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Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1985

TROPO: a microcomputer based troposcatter

communications system design program.

Siomacco, Edward Michael

http://hdl.handle.net/10945/21592

DUDLEY KNOX LIBRARYNAVAL POSTG DUATE SCHOOLMONTEREY, CALIFORNIA 93943

NAVAL POSTGRADUATE SCHOOL

Monterey, California

THESISTROPO: A MICROCOMPUTER BASED TROPOSCATTER

CO^IMUNI CATIONS SYSTEM DESIGN PROGRAM

by

Edward Michael Siomacco

September 19S5

Thesis Advisor: J. B. Knorr

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TROPO: A Microcomputer BasedTroposcatter CommunicationsSystem Design Program

5. TYPE OF REPORT & PERIOD COVEREDMaster's Thesis;September 1985

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Edward Michael Siomacco8. CONTRACT OR GRANT NUMBER!"*;

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Naval Postgraduate SchoolMonterey, California 93943-5100

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Troposcatter; Over-the-Horizon Communications; Height Gain;Tropospheric Ducting

20. ABSTRACT (Continue on ravaraa elda II neceeeary and Identity by block number)

This thesis presents a microcomputer based, computer-aideddesign program for tactical military tropospheric scatter radiosystems. The program has the capability of predicting the systemperformance and reliability for both analog (FM/FDM) and digitaltroposcatter radiolinks. Propagation gain generated by elevatedtropospheric ducting is called height gain. A height gaincomputational model for specific elevated tropospheric ducts

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is derived from statistical radiosonde data. A terrainprofile plot, real-time radiosonde data analysis, andthe probability of error for digital radiolinks areprovided as program options.

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TROF'Q: A Microcomputer Based TroposcatterCommunications System Design Program

by

Edward Michael SiomaccoCaptain, United States Army

B.S., North Carolina State University, 1975

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOLSeptember 19S5

5

ABSTRACT

This thesis presents a microcomputer based,

computer-aided design program -for tactical military

tropospheric scatter radio systems. The program has the

capability of predicting the system performance and

reliability -for both analog (FM/FDM) and digital

troposcatter radial inks. F'ropagation gain generated by

elevated tropospheric ducting is called height gain. A

height gain computational model for specific elevated

tropospheric ducts is derived from statistical radiosonde

data. A terrain profile plot, real-time radiosonde data

=»nalysis, and the probability of error for digital

radial inks are provided as program options.

TABLE OF CONTENTS

I. INTRODUCTION 10

A. PURPOSE 10

B. BACKGROUND 11

C. RELATED WORK 13

II. TROPOSPHERIC PERFORMANCE CONSIDERATIONS IS

A. SCATTER PROPAGATION 18

B. TROPOSPHERIC DUCTING. 22

C. MULT I PATH CONSIDERATIONS 29

III. TROPOSCATTER SYSTEM DESIGN PROGRAM 35

A. GENERAL PROGRAM ALGORITHM 35

B. PREDICTION OF PATH LOSS 35

1

.

General 35

2. Bur-face Refract i vi ty. .................. 37

3. Effect i ve Earth ' s Radi us. .............. 39

4. Terrain Profile Plot

5. Calculation of Angular Distance 40

6. Diffraction Loss. ...................... 50

7. Worst—Hour Loss. 51

8. Aperture-to-Medi urn Coupling Loss. ...... 53

9. Combined Free-Space/Scatter Loss 56

10. Waveguide/Connector Loss 56

11. Absorption Loss..... 56

C. DESIGN PARAMETERS 58

1. Carrier-to-Noise Ratio 5S

2. Digital Radio Link Parameters 59

3. Probability o-f Error Calculations 60

4. Fade Margin and System Reliability 67

5. Diversity Requirements 71

6. Analog Radio Link Parameters 75

IV. HEIGHT GAIN MODEL DESIGN SO

A

.

GENERAL BO

B. MATHEMATICAL FORMULATION. S2

C. RADIOSONDE DATA ANALYSIS 85

7. RESULTS. 87

A

.

GENERAL B7

B. HEIGHT GAIN COMPARISON 37

V I . SUMMARY i 02

A. CONCLUSIONS. 102

B. RECOMMENDATIONS. 103

APPEND IX A 1 04

APPEND IX B 115

LIST OF REFERENCES. . 158

INITIAL DISTRIBUTION LI ST ............ 161

LIST OF TABLES

I

.

VOICE PERFORMANCE CHARACTERISTICS 32

II. RAYLEIGH FADING PROPAGATION RELIABILITY 68

III. ELEVATED DUCT HISTORICAL INFORMATION SI

IV. PROPOSED EXAMPLE SYSTEM SPECIFICATION SS

LIST OF FIGURES

1-1 Distortion Adaptive Receiver Performance 15

2-1 Scatter Volume Geometry 21

2—2 Tropospheric Duct . Descri pti ons 25

2—3 Propagation Effects of Ducts 27

3—1 Program "TROPO" Module Block Diagram 36

3-2 Monthly Surface Re-fractivity (Sea Level ) . 38

3—3 Linear Terrain Profile Plot Example 41

3-4 Terrai n Path Conf i gurat i ons ......... 42

3-5 Typical Path Geometry. . . 46

3-6 Common Scatter Volume Dimension. 43

3-7 Annual and Winter Monthly Standard Deviation... 52

3—8 Aperture—to—Medium Coupling Loss. ..............

3-9 Estimated Atmospheric Absorption. ..............

3-10 Probabi 1 ity of Error (BPSK/QPSK) ............... 62

3-11 Probability of Error (M-ary FSK) ..............

.

64

3-12 DAP Performance (Dual Diversity) ............... 65

3-13 DAR Performance (Quad Diversity) ............... 66

3-14 Approximate Interference Fading Distribution...

3-15 Short-Term Fading (Dual Diversity) .............

3—16 Short-Term Fading (Quad Diversity) 74

3-17 BNR Improvement from Diversity Techniques 73

3-18 Preemphasis Improvement -for FDM Channels 79

4-1 Height Gain Model Flowchart 84

5-1 Example System Design Specifications 90

5-2 Example System Terrain Profile Plot 91

5-3 Radiosonde Environmental Data Listing 92

5-4 M-Profile Plot (Surface Duct) 93

5-5 System Performance Results 94

5—6 Height Gain Model Comparison (Frequency Vary).. 96

5—7 Height Gain Model Comparison (Range Vary)...... 99

A-l Function F(#d) for N = 250 106s

A-2 Function F(0d) for N = 301 107s



A-5 Parameter N Ills

A-6 Frequency Gain Function 112

A-7 Correction Term for N = 301 113s

A-8 Adjustment Factor for Correction Term 114

I. INTRODUCTION

A. PURPOSE

The development of digital transmission techniques in

military communications systems has generated a renewed

interest in tropospheric scatter. Digital troposcatter

radio systems have required changes in the present

planning and engineering design methods. The military

design engineer has the responsibility to predict system

performance and reliability within limited planning

time. Under certain tactical situations, the urgency to

restore vital communications has -forced the engineer to

provide several alternative designs for a single

communications link. These requirements have justified

the need for an efficient, computer-aided design method

to accomplish the task. The purpose of this thesis

research is to develop a tropospheric scatter

communications system design program. The objective is

to design a mi crocomputer—based program which will

predict the path reliability and system performance for

troposcatter radiolinks. This program will introduce

several improvements over the manually generated,

nomograph-based design methods. Speci f i cal 1 y , the

program will estimate the height gain at the average

system antenna height -for specific elevated tropospheric

ducts. Other -features include a terrain pro-file plot,

radiosonde weather data analysis, and the calculation of

the probabilty of error for binary and orthogonal digital

signaling techniques.

B. BACKGROUND

Tropospheric scatter communications systems prdpagats

microwave energy beyond 1 i ne-of -si ght (LOS) or "over the

horizon" by taking advantage of the refraction and

reflection phenomena in a section of the earth's

atmosphere called the troposphere. Typical military

troposcatter systems use transmitter power outputs from 1

to 10 kW, parabolic type antennas, and sensitive

broadband FM receivers with front-end noise figures (IMF)

between 2.0 — 4.0 dB. These systems are most often

employed in military applications because of the limited

available channel capacity [Ref. l:pp. 253-2541. Several

system advantages are summarised as follows:

1. Fewer terminal and /or relay stations are requiredto cover the same transmission path as comparedto tactical microwave 1 ine—of —sight radi clinks.

2. Reliable multichannel communications can beinstalled across long distances of hostile orinaccessible terrain.

3. Standard transmission ranges are suitable for thetactical military -field environmemt -for radiolinksfrom 30 to 200 miles.

A fundamental design parameter for troposcatter links

is the allocation of allowable channel degradation to

each link making up the total communications system. In

analog scatter systems, the quality parameters ar& system

availability and si gnal -to—noi se ratio in the voice

channel. However with the deployment of digital

troposcatter radio systems the performance of the

digitized voice channels under fading conditions is

significantly different than the performance of analog

voice systems under the same conditions. The primary

measure of transmission quality for a digital system is

its error performance. There a.r& two main sources of

transmission errors: (a) long-term error rate which will

occur because of equipment degradation, channel

interference, and long-term power fading; and (b)

multipath fading CRef. 2: pp. 4-53.

C. RELATED WORK

1 . Performance Models for Troposcatter Links

Monsen CRef. 3D has derived performance models

for analog FDM/FM and digital quadrature phase shift

keying (QPSK) systems on troposcatter communications

links. The analysis included the effects of signal level

variations and multipath delay dispersion. His

performance criterion was the outage probability rather

than either average error rate or median signal-to-noise

ratio (SNR) values. Outage probability' performance in a

digital system was derived for two different modems: the

Deci sion—Feedback Equalizer (DFE) and a transmitter-

time—gating technique, the Distortion Adaptive Receiver

(DAR). Analog system performance was determined for the

percentage ' of the time that the voice channel SNR

including thermal noise and multipath delay dispersion

effects were below a specified threshold.

The performance test results for a Distortion

Adaptive Receiver (DAR) was presented in a paper by

Zawislan CRef . 43. The critical problem with digital

troposcatter is inter symbol distortion produced by the

multipath dispersion of the fading channel. To resolve

this problem, the distortion adaptive receiver was

; 3

implemented. The DAR modem employed DPSK modulation with

adaptive matched filter demodulation. A complete

functional description was explained in the reference.

The advantage to this approach was that it did not

require equalization at the receiver to correct

intersymbol interference and it provided near optimum

performance using the adaptive matched filter receiver.

Typical bit error rate performance for the DAR

on a troposcatter channel is shown in Figure 1—1 for

different values of rms multipath delay dispersion. For

low multipath spread, the fading on each diversity

channel has a Rayleigh distribution and the performance

is indicated by the "flat fading" marked curve. Note

that the performance improves rapidly with increasingcvj

multipath spread and, at a 10 error rate a 10 dB

improvement is achieved for multipath curve CBD. However,

as the multipath spread increases (with increased path

length), a irreducible error rate occurs as shown in

curve LCI due to the transmitter time-gate limitation.

To compensate for this problem, the DAR is modified by

utilizing a dual frequency pulse waveform. This

technique is also used in the modem employed by the

AN/TRC-170 tactical digital troposcatter radio set.

1 4

SINGLE PULSE DAR PERFORMANCE

1« 10 20

EB/NO (V6)

(DUAL EXPLICIT DIVERSITY)

Figure 1-1 Distortion Adaptive Receiver Per-farmance

(A-fter Zawislan, Re-f . 4:p. 3)

2. Tropospheric Elevated Duct Models

Several mathematical models have been developed

to calculate the ducted signal -field strength based on

the refractivity pro-file and by modeling the tropospheric

duct as a laterally homogeneous-layer atmospheric

waveguide CRef. 5: pp. 223. A detailed mathematical

analysis was presented by Marcus and Stuart [Re-f. 63.

These authors have developed an effective modal solution

computer program, called "DUCT", which requires a large

processing capabilty of a main—frame computer CRef. 73. A

version o-f this program, called "PDUCT", is available at

the Naval Postgraduate School Computer Center CRef. S3

and CRef. 5: pp. 23-24 3.

Weston CRef. 5: pp. 58-703 has proposed a

statistical model, based on "PDUCT" predictions -for

selected ducts o-f interest. The height gain data, -t-or

these ducts, was used to derive model coefficients.

These unique coefficients were stored according to their

respective transmitter and receiver heights in a matrix

form. Thus, given a receiver height and range from the

transmitter for a selected duct /-frequency data point, the

coefficients for each receiver height a.re obtained and

used to produce the corresponding height gain curve.

This approach required a significant number of main—frame

computer "PDUCT" computations to establish height gain

data for all the ducts of interest.

In December 1983, a microcomputer-based pro-

gram, called "MINI DUCT" Version 1.1, based on Knorr's

mathematical model was developed by Nagel , CRef. 93, at

the Naval Postgraduate School to calculate elevated

ducted signal levels at various frequencies. This

program used either historical radiosonde data or current

elevated duct information CRef. 103. The radiosonde data

represented the atmospheric temperature, pressure, and

humidity at specific altitudes over a five year recording

period. This model was valid for the case where the

transmitter is at the optimum duct coupling height and

the receiver is located either below, within or above the

duct. The optimum coupling height is the altitude above

the surface where the gradient of the modified refractive

index becomes negitive.

II. TRDP05HERIC PERFORMANCE CONSIDERATIONSW^———————^—^1^-^— II ! ! «———li—

A. SCATTER PROPAGATION

1

.

General

At -frequencies above 30 MHz three propagation

mechanisms can carry energy beyond the horizon: (a)

variations in the refractive index in the troposphere can

scatter radio energy, (b) horizontally-stratified abrupt

changes in the refractive index can cause reflection, ana

(c) atmospheric regions of negitive modified refractive

index gradients can introduce ducting. Refractive index

and tropospheric ducting will be thoroughly discussed in

the following section. The forward scattering of radio

signals is the most dominant propagation mechanism at the

frequencies of 0.3 to 10 GHz. CRef . lisp. 13

2. Received Scattered Field

The index of refraction depends on pressure

,

humidity, and temperature. Slight variations in these

quani t i t i es ,, caused by atmospheric turbulence, will

produce random fluctuations in the refractive index. When

an electromagnetic wave propagates through this

i nhomogeneous medium, energy will be scattered out -from

the original incident direction. The

turbulent-scattering theory, CRef. 12:p. 345], has shown

to a -first approximation that the index o-f re-fraction

-fluctuations can be replaced by a model of so—called

"blobs", i nhomogenei 1 1 es o-f di-f-ferent dielectric

constants randomly distributed. I-f these "blobs" are in

the common volume -formed by the transmitter and receiver

antenna beams, the complex received -field can be

described by CRe-f. 13:p. 1463:

Re j*= Ta. e^i*— x (2-1)1 = 1

where m is the number of "blobs" in the scattering

volume, A is the amplitude, and <f> is the phase of a

J J

wave scattered by a single "blob". Assume m to be very

large and the blobs are spherical and uniformly

distributed through the scattering volume. Then the

phase difference of the waves scattered by the

i nhomogenei ti es at the top and bottom of the volume will

be CRef. 13: p. 1473:

A<J> =4 " h sinV (2-2)

19

where y = transmitter, receiver antenna elevation angle

h = mean thickness of the scatter volume (m)

A = transmitter wavelength (m)

The variables in Equation 2-2 are described in Figure 2-i,

By observing the volume geometry, it can be determined

that more "blobs" exist in the central volume region than

at the top or bottom. This indicates a non-uniform

"blob" distribution.

Many phase variations wi 1-1 occur over many

phase cycles of length 2n . The antenna elevation angle

will be less than 2 degrees -for most systems and the

ratio o-F scatter volume thickness to operating wavelength

will be very large. These conditions make the scattered

phases uniformly distributed from zero to 2 n

CRef. 13:p. 14S3.

The amplitude distribution will now be deter-

mined. The real and imaginary components of the complex

received field, Equation 2-1, were resolved into two

random variables X and Y. The number of blobs, m, is

assumed to be large, so by the Central Limit Theorem,

both X and Y will approach a normal "gaussian"

d i st r i but i on . Finally it was shown that these var i ab 1 es

Transmitter

g*;^«»îHMîfl*âûfflMHi*^^

Figure 2-1 Scatter Volume Geometry

(After Beckmann, Re-f . ll:p. 147)

21

are also uncorrel ated and independent. Then their

two—dimensional normal distribution can be trans-formed

into the Rayleigh distribution.

Turbulence, mixing, and wind continuously

change the positions and structure of the i nhomogenei ti es

making the random terms o-f Equation 2-1 functions of

time. The reality of nature is the i nhomogenei ti es do

not vary i sotropi cal 1 y because the index of refraction

changes more rapidly with altitude than with distance.

There can also be a stratification or layering of

i nhomogenei ti es near a particular height (or heights)

that changes the assumed spherical shape of the so-called

"blobs". Under these conditions the uniform phase

distribution may change to an unknown distribution.

B. TROPOSPHERIC DUCTING.

The index of refraction, n, of air is defined as

the ratio of the velocity in a vacuum of electromagnetic

(EM) radiation to the velocity in the medium. A

convenient parameter is ref r act i vi ty , N, defined as

CRef. U:p.l4D:

N = ( n - 1 ) X 106

(2-3)

Another parameter called modi-fied re-f ract 1 vi ty , M, is

de-fined as [Ref. 10:p.9D:

M = N + 0.157 h (2-4)

where h is the altitude in meters above the surface. The

modi-fied re-f racti vi ty accounts -for the curvature of the

earth so the presence of ducting can be easily determined

by observing the M-gradient on the M versus height plot.

Refraction of incident radio waves across a

discontinuity of refractivity is described by the

principles of Snel 1's Law. It is important to remember

that the wave "bends" towards the higher value of

refractivity, and the more dense a material the higher

its n. Since the density of the atmosphere decreases

with height, we expect that a wave will bend back

downward from a geometric straight path. Whenever the

refractive index decreases sharply with height,

radiowaves can be trapped and experience low-loss

propagation -for long distances. This condition is known

as tropospheric ducting CRe-f. ll:p. 29].

The following conditions must be satisfied for a duct

to occur: (1) the modified refractive index gradient

shall be equal to or more negitive than M-units/km, and

(2) this gradient should continue over a height of many

wavelengths, The important duct parameters are the duct

thickness, D, the intensity, M, and the optimum coupling

height, H . A piecewise linear approximation to theopt

madi-fied refractivity (tri-linear) profile -for several

types of ducts are shown in Figure 2-2. There are three

types o-f ducts: (1) surface or ground-based ducts, also

called evaporation ducts when formed over water, Figure

2—2a; (2) surf ace—based ducts from elevated refractive

layers, Figure 2-2b; and (3) elevated ducts from elevated

refractive layers, Figure (s) 2-2c and d. Note that all

positive M-gradients are assumed at 118 M-uni ts/km which

corresponds to a standard atmosphere. Once the slopes

are identified, the important duct parameters are quickly

determined CRef. 9: pp. 8— 123.

Tropospheric ducts more often occur as ground—based

ducts because of both. evaporation and advection.

Evaporation of water vapor from the surface of the sea

may create a zone of high humidity (i.e. high refractive

index) below a region of drier air. Advection, defined

as the movement of one air type over another, may cause

hot dry air (from the land) to be blown over cold wet

air, producing a region of low refractive index above a

region of high refractive index. Such a duct may also

i

(a) (b)

/

•M /co

/o> 1 T 1

Ah \\ \

D I

-)--r(1 '2)D = Ah >

i

S^_ / ?-—JamU- —-IamL-

(q) Ground- based loyer, (b) Elevated layer,

Ground-based duct Ground- based duct

—JAN'U- —J AW' U-

(c) Elevated loyer,

Elevoted duel

( d ) E levated loyer onddud approximated with

on M - discontmui t y .

Figure 2-2 Tropospher i c Duct Descriptions

(A-fter Marcus, Re-f . 7: p. 2-5)

form when warm dry air is blown over cold ground.

Radiation cooling can produce temperature gradients which

cause ground-based ducts. Air next to the ground becomes

cooler and the duct becomes thicker as the night

conti nues.

When morning solar heating warms the air next to the

ground, a region of rapid decrease o-f refractive index

with height produces an elevated duct. However these

ducts quickly disappear because continued ground heating

increases convection mixing and destroys the stable

elevated layer. Elevated ducts may -form -for several days

by a subsidence inversion. Hot air rises at the center

of a high pressure region and spreads out horizontally,

cooling as it slowly descends. This produces a boundary

with the slightly colder air near the surface. The

increasing temperature with height at the boundary forms

the subsidence (temperature) inversion. Changes in

temperature and/or humidity may cause related changes in

the refractive index within the boundary interval

CRef. il:pp. 33-353.

Figures 2—3a thru d illustrate propagating rays

within ground-based ducts. Rays leaving the transmitter

at elevation angles close to the horizontal will parallel

the earth's surface, while other departing ravs 'will

Figure 2-3 Propagation Effects of Ducts

(After Hall, Ref . 9:p. 31)

77

either travel upward or downward. If the li—gradient is

negitive and assumed uniform within the duct, rays

beginning at elevation angles below the critical angle,

defined as CRef. ll:p. 31D:

= \(2 Am X 10' 6)

(2-5)c

will strike the surface, and those above the critical

angle will leave the duct. If ground reflection is

neglected, Figure 2-3a, a shadow region depicts minimum

propagated energy. In the case where surface

reflectivity is high, Figure 2-3b , the rays launched

within the critical angle range will travel beyond the

radio horizon. Figure 2-3c decribes the situation when

the M-gradient is not constant within the duct. If a

transmitter is positioned in the height region h , then

rays within the + 0, = - J(2 AM, X 10 ) range will

remain in the duct with bounces as depicted in Figure

2-3b. Similarly rays transmitted within

the + q^ = - ti(2 AM X 10 ) range are trapped within the

height range h . Finally a surf ace—based duct from anb

elevated layer over rough terrain is illustrated in

Figure 2-3d. In this case the refractive "bending" takes

place at the top of the duct CRe-f. ll:pp. 30-32D.

28

For elevated ducts -formed by advection or subsidence,

the position of the transmitter and receiver relative to

the optimum coupling height, H will influence theopt

propagation effects. The means in which energy enters or

leaves an elevated duct can be described by the duct

acting as a "leaky" waveguide. Energy is "leaked" or

coupled into the duct from the transmitter, and "leaks"

out as the energy propagates along the duct

CRef. 11: p. 36 3.

Because of the non-permanent characteristic of

elevated ducts, their effects a.r& seldom an influence to

troposcatter links, especially if they form above the

common scatter volume. But the presence of tropospheric

ducts can degrade the overall performance of troposcatter

systems by changing the predicted transmission loss. The

term that will change the total path loss is the duct's

height gain, which is derived in Chapter IV.

C. MULT I PATH CONSIDERATIONS

The multipath fading model for a tropospheric scatter

channel produces received signal fading. The received

signal consists of the sum of a large number of

time—variant , complex vectors having amplitudes and

phases. The fading is caused by randomnly time—variant

phases variations. At times the received signal vectors

add destructively to decrease the mean received signal

amplitude. While at other times, the vectors add

constructively, so the received signal is large. Thus

the amplitude variations, or signal -Fading, s.re due to

the multipath characteristics of the tropospheric

channel. The channel can be modeled as a zero mean,

complex-valued gaussian process, with the envelope ot the

instantaneous signal level being Rayl ei gh-di str i buted

.

This Rayleigh -fading channel describes the short-term

fading. When there ^re fixed constant regions of

refractivity or stratified refractive layers in the

vicinity of the common scatter volume the channel cannot

be modeled as having a zero mean. In this case, the

Rayleigh distribution does not apply and the channel

approaches a Rice distribution CRef. 14:pp. 456-4583. All

performance predictions in this study will assume

Rayleigh "short-term" fading as the channel model.

Channel performance will be degraded during periods

of severe multipath fading. With digital systems, the

voice user is unaware of any increase in background noise

until the PCM (Pulse Code Modulation) outage threshold is

broken. Once this threshold is passed the complete

multichannel circuit will be unusable due to noise. The

characteristics of fade outages for a typical digital

troposcatter circuit can experience three (3) primary

categories of fade outage. The first category occurs

when the voice user is subjected to a single fade outage

of duration less than 200 milliseconds. This outage will

be hardly noticed. The second category of outage will

have an outage duration ranging from 1/5 second to 5

seconds. The user will detect this distortion but will

continue to communicate following the outage. When a

recurrence of short duration outages take place (e.g. 2

to 4 outages per minute) annoyance rather than total

disruption will occur. The third category are fade

outages that exceed a subjective level of user patience.

The Defense Communications Agency (DCA) CRef. 153 has

specified five (5) ranges of fade outage conditions,

refer to Table I . DCA has defined the fade outage in

terms of a diversity signal-to-noise ratio threshold-4

corresponding to a 10 bit error probability.

Techniques used to counter multipath propagation are

frequency diversity, space diversity, amplitude

equalization, and channel equalization. If a modulated

signal is simultaneously transmitted over the same

troposcatter radiolink on two or more frequencies, the

correlation between the individual received signals will

31

TABLE I

VOICE PERFORMANCE CHARACTERISTICS

FOR

DCS TROPOSCATTER LINKS

Outage Range Criteria Outage Probability

I See Note See Note-4

II 0.2 sec.< Outage <5 sec. 7.5X10-5III 5 sec.< Outage <1 min. 7.5X10-3IV 2 < Outages/min. < 5 2.5X10-4V 5 < Outages/min. 1.0X10

NOTE:

Range Voice Performance Description

I Outages with adeguate -fade margin,II Outages with adequate -fade margin

and high -frequency o-f occurrence.III Call disruption possible.IV Marginal -fade margin.V Unavailability of circuit.

be small. This method of signal diversity is called

frequency diversity. The important advantage of

•frequency diversity is that it requires a single antenna

at each site. But the need -for additional frequencies

can increase the probability of co-channel interference

among other operating transmitters.

Uncorrelated short—term fading can also be achieved

by separating the receiving antennas in space. This is

known as space diversity. Horizontal and vertical

polarization can "be used to distinguish between two

space—separated signals. However horizontal and vertical

polarization do not provide a satisfactory degree of

noncorrel at i on of signal fading for efficient diversity.

The multiplicity of signals provided by these

diversity methods must be combined. The

diversity—combining techniques ar& classified into: £1)

selection or switching; (2) combining a desirable

weighted combination of received available signals; and

(3) a combination of selection and combining.

In the selection techniques the diversity channels

a.ria scanned until one is found whose level exceeds a

selected threshold. This may not necessarily select the

best available signal. In the combining techniques, all

diversity channels are simultaneously monitored and

equally weighted. This is called equal—gain combining.

In max imal -rati o combining, the weighting -factor o-f each

channel is automatically adjusted to yeild the maximum

signal-to-noise ratio -For the total o-f all the diversity

channels CRe-f. 12: pp. 453-454 3.

Amplitude equalizers a.re designed to properly

equalize the propagation channel for minimum phase

•fading. Channel equalizers balance the channel -for

amplitude and mutlipath delay distrotion. They are

typically adaptive transversal equalizers that consist of

tapped delay lines (TDD with tap-weight multipliers

(i.e., amplifiers or attenuators); and control circuitry

that adapt ively vary the tap-weights in response to

temporal channel variations CRe-f. 16:p. 11 — 123.

III. TRQPQSCATTER SYSTEM DESIGN PROGRAM

A. GENERAL PROGRAM ALGORITHM

The main program, named "TROPQ", is presented as

Appendix B. Figure 3-1 illustrates the program -flow and

the primary computational program modules. The program

development and mathematical approach -for the Radiosonde

Data Analysis and Height Gain modules are described in

Chapter IV. The remaining modules are formulated in this

chapter. A program tutorial and compilation instructions

are contained within the program.

B. PREDICTION OF PATH LOSS

1 . General

The basic median transmission loss will be the

sum of several additive losses, expressed in decibels,

CRef. 173:

LrT=L +L

3+ L +L + L - G„ - G +HG (3-1)Tsdcawtr

where L = free-space propagation/scatter loss (dB)s

L = knife-edge diffraction loss (dB)d

o<

e.

u u

zo -

o

X

Figure 3-1 Program "TROPO" Module Block Diagram

L = medium-to-aperture coupling loss (dB)c

L = atmospheric absorption loss (dB)a

L = waveguide/connector loss (dB)M

G = transmit antenna gain (dB)t

G = receive antenna gain (dB)r

HG = height gain (dB)

2. Surface Re-f r act i vi ty

An adjustment to the average surface refrac-

tivity N , refer to Figure 3-2, is made for the elevationo

at each terminal site. The adjusted surface

ref racti vi ty, N , is CRef. 18:p. 2-12J:

N = N exp(-0 .03222h )(3-2)so s

where N = minimum monthly average refractivityo

h = average antenna height (kft)

If the surface refractivity at each site is significantly

different, an option to calculate the respective N fors

each site can be selected and an average path surface

refractivity can be calculated. The average antenna

height is calculated by averaging the transmit and

receive antenna heights.

•7

o o o o o o o03 ^ CD iD T rO (VI

« Z O <r> 2

gg

o o ooo o o

TT ETTuiVr

ss^ss JL1

1

L£ ME4$H1«« / /;

rT ii\

I i ^QMIIIi^^S 1 -"I '' iji!

-HM "S

,

V"T

Jx^^U'l" rsirH

JSUTrtTJL '\ \

1\

' sj_\_

vV,ifA i /!

Figure 3-2 Monthly Surface Re+ractivity (Sea Level)

(After Panter, Re-f . 12:p. 375)

33

3. Effective Earth's Radius

Changes in the surface re-f racti vi ty will effect

the radio-ray path curvature as the wave propagates over

the earth. To accurately represent the ray-path an

effective earth's radius is calculated as

[Re-f. 12:p. 37411:

a = a 1 - 0.04665 exp(0.005577N )

-1(3-3)

where a = actual earth's radius (6370 km)o

4. Terrain Pro-file Plot

. Several methods are available to plot a«

troposcatter system terrain pro-file. The most

fundamental method is to plot the successive path terrain

elevations along the great circle path. Special 4/3

earth plotting graph paper is required -for this method.

Alternatively, computer graphics technigues which obtain

terrain information -from topographical databases, can

rapidly plot the profile.

The program provides a dot-matrix printer plot.

The terrain profile is linearly plotted by modifying the

terrain elevations, in meters, to include the effect of

39

the average curvature o-f the radio-ray path and the

earth's surfave. Elevations, h , o-f the terrain arei

manually obtained -from topographical maps and tabulated

versus distances, x , -from a selected referencei

terminal. The terrain data points are keyboard entered

into the program. The modified elevations are computed

as CRef. 12: p. 380 3:

x2

y. = h. - (3-4)2a

where a = effective earth's radius (Equation 3-3)

Figure 3-3 illustrates a typical linear terrain plot.

5. Calculation of the Angular Distance

The terrain profile can now determine various

path geometries. The three (3) path configurations

considered arez

a. Smooth Earth Horizons at Both Terminals

b. Obstacle Horizons at Each Terminal

c. Smooth Earth and Obstacle Horizons

The terrain geometries are depicted in Figure(s) 3-4a,

3-4b , and 3-4c. The respective terminal take—off angles

are calculated -for the predicted path type as

CRef. 12:pp. 385-3373:

40

Figure 3-3 Linear Terrain Profile Plot Example

(After Panter, Ref . 12:p. 382)

41

^Xj*

V*."V^-t^,0

a -v/ >^\ ^d-d -d,"~~~-^ y^ (J

v ?\y\ \*^-**^ It lr -a £\ /

\^- -J<£ \ \4^*vv dlt \

dlr S *

Figure 3-4a Smooth Earth Path

(After Ranter, Re-f . 12:p. 385)

42

Figure 3-4b Near Obstacle Path

(After Panter, Re-f . 12:p. 386)

^-\/ 8

hit Vc^T^

««\V // \ /

^"/x \/ X 4

\ \\ \

/

/

/

yv*

\ \ / y\ \ / x\\ 1/

Figure 3-4c Near Obstacle/Smooth Earth Path

(After Ranter, Re-f . 12:p. 385)

44

a. Type I Radio Horizon/Radio Horizon

fi*\:et

= : <3-5a>

f

where h , h = transmitter, receiver terminal elevationts rs

b. Type II Obstacle Horizon/Obstacle Horizon

It ts It

d 2a (3-5c)

h, - h d,lr rs lrOer " ~ (3-5d)

d, 2alr

where h ,d = transmitter obstacle el evat 1 on , di stanceIt It

h ,d = receiver obstacle elevation, distancelr lr

c. Type III Obstacle Horizon/Radio Horizon

= (Same as Equation 3-5c

)

et= (Same as Equation 3-5b)

erThe path type combination may be reversed to satisfy a

Radio Horizon/Obstacle Horizon configuration. Referring

to Figure 3-5, the angles a and R are calculated as:^ oo h oo

S3 B

CM

Figure 3-5 Typical Path Geometry

(After Ref. 18:p.8-6>

46

oo 2a

h. - h-±E Ef + 6 (3-5e)et

P oo 2a

rs ts+ ; + 6>er

<3-5f

)

These angles are modified by correction factors, Aa and

A/3 to allow for the effects of a non—linear

refractivity gradient CRef. 12:p. 3833. The correction

factors can be obtained from Appendix A, Figure A-7,

however for most transhorizon, "over the horizon", paths

these factors are negligible.

The angular distance (often called scatter

angle) is:

w oo a o *oo o (3-5g)

The ratio a OQ and fi co defines the path symmetry factor

CRef. 18:p. 4-7]:

S =a oo

(3-5h)oo

The -following equation will calculate the heigth of the

intersection point of the transmit and receive antenna

beams. This result will estimate the bottom of the

common scatter volume (Refer to Figure 3-6) as

47

Figure 3-6 Common Scatter Volume Dimension

(A-fter Du Castel , Re-f . 19:p. 145)

43

CRe-f. lS:p. 8-8D:

s ad

(1 + S)<3-5i

)

where S = symmetry factor

Du Castel , CRe-f. 19:p 146], approximates

the dimensions of a typical common scatter volume. The

volume height is:

H = 2hh ~ Qo

= 0.3h <3-5j)

where 6 = 1. 150,

6 = scatter angle«

The maximum longitudinal dimension, L, is:

d H

L = = 0.15d2 h

o

<3-5k)

where d = great circle path distance (m)

The center of gravity of the scatter volume is

approximated as:

H = h + 2/3Heg o

(3-51

)

49

6. Pi f fract 1 on Loss

Propagation paths having a common obstacle

horizon, such as a mountain ridge, can be referred to as

an obstacle gain path. It is assumed that the obstacle

will introduce additional path attenuation. However, the

angular distance may be reduced because of the changed

path geometry from the obstacle. The passible reduction

in the scatter loss may be offset by the increased loss

due to diffraction over the obstacle. In some situations

the common obstacle may be visible to both terminals, and

the path loss might be less than the smooth earth path

loss. The International Radio Consultative Committee

(C.C.I.R.) • has developed the following formula for

diffraction loss relative to free—space CRef . 20:p. 1703:

Ld

= 201og1( _V^y-

d + d, ) tan 9 . tan Qa b et er (3->t,di

)

where d = transmitter to obstacle distance (m)

a

d = receiver to obstacle distance (m)

bWhen the take-off angles ar^ less than 10 degrees and

d is greater than 2b then Equation 3-6a can beb aapproximated by:

DU

Ld

= 201og1()

TTdJ- (3-6b)

7. Worst-Hour Loss

Seasonal annual -to-worst month path loss

variations can be determined from a knowledge of the

annual changes in surface refractivity of the atmosphere

over the path. The C.C.I.R. recommends a loss variation

of 0.2 dB (U.S.) and 0.5 dB (Europe) per unit change of

refractive index.

The worst-hour median loss can be derived by

assuming a log-normal distribution during the month. It

was shown by Panter , CRef. 12: p. 401], that on a

log-normal distribution, the 99.9 percent point can be

approximated by the value 3.1<7 in decibels below the

median, where a is the standard deviation of the

log—normal distribution. The worst—hour median loss can

be determined as:

Worst-Hour Median Loss = Median Annual Path Loss

+ Difference of Annual -to-Worst-Month Median Loss

+3.1 o wm

where a = standard deviation of the worst-monthwm

oSTANDARD DEVIATION CURVE 1

a2O5-gQQ <•-

OS

az6-

!

:.

:. ... ->.V ;.. -•-••

LEGENDa ANNUALo WINTER MONTW

•*

" '*."* — * * ;*

f:rf44iTtt

<1 It 38 57 79 M 114 13

ANGULAR DISTANCE (MRAD)

1

Figure 3-7 Annual and Winter Monthly Standard Deviation

(After Ranter, Ref. 12: p. 359)

distribution obtained -from Fiqure 3-7.

8. Aperture-to-Medium Coupling Loss

The parabolic reflector microwave antenna

gain equation, CRef. 12: p. 103], can be expressed in

decibels as:

G = 20log1Q

f + 20log1()

D - 52.6 dB (3-7)

where D = aperture diameter (feet)

An illunimation factor of 0.54 was assumed to derive

Equation 3-7. It would appear that Equation 3-7 depicts

an ever increasing power gain as the antenna aperture

area increases. However the power received by an antenna

does not increase linearly with an increase in antenna

diameter, D. This effect is called aperture-to-medi urn

coupling loss or loss in antenna gain CRef. 12:p. 362].

Aperture coupling loss in troposcatter systems

is caused by a non-planar wave-front due to atmospheric

irregularities, and a geometric effect due to the

decrease in the scattering properties with height inside

the scatter volume. An incoming wavefront consists of

many plane waves, each arriving at a different angle from

the scatter volume. If the arrival angle range variation

is much smaller than the antenna beamwidth the wave-front

will appear nearly plane. If the common volume is much

wider than the receiving antenna's beamwidth a wider

angle range will result, and the wavefront will appear

non—planar

.

Basically, coupling loss can be explained as

limited antenna pickup, as compared to the effective

scatter volume dimensions and the antenna 3 dB

beamwidth. Figure 3-8 compares aperture coupling loss

results between several authors. A unique constant curve

is presented by the C.C.I.R. CRef. 21:p. 1452. This curve

is independent of the scatter angle and is written as:

L = 0.07exp 0.055(GT

+ G )| (3-8)

where G ,G = transmit, receive antenna gain (dB)T R

This empirical formula gives a high coupling loss and

will not be used in the program. The proposed empirical

curve appears as the average of several different

formulas and will be used as a conservative estimate for

the aperture coupling loss.

Figure 3-3 Aper ture-to-Medi urn Coupling Loss

(After Levin, Ref . 21)

9. Combined Free-Space/Scatter Loss

Yeh, CRef. 221 , has derived the following

-formula to calculate the combined -free-space and scatter

loss, in decibels:

Ls

= 30log1Q

f + 201og1

d + 100 + 0.2(N^ - 310) + 57<3-9)

where -f = operating frequency (MHz)

d = great circle path distance (miles)

6 = scatter angle (degrees)

N = surface refractivity5

10. Waveguide/Connector Loss

The waveguide attenuation factor was derived

for standard rigid waveguide. At an operating frequency

of 4.5 GHz the waveguide loss will be approximately 1.25

dB per 100 feet CRef. 18:p. 7-14]. Each waveguide

connection will introduce an additional 0.06 dB per joint

CRef. l:p. 2 10 J.

11. Absorption Loss

Rainfall, snowfall, and fog produce atmos-

pheric absorption loss which depends on the amount of

moisture and on the frequency. Figure 3-9 was used to

^j£>

<?!

<£ 1^&v*>^

4&

\S

y2D 2.6 35 5.0 6.0 7.5 10 12 15

Frequency (GHz)

Figure 3-9 Estimated Atmospheric Absorption

(After Re-F. 18:p. 2-43)

estimate the rain-fall attenuation on a particular

transmission path at four (4) rainfall rates

CRef. 18:p. 2-433.

C. DESIGN PARAMETERS

1 . Carr i er-to-Noi se Ratio

The performance of troposcatter communica-

tions circuits are determined by the minimum acceptable

ratio of hourly median carrier signal to thermal noise

for a type of modulated signal. This ratio, expressed in

decibels, is called the carrier-to-noise ratio (CNR). The

following equation is used to determine the received

carrier power level:

P (dBW) = P (dBw) - LT(dB) (3-10)

where P = transmitter power output (dBW)t

L = total median transmission loss (Equation 3—1)T

The receiver noise threshold level is written as:

p. (dBW) = -20 4 (dBW) + NF(dB) + 101og10

BIp

<3 in

where -204 dBW = thermal noise constant

NF

B

= receiver noise -figure (dB)

= receiver IF bandwidth (Hz)IF

Finally the carrier-to-noise ratio, [Re-f. 10:p. 4113,

1 s:

CNR(dB) = P (dBW) - P (dBW)r n (3-12)

where CNR carr l er-to-noi se ratio (dB)

P = received power level (dBW)r

P = receiver thermal noise level (dBW)n

2. Digital Radio Link Parameters

In digital systems the modem performance is

usually plotted versus average bit energy, E , to theb

receiver noise spectral density, N . The probabilty ofo

error (often called bit error rate) will be determined

from the E /N ratio. The transformation of theb o

calculated carrier-to-noise ratio (CNR) to E /N isb o

written as CRef . 23:p. 15SD:

E,/N = CNR(dB) + 101og 1n B - 101og 1n Rb o 10 w 10

(3-13)

where B = transmission noise bandwidth (Hz)w

19

R = transmission data rate (bit/sec)

3. Propability of Bit Error Calculations

Current military multichannel communications

use Pulse Code Modulation/Time Division Multiplexing

(PCM/TDM) techniques to transmit digital in-formation over

both -frequency modulated (FM) and phase modulated (PM)

troposcatter carrier systems. The quality o-f the

multiplexed circuits is determined by the number o-f bit

errors that occur because o-f the channel -fading and

multipath dispersion. The probability o-f bit errors can

be predicted -for different PCM carrier modulation

methods. Multiphase signaling and M—ary orthogonal

signaling over a Rayleigh -fading channel are derived by

J. G. Proakis CRef. 14:pp. 490-4991.

The bit error rate (BER) -for QPSK (-four-phase phas<

shift keying) and DPSK (differential phase shift keying) i

expressed as:

L - 1

Pb " "J 1 -

V"2 - M'

k =

2k

k 4-2ji(3-14)

where ^ = correlation coefficient

M =

1 +

(for coherent PSK)

60

H = — (-for DPSK)1 + vy c

where y = average received E /N per channelb o

y^ = average received E /N per bitb o

h =L Tc

J

where L = order of diversity

j = 1 (for BPSK signaling)

j = 2 (for QPSK signaling)

Bit error probabilities are depicted in Figure 3-10 for

two-phase and four-phase DPSK signaling with L = 1,2 and 4.

Orthogonal signaling may be viewed as M-ary

FSK (Frequency Shift Keying). The expression for the

probability of symbol error (P ), derived by Proakis,M

assuming no diversity (L = 1) is:

PM

/m-i\

i J 1 + m + m y nm=l c

M-(3-15)

where M = 2 (for BPSK signaling)

M = 4 (for DPSK signaling)

The equivalent bit error rate (BER) can be computed using

k-1

P = i )p

61

—BBS

RAYLEIGH CHANNEL PERFORMANCE(BPSK'/QPSK)

b V •.:

V'i !

LEGENDRAYLEIGH FADING (L=l)

"DUAL DIVERSITY "(1=2)QUAD DIVERSITY Tt^4

C-J\i \

1

l\\!-

oX.

: v \

Ul-V-k

fc-

5u.o>-

1 \x

\\

M » j ; A \< 1

ea co -asa.

: : \

'

'

\

""V"

\1

\

«> \ i\ \

i

1 I

\\

\

\

e \\

\-5.0 10.0 15.0 20.0 25.0 30.0 35 40.0

ED/NO (D3)

. jravy-^jy-rera;^^^^

Figure 3-10 Probability of Error (BPSK/QPSK)

(After Proakis, Re-f. 14:p. 492)

£2

where k = log M•->

The graphs of P versus E /N for M = 2, 4 and L = 1,

M bo2, 4 are shown in Figure 3—11-

The Distortion Adaptive Receiver CDAR] is

currently being used in the military troposcatter digital

radio set, AN/TRC— 170. Experimental modem performance

results are illustrated in the BER versus E /N curves,b o

Figure(s) 3-12 and 3-13. The results are determined for

three (3) different multipath delay values.

Sunde, CRef. 24:pp. 144-2143 has derived a

general expression for the maximum differential

transmission delay. This equation is valid when the

transmitting and receiving antenna beamwidths are

di f f erent

:

8= - e

2f e

et- + e

er,0_

4(3-17a)

where d = path distance (meters)

" = scatter angle (mrad)

6 = transmitter take-off anqle (mrad)et

6 = receiver take-off angle (mrad)er

The time dispersion (multipath spread) relative to the

RAYLEIGH CHANNEL PERFORMANCE(M=2 ORTHOGONAL SIGNALING)

b*

CAOOSOSu— nO i

"

03 -

3 ">•

EhO>

5t_-

<ao0£0.

o

,

orH

O

¥l1 !:#: i

i kvk;1 l\N hi j \; 1 ;....

1 ! \ \\ i

11 MM

i

V! K\l l\

LEGENDRAYLEIGH FADING (L=l)

"TJDaITDIVFRSITY (L=2)_5i;sirDivERsm'ir=4i

—

n0.0 1.0 10.0 15 20.0 25.0 30.0 3!

EB/NO (X>Q)

i.O

Figure 3-11 Probability of Error (M-ary FSK)

(After Proakis, Ref . 14:p. 499)

64

PERFORMANCE OF DUAL PULSE DAR

18.0 20

EB/NO (DB)

(DUAL DIVERSITY L=2)

24.0 28.0 J2.0

Figure 3-12 DAR Performance - Dual Diversity

(A-fter Zawislan, Ref . 4: p. 4)

on

PERFORMANCE OF DUAL PULSE DAR

cX

S3

EhO *i

i

>• -

23<23O

04.0

TT

LEGEND0.29XE-6 SEC

~T3T3fXE-~B~5EC~~~0T019XE^6~5~£~C~

e.o 12.0 16.0

ED/NO (DB)

(QUAD DIVERSITY L=4)

20.0

Figure 3-13 DAR Performance - Quad Diversity

(After Zawislan, Ref . 4:p. 4)

66

average time delay for unequal antenna beamwidths is:

5 5\= = 5 <3-17b>

2c 2(3X10 m/s)

8where c = 3X10 m/sec

In the case of equal transmitting and receiving antenna

beamwidths, Equation 3— 17b is simplified to:

3d#2

A = (3-17c)16c

For a particular order of diversity, the probability of

error can be computed for the AN/TRC— 170 troposcatter

radiolink by evaluating a -least-squares polynomial

equation derived from experimental data curves.

4. Fade Margin and System Reliabilty

The system fade margin, in decibels, is the

difference between the "practical threshold" level and

the median received signal level. The propagation

reliability values for the worst fading condition,

Rayleigh fading, can be compared with their required fade

margins in Table II CRef l:p. 2253. The "practical

threshold", or minimum acceptable received signal level,

cannot be below the FM improvement threshold

TABLE II

RAYLEIGH FADING PROPAGATION RELIABILITY

Single HopPropagat 1 on Reliability Fade Margin

C/.) (dB)90.0 899.0 1899.9 2899.95 3399.99 3899.999 48

>S

[Ref. 25:p. 71]. The -fade margin can be evaluated by:

Fade (dB) = P (dBm) - N (dBm) (3-18)

where N = "practical noise threshold"P

N = P (dBm) + FM improvementP n

P = -174 dBm + 10 log B + NFn 10 IF

W. T. Barnett and A. Vigants of Bell Tele-

phone Laboratories, [Ref 25: pp. 59-60], have developed an

empirical method to determine the nondiversity annual

path availabilty. Barnett 's procedure begins by defining

U as the nondiversity annual outage probability and r

ndpas the fade occurrence factor:

actual f ade probabi 1 i tyr = Rayleigh fade probabilty

If F is the fade margin in decibels:

actual fade probabi 1 tyr =

For the worst month:

-F/1010

r = a x 10m

-5(3-19)

where d = path length (statue miles)

L. CD

f = -frequency (GHz)

F = -fade margin (dB)

a = 4 (for smooth earth, over water, flat desert)

a = 1 (-for average terrain with some roughness)

a = 0.25 (for mountainous terrain)

Considering the annual fade occurrance:

r = br (3-20)yr m

where b = 0.5 (for hot, humid coastal ar&a<a.)

b = 0.25 (for normal, temperate or subarctic)

b = 0.125 (for very dry climate)

Finally the nondiversity annual path outage is:

-F/10ncip yr

U _„. - r ... 10 (3_21)

The annual nondiversity availability percentage i

A = 100(1 - U ) (percent)f -?-*??!nap r Vo -^-'

The percentage of availability is improved

with the use of frequency and space diversity. Figure

3-14 is used to graphically determine the approximate

70

availability improvement -for various percentages of

•frequency separation (F.S.). Figure(s) 3-15 (Dual

Diversity) and 3-16 (Quad Diversity) provide a graphical

method to determine the percent o-f path availability

(percent o-f level exceeded) for different diversity

combining techniques.

5. Piversity Requirements

The antenna spacing, in meters, required for

effective space diversity has been experimentally derived

for frequencies greater than 1 GHz, in the horizontal as

CRef. ll:pp. 145-1463:

/V = 0.36(D 2+ 1600)

1/2 (metersh (3-23a)

and in the vertical as:

A v= 0.36(D 2

+ 225)1/2

(meters,(3-23b)

where D = parabolic antenna diameter (m)

A satisfactory frequency separation, in MHz, for frequency

diversity has been dervied as:

1.44f/ d) (D2

+ 225)1/2

(MHz (3-23c)

71

1.0

\ I I 1 1 !

99

0.5

Rayleigh

^•distribution

—

Percent

of

time

below

level

o

P

F.S. = 3%-rXA \

k~ F s

nondiversity

= 2% \

"™

~

IDCO CO

Percent

of

time

above

level

01

005

F.S. = 4%—X \ \

F.S = 5% or more—-A \

\^^-Dual diversity

\ frequency

\ separation = 1%

99 99

001 ! 99 9993' 15 20 25 30 35 4

IdBI -JFiguru 3-14 Approximate Interference Fading

Distribution versus Order of Diversity

and Frequency Separation

(After Kef. 18: p. 2-4<S)

MM 1 • n

PERCENT OF THt LEVEL EXCEEOEO3 t 0*

I2~

8-maximal-ratio diversity, n = 2 y

6

4-

u

EQUAL-GAIN DIVERSITY, N = 2

i 2z

S •LI:cti )N 01 \*ERS TY,N = 2a5

/ /'

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PERCENT OF TIME BElO* 0RUINA1E

Figure 3-15 Short-Term Fading (Dual Diversity)

(After Ref. lS:p. 4-11)

EOBB B9

MAXIMAL- RATIO DIVERSITY, N = 4 —

^8

EQUAL -GAIN DIVERSITY N-4_"\

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PERCENT OF TIME Bf I l)W ORDINATE

Figure 3-16 Short-Term Fading (Quad Diversity)

(After Ref. 18:p. 4-13)

74

where f = transmitter frequency (MHz)

6 = scatter angle (mrad)

d = path length (km)

6. Analog Radio Link Parameters

The analog radiolink considered will be a FM

transmitter using frequency division multiplexing (FDM)

a. Receiver IF Bandwith

For FM modulation techniques, the re-

ceiver IF bandwidth is computed as [Ref. 18:p. 8-163:

BWIF

= 2( &Fp

+ Fm ) (3-24)

where F = peak frequency deviation (Hz)

PF = maximum modulating frequency (Hz)m

The peak frequency deviation is the product of the

frequency modulation index and the bandwidth of the

modulating signal. The maximum modulating frequency is

computed as the sum of the minimum modulating frequency,

the voice channel bandwidth, and the frequency spacing

between multiplexed supergroups. The calculated IF

bandwidth can now be used to compute the receiver noise

threshold, Equation 3—11. The carr 1 er—to-noi se ratio is

determined by Equation 3-12.

b. Expected Channel Noise

According to DCA System Performance

Specifications CRef. lS:p. 3-113, the channel noise

standard -for a troposcatter link is:

LN(pWpO) = (16,000) (3-25a)

2000

and

N(dBa0) = 10log in (pWp) - 6 dB (3-25b)10

where L = path length (nautical miles)

pWp = picowatts psophometr i cal 1 y weighted measured

at, or referred to, a zero transmission level point.

The term dBa refers to decibels of noise power above a

reference noise power, with an adjustment factor to

compensate for equipment weighting. The referenced noise

power that dBa is referred to is —85 dBm. To obtain

dBaO, it is required to calculate the number of dB above

this reference power the signal is. For flat voice

channels, the corrected reference level is -82 dBm and

the expression for dBaO is:

76

dBaO = 82 - SNR (3-26)

The signal-to—noi se ratio , SNR, must be calculated to

compute Equation 3-26. The channel SNR may be calculated

after the carr ier-to-noi se ratio (CNR) has been

determined by Equation 3-11. The relationship between

channel SNR and system CNR in a FM/FDM system is

CRef. l:p. 2723:

SNR = CNR +D. +FM. -L +P (3-27)ira lm f im

where FM = FN improvement factor (assumed 20 dEOi m

D = diversity improvement -factor (Fig. 3-17)im

P = preemphasis improvement -factor (Fig. 3—18)im

L = -10 + 10 log N (dB)f 10

where N = number of voice channels

0>ccoSIuo

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Figure 3-17 SNR Improvement -from Diversity Technique^

(After Freemann, Re-f . l:p. 207)

78

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PREEMPHASIS IMPROVEMENT

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Figure 3-18 Preemphasis Improvement far FDM Channels

(After Freemann, Re-f . l:p.224)

79

IV. HEIGHT_GAIN_CDMPyiATIQN

A. GENERAL

One of the purposes of this research was to develop

a tactically practical method of calculating the height

gain caused by the presence of an elevated troposhperic

duct. The calculation must provide a result that was

within 10 dB of the PDUCT computer program prediction.

Several related works were investigated for a possible

approach to the problem. Military troposcatter systems

have introduced several constraints to the height gain

problem. These constraints include:

1. The transmitter and receiver terminals a.rs bothlocated outside and below the elevated duct.

2. The operating frequency range was between 4.5 GHzto 5.0 Ghz.

3.. The geographical area of system deployment waslimited to Western Europe (i.e. West Germany).

A statistical analysis of elevated duct histograms

was obtained from several radiosonde recording stations

located throughout West Germany CRef. 26 j. This

information is condensed in Table III. Elevated ducts

that had a percentage of occurrance greater than twenty

percent (207.) over the 5 year recording period were prime

candidates for further study. Eight (8) elevated ducts

were selected as typical for the Area. Their optimum

coupling heights ranged from 951 to 1452 meters above the

surface. The elevated duct intensities were all less

than 6 M-units with 4 M-units being the dominant value.

TABLE III

ELEVATED DUCT HISTORICAL INFORMATION

StationLocation(LAT/LONG)

Mean OptimumCoupling Height

(Meters)

Mean DuctIn ten si ty(M-Units)

Mean DuctThi ckness(Meters)

Stuttgart, FRG(48-49N/09-11E) 1452Essen , FRG(51-23N/06-5SE) 1412Hannover , FRG(52-28N/09-41E) 1376Rheine, FRG(52-16N/07-25E) 1257Idar-Oberstei n , FRG(49-41N/07-19E) 1151Emden , FRG(53-22N/07-13E) 1071Goch, FRG( 5 1 -40N / 06- 1 0E ) 1 044Greifswald, FRG(54-05N/13-22E) 951

115

1 06

1 09

113

88

124

172

119

(After Or tenburger , Ref . 26, Vol. 12)

Height gain values, in decibels, were computed by the

PDUCT program -for each of the eight selected ducts. The

following common input parameters were entered into the

PDUCT program for each duct. CRe-f. 71:

1. The transmitter site elevation was -fixed as thereference at 5 meters above the surface.

2. The receiver site elevation was increased from5 to 280 meters in 25 meter increments.

3. The path distance was increased from 75 to 325kilometers in 50 meter increments.

4. The antenna polarization was set for both hori-zontal and vertical polarization.

5. The frequency of interest Was increased from4500 MHz to 5000 MHz in 100 MHz increments. Thefrequency was changed every PDUCT program runfor each selected duct of interest.

6. The relative permittivity (15), conductivity(0.01 mho/m) , and maximum mode attenuation(1.0 dB/km) were selected for the path character-istics.

B. MATHEMATICAL FORMULATION

The PDUCT height gain results for each duct were

investigated, and the following observations were

discovered. The height gain values increased

exponent i al 1 y as the receiver elevation approached the

bottom of the elevated duct. The other significant

observation was that for any fixed receiver elevation,

the height gain increased linearly with increased path

distance.

Two empirical methods were considered in developing

the height gain prediction model. One method was to

directly store the individual height gain results for

each of the elevated ducts and then to interpolate a

height gain result -from a database. This would have

required an extensive height gain database. The chosen

approach was to approximate height gain curves from the

F'DUCT results using a least-squares curve fitting

program. A second order polynomial equation was derived

for each frequency of interest at the initial

kilometer path length for each selected duct height.

The height gain program module consisted of eight (8)

optimum coupling height decision regions which

cooresponded to the selected elevated ducts. Each duct

height region contained a height gain polynomial equation

for each frequency of interest. For a particular

operating frequency and optimum coupling height, a

baseline height gain was estimated and multiplied by an

incremental range correction factor. This range factor

was the average differential difference in height gain

between the successive 50 kilometer path increments.

Figure 4-1 outlines how the height gain estimate was

computed.

OPTIMUMCOUPLING HT

DUCTTHICKNESS

DUCTINTENSITY

YES

COMPUTEHEIGHT GAIN

EXITMODULE

TRANSMITFREQUENCY

ENTERHEIGHT GAi:

Figure 4-1 Height Gain Estimation Flowchart

3'

C. RADIOSONDE DATA ANALYSIS

Elevated ducts are described by their optimum

coupling height, duct intensity, and duct thickness.

This information can be determined indirectly -from

real—time radiosonde data taken along the system's path

length. The atmospheric pressure, vapor pressure,

temperature and relative humidity readings are used to

calculate the refractive index, N, -for various altitudes

using the expression, CRe-f. 27:p.41:

77.6 48.1 H Pw (4-1

)

N = P +s 273 + T 273 + T

where P = atmospheric pressure (millibars)

T = temperature (celsius)

P = saturated vapor pressure (millibars)w

H = relative humidity ("/.)

The radiosonde information can be entered into the

program. The refractive index values are calculated for

available altitude readings and then converted to

modified refractive index values. At this point a

M-profile plot can be obtained along with a radiosonde

data listing. If an elevated duct does exist, the

optimum coupling height, intensity, and thickness can be

85

determined directly -from the M-pro-fi 1 e. These duct

descriptors must satis-fy the respective limits

established by the height gain prediction model. I-f the

detected elevated duct exceeds the limits o-f the model,

the height gain prediction will become inaccurate. The

program user will be alerted o-f this condition. At this

point the design engineer must decide to obtain the

height gain -From an alternative computation or neglect

ducting e-f-fects.

V. RESULTS

A. GENERAL

For validation purposes, the TROPO Program was used

to determine the design predictions for a typical

tropospheric scatter communications system. Table IV

outlines the proposed system specifications and

assumptions. Both the terrain and radiosonde data have

been assumed to accommodate the program's capabilities.

The program results a.r& illustrated in A Figure (s) 5-1

through 5—4. The Radiosonde Environmental Data Listing

(Figure 5-3) identifies the occurrence of a tropospheric

duct by detecting a "trapped" radio ray path condition.

Other refractive bending conditions identified -are

super-refractive (bending toward the earth's surface),

normal (standard bending), and sub-ret .-act i ve (upward

bending). The M-Profile Plot, Figure 5-4, graphically

verifies the program's computed duct parameters.

B. HEIGHT GAIN COMPARISON

Height gain prediction model results were compared

with the PDUCT program computed values for identical

elevated duct parameters. Height gain curves were

TABLE IV

PROPOSED EXAMPLE SYSTEM SPECIFICATIONS

Site: Transmitter Receiver

Latitude: 36 38' 23"N 37 09' 12"NLongitude: 06 22' 02 "W 05 35' 16"WElevation: 13 meters * 94 meters

Terrain Data Available: Near Obstacle Path Mode

Radio Terminal: Military ( AN/TRC-1 70V3)Diversity: DualFrequency: 4560.0 MH^

Antenna Diameter: 15 Ft. ParabolicWaveguide Length: 25 Ft. per Antenna

Digital Trunk Data Rate: 2.048 Mb/s

Transmission Bandwidth: 3.5 MHz

Radiosonde Data Available: Bur-face Duct Detected

BR

plotted for two test cases: (1) a -fined optimum coupling

height and range with a varying -frequency, and (2) a

•fixed optimum coupling height and frequency with a

varying range. Figure (s) 5-5a thru 5-5c has shown that a

prediction error of approximately 5 dB is possible. The

error increases as the frequency approaches the adjacent

frequency increment. In this case height gain values

al i dated at 4700 MHz have been averaged into .hQSi

computed for 4600 MHz to produce a shift of the

prediction curve. Figure (s) 5—6a thru 5-6c illustrate

the results of only changing the path distance, In this

case the greatest error detected was within 3 dB of

PDUCT , which supports the linearity between height gain

and range.

TRGPCSCATTER SYSTEM DESIGN SPECIFICATIONS

SITE TRANSMITTER RECEIVER

LATITUDE: 36.60 N 37.15 N

LONGITUDE: 6.37 M 5. 53 n

ELEVATION: 13.00 11 94.00 n

TERRAIN PROFILE TYPE: NEAR OBSTACLE PATH NODE

TRANSMITTER TAKE-OFF ANGLE: 4.73 HRAD

RECEIVER TAKE-GFF ANGLE: 4.97 HRAD

SCATTER (ANGULAR DISTANCE): 10.94 HRAD

TRANSMITTER TAKE-GFF ANGLE: .27 DEGREES

RECEIVER TAKE-OFF ANGLE: .23 DEGREES

SCATTER (ANGULAR DISTANCE): 1.20 DEGREES

TRANSMIT FREQUENCY: -1560.00 MHZ

MINIMUM RECOMMENDED FREQUENCY SEPARATION FOR 2UAD DIVERSITY: 52.77 MHZ

AZIMUTH AT TRANSMITTER (TO RECVR!: 48.70(DESREE3 N.)

AZIMUTH AT RECEIVER (TO TRANS): 229. [7 (DEGREES N.

)

GREAT CIRCLE PATH: 57.91 STATUTE MILES / 93.20 KILOMETERS

MINIMUM RECOMMENDED ANTENNA VERTICAL SEPARATION FOR SPACE DIVERSITY: IS. 5 FEET

ESTIMATED SCATTER VOLUME BASE ALTITUDE: 417.09 METERS

Figure 5-1 Example System Design Specifications

90

r— jumg 3B >-^-'iir'^»-'' - hubb HBaaMH—aaM

MODIFIED TERRAIN ELEVATION (METERS)-.372973E+03 -.230794Ef03 -. 13S61SE*03 -,9643SEE*02 -.CSiUEtOI

-.419063E+03 -.32o8S4£t03 -.234704E+03 -.H:525Et03 -.50:45?E*02 ,418334Et02

.0000OOE+O0

.929911E*04

. 1357B2E+05

t, . 278973E+05

u

h .371964E+05QXE-i

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.836929E+05

. 92 c 91 IE+<i5 - *v

TRANSMITTER SITE

//

/

//

//

//

RECEIVER SITE

VER T;CAL AIIS (TOP OF PAGE): TERRAIN ELEVATION METERS)

HORIZONTAL AXIS: PATH EtSTANCE .HE'Ef.S)

"in—nMigwnRaiinr' -, ,*amL tmmmmmmmmmmmmammasmM

Figure 5-2 Example System Terrain Profile Plot

tttt ENVIRONMENTAL DATA LIST tttt

PRESS TEMP VAPOR PRESS ALT N UNITS N/KFT H UNITS CONDITION

LEVEL . (.IB) (0 (MB) (FEET)

1 1008.0 15.1 15.2 60.0 339.7 -26.4 342.6 SUPER

2 1000.0 14.2 14.1 281.

6

jjji3 15.7 347.. 3 SUB

3 993.0 13.9 15.1 476.6 33ui 7 -11.3 359.7 NORMAL

4 9B2.0 13.3 14.3 785.3 Ov*V. 4 -176.3 371.1 TRAP

5 972.0 20.4 6.0 1071.3 282.9 26.6 334.4 SUB

6 962.0 21.5 7 1364.9 290.8 -28.9 v J U * W SUPER

7 949.0 21.5 6.9 1751.3 279.6 .0 ^A"f 7 NORMAL

TROFGSFHERIl DUCT DETECTED, TYPE: SURFACE

QPTIHUH CuUFLING .239 KH

DUCT TH

DUCT IN'

ICKNESS .326 KM

36'ENSI7Y (H -UNITS;...

Figure 5-3 Radiosonde Environmental Data Listing

MODIFIED REFRACTIVITY (M UNITS)

.;:so:7£»03 .345"3E«03 .352719Eh)o .360059E*03 . 2674O0E+-O3

.3343i7E»03 .34t70SE»03 .349048E+U3 .3563S9E*03 .343729E+03 J1370E-J3

.132S41E-01

.698239E-01

. 1213&4E+0Q

.172904E+O0

.22U4:EkO

. 2759B3E+00

S23E+00

.379063EtOO

.4306::e+oo

.482142E»jO

VERTICAL JUS -3P CF FAGEi : 1G3IFIE3 itrr.SCT.VlTK CK-UNITS:

rCRUCMiL AI,i: nLFI TUlE ,"£"f\S

Figur e Lj -4 M-Frofile Plot (Surface Duct)

BASIC MEDIAN TRANSMISSION LOSS FACTORS

~———— — ——————— — T———————————— — ————— — — — ——— ——————•————————— ————— —

,

SYSTEM LOSS FACTORS

FREE-SPACE/SCATTER LOSS 209.4 DB

WAVEGUIDE LOSS 7.4 DB

CONNECTOR LOSS..

4 DB

APERTURE-TD-MEDIAN COUPLING LOSS 1.5 DB

DIFFRACTION LOSS (IF APPLICABLE) NA DB

RAINFFALL ABSORPTION LOSS 3 DB

BYSTEPi GAIN FACTORS

ANTENNA SYSTEM GAIN S8.2 DB

HEIGHT GAIN (IF APPLICABLE) -4.5 DB

TOTAL SYSTEM GAIN B3.7 DB

NET PATH LOSS 135.3 DB

TRANSMITTER POWER 60.0 DBP1

MEDIAN RECEIVED SIGNAL -75.3 DBM

RECEIVED NOISE THRESHOLD -91.5 DBM

FM IMPROVEMENT THRESHOLD -81. 5 DB

THEORETICAL RF CNR 16.3 DB

SYSTEM FADE MARGIN 6.3 DB

Figure 5-5 System Performance Results

SYSTEM PERFORMANCE

SYSTEP! PATH RELIABILITY 87.01 PERCENT

EB/NO (BIT ENERGY/NOISE DENSITY) 21.63 DB

PROBABILITY OF BIT ERROR 13S3E-02

Figure 5-5 System Performance Results (Continued)

95

HEIGHT GAIN MODEL COMPARISON

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M

VI. SUMMARY

A. CONCLUSIONS

An interactive, computer-aided design program -for

military tropospheric scatter communications systems was

developed. The program provides the communications-

engineer with an efficient and acccurate system

performance algorithm that can be used in a tactical

environment on a microcomputer. The following thesis

objectives were accomplished:

1. Both analog and digital troposcatter radioterminals are included as design options.

2. The influence of elevated tropospheric ducting onsystems installed throughout West Germany wasconsidered. A height gain estimation model wasderived using numerical results obtained from thePDUCT ma in-frame computer program.

3. System performance predictions can be calculatedfor the newly deployed digital troposcatter radio,AN/TRC-170.

4. Real—time radiosonde information can be analyzedto determine the presence of both surface andelevated tropospheric ducts.

The accuracy of the height gain model was bounded by

the range of selected duct parameters. However height

gain results of elevated ducts which satisfied the limits

of the model were within 5 dB of the PDUCT computer

102

model. The model did not compute the height gain -for

sur -face-based ducts.

B. RECOMMENDATIONS

Addtional research is required and should -focus

on the -following areas.

1. The validation o-f the computer-derived systemperfomance results can be conducted duringstandard operational testing. Real-time radiosondedata should be obtained from available tacticalweather -facilities and tropospheric ductingphenomena determined. Received signal strengthdata can be recorded and statistically analyzed.

2. The height gain model should be expanded toincluded unlimited duct parameters, e.g. surface-based ducts and elevated surface ducts.

3. The effects of tropospheric ducting can be studiedfurther within the laboratory. Radiated energy,produced by laser light, can be transmittedthrough a fluid medium containing light-scatteringparticles. A common scatter volume can be formedby mirror-like apertures at the laser sources.The refractivity index of the medium could becontrolled to simulate ducting conditions. Thereceived energy could be detected and experimentalresults studied.

APPENDIX A

The -following prediction formulas were developed by

the National Bureau of Standards (NBS) -for calculating

the long-term median basic transmi sssi on loss, L ,

CRef. 12:p. 38911 and CRef. 18:pp. 8-8 thru 8-14].

1. Long-term Median Basic Transmission Loss

bsr

L, = 301og,„f - 201og lA D + F(0d) - F + Hbsr 3 10 10 o o

(A-l)

where f = frequency (MHz)

d = mean sea level arc distance (km)

F (. Q d) = attenuation function (dB)

o

H

= scatter i ng—eff i ci ency' term (dB)

= frequency-gain function (dB)

2. Attenuation Function

For a particular symmetry factor, S, and

approximate surface ref r act l vi t y , N , the followings

figures are used to determine the attenuation factor,

F ( d) :

For a surface ref ract i vi ty

:

N = 250 Refer to Figure A—

1

5

N = 301 Refer to Figure A-2

N 350 Re-fer to Figure A-3

N = 401 Re-fer to Figure A-4s

Scatteri ng-Ef -f icency Term

The -following equation can be used:

F = 1.086

(

o TT^' (ho " h

l " hlt " h

lr>(A-2)

where h = height o-f transmi tter /recei ver antenna beamo

intersection (km)

h = height -from obstacle elevation baseline to1

the antenna beam intersection (km)

h = transmitter obstacle elevation (m)

Ith = receiver obstacle elevation (m)

ir

4. Frequency—Gai n Function

The frequency-gain function is expressed by

as:

H =o

H (r,) + H (r_)o 1 o 2

+ H (dB)o

and r = 41.92 Q -f h1 te

r - 41.92 f h2 re

I5U

-— 1

- --

— rHE PATH DISTANCE

1NO THE ANGUl AHd. IS E'PRESSEO 'N KILOMETERS

DISTANCE. 8. IN RADIANS

160-

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I ? 5 10 2Q 50 100 .'00 500 1000

A 14 A 100

Figure A-l Function F( 6 d ) -For N = 250s

(After Re-f. lB:p. 8-9)

106

2533

Figure A-2 Function F ( 6 d ) for N = 301s

(After Ref. 18: p. 8-10)

10"

Figure A-3 Function F ( d ) for N = 350s

(After Ref. 18:p. 8-11)

108

1X1 — - - \

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Figure A-4 Function F ( d ) -for N = 401s

(After Ref. 18:p. 8-12)

109

and H = <£>C0.6log r\ 1 log S log qo 10 s 10 10

where Q = scatter angle (angular distance) (mrad)

f = frequency (MHz)

h = transmitter elevation (km)te

h = receiver elevation (km)re

S = a / R (symmetry -factor)o o

q = r / (s) (r )

2 1

H (r ) and H (r ) are graphically derived usingo 1 o 2

Figure A-6, with 77 obtained -from Figure A-5

1 10

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Compute Ho(After Ref. 18:p.6-32)

1 1 1

Figure A-6 Frequency Gain Function

(After Ref. 18:p. 8-13)

1 12

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Figure A-7 Correction Terms -for N = 301

(After Re-f . 18:p. 6-28)

1 1

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(After Re-f. 18:p. 6-29)

1 1 4

APPENDIX B

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LIST OF REFERENCES

1. Freeman, R. L. , Tel ecommuni cat i ons Transmi ssi onHandbook , John Wiley & Sons, Inc., 1981.

2. Osterholz, J. L. and Mensch, J. R. , System DesignConsiderations -for Digital Troposcatter Transmission ,

paper presented at the Defense CommunicationsEngineering Center, Reston, Virginia.

3. Monsen , P. , Analog and Digital TransmissionPerformance Models -For Troposcatter Links

,paper

presented at SIGNATRON, Inc., Lexington, Ma.

4. Zawislan, F., GHz Digital Troposcatter Terminal,

paper presented at the Rome Air Development Center,New Jersey.

5. Weston, J.D. , Predicting the Propagation Effects c-f

Elevated Tropospheric Ducts: An Investigation ofOne Tactically Useful Model , M.S. Thesis, NavalPostgraduate School, Monterey, California 93941,March 1983.

6. Electromagnetic Compatibility Analysis CenterTechnical Report ESD-TR-B1- 102 , A Model to CalculateEM Fields in Tropospheric Duct Environments atFrequencies Through SHF , by S. Marcus and W. D.Stuart, September 1981.

7. Electromagnetic Compatibility Analysis CenterTechnical Note, Instructions for the Users of "DUCT"- A Computer Program for Calculating Fields inropospheric Duct Environments , by S. Marcus,

December 19S4.

S. Petke, D. C. , A Numerical Investigation of the PowerDistribution of Signals Propagating Through Elevated"

tropospheric Ducts , FT. W. Thesi s , Naval PostgraduateSchool, Monterey, California 93941, October 19S2.

9. Naval Postgraduate School Technical Report NPS-62—82-045PR, A Simple Model -For the Computation of HeightGain in the Presence of Elevated Tropospheric Ducts ,

by J. B. Knorr, September 19S2.

10. Nag el , L.M. , MINIDUCT: Improvements to a MicrocomputerBased Elevated Duct Circuit Code , M.S. Thesis, NavalPostgraduate School, Monterey, California 93941,December 19S3.

11. Hall, M.P., Effects of the Troposphere on RadioCommun i c at i on s , Peter Peregrinus Ltd. , New York, 1979.

12. Panter , P. F. , Communications Systems Design -

Line-of -Si ght and Troposcatter Systems , McGraw-Hill,New York, 1972.

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tCenter, November 1976.

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IS. Department of the Navy, NAVELEX 0101.112, NavalShore Electronics Criteria - Li ne-of -Si ght andTropospheric Scatter Communi cat i ons Systems ,

Washington, DC, 1972.

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Propagat l on, pp. 143-173, International Telecommuni-

cation Union, Geneva, 1967.

21. Levin, L. , "Troposcatter Aperture-Medium Coupling Loss",A6ARD Con-f . Proc. on Aspects o-f Electromagnetic WaveScattering in Radio Communications , pp. 4.1 - 4.6,September 1977.

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.

24. Sunde, E.G., "Digital Troposcatter Transmission andModulation Theory", BSTJ , Vol. 43, January 1964.

25

.

White, R . F . , Engineering Considerations -for MicrowaveCommunications Systems , Lenkurt Electric Corp., 1975.

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Vol. 12, BTE Sylvania, Inc., December 1987.

27. Naval Ocean Systams Center Technical Report 659, I REPSRevision 2.2 User's Manual , by C.R. Hattan and W.L.Patterson, 21 October 1983.

INITIAL DISTRIBUTION LIST

No. Copies1. Defense Technical Information Center 2

Cameron StationAlexandria, Virginia 22304-6145

2. Library, Code 0142 2Naval Postgraduate SchoolMonterey, CA 93943-5100

3. Department Chairman, Code 62 1

Department of Electrical EngineeringNaval Postgraduate SchoolMonterey, CA 93943-5100

4. Professor Jefferey B. Knorr , Code 62ko 10Department of Electrical EngineeringNaval Postgraduate SchoolMonterey, CA 93943-5100

5. Commander, 7th Signal Brigade 2ATTN: S-3/CSPEAPO New York 0902S

6. CPT(P) Edward M. Siomacco 24913 Ash ton RoadFayettevi lie, NC 28403

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