Role of

Angular Distance in Tropospheric Radio Wave Propagation" at

the West Coast Annual Meeting of the Institute of Radio Engineers at San Francisco in August 1953, and was later presented

in a series of papers to the Eleventh General Assembly of the

International Scientific Radio Union (URSI) at The Hague in

August 1954. In preparation for publication.

F. T. Daniel, W. V. Mansfield, P. L. Rice, and P. J. Short,

"Radio Transmission Loss Versus Angular Distance and Antenna

Height at 63, 100, 195 and 700 Megacycles, " Report prepared

January 7, 1954 for the use of the FCC Radio Propagation

Advisory Committee.

A. P. Barsis, J. W. Herbstreit and K.O. Hornberg, "Cheyenne

Mountain Tropospheric Propagation Experiments," NBS Circular 554, January 3, 19 55 t which is available from the Superintendent of Documents, Government Printing Office, Washington,

D s C.

Kenneth Bullington, "Radio Transmission Beyond the Horizon

in the 40- to 4, 000 -Mc Band. " Proc. IRE, Vol, 41, No. 1,

pp 132-135, January 1953.
- 30 -

transmission loss for tropospheric forward scatter shown on Figs.

3, 4, 5, and 6 cannot necessarily be considered applicable throughout the world. Furthermore, since these levels are extrapolations

from data largely obtained on frequencies above 100 Mc, they

should be verified experimentally in the lower frequency range

with which we are here concerned.

This completes the detailed consideration of the various significant modes of propagation of the interference, and we are now

in a position to consider the interference potentialities of these

last three modes of propagation using the basic transmission loss

levels shown on Figs. 3, 4, 5, and 6. We have already shown that

interference will be present whenever Iu > and, for APr = 0,

this is equivalent to the condition Lbu - Gpu < Lmu, where Lbu

denotes the basic transmission loss on the path between an undesired

transmitter and the desired receiver. Interference will exist for

the percentages of time that Lbu is less than (Lmu + GpU); Table IV

gives the values of (Lmu + GpU ) for the various service-interference

combinations considered in this report.

Reference to Figs. 3, 4, 5, and 6 indicates that the hourly

median basic transmission loss will be less than the values

(Lmu + Gpu) given in Table IV for appreciable percentages of the

time throughout the range of distances up to 1500 miles. Thus we

conclude that allocations, for either of these two types of service,

of more than one transmitter on the same channel at these distance

separations will result in potentially serious mutual interference.

6. TECHNICAL CONCLUSIONS

In the preceding three sections of this report an outline has

been presented of the kinds of information desirable for the determination of the mutual interference likely between radio stations

operating on the same or adjacent channels in the frequency range

25 to 60 Mc.

In particular it was shown that very intense and persistent

interference may be expected whenever the F2 layer of the ionosphere will support propagation between an interfering transmitter

and a desired receiver. The geographical, diurnal, seasonal and

sunspot cycle variations in the occurrence of F2 propagation were

discussed

.
- 31

Table IV

r Source of

Interference Gpu

(Litnu + Gpu i in decibels

Service f=25Mc f=35Mc f=45Mc f=55Mc

Fixed Mobile 4.3 171.6 174.8 177.2 179. 1 to to to to to

24* 191. 3* 194. 5* 196.9* 198.8*

Fixed Fixed 4.3 203. 2 206.4 208.8 210.7

to to to to to

45* 243.9* 247. 1* 249.5* 251.4*

Mobile Mobile 4.3 180.4 183. 5 185.8 187.7

Mobile Fixed 4.3 196.4 199. 5 201.8 203. 7

to to to to to

24* 216. 1* 219. 2* 221. 5* 223.4*

See the footnote to Table III for the qualifications to these

maximum values. When the values in Table IV are applied

to ionospheric forward scatter with high gain antennas,

it must be remembered that Gpu is then a random variable,

and thus the values of (Lmu + Gpu ) will vary between the

limits given above.
- 32 -

The other three modes of propagation: tropospheric forward

scatter, sporadic E, and ionospheric forward scatter were shown

to be less important from the standpoint of their intensity and

probability of occurrence. However, one or more of these modes

of propagation are capable of seriously disrupting communications

in the range of distances out to 1500 miles for brief periods of

time which may occur at any time of the day, season of the year,

or phase of the sunspot cycle.

All modes of propagation of the interference except the tropospheric mode decrease in importance as the frequency is increased.

7. SOME PHILOSOPHY OF RADIO FREQUENCY ALLOCATION

Recently the Joint Technical Advisory Committee of IRE-RTMA

prepared a report entitled "Radio Spectrum Conservation" and made

it available in book form. Section 5. 3 in this book deals with "Technical Measures to Implement Dynamic Conservation. " Since this

provides a good philosophical basis for my later recommendations,

I will quote this section in full:

"5. 3 Technical Measures to Implement Dynamic Conservation

"The limitations governing spectrum occupancy discussed in

the previous section suggest a number of corrective measures,

some rooted in the design and operation of technical equipment,

others in the administration of allocations. The technical measures

comprise the early adoption of methods contributing to spectrum

conservation, with due regard for the benefits and costs involved.

The administrative steps involve applying sound doctrine in comparing the economic and social values of competing services.

"In adopting these measures, great care must be exercised

to avoid foreclosing future developments. The cornerstone of the

conservative program should be the encouragement of and, as far

as possible, advance provisions for new services having more

extensive or comprehensive values than the old. Such unborn methods

and services may have, in fact, at least as important claims on our

natural resources as the services currently occupying the spectrum.

The evaluation of the relative importarce of the old and the new is,

in fact, the most delicate task in the administration of the spectrum.
- 33 -

"The following suggestions are offered, therefore, on the

assumption that necessary steps have been taken and are in continuous effect to encourage experimentation with new services

throughout the spectrum. The suggestions apply in particular to

services which have passed the experimental stage and have entered

or are about to enter regular operation.

"On this basis, the following measures are indicated:

"1. Experimental authorizations to develop new services

should be granted in all regions of the spectrum, subject to reasonable safeguards to prevent interference with existing services.

When a radio service performs a function which can be performed

by nonradio equipment (e.g. , wire lines), the permanent establishment of the radio service, beyond the developmental period, should

not take place until the comparative costs and values of the radio

and nonradio services have been assessed and compared and a determination made of other demands on that portion of the spectrum,

Unless the costs of the radio service are appreciably less or their

value appreciably greater than the corresponding costs and values

of the nonradio service, conservation of the spectrum requires that

nonradio services be used.

"2. The frequency tolerances applicable to carrier emissions

should be a suitably small fraction of the channel width. In most

cases "suitably small" implies as small as the state of the art permits, without incurring undue penalties in size, weight, or ease of

operation and maintenance. Such penalties are not usually the controlling factor. The principal deterrent is cost. After a reasonable

period to amortize the cost of substandard equipment has intervened , it should be replaced by equipment meeting a reasonable standard of

carrier stability.

"3. Off-frequency operation and pirating of frequencies represent a gross derogation of the principles of spectrum conservation

which must be brought under control by improved methods of international cooperation.

"4. The use of guard bands to accommodate apparatus deficiencies (such as excessive carrier-frequency tolerances, improper
- 34 -

or inefficient transmitter modulation, or inadequate receiver

selectivity) should be curtailed.

"5. The use of the most efficient modulation methods, with

respect to uniform frequency occupancy of the assigned channel,

should be encouraged, particularly in the wide -band services such

as FM and television broadcasting.

"6. Every practical method of restricting the extent to which

the interference area of a station extends beyond its service area

should be employed. Specific measures include restricting of

transmitter power to the level required for adequate service,

suppression of harmonic emissions, synchronization of carriers

where practicable ('offset carrier' in television broadcasting), and

the employment of directional antennas. Where the cost of such

measures is substantial, a suitable amortization period should be

allowed

.

"7. Services occupying regions of the spectrum not particularly

adapted to their needs and capabilities should be transferred to other

regions, in accordance with the dictates of full spectrum occupancy,

and outmoded services deleted. Economic resistance to such shifts

can be overcome by announcement of the impending change with a

statement of the technical and economic advantages to be obtained,

sufficiently in advance to permit old equipment to be amortized and

to allow new equipment to be procured and installed. As knowledge

of propagation and equipment improves and becomes stabilized, it

should be possible to establish in advance the basis for such transfers over periods as long as 25 years, although shorter periods

should suffice in most cases.

"8. Frequency assignments should be shared to the fullest

practicable extent. Time sharing of frequency assignments is looked

upon with disfavor by nearly all users of the spectrum and by many

of its administrators, largely as a result of unfortunate experience.

Geographical sharing is common in many services, including all

forms of broadcasting, but is uncommon in others, as, for example,

between military and civilian services. The difficulties of shared

operation are mainly administrative. While not belittling the problems,

we must recognize that the increasing congestion of the spectrum

will eventually force greater reliance on shared operation. The time
- 35 -

is already past when a local assignment made under a military

administration should preclude a similarly local assignment at a distance made under a civilian administration, when interference

does not occur and is not anticipated. "

8. RECOMMENDED ALLOCATION PROCEDURES

a. Since the new High Power Fixed Service (RPIS) provides

a kind of communication facility which cannot readily be duplicated

elsewhere in the entire radio spectrum, it should be favored relative

to other services occupying this particular portion of the spectrum.

b. Because of the ease of jamming by means of F2 propagation, all services likely to be jammed should use frequencies

sufficiently high so that F2 propagation will not occur during most,

if not all , of the time

c. High Power Fixed Services likely to be jammed should be

allocated frequencies sufficiently high so that F2 propagation is not

feasible even at sunspot maximum and geographically separated

(by, say, 1500 miles or more) from other users of these same

frequencies so that other modes of propagation do not cause interference.

d. High Power Fixed Services unlikely to be jammed may

be allocated cleared channels anywhere within the 25 to 60 Mc

range. Such cleared channels would necessarily have to be negotiated and cleared internationally.

e. Since the Land Mobile Services are evidently able to operate

as at present under conditions of fairly severe sporadic interference

such as that caused by tropospheric and sporadic E propagation, it seems likely that many more such stations can be allocated to individual channels in this band before the loss in service suffered by

those stations already on the channels becomes greater than the

additional service provided by the newly allocated stations. Only

when such a balance is struck can it truly be said that efficient use

is being made of this portion of the spectrum.
- 36 -

f. By the use of higher transmitter-carrier-frequency and

receiver-oscillator-frequency stabilities, narrower range modulation schemes and improved receivers, more channels may be made

available per megacycle of this valuable spectrum space.

g. Sufficiently high power should be used by all services so

that noise does not limit the communications at any time in the case

of point-to-point services or at any location within normal operational range in the case of mobile or broadcast services.

h. Many land mobile services can operate satisfactorily in

higher frequency portions of the spectrum and, especially if reliable,

continuous service is essential, should seek channels in these higher

frequency bands.

9. RECOMMENDED FURTHER RADIO PROPAGATION RESEARCH

a. Methods should be developed for predicting F2 maximum

usable frequencies for each two-hour period of the day rather than

by the three geographical zones as at present.

b. Predictions should be made of the expected variance of the

maximum usable frequencies as well as their median values.

c. Work should be expedited on methods for the prediction of

sunspot activity.

d. Many further measurements should be made at as many

locations as possible throughout the world of the tropospheric forward scatter, sporadic E and ionospheric forward scatter transmission losses expected throughout the frequency range 25 to 60 Mc.

afe aBe at ;fe afe T» "* Hf* *T* *i*

Although some of the above work can be done within the present

budgets of the Radio Propagation Engineering and Physics Divisions

of NBS, the proposed additional measurement program would involve

the expenditure of large additional appropriations. It seems likely

that the expenditure of such sums for this purpose are justified in

order to provide ultimately a sound technical basis for the efficient

allocation of radio services to this band of frequencies.
- 37 -

10. RECOMMENDED FURTHER FREQUENCY

ALLOCATION RESEARCH

As demands for various portions of the spectrum multiply,

it becomes increasingly important for allocation engineers to have

a detailed knowledge of the actual spectrum occupancy so that

more services can be accommodated. In particular, it seems

that it will actually be desirable at some time in the near future to

have detailed interference studies made for every channel in the

radio spectrum so as to see how other services may be allocated

to it. These detailed studies should be made using technical data

of the kind included in this report and with the accuracy made

possible by the use of methods of the kind given in Appendix V.

Most government stations are allocated at present on a •'noninterference" basis. In. view of the sporadic nature of the interference, particularly in the 25 to 60 Mc band, this basis for allocation

will often not lead to an efficient use of the spectrum since many

services can tolerate a large amount of sporadic interference

before the degree of degradation of the existing services outweighs

in importance the new services provided by the proposed stations.

Unless detailed and accurate technical information is available

to the allocation engineers, these proposed additional uses of the

spectrum are not likely to be realized.

The implication of the above discussion is that many additional

personnel need to be assigned to allocation engineering if the important objective of efficient use of the spectrum is to be achieved.

1-1

Appendix I

The table in this appendix gives information as to the

number of U.S. assignments (as of December 1954) by classes

of service to the frequency band 25-60 Mc. In the case of the

non- government services, information is also given as to the

nature of the service, i.e. , police, forestry conservation,

broadcast, etc.

It is quite clear from Table 1-1 that by far the majority

(about 93 percent) of all of the assignments are for mobile services, either base stations or mobile stations.
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II

Appendix II DESIRED- CARRIER TO NOISE, R,

AND DESIRED-CARRIER TO UNDESIRED-CARRIER, Ru , RATIOS REQUIRED FOR SATISFACTORY RECEPTION OF

F-S-K TELETYPE AND F-M VOICE COMMUNICATION SYSTEMS

By

A. D. Watt

The following system parameters are assumed for the purpose

of calculating the required ratios:

Mobile F-M Voice Communication System

Voice modulated f-m with a maximum frequency deviation

of + 6 kc, an audio bandwidth of 3 kc and a receiver i-f noise bandwidth of 20 kc. The marginal performance of this system (used in

calculating all the ratios where it is the desired service) is defined

as "Obvious background noise and possible distortion; transmission

understandable. " This corresponds to Circuit Merit 3 of reference

(11).

Fixed System

Frequency-shift-keyed teletype with a frequency deviation of + 150 cycles, an equivalent square -wave keying rate of 60 cycles

(i.e. , multiplex operation), and a receiver i-f noise bandwidth of

500 cycles. The marginal performance of this system (used in

calculating all the ratios where it is the desired service) is defined

as a 1 percent binary error rate which corresponds to a synchronous

teletype error rate of 50 characters per 1000.

The various conditions which can cause marginal performance

are listed in table II- 1 along with their corresponding unmodulated

carrier ratios which are derived in the following paragraphs,,
II-2

Table II -1

1 Source of Marginal R or Ru

Case Service Interference db

Fixed* Noise 16,9

2 Fixed* Mobile* 1.3**

3 Fixed* Fixed* 16.9

4 Mobile Noise 3.6

5 Mobile Mobile* 6.6

6 Mobile Fixed* 6.6

The star indicates that the received power is fading in

accordance with a Rayleigh distribution at the receiver

site; the ratios, r and ru , in these Rayleigh fading

cases are in terms of the squares of the unmodulated

carrier voltages averaged over a period of several

minutes.

** This value applies during the time that the mobile transmitter is modulated; it provides a realistic measure of

the interference on the assumption that the unmodulated

carrier is offset so as to fall outside the Fixed service

receiver pass -band.
II-3

Case 1. Fixed#/Noise.

From reference 9, equation (13) we find that the binary error

rate for a narrow band f-s-k system with a Rayleigh fading carrier

and random noise is:

P6 = 1 (II-D

2(l+r)

where r is the ratio of the mean square carrier to mean square

noise. When Pc = 0. 01 , we obtain r = 49, i. e. , R = 16. 9 db.

Case 2. Fixed */Mobile*

There are three possible conditions for this case: (a) if the

Mobile service carrier is offset relative to the Fixed service

carrier and stabilized so as to remain outside the pass -band of

the Fixed service receiver, then during periods when the Mobile

service carrier is unmodulated there should be no interference,

(b) whenever the unmodulated Mobile service carrier drifts into

the Fixed service receiver pass -band, there will be substantial

interference and Ru = 16.9 db, (c) when modulated, regardless

of the precise location of the Mobile service carrier within its

allocated band, Ru

= 1. 3 db. Since a combination of (a) and (c)

results in the least interference and since it is technically possible

to realize condition (a), it is assumed in this report that Ru =1.3

db is a representative value for this case.

The basis for the above conclusions follows. Because of the

nature of the Fixed service receiver, it is possible to assume a rather sharp transition (capture) point and, as a result, we can

assume, for all practical purposes, that errors will result 50 percent of the time that the instantaneous -undesired -signal-power

exceeds the instantaneous-desired-signal-power in the pass-band

of the Fixed service receiver, and that no errors will occur in

the converse situation.
II-4

The Mobile service signal power in the Fixed service receiver

pass-band for condition (b) will be equal to the unmodulated carrier

power, but for condition (c) will be 15.6 db (10 logio (18000/500))

less since the Mobile service transmitter carrier energy is spread

out over an 18 kc band under conditions of full modulation.

Finally we must consider the probability (percentage of time/

100) that the instantaneous-undesired-carrier-power exceeds the

instantaneous-desired-carrier-power; for two Rayleigh fading

carriers it has been shown fy that this probability may be expressed:

p " -JTT7) < n" 2>

We find then for the probability of error in case 2(b):

Pc = —r-± (II-3)

€ 2(1 + r)

'

Since this is numerically the same as (II- 1) we find that Ru

= 16.9 db for the protection ratio against an unmodulated FM carrier

in the pass-band of the Fixed Service receiver.

When the FM carrier is modulated this ratio becomes for

case 2(c) 1^ = 16. 9 - 15. 6 = 1. 3 db.

a/

Kenneth A. Norton, "The Effect of Fading on the Desired-toUndesired Signal Ratio Required to Provide a Specified Grade

of Service for a Given Percentage of a Specified Period of

Time, " Private Communication, Feb. 3, 1948.
II

Case 3. Fixed */Fixed*

This case is similar to the preceding one except that the

desired and undesired carriers are always equally effective in

capturing the receiver limiter system. Because of this (II-3)

is applicable.

Case 4. Mobile/Noise

The marginal performance specified for the mobile service

requires operation of the FM receivers at input carrier-to-noise

ratios where a gaussian input noise produces impulsive noise in

the audio output, b/ Because the degree of impulsiveness is a

function of the receiver characteristics as well as the input

carrier-to-noise ratios for ratios less than 9 db, we shall not

try to determine the rms signal-to-noise improvement over the

input carrier-to-noise ratio as we would normally do at the higher

input carrier-to-noise ratios where the audio noise is essentially

gaussian. We shall instead consider a different method for determining the desired carrier-to-noise ratio. Since a typical good

quality FM receiver provides an average instantaneous frequency

equal to that of the strongest of two input voltages, we can consider

that serious noise impulses occur only when the instantaneous - input-noise -envelope voltage is equal to or greater than the carrier

envelope voltage, by The grade of service specified corresponds

to the condition where noise pulses occur approximately 10 percent

of the time, and the probability that the instantaneous -noise -envelope

voltage exceeds its rms value by the ratio x is given by the cumulative Rayleigh distribution: + y A. D. Watt, "Statistical Characteristics of Sampled and Integrated AM and FM Noise, " Naval Research Laboratory

report No. 3856, October 22, 1951.

It should be noted that x is the ratio of the noise envelope to

the rms value of envelope , and not to the rms value of the

input noise. This formula can, however, be used directly

because the envelope of the carrier is equal to yZ times the

rms carrier, and similarly the envelope noise rms value is

equal to yZ times the input noise rms value.
II -6

-x2

P = e (II-4)

For P = 0. 1, x = 2. 3 and the rms carrier-to-noise ratio

R = 3. 6 db. It is interesting to note that although the 10 percent

value chosen may seem arbitrary, the 3. 6 db value is in good

agreement with values obtained experimentally with a particular

narrow-band FM system. _£/

Case 5. Mobile/Mobile*

An exact solution in this case, as in the preceding one, would

require the development of a new distribution by combining the

capture characteristics of the receiver with the differential Rayleigh distribution; however, in this case, as before, we shall consider the capture transition as being very abrupt, which yields the

conventional cumulative Rayleigh distribution (II-4).

Fading of the Mobile interfering carrier requires that the

desired carrier exceed the instantaneous fading carrier about 99

percent of the time. This percentage value is considerably greater

than the 90 percent used in case 4 above because of the greater

effective loss, produced during a prolonged period where the desired

carrier is exceeded, than is caused by short bursts of impulse

noise. The distribution which results is the same in both cases;

however, the signal fading rate in the VHF range is low enough to

cause the loss of whole words rather than having very short portions

of a syllable omitted as is the case with the much higher frequency

noise. + Using P = 0.01, we obtain x2 = 4. 6 and Ru

= 6.6 db for

the required protection ratio.

c/

~" E. Toth and J. D. Wallace, NRL Report No. 3230, June 1952.

"*" This is demonstrated by the well known fact that a considerable

portion of a speech wave can be chopped out without affecting

its intelligibility if the chopping rate is high enough and the

chopped interval small enough.
II-7

Case 6. Mobile/Fixed*

The same method and answer of Case 5 apply here,

Ill

Appendix III SPORADIC E COMPUTATIONS

by

E. K. Smith

A. Introduction

This appendix describes the sources of sporadic E data used

here and also the methods employed to reduce these data to a form

suitable for obtaining the mean curves of sporadic E transmission

loss which appear in the body of this report. The base data utilized

are described in section B of this appendix. Section C considers the

normalizing procedures employed to adjust data taken for a few hours

of the day and over only part of the year to a twenty-four hour day

over a full year. The method used here to extrapolate Es data taken

at one frequency to a different one is discussed under section D. A

justification of this relation is also shown in the same section. Section

E describes the base data adjusted to fheir final form: instantaneous basic

transmission loss on the desired frequencies of 25, 35, 45 and 55 Mc.

B. Description of Data

The only usable transmission loss data pertinent to sporadic E

transmission at oblique incidence stemmed from two sources. The
Ill2

first of these consists of a series of reports—' released by the FCC

in connection with the reallocation of the F. M. band after the last war.

These describe transmission loss measurements of station WGTR

Paxton, Mass (44. 3 Mc, 340 kw) made at a series of FCC monitoring

stations in the period 1943 through 1945. The second source is found

2/ in a recent paper in a Japanese journal. -/ Following the recommendation

of Study Program No. 22 of the Geneva Meeting of CCIR, a recording

program was undertaken in Japan during the period of June through

August 1952. Transmitters on 31.55 Mc, 43.85 Mc, and 65.82 Mc

were located at Hiraiso on the northeastern coast of Honshu. Transmission loss measurements were then made at seven monitoring

stations at distances of 302 to 674 miles from Hiraiso. The particulars

of both of these sets of data are given in the table below.

-=/ "Report on VHF Field Strength Measurements 1943-1944,"

FCC Docket No. 6651, Exhibit 4, Sept. 28, 1944;

"Measurements of Sporadic E Field Intensities,"

FCC, 14100.

-/ "Study of Long Distance Propagation of VHF Waves by Sporadic E

Ionization," by T. Kono, Y. Uesugi, M Hirai and G. Abe,

Journal of the Radio Research Laboratories, Tokyo, Japan,

vol. 1, pp. 1-10, March 1954.
Ill -3 oa

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Ill -4

C. Normalizing Procedure

It will be noticed in the table above that none of the measurements

of sporadic E transmission loss were made for a full day over a period

as long as a year. The FCC data which are mostly for a year's duration were taken only 18 hours per day. The Japanese data which are

assumed to be 24 hours per day, on the other hand, are limited to

three summer months. To make these data more readily usable and

also to put them all on a comparable base, they have been normalized,

in each case, to a full year. The U.S. data in normalized form refer

to what would probably have been observed during the period September

1943 through August. 1944 for a 24 hour day. The normalized Japanese

data apply correspondingly to the calendar year 1952. No effort has

been made to reduce the two sets of data to a common year, as this

involves a possible error of a greater order of magnitude.

The normalizing procedure assumes that the seasonal or diurnal

distribution of sporadic E observed over the oblique VHF path is

proportional to that obtained for fEs > 7 Mc on the nearest vertical

incidence ionosphere sounder for the period in question. The Washington,

D. C. ionosphere sounder results as published in the CRPLi -F series

were used for the FCC paths. Data from the Yamagawa sounder was

employed for the Japanese paths.
Ill -5

We may define:

pi = probability that the transmission loss is less than

a given level for the year September 1943 - August 1944,

r j = measured fraction of the time that transmission loss

is less than a given level for June, July and August,

06-24 hours in the United States,

ri = measured fraction of the time that transmission loss

is less than a given level for September 1943 through

August 1944 in the U.S.

Then for the FCC paths where Washington, D.C. data is used:

P1 = 0.250 r L (IH-1)

Pl = 0.782 r 2

(III-2)

Correspondingly for the Japanese paths let

P2 = probability that the transmission loss is less than

a given level for the calendar year 1952,

r$ = measured fraction of the time that transmission

loss is less than a given level during June, July

and August, 1952, in Japan.

Then, when the Yamagawa sounder data is used:

p 2

= 0.391 r

3 (HI-3)

These normalized data are presented in form of a series of

broken-line curves of instantaneous basic transmission loss versus

distance with probability of occurrence as parameter in Figs. Ill- 1

,

III- 2 and III- 3. These data refer approximately to the frequencies of

SPORADIC E BASIC TRANSMISSION LOSS VERSUS DISTANCE AT 32 MC

The Labels on the Curves Refer to the Probability, p, During a Period of One Year that the Observed

Basic Transmission Loss will be Less than the Ordinate Values

CDo

a> Q

o

V>o

QDo

<uco

o

toc

p = 0.000 p=OOOI

p=0.9

p=0.99

Distance in Statute Miles

Figure m-l
SPORADIC E BASIC TRANSMISSION LOSS VERSUS DISTANCE AT44MC

The Labels on the Curves Refer to the Probability, p, During a Period of One Year that the Observed

Basic Transmission Loss will be Less than the Ordinate Values

a> -Qo

a> Q

o

00

IIU \ — Japanese Data 43.85 Mc

\

tarly r-.u.u. Data <+4 o Mc

• Tropospheric Forward Scatter

120 v>"-. s~ - "" —

P

=0.0005

130 /

X

1 S p p=oooi " -c ^Basi c Tra nsm/s.?/or? Loss in Free Space

S

1 i/

/ P

"""" p=O002 ~~ ——--

140 p=O.OC

— — .

I 7 r

p=0.00

1

5

)OI

•" / J /

p=O.OI

p=O.C

150 p=0

101 V <---' /

J "p=O.C>2

01 • .. /

/

\\ F>=0.000l

160p=

\ \

p=0.05 / \\ P=0.0002 \ p=0.0005 \ p=0.00l

D.I : / /

F'^O.OO 2

170p=<

——-

-~S _ - —

\

/ ^pr0.01

N

D.5

::' \ \\ N

P=0.1 N r

) = O.OC 5

p=c

180 P=0

)9: *•

99 1\ \

'• '•'•

|

1 T

3.

190

: \

1

1

<3 ^f

\. -5 a

'• "• ' 5

Si s I

^ 1 1

400 1,400

Distance in Statute Miles

Figure KL-2 <NBS>
O

Q

o

enO

GO

torjo

<D

szo

D

ir> a

SPORADIC E BASIC TRANSMISSION LOSS VERSUS DISTANCE AT 66 MC

The Labels on the Curves Refer to the Probability, p, During a Period of One Year that the Observed

Basic Transmission Loss will be Less than the Ordinate Values

IIU \ — Jc

1 panese Date

1 65.82 Mc

120 ^

" EcEx

rly FCC. Data 44.3 Mc

trapolated to 66 Mc

=r

••• Tropospheric Forward Scatt

130 ^^

-Basi c Trar smission Loss inFree Space

~~- —~~~ - ~~— _

140 p=0.0(

F = O.OC105

1

>oi-

:

_.. ,.*--"

*"

*"*""

p = 0.001

p=0.0

150 p=0

oi

: / 1 1 / 1 1 / p = 0.002

.01-'' / // 1 /

160

p=O.I s / p=0.005 /

/ /

/ /

-~-^p=0.01 /

*— p= 0.000 =5 x. ^ p= O.OOOI

170 p = 0.5 \\\

/ / /

/

s N

p=0O2

^ p= 0.0002

p=0.05

> > p =0.001

p=

180 p=0.

3.9: —

1 — — p=O.I y • p=0 002

99 :\

t

t t

oj190 t

t $

§

^£

*. -* s • -. •

<: '. 3

1 —5- 5

<0 5&

-9

?nn Ov* $

1 1 1

200

Distance in Statute Miles

Figure m-3

<NBS>
Ill -6

32 Mc, 44 Mc and 66 Mc, The dotted curves of tropospheric forward

scatter are theoretical values added for reference.

D. Variation of Es Incidence with Frequency

The relation derived by Mrs. Phillips~"from the distribution of

fEs at vertical incidence stations had the form

log p = a + bf (IH-4)

where p = probability that fEs > f

a, b are adjustable constants.

If we make the assumption a = in (III-4), the relation becomes a

simple proportionality. The constant b can be eliminated by dividing (III-4) by the same relation referred to a different frequency and

value of p. Thus

log pi fi where p,, p? = probabilities

T

JL±1 = ~ r < (IH-5)

io g P2 f2 i 1' 1 Z ~ frequencies

This relation has no arbitrary constants but does, of course, contain

the implicit assumption that a = in (III-4). Its use in this section

will be demonstrated through a numerical problem. For example,

for any given level of transmission loss relative to the expected free

space transmission loss, if a level of 30 db below free space were

observed on a frequency f , = 60 Mc at a probability of p^ = 0. 01 or

1% of the time, then at i? = 30 Mc we may solve for p£ from (III- 5):

—' "Variations in Sporadic E Ionization," by M.L.Phillips, Trans. AGU,

Vol. 28, p. 77 (Feb. 1947); IRPL "Radio Propagation Conditions , "—

Oct. 14, 1943, pp. 3-4, and Feb. 14, 1944, pp. 3-4.
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SSCT] UOISSIUJSUDJJ_ OlSDg
COMPARISON OF PREDICTED FIELD INTENSITY WITH

THAT OBSERVED AT YAMAGAWA

Prediction Relation: f. log P2

= f2

log P. Observed Level Probabilities at 43.85 Mc Were Used as Reference

Yamagawa Data Normalized to Represent Full Year 1952

0.7

0.5

0.3

0.2

to

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=>

0.1

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>

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0.0005

0.0003

0.0002 oo

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0_ 0.0001

0.00007 0.00005

0.00003

0.00002

20 40 50 60 70

Frequency in Megacycles

Figure IE -5
III-7

log p 2 = li log Pl = |0 ( . 2) = _j (m. 6)

f 1 60

Thus for p£ = 0. 1 or 10% of the time, we would expect by this method

of extrapolation a transmission loss relative to free space less than

30 db on 30 Mc if, during the period in question, these levels relative

to free space were observed for 1% of the time on 60 Mc.

To the best of our knowledge the Japanese data"/ present the

first Opportunity to test this relation for oblique incidence transmission loss data at VHF frequencies. The basic data are given on Fig. III-4

which presents the measured distributions of basic transmission loss for

three frequencies near 32 Mc, 44 Mc and 66 Mc. The Japanese data

represent a coherent set of measurements all taken during the same

period. Three stations, Yamagawa (674 mi. ), Kochi (447 mi. ) and

Osaka (302 mi. ), have distributions available for all three frequencies.

Osaka and Kochi are at distances such that one might suspect tropospheric contamination to the 66 Mc data, but Yamagawa should be pure

sporadic E on all three frequencies. Therefore it was selected for a

test of relation (III- 5). The results of this comparison of prediction

and measurement are given in Fig. III-5. It should be stressed that

the transmission loss levels held constant here were in terms of "db

below free space" and not "basic transmission loss. " In terms of the

relation for basic transmission loss L^ in db we have:
Ill -8

Lb

= 20 log 10 d + 20 log 10 f + A + 36. 58 (IH-7)

where d = distance in miles,

f = frequency in Mc,

A = propagation path attenuation in db

relative to the free space value.

The term which is set constant in (III- 7) when the relation

(III- 5) for probability at a different frequency is to be used is A, the

attenuation relative to free space. Relation (III- 5) was also applied

to basic transmission loss, but there was a systematic deviation by

the amount of the variation of the frequency term in (III- 7) with frequency.

As relation (III- 5) appeared to meet the test through comparison

with the Yamagawa data, it was then used to extrapolate the FCC data

from 44. 3 Mc to both 32 Mc and 66 Mc in terms of db below free space,

which was then reconverted to basic transmission loss and entered on

Figs. III-l and III- 3.

E. Estimates of the Distributions of Instantaneous Basic Transmission

Loss at 25, 35, 45 and 55 Mc

If it is assumed that distribution of instantaneous sporadic E

transmission loss relative to free space obeys, at least to some

extent, the law of (III- 5), we may use this law to derive probability

distributions at the desired frequencies of 25, 35, 45 and 55 Mc. Thus

we can extrapolate each measured distribution to four frequencies, in
III-9

exactly the same way that the FCC data were extrapolated to 32 and

66 Mc in Figs. Ill - 1 and III - 3 respectively. These extrapolations for

the ten paths (six Japanese and four U.S.) are shown in Figs. III-6

through III- 10, arranged in order of increasing distance. There is

some indication in the Japanese data that the applicability of (III- 5)

increases with decreasing f cosi where f is the frequency at which

the data were taken and i the incident angle on the sporadic E region

of the ionosphere (f cosi is, of course, the equivalent vertical incidence frequency if the cosine law is assumed to apply). This appears

particularly true from the derived distributions for Osaka (poor

agreement for all three data frequencies), Kochi (some agreement

between the curves for the two lower data frequencies), and Yamagawa

(good agreement for all three data frequencies). Fig. Ill- 11 illustrates

the variation of f cosi for the four frequencies on which data were

recorded. If we limit f cosi to values, say less than 16, we see from

Fig. Ill- 11 that our cases of poor agreement are eliminated. The

success of this limit is possibly fortuitous md thus should not necessarily

be taken literally for application elsewhere.
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IN TERMS OF GREAT CIRCLE DISTANCE

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200 400 600 800 1,200 1,400

Distance in Miles

Figurem-ll

:nbs:

Appendix IV

LONG-TERM CUMULATIVE DISTRIBUTION

OF INSTANTANEOUS RECEIVED POWER

By

Garner McCrossen

1. INTRODUCTION

For certain analyses, the Central Radio Propagation Laboratory of the National Bureau of Standards has found it convenient to

tabulate data in the form of hourly median values of transmission

loss. It is observed that the hourly medians of received power

are approximately log-normally distributed in time.Jy

Other types of analyses, however, require statistical characteristics of transmission loss within each hour. These analyses

indicate that, where scattering is predominant, the instantaneous

received power is approximately Rayleigh-power distributed for

certain periods of time. J_/

It is the major intent of this note to derive, under certain

restrictive conditions, a cumulative distribution function for the

instantaneous received power, expressed in decibels above unit

power, over an indefinitely long period of time for regions where

scattering is the only important propagation mechanism. Such

a cumulative distribution function will have a form which involves

an improper integral. Another intent of this note is to indicate a

numerical method for obtaining the cumulative distribution o£

instantaneous received power in decibels above unit power.

1/ _' NBS Circular 554, "Cheyenne Mountain Tropospheric Propagation Experiments ," by A. P. Barsis, J. W. Herbstreit, and

K. O. Hornberg, issued January 3, 1955,
IV-2

2. THE CUMULATIVE DISTRIBUTION FUNCTION

The assumption is made that the fields dealt with are ones

where scattering is the only important propagation mechanism.

It is further assumed that at a given instant and at a given receiving

point, a large number, m, of independent vector voltages v\ f . . . , vm of approximately equal amplitudes xj, . . . , xm arrive in random

relative phase. The theoratical instantaneous received power is

v^/t,, where

v = m

i

1X1 Iand £ is the impedance at the point of measurement. The phase

of v is random. The quantity x^/t, is defined as follows:

m

x

2

1 V

i I "1 W

i=l

We now define the Rayleigh-voltage distribution of v as that

listribution whose frequency function is

[v|x) = *L exp {-v2/x2

}, (3)

x2

where x is considered constant.

As mentioned previously, analyses of transmission loss data

indicate that instantaneous received power has a Rayleigh-power
IV -3

distribution for certain periods of time which are of the order of

10 minutes to one hour. If r E v^/t, represents instantaneous received

power, then (3) leads to a definition of the Rayleigh-power distribution of r as that distribution whose frequency function is

f(r |q) = - exp { -r/q } , (4)

where q E * /t is considered constant. In this note the period of time

during which r is Rayleigh-power distributed with a distribution

function (4) will be assumed to last as long as q is constant. If in

(4) q varies, then f(r jq) must be interpreted as a conditional frequency function.

If z is the median value of r when q is constant, then

CO

i

A exp {-r/q}dr = 1 . (5]

q 2

Integrating the left member of (5), it is seen that z satisfies the

relation

z = q loge 2 . (6)

But the relation in (6) is one between q and the median z. As

mentioned previously, it has been observed that hourly medians

of received power have approximately a log-normal distribution.

It will now be assumed in this note that Z 5 10 login z has a normal distribution with mean Z in decibels above unit power

and standard deviation a 7 in decibels. The frequency function

of Z is
IV-4

f(Z) =

l-==r exp J W Z - Z

crz

/2tt 2 \ cr i (7)

Using (7) and the relation z = 10 we obtain

-Z/10 -Z/10

f(r|Z) = (loge 2)10 exp<|-(loge 2)10 r >

as the conditional frequency function of r in terms of Z.

Letting f(r,Z) denote the joint frequency function of r and

Z and using the relation f(r,Z) = f (Z) f (r | Z), we write, by (7)

and (8),

f(r.Z) =

o" 7

]/Ztt

1 /Z - Z

exp < - -

2 cr

log 2

exp

J-rlog e

2

10 Z/10 in Z/10 .(9)

We desire the probability that r exceeds r Q

. This probability

is obtained by integrating f( r, Z) over the region defined by

r > r , Z > i co. Thus, using (9),

oo CO

p(,> ,„)._* fexpJ-ifZ^Z.) dZ Ci^Aexp }.US*Sl dr. (10) ° crzl/27, J 1 2 r, / | J 1^Z7I0 H 10 Z/10 f

' CO -r.

or

CO

P(r>r ) = exp

r Q lo

^z/^r J I 10 z/io

- CO v <—

ge 2 + ]_]

1

2 \ o- dZ. (11)
IV-5

If R : 10 log^Q r is the instantaneous received power expressed

in decibels above unit power, then it follows immediately from (11)

that

p (R > R ) = ~7=

J

exp l-\ do

- CO v <—

(Ro -Z)/l0 1 Z- Z

g e 2)10 ° +-

Z \ (T Z

dZ, U2)

which yields the desired cumulative distribution function.

In practice, Z may be regarded as the theoretical mean of

hourly medians Z of transmission loss in decibels above unit power

and (y^ as the theoretical standard deviation of these hourly medians

The integral in (12)vvas evaluated by numerical methods of

integration for ir^ = 1, 2, 4, 8 and Z = 0, and curves were obtained

of the theoretical cumulative distributions of instantaneous received

power in decibels above unit power, R E 10 log^nr, and of hourly

medians of transmission loss above unit power, Z = 10 log^Q z (Fig.IV-1).

3. METHOD FOR APPROXIMATING THE CUMULATIVE DISTRIBUTION FUNCTION FOR LARGE VALUES OF <r z

The numerical method, mentioned in the introduction, for

obtaining curves of the theoretical cumulative distribution of instantaneous received power in decibels above unit power will now be

described assuming, without loss in generality, that Z = 0. The

method is due to P. L. Rice of the Central Radio Propagation

Laboratory. Its graphical analogue has proved to be highly accurate

and efficient for large vaiues of a Z . The interval (0, 1) is divided

into n equal sub-intervals with midpoints pi(Z > Z j) = (2i - l)/(2n)j,

i = 1, . . . , n. As discussed later, n must be sufficiently large to

yield adequate accuracy in the final calculations. In practice,

pi (Z > ZQ^) is interpreted as the probability that an hourly median

Z will exceed ZQj. If
LONG-TERM CUMULATIVE DISTRIBUTION

OF INSTANTANEOUS RECEIVED POWER

R= 10 log, r

Hourly Medians z are Log -Norma My Distributed (Z = IOIog lo z)

Within -Hour Instantaneous Rayleigh-Power Distribution is Assumed:

p(r> r )=exp(-r /q)

a>

ZJoI

a>

>o

-Q

oQ

o

or

40

30

20

-20

-30

\\

— L one7-tern7 distruwtion oth our/y meyians ^

\\

\

\

\*

s <*

\ > \ \

3HJ ^^4;S \

V j \ — -~- \ss

St; V

^

V X

-v > ^

-^f2

^S '-»«

^

\

V

0.9 095 098 099 0.9980999 0.9999

Probability p that Ordinate is Exceeded <nbs>

0.001 0005 0.02 0.05 01 0.2 0.3 0.4 0.5 06 0.7 00005 0.002 0.01

Figure E - I
IV-7

W

2

P 2 (W)=—L- f exp {- a

2-/Z}da s (13]

/2tt J

o

then the following relations exist between p^ and p 2

: If 1 - 2pi(Z > Zoi ) > 0, then Zoi > and

P2(Woi )= 1 - 2Pl (Z > Zoi ), Zoi = a z WQi ; (14)

If 1 - 2pi (Z > Z j) < 0, then Zoi < and

P 2< Woi> = 2Pl< Z > Zoi> " 1. Zoi

=

- ^Z Woi • < 15 >

Tables can be used to calculate each W j. Then the relations

Zoi = a Z ^oi or Zoi ~ _cr Z ^oi are usec* *° calculate each ZQj.

The Z j are levels which the hourly medians exceed with

a probability (2i - l)/(2n). We now use the Z j as median values

of received power in decibels, and assume that over a long period

of time these values of Z are actually taken on for an hour at a time with a probability l/n, i. e. , we assume p(Z = Z i) = l/n.

The next step is to pick a level of instantaneous received

power in decibels, R = 10 log^o r . For a fixed Z i we seek the

probability, p(R>R |Z i) , that R exdeeds R on the hypothesis

that Z = Zoi . Now r Q

= 10 Ro/10 and, by (6) and the definition of

Z i, qj = {l0 Zoi/l0}/i O g e

2. By the preceding relations and (8)

we may write, since p(r > r | Z Q ^) = p (R > R J Z j),
IV-8

> R |Z Qi ) == exp<J -r o (log e 2)/l0 Zoi/l °

\ 10 (Ro-zoi )/io

I\ (16)

Thus if Z = Z j, then R exceeds RQ with the conditional probability given in (16). Now the total probability that R exceeds R

is approximated as follows:

n p(R > RQ ) = V p(R > R , Z = Z oi ) (17)

i= 1

Using the relation p(R > RQ

, Z = Z oi ) = p(R > R | Z oi )p(Z=Z i)

we get, from (16), (17), and the assumption that p(Z = Z {) = l/n,

« , v 10 (Ro -Zoi )/l0

p(R>Ro)

=I ^(ij (18,

i = 1

where p(R > R ) is the probability that the instantaneous received

power in decibels above unit power exceeds RQ

. It may be shown

that (18) approaches (1Z) in the limit as n approaches infinity.

Using (18), curves of the theoretical cumulative distribution

of instantaneous received power in decibels above unit power, for

probabilities less than 0. 5, were obtained for values of (r^ = 15,

20, 30, and Z = (Fig.IV-2).These curves were obtained by letting
LONG-TERM CUMULATIVE DISTRIBUTION

OF INSTANTANEOUS RECEIVED POWER

R = IO log

lo

r

Hourly Medians z ore Log-Normally Distributed (Z= 10 log z

)

Within- Hour Instantaneous Rayleigh-Power Distribution is Assumed:

p(r>r ) = exp (-r /q)

120

to

cza

CO

Z3oX

czo

co

CD>o

-Q

<

<DO

a> Q

Klo

or

110

100

90

70

60

50

40

30

20

10

-10

' waging1 I 1 -10 lc

-101c \

— Lc tern? distr'bution of Z-

%o'

?>oz

\

\\

\X

X

-°z= 30 db

r=2C^db

%.

*

k vV V

s \

V

N \

\

0.00050.0010.0050.01 0.02 0.05 0.1 0.2 0.3 0.4 05

Probability p that Ordinate is Exceeded

Figure 12 - 2

<NBS>
IV-10

n = 10,000 for those calculated points lying to the left of the

p = 0. 002 vertical line, n = 1, 000 for those calculated points

lying between the p = 0. 002 and p = 0. 05 vertical lines, and

n = 100 for those calculated points lying between the p = 0.05 and

p = 0. 05 vertical lines. It was found that the usually required

accuracy of about 0. 1 decibel was obtained by retaining only a

relatively small number of terms in (18), e.g. , with m = 1,000,

<r = 30 db, R = 80 db, the use of 11 terms yielded an accuracy

of better than 0. 01 decibel.

From the curves representing the cumulative distribution

of instantaneous received power in decibels aboveunit power

(for (r^ = 0, 1, 2, 4, 8, 15, 20, 30, and Z = 0) other curves were

obtained as follows: The difference between levels of instantaneous

received power R and hourly medians Z, each exceeded with the

same probability p (p = 0.0001, 0.001, 0.01, 0.1), was plotted

versus the standard deviation &% °* hourly medians Z (Fig. IV-3).

The difference between two levels of instantaneous received power

R, corresponding to two given probabilities, was plotted versus the

standard deviation crz of hourly medians Z; also, the difference

between two levels of hourly medians Z, corresponding to two

given probabilities, was plotted versus the standard deviation

<TZ of hourly medians Z (Fig. IV-4).
Cl

cr t

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R(p):

Level

exceeded

by

instantaneous

received

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with

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<b

!' -' ^

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III

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withprobabili

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kill*,,

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Appendix V

ACCURATE EQUATIONS FOR DETERMINING

THE INTERFERENCE TO BE EXPECTED

BETWEEN RADIO SERVICES OPERATING

ON THE SAME OR ADJACENT CHANNELS

Let Pa

= 10 logjQpa denote for the desired station the

average available power from the receiving antenna, expressed

in decibels above one watt, and assume initially that the reception

of this desired station is limited by noise alone, i. e. , that signals

other than the desired signal are not perceptible in the noise. If

the desired station transmitter power is now varied up and down,

it is possible to determine the minimum value, R, of the signalto-noise ratio which will provide reception of a given grade, e.g. , reception over short periods of time with less than 1 percent

binary error rate.

Thus, if we use a prime to denote instantaneous values, and

let R' denote the instantaneous ratio of the desired signal power

to undesired noise power, we may write:

R1 = Pa

- 10 logxo (f* ktb) = Pa- F' - B + 204 (V-l)

Note that both Pa and F1 will vary with time. Over short periods

of time of the order of from 10 minutes to an hour, pa and f* may

be considered to be independently distributed in accordance with

the Rayleigh distribution, and on this assumption a formula (II- 1)

was derived in Appendix II giving the value of R for various grades

of service. Note that these values of R correspond to the values

pa and f averaged over these short intervals of time. Thus it is

convenient to write:

R' = Pa

- F - B + 204 (V-2)
- V-2 -

Over long periods of time of the order of days, months, or years,

it has been observed that Pa and F may be considered to be normally distributed variates, and thus R' will be a normally distributed

variate. If we let cr^i , <r , and crp denote the standard deviations

of these normal distributions, then we see that:

aR>

= "I

+ 4 " ^aF^aV (V" 3)

In the above p a p denotes the correlation coefficient between

the variations of Pa and F. We now have a means for determining

the average available power of the desired station, Pn, required

to provide service (in the presence of noise alone) of a given grade,

R or better, with a given probability, (1 - p), or for a given percentage, 100(1 - p), of a long period of time:

Pn

= F + B - 204 + R + X(p)<r£, (V-4)

The function X.(p) may be determined inversely from the cumulative

normal distribution:

co

P = J7JJ- J

exp ( - t 2/2) d t (V-5)

Mp)

For example \(p) = 2.326 for p = 0.01, i.e. , service of grade Re or better, for 99 percent of the time.
- V-3 -

Consider next the case in which the signal power, pau» from

the single undesired station, u, is so strong as to completely override the noise and any other undesired signals. If the desired

station transmitter power is now varied up and down, it is possible

to determine the minimum value, Ru , of the desired signal to

undesired signal ratio which will provide reception of a given grade.

In a manner similar to the above we may determine the average

available power, Pu

, of the desired station required to provide

service of a given grade, R^, or better, over short periods of time

with a probability, (1 -p), or for a percentage of time, 100 (1-pJ:

P

u = P

au +Ru+MPKR»

where a— = (r 2 + q- 2 - Zp Q- or {V-7J R" a u au a u

In the above <ra denotes the standard deviation of the normally

distributed variate, Pa , <r u denotes the standard deviation of the

normally distributed variate Pau ana Pau denotes the correlation

coefficient (usually positive) between Pa and Pau.

In order to generalize the above special cases to the actual

situation in which noise and several undesired signals may be

present simultaneously in the pass band of the desired station

receiver, we may let R,,B denote the instantaneous ratio of the

desired signal power to the sum of the undesired noise and undesired

signal powers:

m

R"« = Pa

- 10 log10 (f'ktb + S Pau ) (V-8J

u=l
- V-4 - When we note that P^, f '

, and p^u

all vary with time, it is evident

that the solution of (V-8) will, in general, be much more complex

than the corresponding solution of (V-l). The above may be solved,

however, in the following important special case. Assume that f

1

, p' , and p^u are all Rayleigh distributed over short periods of

time. It is shown in Appendix II that R and Ru are the same,

(II- 1

) and (II-3), respectively, in that case. Thus we may write

(V-8):

m

Pm = R+ 10 log 10 (fktb + S p au ) (V-9)

u=l

In (V-9), as before, Pa , F, and Pau may be considered to be

normally distributed variates. Norton, Staras and BlumJ/ have

developed a method for determining the average value Pm required

to provide service of a given grade R, or better, in the presence

of noise and m undesired signals for a given percentage of a long

period of time; this method allows for the correlations between

Pa , F, and Pau .

Equation (4) in the body of this report was obtained by arbitrarily introducing r and ru as multipliers to f and pau in (V-9)

when r and ru are not the same and even when f and pau are

not both Rayleigh distributed. The above mentioned method_V of

solving (V-9) may then also be used for solving (4).

In view of the great complexity of (4) or (V-9), it is often

sufficient to solve (V-4) and (V-6) separately for all values of u and

then simply use the largest of the resulting values of Pn

and Pu .

In the body of this report the further approximation was made

of neglecting the correlation between the long term variations of

the desired and undesired signals. A correction for this particular

approximation can, in principle, be made by adding:

1/ K. A. Norton, H. Staras, and M. Blum, "A Statistical Approach

to the Problem of Multiple Radio Interference to FM and Television Service, " Trans. IRE, PGAP-1, February 1952.
V-5 -

C = \(p) (<ra + <ru

- o-r,,) (V-10)

to the hourly median values of L^ given on Figs. 3, 4, 5, and 6.

This will have the effect of reducing the interference expected by

C decibels. Unfortunately, the value of p au to use in various

cases is not well known so that this correction factor will be

difficult to apply in practise. In order to obtain some idea of the

possible magnitude of C in a particular case, assume (a) that the

desired signal is received by ionospheric forward scatter and has

a standard deviation cra

= 7 db, (b) that the undesired signal is

received by sporadic E and has a standard deviation <r n

= 15 db,

and (c) that p au = +0. 2. For a 99 percent service, i. e. , p = 0. 1,

we obtain C = 2. 326 (7 + 15 - 15. 23) = 15. 7 db; for p au = +0. 5

this would increase to 20.9 db, and for p au = 0, C = 12. 7 db.

It should be clear from the above discussion that the use of

approximate statistical methods of the kind used in the body of this

report may lead to substantially incorrect conclusions. This fact

lends force to the recommendation made in Section 10 of this report

that much further frequency allocation research be carried out.

Appendix VI

THE CARRIER FREQUENCY DEPENDENCE OF THE TRANSMITTER

POWER REQUIRED TO PROVIDE VARIOUS TYPES OF SERVICE

IN THE PRESENCE OF NOISE

A general equation was developed in Section 4 for the radiated

power, Prr » required to just over-ride the noise in the absence of

other forms of interference. If we add a term L,£ to (5), this general equation may be written:

Pt ^R + B-204 + l^+F+L (VI- 1)

In the above the required transmitter power, P. , is expressed

in decibels above one watt; the minimum signal-to-noise ratio,

R, required for satisfactory reception is expressed in decibels,

B E 10 logjob where b is the effective receiver noise bandwidth

in cycles per second; L^ is the transmission line and circuit loss

at the transmitting end of the circuit which is expressed in decibels and allows for the usually small difference between the total

power actually radiated from the antenna and that available from

the transmitter; F is the effective receiver noise figure expressed

in decibels and allows in an appropriate way not only for the actual

receiver noise figure but also for the noise picked up externally

by the receiving antenna as well as for any transmission line and

receiver input circuit losses at the receiving end of the circuit.

A brief discussion of the effective receiver noise figure, F, is

given by the author in reference 2 and in more detail by Crichlow,

Smith, Morton, and Corliss in reference 7.

In the above equation R and B will not vary appreciably

with the carrier frequency and may be considered constant for any

given type of service. The terms (L^ + F) may be expected to be

of the order of 25 db at 25 Mc, will decrease with increasing

frequency reaching a minimum value of the order of 7 db in the

neighborhood of 100 Mc, and will then increase again at higher

frequencies approximately in accordance with the relation:
VI-2

(L|+ F) = 6 1og 10 f Mc - 5 (fMc > 100) (VI-2)

The value of (L^ + F) will vary significantly with the engineering

design and the components used in the equipment, and the above

estimates are based on the assumption that the best available

equipment is used. Below 100 Mc, cosmic noise largely controls

the value of (Ljg + F), while above 100 Mc this value is largely

determined by the equipment and is essentially independent of

external noise. The above estimates of (Ljg + F) were based on

the assumption that a quiet receiving location, free from man-made

noise, is available. Man-made noise levels are likely to limit

reception at least part of the time for some types of service and,

when these man-made noise levels are high, we may expect

(!_»« + F) to be roughly of the form:

(L|+ F) =N - 27 log 10 f Mc (N>65) (VI-3)

for frequencies up to that frequency at which (VI-3) gives the same

value as (VI-2); at still higher frequencies (VI-2) will again be

applicable.

Consider next the remaining variable, L, in (VI- 1). In

free space the transmission loss, L, is given by:

Lf = 36.58 + 20 log 10 fMc + 20 lo gl0 D " Gt " Gr < VI" 4 >
VI-3

In the above D is the path distance expressed in statute miles.

It is convenient to consider three different cases corresponding

to three types of service in which (a) non-directional half-wave

dipole antennas are used at both ends of the path, (b) a nondirectional half -wave dipole antenna is used at one end of the path

while a directional antenna is used at the other end, and (c) pointto-point services in which directional antennas may be used at

both ends of the path. For the half- wave dipole G = 2.15 db,

while a directional antenna with an effective absorbing area of

A square meters has a gain:

10 1og

10

A

e+

20 1og

10

fMc -38.54 (VI-5)

where f , > 100 \I~A~ Mc e

Using the above gains in (VI-4) we obtain the following relations

for the transmission loss expected in free space for the three

cases described above:

Case (a) Half-Wave Dipoles at Both Terminals

L

f = 32. 28 + 20 log

1() D + 20 log1() f^ (VI-6)
VI-4

Case (b) Directional Antenna at One Terminal and a

Half-Wave Dipole at the Other Terminal

Lf = 72.98 + 20 log 10 D - 10 log 10 Ae (VI-7)

Case (c) Directional Antennas at Both Terminals

Lf = 113.67 + 20 1og 10 D - 20 log 10 Ae - 20 log 10 fMc < VI" 8 )

Note that the free space transmission loss increases with frequency in case (a), is independent of frequency in case (b), and

decreases with frequency in case (c).

Finally, to determine the actual transmission loss, L, it

is necessary to add to the above free-space transmission losses,

Lf, the attenuation A, relative to these free-space values. This

will be different for the different modes of propagation. The

following discussion will be confined to the range of frequencies

above 25 Mc. For propagation via the F2 layer of the ionosphere

A is essentially zero for frequencies up to the MUF (maximum

usable frequency) of the F2 layer, and then increases rapidly with

increasing frequency until a final practical cut-off is reached at

frequencies of the order of 10 to 15 percent above the MUF. £/

For the ionospheric forward scatter mode of propagation A depends on frequency in the following way:

2/~~ This phenomenon of F2 propagation just above the MUF has

recently been explained by D. R. Bailey, first in a paper on

forward scattering in the ionosphere presented at the Xlth

General Assembly of the URSI at The Hague in August 1954,

and more recently and in much more detail in a colloquium

talk entitled "The Role of Ionospheric Forward Scatter in

Oblique Incidence MUF" which was presented on February 24,

1955 at the Central Radio Propagation -Laboratory in Boulder,

Colorado.
VI-5

A = A(f ) + 84 log 10 (f/fo ) (VI-9)

For ground -wave propagation over a smooth flat earth:

A = A(fQ

) - 20 log 10 (f/fo) (VI-10)

The curvature of the earth A/ and terrain roughness _/ introduce

additional frequency effects so that the attenuation, A, for the

ground wave usually decreases only slightly with increasing frequency at points within the line of sight and increases slightly with

increasing frequency at points just beyond the line of sight. At

points far beyond the line of sight in the tropospheric forward

scatter region the attenuation, A, is independent of the frequency.J/

However, when high-gain antennas are used, with a fixed size,

the "loss in antenna gain" will increase with increasing frequency

for either ionospheric or tropospheric forward scatter, and additional transmitter power must be allowed for this effect.

At sufficiently high frequencies atmospheric absorption^/ may

become an important factor and, in the range above, say, 2000 Mc,

A increases rapidly with increasing frequency.

3

-L K. A. Norton, M. Schulkin, and R. S. Kirby, "Ground-Wave

Propagation Over Irregular Terrain at Frequencies above 50

Mc, " Reference C to the Report of the FCC Ad Hoc Committee

for the Evaluation of FM and TV Propagation Factors Between

50 and 2 50 Mc, June 6, 1949; also, K. A. Norton, "A Formula

for the Transmission Loss of Space Waves Propaged Over

Irregular Terrain," Trans. IRE, PGAP-3, August 1952.

Zf Howard E. Bussey, "Microwave Attenuation Statistics Estimated from Rainfall and Water Vapor Statistics, " Proc. IRE,

Vol. 38, No. 7, p. 781, July 1950; see also NBS Tech. News

Bulletin, Vol. 33, No. 12, p. 144, December 1949.
VI-6

It should be clear from the above discussion that the required

transmitter power, Pf r

. may either increase or decrease with

increasing frequency, depending on the type of service or mode of

propagation.