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SU-SEL-70-037

Irregularities in the Quiet ?2 Ionosphere and Their Effect on ^ Propagation

N. by

Philip A. Fialer

August 1970

Technical Report N0 156

This document has been approved for public release and sale; its distribution is unlimited.

Prepared under

Office of Naval Research Contract Nonr-225(64), NR 088-019, and Advanced Research Projects Agency ARPA Order N* 196

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SEL-70-037

IRREGULARITIES IN THE QUIET IONOSPHERE AND THEIR EFFECT ON PROPAGATION

by

Philip A. Fialer

August 1970

f-

This document has been approved for public release and sale; its distribution is unlimited.

Technical Report No. 156

Prepared under

Office of Naval Research Contract Nonr-225(64), NR 088-019, and

Advanced Research Projects Agency ARPA Order No. 196

^ Radioscience Laboratory Stanford Electronics Laboratories

^ Stanford University Stanford, California

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ABSTRACT

The primary purpose of this investigation was to determine the

nature and characteristics of a class of large, weak ionospheric irregu-

larities which in certain circumstances significantly affects long-dis-

tance HF radio-wave propagation. A further purpose was to determine the

relative practical importance of the diffraction produced by these inho-

mogeneities, in relation to the influence of other mechanisms such as

Faraday rotation and scattering by small irregularities.

Measurements of quasi-periodic variations in phase-path length have

been made on a 2600 km one-hop lower-ray F-region path. Variations of 8

to 75 wavelengths are regularly observed during winter daylight hours.

They have a quasi period of about 20 minutes. Correlations of measure-

ments made at spaced receiver locations indicate that these variations

in phase-path length are produced by irregularities having a horizontal

scale size of about 35 km. Multiple frequency measurements show a verti-

cal scale size of about 15 km, with a maximum in the lower F region. A

lower limit of 65 m/sec is determined for the horizontal velocity of the

irregularities. A downward vertical velocity of 30 to 40 m/sec is ob-

served. The irregularities limit achievable bandwidth and spatial reso-

lution for one-hop HF ionospherically propagated waves under quiet iono-

spheric conditions.

A model of the irregularities has been devised and has been used to

predict the signal-strength fluctuations which would result from propaga-

tion through a medium described by the model. Two classes of signal-

strength behavior are predicted and observed experimentally, depending

on the relative magnitude of the phase-path variations within the limits

mentioned above. Signal-strength variations of a few dB, having a 20 min

period, are observed when the changes in phase-path length are small, and

are attributed to focusing caused by the irregularities. Larger, more

rapid signal-strength fluctuations are also observed. These are attribu-

ted to multipath interference between several rays propagating through

the same irregularity. Taken together, these rays make up what would be

identified as the one-hop lower-ray F-layer mode, which is seen to be

less homogeneous than had previously been supposed, for propagation over

2000-4000 km distances.

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CONTENTS

Page

I. INTRODUCTION 1

A. Purpose 1

B. Background 1

1. Features of the Quiet Ionosphere 4 2. Sources of Wavefront Distortion in the

Quiet Ionosphere 4

a. Traveling Ionospheric Disturbances 7 b. Multi-mode Observations 7 c. Single-mode Oblique-incidence Measurements ... 7

C. Approach in Present Study 9

II. PHASE-PATH MEASUREMENTS 11

A. Conditions of the Measurements 11

B. Phase-Path Measurement Method 12

C. Multiple-Location Measurements 20

D. Horizontal Scale Size of the Observed Irregularities . . 26

E. Vertical Scale Size 29

F. Conclusions from Phase-Path Measurements 32

III. MODEL OF THE IONOSPHERIC IRREGULARITIES 37

A. The Ray-Theory Approximation 37

B. The Effects of a Single Irregularity 38

1. Nature of the Wave Field Produced by a Single Irregularity 38

2. Relation of Variations in Phase-Path Length to Variations in Refractive Index and Electron Density 41

3. Modifications of the Simple Two-Dimensional Model to Account for Background Variation in |i . . 48

C. The Effects of Multiple Irregularities in Three Dimensions 50

1. The Effect of the Presence of Multiple Irregu- larities on the Calculated Change in Electron Density 50

2. The Range of Phase Changes Produced by the Observed Irregularities 51

3. The Effects of the Observed Phase Changes 54

D. Effect of the Earth's Magnetic Field 57

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CONTENTS (Cont)

Page

IV, SIGNAL-STRENGTH FLUCTUATIONS 59

A. Multiple Weak-Scattering Interpretation of Amplitude Fluctuations 60

B. Interpretation on the Basis of Large Irregularities ... 64

1. Focusing 65 2. Multipath Interference ...... 65 3. Polarization Mismatch 67 4. Absorption 69

C. Survey of Amplitude Distributions 69

D. Relation of Signal-Strength Fluctuations to Phase- Path Fluctuations 80

E. Measured Amplitude Histograms 83

F. Conclusions from Signal-Strength Analysis 96

V. OTHER CHARACTERISTICS OF THE IRREGULARITIES 99

A. Horizontal Motion of Irregularities 99

B. Vertical Motion of Irregularities 102

C. Diurnal and Seasonal Variations 105

D. Antenna Performance , 105

E. Bandwidth Limitations 108

VI. SUMMARY AND RECOMMENDATIONS HI

A. Summary HI

B. . Recommendations 112

Appendix A. CW PHASE-PATH MEASUREMENTS 117

Appendix B. THE EFFECT OF CHANGES IN RAY REFLECTION HEIGHT .... 131

REFERENCES 135

TABLES

Number

1. Aircraft tracking system errors 127

2. Data recorded on analog tapes 128

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ILLUSTRATIONS

Figure Page

1. Ionospheric electron density profile 2

2. High-frequency radio ray paths in the ionosphere 3

3. Sweep-frequency soundings—Bearden, Ark. to Los Banos, Calif 5

4. Vector representation of received signals 16

5. Alternate capture of phase-path measurement by two rays 18

6. Two-point wide-spaced phase-path records 24

7. Doppler correlation coefficient for wide-spaced phase-path measurements 27

8. Ionospheric ray paths joining two points for several frequencies 31

9. Doppler correlation coefficient for multiple- frequency phase-path measurements 33

10. Two-dimensional scattering geometry 36

11. Computed raypaths through a gaussian irregularity 39

12. Computed received wavefronts for waves propagating through a gaussian irregularity 42

13. Computed received amplitude for waves propagating through a gaussian irregularity 43

14. Change in electron density required to produce a one per cent change in refractive index 45

15. Computed Fresnel zone length at the reflection height for rays in the ionosphere 49

16. Phase-path length measuremert for very quiet ionospheric conditions 52

17. Phase-path length measurement for fairly quiet ionospheric conditions 52

18. Phase-path length measurement alternately captured by two rays of comparable amplitude 53

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27.

28.

29.

30.

31.

32.

33

34.

ILLUSTRATIONS (Cont)

Page

Phase-path length measurement for disturbed ionospheric conditions 53

Expected number of rays for the given path and measured irregularity scale sizes 56

Amplitude distributions as derived by Rice for a specular ray and a cone of scattered rays 62

The relation of wave coherence, ß, to amplitude fluctuation, FP/R2, for the small scattering model .... 62

The Rice amplitude distribution computed using the Monte Carlo method and plotted with the mean envelope amplitude E as a scale factor 63

Observed signal-strength fluctuations for the Arkansas--Los Banos path 66

Computed amplitude distribution for the random vector sum of rays 68

Computed amplitude distribution for the random vector sum of two rays 70

Computed amplitude distribution for the random vector sum of rays 71

Computed amplitude distribution for the random vector sum of three rays 74

Computed amplitude distributions for the random vector sum of five or more rays 76

Computed amplitude distributions for the random vector sum of rays, including the effect of polarization mismatch 79

Observed signal-strength fluctuations vs. observed phase fluctuations 81

Observed signal-strength and phase-path-length fluctuations over two paths at the same time 84

Observed amplitude density distributions W(E/E) for the period shown in the records of Fig. 33 86

Observed amplitude density distributions exhibiting multiple peaks 88

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42.

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48.

49.

50.

ILLUSTRATIONS (Cont)

Page

Observed amplitude density distributions for short analysis times 89

Amplitude distributions exhibiting the effect of changing signal energy 91

Measured amplitude distributions showing the effects of Faraday rotation 92

Measured amplitude distribution for three consecutive 10-min intervals, and for the whole 30-min interval, showing the effect of analysis time on observed dis- tributions 93

Measured amplitude distributions and signal-strength record relating amplitude distribution to ooserved signal fluctuations 94

Doppler correlation versus time lag for wide-spaced phase-path measurements made with receiving antennas at Los Banos, Calif, and on an airplane 98

Cross correlation of signals on antennas spaced 2.5 km apart 100

Cross correlation of phase-path length changes observed on the Bearden-Los Banos path for two frequencies separated by 2 MHz 103

Time lags required to produce maximum cross correlation of phase-path length changes for spaced frequencies 104

Variation of phase fluctuations with time of day 106

Variation of phase fluctuations with time of year 107

Map showing the area of the experiments 120

Exterior of aircraft 121

Interior of aircraft 121

Block diagram of major equipment of the aircraft 124

Ionospheric ray paths showing a change in reflection height caused by an irregularity near region of sig- nificant ray bending 132

ix

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ACKNOWLEDGMENT

I wish to express special thanks to Professor 0. G. Villard, Jr.,

for his guidance and encouragement throughout this work. I am also

grateful to Professor L. A. Manning and Professor Thomas M. Cover for

their suggestions in improving the technical quality of the manuscript,

I gratefully acknowledge the assistance of Doctor Thomas A. Croft who

developed most of the computer raytracing techniques which were used

in this work. My thanks also go to Mrs. Mabel Rockwell and to Miss

Jane King for their help in preparing the finished report.

This research was supported by the Advanced Research Projects

Agency through the Office of Naval Research, Contract Nonr-225(64).

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INTRODUCTION

A. PURPOSE

The purpose of the work described in this report was to determine

the large-scale spatial properties of high-freqiiency (HF) radio waves

which had propagated over an undisturbed (quiet) one-hop F-layer iono-

spheric path. These large-scale properties limit the maximum antenna

size which may be efficiently employed in HF systems. A further purpose

of the work was to determine the importance of ionospheric irregularities

relative to other mechanisms in producing spatial distortions in HF waves,

B. BACKGROUND

Ionospheric communication is made possible by the refracting region

of free electrons which exists at altitudes of about 70 to 300 km above

the earth. Figure 1 is an example of a profile of electron density vs

height which might be observed over a fixed point on the earth. This

electron-density profile is typical of the midlatitude winter daytime

ionosphere. Radio waves in the range of about one to thirty MHz are

bent sufficiently that they will return to the earth at a considerable

distance from the point of transmission. Figure 2 shows the paths of

rays at a fixed radio frequency for an ionosphere which is described

everywhere by the electron-density profile of Fig. 1.

At the point of return, the waves may be received, or they may be

reflected from the surface to make additional "hops", often reaching

distances two, three or four times those for a single hop. While tra-

versing the ionospheric portion of their path, these waves are affected

by any variations in electron concentration (and hence in refractive

index) which they may encounter.

Variations (with time of day, season of the year, and location on

the earth) in the angle at which the sun's energy is incident upon the

ionosphere cause spatial variations on a global scale in observed pro-

files of electron density versus height. These spatial variations can

contribute to small frequency shifts in the received signals and to

small effective "tilts" in the refracting layer. Such frequency shifts

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and tilts do not generally cause difficulty in the operation of high-

frequency communication circuits.

More important degradations in the smoothness of received wave

fronts (surfaces of constant phase) can be produced by localized varia-

tions in the electron-density profile of the ionosphere. These localized

variations (ionospheric irregularities) scatter or refract the incident

waves. If the irregularities are moving, they cause the amplitude and

phase of the received signals to vary with time. Variations of this

sort limit the useful bandwidths and antenna apertures that may be em-

ployed in HF communication systems.

1. Features of the Quiet Ionosphere

The gross characteristics of the ionosphere, through which ray

paths joining any two points on the earth travel, may be determined from

a sweep-frequency sounding over the path (an "oblique ionogram", Fig. 3).

In such a record the time required for a group of waves to travel from

transmitter to receiver is measured over a wide interval of radio frequen-

cies (Barry and Fenwick '65). Figure 3a shows such an ionogram for a mid-

latitude path on a typical winter day. Some important features are indi-

cated in the figure. In the frequency interval labeled "single mode",

only one major ionospheric path exists between the transmitter and the

receiver. The ionogram of Fig. 3a was made during a period of undis-

turbed or "quiet" ionospheric conditions. Figure 3b shows the effect

that an ionospheric disturbance produces in an oblique ionogram.

All of the experimental work in this paper was performed under

the following conditions :

1. One-hop, lower-ray, F-layer propagation only.

2. East-west, midlatitude path.

3. Quiet ionospheric conditions.

2. Sources of Wavefront Distortion in the Quiet Ionosphere

Information on the spatial characteristics of HF ionospherical-

ly propagated waves is available in a variety of forms and representing

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a wide range of ionospheric conditions. In this section some of the pre-

existing relevant information and its relation to the present work are

discussed.

a. Traveling Ionospheric Disturbances

Traveling ionospheric disturbances produce large ionospher-

ic irregularities having horizontal spatial periods ranging from 50 km to

over 1000 km. The disturbances occur at rates of a few per day for smal-

ler disturbances to a few per month for larger ones. Munro ('50, '58),

Georges ('67), Chan and Villard ('62) and others have studied such dis-

turbances. The wavefront distortions which result are reasonably well

understood. The low rate of occurrence of traveling disturbances decrease

their influence on the performance of HF systems. The observations de-

scribed in the present work were made under conditions when no large

traveling disturbances were influencing propagation over the path (as

determined by the absence of "kinks" in ionograms over the path—see Fig.

3).

b. Multi-mode Observations

The spatial characteristics and motion of the fading pat-

tern produced by the interference of rays propagating over different

ionospheric paths, that is, by different modes, has been studied by Ames

('64). The observed fading rates and motions of the fading patterns are

adequately explained in terms of large-scale tilts and motions of the

ionospheric layers. The observations of the present study are limited

to the frequency range where only a single mode is propagating.

c. Single-mode Oblique-incidence Measurements

Measurements during periods of quiet ionospheric conditions,

using frequencies for which only a single mode is propagating (or where

modes are resolved using pulse methods), have been made by a number of

investigators. Such measurements permit the most direct interpretation

in terms of causative mechanisms in the ionosphere.

One category of single-mode oblique-incidence studies con-

siders the scattering produced by large numbers of small (less than 5 km

7 SEL-70-037

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horizontal extent) weak irregularities. The statistical properties of

the resulting field are measured to determine the statistics of the scat-

terers. It is assumed that the received wave is composed of a single

specular component plus a large number of weak scattered waves. The

Bc&ttered energy introduces amplitude and phase fluctuations in the re-

ceived signal which are statistically distributed in a characteristic

manner that defines the ratio of the unscattered (appcular) energy to

the scattered energy. This ratio (ß) is often referred to as the

coherence ratio of the received signal. Al'pert ('63) summarizes a

number of amplitude-distribution measurements of ionospherically propa-

gated waves. Whale and Gardiner ('66) derive relations between the

statistics of the phase difference measured on two spaced antennas,

and the coherence of the received wave field. Coherence measurements

have not produced a clear description of the influence of small irreg-

ularities on ionospheric communication. Phase measurements usually

indicate much larger values for the coherence ratio than are found

using amplitude measurements.

A ■•cond category of studies considers the effect that

a smaller number of larger irregularities has on waves propagating

through the ionosphere. The effect« of each individual irregularity

are measured, frequently at widely separated locations. These studies

have mainly been concerned with irregularities in motion, primarily

because the observation of temporal variations is experimentally easier

than the observation of spatial variations. The velocity and size of

large irregularities have been determined by measuring the time separa-

tion of the effects of a given irregularity at spatially separated points.

The measurements of traveling ionospheric disturbances described above

fall into this category. Also, Bramley ('53, '55) has studied variations

in the angle of arrival of obliquely propagated waves at sites separated

by 27 km to 213 km. He measures angular deviations in azimuth of about

a degree, having a pseudo-period of about 20 minutes. These deviations

are highly correlated at 27 km, but are nearly uncorrelated at the 213 km

spacing. Although it is difficult to determine the shape and strength of

irregularities from angle-of-arrival data only, Bramley attributes the

observed variations in angle of arrival to weak traveling irregularities

having spatial periods of 50 to 200 km.

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A third category of measurements of the spatial properties

of ionospherically propagated waves involves measuring the amplitude and

phase of the waves at a large number of spatially separated points. (The

multi-mode work of Ames, described above, used this technique.) The major

work of this type for single-mode propagation under quiet ionospheric con-

ditions is that of Sweeney ('70),, He employed eight receiving elements

equally spaced along a line 2,5 km long. He observed relatively linear

wavefronts having mean angle-of-arrival variations similar to those ob-

served by Bramlcy. In addition, Sweeney observed amplitude differences

of about 10 dB and phase fluctuations of about ±20° on the individual

elements. These fluctuations are more rapid (having periods of less than

1 min) than the variations in the mean angle of arrival. The mechanism

that produces the more rapid fluctuations is not determined.

C. APPROACH IN PRESENT STUDY

This report describes a series of experiments performed to determine

the large-scale (large compared with the 2.5 km aperture used by Sweeney)

spatial properties of ionospherically propagated waves. A new phase-mea-

suring technique is used to study the shape of the observed wavefronts.

Phase measurements are made using a fixed receiver site plus an airborne

receiving system. The use of an airborne receiving system allows phase

changes to be measured simultaneously at two points whose separation may

be changed rapidly. The moving airborne receiver is sensitive both to

moving disturbances and to wavefront distortions which are fixed in space,

that is, not varying significantly with time.

Data gathered by use of this technique reveal the presence of a new

class of ionospheric irregularities, which appear to be a continuation

to smaller sizes (approximately 35 km) and weaker strengths (approximately

1 per cent change in electron density), of the irregularities observed by

Bramley and others. Simultaneous measurements with several radio frequen-

cies are used to determine the vertical size (about 15 km) of these new

irregularities. A computer model is then used to predict the influence

of the irregularities on propagation. Amplitude fluctuations which re-

sult from propagation through such irregularities are predicted from the

9 SEL-70-037

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model, and are compared with the fluctuations observed experimentally.

The occurrence of these weak, medium-sized irregularities is shown to

coincide with signal-strength fluctuations. The statistical distribu-

tion of amplitude fluctuations at the receiver is measured and compared

with amplitude-fluctuation distributions predicted from the model. The

predicted and measured amplitude-fluctuation distributions are in turn

compared to distributions predicted by other models of fading mechanisms

such as 0-X interference and scattering by numerous small, weak irregu-

larities. This analysis can explain some ambiguities in previous studies

which attempted to explain amplitude fluctuations using a model based on

the assumption of many weak irregularities.

Determinations of the apparent vertical velocity and a lower limit

for the horizontal velocity are also drawn from the measurements. Fi-

nally, the performance of wide-aperture antennas in the presence of large

irregularities is discussed. Appendix A provides a detailed description

of the experimental method, together with the accuracy requirements of

this method.

SEL-70-037 iO

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II. PHASE-PATH MEASUREMENTS

The experiments described in this report were performed in two

series of measurements. The objective of the first was to establish

a general understanding of the wave field of energy which has propaga-

ted over a one-hop lower-ray F-layer path through the ionosphere. The

results of this first series of measurements showed that the major dis-

tortion of the received wave fronts appears to be caused by ionospheric

irregularities having a temporal variation with a period of about 20 min,

a horizontal scale size of approximately 35 km, and a maximum deviation

of electron density in the range of 0.6 per cent to 6.0 per cent.

The second series of experiments, performed about one year after

the first series, was concerned with determining the vertical scale size

(determined to be about 15 km), and the range of magnitudes of the vari-

ations observed. In addition, data from the second series of experiments

were used to study the signal-strength fluctuations produced by the ir-

regularities, and to determine any observable motion of the irregulari-

ties .

A. CONDITIONS OF THE MEASUREMENTS

In order to minimize the possibility of ambiguities in the experi-

mental side of this work and in the interpretation of the data, the mea-

surements were performed under conditions which were expected to produce

relatively smooth wave fronts. The path employed joins transmitters at

Bearden, Arkansas and receivers at (or near) Los Banos, California (see

map. Fig. 46 in Appendix A). The use of this midlatitude path avoids

equatorial and polar anomalies. The great-circle distance from Bearden

to Los Banos is 2600 km.

Measurements were made during winter daytiue periods. At these

times, ionospheric disturbances are infrequent, and a wide range of

frequencies could be used which propagated by the one-hop lower-ray

F-layer mode only. For unambiguous results, the measuring technique

that was used requires single-mode propagation. Frequencies as low

as 18 MHz (limited by tie appearance of the two-hop F-layer mode or

11 SEL-70-037

.^■^,■..,...-.,....^,„„^„..,„1^..,...., mi^i^ai^u^^w^.«^^^^ ahfttiiiABkj.t.^..,.,.»-,.,^!

li^HpBip);^^!^^^^ i.l,..>,.Mi^upwijjii.i..iv,, J'W).W»WW^^ ' ■l-lJI!J»IMy

the ono-hop E-layer mcxie) and as high as 28 MHz (limited by the appearance

of the one-hop F-layer upper-ray mode) were used. On most days a range of

between 3 and 10 MHz was available, for which propagation was by the one- » -

hop lower-ray F-layer mode only. During winter nights and during the sum-

mer, there are usually no frequencies which propagate by only a single

mode over the Bearden-Los Banos path.

A high-resolution FMCW ("chirp") sounder was ussd to monitor condi-

tions over the path. This sounder provides oblique ionograms having 8

usec resolution in group time delay. Ionograms were made routinely, at

Intervals of a half hour to an hour and a half, to determine the "single-

mode" frequency range and to check for the presence of large ionospheric

disturbances. Additional ionograms were made if the phase-path measure-

ments (described below) indicated that any ionospheric disturbances might

be present on the path. Any traveling disturbances (as studied by Munro

and others) produce noticeable "kinks" in the high-resolution ionogram.

No data from the phase-path measurements were used for periods when iono-

spheric disturbances could be detected from the ionograms.

B. PHASE-PATH MEASUREMENT METHOD

The selection of a measuring technique to be used for this work was

made on the basis of the known characteristics of wave fronts propagated

over long, single-mode, one-hop F-layer paths—plus a desire to determine

the nature of the mechanism producing wave-front distortions. The use of

pulse measurement techniques was rejected because it was felt that the

resolution possible with ionospherically propagated pulses (approximately

2 pisec at best) was not sufficient to provide any new information about

small variations in wave-front tihape. Angle-of-arrival measurements were

considered impractical in view of the desire to make measurements at a

wide variety of receiver spacings. (Accurate angle-of-arrival measure-

ments require very carefully selected receiver sites.)

The use of continuous-wave (CW) measurements was selected for the

following reasons:

SEL-70-037 12

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^«'•«i^uwwTOiyw^Wif«!^

1. Measured phase changes may be more simply interpreted in terms of refractive-index variations in the ionosphere, than is the case for group-path measurements,

2. The sensitivity of the measuring system to small phase changes is limited only by the stability of the frequency standards em- ployed .

3. Dispersion—i.e., the propagation of different frequency compo- nents of a pulse over different paths—need not be considered.

4. The narrov/ bandwidth required allows the use of low peak power and reduces the system's sensitivity to interference.

The major disadvantage of CW measurements is that frequencies must

be chosen at which only a single mode is propagating. The path used in

the present study allowed the use of single-mode frequencies during win-

ter daylight hours. The methods of acquiring and analyzing the data are

described below.

Changes in the phase-path length (P) of rays propagated obliquely

over a 2600 km ionospheric path were used to study irregularities in the

received wave fronts and to infer some of the characteristics of the

source mechanism in the ionosphere. The measured rays propagated over

a "single-mode", one-hop, lower-ray F-layer path. In the absence of ir-

regularities in the ionosphere, the resulting field at the receiver,

produced by such "single-mode" propagation, consists of an ordinary and

an extraordinary magnetoionic ray. As a result of the irregular bending

of rays by ionospheric irregularities, more than one such pair of rays

may arrive at the receiver.

The phase-path length of a ray propagating from transmitter to re-

ceiver through a medium of varying refractive index is defined by the

relation

-i V-ds , (1) RAY PATH

where \i is the refractive index of the medium and ds is an incremen-

tal distance along the ray path. P is directly related to the phase

cp of the received wave by

13 SEL-70-037

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^ww ^ppglBPPPPBPPIP ■Jli-'li'UI^AftliMPffWiWipMilllWPWi^^

CD 2nP

A

where A is the wavelength in the medium and equals 7\ /u, in which ^ o o is the free-space wavelength. If changes in phase-path length (AP) are

measured in free space (}.; = 1), A may be used in relating Acp to AP.

In this context, cp is not periodic in 2n rariians. The measurement of

changes in P as a function of time is made by observing the changes in

cp as a function of time—i.e., by counting the number of cycles (an in-

tegral number plus a fraction) of the received signal which occur during

some sample interval (usually one second), and comparing this with the

transmitted frequency. Such a measurement is unambiguous (unlike a sim-

ple phase measurement). That is, the resulting phase measurement is not

limited to the rangu 0 to 2it radians.

The received signal is converted to an audio frequency by a phase-

coherent receiver, and it is this audio signal which is measured. The

use of an audio frequency much higher than any possible frequency shift

in the received signal avoids any potential plus/minus ambiguity. The

equipment and processing used in these measurements, and the accuracy

of the measurements, are discussed in the appendix,

If only a single ray path joins the transmitter and the receiver,

the meaning of such a measurement is clear. Let the received signal,

E , be described in the form r

E = E(t) sin r pnf t + cp(t) , (2)

where t is time, f is the transmitted frequency (carrier), E(t)

is a slowly varying (compared to the carrier frequency) "envelope" am-

plitude, and cp(t) is a slowly varying phase angle measured with re-

spect to the carrier. The quantity cp will be referred to as the

measured phase of the received signal. Again, note that the range of

T' is not restricted to 2K radians. E(t) is also measured at the

sampling interval. A one-second sampling interval has been found to

be satisfactory for the relatively stable signals observed under the

measurement conditions.

SEL-70-037 14

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P?"'1 '■' IU '''f^**1^****1*^*'^^ "TTJP

The received signal E can be represented as a vector of length

E at an angle cp relative to a coordinate system rotating at 2«f

rad/sec (Fig. 4a). If truly only one signal is present, this picture,

together with the meaning of the measurement, is clear. If the received

signal is shifted in frequency from the carrier frequency, e.g., if a

doppler shift is caused by motions in the ionosphere, then

cp(t) = 2«fdt , (3)

where f (commonly called "doppler") is the difference between the

transmitted and received frequencies.

If the received signal is produced by a summation of several rays,

the interpretation of the measurement may or may not be clear. The

phase measured is that of the vector sum of all components present.

Some possible types of sums are shown in Figs. 4b and 4c and are de-

scribed below.

Consider a received vector composed of a large signal vector (E )

plus a small randomly phased vector (E ). As has been pointed out, the

measurements made in connection with this work were carried out under un-

disturbed ionospheric conditions, using frequencies for which only a sin-

gle mode was propagating. Measurements by Sweeney (''0) and others show

that under such conditions, phase changes are generally smooth for peri-

ods of several minutes, but that small, more rapid (5-20 sec period)

phase fluctuations of about 10 deg are observed. Such fluctuations might

arise from noise, interference, or scattering by small irregularities in

the ionosphere. This type of fluctuation may be represented by a small

random vector E added to the main signal vector (Fig. 4b). The mea-

surement of phase is still unambiguous; however, a phase error is intro-

duced. As long as the actual phase error introduced into the vector sum

is not significant to the data derived from the measurement, the effect

of such perturbations is not important, and does not modify the concept

of the measurement. Actually, if one received signal vector is larger

than the sum of the magnitudes of all other vectors, the unambiguous mea-

surement is a meaningful representation of the larger (dominant) vector

as long as an error in measured change in P of ±A/4 (equivalent to a

change in cp of ±n/2 radians) is acceptable. While an error of 7t/2

15 SEL-70-037

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E(t)

270*

Figure 4. Vector representation of received signals.

(a) Single ray. (b) Small perturbing

component. (c) Two rays of comparable

amplitude.

SEL-70-037 16

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radians might invalidate a simple phase measurement, errors of this

magnitude will be negligible in the unambiguous phase-path-length mea-

surements .

Now consider a measured resultant vector made up of two vectors of

similar magnitude, E and E , whose lengths vary with time (Fig.

4c). 5.uch a situation might represent two magnetoionic components (see

Chapter III); or propagation by more than one mode; or "internal multi-

path" effects produced by ionospheric irregularities. In the case of

the ordinary and extraordinary magnetoionic components, the relative po-

sition and strength of the two component vectors will vary only slowly

with time. With the exception of a complete cancellation, the measured

phase and frequency shift of the resultant vector will be a reasonable

estimate of the performance of either of the two rays. For rays of com-

parable amplitude which do not behave similarly to each other, we will

observe the variations in length of phase path P for the stronger ray,

within an accuracy of ±A/4. Since the relative amplitudes of the rays

may vary with time, one ray and then the other may successively dominate

the measurement. If such relative changes in amplitude occur slowly

enough (i.e., if many samples are taken between changes), and if the

frequency shifts f along the ray paths are different enough for the

two rays, we will be able to observe an abrupt change in the slope of

the phase-path record as the change occurs. Figure 5 shows the type of

changes we would expect under these conditions.

For larger numbers of components, a simple intuitive understanding

cannot be continued unless one of the above conditions can be approxima-

ted; i.e., unless one ray or several rays with very similar frequency

shifts dominate the resultant vector for reasonably long intervals of

time. Ultimately, the analysis of the amplitude and phase measurements

will be limited by sampling theory and measurement noise; however, in

this work the technique is applied only under conditions when the simple

intuitive approach is applicable.

The term internal multipath' is used to describe multiple rays which propagate from a transmitter to a receiver via a single ionospheric mode. Internal multipath is present if ionospheric irregularities produce suf- ficient differential ray bending that rays cross before reaching the re- ceiver location.

17 SEL-70-037

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SEL-70-037 18

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Using the measurement described above, it is possible, under certain

conditions, to determine changes in P for the ray path joining a trans-

mitter and a receiver, and conversely, it is frequently possible to deter-

mine from the measurement record whether the necessary conditions exist

at the time of the measurement. Several implications of such measurements

will now be discussed.

Variations in the phase-path length of an ionospherically propagated

ray can occur in two ways. From Eq. (1) it is seen that variations in P

may be caused both by variations in ^ along a fixed path, and by changes

in the position or length of the physical path. The frequency shift (dop-

pler) which is produced by varying the phase-path length of a ray is

d c dt

where c is the speed of light and f is the transmitted radio fre-

quency. By measuring the slope of a phase-path record, we may determine

the doppler shift of the ray that dominates the measurement.

An additional and perhaps unexpected relation for rays propagating

between two fixed endpoints, through a medium in which the refractive

index varies with time, is derived by Bennett ('67)

= - T L „.„„ i fd = -TJ *ti5 ■ <5)

■mv PATH

This relation states that the instantaneous frequency shift is a function

only of the instantaneous rate of change of refractive index along the

present ray path, and does not include a contribution due to the simul-

taneous change in the position or length of the ray path which may be

occurring. This fact will provide a more direct interpretation of our

measurements in terms of the irregularities which cause them.

More precise statements ox Eqs. (1) and (5), which account for the an- isotropy of the ionosphere, include an additional term, cos a, within the integral, where a is the angle between the ray direction and the wave normal (see Budden, 1961). When considering small changes in long- range oblique ray paths, the error introduced by neglecting this term is negligible.

19 SEL-70-037

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j^aiW^yW^MIUm^^^

It is also useful to consider the technological constraints which

will influence the usefulness of the measuring technique. The measured

changes in phase-path length are not expected to occur at a rapid rate,

since frequency shifts greater than one or two tenths Hz are rare under

the stated experimental conditions. An error in integrated phase aris-

ing from the frequency sources used for transmitting and receiving will

be reflected in a like error in the measured phase-path length. The

more rapidly phase-path changes introduced by the ionosphere occur, the

less rigid will be the requirements on the frequency sources used. Fre-

quency errors (linear changes of phase) can be tolerated if a linear

trend may be removed from the resulting data without loss of information.

Instability in frequency, however, will degrade any data that make use

of measurements of changes in P. Crystal frequency standards having a -9

stability of about 10 will introduce errors in the measurement of P

at a rate of about 1000 m/hr. Portable cesium-beam frequency standards

having a stability of 10 will allow measurements with an error of

about 10 m/hr. For the observed variations of the present experiments,

this gain in accuracy is crucial.

C. MULTIPLE-LOCATION MEASUREMENTS

The effect of refractive-index irregularities on waves propagating

through them is principally determined by the strength (per cent altera-

tion of the refractive index) and the spatial extent of the irregulari-

t ies .

The first series of measurements performed in this study was primar-

ily concerned with determining the strength and horizontal scale size

(or sizes) oi the ionospheric irregularities believed to be present under

quiet ionospheric conditions. Since the size range of possible irregu-

larities was not known a priori, measurements were made at as wide a

range of spacings aj possible. The work of Bramley, carried out under

quiet ionospheric conditions, indicated that the probable range of sizes

of irregularities to be encountered would lie between 30 and 200 km.

Making use of these observations, and considering some practical experi-

mental limitations, a single stable-frequency CW transmitter was used,

SEL-70-037 20

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i.lWgWp.ft^WP#i^r""w

and phase-path measurements were made simultaneously at two receiving

points separated by distances which varied from 50 to 170 km. This

provided two ray paths in the ionosphere which were separated horizon-

tally by 25 to 85 km at the maximum height of the rays. One receiving

system was located at the Stanford University Wide-Aperture Research

Facility near Los Banos, California, while the other receiver was in-

stalled aboard a DC-3 aircraft. The aircraft was also equipped with

an accurate tracking system which, in conjunction with two line-of-sight

stable-frequency transmissions, allowed continuous (though not real-time)

tracking of the plane's position. The equipment and data-processing

method employed are described in detail in Appendix A. The resulting

records show the variation in phase-path lengths between the transmitter

(located in Bearrien, Arkansas, 2600 km east of Los Banos) and each of the

receivers. The records from the aircraft are corrected to compensate for

the variation of the aircraft's position from a constant radial distance

to the transmitter and from a constant altitude. For most of the experi-

ments, the aircraft flew a course running from 50 to 170 km north of Los

Banos. The course was flown in both directions.

The choice of this method of observation results in the ability to

explore wave fronts at various receiving-antenna spacings without the

necessity of establishing numerous field sites, and allows the detection

of fixed irregularities. It does, however, suffer a decrease in the num-

ber of measurements that may be made at any given spacing, for the sake

of an increase in the number of spacings that may be employed. The re-

cords show

P(t) - PQ a for the fixed receiver, and

r = constant 6 = constant

p(t,e) - Pb for the aircraft receiver, r = constant

21 SEL-70-037

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!t;^^.VWWW*^WWWIWlB><?MW^ ..--r.-^-, -^ r^rT7jIWTOB^EW?™TO?^^pE»TOBPW?

P = phase-path length,

r = great-circle distance from the transmitter to the receiver,

9 = bearing from transmitter to receiver, and

P and P = unknown constants at the start of each measurement.

The slopes of these functions correspond to the observed frequency shift

(doppler) of the signal and are given by

dP — , with r and 0 constant, for the fixed receiver.

and

ÖP ÖP d0 J L d6 *yt + ^9 ' dt ' with Ht" and r constant, for the aircraft. (6)

The second term in the doppler expression for the aircraft arises from

the aircraft velocity.

Two sources of error in interpretation of these data will now be

mentioned with reference to their effect on our observations. The first

is that the ray path Joining the transmitter and the receiver does not

lie in a plane containing the transmitter, the receiver, and the center

of the earth, because of the tilts in the ionosphere produced by the ir-

regularities we are studying. Therefore, the exact ray path is not known,

and the measured doppler is that corresponding to a point in the iono-

sphere whose location is not precisely known. The error introduced by

this deviation can be estimated by making use of angle-of-arrival mea-

.-.urements made by Sweeney ('70). He used a broadside antenna array which

was 2.5 km long, and which received over the \rkansas-Los Banos path.

HL> found root-mean-square (rms) angle-of-arrival fluctuations of about

1/4 deg, which implies that the ionospheric ray path has an rms devia-

tion from the great-circle plane containing the transmitter and receiver

oi about 7 km at its maximum height.

SEL-70-037 22

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The second source of error is introduced by the aircraft's motion

(the OP/00 term in Eq. 6). The effect of this error can also be de-

termined from the known angle-of-arrival deviation. For a 15 m wave-

length (20 MHz), a 1/4 deg change in angle of arrival will produce a

phase variation normal to the nominal ray path of one cycle in 3 km.

At the nominal aircraft velocity of 60 m/sec, this will result in a

frequency shift of 0.02 Hz. As is indicated by the measured data pre-

sented in the next section, these zero-mean errors introduce only minor

errors in the results for the values of frequency shift measured in

these experiments, and for the number of points averaged in computing

correlations.

Measurements using the aircraft receiver and the Los Banos receiver

were made during April of 1969. A total of ten flights yielding satis-

factory data were made. Frequencies between 20 and 25 MHz (wavelengths

A between 12 and 15 m) were used for these measurements. Each flight

covered a path between a point 170 km north of Los Banos and a point 50

km north of Los Banos, and required between 20 and 40 minutes. On any

given day, one or two flights over the path were made. If two flights

were made on one day, they were made in rapid succession. (The data from

two of the ten flights were later discarded because of interference on

the tracking system frequencies in one case, and evidence on an ionogram

and in the phase-path measurements of an ionospheric disturbance in the

other.)

A typical pair of records from the fixed and airborne receivers is

shown in Fig. 6. For each pair of records, a constant doppler (constant

frequency shift, indicating a linear time rate of change of phase-path

length) has been subtracted from both records. This removes the effect

of large-scale ionospheric layer motions which do not influence the shape

of the wave front. The most striking feature of the records is the quasi-

periodic variation in phase-path length seen consistently in our observa-

tions. The time between peaks of these variations ranges from 15 to 25

min. The peak-to-peak phase-path length variations seen in these records

ranged from about 8 7\ (approximately 100 meters) to about 50 A (approxi-

mately 600 meters). These length variations produced maximum frequency

shifts ranging from about 0.05 Hz to 0.20 Hz. Analysis of these data

23 SEL-70-037

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SEL-70-037 24

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(see Section D of this chapter) indicated the presence of large, weak

irregularities.

The small size of the measured frequency variations reveals some

of the experimental difficulties which may be encountered in studying

them. In order to make relative phase-path-length measurements at two

separated points, the frequency standard at each point must be suffi-

ciently accurate and stable that the desired measurement is not masked

by variations in the standard. For variations of the order of 10 A per

20 min, at an operating frequency near 20 MHz, we would like the stan-

dard to introduce errors no greater than 10 per cent of the desired

measurements This means one cycle per 20 min at 20 MHz, or a stability

(Af/f) of about 4 X 10 . If the two measurements are made only a

short distance apart, a common frequency standard may be used, making

possible relative phase measurements that are as accurate as may be de-

sired. However, if the effect being investigated produces only an in-

significant difference in length of phase path at points separated by

the small distances which may reasonably use the same frequency standards,

independent standards of the above accuracy must be used in order to

enable observation to be made at more widely separated receiving points.

It is only recently that portable cesium-beam standards have been avail-

able which meet this requirement.

A second difficulty is encountered if doppler measurements are to

be made using a Fourier analysis technique (instead of measuring the

instantaneous slope of the phase-path variations). The smallest fre-

quency interval Af which may be resolved by Fourier analysis is 1/Tr

where T is the length of the data sample. If ten independent frequency

intervals are dasired in the range of dopplers produced by weak irregu-

larities, i.e., f = 0.05 Hz, then Af = 0.005 Hz, and T = 200 sec.

During this 200 sec interval, for the observed variations, the frequency

will have shifted through several frequency-resolution cells, producing

a poorly defined spectrum. If only a single signal component is present,

we may use a shorter analysis time and interpolate between frequency in-

tervals; however, this condition is rarely met for ionospherically propa-

gated signals. When multiple, comparably strong (within an order of mag-

nitude) components are present, the doppler method can separate them only

when the frequencies change slowly enough to be resolved.

25 SEL-70-037

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^^l^W^^WWWW^^ BBIM^IHWSiHIW1-'." '"Wl'.^'l' 1^ " lfi^-"M"''Witf^l^5J'IH^f.'.Wll!IV,'''*ll'.'i

D. HORIZONTAL SCALE SIZE OF THE OBSERVED IRREGULARITIES

An estimate oi the size (horizontal extent) of the irregularities

being investigated was made from the above data by computing a correla-

tion coefficient "'or the variation of the doppler from the mean, measured

at various spacings of the two receivers. The doppler was measured graph-

ically from the phase-path records. A total of eight pairs of records

was found suitable for use in this correlation. For each pair of records,

P^Ax) ^dl "d2

(7)

dl

was calculated, where

.th o (Ax) is a sample of the correlation for the i flight at a

receiver spacing of Ax,

f., is the scaled doppler value for the fixed receiver, dl

f is the scaled doppler value for the airborne receiver, and

f is the mean-squared doppler for the fixed receiver for the length of the record.

The estimate of correlation was then calculated as

8

p(Ax) = 2. — i=l

p. (Ax)

8 (8)

The calculated points are plotted in Fig. 7. The error bars indicate the 2

estimated variance (s' )'J of the correlation [as defined by Eq. (7)]

calculated from the measured values by

2 2 (s-r = s n-l '

SEL-70-037 26

''tifrtflryiMtftriW^tiMim^ mmtim . I llll

FPWPPI|||Wf|!PPPP^PIBPPPIP»WP*P!l|PI»«P!P pgpppj i tp"iJi««UliLli!VUI.iiiJUPlll^||||p|||pipp PIPPMilPIPllJILIIIIUIllllllJII I

:

I

t-O*

oj <

o - 00 o z

1

^p2; s< ,——o^^ V) ^N X o

(0

7 o m

/ / liJ o UJ o z < (r A

N

OF

^E

AS

UR

N

TS

o rO

<T UJ —u > 50C5 o

J- W

O

1 1 1 J 1 O CO

- d 6 6 6 o d d

oo c

•r-l XJ a (U • XI

c o >,

•r-l to i-l i-i O e i—i

to •u u

-n U-l C m to Ü u M N

m o •rJ

0. u >-l

m •l-l Ü i to x;

<1J T) o ü •r^ 4.) 4J

? 0) 01

M a D 0 ■o T3

U-l

J-i C

CL < (1)

■ r-l c c Ü •l-l •r-l

•i-l V-) (-1 )-l

M-l • o O

(1) C/3 S-l !-i

O U >-l >-i

O C 0)

OJ QJ

c fi T3 •a 0 Oi tu OJ

•l-l 1-1 J-I a 4-1 D to to m tn E e --I nl •rl •l-l

en OJ XJ 4J

M R tn tn u w CJJ o Ä o 4J

1 , M a OJ i

I—i OJ a en " a to (-4 ü 4= Q a J"

<u n D eo

•■-I

(«7)^ 'lN3IOIiJ30D N0liVn3ad0D

27 SEL-70-037

■'■ • ■■:-''-' ■ - ■ ■' ■ " -^^^^^^'ti^^iüiiJmiii ̂ i.,-^i.^.. ̂ ^MtM**^..^^^.^^^^^*^^^ : .; tkum

»S?lOT'-7«c?™*sra?»!!Hn^>=WW5^^ ■ - -'„» JT" " .,r.-L^.!,^...i ,......,•,,jy^~^r.i..J(,!j,t,,„,.i.,.,v,,5W.,n,,, l^m^mnnmn^meRism i ww im

wlie rt' n und is the sample variance.

l^'o sources oi error in the measurements of p. were mentioned in i

Section C. Unc is introduced by the motion of the aircraft, which was

sho^n to introduce an rms error into the doppler measured by the aircraft

(f ,9) of about 0.02 Hz. The rms measured doppler averaged over all

flights was approximately 0.1 Hz. Therefore the expected error in p.

is 0,2 for this source. The expected error in p is then 0.2/ 8, or

approximately 0.07.

The other source of error is introduced by the horizontal bending

of ray paths by irregularities, which was shown to introduce an uncer-

tainty in the location of the ray path of about 7 km near the reflection

height of the rays. This can be represented as an error on the ground

oi 11 km for each ray. The error in Ax will depend on how the devia-

tions of the two rays are correlated. At very small (compared to the

.-,ize of the irregularities) spacings the deviations are positively cor-

related, decreasing the error in J^x. At very large spacings, the devia-

tions will be independent. At some intermediate spacings, the two rays

will bo deflected oppositely by the two sides of each irregularity, caus-

ing the deviations to be negatively correlated, thus increasing the error

in Ax. On the basis that the deviations are uncorrelated, the expected

error in p is represented as an error in the location of p(Ax). This

error is approximately 7 km (14 \j2/'^8). The effects of this error and

the error due to aircraft motion are shown in Fig. 7.

The data of Fig. 7 show a correlation greater than 0.8 for the dop-

pler measured at spacings of 60 km or less. At spacings greater than üO

km, the correlation is less than 0.3. This indicates that the irregular-

ities producing the major component of the observed dopplers are of limi-

ted extent, and that the experimental configuration covered the size range

uf the major irregular structure. At a receiver separation of 70 km, the

average correlation has dropped to about 0.5. This gives us a reasonable

first estimate of 35 km for the horizontal extent of the irregularities

in the ionosphere. This scale size will be used as a typical value in

predicting the expected effects which these irregularities are expected

to produce on wave fronts.

SFL-70-037 28

■ >-.»^-~- --^-^ '■■ - ■ .-.■■■..i— ■- . .-. - ■■■„.n.»...' , .,,L,^..tfrB^^.A:.;A^j,i;..i^<^ ,^-x.t^i..^..^.^^.»^..

^>^^»U^!Ulll||ll.).^BJIUlJlil lljllinj^^jg^jy^^ip, -' .. .-:.-—^—o;,., , ,.l-^^^

^^^I.Jia-ll.lll»MI.IW^^IBi^)yffliwftayj^^ujwu^,j^^^

As was noted above, the doppler measured by the aircraft is a func-

tion not only of the time rate 01 change of ray path length at a fixed

point, but also of the spatial variation of refractive index caused by

the irregularities. The ef^L-ct of the spatial structure of the irregu-

larities of 20 min period, identified in the above doppler correlation

study, was estimated earlier in this section using Sweeney's angle-of-

arrival measurements, and was found to introduce only a small unbiased

error term in the estimate of correlation. The possibility of the exis-

tence of a fixed irregular structure (or structure varying with a period

much greater than the observed 20 min period) was examined by correlating

the doppler measured on two pairs of consecutive flights over the path

(spaced in time by about 30 min). Doppler correlations were computed

from the data obtained on each pair of flights. The correlation coeffi-

cients of 0.13 and -0.05 for the two pairs of flights indicate that no

fixed or semi-fixed structure was present with a magnitude comparable to

that of the irregularities having the 20 min period variations.

A more accurate measure of the scale size of the irregularity struc-

ture could be obtained if it were possible to make prolonged measurements

at fixed receiver separations. If multiple spacings were employed, some

estimate of the spatial spectrum of irregularities could be obtained.

Such a program could prove costly because of the large spacings needed

and the high stability requirements of each receiving system. For the

purposes of this work, the approximate scale size of the irregularity

structure determined above will be used to study the effects to be ex-

pected in the presence of such irregularities.

E. VERTICAL SCALE SIZE

Having determined a reasonable estimate of the strength and of the

effective horizontal scale size of the most significant irregularities

for the oblique path, it was then necessary also to determine the approx-

imate vertical extent of the irregularities in order to model their ray-

beinding effects. The most convenient technique for probing the iono-

sphere at various heights, for a path joining two points, is to make use

29 SEL-70-037

i;i^rilH;j^.ii.e.1»^Ji.i...i.iij.i--..i..,.:-v-|l|„.t(||| - ■-—aoaiiaiaiaaiiatttt^^ ■ ■•■ ' ■t-W —, ! V L_*L

ÜWPIBIIIliPÜWW' ■,«^*WWB«|P»WPP!^!IIW . uiililUMPNI VPIBIIIII.IMI kiuiuiiii.i.iiiii ül.l ii in... .».in i -.«-.■v-ru'—~-Tn

01 a ran^u 01 radio Irequencios which will penetrate to various heights

Into the ionosphere. Figure 8 shows the geometry of ray paths of various

frequencies between two points, and gives the values of ray height at

dilferont points along the path, as computed by raytracing techniques

(Croft '69), lor an ionosphere typical of that over the path under study.

These heights arc used in estimating the vertical scale size of the ir-

regularities .

During the winter and spring of 1969-1970 another series of experi-

ments was performed over the same path used in the previous work, with

the objective of determining the vertical scale size of the irregulari-

ties previously observed. Only the Los Bp.nos receiver site was used for

these measurements. Transmissions on two single-mode frequencies were

made from Bearden and received at Los Banos, The two frequencies were

received on a single whip antenna. One of the frequencies was also re-

ceived on a whip antenna located 2.52 km north of the first antenna, for

use in measuring the north-south velocity component of the irregularities.

The outputs of the three receivers were recorded using the same phase-

moasuring technique used previously (see Appendix A). During the period

from November 1969 to April 1970, measurements were made one or two days

per week. Each day, from two to six hours of operation were possible

(periods when single-mode propagation was possible and no irregularities

were observable on ionograms over the path). The data collected in the

course of these measurements were also analyzed to determine the vertical

and north-south velocity components, seasonal occurrence, and signal-fad-

ing effects of these Irregularities. These results are discussed in later

chapters of this report.

Frequency separations in the range of 100 kHz to 6 MHz were used to

achieve various ray spacings in the ionosphere. Doppler correlations

similar to those employed in the determination of horizontal scale size

were performed on pairs of frequencies using 1.2 hr segments of data. A

considerably greater quantity of data were available for this work (75

segments of 1.2 hr each) than were available from the aircraft measure-

ments ,

Similar phase-path variations were observed at all frequencies used

In those measurements. (Examples of the phase-path records are shown in

SEL-70-037 30

&i-....-.^.-^^toi.^v.^^.to^,„_.^^^.^^ r/ftliii •iri'miiiiiirtfi ti

<£>

UJ (SI

tr

<J3

en 0)

•H Ü c 0) 3 D" OJ )-i

M-l

■—1 nj j= B M •u X OJ ra > a <!• <f co <r ^3 rn 01 •o oo a\ n co in oo tn •H

s <]■ oo n oo n CN U x: ci rsi ro ro ^ "^ 0 4J c^ rg CS CN CM CM

M-l < W ij

4J JZ C 60

•H •^ 0 OJ a ffi

6 o >, ^ S « 4J a! O OJ

O 00 00 oo a c r-i CO B

•H Pi ^ c T)

•l-l c -a t—i in o o r— vo o to c "-1 3 i-i m o vo vt vo

o o co m <f -J" m vo w O l-l r-l i-t i-l t-( 1-4 r-l

-C 00 o 4J « 4-1

a < >. ni !-i

u >> •H U N

C OJ §

J 3 a. cr o .-i CM en <t- m en 0) <N CM CM CN CM CS

o u c fe 0 H

(1)

3 M

:

31 SEL-70-037

.... .. .:^,^..^...^^ ^J.t.i.^.i^^^:^...,:^^ ,l:..^..^^^. . . 2<...,..:*,...^^.*k.<'.^; UfrOük . ,i. ..:. ^..-. tiMittaniauittiii in i ■ .^^~-.iii

m^G*ffHmmmm*mmfmmm&!fi*!'i^*'*mm UI(j.MW^a,WHW!pWBi|Wii^^

Chapter III, Figs. 17-20.) Frequently, however, the amplitude of the

phase-path changes decreased with increasing frequency. This information

may be of use in determining the mechanism responsible for the observed

variations; but for the present, only the vertical scale size of the ir-

regularities is of Interest. The form of the correlation computed was

slightly modified in order to utilize the greater quantity of data avail-

able and to compensate for the general decrease in magnitude with frequency,

The denominator used in calculating the correlation coefficient was changed

This form of the correlation func- from f?, dl

as in Eq. (7) to if? . f si dl

2 d2■

tion has the property that two functions differing only by a constant fac-

tor will have a correlation coefficient of 1.0. For each sequence of data,

taken at a fixed frequency spacing, a correlation was calculated from 64

doppler measurements during the 1.2 hour period. In Fig. 9, the correla-

tions are plotted against the frequency separation used. On the assump-

tion (supported in the next chapter) that the irregularities have their

maximum effect near the maximum altitude of the rays, spatial separations

are also assigned to the frequency axis in Fig. 9 by using an average

value of 4 km per MHz. The error in this average spacing as determined

by raytracings in several representative model ionospheres (see Fig. 8)

is indicated on the figure.

Again, a smoothly decreasing correlation is observed as the spacing

increases. The average vertical distance required for the doppler cor-

relation to drop to 0.5 is about 15 km, based on the assumed ray separa-

tions. This considerably smaller vertical scale size of the irregulari-

ties, in comparison to horizontal scale size, will be of importance in

determining the effects produced by these irregularities.

F. CONCLUSIONS FROM PHASE-PATH MEASUREMENTS

The important parameters of the irregularities observed will now be

summarized in a form which will allow an investigation in the following

chapters of the expected effect of these irregularities on wave front

characteristics and antenna performance. All of the observations of ir-

regularities during the course of this work were made under undisturbed

winter daytime conditions over a 2600 km path at frequencies for which

SEL-70-037 32

„ ■., ../.^.^-^t.^-,.,..;..;^.^...^..^..., ^.^u-i-^.^^^-^^^.^^^.».»«^

p!^IU^■l.Vl"i»«*IJlill»JI!■^!l^)lJft■il!l.J,ll!,Jl■??»^ ilM.^^MIWJIlU^jUji^llHB^^

< üJ 0.00 oc tr o o

-0.2S

PROBABLE RANGE OF ERROR IN RAY SPACING (km)

J.

QO o

12 3 4 5 FREQUENCY DIFFERENCE. Af (MHz)

I I I I L_ 4 8 12 16 20

APPr^OX. RAY SPACING AT MAX. HT. Ah (km) 24

Figure 9. Doppler correlation coefficient for multiple-frequency phase-path measurements.

33 SEL-70-037

^to;at,to.ni^.^^^a<^,.^^ -.^^.■..^;,^.^«,aMiiJ^^;i^^ tMi^W^tt.^^iL

lumwmw^iitijij.ijiii^^^ lUiiiirjiiiiiuu^ii^ffiwWWWJIW^^

only the one-hop lower-ray F-layer mode was propagating. No data were

taken during periods when larger irregularities (which are visible as

"kinks" in the tonogram—Fig. 3b) were present. The conditions represent

the most promising conditions for high-performance IIF propagation, and

are therefore of great practical interest. Such conditions also allow

the use of the most direct measurement methods. Furthermore, the appli-

cation of the knowledge gained under these conditions will help to clar-

ify the results of observations made under more complex conditions.

During about 100 hours of observation in the spring of 1969, and in

the winter and spring of 1969-1970, phase-path variations having a dis-

tinct period of 15 to 25 min were always observed. The amplitude of these

variations ranged from about 8 A to 75 A peak to peak. The horizontal

spatial correlation of the doppler produced by these variations indicates

a correlation of 0.5 for receiver spacings of about 70 km on the ground.

This implies a horizontal scale size for the irregularities of about 35

km. (If scale size is defined for a correlation of 1/e, where e is

the base for natural logarithms, the scale size would be about 43 km.)

A similar calculation of vertical scale size indicates a vertical extent

of about 15 km, assuming the effects are produced at the maximum height

of the rays. Also, for a fixed ionosphere, a decrease in magnitude of

the phase-path variation with increasing radio frequency has been noted.

SEL-70-037 34

tfljijjijfrliiitij&äfä^^ iiiiiiriiJHriiiiairiiiiiiitiriiiiiiiiii'iiiiiiiiiii j

Bp'^rww^flNVW'BJMWlJIIMJHW.!^

SCATTERING REGION 44612

Figure 10. Two-dimensional scattering geometry,

SEL-70-037 36 Preceding page blank

— -^---■"■"-^ -^—,..-■■--^ ■■.--■■.. ■.K..,....-.!.^.,.^.. ../.t ,....-.,..,v||M||i||lV|^|r||^4l^-JJM^^^^^..^^ _^Ä , - I - -H

wrnvm^mmmmmmm^mmmmmmm^m^mmmm^ |1<|P«.SH"!W«>W!1.i,i!„.|,lJ,.!.ll!«j piplilpipppjlpipipppi

III. MODEL OF THE IONOSPHERIC IRREGULARITIES

The p'iase-path-length measurements described in the preceding

chapter were used to determine the strength and spatial extent of the

irregularities producing the measured variations in phase-path length.

The measurements do not, however, provide a complete description of the

received wave field. In fact, the measuring technique intentionally

rejects amplitude fluctuations and small phase fluctuations in order to

provide measurements which describe the causative mechanism (the irregu-

larities) most directly. In this chapter, irregularity models are used

to determine the nature of the total wave field expected in the presence

of the weak, medium scale irregularities.

A two-dimensional representation of ray bending, as shown in Fig.

10, will be used. In the figure, r is the distance from the scatter-

ing region to the point of observation, and e is the angular deviation

imposed on the ray by the irregularities. This representation will be

applied to diffraction in both the vertical and horizontal planes.

A. THE RAY-THEORY APPROXIMATION

The spatial extent of an irregularity strongly influences its effect

on waves which propagate through it. In particular, the relation between

the transverse scale size (A^J of the irregularities (measured trans-

versely to the ray path) and the length of the first Fresnel zone (F)

determines the suitability of a ray-theory treatment (A,^ » F) or a

diffraction theory treatment (F »A™)- If it is assumed that parallel

rays are incident on the scattering region, then

F = \IPh O)

where r is the distance from the receiver to the scattering region and

A is the wavelength. For the parameters of the measurements in this

work, r ~ 1300 km and 7v =a 12 m. Therefore, T ~ 4 km. Since the

scale size of the irregularities in question was determined in the pre-

vious chapter to be considerably larger than 4 km, a ray-theory treat-

ment is appropriate.

37 SSL-70-037

!BtateMuMidiiMaflaittaia.i^^

WJgWllUl^iMill'WWJpHWW.»

13. TllE EFFECTS OF A SINGLE IRREGULARITY

In this section it is assumed that the observed variations in phase-

path length are caused by single isolated circular irregularities. The

refractive index within the irregularity is given by

M - Mb + max

^b

where ^ is the ambient (background) refractive index of the ionosphere,

An is the refractive index change at the center of the irregularity

(the strength of the irregularity) and z is distance from the center

of the irregularity.

1. Nature of the Wave Field Produced by a Single Irregularity

Computed ray paths through a single circular irregularity are

shown in Fig. 11 for three different values of irregularity strength.

Figures 11a, b and c illustrate the effect of successively stronger ir-

regularities. The scales are greatly compressed in the direction of

propagation in order to provide a convenient format.

The angle e through which rays are bent when passing through

such an irregularity is a function of the phase change, cp, produced by

the irregularity and of the transverse scale size A- of the irregular-

ity. The wave field at the receiver plane is determined by the angular

deviations of the rays and by the distance from the irregularity to the

receiver. If the phase change of a ray passing through the center of an

irregularity is defined as cp , the nature of the received wave field 6 J Ymax is determined by the ratio of cp to A^/F. If cp is small com- J max T Tmax pared to A_/F, only a single ray will arrive at a given point on the

ground (Fig. 11a). However, if cp is large compared with A~/F,

rays will cross before reaching the receiver (Fig. lie), thus producing

a field at the receiver plane which may be composed of three separate

waves having slightly different arrival angles.

By calculating points of constant phase-path length (i.e.,

fpcls- constant) along each ray path, the shape of the resulting wave

SEL-70-037 38

gp.-"TTO, i,',...HWfl.J|n.^W;...j - lit. i .■.■■■, ..„i^-p^.^ .. , ..v..!tr.,„ i»HU»#WjMWWtwiiy^w

(a)

^-.1-

x|<

h- o: <

LONGITUDINAL DISTANCE

Figure 11. Computed raypaths through a gaussian irregularity.

(a) cp

(b) cp

(c) cp

max

max

max

< AT/F

« AT/F

> AT/F

39 SEL-70-037

-— W^Mii^^^MM^^ffl,.»^^

tJiiu-wwpwjaiiiw^^^

fronts may be determined. By computing the change in area of each flux

tube (an arbitrary volume bounded by rays), the resulting distributions

of field amplitude may be determined (with some restrictions in regions

where rays are focused). Examples of the results of such calculations

are shown in Figs. 12 and 13 for irregularities which produce maximum

phase changes, cp , of cp , 4rp and 6.5rp where cp is chosen rticix J. J. i 1

arbitrarily simply to illustrate the effects of varying irregularity

strengths. Note that the wave-front plots. Fig. 12, could be plotted on

the ray tracings. Fig. 11; but the scale of interest is drastically dif-

ferent. For the irregularities we are studying, the total ray-path

length is over 2600 km, while the maximum wave-front deviation is about

1 km.

In the presence of a single irregularity, the field at the re-

ceiver will be composed of one or three waves, depending on the strength

and position of the irregularity. If multiple waves are present, the

amplitudes of the waves will be similar, differing by only a few dB. As

the strength or position of the irregularity changes with time, deep

fades will be observed as the relative phase of the similar amplitude

waves changes with time.

2. Relation of Variations in Phase-Path Length to Variations in Refractive Index and Electron Density

The two-dimensional single-irregularity model just described

will now be used to estimate the variations in refractive index and elec-

tron' density required to produce the experimentally observed variations

in phase-path length. The calculations ignore the ray curvature produced

by the slowly varying background refractive index. However, it is shown

in Appendix B that these calculations nevertheless provide a valid rela-

tion between observed changes in phase-path length and changes in refrac-

tive index. Since the simple model assumes that all observed phase-path

variation is caused by one individual irregularity, this calculation will

set an upper bound on the electron-density variation. The peak-to-peak

variations in P observed experimentally were in the range of 100 to

1000 m. Assuming that the irregularities are roughly circular in plan

view (as was assumed in the raytracing), the length of the ray path in

41 SEL-70-037

a^aiu^^^V.v/wHM^Y^^^ -IK nlr.-l.i, , ; i ; ;

WfMWWMJlfH^WItti'.MIWt««^.»» rMwiuai.'"^'^ *. ■ ■^g^yp^r.^'-^'!'^.-- ;>.i"-.:--i-,v"-.w.A.|iiWBT

8-19- d

to i < X CL 0 Q

(0)

<-2h o: 0 - 31-

1 -

s-ls: o ^ UJ s tn - | l~ >/ < yS I jS

Q. .2 y/

Q s'

UJ , N J ^^ _J ^ 2 -4 1 -——

2 o: O -5

i L , 1 \

0 I 2 3 _ NORMALIZED DISTANCE FROM CENTER OF IRREGULARITY, AT

Figure 12. Computed received wavefronts for waves propagating through a gaussian irregularity.

(a) cp = cp.

4(p (b) cp

(c) 9 max i

max 6.5cp1 (cp max

r

»AT/F)

max (cp > AT/F) Tmax '

SEL-70-037

-'■'■ •- ■ ^.■M^^-....'r..«..>S^J**^^ ■.....-„...-.-..■

Wt 1UIU. .I.IIIIUI ■mn^ffinpEppnmi yjpilliin. .uMU«, SWiy.^^MHlülMii.JWIBWillUiHll#f^/lipMiP!liy^^

2 0

ÜJ Q p-4

CL

-8

(o)

NORMALIZED DISTANCE FROM CENTER OF IRREGULARITY, AT

Figure 13. Computed received amplitude for waves propagating through a gaussian Irregularity,

(a) cp = cp max Tl

(b) cp max

4q31

(c) cp = 6.59, Tmax Tl

Ka* < AT/F)

^max > AT/F)

^max>>AT/F)

43 SEL-70-037

*^—;"—--^ mm ^.■^■-. .^ ■■^..u.,.^^ üj) L>

mmmi w^^mipmiimmmmii^mm^m^ PPiPflWWWHWfflpifPWWl^lt^'WiWWIilU.lfln*'1'11!»^^"^^^^

Lhu irregularity is :ibout 35 km. Therefore, the ray path is modified by

about 100 to 1000 m in a distance of 35 km. From the defining equation

of the ray-path length, Eq. (1), it is seen that ^P/P is proportional

to liw'u. Therefore, the variations of refractive index are in the range

ol 0.3 per cent to 3.0 per cent. The relation between the electron den-

sity variation, ^N/N, and the refractive-index variation, AlVfi, is a

function of the background refractive index, \i.

For the ionosphere, neglecting electron/ion collisions and the

effect of the magnetic field (which are unimportant for this calculation)

the refractive index is given by

= ;1 80.6 N

(10)

where N = electron density in electrons per cubic meter, and f = fre-

quency in MHz.

Figure 14 is a plot of the per unit change in electron density,

,\N/N, required to produce a one per cent change in refractive index,

plotted against the background refractive index, |i. For the path and

frequencies under investigation, the refractive index along the ray path

varies from 1.0 to a minimum of about 0.7 at the maximum height of the

ray. At a background refractive index of 0.7, a one per cent change in

refractive index requires about a two per cent change in electron density.

At points of lower height along the ray path, the refractive index is

greater, and larger changes in electron density are required to produce

the same modification of refracti-'e index and hence of the ray path length.

For the changes in refractive index observed in the present studies, elec-

tron density variations of 0.6 per cent to 6.0 per cent are required at

the reflection height. Considerably greater changes would be required

at other points on the ray path.

The calculated changes in electron density may be compared with

the variations observed by others. A great deal of the information avail-

able on ionospheric irregularities has been acquired with vertical-incidence

pulse sounders. However, ionospheric dispersion limits the time delay

(range) resolution of measurements made with these sounders. Also, antennas

SKL-70-037 44

^.ajjifea»^^.,^:^,^^

IBl^WPUl» mmmmm^^^^^m^ ■" i'^MWupwiffppipiiiiiiiiiiis^^

d- 0.10

z UJ

z < x

0.09

0.08 o

0.07 UJ o UJ a.

0.06

< 0.05

UJ o 3 0.04

s tr. a. 0.03 O t-

0.02

l|Z

0.01

0^2 0.3 0.4 0.5 0.6 0.7 BACKGROUND REFRACTIVE INDEX, /x

0.8 0.9

Figure 14. Change in electron density required to produce a one per cent change in refractive index.

45 SEL-70-037

^—c^^^^-......^.^.—..,-...,. ^„A^.^.to^J.Mi .„:..;■.:. :.'..i..^-J--.> mritirtiirtimiliiinfiimtfiiirtiiiiHTB

p.j.j.iu.VPHIMIIL.ipilPJl mm wmmmm ■PPJWWWPWWBIWH^

having little directivity are usually employed with such sounders, caus-

ing their sensitivity to decrease for spatially small irregularities be-

cause of the spatial averaging effect of the antenna. According to Munro

('58), the lower limit for detection of medium-scale irregularities with

vertical-incidence pulse sounders is "a few per cent" of the background

electron density. It is therefore reasonable to assume that if the ir-

regularities most prominent in our measurements are located near the ray

reflection height, they would not bo seen by vertical-Incidence sounders,

or at best would be at the lower limit of resolution for vertical-incidence

techniques. We have already noted the difficulties involved in observing

such irregularities using doppler Fourier analysis methods, and we have

concluded that the irregularities we observe are at or below the lower

resolution limit of this method.

The use of satellite signals in measuring small or weak irregu-

larities is also limited. Satellite measurements indicate variations in

the total electron content of the ionosphere between the observation point

and the satellite, and hence are somewhat less sensitive in detecting ir-

regularities of limited vertical extent than are ground-based measurements.

Also, satellite measurements do not directly yield the altitude at which

irregularities occur. Titheridge ('63) observed variations in total elec-

tron content in the range of 0.05 per cent to 7,0 per cent, which for the

size, shape and altitude (somewhat below the F-layer peak) of the irregu-

larities we observe, would require variations in electron density, with

reference to ,the ambient background, of 0.5 per cent to about 25 per cent.

It is likely that some of the smaller irregularities observed by Titheridge

were the same type observed in the present work. However, satellite methods

do not frequently observe irregularities as small (horizontally) as those

observed here, because of the low probability that a ray path between a

satellite and a ground station will pass through a given irregularity.

In summary, then, it appears that the irregularities whose ex-

istence and characteristics are proposed from the two-dimensional, single-

irregularity model are of a size and strength range not readily observed

using other techniques. Such irregularities are, however, very significant

in their effect on HF oblique-incidence radio communication, as will be

seen in Chapter IV.

47 SEL-70-037

naiyfragaaiaia ..^.iJ^..,i.,w.ai.';,-..^.-.....J.J::v......:-:^.,^,;:.-,^.t...^.--^w. |jg|j|i

7-- - .^.^flWM'.IM^^^^^

3. Modif icat ions of the Simplu' Two-Dimensional Model to Account lor Background Variation in u

Su tar, the effects of the curvature of the ionospheric ray

paths in the vertical plane (vertical focusing), arising from the slowly

varying refractive index of the background as the ray travels upward have

not been considered. The simple model of Fig. 10 is directly applicable

to horizontal (azimuthal) ray bending, if the value of F is modified

appropriately for rays diverging from a point source. In this case

F = VrA/2, ignoring a minor error due to the curvature of the earth and

the ionosphere. However, a realistic model for vertical ray beinding

should include vertical focusing effects caused by the smooth variation

with height of the ionospheric refractive index.

While ray bending effects may be determined for any specific

irregularity distribution using computerized raytracing methods, it is

of greater value in the present research to develop an analytical descrip-

tion of these effects. The correction for ionospheric focusing in the

vertical plane may be made by determining the length of the first Fresnel

zone (K) in the vertical plane for the region where the ray paths are

affected by irregularities.

The fundamental definition of F is the distance along a wave

front at which two ray paths to a receiving point differ by one-half

wavelength (Born and Wolf, '64), The parameter F therefore describes

the effect that phase changes introduced at different points across the

wave front will have on the field at large distances from the phase-

changing region. By computing wave fronts produced by radiation from a

transmitter on the ground, using rays traced through a typical ionosphere,

the distance F may be determined at various points along the ray paths.

This was done to determine the value of F near the reflection height

for a number of ranges and frequencies typical of Ipng-distance HF com-

munication. In Fig. 15 the ratio of the actual value of F to \fP\ at

the reflection height is plotted for various ranges and frequencies. For

the conditions of our measurements, the ratio of F to vrA is less

than 2,0. The use of the actual value of F will allow the inclusion,

in the following calculations, of the focusing effects produced by the

smooth variation with height of refractive index in the ionosphere.

SEb-70-037 48

.....„^^T^^^.^^:^ .-■._ ^^ - AL ,.

I

s 2.0r-

^ 1.0

0.0

15 MHz

± ± 1000 . 2000 3000

DISTANCE FROM TRANSMITTER TO RECEIVER (km)

Figure 15. Computed Fresnel zone length at the reflection height for rays in the ionosphere.

49 SEL-70-037

■ ■■■i^;^;,,,.^. -,'; ' ...i.ia^J.^^l*. .tt^^^^^^^.^.,^^.^....*^,^ iBtmttiiBtirhiaa

C. THE EFFECTS OF MULTIPLE IRREGULARITIES IN THREE DIMENSIONS

The two-dimensional representation of propagation and as affected

by irregularities (as in Fig. 10) will now be applied to both the hori-

zontal and vortical axes of the irregularities, including the corrections

for focusing determined in the previous section. The effects of multiple

irregularities will also be included.

1. The Effect of the Presence of Multiple Irregularities on the Calculated Change in Electron Density

The raytracings shown in Fig. 11 are the results of raytracing

through a single irregularity. There may be more than a single irregu-

larity that influences wave field at the receiver. However, the number

of such irregularities is probably not large, as the region where the

ray path is most susceptible to irregularities of a given percentage de-

viation in electron density is limited to the region near the maximum

height of the ray. In the presence of an isolated two-dimensional gaus-

sian irregularity, the number of rays at the receiver will be one or

three, depending on the strength and size of the irregularity (see Fig.

11), In the presence of more than one irregularity, a larger number of

rays is expected to reach the receiver.

Chernov ('60) calculates the mean squared phase fluctuation 2

cp , due to propagation through an irregular medium described by a spa-

tially stationary gaussian correlation of refractive index with distance,

as

cp2 = -^ (Au)2 k2ALL , (11)

where

Afi = the change in refractive index,

k = 2 JT/A,

L = the length of the scattering region,

AT = the longitudinal scale size of the irregularity, Li

SEL-70-037 50

L ..^^..^^^,^,^^.^l.^^,^^ - -

2 From the measurements made in this work, cp may be calculated.

Using this estimate in (11), (A|i)2 can be estimated, assuming that the

longitudinal and transverse scale sizes of the irregularities are known.

For the single-irregularity model used previously, it was assumed that

TV = A, = L. While these assumptions cannot bo verified with the experi-

mental geometry used, they do however produce reasonable values for AM-

If more than one irregularity affects a single ray path (L >AT), or Li

if thö irregularities are elongated in the direction of propagation

(A- > .A-.), smaller values of A|i result. This would be acceptable in

terms of known ionospheric characteristics.

2. The Range of Phase Changes Produced by the Observed Irregularities

Ray bending effects caused by irregularities are determined

mainly by the phase change produced by the irregularities and the trans-

verse (to the ray path) scale size .A of the irregularities (horizontal

and vertical), A variety of data taken during the experiments of this

work, v/hich is representative of the range of phase-path variations ob-

served, is presented here. Figure 16 is an example of data representing

quiet conditions. Phase-path length changes are expressed in wavelengths.

Tue record shows a maximum change in phase-path length of about 20 wave-

lengths peak-to-peak. The trace is smooth, indicating that a single ray

was dominating the measurement throughout the period of the observation.

Figure 17 is a similar record, but with a greater observed deviation in

phase-path length. The record is still dominated by a single ray through-

out .

Some other effects occasionally appear in the records. Figure

18 shows the effect of alternate capture of the measurement by two rays

having different doppler shifts. The record which would be produced by

either of these rays separately is shown by the dotted lines. In this

record, the measurement is still yielding a useful description of the

changes in phase-path length for the rays. Finally, Fig. 19 is an exam-

ple of a record taken under conditions in which the usefulness of the

measuring technique has broken down because of the presence of a number

of rays of different doppler shifts, each of which dominates the measure-

ment for short periods of time.

51 SEL-70-037

!

ygjQI&tfgvgfg!*!^^ :......... ..^aüi

25

* Q. i

T (- 10 0 7 Irl _J \

\ ft N.

a w < T Ü.

-25 " _i6o

\

500 1000

TIME (sec)

1500 2000

Figure 16. Phase-path length measurement for very quiet ionospheric conditions.

1000 TIME (sec)

2000

Figure 17. Phase-path length measurement for fairly quiet ionospheric conditions.

SEL-70-037 52

'Aiitm&iiMUmbilu^

5000 TIME (sec)

5500

Figure 18. Phase-path length measurement alternately captured by two rays of comparable amplitude.

25r

g Q.

I

Z UJ

S3

-25

/

A

u H/II

100 500 TIME (sec)

1000

Figure 19. Phase-path length measurement for disturbed ionospheric conditions.

53 SEL-70-037

^■;...-;„,.....^;...„^,„.......,J..^, ^ü..,.,.^..,:^.,;^^,..../.-,^^^.'..^ ..;.....:-. : ..„,„:...f..;i>,„..,.. .,...: i..^,..^,...,-.,:. ..^...■.. -.. . ^..■.i,. 0.^ ,.jk^^kA^.^..C ^ - ..^-^ ' ^-^-^^i,. .

3. The Effects of the Observed Phase Changes

With the observed range of phase variations, cp2, in mind,

the theoretically predicted wave-front effects in the presence of multi-

ple irregularities can be determined. Chernov calculates the mean squared

angular ray deviations e2 as a function of cp2 and of A , the trans-

verse scale size of the Irregularities.

(12)

Rays emerging from the scattering region are unchanged in am-

plitude or position, but have a change in angle imposed upon them. As

the wave propagates through space to the receiving location, the rays

converge or diverge (Fig. 11), Also, as the wave propagates, the ampli-

tude at various positions across the wave will change due to the conver-

gence and divergence of the rays. Manning ('68) describes two classes

of wave fields which result from this process. The distinction is based

upon the number of rays which are expected to arrive at one point on the

ground. For weak, large or nearby irregularities, only a single ray will

be expected to arrive at any one point on the ground. For stronger, smal-

ler or more distant irregularities, rays will cross before reaching the

plane of the receiver, and multiple rays will arrive at least some points

on the ground. Manning calculates the expected number of rays at a given

point (for the two-dimen ional geometry) as

E[R] = 1 + -&f-Jcp2 , (13)

3/2 i— where £[•] denotes expectation. The factor (n /N2) »4. So, if ""5" 2 qr « 16(.A/F) , it is probable that only one ray will arrive at a given

point on the ground; whereas if cp2 » leC/Vp/F) , more than one ray can

arrive at the same point.

SEL-70-037 54

^•- ^aaaiaMi ^■- -^ ■..:^^-. -^^^y^,,..i,,,..,,.,,,,,.,,^,,t^^^.^^^

For the case where the scattering region contains irregulari-

ties which have variations in two dimensions transverse to the ray path,

Manning further shows that

E[R] = ECRy] • E[R ] , (14)

where E[Rl = the expected number of rays produced by vertical bending,

and E[R ] = the expected number of rays produced by horizontal bending.

As was previously pointed out, the effective value of F is

modified in the case of vertical ray deviations by the focusing effect

of the smooth variation in \i with height in the ionosphere. By using

the corrected value of F for vertical bending as plotted in Fig. 15,

and F = vrA/S for horizontal bending, the calculations of the expected

number of rays, as well as the signal strength calculations (Fig. 13),

can be corrected for the effect of vertical bending in the ionosphere.

For the observations made in this work, Cfr was found to vary

over the range of approximately 100 to 10,000 radians squared. For a

horizontal scale size of 45 km and a vertical scale size of 20 km, E[R],

E [R ] and E [R ] are plotted against vcp2 in Fig. 20. It can be seen V H

that the major contribution of the ionosphere to the multiple rays arriv-

ing at the receiver is refraction in the vertical plane, and that for all

but the quietest conditions seen during our observations, E[R] is

greater than 1, but usually less than 10. The value of E[r] from Fig.

20 can be regarded as an upper limit on the expected number of rays reach-

ing the receiver. Therefore it is expected that wave fields such as those

of Figs, lib and lie will be common, and in the presence of more than a

single irregularity, somewhat more complex.

The total amplitude and phase of the wave field at a point on

the ground can now be described in terms of the summation of R waves.

The relative amplitudes of the waves will be in the range shown in Fig.

13. The resulting total amplitude and phase fluctuations are described

in Chapter IV.

55 SEL-70-037

J^^^^aaL-^iM-itMii^ikt^^ - ■ ■■■ ■■• ■■ ■■J.^JVfi^^:.i^,i.^...:^<i»^^^'-'.^»-.^.'->^a^^>»..,.>...gJ.......^^^:.,.j,.^.^:^.

60 80 100 120 140 RMS PHASE FLUCTUATION, ^/^^(rodlans)

Figure 20. Expected number of rays for the given path and measured irregularity scale sizes.

SEL-70-037 56

^^■..ki...hic.-»^ >, ^...M.i .i^-^^ax:. ^„[..f. ii^TrMiWfaitiyim^iffii^^ .-•*-,■.. .^..■.■.

D. EFFECT OF THE EARTH'S MAGNETIC FIELD

Thus far the effect of the earth's magnetic field on oblique-inci-

dence HF ionospheric propagation has been ignored. This effect may be

described either in terms of the rotation oi the plane of polarization

of a linearly polarized wave (Faraday rotation) or in terms of splitting

of the wave incident on the ionosphere into two components, each of which

exhibits one of two possible characteristic polarizations for a wave of

that direction and frequency in the ionosphere, and propagates over a

slightly different path. The field produced by the combination of these

two component waves at any point on the path produces the linearly polar-

ized wave described by the first method.

The concept of Faraday rotation is frequently valid for oblique-

incidence ionospheric propagation. As a wave propagates through the

ionosphere its plane of polarization (assuming that the transmitted wave

is plane-polarized) rotates slowly with distance in the refracting region

of the ionosphere. This rotation causes the wave arriving at the receiver

to have a plane of polarization determined by the amount of Faraday rota-

tion which occurred in the ionosphere. If the receiving antenna is lin-

early polarized, the received signal strength will vary as the plane of

polarization of the received wave rotates. For the path used in our ex-

periments, the total number of rotations of the plane of polarization

along the path of the ray is calculated by raytracing (Croft '69) to be

about 20 turns under typical daytime conditions.

It is not possible to develop a simple relation between variations

in the total phase-path length and changes in the number of Faraday turns,

for a ray in the ionosphere. Therefore, various assumed ionospheric elec-

tron density profiles, representative of various times of day, were used

for tracing rays, while calculating both the total phase path and the total

number of Faraday turns. A variation of 50 to 100 wavelengths in P pro-

duced a change of one turn in Faraday rotation. This implies that for

smooth changes in the ionosphere, only one or two nulls in received signal

strength should occur for each 50 to 100 wavelengths of observed change in

P.

When considering the effects of irregularities, it is more revealing

to consider the model consisting of two component rays propagating over

57 SEL-70-037

^a—'"^"t——■ ^...^..-.;... '■ ammmm■ m M tjMMm m Mk mm lii i i ^:^.'H.^^^^^^^^i^^fr-..■ ,

slightly different paths, than it is to use the concept of Faraday

rotation. The two rays are customarily denoted as ordinary (0) and

extraordinary (X). If these rays have phase-path lengths P and P ,

a change in the difference between the two phase-path lengths (P - P )

of one wavelength will cause one Faraday-turn null at the receiver. By

tracing rays using the ESSA three-dimensional ray-tracing program (Jones

'68'», it was determined that for the conditions of our measurements, the

0 and X components will be separated vertically by a maximum of 0.5 km

to 1,0 km at their greatest height in the iorjosphere. Laterally, they

will be separated by no more than 200 m. These numbers represent the ray

spacings under undisturbed ionospheric conditions, i.e., with no irregu-

larities present. If an irregularity causes the phase-path length of one

of the rays to change with respect to that of the other ray by one wave-

length, one null will be observed at the receiver. Based on the measured

irregularity scale sizes, and assuming gaussian irregularities, the changes

in phase-path length for two rays spaced by about 1 km vertically are

highly correlated—of the order of 0.98, Therefore, for irregularities

such as those studied and modeled in this work, about one Faraday null is

expected for each 50 wavelengths change in P due to irregularities.

Based on the above calculations, then, both irregularities and smooth

variations in the ionosphere are expected to produce variations in the

received polarization which will cause one receiver null for each 50 to

100 wavelengths change i?i P. This sets an upper limit to the number of

such nulls which can be explained on the basis of the measured irregular-

ity sizes.

SEL-70-037 58

)^^ait^Wa^.A.^i^i^^'^^i:i^^.>=.V^^t^-i! :.^Vj-^l»£^^iA^ h^>a,.ifa,^'.itM i ^r.>v:«^^-„J..A>Wt.l.ai.».rf^^;^

IV. SIGNAL-STRENGTH FLUCTUATIONS

In Chapter II a series of measurements of the phase characteristics

of HF obliquely propagated ionospheric waves was described. These mea-

surements allowed a determination of the size and strength range of ir-

regularities which are present in the ionosphere under quiet conditions.

In Chapter III the effects which would be anticipated for waves propagat-

ing through such irregularities were examined. The expected number of

rays which would be produced by these irregularities was determined and

the expected relative magnitudes were found. In the present chapter,

the amplitude variations which are observed under quiet ionospheric con-

ditions are examined to verify that observed amplitude fluctuations are

explained in terms of interference of rays. In addition, other possible

causes of the observed amplitude fluctuations are discussed.

The envelope-amplitude fluctuations of a received signal can be de-

scribed by their statistical distribution. The probability density func-

tion for the envelope-amplitude, <I>(E), will be calculated for various

assvunptions about the received waves. These calculated distributions

will be compared with histograms of observed envelope-amplitude fluctua-

tions. The histograms are plotted so that the densities of the measured

values of envelope-amplitude, W(E), are directly comparable with the

computed probability-density functions. The mean envelope amplitude E

is used as a scale factor in plotting both the computed and observed en-

velope-amplitude distributions.

In addition to the density functions themselves, the normalized 2

variance of the envelope amplitude, a , will be calculated for both 2

predicted and observed amplitude fluctuations. The value of a is

given by

2 E2 1

(E)

A second statistic, qr, is also calculated for each of the assumed

forms of the received wave field. Here cp is the difference between

the phase of the received signal at any instant of time and the phase

59 SEL-70-037

üari^aMaiai^^

MimiMiW}iiip.wiH^^

2 of the strongest of the signal's component waves. The values of 0 and

-p2 nuiy be used to dotermine the efficiency of receiving antennas under

certain conditions. This subject will be discussed briefly in the next

chapter.

A. MULTIPLE WEAK-SCATTERING INTERPRETATION OF AMPLITUDE FLUCTUATIONS

Booker, Ratcliffe and Shinn ('50) applied diffraction theory to the

ionospheric propagation problem by describing scattering in the ionosphere

in terms of a scattering region composed of a thin screen of small, weak

phase-changing irregularities. The signal which emerges from such a scat-

tering region can be characterized in terms of a specular component and

a cone of scattered rays. The "coherence ratio", ß, is used to describe

the ratio of the energy of the specular component to the energy of the

scattered rays. The width of the cone of scattered rays is determined

by the size of the irregularities in relation to the wavelength employed.

The cone of rays is made up of a large number of rays having random am-

plitudes and phases. If the number of scattered rays reaching the re-

ceiver is statistically large, the expected envelope-amplitude distribu-

tions for the sum of a sine wave and narrow-band random noise, as derived

by Rice ('45), may be used to predict analytically the amplitude fluctua-

tions produced by the specular and scattered components of ionospherically

propagated waves. Rice derives the probability density for the envelope-

amplitude of such a signal as

/ E2 + E2\ /2E E

n \ n / \ n

where (in the notation used in the present report):

E = the envelope amplitude of the received signal,

E = the amplitude of the specular component, o

E = the amplitude of the scattered component, n

SEL-70-037 60

buHjfr^i^^^-i^L^^ifr^J^jtifr^^ i- O ..v^ v»'VU-, ... vV. ■ Y.L JliliH^V*'rv--^t;■-'"-VT}tifc-^**&''-'"'■--^^/^l'*l^Vi;t^t*.fa^Ji^ia^lfa.lWaiM&>a*>tli.iiiili*.**,Lii&^&BiutiiJi.iii*ii*i*iii*tnhJAwltki^Mmii 11'■ WtMiri't)m*u*k&Üä&iil

* nmm^mammmimmmimmmiGi** JUill^llJUII.. ^.''."».J^^.M'MWWlIW^JHWW^MJIIfM^ffW^M^^^^^^

and

I is the zero-order Bessel function of imaginary argument,

Curves of 0(E), using the normalizations employed by Rice, are shown

for different values of the parameter s = N/2(3 in Fig. 21. Before an

experimental amplitude density distribution may be compared with these

curves, the parameter (3 must be determined, ß is related to the mea-

sureable quantity E2/(E) , the ratio of the mean squared amplitude to

the squared mean of the amplitude, by the relation

E

(i)2 4(1 + g2) exp(ß2)

(1 + ß )I

(16)

where I and I are Bessel functions of imaginary argument. This

function is plotted in Fig. 22. E2/(E) must lie in the range

1 < E2/(E)2 < 4/n.

Experimentally determined amplitude distributions may be compared

with the Rice distributions in order to determine the applicability of

the multiple weak-scattering theory proposed by Booker, Ratcliffe and

Shinn. Because of the necessity for calculating ß before plotting the

experimental distributions, Rice's method of displaying amplitude dis-

tributions (Fig. 21) is not suitable for conditions where Eq. (15) may

not apply. Therefore, the Rice distributions are replotted in Fig. 23

for various values of ß, using the mean amplitude E as a scale fac-

tor. These graphs were computed using a random-number generator and the

Monte Carlo method. This computation method will be used later in con-

nection with other models of amplitude fading. Note that for ß equal

to 0 (a random component only), the distribution is the Rayleigh distri-

bution.

The results of applying the multiple weak-scattering theory to ob-

lique F-layer ionospheric propagation have not provided a consistent

picture of the ionospheric mechanism responsible for the observed signal

fluctuations. Al'pert ('63) discusses some of the results of such mea-

surements and some of the problems encountered in their interpretation.

61 SEL-70-037

^■r.-^.J^^te.^.^.-.^I^..-.^^^.-.....^^ l-t-. -l,.^,. -1 ....Wl-lij^:..j,...^^„lL.<.„.:k..,l,«.',|HB||ft^1f|,|.|' i|,ilfltlM■r':^tga'^>rifti'ilflW|:|i^^^'--~^'^,♦^'^ "• -"l«if 11 il ff I I I If' < ■ ■' -■i^n-.-^M^ ^..-^l^ÜU

ym«iiny^r»»r'^?y<.«'vvvv-'v.-v?'-T<;w^^^^^

n 1-1 <u o u <4-( n 0) #* M OKN

■g^ T* <u > ™ •» 3 g*.

4-1 .n< .-1 • o

CO t1

c 3 O CM o ■w B

CN ^. »■■ *, •r4 o W ltd •u 3 00

CO r-l Ö l-i U-l -^ 0) M

II M (U (U

OJ 3 -U IN Icsl x: 4J to

Kil \Di H

rapl

i 1

sc

a • t0 t-i o N to

•r^ N o ß w 4J CO u 0) (U M « (1)

> 3 J2 d M ax -u o ■rJ o fe

c

tn w 3

e o u

M-l

c o

•l-i ■u

CO c to 1-1

4-1

4J M HI

CO 5«

:

jH»^

/

/ /

- II /I -X*

/

v^ M en /^ im l?5><^\

•<

II n^\ ^ \

^ ^^^

\ Ü

. ^

w Cd --^ td

[ft levj

•o C3- a"

w X

-a

> •i-i n ai iw

•o o CO OJ CO C

o

tn •r4 TD

CU •a 3 4J •r4 I-I a

I

<U u 3 00

•r4

CO l-l

1-1 to

3 Ü 0) Du* to

Pi 4J tti

J3 U)

OJ x: o to o a o H

to Ü OJ • C .c CO O CO 4J VO

•M cr> u •a -a 1—1

3 c a XI to to *

o •r4 ■U

™. M to

o u

to <u to >^ >

to tfl 1-1 u S Ü m •a 0

0) •H OJ u TJ 0 0) CO

•r4 4J OJ

o 1-1 fa o *

3 to 01 1-1 3

PQ

w J-l C to 4J l-l 3 to C O

SBL-70-037 62

,■■,.! ^.^.. „■.^^^ ■■ , ■ .V.. , 1;-- ■■■ ., -^^ä,.^^ ...■„^^^ ,■,..■■■■■...>.■> ^.....r,.,-^..^..^-:.. ■.--v.:..^^tl.^/-^I.^^A^^^W^^H.,^.A^^A^^^

JW>^?*!*#<WI<«m

ENVELOPE AMPLITUDE (4) ENVELOPE AMPLITUDE (4)

I 2 ENVELOPE AMPLITUDE (|-)

2.0

- 1.5 UljlUJ

UJ Q

Q LU h-

Q.

o o

1.0

0.5-

(d)

ENVELOPE AMPLITUDE {^)

Figure 23. The Rice amplitude distribution computed using the Monte Carlo method and plotted with the mean envelope amplitude E as a scale factor.

(a) 0 = o, 0 = 0.272

(b) 0 = 2, a2 = 0.101

(c) P = 3, a2 = 0.054

(d) e = 5, a2 = 0.024

63 SEL-70-037

AB^ya^ta^^Au^^^^a!^^ .„n, »,r ■ ,LL

WWJ^^fWlMawWPWJ.'W'-'.111 ■-'M'wiiw^'M^www^witfH^^^^

Measurements of ß are reported in the range from 0 to 10, with usual

values in the range of 2 to 4. No numerical evaluation of how well the

observed data fit the predicted results of the multiple weak-scattering

theory is presented. However, Al'pert notes that in about 30 per cent

of the observations, the value of E2/(E) exceeds 4/it, the maximum

value permitted by the theory. Also, in about 20 per cent of the obser-

vations, distributions with more than one maximum are observed. These

discrepancies lead Al'pert to conclude that some other mechanism must be

contributing to the observed signal-strength fluctuations.

The same ionospheric scattering model used in the amplitude fluctua-

tion studies discussed above has been applied by others in analyzing the

phase fluctuations observed on pairs of spaced antennas. Whale and Gar-

diner ('66) derive unique probability distributions for the difference

in phase measured at two spaced antennas as a function of ß and the

spatial autocorrelation function of the scattered component alone. Whale

and Boys ('68) and Boys ('68) use this method and find for one-hop propa-

gation, that ß is usually quite high with measured values of 10 or more,

indicating that the received wave is highly specular. The results of

these phase measurements are not compatible with those commonly obtained

from amplitude measurements using the Rice theory.

B. INTERPRETATION ON THE BASIS OF LARGE IRREGULARITIES

The signal-strength fluctuations which are expected in the presence

of large irregularities will now be examined in terms of the amplitude

distributions which could be produced by such irregularities. Computed

envelope-amplitude probability-density distributions <I>(E/E) will be

used to gain some insights into the effect of varying parameters on the

shapes of these distributions. Also, the normalized variance of the am-

plitude fluctuations will be computed for comparison with the known lim-

its for this statistic under the random-noise (multiple weak-scattering)

representation. Measurements of the density distribution of observed

amplitude fluctuations, W(E/E), will be compared with the computed pro-

bability-density distributions. Four different possible sources of sig-

nal amplitude variation will be discussed. These are focusing, multipath

interference, polarization mismatch, and absorption.

SEL-70-037 64

>wjfc^j,i.^.-.u^a^^Ai>J.»w:,.^.~A.^,i.^^^

WWiW^i^lWIWWWilPI^ ■ -^V -' ..--.WJ^wK^^^fF^rM^^^rnKmav^'f^'^mv'-myvwr'

1. Focusing

The spatial variations in refractive index produced by iono-

spheric irregularities cause changes in the convergence or divergence of

rays. This in turn causes variations in the energy density between adja-

cent rays. This change in energy density will produce variations in the

observed strength of a given wave at a distance from the refracting region.

As can be seen from the raytracings in Fig. 11, the variations in amplitude

increase with distance from the scattering region. These variations are

in the range of a few decibels for the irregularities which we have pro-

posed. (See Fig. 13.) In cases where only 3 single ray is present at

any point in the receiver plane, we would therefore expect to see signal-

strength variations of this order of magnitude. In the case of multiple

rays, it is noteworthy that the difference in amplitudes for the various

components is again only a few dB. This fact will be of considerable im-

portance in considering multipath interference.

If changes in received amplitude are attributable only to varia-

tions in the strength of a single component due to focusing, the expected

fluctuations in signal strength would be a few dB. This is observed at

times on HF paths. It has also been noted in ground backscatter radar

observations. Figure 24a is a record of signal-strength variations of

the type observed over the path used for the phase measurements of this

report. However, signal-strength fluctuations as small as these are much

more the exception than the rule. Figures 24b and 24c show examples of

more typical signal-strength records over this path. Variations such as

these cannot be explained on the basis of focusing due to irregularities.

2. Multipath Interference

Inasmuch as the irregularity model developed in Chapter III

predicts that because of the effect of even a single irregularity, the

expected number of rays at the receiver location will frequently be

greater than one, the effects on total signal strength which will be

produced by the summation of several rays must be considered. As can

be seen from the amplitude plots in Fig. 13, the amplitudes of multiple

rays are not very different from one another. Considering the vector

addition of rays, as was done in Chapter II, it can be seen that the

65 SEL-70-037

- — — •■■ "•■■■■'-•■ ■■'-■- - .■■■^■,.. r..;,;,- - .- ■■ ■■..-■..,i:^,-.,-;.—>. ..^ _......^,., v.t.^^.^ali^itaAdkiaaa&l^^ -- ■

---.---^j.WMWWWj'^^

0

-10-

-20

-30

(a) 100 200 300 400 500 600 700 800 900 1000

100 200 300 400 500 600 700 800 900 1000 TIME (sec)

Figure 24, Observed signal-strength fluctuations for the Arkansas- Los Banos path.

(a) Little fading, (b) Moderate fading. (c) Severe fading.

SEL-70-037 66

ateii ^■-^^^.^,-v,.-.^-.. ^...-^w^^ MUiäiittMaÜi WHttafl

I^-^M^^^^

1 -

possible range of amplitudes for the sum will be bounded by the summation

of the ray amplitudes as an upper limit, and by the difference between

the largest ray and the summation of the remaining rays as a lower limit.

If the lower limit is negative, then all values from zero to the upper

limit are possible (as we are interested in the envelope amplitude). The

phases of the multiple rays vary sufficiently that in performing the vec-

tor summations, it will be assumed that the phase of each ray is uniformly

distributed in the range of zero to 2Tt, This assumption is usually valid

for the measurement periods used in this work, which span a number of sig-

nal minima. Computed amplitude probability-density distributions calcula-

ted for two rays and three rays having amplitude differences of a few dB

(such as we expect to encounter based on the work of the previous chapter)

are shown in Figs. 25a and b. Note that these amplitude distributions are

quite different in appearance from those calculated using the random-noise

representation for a large number of small scatterers and a strong specu-

lar component (see Fig. 23).

3. Polarization Mismatch

As was pointed out in Chapter III, the ionosphere is birefrin-

gent because of the presence of the earth's magnetic field. Therefore,

if a linearly polarized wave is incident on the ionosphere, it will be

split into two components of differing elliptical polarization, and each

component will travel a slightly different path through the ionosphere.

Upon emerging from the ionosphere, these two components (the ordinary

and extraordinary rays) will add to produce some resultant polarization

which is a function of the difference in path lengths for the components,

and of the difference in strength of the components. At the end of Chap-

ter III, it was shown that very little differential in path length or

signal strength between the ordinary and extraordinary rays was expected

to be introduced by ionospheric irregularities. If this is the case,

the emerging waves will sum to form a linearly polarized wave (still

assvuning that the incident wave was linearly polarized). However, the

plane of polarization will no longer be the same as that of the incident

wave; and furthermore, it will be time-varying. If a circularly polar-

ized antenna is used to receive such a wave, its response will be constant,

67 SEL-70-037

- .;-■,. i I.,J i ■- -.-. — ^^..^■■■.l^^friv.ifr,..^^^^ ^^^^.^ || . J

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T 1.51 UJ|IUJ

8 Q

Ö 05

(a)

M1

ENVELOPE AMPLITUDE (|r) I 2

ENVELOPE AMPLITUDE (|r)

Figure 25. Computed amplitude distribution for the random vector sum of rays.

(a) Two rays, amplitudes = 1.0, 0.7.

a2 = 0.175, cp7 = 0.53.

(b) Three rays, amplitudes = 1.0, 0.7, 0.5. -

a2 = 0.200, cp7 = 0.80.

SEL-70-O37 68

. ■ ■ - ' ■ --■■^ ■ - --t'- ---■■- -^..^ -■■ ■^■'■•^'■||t■'||||»rn[tTli^--•^-"-^■'^■, -:■■—'^*^.J-.L^.. . ■.■^.—^j- iii

p^^^(ij.tijm,u^|^^

regardless of the plane of polarization of the wave. In practice, it is

difficult to construct and test an antenna designed to be sensitive to

circular polarization for the frequencies and low radiation angles used

for long-range HF conununication. If a linearly polarized receiving an-

tenna is used, a polarization mismatch will result, producing variations

in response depending upon the instantaneous plane of polarization of the

received wave. The signal amplitude from such an antenna will be propor-

tional to cos cc, where a is the angle between the planes of polariza-

tion of the incident wave and the antenna. The two components (0 and

X) arriving at a linearly polarized receiving antenna may be represented

by two linearly polarized waves having amplitudes equal to the fraction

of each wave's energy which lies in the plane of polarization of the re-

ceiving antenna. The amplitudes will remain fixed over long periods of

time, since the polarization of the received components is determined

primarily by the ray direction and the earth's magnetic field. Figure 26

shows the calculated amplitude distributions which would be expected for

two waves of differing relative amplitudes. The distributions show sharp

upper and lower limits in amplitude, corresponding to the sum and differ-

ence of the two rays.

4. Absorption

Waves propagating in the ionosphere also suffer losses due to

absorption of energy associated with particle collisions. With the excep-

tion of periods of severe solar storm activity, the loss due to absorption

is very small for frequencies above a few megacycles. Variations in loss

from this mechanism are neglected in this work.

C. SURVEY OF AMPLITUDE DISTRIBUTIONS

We shall now examine a number of computed amplitude probability-

density distributions in order tc understand the characteristics impar-

ted to such distributions by various signal combinations. We have already

seen some distributions in the discussion of fading mechanisms.

A single ray of constant amplitude will naturally produce an impulse

in amplitude probability density at the mean value (Fig. 27a). Combinations

69 SEL-70-037

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1^

I 2

ENVELOPE AMPLITUDE (-|-)

8 0.5

(d)

ENVELOPE AMPLITUDE (4)

ENVELOPE AMPLITUDE (-I")

Figure 26. Computed amplitude distribution for the random vector sum of two rays.

2 ""7 (a) Amplitudes = 1.0, 1.0. - a = 0.233, cp = 0.90.

(b) Amplitudes = 1.0, 0.9. a2 = 0.231, cp = 0.74. 2 "7

(c) Amplitudes = 1.0, 0.8. - a = 0.205, cp = 0.63.

2 ~T (d) Amplitudes = 1.0, 0.4. - a = 0.073, cp = 0.29,

SEL-70-037 70

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71 SEL-70-037

^.0,-„l.^^,wJ^^.,i, A ■ It ^-"iMiirimiimiiiiiiiiiriiiifiiiitiiriiiiwiifii'rl ..^^.^^^^.,.^^.^.^ ü teMÜÜÜii

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of two or three rays of equal amplitude produce the distributions shown

in Figs. 27b and 27c. The case of two unequal rays has already been seen

in connection with the discussion of polarization effects (Fig. 26), The

two-ray distributions exhibit a double peak, with tht; spacing between the

peaks inversely related to the difference in the strengths of the two

rays.

In Fig. 28, the amplitude distributions produced by three rays of

various relative magnitudes are plotted. They tend to exhibit the double

peaked nature of the two-ray distributions, but are considerably smoother,

and do not have the sharp upper and lower amplitude limits of the two ray

distributions. The spacing of the two peaks is seen to increase as the

relative strength of the middle amplitude component increases, or as the

weakest component decreases. The clarity of the peaks is affected by the

strength of the weakest component and by the separation of the peaks.

As more components of comparable magnitude are added, the character-

istic features of the distributions decrease, approaching the Rayleigh

distribution. Figure 29a shows a distribution produced by six rays. When

the number of rays becomes large, it is not possible to interpret a mea-

sured amplitude distribution in terms of known distributions, other than

to say that a large number of rays appears to be present. An exception

occurs if the distribution is dominated by a few strong rays, but other

rays of considerably lower amplitude are present. The weaker components

then may not mask the features of the distribution, but only smooth out

the features. Several distributions of this type are shown in Fig. 29.

In the discussion of polarization mismatch, amplitude distributions

which would be expected if only one ordinary and one extraordinary ray

should arrive at the receiver were discussed. If multiple ray paths ex-

ist, each composed of an ordinary and an extraordinary component, then

at least four rays will arrive at the receiver. This circumstance will

increase the likelihood of having distributions which resemble the Ray-

leigh distribution. Figures 30a and 30b show examples of this type of

distribution for equal ordinary and extraordinary component strengths.

The representation used in calculating these distributions for multi-ray

propagation with both ordinary and extraordinary components assumes that

the polarization of each of the paths is independent. Because of the

73 SEL-70-037

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SEL-70-037 74

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75 SEL-70-037

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SEL-70-037 76

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77 SEL-70-037

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Figure 30. Computed amplitude distributions for the random vector sum of rays, including the effect of polarization mismatch.

(a)

(b)

(c)

(d)

Ray polarization-independent, two rays, amplitude = 1.0, 0.7, a2 = 0.232, cp? = 0.89. Ray polarization-independent, three rays, amplitude = 1.0, 0.7, 0.4, a2 = 0.239, cp^ = 0.97. Ray polarization-equal, two rays, amplitude = 1.0, 0.7, a2 = 0.453, cp2 = 0.53. Ray polarization-equal, three rays, amplitude = 1.0, 0.7, 0.4, a2 = 0.470, 5p2 = 0.71

79 SEL-70-037

,;■.»,■.-■...i.iv., wJiVM.rim^i^rimrtili^mWftlfhrt«»^^ -'■■''■"''■'■■'^^''■■^■■""^-'^-■Ml^ - i ■*-■'«

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I

differences in path lengths suggested by our model for the rays, it is

anticipated that the resulting polarizations would be independent. If

this is not the case, the polarization mismatch for the various paths

will be related. If this assumption is used in computing the expected

amplitude distribution, the curves of Fig. 30c and 30d result. These

distributions have a very distinctive appearance when compared with the

other distributions we have examined, in that they are almost always

monotonically decreasing. Another characteristic of these distributions

is that the normalized variance usually exceeds (4/3T) -1.

The amplitude probability-density distributions computed above give

an idea of what can be expected of measured amplitude distributions under

various conditions. These computed distributions will be compared with

experimentally observed amplitude variations in the following sections.

D. RELATION OF SIGNAL-STRENGTH FLUCTUATIONS TO PHASE-PATH FLUCTUATIONS

In this section a relation between the occurrence of phase-path

variations and fluctuations in the strength of the received signal is

established. This relation is to be expected on the basis of the irreg-

ularity model and its prediction of raultipath interference during periods

of high irregularity activity. Using measured signal-strength and phase-

path data acquired during the winter and spring of 1969-1970, about ninety

hours of data were examined for this purpose. For each 1.2 hr segment of

data, the rms phase fluctuation sjcfr (with mean and linear trend removed)

was computed. These segments were grouped into ten intervals according

to the computed value of N/Cfr1. For all of the data segments in each in-

terval, the measured normalized variance a = [E2/(E)2J -1 of the

observed signal-strength fluctuation was calculated for 200 sec periods

(this period includes a number of signal-strength minima under most con-

ditions). The mean and the standard deviation of the amplitude variance

were computed for each interval of Vcp2. These values, and the number of

data segments in each interval, are shown in Fig. 31. Although a wide

range of signal-strength fluctuation is observed at any measured value

of phase fluctuation, a strong dependence between phase fluctuations and

amplitude fluctuations is seen. This indicates that the presence of the

SEL-70-037 80

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IUJ IUJ 0.3-

to z o < 3 I- O 3 _i

ID Z UJ tr i-

_j < z o V)

0.2

0.0

MEAN OF NUMBER OF SEGMENTS INDICATED-

17

14

T STANDARD DEVIATION

1

<20 20-30 30-40 40-50 50-60 60-80 80-100 100-150 RMS PHASE FLUCTUATION, /^ (radians)

>I50

Figure 31. Observed signal-strength fluctuations vs. observed phase fluctuations.

81 SEL-70-037

^. .--..-■....■^.■■■-. ..^■.^..■^.. -..^^wi^w^^....^-^^.^o^^,in^ fiMMlllii '■^—-"lt-"--;-----

,II,UI . ., .|IIJ.I..;IILI.IUI.II.I,...J .1 | ||..U-.-.U...-.,-IMIHPII,,, .Uli , ii.ii,iiiuipi||iiu,|i. ill). ,111,11 III.W|||||WM,II||,. i,^.pmwy^i^^M-1|P,-ui»iMPM,i.^^^..,^

irregularities which produce the observed phase fluctuations strongly

influences the fading observed.

In order further to verify the predicted effect of phase fluctua-

tions on observed signal strengths, a few measurements were made over a

shorter path. It is expected that for shorter paths, the effect of ir-

regularities of a given size and strength on signal-strength fluctura-

tions should not be as great. This can be seen from Eq. (13), which

shows that the expected number of rays reaching a point on the ground

is a function of F/A-. By decreasing the range, we reduce F. In ad-

dition, the focusing arising from smooth ionospheric variations (Fig. 15)

will be less, further reducing the effective value of F.

Simultaneous observations were made over the path used for the other

measurements of this work, and over the path from National Bureau of Stan-

dards Station WWV at Fort Collins, Colorado to Los Banos, California, in

order to compare the influence of path length on signal-strength fluctua-

tions. Changes in phase-path length were also recorded simultaneously.

The distance from Fort Collins to Los Banos is about 1430 km. The differ-

ence in distance, plus ionospheric focusing, should produce an effective

Fresnel-zone size for the WWV path about half that for the Arkansas path.

This would be expected to produce a significant decrease in amplitude

fluctuation effects.

Because no sounder was available over the WWV-Los Banos path, it was

not possible to determine positively that only one mode was propagating

over this path. However, ionograms over the Arkansas path were examined

to determine the most likely times and frequencies for single-mode propa-

gation from Fort Collins. This type of propagation occurred most fre-

quently for WWV at 15 MHz. A single-mode frequency for the Arkansas path

was chosen to provide a reflection height which was comparable to that on

the WWV path based on nominal ionospheric conditions. This was usually

about 24 MHz. (The difference in frequencies will cause the Fresnel-zone

length for WWV to be slightly larger than halo, the Fresnel-zone length

for Bearden.)

In all observations, fading on the WWV path was significantly less

than on the Arkansas path. At times the WWV path exhibited almost no

SEL-70-037 82

HfttWilHffitflitVfl^ ItltttVi»WffitltMBilflWttlWiltWfrliWftilfcifcTirii'iiii' 1 rr'""'i '""-iiiii1- ni'iii i iii'i"^" l;,l'--'"-ffiiirir,-'infrhhiltlilf^'''-;'''"iAta*'J^'m'm"ax'>"

^flNWUflllJ!!. Jl-W l*(JU)l(i!l4JIM| ?!lgWr^»l«l'lftl'JHt^!^^'."''""-'CT"^vi-ctlJJMli;u.«W.lWCT»;^T!r^^

noticeable fading. Figure 32 is typical of the data obtained under such

conditions. The phase-path variations are similar in magnitude, although

uncorrelated. The signal fluctuations on the W\VV path are considerably

weaker. In addition, the measured amplitude density distributions for

the period of the records (Fig. 33) shows that the WWV signal is much

more constant in amplitude. Again, this verifies our interpretation of

the phase fluctuations observed.

E. MEASURED AMPLITUDE HISTOGRAMS

We shall now examine a number of amplitude histograms calculated

from the measured signal-strength records, and attempt to infer some

characteristics of the rays producing the observed distributions. A

major difficulty in this task is presented by the discreteness of the

irregularities and the small number of rays. Under these conditions,

the number and amplitudes of the rays are expected to vary significantly

with time. For irregularities having a 20 min period, it is net likely

that the situation will remain stationary for more than a few minutes.

For observations to represent conditions at any one particular time, the

conditions should remain relatively constant for the period of the mea-

surement . The measuring period will therefore be a compromise between a

period short enough to provide stationarity and a period long enough to

permit obtaining the reasonably large number of samples required to pro-

duce valid distributions.

Measurements of amplitude were made at intervals of 0.1 to 1.0 sec.

There is a limit to the amount of information to be gained by sampling

more rapidly. If the observed distribution is to be valid, the rays must

have doppler shifts sufficiently large and sufficiently different from

each other that a random phasor sum of the rays will be observed. The

effects of different sampling intervals will be discussed together with 2

the observed amplitude distributions. Also, the variance o of the

observed amplitude fluctuations will be noted for comparison with those 2

predicted in the computed distributions. The values of a are indica-

ted in the captions for each of the computed and measured distributions.

If the distributions result from a random phasor sum of sine waves whose

83 3EL-70-037

——: -^«^Irt^awäM^^ ,.t^^

^»'«W^^g^.'M'^yi^ii^iw^pi«!»^^^ agapB^ffl^iapipiBWIpii^ipipp^^^

5 -IOI , 20'

|-JOt

lu) IOC 200 300 400 500 600 700 800 900 1000

25

<

-25'

(c)

100 500

TIME (sec) 1000

Figure 32. Observed signal-strength and phase-path-length fluctuations over two paths at the same time.

(a) Signal strength, WWV-15, Fort Collins, Colorado to Los Bancs, Calif. (1430 km),

(c) Phase-path-length fluctuations--Fort Collins,

Continued on next page.

SEL-70-037 84

ri^^^WtiitiW^mliiiViifi-im«^

~^r7™^V,:™..,~,r^^W..t.,VWJ.^W

1-30 fY U /:■ r '■ ,"'' h i 'i f

(b) 100 200 300 400 500 600 700 800 .900 1000 TIME (sec)

25

Q. [

LEN

GT

H,

o

PA

TH

PH

AS

E

-?fi' 100

(d)

500 TIME (sec)

1000

Figure 32. Continued,

(b) Signal strength--22.81 MHz, Bearden, Arkansas to Los Banos, Calif. (2600 km),

(d) Phase-path-length fluctuations--Bearden,

85 SEL-70-037

toi^mii^'i.-'-ijij-"'». - >»-^'--~— ■■- - ' -" - -■ II '- •-■■■■ ■- ■ ------ ■-■^^^-'ü*^:-aUhJaari^Jfl^^,WM^h^^^^

il.lpi^i.]iUipi»»a^iWW.>aii>|.wiifliLL. »■■■'■»■HI ""■"■ , ■ "'"■ • " ■ w^iaWffip»W^^lWWWPWII!^,llllii.ill|i!lW.II (ilW^.wiJ-i'V V''»'-''^^»'"'"^-'"»«»;»^™««^»^''-.^!^^,.^^!'.^*^;

1 5 1 '

UJ|IIJJ 1

—, i

s jL

> (- tn ] z Ixl 10 1

Q t

Q n! Hi i u

CE 3 cn < ^ 05

;' - _ J

■

1

2.0.

ENVELOPE AMPLITUDE (-t)

T L5 ÜJIIU

V

in 5 i.o Q

Q UJ tr

< ^ 0.5

(b)

[L OJ

"H "L

I 2 3 ENVELOPE AMPLITUDE (4)

Figure 33. Observed amplitude density distributions W(E/E) for the period shown in the records of Fig. 33.

2 (a) Fort Collins path. - a = 0.081 .

(b) Bearden, Arkansas path, = 0.204

SEL-70-037 86

il:-."^""'"'- ■'■■■ w»-...:...u^;^.<.v^....^-^.rijiu^...:^;1L..:/.:^.,,lj.J.!;^

^«^■y-w ..ijuiwim^ji^

2 amplitudes do not vary, the variance a is restricted to lie in the

range from 0 to 0.273 [(4/«)-!]. Greater values may occur if the sig-

nal energy changes during the analysis interval. Such variations in en-

ergy would be expected, based on our irregularity model.

The examination of a large number of measured amplitude distributions

reveals some general characteristics. First, no distribution curve shape

may be said to be typical. The shape of the distributions is a strong

function of the analysis interval and the nature of the signal fluctua-

tions during the analysis interval. The second general characteristic 2

of the data is that a frequently exceeds 0.273, Indicating that for

analysis times long enough to produce valid random phasor sums, signifi-

cant energy changes occur. Finally, only when fading is quite rapid and

severe do the measured distributions resemble any of the Rice distribu-

tions shown in Figs. 21 and 23, and then only the ß = 0 distribution,

which is equivalent to the computed distributions for more than a few

rays of comparable magnitude.

A frequently noted characteristic of the observed amplitude distri-

butions is a double-peaked form. Three such distributions are shown in

Fig. 34, which displays the observed amplitude density, W(E/E), versus

E/E. These distributions are measured from data taken during 10 to 15

min intervals. These double-peaked curves resemble the 2-ray and 3-ray

distributions of Figs. 26 and 28. They differ from the latter distribu-

tions in having more elongated high-amplitude "tails". Such long tails

are frequently observed, and are assumed to be caused by changes in the

amplitudes of the rays being received.

In an effort to verify this assumption, some data were analyzed for

a 2.5 min period. These data were sampled at 10 samples per sec, so that

enough points to produce a smooth distribution could be obtained. Records

such as shown in Fig. 35a were produced under these conditions. This

distribution has a sharp upper limit. It does not, however, appear to

be a satisfactory random vector sum, and while ray amplitudes are prob-

ably relatively constant for this interval of 2.5 min, the frequency

shifts of the various rays are apparently not sufficient to produce the

desired random vector sum. Figure 35b shows the distribution produced

by analyzing a 5 min period which included the period used for Fig. 35a.

87 SEL-70-037

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(U CIJ OJ tu TJ B 6 B 3 •r-l •i-i •rJ 4J ■U 4J 4J •i-l

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OJ !-i 3 60

•P-I

PM

(-=-)M AiiSN3a aaynsvsw

SEL-70-037 88

:-.:.J..,-.^,.;-^.^.-^^^^- ^attwifeaM ■"--■■- e^mmaäiaäiäi^UM M ~..^-±>^...^^-*^^<^.-.^~^.-M*^^<^^ J

■.IH;.^gy.n^rT^««>l!lni,,^w»lJl..pj|.ilwlJ1-iiu»..i. m.»..!.!,..;.!!!—n^yi.i^njjjujiiiiji. I ,LI .yiu^u^i,^^^.^g^iy^^g^^^i^

2,0

T L5 Uj|lLÜ

UJ Q

Q

cc

< 5 0.5

(a)

20

T 1.5 llj|lUJ

i >-

to L'J Q

Q LU 01

m <

1.0

ENVELOPE AMPLITUDE (-t)

2 0.5

(b) ENVELOPE AMPLITUDE (|r)

Figure 35. Observed amplitude density distributions for short analysis times.

2 (a) Analysis time = 2.5 min. - a = 0.194

2 (b) Analysis time = 5-.0 min. - a = 0.238

89 SEL-70-037

-. ■ -■- ..-■....,.■■^^..^■... :ik^:»^w.^^...^^^wi-^^^ ,:j.v....-:^,_.v.^ ..,- ... ...■.■. -•..■-.. ^■^■■.:ür.^tJ..jy;^^^i^^^-.^-^V:<i,i|iiiSBiriiiri-ii»lhlili -•^-■:-^i.>.^-^.^.'..... .

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Note that tlio tall of the distribution is growing, indicating a change

in the amplitudes of some of the component rays.

To further investigate the effect of changing ray amplitudes, a

distribution was computed for which one ray was present for half of the

samples and three rays wore present for the other half. Such a stepwise

change Is not realistic, but the resulting computed distribution, shown

in Fig. 36a, gives an insight into the effect of changing energy. A

measured distribution exhibiting a similar effect is shown in Fig. 36b.

All of the above measured distributions were taken during periods

of relatively rapid fading, as observed on the signal-strength records.

If the observed fading were the result of interference between two rays

of about equal amplitude, such as would be the expected result of magne-

toionic splitting, distributions similar to those of Figs. 26, 30a and

30b should be observed. Records such as these, however, are not observed

during periods of rapid signal-strength fluctuation, indicating that

Faraday rotation is not the dominant mechanism in producing these fades.

Observations made over long periods of time when little fading is present,

do however appear quite similar to the computed distributions for two

rays of similar strength. Figures 37a and 37b show two such measured

distributions, where the analysis time is 20 min. This indicates that

the effects of Faraday rotation are seen over longer time intervals, but

not for short intervals. This is consistent with predicted behavior for

the ordinary and extraordinary rays.

Additional examples of some observed distributions are shown in Fig.

38. These distributions were measured during three consecutive 10 min

periods under conditions of moderate fading. They show the change in 2

the dominant rays during the interval. In all cases a is less than

0.273, indicating that energy was relatively constant during each 10 min

period. Figure 38d shows the amplitude distribution for the entire pe-

riod, indicating the loss of information due to changes in the ray struc- 2

ture. Also, for this record, a is greater than 0.273.

Finally, we show three more measured distributions in Fig. 39. These

are the result of analyzing 20 min segments of data during a one and a

half hour period. The signal-strength record for this period is shown

in Fig. 39d. The three distributions correspond to periods of time when

SEL-70-037 90

—-^iAi*i^ii«ife>*^^v^y^^^ HMMwirf'.b fatti'-Aifc^fchtei^iai

mmi- m^mmnmwimnmmiKmmm. Plii«.,upjwii!iiwifmwj.«ii'i ^w^-,,.,^^^^ . v i ppppppipipppipjiiigiipjp m*nmfm

fs

2.0

^ 1.5 UJ|ILJJ

e

CO z LLI Q

Q UJ

a. o

i.O

0.5

(a)

ENVELOPE AMPLITUDE (■^) 2 3

ENVELOPE AMPLITUDE (-t)

Figure 36. Amplitude distributions exhibiting the effect of changing signal energy.

(a) Computed distribution with one ray (amplitude = 1.0) present for half of the analysis interval and three rays (amplitude - 1.0, 0.85, 0.7) present for the other half of the analysis interval. - a - 0.288, T cp = 0.79 .

2 (b) Measured distribution. - a = 0.26 .

91 SEL-70~037

__.*■■ n n'.i.iM n n in ■(■■liii.tiinJi.ir i ----■■ -:---......-»■ ..-- ■ . - in. - ..'■■v. ,..v,...-^ ^-t-^j^m.a^»...,.^^ ,, . . . .„

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UJ|IUJ

8 10

< ^ 0.5

(a)

f"

i

ENVELOPE AMPLITUDE (4)

2.0

lJj{lLU

i >- t § i.o o

<

^ 0,5

(b) ENVELOPE AMPLITUDE (4)

Figure 37. Measured amplitude distributions showing the effects of Faraday rotation.

2 (a) Analysis time = 20 min. - a = 0.14

2 (b) Analysis time = 20 min. - a =0.20

SEL-70-037 92

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2.0

ENVELOPE AMPLITUDE (4)

T 1.5

>-

<

1.0

5 0.5

(b)

fu

m k

JL

ENVELOPE AMPLITUDE (|r)

2.0

T '^

>-

^

Q LÜ (T.

<

1.0

0.5

(c)

{I fl

P ENVELOPE AMPLITUDE {&■)

20

T L5 Üj|lllJ

CO z LÜ Q

Q W (T

<

1.0

2 0.5

(d) ENVELOPE AMPLITUDE (-|-)

Figure 38. Measured amplitude distribution for three consecutive 10-min intervals, and for the whole 30-min interval, showing the effect of analysis time on observed distributions.

(a) First 10 min.

(b) Second 10 min.

(c) Third 10 min.

(d) Total 30 min.

- a

- a

0.238

0.206

0.197

0.433

93 SEL-70-037

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4J £ f= B u •a 3 i i c

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05 co 0) t-1 3 00

SEL-70-037 94

rr'-r ir'tiiS-friniMT-W/Kk"Wlrito^iY<.;^iiiHiJbl1l^

i«|!>ipp.^l»ii!pili^^

N

o o o o T ~ 10

o o o o -r W lO

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>, 0) J3

TJ 3 -O U 01 •r-l i-l r-l [0 a. O e -H « -a

c QJ •(-(

x: 4-1 <U

)-l n w 0

m OJ M

TJ 3 aj oo N -^ ^M-l

■—(

n en C T-l n) XI

4J (0 •o m O O

•r^ M U <U D-'O

C (U TO x: H XI

i •> , rt tn

•H TJ W X u JJ « o n u n] OJ QJ a- (3 n •H

•4-1 4-1 Xi o w cu öo w x: c c 4J OJ o M --l OJ 4J 4J > cn 3 0 1 XI XI

t-H -H TO • (0 U TJ C 4J tn

(1) 60 en U 3 .r4 .!-( (TI C I/) T) XI

•H AJ c ^-N 0 TJ u ^-^

05

cu u 3 M

•i-l

95 SEL-70-037

..-..^.■„■L..,^ ■. ■. -.1, :..-,■,..^„..V.W1.^^^>;^.r,.-..A-..~^^^^.^,^^^.^».^^^W.Wvai^^^....^ ^..../.U^i-.U^^a^iSte^^^.^,.^.,..,,,..,^.;,,.,,..,...:,....

pp <Kwmm^£^m»kmm^Mmmh»<m» [a-w ^ fi mui. m^mmmc^mwmmmH j^fg^nmmimnmm^mismm^

the signal-strength record had different appearances. Figure 39a appears

to resemble the amplitude distribution produced by two or three rays (Fig.

26K During the corresponding interval the signal-strength record shows

a moderate amount of fading. Figure 39b, the distribution for a more dis-

turbed period on the signal strength record, more closely resembles compu-

ted distributions for a larger number of rays. Figure 39c shows a very

strong component indicating that a single ray was prominent during this

period. The signal strength during this latter time was very stable.

F. CONCLUSIONS FROM SIGNAL-STRENGTH ANALYSIS

The observed amplitude distribution data presented in the above ex-

amples are similar to a majority of the observed amplitude distributions

examined. Analysis times were chosen to emphasize certain features of

the data. For all data taken during the course of the experiments, sim-

ilar distributions were produced when analysis intervals were chosen long

enough to give reasonably smooth distributions, and short enough to avoid

encompassing widely varying situations which produce distributions ap-

proaching the Rayleigh. From these analyses, the following conclusions

are drawn:

Signal-strength fluctuations observed for single-mode iono- spheric propagation under quiet ionospheric conditions are adequately described in terms of the multipath interference resulting from vertical ray bending caused by large, weak ionospheric irregularities.

Under most conditions, fading due to O-X interference is not significant compared with that arising from the vertical ray bending caused by the irregularities being investigated.

Measured amplitude histograms for ionospherically propagated rays are highly time-dependent because of the variability of the causative mechanism.

Weak scattering caused by a large number of small scatterers does not produce the major portion of the fading observed on single-mode one-hop ionospheric propagation. We do not know whether such weak scattering occurs in some smaller degree which is masked by the multipath-interference effects. Ex- periments to answer this question must consider the effects

SEL-70-037 96

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i mumm mmmm mm auWJMlUyiM^lWW^Wj'.^IIJiMl ^^^

of multipath such as we observe. Such experiments would promise most success if performed for shorter paths, where multi-ray in- terference is less, and during periods of low fluctuation in phase-path length.

97 SEL-70-037

i^tiaWMi.tM.Wl'.i^MnilBHi-.Jl,^^^ .:.^**.;..^,L*iJiib

.^■iw.».-. ■■-..ür -^-w^w^n*,,., U..-.^i,.ffl,»y;i..ii..u.:uv ^,|4. i.^tw.ijj^j^^, Wyi..i14<^.nf-.j;H<.WWi|W^I*';,^il<iff^W<iWJ.tJ^^^

5 0.8

z" o fl 0.6 < iij

|o,4 o o: ÜJ 5^0.2 a. o Q

0.0

SPACI

-200 -150 -100 -50 AIRCRAFT LEADhMG

LAG, 6t (sec)

50 100 150 200 LOS BANOS LEADING

Figure 40. Doppier correlation versus time lag for wide-spaced phase-path measurements made with receiving antennas at Los Banos, Calif, and on an airplane.

f SEL-70-037 98

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jjp^fffy.wJiV^^Mfpw^^^

V. OTHER CHARACTERISTICS OF THE IRREGULARITIES

A, HORIZONTAL MOTION OF IRREGULARITIES

Some of the phase-path data acquired in this work have been examined

with the object of determining whether the observed irregularities exhibit

any preferred direction and velocity of motion. The observational geometry

used in this work was sensitive to horizontal motions in the north-south

direction, and also to vertical motions (when more than one radio frequency

was used simultaneously).

The records obtained from the wide-spaced CW measurements, using re-

ceivers at Los Banos and on an airplane, were examined in an attempt to

identify a consistent horizontal velocity component of the irregularities.

The aircraft doppler measurements taken at spacings of 60, 65 and 70 km

were correlated [as in Eqs. (7) and (8)] with the fixed receiver-site

measurements using time lags of ±50 sec to ±200 sec for the fixed site,

to determine whether the highest correlation occurred at a time lag other

than zero. The results of these correlations are shown in Fig. 40. In

all cases, the correlation decreased for time lags other than zero, indi-

cating no preferred horizontal motion.

The above test involved averaging data over eight observations, and

therefore would sense only a preferred direction of motion. It is possi-

ble that each of the irregularities is moving, but that the directions

of motion vary widely. In order to observe the motion of individual ir-

regularities, use was made of the data gathered during the winter and

spring of 1969-1970. Changes in phase-path length measured on two ver-

tical monopoles spaced 2.5 km apart were cross-correlated to determine

the time shift of maximum correlation. Figure 41a shows a typical result

of this correlation. The phase of the signals at this spacing was highly

correlated (greater than 0.97 in all cases). The maximum phase-path cor-

relation pp(At) occurs for a time shift of 0 ± 5 sec for all records

examined. Because of the slow decorrelation of phase with time, it is

difficult to assign a value of north-south velocity component from these

records, and no attempt was made to do so.

Similar correlations were performed on the amplitude data available

from the experiments. As shown in Fig. 41b, the amplitude correlation

99 SEL-70-037

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101 SEL-70-037

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f, (^t) decreases much more rapidly with time than does the phase-path

correlation. Offsets of the peak amplitude correlation (from zero lag)

ranged from 0 sec to t20 sec. The interpretation of these time lags is

difficult for two reasons. First, only one component of the velocity is

observed. This allows us only to place a lower limit on the velocity of

the fading pattern. Second, horizontal motion of the fading pattern can

result from vertical motion and deformation of the irregularities as well

as from their horizontal motion.

If we assume that horizontal irregularity motion, rather than verti-

cal motion or deformation, is responsible for the motion of the fading

pattern, we find (based on the antenna spacing and time lag given above)

a lower limit for the horizontal velocity of the irregularity of about

65 m per sec .

B. VERTICAL MOTION OF IRREGULARITIES

By making use of simultaneous transmissions on two frequencies over

the Arkansas-Los Banos path, changes in phase-path length could be mea-

sured on two vertically separated paths simultaneously. Approximately

thirty hours of such two-frequency data taken during the winter-spring

1969-1970 period were analyzed to determine whether the observed irregu-

laritie£5 moved vertically. The analysis was performed by cross-correla-

ting the phase-path variation records for the two paths. Data segments

of 1.2 hours were used for each correlation. Frequency separations be-

tween 100 kHz and 5.1 MHz were used. A typical record for a 2 MHz fre-

quency spacing is shown in Fig. 42. The peak correlation occurs at a

time lag of 240 sec for the lower-frequency path. Assuming the vertical

ray spacings given in Fig. 8, this corresponds to a downward velocity of

about 33 m/sec. All of the data analyzed in this manner (shown in Fig.

43) indicated a downward velocity of between 30 and 40 m/sec. We there-

fore have considerable confidence in this measurement.

SKL-70-037 102

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103 SEL-70-037

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FREQUENCY DIFFERENCE. Af(MHr) J I I L_L 4 8 12 16

APPROX. RAY SPACING AT MAX. HT.(km) 20 24

Figure 43. Time lags required to produce maximum cross correlation of phase-path length changes for spaced frequencies.

SEL-70-037 104

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C. DIURNAL AND SEASONAL VARIATIONS

The measuring technique used in the course of this work could be

regularly employed only during winter daytime periods for the path in-

volved, To determine any diurnal variation which might be observable

during these limited periods (about 10:00 am to 4:00 pm local time at

midpath) the rms phase fluctuations observed for each 1.2 hr segment

of data analyzed in Chapter III, Section D (Fig. 31) are grouped into

1 hour intervals (according to the time of day at the middle of the

segment) and an average is calculated. These averages and their stan-

dard deviations are shown in Fig. 44. They indicate that large phase

fluctuations are most common in the morning, and least common near noon,

To examine the seasonal variations of N/CP^ this quantity is aver-

aged for each day of available data. These averages are shown in Fig.

45, for the period from November 1969 through April 1970. Single-mode

phase-path measurements are not possible on a regular basis over the

Bearden-Los Banos path at other times of the year. For the period of

the data, a small decrease in the magnitude of the phase-path-length

fluctuations is observed during the latter portion of the period.

D. ANTENNA PERFORMANCE

If it is desired to make use of very large apertures (greater than

one km) for HF communication systems, in order to increase antenna gain

and reduce interference, the irregularities described in this work will

strongly influence the design and performance of such antennas. The

strength and horizontal scale size of the irregularities will determine

the wave-front curvature for rays arriving at the receiving antenna.

This will limit the length of antennas which may be employed without

compensation for the varying curvature of the wave fronts. It is found,

however, that antennas having lengths up to about 20 km will be useful

under many circumstances without compensation for wave-front curvature.

Such antennas must, however, be able to track the changing apparent

azimuthal angle of arrival of incoming rays.

105 SEL-70-037

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MEAN OF NO. OF PTS SHOWN

X J_ X 9-10 AM 11 AM-NOON 1-2 PM 3-4 PM

10-11 AM NOON-IPM 2-3 PM 4-5 PM LOCAL TIME AT MIDPOINT OF PATH

Figure 44. Variation of phase fluctuations with time of day.

SEL-70-037 106

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Figure 45. Variation of phase fluctuations with time of year.

107 SEL-70-037

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|pWj^iIV»rpv.'l»^T:?uv..tJ^i.j^^

Signal-strength fluctuations will produce fading on any antenna

that is short compared with the dimensions of the ray interference

pattern on the ground. Measurements made during the course of this

work show that the correlation coefficient for amplitude fluctuations

on two spaced antennas perpendicular to the ray path is 0.8 to 0.95 at

spaclngs of 360 m and 0.4 to 0.8 at spacings of 2.5 km (Fig. 41b).

Larger horizontal spacings, vertical spacings, or spacings which are

not normal to the ray path may provide more rapid decreases in the

amplitude correlation with distance. If the antenna can be made large

enough so that it is composed of a number of cells (subdivisions) each

of which observes amplitudes independent of those observed by the other

cells, the antenna performance may be predicted using the methods of

Dracewell ('60). With this method, the field at the receiving antenna,

E, is represented as the sum" of the strongest ray arriving at the an-

tenna, E , and a superimposed random component, ^E , where ^ is

the complex deviation factor of the field from its average value. The

efficiency of the antenna is then given by

1 + var | (20)

2 In Chapter III the variance of the amplitude fluctuations (a )

for each measured and computed distribution, and the variance of the

phase fluctuations (cp2) for the computed distributions were calcula-

ted. These variances may be used to predict the efficiency of large

antenna systems if the antenna is large enough that the required inde-

pendent cells are present. Fading would not be observed with such an

antenna, although its efficiency would be reduced by the multiple in-

c ident rays.

E. BANDWIDTH LIMITATIONS

The multiray representation of the field resulting from propaga-

tion through ionospheric irregularities may also be used in describing

the bandwidth characteristics of the channel. At any given frequency,

SEL-70-037 108

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tw,^.»^..^^,^^^^

the channel transfer function is described by the relative amplitudes of

the rays and by their differential time delay, AP/c. The manner in which

these quantities vary with frequency has not been investigated in this

work.

If the directivity of an antenna can be made high enough so that

only one ray is accepted, the interfering rays will not be admitted to

the receiver. This would eliminate the fading and the bandwidth limita-

tions described above. In the vertical (elevation) plane, rays will

originate at heights which differ by about 15 km at the reflection height.

For a path of the length used in our measurements, these rays will arrive

at the receiving antenna with a separation in elevation angle of about a

half degree. A vertical aperture of over 1 km would be required to sepa-

rate these rays. Therefore, it does not appear practical to reject inter-

fering rays by the use of large vertical apertures. However, large hori-

zontal antennas might be able to reject multipath rays, if the rays have

sufficiently different azimuthal angles of arrival.

109 SEL-70-037

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VI. SUMMARY AND RECOMMENDATIONS

A. SUMMARY

High-frequency ionospheric radio propagation over a one-hop lower-

ray F-layer path has been studied under "quiet" ionospheric conditions,

i.e., during periods when high-resolution oblique-incidence soundings

over the path showed no evidence of ionospheric irregularities. Changes

in the phase-path length of rays propagating over the path were measured

using a technique which is sensitive to changes occurring as slowly as

ten meters per hour. Under quiet conditions, the technique allows mea-

suring ionospheric refractive-index irregularities with a sensitivity

about an order of magnitude better than that of other methods, e.g.,

pulse sounders, satellite Faraday rotation measurements and doppler

spectrum analysis.

Analysis of the data produced in these measurements revealed a

class of weak slowly-varying irregularities which were present during

all of the observations. The data were taken during daylight hours in

the spring of 1969 and the winter and spring of 1969-1970, over a 2600

km mid-latitude east-west path. A variety of experimental configura-

tions were employed. The major physical characteristics of the irre-

gularities are:

1. Horizontal scale size of about 35 km.

2. Vertical scple size of about 15 km.

3. Electron-density changes of 0.6 to 6.0 per cent,

4. Horizontal velocity of 65 m/sec (lower limit)—no preferred direction.

5. Vertical phase velocity of 35 m/sec—downward.

Using these parameters, we may classify the new irregularities as

smaller, weaker, and somewhat slower-moving than those studied by Munro,

Titheridge and others. Their continuous presence and comparatively large

effects make them quite significant in ionospheric radio propagation over

long one-hop F-layer paths.

Ill SEL-70-037

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A mtxlel was developed, and was shown to predict correctly the

amplitude fluctuations most commonly observed for long-distance sin-

gle-mode KF propagation. These fluctuations had not been satisfacto-

rily explained previously. The irregularities also impose fundamental

limits on the spatial resolution and bandwidth which may be achievable

in HF ionospheric propagation.

No attempt has been made to determine the origin of these irregu-

larities, but their characteristics are consistent with effects which

might be produced by internal gravity waves. Georges ('67) in studying

large- and medium-scale traveling ionospheric disturbances points out

that preferred periods for gravity waves in the F-region are close to

20 minutes. He also shows that for internal gravity-wave energy propa-

gating vertically upward, the phase velocity of the resulting distur-

bances is vertically downward. If the irregularities observed in this

investigation result from internal gravity waves, there is reason to

believe that the source of energy producing them lies below the F region,

and possibly within the upper atmosphere. Georges notes that thunder-

cloud tops are observed to oscillate with periods of about 20 min, and

that attempts have been made by others to detect ionospheric effects

which might be produced by these oscillations. The phase-path measure-

ment method used in this work offers considerable potential for observ-

ing such a relation if it exists.

B. RECOMMENDATIONS

The bandwidth limitations imposed by weak ionospheric irregularities

are not yet fully understood. They are, however, an important result of

propagation through such irregularities. Additional information concern-

i: g the characteristics and occurrence of these irregularities is needed

in order to form a complete description of their effect on HF propagation

under varying circumstances. The stable-frequency phase-path measuring

system employed in this work would be particularly suitable for additional

investigations of the motion, the solar-cycle dependence, and the seasonal,

diurnal and global frequency of occurrence of these irregularities. For

use in potential development of large antenna systems, more detailed infor-

mation on the azimuthal-angle distribution of multiple rays is needed.

SEL-70-037 112

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r v - - - ■ v ■ - ■

The major degradation of HF communication-system performance produced

by those irregularities is multipath interference within a single mode.

Since the extent of this interference is a function of the distance from

the scattering region to the receiver, it may be possible to optimize the

design of a high-performance communication system by selecting paths suf-

ficiently short that such interference is minimized to the greatest possi-

ble extent. More data is required on the occurrence and global distribu-

tion of the irregularities if such an optimization is to be used in prac-

tice .

113 SEL-70-037

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APPENDICES

115 SEL-70-037

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APPENDIX A

CW PHASE-PATH MEASUREMENTS

A. THE BASIC MEASUREMENT

The phase-path measurements of this work were made using CW trans-

missions from stable-frequency transmitters. The transmitted frequencies

were synthesized from a cesium-beam frequency standard (or in some cases,

from a highly stable crystal frequency standard). The signals were re-

ceived using standard HF receivers. All of the conversion injection fre-

quencies of these receivers were synthesized from cesium-beam frequency

standards. The audio-frequency output of the receivers was sampled by a

computer with an analog-to-digital converter. Zero crossings of the au-

dio signal were counted continuously from the start of each data-gather-

ing run. At each "sampling interval" the computer subtracted a number,

n, from the running total of zero crossings. The value of n was

n = 2f t , a

where f is the nominal audio output frequency of the receiver, as

determined by the receiver conversion frequencies used, and t is the

sampling interval used. Sampling intervals between 1/10 and 1 sec were

used. The sampling rate and the length of the sampling interval were

controlled by pulses derived from digital dividers clocked by the cesium-

beam frequency standard.

In addition, at the end of each sampling interval the instantaneous

phase of the audio signal was calculated by measuring the fractional part

of a half-cycle as

f t ^ fract. = — , t2

where t is the time between the end of the interval and the zero cross-

ing immediately prior to the end of the sampling interval, and t_ is

the time between the zero crossings immediately preceding and Immediately

117 SEL-70-037

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pppBWBWiBpp m a Wig ll|iPv'Mwpu.uia.vi'JiituwüMW!ai!pip)!i»WJiM^!il .. .... ,u,.iati.yff i.j.j.-Mj^.^i.iuwmHjijyp!^^ ,JM'tfi'"'.uuji!-.Lii,»u^u4W!^iiiiv^w^,wu.ii.i^iipw<w»^wHu^!^

following the end of the sampling interval. The sum of the running total

of zero crossings and the measured fraction is the desired measurement of

phase-path length in units of A/2, where A is the wavelength of the

transmitted frequency. Using this technique, errors in the measurement

of the fractional part of a half-cycle do not accumulate, as the output

at each sampling interval is the running total of zero crossings for the

entire measurement period (an integer number) plus the fraction measured

at the end of the specific interval.

The envelope amplitude of the signal was determined by measuring the

slope of the audio signal at the zero crossings immediately preceding and

following the end of the sampling interval. For narrow-band signals, this

slope is directly proportional to the envelope amplitude of the signal.

Errors in these measurements are introduced by instabilities in the

frequency standards and in the other equipment (e.g., receiver phase drift,

digital-circuit jitter). As stated in the body of the report, errors in

the frequency standards introduce an error of about 10 m/hr in the mea-

surement of phase-path length. Tests were made to determine the total

system error by introducing synthesized standard frequencies directly

into the input of the receivers. The long-term phase drift observed was

less than 10 m/hr (equivalent phase-path length) when the receiver input

was derived from the same frequency standard used to synthesize the re-

ceiver injection frequencies, or from another independent cesium-beam

frequency standard. When a stable crystal frequency standard was used

to supply the receiver input, a linear long-term drift was observed due

to the frequency error of the crystal standard. Departures from a linear

drift were less than 20 m/hr.

Short-term phase errors, arising primarily from noise and digital

circuit jitter, were less than 2 deg at the maximum receiver input level,

and less than 10 deg (~ 1/3 m) at a receiver input 40 dB below the maxi-

mum level. The amplitude measurement was accurate to within 1 dB over

the 40 dB range of input levels.

During the first series of measurements, involving the airborne and

Los Banos receiver sites, some additional short-term errors were intro-

duced by the intermediate analog magnetic tape recording. These errors

are discussed in the next section.

SEL-70-037 118

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. J.-.^^WIlMiWMili^ ?WWR

B. WIDE-SPACED MEASUREMENTS

Initial determinations of the strength and horizontal size of the

observed weak irregularities were made using a transmitter in Bearden,

Arkansas, a fixed receiving site at Los Banos, California, and a receiv-

ing system in an aircraft. The path length is about 2600 km. This con-

figuration was used to allow a relatively rapid determination of the ma-

jor characteristics of the received wavefronts. Flights were made in a

generally north-south line, from 30 to 170 km north of the fixed receiv-

ing site (see Fig. 46). Each flight took between 20 and 40 min, and

covered from 100 to 140 km. Ten flights were made, of which the eight

most successful were used to determine the parameters of the irregular-

ities. This section describes the equipment and methods used in making

these measurements.

A DC-3 aircraft was used for the experiment. It was equipped with

two monopole antennas, approximately 1/4 wavelength long. These were

tuned so that a low VSWR was obtained over frequencies from 20 to 26 MHz.

The same signal was received on both of the antennas and separately re-

corded. The results of processing data from both antennas were compared

to eliminate any ambiguities resulting from fades due to ground reflec-

tions or incoming polarization changes. Generally, the data from the

vertical antenna were used. Figure 47 is a photograph of the exterior

of the aircraft. The antennas may be seen at the rear.

Figure 48/ shows the interior of the aircraft with the equipment in-

stalled . All receivers were modified so that all conversion frequencies

were synthesized from the cesium standard. The receiver audio outputs

were recorded on analog magnetic tapo. In addition, a 50 kHz signal de-

rived from the cesium standard was recorded on the tape. This signal was

used during data reduction to control the sampling of the data channels,

thereby greatly reducing the effects of short-term tape speed fluctua-

tions, ard eliminating the effects of long-term fluctuations. A one

pulse per second (pps) signal derived from the cesium standard was also

recorded on the tape. This permitted precise synchronization of the

tapes from the aircraft and from Los Banos, and prevented dropouts in

the 50 kHz signal from degrading long term accuracy. Voice countdowns

on the tape allowed exact matching of the time between Los Banos and the

119 SEL-70-037

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aircraft. Tests of this method of recording and the associated data-

reduction process showed that a phase accuracy of better than ±5 deg was

maintained for the data channels (where only a single frequency component

was present) and ±10 deg for the tracking channel (two frequencies, dif-

fering in strength by up to 30 dB, were used for the tracking system as

described below). Figure 49 is a block diagram of the equipment on the

aircraft.

The receiving equipment at Los Banos used basically the same tech-

nique, A single 1/4 wavelength vertical antenna was used. Again, all

conversion frequencies were derived from a cesium beam frequency stand-

airi. The same data recording scheme was used.

CW transmissions from Bearden, Arkansas were provided by a crystal

frequency standard, a frequency synthesizer and a 1000 watt linear ampli-

iier. The antenna used was a vertical monopole. The frequency stability -10

of the crystal frequency standard is specified as 10 for averaging

times from 1 sec to 1 hr. This can introduce an uncorrected doppler fre-

quency of up to 0.0025 Hz for a typical pass. The peak-measured doppler

(dP/dt) for all flights ranged from 0.05 Hz to 0.2 Hz. Errors in rela-

tive doppler between Los Banos and the aircraft are determined by the

stability of the cesium standards at Los Banos and on the aircraft. These

errors were of the order of 0.00025 Hz.

C. AIRCRAFT TRACKING SYSTEM

An accurate determination of wave-front shape from a moving aircraft

requires an accurate means of determining the location of the aircraft.

The accuracy with which the position of the aircraft can be determined

sets a limit on the accuracy of the measurements which can be made. A

tracking system was used for these experiments which provided continuous

measurements of the position of the aircraft. The estimated accuracies

for this tracking system are discussed below and summarized in Table 1.

The tracking system consisted of a CW doppler system, an aneroid

differential altimeter, ard an aerial camera. The CW doppler system mea-

sured changes in distance to the aircraft from two ground points within

a direct line-of-sight of the aircraft. r;wo doppler transmitting sites

123 SEL-70-037

»rtfaWMa^HitiiMaMiltMili^

VERTICAL ANTENNA V HORIZONTAL

ANTENNA V

TRACKING RECEIVER

TO ALL RECEIVER LOCAL OSCILLATOR

INJECTIONS

CESIUM BEAM FREQUENCY STANDARD

DATA RECEIVER

DATA RECEIVER

pps

50 kHz

ANALOG TAPE

RECORDER

FREQUENCY SYNTHESIZERS ALTIMETER

Figure 49. Block diagram of major equipment of the aircraft.

SEL-70-037 124

^■^^i^^^^^v..*..:.,^^*.^^^

were used (see Fig. 46), one located near the southern end of the flight

path (Los Banos), and one to the east of the flight path in the Sierra

foothills (Bear Mountain), Both transmission paths to the aircraft were

unobstructed along the entire flight path. Frequencies near 25 MHz were

used for reasons of simplicity and economy in the transmitting and re-

ceiving equipment. The frequencies of the two transmitters were offset

by 3.0 kHz. The signals were received in the aircraft using the same

vertical antenna that was used for receiving the ionospherically-propa-

gated signals. Both tracking signals were received by a single receiver

having a 6 kHz bandwidth. The audio output of this receiver (at 3 and 6

kHz) v/as recorded on one track of the analog tape recorder. All trans-

mitting and receiving mixing frequencies for the tracking system were

synthesized from a single frequency standard at each location. The fre-

quency standards in the aircraft and at Los Banos were cesium-beam stan-

dards. A crystal frequency standard was used at the Bear Mountain trans-

mitting site, in order to remove the effect of frequency fluctuations

in the crystal frequency standard, the signal transmitted from Bear Moun-

tain was also received at Los Banos, using a receiver having all conver-

sions synthesized from the Los Banos cesium standard, and recorded for

use during the tracking data reduction.

The specified accuracy and long-term stability of the cesium-beam

frequency standards is ±1 X 10 . Short-term stability is such that

the accumulated phase error never exceeds that due to the accuracy spe-

cification by more than 1 milliradian at 25 MHz. Measurements made on

the two cesium standards that were used indicate a relative drift of

less than 1 |asec/day between them. This is within the specification

value. A typical pass over the flight path requires about 1/2 hr. Dur-

ing this period, the total phase change is approximately 25 X 10 X

2Jt x IfiOO rad. The phase error expected would then be

6 —11 25 X 10 X 27t X 1800 X 10 = 2,8 rad

For a frequency of 25 MHz (A = 12) this corresponds to a distance error

of 5 m over a 30 min flight, and proportionally less over shorter portions

of a flight.

125 SEL-70-037

^aj^idfr^^^i^aa^^ 'IBrtiBHgiifi r iri in i

Changes in the height of the aircraft were measured with a precision

aneroid altimeter. It was used in a differential mode with a full-scale

output of ±40 m. In this mode the primary source of instrument error is

hysteresis, which is specified at ±3 m. Corrections for variations in

air pressure with time and along the flight path were made when necessary,

using temperature-corrected barometric readings from the Sacramento and

Stockton, California, Weather Bureau stations. These readings were taken

at half hour intervals during the period of the flights. For a majority

of the flights no correction was made, as the indicated correction was

less than 10 m. Because the elevation angle~of-arrival for the ionospher-

ically propagated signals from Bearden is low (~ 10 deg), errors in alti-

tude affect the phase-path measurements by less than 1/5 as much as do

errors in horizontal position.

The three measurements made by the doppler system and the altimeter

are sufficient to determine the location of the aircraft, continuously

if an initial location can be determined from other means. For the mea-

surements involved in these experiments, although it is important to know

accurately only changes in the great circle distance to the transmitter

and changes in altitude, the geometry of the doppler system requires that

a fixed point be used as a starting reference. The error in change of

distance will be about half the error in the location of the fixed point

for the transmitter locations employed. (If only portions of the flight

path near the center are used, where the angle between the flight path

and the transmission from Bear Mountain is reasonably large, less error

in change of distance will result.)

Photogrammetrie reduction of the aerial photographs taken over two

"photo points" (Fig. 46) on the flight path (a stereo pair at each point)

was used to establish the fixed point required by doppler/altimeter sys-

tem, and to check the closure error of the tracking system. The stated

accuracy of the photographic position determination is ±50 m in the hor-

izontal plane, and ±100 m in altitude.

The final accuracy of the tracking system is estimated in terms of

the effects of various errors on relative position, rather than absolute

position determination which is not important for the experiments. Table

1 sununarizes the various sources of error in the tracking system, and

their contribution to relative position error.

SEL-70-037 126

> ..»^i^-,^..c«..M,,^ A^jt^.o^...^4ü.jjir.^iit.i. ̂s.v.^,:..^,........^.. ■■,..--.,-^,..^^

TABLE 1

AIRCRAFT TRACKING SYSTEM ERRORS (30 Min. Flight Time)

Error Source

Frequency Standards Altimeter (3.0/5) Air Pressure Changes (10.0/5) Photogrammetry—Horizontal (50/2) Photogrammetry—Vertical (100/10) Tracking Frequency Ground Reflections (A/S) Phase Measuring System (Insignificant)

TOTAL

Estimated rms Error (m)

5 .0 0 .6 2 .0

25 .0 10 .0

2 .0 — -

27.4

As a check on long-term error, photographic position determinations

were made at both ends of the flight path for four flights. These were

compared with the positions determined by the tracking system. Closure

errors were 20, 25, 35, and 60 m for these flights. No systematic er-

rors were visible on the data. It is therefore believed that tracking-

system errors contributed an rms error of about 10 per cent to the ex-

perimental data from the aircraft.

D. DATA PROCESSING

Each pass over the flight path resulted in one analog tape each from

the aircraft and from Los Bancs. Table 2 lists the channel assignments

for these tapes. The first step in the data reduction was to play back

the tapes, and, using a Scientific Data Systems Sigma V computer with an-

alog-to-digital converter, convert the audio signals to a digital tape

which represented the total number of cycles (including fractions) from

the start of the tape. This was done for each of the six audio signals

on the tapes. Sampling of the signals was clocked by the 50 kHz or 25 vHz tones on the tapes. The one pps signal was also sampled to indicate

the start of each second, in the event that dropouts occurred in the 50

kHz signal. A test was made during sampling to assure that between 0.8

and 1.2 seconds of real time elapsed between occurrences of the 1 pps

127 SEL-70-037

^ ■:- - - - - ■ • • -■ ■ ■-■^^-^^"^^■■—-'^^^j^-iiiOTirtH"- m i ■ ■■■■■^-■^^*^^ -m

TABLE 2

DATA RECORDED ON ANALOG TAPES

Aircraft Tapes — 30 in ,/sec — Direct record (except FM where marked with asterisk)

Track

1.

2.*

3,

4.*

5.

6.

7.

Tracking Receiver Output - 3 & 6 kHz

Voice commentary & countdowns, & camera exposure tone

1 pps from cesium standard

Differential altimeter - ± 40 m

50 kHz sine wave from cesium standard and divider

Horizontal antenna data-receiver output - 3 kHz

Vertical antenna data-receiver output - 3 kHz

Los Banos Tapes^ — 15 in./sec

Track

i .

2.*

3,

5.

7,

4 & 6.

Beam Mountain tracking correction signal - 3 kHz

Voice commentary and countdowns

1 pps from cesium standard

25 kHz sine wave from cesium standard and divider

Data receiver output - 3 kHz

Not used.

signal from the tape. This insured that seconds would not be "lost" if

there were dropouts in the 1 pps channel. Finally, the altimeter channel

and its calibration were sampled each second.

The resulting digital tapes were listed, and a test was made to de-

termine that the doppler frequency each second was within 1/2 Hz of the

doppler frequency for the preceding second. If not, the data were flag-

ged at that point to indicate a tape or signal dropout. Between 0 and

40 points for each tape (in a total of about 1500 points) were flagged.

An editing program was then used to correct flagged points, align all

tape playbacks to a common starting point, and convert from cycles to

distance. The latter conversion required inversion of some of the

SEL-70-037 128

^inntotf^A"——'-■■--^"—"^^ ' t^.^....^^^^^u^.^:^^.^...^^..^^^ ^..„,.,. :-„^:.^...,...,-v,.^....„-^..^^„..!..„,.,^..^..^^

frequencies (where the receiver used an odd number'of inverting conver-

sions), and multiplication by the particular wavelength for the frequency

involved. The resulting tape was then processed to obtain the required

results in terms of changes in phase path length. *£o the transmitter.

Three of the six audio frequencies on the analog tapes result in two

records, describing changes in distance between the aircraft and Los

Banos and between the aircraft and Bear Mountain. The altimeter samples

result in a record of changes in altitude of the aircraft. (Corrections

for changes in barometric pressure are also included in the editing pro-

gram.) These three records are used, together with an initial point de-

termined from photography, to calculate the location of the aircraft each

second, and to calculate the great circle distance to the transmitting

site each second.

The remaining three audio frequencies produce records representing

the change in phase path length of the ionospherically propagated signal

received at Los Banos and on the aircraft horizontal and vertical anten-

nas. The data from the aircraft are then corrected for the effect of

changes in aircraft distance from the transmitter and changes in altitude.

The resulting records for the aircraft represent measurements comparable

to the Los Banos measurements. Finally a constant doppler (linear phase-

path change) term is subtracted from all the data for a given flight.

-The quantity subtracted is the average doppler at Los Banos for a period

of a half hour to an hour, including the time of the flight. The result-

ing records show changes in phase-path length between the transmitter and

Los Banos, and between the transmitter and the aircraft, with a linear

term removed from both. Typical records are included in Chapter II. The

difference in doppler at varying separations of receiving sites is deter-

mined by measuring the slopes of the two curves at various times and cor-

responding separations.

E. LATER LOS BANOS MEASUREMENTS

The measurements made during the winter and spring of 1970 involved

only the Los Banos receiving site and the Bearden transmitting site.

The basic measurement was the same, but the equipment used was somewhat

129 SEL-70-037

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different. The transmitting rfite transmitted two synthesized frequencies.

The receiving site was equipped with a small computer with an analog-to-

digltal converter and a digital tape recorder. These were used to con-

siderably simplify the data processing. Receiving antennas were availa-

ble which were located on a line perpendicular to the direction of the

transmitting site. These were eight vertical monopoles spaced 360 m be-

tween each element. A maximum of three elements was used at any one time.

SEL-70-037 130

. .■^■^,:^.^^.^.,^I;......u.^..^^^^

APPENDIX B

THE EFFECT OF CHANGES IN RAY REFLECTION HEIGHT

This appendix discusses the possibility that the relation which was

derived between the measured changes in phase-path length, and the changes

in refractive index and electron density which are required to produce

them, may not be accurate. Two distinct simple models of the ionosphere

are commonly used in considering the source of doppler effects on iono-

Ispherically propagated waves (Davies '65). The first assumes that vari-

ations in refractive index occur along straight (non-deviating) portions

of the ray paths (i.e., not near the reflection height). This is the

assumption made in the two-dimensional model used in Chapter III. The

second commonly-used model assumes that if there are ionospheric varia-

tions near the reflection height (where in fact it appears that the ob-

served irregularities are located), these can be analyzed in terms of a

change in height of a reflecting mirror. This latter idea implies that

an irregularity may change the height at which a ray is reflected. The

effect of such a change in reflection height is now to be considered.

It might be anticipated that when an irregularity disturbs the path

of a ray in the ionosphere, causing a change in the reflection height of

the ray, the measured change in path length may be greater than that

which would occur for a ray passing directly through the irregularity

when the latter is so located as not to affect the reflection height—

i.e., when the irregularity is on the ray path but not near the region

of significant ray bending. Figure 50 shows the effect of a change in

reflection height caused by the presence of an irregularity near the

region of significant ray bending. From Eqs. (5) and (4) we have

dP f 1^ ds . (B.l) RAY PATH aZ

It will now be shown that the change in reflection height does not affect

the relations which were used in determining changes in refractive index

and electron density.

131 SEL-70-037

ifaü^aMY,i^^^^i^i»^^

P^JfWiiNmilM.I'MiW.iMf^ N.a.ii .ti^Ji.iii.;.iii^ijHy)ffi^iyiu.i,HH^HVi1HfUHuiiuJ.'.w^vs..Mi!!y-i'M"«('W

PATH IN THE PRESENCE OF AN OVERDENSE IRREGULARITY

Figure 50. Ionospheric ray paths showing a change in reflection height caused by an irregularity near region of sig- nificant ray bending.

SEL-70-037 132

^Mliri^tJiiafcMfchBiiliiMtM^MiltlMWi^aiflt^ ..^i.;/ ,r>.'V-.t. ■V;-^-,J ,.:■■;,U-.^aa/.-..:.-^>^-.----||i||imrit^aifniV ■ , ■.Ji.«.J..v.:........;«.Mj.Jt^.v^k^.-;1

Wi)k^iwjTOijji.i!Ly.^py))^^^^^ mf^w^^^f^^^if/a

Consider first a non-moving irregularity described by

f(t) • g(x,y,z)

In this expression g(x,y,z) describes a fixed shape for the irregular-

ity, and f(t) describes some time function. Let the irregularity be

isolated from the slowly varying ionospheric background, i.e., let it be

immersed in a medium of constant refractive index. At any time t, de-

fine a geometrical ray path G within the irregularity as the path

which exhibits the maximum doppler at the time. That is.

l ■^r ds = max (B.2)

m

Now at any instant t, the rate of change of phase path, dP/dt, along

the geometrical path G will correspond to the maximum possible value m

of the integral in Eq. (B.l). If the irregularity is now immersed in

the ionosphere, the only portion of any ionospheric ray path which can

contribute to a change in the value of the integral is the portion (if

any) which lies within the irregularity, since outside the irregularity,

ö|j/öt = 0. Therefore, at any instant, the doppler over the ionospheric

path must be less than or equal to the doppler along G within the

isolated irregularity. For simple shapes of irregularities of arbitrary

strength (excluding the possibility of total ray reflection) and for ar-

bitrary shapes of weak irregularities, we can show that G is a fixed

path. In the case of a spherically symmetric irregularity, G is any

diameter of the irregularity. For an ellipsoidal irregularity, G is

the major axis of the irregularity. In the case of weak irregularities,

where in this case 'weak' implies that rays are not displaced within the

irregularity, but only deflected in angle, all ray paths within the ir-

regularity are straight lines, and every straight line is a ray path.

G is then a fixed straight line defined by m

133 SEL-70-037

-^.....■-■■^.■^■.^.^--J^,:...,^.—.. ..^■.■-»..■^.:..,i «i^l^a^.^^^»^.*^^.;^^^^/^^ "--'-^— -

■ppiSllBI!!BiipppW,WWllW!MJ*<^^ ■ J.-i v.iWllliW^IM^^

/ g(x,y,z) = maximum . (B.3) •'STRAIGHT

LINE

The irregularities which were described based on the ionospheric

measurements of this work satisfy the 'weak' approximation with little

error. The result states that regardless of the smooth bending geometry

of the ionosphere itself, irregularities produce a doppler which is at

every instant less than or equal to the doppler that would be measured

for a path G in the irregularity when the latter is isolated from the

ionosphere. Therefore, the total measured change in phase-path length

when the irregularity is in the ionosphere will be less than or equal to

the change in phase-path length along a path G through the isolated

irregularity. So, despite the fact that an irregularity may change the

reflection height of a ray in the ionosphere, and therefore also change

the phase-path length of the ray outside the region of the irregularity,

the total measured change will be no greater than the change which would

be predicted from propagation through an isolated irregularity, having

the same profile, which is not close to the reflection height.

If the irregularity is assumed to move, little is changed in the

argument. Since the total ionospheric ray path at a given time is not

a function of its history, the integral of dP/dt will be the same

whether the irregularity reached its present position by moving there

or by developing there. This leads to the conclusion that the method

used in relating AP to An is valid.

SEL-70-037 134

Bt ■.*MW.»U»Wi,>....;»Jlli^».Mr ,^^^ „■.... .^..... — . ..-..■---..

T^MyilU'JiM|W|-iii.iJl)l^

REFERENCES

Al'pert, Ya. L., Radio Wave Propagation and the Ionosphere, (Authorized Translation fron the Russian), Consultants Bureau Enterprises, Inc., New York, 1963.

Barry, G. H. and R. B. Fenwicl:. "Extraterrestrial and Ionospheric Sounding with Synthesized Frequency Sweeps," Hewlett-Packard Journal, Vol. 16, No, 11 8 (1965),

Bennett, J. A., "The Calculation of Doppler Shifts Due to a Changing Ionosphere," J. Atmos. Terrest, Phys,, Vol. 29, 887 (1967),

Booker, H. C, J. A, Ratcliffe and D. H. Shinn, "Diffraction from an Irregular Screen," Phil. Trans. Roy. Soc. London, Vol. A-242, 579 (1950).

Born, M. and E. Wolf, Principles of Optics, Pergamon Press, New York, 1964.

Boys, J. T., "Statistical Variations in the Apparent Specular Component of lonospherically-Reflected Radio Waves, " Radio Sei., Vol. 3 (New Series), 984' (1968).

Bracewell, R. N., "Antenna Tolerance Theory," Statistical Methods of Radio Wave Propagation, Pergamon Press, London, 1960.

Bramley, E. N., "Direction-Finding Studies of Large-Scale Ionospheric Irregularities," Proc. Roy. Soc, Vol, A-220, 39 (1953),

Bramley, E. N., "Some Comparative Directional Measurements on Short Radio Waves over Different Transmission Paths," Proc. IEEE, Vol. 43, 544 (1955).

Budden, K. G., Radio Waves in the Ionosphere, The University Press, Cam- bridge, 1961.

Chan, K. L. and 0, G. Villard, Jr., "Observation of Large-Scale Traveling Disturbances by Spaced-Path High-Frequency Instantaneous-Frequency Measurements," J. Geophys. Res., Vol. 67, 973 (1962),

Chernov, Lev A., Wave Propagation in a Random Medium, McGraw-Hill Book Company, New^York, 1960.

i' Croft, T. A., "Methods and Applications of Computer Raytracing," Report

SEL-69-007 (TR No. 112), Stanford Electronics Laboratories, Stanford, California, 1969.

Davies, K., Ionospheric Radio Propagation, U. S. Govt. Printing Office, Washington, D. C, 1965.

135 SEL-70-037

■ — ■ " ■ '•- ' 1 i n ii ^I.Ai.n.i. Hi. -■-■- ■ - - -^ —' -' ■■" -' ' •" m, i

WiWPii^JliPBBpWltPWitiWMW

REFERENCES (Cont)

Dleminger, W., "The Scattering of Radio Waves," Proc. Phys. Soc, Vol. B-64, 142 (1951),

Georges, T. M., "ionospheric Effects of Atmospheric Waves," IER 57- TTSA 54, Institute for Telecommunication Sciences and Aeronomy, Boulder, Colorado, 1967.

Hines, CO., "Atmospheric Gravity Waves: A New Toy for the Wave Theorist," Radio Sei., Vol. 69D, 375 (1965).

Jones, R, M., "A Three-Dimensionul Ray-Tracing Computer Program," Radio Sci., Vol. 3 (New Series), 93 (1968).

Kato, S., "A Contribution to the Theory of Irregularities in a Medium with a Mean Density Gradient," J. Atmos. Terrest. Phys., Vol. 27, 367 (1965).

Lee, R. W. and J. C. Harp, "Weak Scattering in Random Media, with Appli- cations to Remote Probing," Proc. IEEE, Vol. 57, 375 (1969).

Little, C. G, and 0. K. Garriott, "The Use of Geostationary Satellites for the Study of Ionospheric Electron Content and Ionospheric Radio Wave Propagation," J. Geophys. Res., Vol. 65, 2025 (1960).

Manning, L. A., "The Effects of Irregularity Scale on Usable Antenna Aperture," Report SEL-68-051 (TR No. 141), Stanford Electronics Laboratories, Stanford, California, 1968.

Munro, G. H., "Travelling Disturbances in the Ionosphere," Proc. Roy. Soc, Vol. 202, 208 (1950).

Munro, G. H., "Travelling Ionospheric Disturbances in the F Region," Aust. J. Phys., Vol. 11, 91 (1958).

Peterson, A. M., "The Mechanism of F-Layer Propagated Back-Scatter Echoes, J. Geophys. Res., Vol. 56, 221 (1951).

Rice, S. 0., "Mathematical Analysis of Random Noise, Pt. Ill," Bell Sys- tem Tech. J., Vol. 23, 282 (1945).

Sweeney, L. E., Jr., "Spatial Properties of Ionospheric Radio Propagation as Determined with Half-Degree Azirauthal Resolution," Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy, Stanford University, Stanford, California, 1970.

Tatarski, Wave Propagation in a Turbulent Medium, McGraw-Hill Book Com- pany, New York, 1961.

SEL-70-037 136

».aiit^.....^...,;.-!..;, .-...1.'.^..|.-*-'■-•'■'T-"-V '■■•■\Mlr't"r ■ hv;ifiifiirfiiitlhOiU-wi^^ririTi»i---'^'^^'^.'-^----iil.'B>tt»^r in t (il »tfliii'ltiiitftirnr vi-^! 'nt^^n^H '

REFERENCES (Cont)

Titheridge, J. E., "Large-Scale Irregularities in the Ionosphere," J.

Geophys. Res., Vol. 68, 3399 (1963).

Titheridge, J. E,, "Periodic Disturbances in the Ionosphere," J. Geophys,

Res., Vol. 73, 243 (1968).

Whale, H, A. and J. T. Boys, "Measurements of the Coherence Ratio of lonospherlcally Propagated Radio Waves," Radio Sei., Vol. 3 (New

Series), 977 (1968).

Whale, H. A. and C. W. Gardiner, "The Effect of a Specular Component on the Correlation Between the Signals Received on Spaced Antennas,"

Radio Sei., Vol. 1 (New Series), 557 (1966).

■L37 SEL-70-037

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1111 "H ' ■! U ■pppHMm 1 " Ill< ' "HIIW? . - t'^pf'.-r^pr;; T ■;■■■. *..

rNCkASSIFIKl) Security Classification

DOCUMENT CONTROL DATA • R&D (Security clücatticatlon of title, body ot abstract and indexing annotation muaf bs enferec/ when the overall report la claaailied)

I ORiniNATIN G ACTIVITY fCorporat« aurhor;

Stanford Klectronics Laboratories Stanford University, Stanford, Calif 94305

2« REPORT SECURITY C U A»5I F1C * TION

Unclassified Zb GROUP

3 REPORT TITLE

IRREGULARITIES IN THE QUIET IONOSPHERE AND THEIR EFFECT ON PROPAGATION

4 DESCRIPTIVE NOTES (Type ot report and Inclusive datea)

Technical Report No. 156, August 1970 5 AUTHORrSJ O-ai"! name. «r»l name. Initial)

Philip A. Fialer

6 REPORT DATE

August 1970 7p. TOTAL NO. OF PAGE»

137

7b. NO. OF REF3

32 8a CONTRACT OR GRANT NO.

Nonr-225(64) b. PROJECT NO.

3808

9a. ORIGINATOR'S REPORT NUMBERfSJ

TR No. 156 SEL-70-037

9b. OTHER REPORT HO(S) (Any other number« that may be •aaldnecf Ulla raporü

10. AVA IL ABILITY/LIMITATION NOTICES

This document nas been approved for public release and sale; its distribution is unlimited.

II. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

Office of Naval Research

13 ABSTRACT , J_, j J

The primary purpose of this investigation was to determine the nature and characteristics of a class of large, weak ionospheric irregularities which in cer- tain circumstances significantly affect long-distance HF radio-wave propagation. ti further purpose was to determine the relative practical importance of the dif- fraction produced by these inhomogeneities, in relation to the influence of other mechanisms such as Faraday rotation and scattering by small irregularities.

Measurements of quasi-periodic variations in phase-path length have been made on a 2600 km one-hop lower-ray F-region path. Variations of 8 to 75 wavelengths are regularly observed during winter daylight hours. They have a quasi period of about 20 minutes. Correlations of measurements made at spaced receiver locations indicate that these variations in phase-path length are produced by irregularities having a horizontal scale size of about 35 km. Multiple frequency measurements show a vertical scale size of about 15 km, with a maximum in the lower F region, A lower limit of 65 m/sec is determined for the horizontal velocity of the irreg- ularities. A downward vertical velocity of 30 to 40 m/sec is observed. The irreg ularities limit achievable bandwidth and spatial resolution for one-hop HF iono- spherically propagated waves under quiet ionospheric conditions.

A model of the irregularities has been devised and has been used to predict the signal-strength fluctuations which would result from propagation through a medium described by the model. Two classes of signal-strength behavior are pre- dicted and observed experimentally, depending on the relative magnitude of the phase-path variations within the limits mentioned above. Signal-strength

DD /Ä 1473 j

Security Classification

-■ '- * .■. — -........ w.^„. .^■.-^^^.^.„..^...>.i.t.^...:^.,^,....-..t.,.....k.....,..^..-.^^^.»^,-,.J,.... /.„«.t, ,... - >..■,.-■■..,...:.^..-J.^^^.>^t^1^.,.^AL.

L- " M.wp/pppiippppippjpBJp^ ! ^^w^fww^'^^y>M.TW.^^W» ru-JWi i .1 !,uiiW^tWipiVM,W^^t!p;tlipffiM J^u.J|..^tiuW!i|WI»,wvi^

Security Classification

K F V W (j w o 5

FOCUSSING MULTIPATH SINGLE-MODE HIGH-FREQUENCY RADIO RAY-TRACING COHERENCE ANTENNAS

HOLE WT

ABSTRACT (Cont)

variations of a few dB, having a 20 min period, are observed when the changes in phase-path length are small, and are attributed to focusing caused by the irregularities. Larger, more rapid signal- strength fluctuations are also observed. These are attributed to multipath interference between several, ray propagating through the same irregularity. Taken together, these rays make up what would be identi- fied as the one-hop lower-ray F-layer mode, which i seen to be less homogeneous than had previously been supposed, for propagation over 2000-4000 km distances.

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