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1985 TROPO: a microcomputer based troposcatter communications system design program.
Siomacco, Edward Michael http://hdl.handle.net/10945/21592
DUDLEY KNOX LIBRARY NAVAL POSTG DUATE SCHOOL MONTEREY, CALIFORNIA 93943
NAVAL POSTGRADUATE SCHOOL Monterey, California
THESIS
TROPO: 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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I. REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER
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7. AUTHORf«> 8. CONTRACT OR GRANT NUMBER!"*; Edward Michael Siomacco
9. PERFORMING ORGANIZATION NAME ANO ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASK AREA & WORK UNIT NUMBERS Naval Postgraduate School Monterey, California 93943-5100
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10. SUPPLEMENTARY NOTES
19. KEY WORDS (Continue on ravaraa aide II neceeeary and Identity by block number) 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-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 radiolinks. Propagation gain generated by elevated tropospheric ducting is called height gain. A height gain computational model for specific elevated tropospheric ducts
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is derived from statistical radiosonde data. A terrain profile plot, real-time radiosonde data analysis, and the probability of error for digital radiolinks are provided as program options.
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TROF'Q: A Microcomputer Based Troposcatter Communications System Design Program
by
Edward Michael Siomacco Captain, United States Army B.S., North Carolina State University, 1975
Submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN ELECTRICAL ENGINEERING
from the
NAVAL POSTGRADUATE SCHOOL September 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-fr activity (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 = 250 106 s A-2 Function F(0d) for N = 301 107 s A-3 Function F(0d) for N = 350 108 s A-4 Function F(0d) for N = 401 109 s A-5 Parameter N Ill s A-6 Frequency Gain Function 112
A-7 Correction Term for N = 301 113 s 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 required to cover the same transmission path as compared to tactical microwave 1 ine—of —sight radi clinks. 2. Reliable multichannel communications can be installed across long distances of hostile or inaccessible terrain.
3. Standard transmission ranges are suitable for the tactical military -field environmemt -for radiolinks from 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 increasing c vj 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 CONSIDERATIONS W^———————^—^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
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:
4 h sinV = " (2-2) A
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*;^«»^iHM^ifl*^a^ufflMHi*^^
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:
6 N = ( n - 1 ) X 10 (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 the opt 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 (a) (b)
i
/ •M / c o o > 1 1 / T Ah D I \ \ \ -)--r (1 '2)D = Ah > S^_ ?- i / —JamU- —-IamL-
(q) Ground- based loyer, (b) Elevated layer, Ground-based duct Ground- based duct
—JAN'U- —J AW' U-
(c) Elevated loyer, ( d ) E levated loyer ond Elevoted duel dud 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:
= 10' 6 (2-5) \(2 Am X ) 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 an b 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 the opt 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. 7.5X10-5 III 5 sec.< Outage <1 min. 7.5X10-3 IV 2 < Outages/min. < 5 2.5X10-4 V 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:
L + L +L + L - G„ - G +HG (3-1) TsdcawtrrT =L +L 3
where L = free-space propagation/scatter loss (dB) s L = knife-edge diffraction loss (dB) d o < e. u u z o - 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 elevation o at each terminal site. The adjusted surface
ref racti vi ty, N , is CRef. 18:p. 2-12J:
(3-2) N = N exp(-0 .03222h ) so s
where N = minimum monthly average refractivity o h = average antenna height (kft)
If the surface refractivity at each site is significantly
different, an option to calculate the respective N for s 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 1
o o o o o o o « Z
o o ooo o o TT E gg TTuiV JL 1 r L£ ss^ss / /; ME4$H1«« i rT i\
'' ij I i ^QMIIIi^^S 1 -"I i! Jx^^U'l" rsirH -H JSUTrtT
JL '\ ' "S , \ \ M 1 s V"T j_\_
,ifA i /! vV
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:
-1 a = a 1 - 0.04665 exp(0.005577N ) (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 are i manually obtained -from topographical maps and tabulated
versus distances, x , -from a selected reference i 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^-t^ ,0 y^ (J a -v/ ^-**^^d-d -d,"~~~-^ V*. >^\ It lr v ?\y\ \* -a £\ / \^- -J<£ \ d \4 ^*vv dlt \ lr 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
h it Vc^T^ ««\
V // \ / / \ X 4 ^"/x / 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*\: = : <3-5a> et
f
where h , h = transmitter, receiver terminal elevation ts rs
b. Type II Obstacle Horizon/Obstacle Horizon
It ts It d 2a (3-5c)
h, - h d, lr rs lr Oer " ~ (3-5d) d, lr 2a
where h ,d = transmitter obstacle el evat 1 on , di stance It It h ,d = receiver obstacle elevation, distance lr lr
c. Type III Obstacle Horizon/Radio Horizon
= (Same as Equation 3-5c et = (Same as Equation 3-5b) er The 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 )
h. - h -±E Ef + 6 (3-5e) oo et 2a
rs ts <3-5f + ; + 6> er P oo 2a
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:
(3-5g) w oo a o *oo o
a The ratio OQ and fi co defines the path symmetry factor
CRef. 18:p. 4-7]:
a = oo S (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 <3-5i (1 + S)
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 ~ Qo H = 2h = 0.3h <3-5j)
where 6 = 1. 150,
6 = scatter angle
« The maximum longitudinal dimension, L, is:
d H L = = 0.15d <3-5k) 2 h o
where d = great circle path distance (m)
The center of gravity of the scatter volume is
approximated as:
H = h + 2/3H (3-51 eg o
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:
d + d, ) tan 9 . tan Q a b et er (3->t,di L = 201og d 1( _V^y-
where d = transmitter to obstacle distance (m) a d = receiver to obstacle distance (m) b When the take-off angles ar^ less than 10 degrees and d is greater than 2b then Equation 3-6a can be b a approximated by:
DU L = 201og TTdJ- (3-6b) d 1()
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-month wm STANDARD DEVIATION CURVE 1 o
! LEGEND :. a :. ... ->.V ;.. -•-•• ANNUAL a o WINTER MONTW 2 O 5- g Q Q <•- OS a z •*
" '*."* — * * ;* 6- 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 = 20log f + 20log D - 52.6 dB (3-7) 1Q 1()
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(G + G (3-8) T )|
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:
L = 30log f + 201og d + 100 + 0.2(N^ - 310) + 57<3-9) s 1Q 1
where -f = operating frequency (MHz)
d = great circle path distance (miles)
6 = scatter angle (degrees)
N = surface refractivity 5
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£> 50
20
10 &
,\/f
s&f fc4
0.5 ,*>
•H 0.2 ^ 4 0.02 \S 0.01 0.005 0.002 y O.OOi 2D 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: = (dBw) - L (dB) P (dBW) P T (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: 3 in + NF(dB) + 101og B < p. (dBW) = -20 4 (dBW) 10 Ip where -204 dBW = thermal noise constant NF = receiver noise -figure (dB) B = 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 the b receiver noise spectral density, N . The probabilty of o error (often called bit error rate) will be determined from the E /N ratio. The transformation of the b o calculated carrier-to-noise ratio (CNR) to E /N is b o written as CRef . 23:p. 15SD: E,/N = CNR(dB) + 101og B - 101og R (3-13) b o 101n w 101n 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 2k P " 1 - (3-14) b "J k 2 - M' 4-2ji V" k = where ^ = correlation coefficient M = (for coherent PSK) 1 + 60 H = — (-for DPSK) 1 + vy c where y = average received E /N per channel b o y^ = average received E /N per bit b o L Tc h = 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: /m-i\ M- (3-15) PM i J 1 + m + m m=l y cn 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 : LEGEND V'i ! RAYLEIGH FADING (L=l) "DUAL DIVERSITY "(1=2) QUAD DIVERSITY Tt^4 \i \ C-J 1 - l\\! o : v \ X. k - Ul-V- 5fc x ou. >- \ 1 \ \ » M j ; A \ < 1 ""V" eao -c : \ as : a. \ 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 bo 2, 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 e 0_ 8= - f e - + e (3-17a) 2 et er, 4 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* ¥l 1 ! :#: i CAO OS uOS i — n " i kvk; O 03 - 3 " >• EhO > 1 l\N h 5t_- i j \; 1 ;.... < i a 1 ! \\ o \ 0£ 0. 1 o 1 i MM o rH LEGEND V! RAYLEIGH FADING (L=l) K _"TJDaITDIVFRSITY (L=2) 5i;sirDivERsm'ir=4i O \l l\ n 0.0 1.0 10.0 15 20.0 25.0 30.0 3!i.O EB/NO (X>Q) Figure 3-11 Probability of Error (M-ary FSK) (After Proakis, Ref . 14:p. 499) 64 PERFORMANCE OF DUAL PULSE DAR 18.0 20 24.0 28.0 J2.0 EB/NO (DB) (DUAL DIVERSITY L=2) Figure 3-12 DAR Performance - Dual Diversity (A-fter Zawislan, Ref . 4: p. 4) on PERFORMANCE OF DUAL PULSE DAR TT LEGEND 0.29XE-6 SEC ~T3T3fXE-~B~5EC~~ ~0T019XE^6~5~£~C~ c X S3 Eh O *i i >• - 23 < O23 04.0 e.o 12.0 16.0 20.0 ED/NO (DB) (QUAD DIVERSITY L=4) 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) 8 where 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 Hop Propagat 1 on Reliability Fade Margin C/.) (dB) 90.0 8 99.0 18 99.9 28 99.95 33 99.99 38 99.999 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 improvement P n P = -174 dBm + 10 log B + NF n 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 ndp as the fade occurrence factor: actual f ade probabi 1 i ty r = Rayleigh fade probabilty If F is the fade margin in decibels: actual fade probabi 1 ty r = -F/10 10 For the worst month: -5 r = a x 10 (3-19) m 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 b = 0.25 (for normal, temperate or subarctic) b = 0.125 (for very dry climate) Finally the nondiversity annual path outage is: -F/10 U _„. - r ... 10 _ ncip yr (3 21) The annual nondiversity availability percentage i A = 100(1 - U ) (percent) -?-*??! nap r fVo -^-' 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: 2 1/2 /V = 0.36(D + 1600) (meters h (3-23a) and in the vertical as: 2 = 0.36(D 1/2 (3-23b) A v + 225) (meters, where D = parabolic antenna diameter (m) A satisfactory frequency separation, in MHz, for frequency diversity has been dervied as: 2 1/2 1.44f/ d) (D + 225) (MHz (3-23c) 71 ~ I I \ 1 1 ! 1.0 99 0.5 — Rayleigh ^•distribution nondiversity level level P "™ IDCO CO above below time time o F s = 2% \ of of k~ = F.S. 3%-rXA \ Percent Percent 01 99 99 \^^-Dual diversity F.S. = 4% —X \ \ \ frequency separation = 1% 005 \ F.S = 5% or more—-A \ 001 ! 99 999 ' 15 20 25 30 35 4 3 IdBI -J Figuru 3-14 Approximate Interference Fading Distribution versus Order of Diversity and Frequency Separation (After Kef. 18: p. 2-4 I2~ 8- maximal-ratio diversity, n = 2 y 6 EQUAL-GAIN DIVERSITY, N = 2 4- u i 2 z a S •LI:cti )N 01 \ *ERS TY,N = 2 / /' 5 / / / £ -2 > — 6 u 2 -e RAYLEIGH FAOING u / z ff -e / Ul r u. r m * / / 28d8 AT 99 9% " -12- (l 1 - 38 d B AT 99 99 % -20 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 — ^ EQUAL -GAIN DIVERSITY N-4_"\ 8 \ \,A 6 j 2 ^- SELECTION DIVERSITY N = 4 - - — — — £- - - — 4 — RAY I EIGH FADING a -10 -12 — — — - 010 05 2 Ob 1 2 5 10 20 JO 40 50 W »0 80 90 95 98 99 99 8 99 9 99 99 PERCENT OF TIME Bf I l)W ORDINATE Diversity) Figure 3-16 Short-Term Fading (Quad (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: BW = 2( &F + F ) (3-24) IF p m where F = peak frequency deviation (Hz) P F = 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: L N(pWpO) = (16,000) (3-25a) 2000 and = 10log (pWp) - 6 dB (3-25b) N(dBa0) 10in 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 dEO i 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 « u 1-'" ^ 1 9 " " MQxjmai-ratiO Oiversity —r-*^ i " 0> c c 1 o , .-r r'-r SI e • u 1 t x s j ' s / /• o 2 u / a / s "~Equai-gain diversity -O ' / 1 5 1 1 » / —* _ - » — / / «--*• / 4 1 / / „, o 1 c 2 /' 1/ /// y/ 1 a 1 r~ 34567 89 10 Number of cnannets N Technique^ Figure 3-17 SNR Improvement -from Diversity 207) (After Freemann, Re-f . l:p. 78 "iv. wmw PREEMPHASIS IMPROVEMENT o • " m° a" H 2 U S UJ o > -» O cc 0. s r' a C3 •• •• V O M ' ' ' 1 1 1 1 1 1 1 1 1 1 1 'III! s itf 10* 10 10* NUMHER OF VOICE CHANNELS m[m.imi)iwim.v^ jap—BBB3BW8—BM—BMBW Ji,timw,tiLWM i ff .f 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 both located outside and below the elevated duct. 2. The operating frequency range was between 4.5 GHz to 5.0 Ghz. 3.. The geographical area of system deployment was limited 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 Station Mean Optimum Mean Duct Mean Duct Location Coupling Height In ten si ty Thi ckness (LAT/LONG) (Meters) (M-Units) (Meters) Stuttgart, FRG (48-49N/09-11E) 1452 115 Essen , FRG (51-23N/06-5SE) 1412 1 06 Hannover , FRG (52-28N/09-41E) 1376 1 09 Rheine, FRG (52-16N/07-25E) 1257 113 Idar-Oberstei n , FRG (49-41N/07-19E) 1151 88 Emden , FRG (53-22N/07-13E) 1071 124 Goch, FRG 1 ( 5 -40N / 06- 1 0E ) 1 044 172 Greifswald, FRG (54-05N/13-22E) 951 119 (After Or ten burger , 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 the reference at 5 meters above the surface. 2. The receiver site elevation was increased from 5 to 280 meters in 25 meter increments. 3. The path distance was increased from 75 to 325 kilometers in 50 meter increments. 4. The antenna polarization was set for both hori- zontal and vertical polarization. 5. The frequency of interest Was increased from 4500 MHz to 5000 MHz in 100 MHz increments. The frequency was changed every PDUCT program run for 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. OPTIMUM COUPLING HT DUCT THICKNESS DUCT INTENSITY YES COMPUTE TRANSMIT HEIGHT GAIN FREQUENCY EXIT ENTER MODULE HEIGHT 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 P w (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"N Longitude: 06 22' 02 "W 05 35' 16"W Elevation: 13 meters * 94 meters Terrain Data Available: Near Obstacle Path Mode Radio Terminal: Military ( AN/TRC-1 70V3) Diversity: Dual Frequency: 4560.0 MH^ Antenna Diameter: 15 Ft. Parabolic Waveguide 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 — jumg 3B >-^-'iir'^»-'' - hubb HBaaMH—aaM MODIFIED TERRAIN ELEVATION (METERS) -.372973E+03 -.230794Ef03 -. 13S61SE*03 -,9643SEE*02 -.CSiUEtOI r -.419063E+03 -.32o8S4£t03 -.234704E+03 -.H:525Et03 -.50:45?E*02 ,418334Et02 .0000OOE+O0 TRANSMITTER SITE .929911E*04 . 1357B2E+05 t, . 278973E+05 u h Q .371964E+05 X E-i * a, ^ .464955E+05 u / / 55794iE+o5 / / / / ^O^BE'dS / / / .743929E+05 .836929E+05 c v RECEIVER SITE . 92 91 IE+ T VER ;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 6 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. 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 7 6 962.0 21.5 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: SU RFACE QPTIHUH CuUFLING .239 KH DUCT TH ICKNESS .326 KM DUCT IN' 'ENSI7Y (H -UNITS;... 36 Figure 5-3 Radiosonde Environmental Data Listing MODIFIED REFRACTIVITY (M UNITS) .;:so:7£»03 .345"3E«03 .352719Eh)o .360059E*03 . 2674O0E+-O3 J1370E-J3 .3343i7E»03 .34t70SE»03 .349048E+U3 .3563S9E*03 .343729E+03 .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 2 — «r» o UJ X 9 6 LIGEND TR OPQ o o d 1 i i ' - ' — r -25.0 -20.0 -13.0 -tO.O -5.0 o.o HEIGHT GAIN (DB) H:1.352KM F-.4625MHZ R:75KM 2K3Z2£^£ Figure 5-6a Height Gain Model Comparison (Frequency: 4625.0 MHz) BESEEEBSZEEl HEIGHT GAIN MODEL COMPARISON P r i i i 9 \ • « ', / o f ..Pi.... * 4 f : © » _ ....'...... :/"• O UJ : : ... / y ; y ' , $ LEG END o 1 $-; - d TFtOPO 6 o \ DlJCT o X; o d a ( ' r— r -20.0 -15.0 -10.0 -5.0 0.C HEIGHT GAIN (DB) H.-1.352KM F:4650MHZ R:75KM —i m —^M———CS » Figure 5-6b Height Gain Model Comparison (Frequency: 4650.0 MHz) 97 i mt .*^««!i..v^.!> .?.».> j i - -^* flgagaBaaB aan a acae amaaaaca HEIGHT GAIN o MODEL COMPARISON $ o § > M d"" P / : / o • / d~ •••:• c i i O t UJ \*\ x e : t : d" T 1 LEGEND o a TROPO o DUCT i o d. i — —1 1 -25.0 -20.0 -13.0 -10.0 -5.0 HEIGHT GAJN (DB) H:1.352KM R4675MHZ R:75KM Figure 5-6c Height Gain Model Comparison (Frequency: 4675.0 MHz) •'• '.' : ..*»Xi!«7i":«H: K"S? "W»li Wi*» ; aBaaaaaagEaas HEIGHT GAIN MODEL COMPARISON -20.0 -15.0 -10.0 HEIGHT GAIN (DB) H:1.257KM R4990MHZ R:75KM —BB Figure 5-7a Height Gain Model Comparison (Range: 75 Kilometers) OQ : aaaaHBBBB m« aaaa ESSSEEEST HEIGHT GAIN o MODEL COMPARISON s "' ©~ -} ! 1 :- • i i : ~! i ij/\ : : : : : j : : : : : : •/ :::::::::• ::::::. */: ::::::::::: o r o • JT' • • ... I 2 *~'«n : : : :// ;::::::::::::: X 6 UJ I i py I ; ' ' / ' O - \ JP - / ] ::::: — «1 LEGEND q a TR0P0 d : : 7 Qi ::::::::! _?__P_UCT___. o : : : N :::::::;: : q v ; ; -a o ; ; ; ; • ; ; ; r r -43.0 -40.0 -33.0 -30.0 -25.0 B HEIGHT GAIN (DB) H:1.257KM F:4990MHZ R:T75KM 1 : f « : -.- -.-™" » . ^-TTtf KUE1- ». J.a3T^J mfcit'****t*>£? Figure 5-7b Height Gain Model Comparison (Range: 175 Kilometers) •< < I 1 — — nmtmuumium r>« '< Wli 3 HEIGHT GAIN o MODEL COMPARISON 0. 9 i / '• : "'(b"':' 0.25 V i t '. ', * / 0.20 (KM) 0.15 HEIGHT 0.10 r. ... • / : & LEGEND o TROPO o DUCT o ( D d ; ' r — i -75.0 -70.0 -65.0 -60.0 -55.0 HEIGHT GAIN (DB) H:1.257KM F:4990MHZ R:275KM WBmnaBBBmsaMamttti* Figure 5-7c Height Gain Model Comparison (Range: 275 Kilometers) 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 radio terminals are included as design options. 2. The influence of elevated tropospheric ducting on systems installed throughout West Germany was considered. A height gain estimation model was derived using numerical results obtained from the PDUCT ma in -frame computer program. 3. System performance predictions can be calculated for the newly deployed digital troposcatter radio, AN/TRC-170. 4. Real—time radiosonde information can be analyzed to determine the presence of both surface and elevated 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 system perfomance results can be conducted during standard operational testing. Real-time radiosonde data should be obtained from available tactical weather -facilities and tropospheric ducting phenomena determined. Received signal strength data can be recorded and statistically analyzed. 2. The height gain model should be expanded to included unlimited duct parameters, e.g. surface- based ducts and elevated surface ducts. 3. The effects of tropospheric ducting can be studied further within the laboratory. Radiated energy, produced by laser light, can be transmitted through a fluid medium containing light-scattering particles. A common scatter volume can be formed by mirror-like apertures at the laser sources. The refractivity index of the medium could be controlled to simulate ducting conditions. The received energy could be detected and experimental results studied. : 1 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 , bsr CRef. 12:p. 38911 and CRef. 18:pp. 8-8 thru 8-14]. 1. Long-term Median Basic Transmission Loss L, = 301og,„f - 201og D + F(0d) - F + H (A-l) bsr 3 10 10lA o o where f = frequency (MHz) d = mean sea level arc distance (km) F (. Q d) = attenuation function (dB) = scatter i ng—eff i ci ency' term (dB) o H = frequency-gain function (dB) 2. Attenuation Function For a particular symmetry factor, S, and l , approximate surface ref r act vi t y N , the following s figures are used to determine the attenuation factor, F ( d) : For a surface ref ract i vi ty N = 250 Refer to Figure A— 5 ( N = 301 Refer to Figure A-2 N 350 Re-fer to Figure A-3 N = 401 Re-fer to Figure A-4 s Scatteri ng-Ef -f icency Term The -following equation can be used: (A-2) F = 1.086 (h h " h " h o TT^' o " l lt lr> where h = height o-f transmi tter /recei ver antenna beam o intersection (km) h = height -from obstacle elevation baseline to 1 the antenna beam intersection (km) h = transmitter obstacle elevation (m) It h = receiver obstacle elevation (m) ir 4. Frequency— Gai n Function The frequency-gain function is expressed by as: H (r,) + H (r_) o 1 o 2 H = + H (dB) o o and r = 41.92 Q -f h 1 te r - 41.92 f h 2 re — I5U — 1 — - rHE PATH DISTANCE d. IS E'PRESSEO 'N KILOMETERS - -- 1NO THE ANGUl AH DISTANCE. 8. IN RADIANS 160 ' - - - ...... - -' . . ,..__.. iro — - — — — . no __. : 190 - — m ,v: — "J" V -- - ?I0 T? Ml) - - - — - • — — m s=ooi| 1 v\\ %0 - - ' - • - - — 5-0 51 : ?50 ^. -- — v \ \ \ E \ k ?40 ^ — — - \ 1 T _. » 1 — - 4 \-V \_ 750 Til - |s4M t — — . .. . E T ?60 IsO'iO ._. - __. - ' 4 V — IJsmoo \r M \ \]_ v\j T - i _ - V 1 1 \ \ — — — l\ , \ ~ \ J90 »\ \ — - \ ...... _ iUA-_l!i1 .'00 1000 I ? 5 10 2Q 50 100 500 A 14 A 100 Figure A-l Function F( 6 d ) -For N = 250 s (After Re-f. lB:p. 8-9) 106 2533 Figure A-2 Function F ( 6 d ) for N = 301 s (After Ref. 18: p. 8-10) 0" 1 Figure A-3 Function F ( d ) for N = 350 s (After Ref. 18:p. 8-11) 108 —V 1X1 — - - \ I I ! I I I III II I I I II J ThC PATH DISTANCE, d. IS EXPBESSEO IN KIUOKTEBS - \ J ANO THf ANGULAR DISTANCE. 9. IN RAOIANS. ICO — - \ . ITO | — - - - - . _ . 180 \V — - , — — 4 . — - . .. ^ 190 — — — — — — w>. 1 \ \ 200 s ill i .\ — — v M V v x™ r sooi - S'002 210 p-V-Y _ C L -SO OS -1« O 10 a - — -. \ t: L. 10 V* <\ * V. "V \ \ UJ 1 ^ — Q \ — — r- J - r- - ?30 .. — — " t" '"" ' CD A U. — — .__._ —A \ WO u t— S<20 \ 250 SO SO - ^ - \ soao ^ \ 1 SO 70 V'-A S'i oo I- 260 V" ~* IT 1 - 1 — — ' V Y — \ \ \ \ \ 2/0 1 \ . \ ' •v -- 280 — k_. _ - -=- 290 \f'v X 1I \ - --- __ inn I 2 5 K> 20 100 200 500 1000 Figure A-4 Function F ( d ) -for N = 401 s (After Ref. 18:p. 8-12) 109 and H = <£>C0.6log r\ 1 log S log q o 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 using o 1 o 2 Figure A-6, with 77 obtained -from Figure A-5 1 10 r aaEaaaanBaasfflagg^ag^ -i —— — - _ 5 5Jh»"° n,'0 5696h. ((0.031- 2 32N,ild » 3 67NjilO'*)«" 1—1—1—1—1— - h » Sd»/(l*S) km =0 5696h ']*,, (- — ._. — — — 4 — -- - — - < V ^ # /^ z I */ /z1 - 400 A 3 - 530 ,/ — — - / c ; 301 230 - — l I I \ < 5 I I I 9 10 II I? 13 H MIMiaiffiaBMMaB Figure A-5 Parameter N Ch 3 Used to s o 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 — \ fa—— affiffiBMIIgrsnaBliBBT^^ Figure A-7 Correction Terms -for N = 301 (After Re-f . 18:p. 6-28) 1 1 iFBMBBww«Bmw»miwft^ )' aaa MawaE Figure A-8 Adjustment Factor -for Figure A-7 (After Re-f. 18:p. 6-29) 1 1 4 APPENDIX B 2 ***** C3 ***** 25 25 ***** * * H * * H •=»! * * * * to * * o«u * * * * W * * 25 UDUrjUCJUUUUUUUOUUUOUUUUUUJUUjUU'jUUUU'JUU UCJU'JU 115 . o'. h — * * * t- *rvj » «. % * * O"— — %*3c/)*:ai *- w * * =ra U L) ucjcjuoucjucjuucjcjcj 116 . 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Wi_4W en 03 ^ ~* &3 63 Ml ,»» - HJ. hh* H .-» tn • u O 63 • 03 3 < «— o a- o <— =r too o <— cn "Mm— m cno'~ t"' ^- * old en cr> cj> uuuuuuuuuuuuu 122 » ^, »— , * CN # *-* * -»• O * as * * * \ •* — * H * »- ^-* -* * W •M- * W * CO — * Pn # pq CO * »• cd tt Pn - cq tt O 0- Eh «*• • f •a} 3 rq -* co SoZ H cq cn a * q oO *<«< 2;z * H Q * * << hH 11II . . ^s H •>* CO 123 ' » » ' > Q » ^, * ^» ^ * -J0 CM * ^^ 00 -M 1 * \ - • cq # tS * • NCO OH * *"* * S- 03 r-^j »• »— * OCqpq 44 S > * 2333 EH k^-* 33 cq * Cm cq —X CJ q * \ HS • rqe-t 33 cq * \cqcoo «» »33 < S h «_» k - cors-q "\3o-| CJ jJ k m ^m. » « ^c «» * » * * ' D tfllfl f i i CJ CJ no v£> 3-* rn C3t— no zrinvor^o* 3 CO 33 in uO* oo O OOOOr--* PQ CQ r* r** r«»r* r* t^(^»r^r»r** «j tf-4 cq Q U UU UUD U 124 . « I eg * * * * * *o* # * •* *o# tt > * *o* * 03 05 #T-tt « s> iq * * # u H w * * o* * uq H s * * H* •«• 05 H * o* •»• s • * * C3# * H "to * # * < S3 X ~*# * -=S — * I! 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" X X in C-t k H r— > uq % <: H •3 ^ o H -1 ^N o CJ >-A » as oj *— X PM w % sr w ttl 03 II a M ,_^ Q «a! » o ^^ pq ms 33 — • un H • U H CN O o o H CO CN a W CN k Q « fO w % T— 3 cq T" S3 2 X O II EH • II X 00 EH « >— A H H *•* bj • S3 *^ a k ^o O ««, ^-» ^» H _ D CD H LO cq ^3 — fN X *-» O l3 'J *" cum ki 3) «-*» o « < Q >^ r— o \ ,_» CT» «• a, 33 CO*— *™ -« •-5 ^~ » f" EH **" cow » ^O X II b H CU«3J CN • X • O w H O cH h WSJ II iN lO EH Q -1 CKCJ M T— H«- H .-«. Oi < S3 » % w M* r- a •>«-» H o w *-• o-. ,^ % • X Q u> o ^^T— CN H • • -^ ur- X O—v««J r» IT) T-* -«= ^ O en CO H «^>^ CN ^-tHCO Oh^\ II — CN o Tin o H O w QO^ CNX^s u M rn '-O ••< m o CO X c-l «. r— a, HlO Of\ X »z -O* ^r» 2 ,«», a o , o _ __ CJ- O r- »*"" wr*»- CO w >* 156 » * w 55 H J W05 « <-< 33 U O 00 I! V 25 ^ rs Oi t- H .-VJ OM fcH *-a« O—. t^ N. ra c/)--» «" in hoi Q3 03 • O^J w # h-3«C \ O ON H <$:c h — H a EU SO* * WN Oi * ^ =5 Q3 » «H ax ti\ r- L0 03=1- 0^» was H'-O I 55P- fc-tO 0> "-^302'-' Otn + <-=3 * HQ3 s * O X ocq co>p*- S3 * w -=»i— ds h o *+h —* a «r* « tjm \ 0333'- C0LT> —. OH St* X 23=3 • WtO ^ "** au r\j W!j II t || • || =5 03 tHW-3505 HO OHCOH^OH II 03 HO O'-O M H23=> U K»^*j: X XII S3 ZD U W>-3«S II 1-HWDHU3 hho3Hq 55 h<:h ch^*-.'-* sw ii 11 chhq 55 h< 157 LIST OF REFERENCES 1. Freeman, R. L. , Tel ecommuni cat i ons Transmi ssi on Handbook , John Wiley & Sons, Inc., 1981. 2. Osterholz, J. L. and Mensch, J. R. , System Design Considerations -for Digital Troposcatter Transmission , paper presented at the Defense Communications Engineering Center, Reston, Virginia. 3. Monsen , P. , Analog and Digital Transmission Performance -For Models 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 of One Tactically Useful Model , M.S. Thesis, Naval Postgraduate School, Monterey, California 93941, March 1983. 6. Electromagnetic Compatibility Analysis Center Technical Report ESD-TR-B1- 102 , A Model to Calculate EM Fields in Tropospheric Duct Environments at Frequencies Through SHF , by S. Marcus and W. D. Stuart, September 1981. 7. Electromagnetic Compatibility Analysis Center Technical Note, Instructions for the Users of "DUCT" - A Computer Program for Calculating Fields in ropospheric Duct Environments , by S. Marcus, December 19S4. S. Petke, D. C. , A Numerical Investigation of the Powe r Distribution of Signals Propagating Through Elevated " tropospheric Ducts , FT. W. Thesi s , Naval Postgraduate School, Monterey, California 93941, October 19S2. 9. Naval Postgraduate School Technical Report NPS-62—82- 045PR, A Simple Model -For the Computation of Height Gain in the Presence of Elevated Tropospheric Ducts , by J. B. Knorr, September 19S2. 10. Nag el , L.M. , MINIDUCT: Improvements to a Microcomputer Based Elevated Duct Circuit Code , M.S. Thesis, Naval Postgraduate School, Monterey, California 93941, December 19S3. 11. Hall, M.P., Effects of the Troposphere on Radio Commun 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. 13. Beckmann, P. , Probability in Communications Engineering Har court , Brace & World, Inc. , New York, 1967. 14. Proakis, J. G. , Digital Communications , McGraw-Hill Book Co. , 19S3. 15. Technical Report No. 12-76, DCS Transmission System Performance , Defense Communications Engineering t Center, November 1976. 16. Siller, C. A., "Multipath Propagation," IEEE Communications Magazine , v. 22, pp. 11-12, February 19S4. 17. Knorr, J.B., Unpublished ECE 3600 lecture notes. Naval Postgraduate School, Monterey, California 93940, November 1984. IS. Department of the Navy, NAVELEX 0101.112, Naval Shore Electronics Criteria - Li ne-of -Si ght and Tropospheric Scatter Communi cat i ons Systems , Washington, DC, 1972. 19. Du Cast el , F. , Tropospheric Radiowave Propagation Beyond the Horizon , Pergamon Press, New York, 1966. 20. International Radio Consultative Committee, Vol. I I_. , l Propagat 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 Wave - Scattering in Radio Communications , pp. 4.1 4.6, September 1977. 22. Yeh , L. P., "Simple Methods -for Designing Troposcatter Circuits", I.R.E. Trans. C.S . , pp. 193-198, Septmeber 1960. 23. Feher , K. , Digital Communications: Satellite/Earth Station Engineering , Prentice-Hall, Englewood, NJ . , 1 981 24. Sunde, E.G., "Digital Troposcatter Transmission and Modulation Theory", BSTJ , Vol. 43, January 1964. 25 White, R . F . , Engineering Considerations -for Microwave Communications Systems , Lenkurt Electric Corp., 1975. , , Analysis II 26. Ortenburger L.N., et al Radiosonde Data , Vol. 12, BTE Sylvania, Inc., December 1987. 27. Naval Ocean Systams Center Technical Report 659, I REPS Revision 2.2 User's Manual , by C.R. Hattan and W.L. Patterson, 21 October 1983. INITIAL DISTRIBUTION LIST No. Copies 1. Defense Technical Information Center 2 Cameron Station Alexandria, Virginia 22304-6145 2. Library, Code 0142 2 Naval Postgraduate School Monterey, CA 93943-5100 3. Department Chairman, Code 62 1 Department of Electrical Engineering Naval Postgraduate School Monterey, CA 93943-5100 4. Professor Jefferey B. Knorr , Code 62ko 10 Department of Electrical Engineering Naval Postgraduate School Monterey, CA 93943-5100 5. Commander, 7th Signal Brigade 2 ATTN: S-3/CSPE APO New York 0902S 6. CPT(P) Edward M. Siomacco 2 4913 Ash ton Road Fayettevi lie, NC 28403 i ,:. I. cO'. ThesjThesis S538 25^ Thesis S53865 Siomacco c.l TROPO: a microcom- puter based troposcat- ter communications sys- tem design program. >»"«*£ .^pw mwuh a 03WQ(J5 o z HhIO-^ShW H 55 55 EH tqSWHCq tri « Q H^ 55 55 OI LO WQZXQ O 550 CO ^OCN hwh-ssseh u OCU r~<"0 uu^w ,—3 — H 53 H 55 QHEHMMEHEHM WaW^xUWM a pb| «3j tet, 7zJ MEhEhEh O"^M=H03W ———1- —'II T-" 33 03 —Mowacju * CO z < «s «u «sj «c «=c <] ...... «»: «$ «t« «j ii]^HHffifeO(HHXOHHIOHHKOHHI!E < II WWHQO-J WHEhWSHQSHW "-WWHOHCqi^HHlilWHHWWHBWrt^^ + bn + W II 0303' Ha3033W'1 Z a< H CO CJ H 022 O Ct)>J30>^EHH CO 3 3 to tx.1 z O CO 33 O^Hrc^S w o w o 3 w ^5 Z 03 tiit-Ji-aw^o^ as cu H-q 3 w =0 COt-3CJ33«H % to
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