NTIA-REPORT-79-18

Automated Digital System

Engineering Model

L.G. Hause

D.R. Wortendyke

u.s. DEPARTMENT OF COMMERCE

Juanita M. Kreps, Secretary

Henry Geller, Assistant Secretary

for Communications and Information

March 1979

TABLE OF CONTENTS

Page

ABSTRACT 1

1. INTRODUCTION 1

2. PROGRAM NO. 1., EARTH GEOMETRY AND PROGRAM NO. 2, PATH

PROFILE A..~D RAY-PATH CHARACTERISTICS 7

3. PROGRAM NO. 3, MEDIAN BASIC TRANSMISSION LOSS MODEL 25

4. PROGRAM NO. 4, PATH-LOSS VARIABILITY MODEL 33

5. PROGRAM NO. 5, LINK EQUIPMENT GAIN 51

6. PROGRAM NO. 6, LINK PERFORMANCE CALCULATIONS 59

7. PROGRAM NO. 7, SYSTEM PERFORMANCE 80

8. RECOMMENDATIONS 84

9. REFERENCES 85

LIST OF FIGURES

Figure 1-1.

Figure 1-2.

Figure 2-1.

Figure 2-2.

Figure 2-3.

Figure 2-4.

Figure 2-5.

Figure 3-1.

Figure 3-2.

Diagram for the design of a microwave radio

communications system.

Automated system engineering model.

Earth geometry model.

Earth geometry program flow chart.

Spherical triangle for great-circle path

computations.

Terrain profile and ray-path model.

Example of terrain profile and ray paths.

Median basic transmission loss model.

Mean temperature values (use July values for

the Northern Hemisphere and January values

for the Southern Hemisphere). (From "Climates

of the World", U.S. Dept. of Carom., ESSA,

Environmental Data Service, January 1969.)

iii

3

4

9

10

14

18

19

26

28
Page

Figure 3-3. 'Contours of average absolute humidity (g/m3) for

a summer month (August for the northern hemisphere and February for the southern hemisphere)

(Bean and Dutton, 1966). 30

Figure 4-1. Path-loss variability model. 34

Figure 4-2. Comparison of prediction methods with one year

of data from an LOS path across the English

Channel (88 km, 5 GHz) . 35

Figure 4-3. Example basic transmission loss variability

distributions. 38

Figure 4-4. Annual precipitation, M, in millimeters, for

an average year in Europe. 41

Figure 4-5. Mean annual thunderstorm ratio, S, for Europe.

(Dashed contours indicate regions of sparce

data.) 42

Figure 4-6. The estimated number of rainy days, 0, for an

average year in Europe. 43

Figure 4-7. 30-year mean c3nnual precipitation, M, in

millimeters, for the U.S.A. 44

Figure 4-8. Mean annual thunderstorm ratio, (3, for

the U.S.A. 45

Figure 4-9. 30-year annual number of days, 0, with prec~pl.-

tation greater than 0.25 rom for the U.S.A. 46

Figure 4-10. Mean annual thunderstorm ratio, S, for the

world.

Figure 4-11. Example point rain rate distribution.

Figure 5-1. Link equipment gain.

Figure 5-2. Microwave waveguide attenuation.

Figure 5-3. Time availability of received signal level.

Figure 6-1. Link performance evaluation.

Figure 6-2. Waveguide velocity curves.

Figure 6-3. Maximum distortion to signal ratio due to echo.

iv

47

48

52

54

58

60

67

69
Figure 6-4. Example of a worst channel FM-FDM receiver

transfer characteristic.

Figure 6-5. Example of a digital receiver transfer

characteristic.

Figure 7-1. System performance evaluation.

LIST ·OF TABLESTable 2-1. Example of an Earth Geometry Tabular Output

Table 2-2. Earth Radius For Various Spheroids

Table 2-3. Example of Microwave Path Tabulation

Table 3-1. Oxygen Lines

Table 3-2. Water Vapor Lines

Table 3-3. Example of the Tabular Output Format From the

Median Basic Transmission Loss Model

Table 4-1. Example of Tabular Output of Path Loss

Variabi~ity Information

Table 5-1. Sample Summary of Basic Link and Equipment

Gain Parameters

Table 6-1. Example of the Link Performance·Summary

Table 7-1. Example FM/FDM SY$tem Performance Table

Table 7-2. Example Digital System Performance Table

v

Page

72

74

81

11

12

20

29

31

32

39

56

75

82

83

AUTOMATED DIGITAL SYSTEM ENGINEERING MODEL

L.G. Hause and D.R. Wortendyke*

This report describes a desk-top computer system and

mathematical models which were used in seven of its programs. These programs make key calculations in the design

of line-of-sight microwave systems. The models have the

following ranges; bit rates up to 50 Mbits/s, carrier

frequencies from 1 to 40 GHz, and path distances up to

150 km. The programs calculate, tabulate and plot

information about earth geometry, path profiles and

ray paths, median basic transmission loss, path-loss

variability, equipment gain, link performance, and

system performance. Models were chosen based on their

wideness of acceptance and the size and type of data

base substantiating the model. Any design engineer using

this model can have immediate access to calculated

results corresponding to changes in design parameters.

The reasons for this capability are that the programs are

written for use in an interactive mode and the programs

can be used by people with no experience in programming.

Key words: Line-of-sight microwave, computer programs,

earth geometry, path profiles, basic

transmission loss, digital systems, microwave link performance, multipath fading,

rain attenuation

1. INTRODUCTION

The purpose of this report is to describe a program which developed an

interactive automated engineering model used in the design of line-ofsight microwave communications systems. The c~ncept of this engineering

model is based in large part on the information and methodology contained

in MIL-HDBK-416 (1977) which was prepared by the Institute for Telecommunication Sciences (ITS), under an Air Force contract. The handbook was written

several years ago.; consequently, emphasis was placed on analog systems

(FM/FDM) with little information on digital systems. With the passage of

time, many of the original models used to predict path-loss variability

and other factors affecting performance have been improved.

*The authors are with the National Telecommunications and Information

Administration, Institute for Telecommunication Sciences, U.S. Dept. of

Commerce, Boulder, Colorado 80303.
Much emphasis in this program (sponsored by USACC EED-PED) is placed on

adding needed models and updating ones which have been improved.

Obviously not all aspects of a line-of-sight system design can be

automated and such things as procedures for making a field survey of

potential terminal sites are much the'same.as described in MIL-HDBK-4l6.

These topics were not reexamined during this program. The primary objective

for this project is to automate tedious calculations within various models

which are compatible with a calculator* based system operated in a highly

interactive mode. This type of operation permits the system design engineer

to evaluate many different configurations with immediate feedback in terms

of system performance and tradeoffs. Among the benefits from this kind of

automation are the time saved when batch processing is not necessary and

a more nearly optimum design choice that results from the capabilitY,of the

system designer to view the results of design changes immediately.

This report discusses three topics:

1. A brief description of the Hewlett-Packard 9825A** calculator

system is presented.

2. A block diagram and description is presented of the various stages

of the microwave system design (Figure 1-1). The blocks are

selected to follow the evolution of the design. A second diagram

of the automated system is presented with blocks representing

segments of effort that terminate at logical reporting times

(Figure 1-2). The second diagram includes only that part of the

design which is compatible with the calculator based system.

3. Flow diagrams and descriptions of the various particular models

are presented with the reasonS why some models were added, others

modified, and some left essentially unchanged from their orig'inal

presentation inMIL-HDBK-4l6.

*For desk-top computers,.. the terms calculator and computer have become

interchangeable in usage by both manufacturers and government agencies.

**The use of trade names in this volume is necessary since the computer

system and language are unique to the manufacturer who provided them.

Such use of the trade name does not constitute a product endorsement.

2
DETERMINE

COMMUNICATION

REQUIREMENTS

1 REEXAMINE

REQUIREMENTS

AND liMITATIONS

NO

DETERMINE

RESOURCE

LIMITATIONS

IS A

DESIGN

FEAS IBlE 1

NO

SHOULD

THE PROJECT BE

ABANDONED?

YES RECOMMEND

ABANDONING

THE PROJECT

YES

ARE

STUDY ROUTE THERE ANY NO

ALTERNATIVES VIABLE

ROUTES?

YES

SELECT A

ROUTE AND NO

MAKE A FIE~D THE. DESIGN

SURVEY FEASIBLE?

YES

DO INDIVIDUAL

LINK DESIGN

ANALYSIS

ARE.

All liNKS AO~QUATE?

NO

YES

Figure 1-1. Diagram for the design of a microwave radio

communication system.

RECOMMEND

IMPLEMENTATION

NO

3

DO A

COMMUNICATION

SYSTEM

ANALYSIS
CALCULATE

EARTH PROGRAM NO. 1

GEOMETRY

TABULATED

OUTPUT

DETERMINE

PATH PROFILE

AND RAY PATH PROGRAM NO. 2

CHARACTERISTICS

RAY PATHS

PROFILE AND

TABULATED

OUTPUT

CALCULATE

MEDIAN BASIC

TRANS" ISS ION PROGRAM NO. 3

LOSS

TABULATED

OUTPUT

CALCULATE

PATH LOSS PROGRAM NO. ,. VARIABILITY

DISTR'BUTIONS

OF

TRANSMISSION

LOSS

CALCULATE

LINK PROGRAM NO. 5 EQUIPMENT

GAIN

DiSTRIBUTIONS

OF RSL ALSO

FADE MARGIN

CALCULATION

CALCULATE

LINK PROGRAM NO. 6

PERFORMANCE

LINK

OUTAGE

TIME WITH

TABULATED

OUTPUT

CALCULATE

SYSTEM PROGRAM NO. 7

PERFORMANCE

SYSTEM

OUTAGE

TIME WITH

TABULATED

OUTPUT

Figure 1-2. Automated system engineering model.

4
Calculator Based System:

The system has five major hardware components:

,

.J.. The Calculator

2. An Impact Printer

3. An X-Y Plotter

4. A Flexible Disc Drive

5. A Hopper Card Reader

The calculator uses the HPL language (Morris et al., 1976) and has these

other useful characteristics:

1. 24,000-byte working memory,

2. Built-in tape cartridge drive,

3. All of the peripheral equipment can be simultaneously connected

making it possible to have the hardware always in the ready

condition.

The impact printer will print the 96 ASCII (American Standard Code for

Information Interchange) characters at 30 characters per second. This form

of printed output was selected -because it provides report-ready copy.

The X-Y plotter also provides report-ready copy. One of its features

is that it can be used to digitize coordinates on the platten surface.

Some of its other major characteristics are:

1. It can draw at a rate of approximately 20 ips.

2. It is microproc:essorcQntrolled,which makes the programming of

many drawing patterns and techniques practical.

3 . The repeatability of pen po~itions is goo:dto less than

0.01 inches.

To expand the capability of the system to handle large blocks of data,

permit convenient use, and handle large numbers of complex programs, a

flexible disc mass storage system was obtained. This system makes available 400,000 bytes of conveniently available memory. Each memory disc

costs approximately $10.

A hopper card reader was acquired which permits obtaining blocks of

data from a large computer and entering the data into the calculator system

automatically. Some examples of data which can be entered in this manner

are meteorological parameters for rain--attenuat-ion models and terrain

information for plotting path profiles.

5
Engineering Model Design:

The design model for a line-of-sight microwave radio communications system involves much more than making mathematical calculations and feeding in

numerical values of parameters which are compared with values from standards

and specifications. Figure 1-1 shows a simple diagram for the design of a

microwave radio communications system. Much of the first part of the design

involves making user surveys and considering lead times, funding, spectrum

availability, and political realities. At the point in the evolution of

the design where route alternatives are being considered, the calculator

based system becomes a very useful tool for the remainder of the design

process. Figure 1-2 shows a block diagram of the automated system engineering

model. We will point out where the 'various outputs from the automated

model become particularly useful in the overall design illustrated in

Figure 1-1. After communications requirements and some of the resource

limitations are known, calculator program Nos. 1 and 2 become useful in

making preliminary studies of route alternatives from maps and other locally

available sources of information. Program 2 provides information and forms

vitally necessary for obtaining maximum information during the field

survey. This program could be run prior to the survey. It should be rerun

again after the field survey since more accurate and detailed information

will then be available. If path loss measurements are going to be made during the field survey, it is also important to run programs 3 and 4 to

determine expected transmission loss characteristics prior to the survey.

To select equipment properly for use on a given link, programs 2, 3, 4,

5, and 6 are necessary for rapid optimization of such things as antenna

heights, antenna gains, diversity spacing, transmitter power, transmission

line type, maximum transmission line return loss requirement and receiver

noise figure. In the case of new systems, it is usually necessary to rerun

programs 5, 6, and 7 a number of times to provide adequate system performance within reasonable cost. In the following sections, we will discuss

each of the 7 basic sets of calculations and data indicated in Figure 2.

6
2 . PROGRAM NO.1, EARTH GEOMETRY AND PROGRAM NO.2,

PATH PROFILE AND RAY PATHS

The earth Geometry Program and the Path Profile and Ray Paths Program

that will be discussed in this section are interdependent in that:

1. The Earth Geometry Program must be run before the Path Profile

and Ray Paths Programs can be run.

2. The output tabulation from the Earth Geometry Program, except

for map crossings, is included in the output tabulation of the

Path Profile and Ray Paths Programs.

3. These two programs provide checks on each other by indicating

differences in path length obtained by calculation from site

coordinate information and path length obtained from path profile

information.

The Earth Geometry Program uses the flexible disc to store data

required for the execution of Program No.2. If the data and disc are

not available to Program No.2, Program No. 2 automatically loads

Program No.1.

Program No. lis primarily intended as a preliminary design step

for 01:>taining the parameters for drawing the path profile. The output

of Program No. 2 is designed to provide report-ready documentation of the

physical characteristics of the path profile and ray path.

A check of the great-circle path length calculated from site

coordinates and the value obtained from the path profile data is desirable since path profile information and coordinates are often obtained

from sources .not readily accessible to the link designer. The importance

of this check should not be underestimated. It has been our experience

that often several sets of site coordinates are mistakenly recorded for

a given site. It is the actual tower coordinates that are required.

Many times named locations have more than one radio tower, several survey

control points, and several surveyed structure locations. These locations

lend to the confusion in specifying the proper tower coordinates.

7
Program No. 1 Earth Geometry:

The purpose of the Earth Geometry program is to provide a tabulation

of the following data:

1. Tower (or potential tower) designations.

2. Tower base elevations above mean sea level.

3. Tower location (latitude and longitude).

4. The distance between towers.

5. Azimuth from true nort11 at each tower to the other tower.

6. Magnetic azimuths at each tower to the other tower.

7. Map crossings (latitude and longitude).

8. Distances from map crossings to the towers.

Figure 2-1 shows a simplified block "diagram for this initial program.

Because the output of this program is short, it has been used as an example

of program documentation and tabular output format (see Figure 2-2 and

Table 2-1).

The model which we use tocomPllte,ea:rth geometry is unavoidably inexact but should be very satisfactory for engineering line-of-sight

paths. Spheroids in use today include the Clark Spheroid of 1866, the

Malayan Spheroid, the Bessel Spheroid, the Australian National Spheroid,

and the International Spheroid. Table 2-2 lists the equatorial and polar

radii in kilometers and an arithmetic average of these. Conversion factors

between degrees and distance on the surface of a sphere of radius equal to

either the equatorial or polar radius are included, as well as an arithmetic

average of the factors for each spheroid. These conversion factors are

only valid exactly at the pole or at} the equator, but the American Ephemeris

and Nautical Almanac for the ye'ar 1975 (1973) page 528, gives equations for

approximating the true arc length of the International Spheroid.

1° latitude = 111133.35 - 599.84 cos 2¢ + 1.17 cos 4¢ meters, and (2-1)

1° longitude = 111413.28 cos ep - 93.51 cos 3¢ + 0.12 cos 5¢ meters (2-2)

where ¢ is the mid-latitude of the arc.

8
START

INPUT TOWER

DESIGNATIONS AND

LOCATIONS

CALCULATE

AZIMUTHS AND

PATH LENGTH

CALCULATE

MAP CROSSING

AND DISTANCES

TABULATE

INFORMATION

Figure 2-1. Earth geometry model.

9
1-22

1-18

1-13

CALCULATE CALCULATE INTERMEDIATE 1-14 INTERMEDIATE 1-19

LONGITUDE LATITUDE

1-4

CALCULATE 1-15 TRY DIFFERENT G.C.O. TO BOTH 1-2' CASE 'SITES

1-7

1-8

1-'

CALCULATE

G.C.D. AND

AZIMUTHS

WRITE OUT

THE INPUT

PARAMETERS

HOUSEKEEPING 1-1

ARRANGE SITES IN 1-6

ORDER (CLOSEST TO

EQUATOR. FIRST)

WRITE OUT THE

CALCULATED

PARAMETERS

1-9

1-25'

1-26

WRITE

ON DISK

WRITE OUT

ENDING AND

FORM FEED

CALCULATE

CONSTANTS

FOR HAP

CROSSINGS

Figure 2-2. Earth geometry program flow chart.

10
Table 2-1. Example of an Earth Geometry Tabular Output

Earth Geometry for the LANGERKOPF-FELDBERG Path

31 Jan 78 - Project No: 789456123 - DRW

(MKS uni ts)

Tower Name Desig- La ti tUde

nator deg min sec

Longitude Elev(MSL)

deg min sec meters

LANGERKOPF

FELDBERG

LKF 1

FEL 0

49 18 04.0N

50 14 33.0N

7 50 47.0E

8 29 49.0E

602.0

688 .8-

Great circle distance between towers is 114.55 kilometers

Azmuths from TRUE NORTH:

Azimuth from LKF to FEL is

Azimuth from FEL to LKF is

deg min sec

23 48 13.55

204 18 01.69

Declination: of MAGNETIC NORTH from TRUE NORTH:

deg min

At LANGERKOPF 12 07.0W

At FELDBERG 12 03.0W

Azimuths from MAGNETIC NORTH: deg min

Azimuth from LKF to FEL is 11 41.2

Azimuth from FEL to LKF is 192 15.0

Intermediate coordinates (Map crossings) :

Distance (km) from:

LKF FEL

Latitude Long i tude

deg min sec deg min sec

49 30 OO.OON 7 58 53.53E

50 00 OO.OON 8 19 36.08E

49 31 37.33N 8 00 OO.OOE

(Program Version: 24Jan7a)

II

24.16

85.00

27.45

90.39

29.55

87.10
Table 2-2. Earth Radius For Various Spheroids

Equ'atoria1 Polar Average Conversion

Spheroid Radius' Radius Radius Equatorial/Polar Average

International 6378.388 6356.912 6367.65 111.3239 110.9490 111.1365

Clark 1866 6378.2064 6356.5838 6367.3951 111.3207 110.9433 111.1320

Clark 1880 6378.249145 6356.514869 6367.382005 111.3214 110.9421 111.1318

Everest 6377.276345 6356.075415 6366.67588 111.3045 110.9344 111.1195

Bessel 6377.397155 6356.078963 6366.73806 111.3066 110.9345 111.1205

Australian National 6378.160 6356.7745 6367.46735 111.3199 110.9466 111.1333

t--J

t'V Airy 6377.563396 6356.256910 6366.910155 111.3095 110.9376 111.1235

Fisc'her 6378.155 6356.77332 6367.46416 111.3198 110.9466 111.1332

Malayan 6377.304063 6356.103039 6366.70355 111.3050 110.9349 111.1199
At a recent meeting of the International Astronomical Union, the

system of Astronomical -Constants was revised to reflect the adoption of

the values of the Australian National Spheroid as the current standard

in the System of Astronomical Constants. Although there are differences

in the several spheroids in present use, these differences are still not

resolved, nor perhaps resolvable since satellite measurements indicate

that the Earth is not a true spheroid. For a further discussion of the

determination of the various spheroids see for example "Dynamic Geodesy"

by Kamela (1964). A map showing which areas of the world are based on

the various spheroids is contained in u.s. Army TM 5-241-1 (1967). Thus,

for greatest accuracy, the applicable spheroid constants can be used in

any particular area of the world.

However, lest we lose sight of the relative importance of the accuracy

and precision required of the spheroid constants, it should be pointed

out that the distance factor derived from the equatorial and polar Earth

radii is used in LOS system calculations primarily to determine transmission loss in free space. The distance term in this equation is 20 log d

and the error introduced into the transmission loss value by using the

widest spread of values from Table 2-2 is bounded by

111.3239

20 log 110.9344

which is of the order of 0.03 dB.

The information used to compute azimuth from true north and path length

is essentially the same as that in MIL-HDBK-4l6 (1977) pp. 4-36 thru 4-39.

The spherical triangle on a unit radius sphere used for the computation of

points on a great circle path is identified on Figure 2-2 as PAB. Points

A and B are the antenna terminals, and P is the north or south pole. Point

B is selected to have a greater latitude than A. The triangle shown is for

the northern hemisphere but may readily be inverted to apply to the southern

hemisphere. The latitudes of the points are denoted by LA and LB, while

C is the difference in longitude between A and B. Angle Z multiplied by

the Earth's radius is the corresponding great-circle path length. The

following formulas are practical for hand computations as well as for

digital computers. Equations 2-3 to 2-7 have been taken from ITT (1975)

(pp. 28-9 to 28-11).

13
EQUATOR

Figure 2-3. Spherical triangle for great-circle path computations.

14
Y + X

tan 2

The initial bearings or azimuth values (X from terminal A, and Y

from terminal B) are measured from true north, and are calculated as

follows:

tan _Y_;_X = ( cot %) (Sin LB; LA) / (COS LB LA)

(cot %) (COS LB; LA) / (Sin LB LA)

(2-3)

(2-4)

Y + X Y - X Y + X

2 + 2 = Y, and 2 y - X

2 X. (2-5)

The great-circle distance, Z (in degrees), is given by

z ( LB - LA) ( Y + X\ / l Y - X) tan 2 = tan 2 sin 2 J ,in 2 ·

To convert the angle Z obtained in degrees to kilometers, the

following is used:

(2-6)

D·km 111.12 ZOe (2-7)

The following formulas show how to calculate either the latitude or

the longitude of a point on the great-circle path, when the other coordinate is given. The given coordinates often correspond to the edges of

detailed maps, and to intermediate points usually about 7.5 minutes apart,

so that straight lines between points will adequately approximate a

great-circle path.

The basic map crossing equations may be derived by calculating the

intersection of the equation of a sphere and the equation of a plane

through the origin at the center of the sphere in terms of latitudinal

and longitudinal coordinates. The symbol for latitude is L and for

longitude A. The angle values for north latitude are considered positive

and for south latitude they are negative. The angle values for east

longitude are positive and for west longitude they are negative. The

equation for this intersection (all great-circle paths) is:

tan L (2-8)

where k l and k 2 are constants for any particular great-circle path. Another form of this equation is:

15
(2-9)

where k3 and k4 are also constants for any particular great-circle path.

The relationship between the two sets of constants are:

k = k2 k 3

k 1

or = 3 sin k

4 cos k 4

and

k 4 tan-1 (k2/kl = ) •

( 2-10)

(2-11)

Since the tower coordinates for A and B are usually known, these coordinate values (LA' AA) and (LB, AB) may be used to calculate the greatcircle path constants:

( 2-12)

(2-13)

(2-14)

With values for these constants, the intersection of the great-circle path

with any value of latitude or longitude may now be calculated provided

that it exists (some great-circle paths do not intersect some latitudes) •

The explicit expressions for latitude in terms of longitude and longitude in terms of latitude are:

L = tan-1 [k3 sin 0. + k 4}]

and

(2-15)

16
Program No.2, Path Profile and Ray Path Characteristics:

The purpose of this program is to help provide the designer with an

accurate set of information about the radio path. The goals are optimum

selection of antenna heights and the preparation of foundation information

to estimate the radio path reliability.

Figure 2-4 is a diagram of the terrain profile andray-pa'th model. The

ray paths are calculated in accordance with the procedures in MIL-HDBK-4l6

(1977) .

Initially, the program should be used to help with the process of

route selection. After a route has been selected, the program can be used

to supply forms and information for the field survey. Often preliminary

information is not accurate and such forms prompt the field survey engineer

to obtain both accurate and complete information. For example, coordinates

for one of the towers obtained early in the design process may turn out to

have been coordinates for an older tower. Such discrepancies often become

apparent on the site survey and a complete set of forms prompts a thorough

search for the required information especially if the information input to

the calculator is printed out in the same format as that required for filling

out the site survey forms. After the field survey has been completed, this

program should be rerun using the new information to insure an accurate

foundation for link outage time ·predic;tions.

The output of this program is in two parts; one part is a path

profile with ray paths drawn for a diversity configuration (normally on

11 x 17 inch paper) and the second part is a tabular summation of meteorological, geographical and other required information about the path (see

Figure 2-5 and Table 2-3). Some information common to the output from

Program I is presented again on the tabulation (coordinates, heights, etc.).

Several sL~ple models are used to find parameters that are used in

various steps of the system design. These models are needed to calculate

ray path geometry, Fresnel-zone clearance, minimum path clearance above

obstacles and terrain, ray take-off angle at the antenna, minimum atmospheric

layer penetration angle,* mean atmospheric pressure along the ray path and

mean height of the ray path above ground.

*The term penetration angle as used here means penetration angle of atmospheric layers concentric with the center of the earth.

17
START

INPUT OTHER PATH J--~~INFORMATION (TREE

HEIGHTS, ETC.)

INPUT TERRAIN

PROFILE DATA

INPUT SITE

DESIGNATIONS

AND ANTENNA

COORDINATES OR

PATH LENGTH

PLOT TERRAIN

PROF I LE AND RAY ....----- PATHS

CALCULATE

FRESNEL

ZONE

BOUNDARY

CALCULATE

RAY PATHS

CALCULATE TERRAIN

CLEARANCE

CALCULATE

ANGLES OF

PENETRATION

PRINTOUT

TABULATION OF

PATH INFORMATION

CALCULATE

MEAN RAY

PATH HEIGHT

CALCULATE

MEAN

ATMOSPHERIC

PRESSURE

END

Figure 2-4. Terrain profile and ray-path model.

18
DISTANCE (miles)

1""" 0. "m 12.43 24.86 37.29 49. 72 62. 15 328" Ei •••••••••••••••• '.,••••••••••••••••• '.,•••••••••••••••••••,•••••••••••••••••••,••••••••••••,••••••,•••••••••••••••••'.,•••••••••••••••••••,••• '•••• , "'!f

Latitude . Longitude Elevation (m)

----.----- k- 4/3 LKF 49 lS'04'·N 75S'47"E 682.8

----k- 4/3 FEL 5814'33"N 829'4911E 688.8

90B t:.... kc:a 4/3 Pat.h Length _ 114. 55 kill ..,j. 2952

- - - k- 2/3 25 April 18 ProJeot. No. 9183504 DRW

. . . . . . . .. 8.68 Freenel Zone

900 L l~ at. 8.32 GHz ..:.12624

.\

188 L M. .. \. 115 ..j 2296

.~ I

~. 690 \ I \ •••\ !" ( 1968 ""'

+>.~

CD '~ \\ • '- /. . LKF +> .' CD

(I) \.'- /. (I) E ." . 4- 'V 588 ...'. ~. . I 1640 'V

(J)

-.J

\.

. " / ~.!.....J .~ j (J) \.O:E ~." ",..! :E

400 \. . ,/. : 1312

W I W

> \ >

300 \ I t\ 984

a \~/\ a

200 \, ./ \; 656

< \ / < > \ /,.... >

W 188 328 W

B " 8 28 48 68 88 188 120

DISTANCE (kilometers)

Link Profil~ from FELDBERG to LANGERKOPF

Figure 2-5. Example of terrai:n profile and ray paths.
Table 2-3. Example of Microwave Path Tabulation

Terrain Profile and Ray Path Information

for the FELDBERG, LANGERKOPF Link

27Ju178 Project No. 9103504 THH

COORDINATES:

Site

FEL 0:

LKF 1:

Latitude

50 14 '33"N

49 lS'04"N

Longitude

8 29, '49"E

7 SO'47"E

Elevation

above l-lSL

688.8m

602.0m

Heights Above Ground

Upper Ant Lower Ant

120.0m l03.0m

lOS.Om 90.0m

PATH LENGTH:

Path Length is 114.55 kilometers

PATH AZIMUTHS:

Azimuths from True North:

LKF 1 to FEL 0 23 48'14"

FEL 0 to LKF 1 204 18'02"

Azmuths from Magnetic North:

LKF 1 to FEL 0 11 41. '14"

FEL 0 to LKF 1 192 15'02"

RAY PATh MINIMUM CLEARANCE:

For an Earth Radius Factor of k= 0.67:

Absolute clearance is 24.37 meters at 93.18 km from FEL.

Minimum clearance is 0.94 Fresnel Zones at 8.20 GHz~

and 93.18 km from FEL.

20
Table 2-3. Example of Microwave Path Tabulation

(Sheet 2)

Terrain Profile and Ray Path Information (continued)

for the FELDBERG, LANGERKOPF Link

ANGLES OF ATMOSPHERIC PENETRATION:

FOr an Earth Radius Factor of k= 1.33:

Take off angle at LKF I is -0.44 degrees.

Take off angl e at FEL 0 is - O. 34 deg rees.

Minimum angle of penetration is 0.00 degrees.

PATH NOTES:

1. Mean atmospheric pressure on the path is P

m

= 9,3.96 kPa

2. Mean Path height for k=4/3 is h

m

= 321.20 meters.

3. Has an allowance for growth been included in the

tree heights shown on the profile ? '

4. The terrain is typical of Mountains.

5. The estimated annual worst month average

snow depth at the location of minimum

clearance is 3.00 m.

6. Additional comments: (entered by operator)

New construction -is planned near LKF site.

21
Table 2-3. Example of Microwave Path Tabul~tion

(Sheet 3)

Profile Data for the Path from

FELDBERG Tower 0 to LANGERKOPF Tower 1

25 April 78 Project "No. 9103504 DRW

Metr icUni ts

Point Dist Elev Code Height

No. (km) (m) (m)

Eng 11sh Uni ts

Dist E1ev Code He ight

( mi ) ( f t) ( f t)

1 0.00

2 2.35

3 3. 56

4 8.85

5 11. 53

6 12.85

7 14.35

8 17.15

9 24.55

10 24 .65

11 24.85

12 25.67

·13 27.35

14 28.92

15 32.20

16 33.43

17 37.95

18 40.95

19 46.34

20 63.25

21 65.95

22 67.15

23 68.97

24 73. 05

25 79.00

26 81.23

2782.67

28 87.65

29 90.10

30 93.18

31 98.00

32 98.50

33 106.29

34 108.54

35 111.35

36 113.55

37 114.85

689

500

690

290

235

380

179

330

136

136

135

130

115

85

85

180

168

211

120

210

299

300

285

169

238

339

250

240

280

440

300

310

430

290

547

593

602

o

o

Tree 28

o

o

°0

o

o

Bldg 34

Bldg 34

a

Bldg 28

o

Water 0

Water 0

o

o

o

o

o

o

Bldg 18

o

o

o

Obst 25

o

o

o

Tree 12

a

o

o

o

o

o

o

22

0.00

1.46

2.21

5.50

7.16

7.98

8.92

10.66

15.25

15.32

15.44

15.95

16.99

17.97

20. 01

20.77

23.58

25.45

28. 79

39.30

40.98

41.72

42.86

45.39

49.09

50.47

51.37

54 .46

55.99

57.90

60.89

61.20

66.05

67.44

69.19

70.56

71.36

2261

1641

2264

951

771

1247

587

1083

446

446

443

427

377

279

279

591

551

692

394

689

981

984

935

554

781

1112

820

787

919

1444

984

1017

1411

951

1795

1946

1975

o

o

Tree 92

o

o

o

o

o

Bldg 112

Bldg 112

o

Bldg 92

o

water 0

Wa ter 0

o

o

o

o

o

o

Bldg 59

o

o

o

Obst 82

o

o

o

Tree 39

o

o

o

o

o

o

o
The geometry of the ray path is considered in section 4.2.15 of

MIL-HDBK-416 (1977) and the expression for the height of the ray path, h,

in meters above mean sea level (m.s.l.) is as follows:

h 1

12.75k (2-16)

where hI the antenna height in meters above m.s.l. where d o.

h 2 the antenna height in meters above m.s.l. where d D.

d the distance along the path in km.

D the length of the path in km.

k the Earth's radius factor.

In MIL-HDBK-416, (1977) section 4.2.18 an equation is provided for

calculating the nth Fresnel-zone radius, R , on a plane perpendicular to

n

the path:

R

n (2-l7)

where f = frequency in GHz.

The clearance, C, is the distance between the top of the obstacle

directly beneath the ray path and the ray path in meters.

The number of Fresnel zones, n, is given by the following expression:

3.34 fDC2 -3 n = x 10 .

dD - d 2

For all entered values of d along the path, n is calcd1ated and the

minimum value of n with the corresponding value of d is recorded.

The take~off angle, S, is the angle between the horizontal plane

and the tangent to the ray path at an antenna.

When d 0,

-1 h 2 - hI D

tan ( - ---) 1000 x D l2750k·

When d D,

-1 D h2 - hI

-tan (12750k + 1000 x D)·

23

(2-18)

(2-19)

(2-20)
If Sl < 0 and (32 < 0, then the minimum angle of penetration is o.

If If\1 < 1S21, the minimum angle of penetration is Isli for k > o.

If Isli > IS21, the minimum angle of 'penetration. is Is21 for k > o.

To calculate the mean atmospheric pressure along the path, we will

use the expression t:or pressure, p, as a function of altitude, h, in meters

above mean sea level provided in List (1951), pp. 266.

p

-5 5.2553

101.3 (1 - 2.26h x 10 ) (2-21)

where p is the atmospheric pressure in kilopascals (kPa), the mean

pressure p can be calculated by av~raging the 10 values of p calculated

for 10 equidistant points along the path calculated for k = 4/3.

To estimate the average height above ground, ~h, we calculate

the difference between h and the terrain height above mean sea level, h t ,

at 10 approximately equidistant points along the path and calculate the

arithmetic average, ~h, in meters.

24
3 • PROGRAM NO.3, MEDIAN' BASIC TRANSMISSION LOSS MODEL

The model for calculating median basic transmission loss is similar to

the model in MIL-HDBK-416 (1977). It is based on the inverse square law and

the gas absorption model (Figure 3-,1). Terrain reflections are not a part of

this model although for low antennas and particularly smooth terrain, reflections can strongly influence the median received signal level. Over

the frequency range of interest here (1 to 50 GHz), the adverse effects of

terrain reflections on signal level are usually overcome by using space

diversity. For this reason, we are not including terrain reflection effects

in the median basic transmission loss calculation. We do not want to imply

that terrain reflection effects should be ignored in the design of a system.

Aside from affecting received signal level, reflections may cause a delayed

signal distortion of the desired signal, therefore they should be avoided

if possible. Another factor which will affect median basic transmission

loss is partial blocking of the ray path by an obstacle. Such an obstacle

produces a diffracted field. Basic transmission loss may be estimated for

the diffraction path using the diffraction theory included in MIL-HDBK-4l6

(1977) but these estimates are not included in the calculator model.

The basic free-space transmission loss, ~f' is calculated as follows:

~f = 92.45 + 20 log f GHZ + 20 log dkm

dB (3-1)

where ~m is distance in km and f is frequency in GHz~

The atmospheric absorption loss component due to oxygen is dependent

primarily on air density and path length and is fairly stable as a function

of time. The component due to water vapor absorption, on the other hand,

varies with air density, temperature, and humidity which requires a more

complicated model to predict a median value. The first water vapor line

occurs at 22 GHz with substantial effects at frequencies above 15 GHz. The

graph often used to estimate water vapor absorption assumes a value of abso- , 3

lute humidity of about 10 glm (MIL-HDBK-4l6, 1977, p. 4-49). In many parts

of the world absolute humidity will remain between 20 and 30 g/m3 for weeks

at a time, therefore a better model than the one used in MIL-HDBK-4l6 (1977)

is required. The model which we use for calculating atmospheric absorption

is one prepared by H.J. Liebe and G.G. Gimmestad (1978). Atmospheric absorption, A , is calculated by adding the components due to oxygen and water

a,

vapor:

25
INPUT PATH LENGTH

TEMPERATURE, PRESSURE

AND ABSOLUTE HUMIDITY

CALCULATE FREE

SPACE BASIC

TRANSMISSION LOSS

CALCULATE

OXYGEN

ABSORPTION LOSS

CALCULATE

WATER VAPOR

ABSORPTION LOSS

CALCULATE MEDIAN

BASIC TRANSMISSION

LOSS

TABULATE INPUTS,

INTERMEDIATE RESULTS

AND MEDIAN BASIC

TRANSMISSION LOSS

Figure 3-1. Median basic transmission loss model.

26
A

a (3-2)

To calculate 02 absorption per unit length, 0,1' to 50 GHz:

S

a

a = 36

1::

a = 1

S F"

a a (3-3)

(3-4)

F"

a

I

a

f

(

y - (f - f) I Y - (f + f) I ) a a a a a a

-------- + -------- f 2 2 2 2 a (f - f) + Y (f + f) + Y

a a a a

A3 (p + 1.3 pw) to. 9

A4 pt

2

(3-5)

(3-6)

(3-7)

f frequency in GHz. (1<f<50)

f line frequency (see Table 3-1) a

300

T+273.16 where T = temperature in °c.

(-98<T<37)

(3-8)

T is the median path air temperature.

For the value of T, a world map of mean

temperature values is provided (Fig. 3-2). A

default value* is T

(60<p <101.3) . m (3-9)

Pm is the mean air pressure on the radio path.

It is provided as an o~utput of the path profile

and ray path program. A default va1ue* is p = m

101.3 kPa (pressure at mean sea level).

*The term default value as used here means a value for making an estimate

when a more accurate value is not available.

27
AVERAGE JULY TEMPERATURE (F·)

o

10

150 180

• . .l'= ---.....--------__---

.. , -~ ~" .. ' .

~..:-:-' ·""=~ .. ~Ait· , " , y

»--=:::::::: ::... -:-.. __ .,,~._ .. ~311 10 IO~:-!":' .' .. " •.•..... ~olO

5 •.. . Degrees Celsius = 9 (OF-32)

.. . 50

... - . &0------.

AVERAGE JANUARY TEMPERATURE (F'

o

10

20

Figure 3-2. Mean temperature values. (use July values for the Northern

Hemisphereand:January values for the Southern Hemisphere) 0

(From "Climates of the World", u.s. Dept. of camIn., ESSA,

Environmental Data Service, January 1969.)

28
pw =0.00046151 P (T + 273.16) (3-10) w

P = air water vapor density ing/m3. (O<P < 40) w w

For the value of Pw' a world con'tour map is provided (Fig.

3-3) • A default value for water vapor density is 15 g/m3 P = . w

For values of f a' AI' A2 , A3 andA4 , see Table 3-1.

Table 3-1. Oxygen Lines

Center

Frequency Strenqth Width Interference

f Al A2 A3 A a 4

(GHz) kHz (GHZ) 1

(kPa) kPa (kPa)

50.9873 2.44 E-6 8.69 8.7 x 10-3 5.5 x 10-3

51.50302 6.04 E-6 7.74 8.9 " 5.6

52.02117 1.41 E-5 6.84 9.2 " 5.5

52.54223 3.08 E-5 6.00 9.4 " 5.7

53.06680 6.37 E-5 5.22 9.7 " 5.3

53.59572 1.24 E-4 4.48 10.0 " 5.4

54.12997 2.265 E-4 3.81 10.2 " 4.8

54.67116 3.893 E-4 3.19 10.5 " 4.8

55.22136 6.274 E-4 2.62 10.79 " 4.17

55.78380 9.471 E-4 2.11 11.iO " 3.75

56.26478 5.453 E-4 0 .. 0138 16.46, " 7.74

56.36339 1.335 E-j 1.66 11.44 " 2.97

56.96818 1.752 E-3 1.255 11.81 " 2.12

57.61249 2.126 E-3 0.910 12.21 " 0.94

58.32389 ~.369 E-3 0.621 12.66 -0.'55 " 58.44660 1.447 ,E--3 0.0827 14.49 5.97 " 59.16422 2.387 E-3 0.386 13.19 -2.44 " 59.59098 2.097 E-3 0.207 13.60 3.44

60.30604 2.109 E-3 0.207 13.82 -4.35

60'.43478 2.444 E-3 0.386 12.97 1.32

61.15057 2.486 E-3 0.621 12.48 " -0.36

61.80017 2.281 E-3 0.910 12.07 " -1.59

62.41122 1.919 E-3 1.255 11.71 " -2.66

62~48626 1.507 E-3 0.0827 14.68 " -5.03

62.99800 1.492 E-3 1.66 11.39 " -3.34

63.56854 1.079 E-3 2.11 11.08 " -4.17

64.12778 7.281 E-4 2.62 10.78 " -4.48'

64.67892 4.601 E-4 3.19 10.5 -5.1

65.22408 2.727 E-4 3.81 10.2 -5.1

65.76474 1.52 E-4 4.48 10.0 -5.7

66.30206 7.94 E-5 5.22 9.7 -5.5

66.83677 3.91 E-5 6.00 9.4 -5.9

67.36951 1.81 E-5 6.84 9.2 -5.6

67.90073 7.95 E-6 7.74 8.9 -5.8

68.4308 3.28 E-6, 8.69 8.7 ...5.7

118.75034' 9.341 E-4 0.0138 15.92 -0.44 "

29
30'

so40'

60'

10'

20'

60'

40' 60

40'

~--t---t-::: I I i faI 40'

20' WEST O' EAST 20'

20' lEST 0' EAST 20'

, ~-_:t=t-~ 5 160'

40'

60' 40'

80' 60'

80'

100'

100'

120'

120'

140'

140'

160' (AST ISO'IEST 160'

i60' fAST 180' lEST 160'

140'

140'

100' 120'

,....- 120' iii iii iii I , i I t I I I; I I I go' , , iii i , iii • I

10'

x

~I j--l I 'I~/"K<..1 J I I I I I 1__L;;l'l " I I ..r-1r %

i

2()t~

60' SO'

20'

10'

50' --

JO'

60' • I

60'

SO'

10' I l::::::aw t 4C.-~ 51 I I I +-----1-- .. t . t

% OO~ , 9 .' - O' , " 0-

!-. % . . %- ---~... -- -- J

·40'

w

o

Figure 3-3. Contours of average absolute humidity (g/m3) for a summer mon·th (August for

the northern hemisphere and February for the southern hemisphere) (Bean and

Dutton, 1966)'.
To calculate water vapor absorption per unit length, 0,2' to 50 GHz:

0.1820 f [: : SbFb] + 0.1820 f N~ (3-11)

(see Eq. 3-8) (3-12)

(3-13 )

(3-14)

Nt'

W

-5 3 1 1.87 x 10 P pt • f.

.w (3--15 )

For values of f

b , B1 , B2 , B3 , and B4 , see Table 3-2.

TABLE 3-2. WATER VAPOR LINES

f,·····, B1 B2 B3 B b 4

22.23508 0.112 2.143 28.1 x 10-3 0

68.052 0.018 8.75 28 " 0

183.31009 2.41 0.653 28.2 " 0

321.22564 0.044 6.16 22 " 0

325.15292 1.59 1.52 29 " 0

380.19737 12.40 1.02 28.5 " 0

Table 3-3 is an example of the output format for Program No.3. The

primary output is one number (the estimate of median basic transmission

loss). The median basic transmission loss is estimated by adding ~f and

A as was done in MIL-HDBK-416 (1977). Using this value, Program No. 4

a,

will calculate the time distribu.tions o~ basic transmission loss due to

rain and mu1tipath.

31
Table 3-3 Example of the. Tabular Output Format From

the Median Basic Transmission Loss "odel

Median Basic Transmission Loss for the

Path from LANGERKOPF to FELDBERG

(June 8, 1978 - Project No: 9103504 - DRW)

Path Length = 114.55 km

Carrier Frequency = 8.20 GHz

Mean Path Temp·era tur e = 20.0 C

Mean Path Pressure = 95.07 kPa

Mean Absolute Humidi ty = 12.00 9/ CU m

-----------~--~--~~----~---~--

Free Space Basic Transmission Loss

Oxygen Absorption Loss

Water Vapor Absorption Loss

Total Median Transmission Loss

from LKF to FEL

(Program Version: 17May78)

32

=

=

=

=

151.91 dB

0.73 dB

0.64 dB

153.27 dB
PROGRAM NO.4, PATH-LOSS VARIABILITY MODEL

. There are essentially two components of temporal path-loss variability

that can"be estimated in a quantitative way. These components are multipath

fading and rain attenuation and they appear in the path-loss variability

flow diagram in Figure 4-1. There are other causes of path-loss variability

besides these two mechanisms but for a line-of-sight (LOS) microwave path

designed with proper antenna characteristics and sufficient terrain clearance, these other causes are of less importance. Two of these "mechanisms

are defocusing and diffraction fading.

In MIL-HDBK-4l6 (1977), the Barnett model was used for multipath

effects. In the automated digital system engineering model, we use an

updated version of the Barnett model which appears in an article by

A. Vigants (1975) entitled "Space-Diversity Engineering". This model for

calculating multipath effects on LOS systems has become widely accepted for

paths between 20 and 60 km long. For long paths, we used the Japanese

model, Morita (1970). This model was developed from a data base including

much longer paths than the Barnett model included.

One year of data for 5 GHz paths across the English Channel (88 km from

Swingate, England to ".,Houtem, Belgium) has recently been obtained. This set

of data is useful for comparison with long LOS multipath attenuation models.

The data set indicates that the temporal distribution of signal levels

(Figure 4-2) was much less severe than wo:uld be predicted from a simple

extension of the Barnett model. Barnett (1972), pages 332-333, states

reasons why the Barnett model should not be extended in a simple manner to

long paths.

Analysis of the Swingate-Houtem data indicates that the multipath

model may relax to a Rayleigh distribution as path length increases.

This Rayleigh distribution can be expressed as follows:

P = l-exp { -Mf/IO} " -In 2 • 10 (4-1)

where P is the fraction of time during which the signal is Mf dB or more

below the long-term median.

33
4-19

PLOT

2>L S AND LABEL RAIN

AND MlLTIPATH

LOSSES

4-17

-4-13

CALCUl.ATE TIME

PERCEHTS FtR

MULTIPAnt

CALCUl.A1£ RAIN

LOSS FtR VARIOJS

RAIN RATES

CALCUl.A1£ TIME

PERCENTS FtR 1HlSE

RAIN· RATES

4-18

PUrr

RAIN RATES. lRATES

LABEl. AND ANNOTATE

READ DISC

NO REDRJ

1

4-4

Figure 4-1. Path Loss Variability Model.
-18

Ie

Barnett Model

- - - Morita Model

o English Channel Data (Receiyer A)

C English Channel Data (Receiver B)

,--..

CJ::)

--C

'-'"

2B o D Cot-

'. :::E: '"

o c

" .

s::

0 (I]

"-

" .....

-0

o " CD 0 ::E: 30 "

31= t) 0 D "-

" ..--t

Q) 0 D

" c:c

..--t "-

Q) 0 c

>

Q) 48

--J

B. 99 B. 9 B. 5 H. 1 ~. B1 a. BB1

Fraction of Time, P, Below Level

Figure 4-2. Comparison of prediction methods with one year of

data from an LOS path across the English Channel

(88 km, 5 GHz) .

35
The Barnett model may be presented in the following form:

P

m (4-2)

where

0.24(c) < 1

P

m

the fraction of time that the signal fades to a depth

greater than Mf during the worst fading month.

Mf the fade depth exceeded

level in dB. Mf > 20.

d the path length in kIn.

f the frequency in GHz.

c = the climate factor

referred to the median signal

15 < d < 50.

1 < f < 50.

1 average terrain

c 4 over-water and coastal areas

0.25 mountains and dry climate

The Morita model presented in Morita (1970), page 810, predicts the

fraction of time that a microwave path is in a Rayleigh fading mode. A

translation of this model in terms of the same P, d, f, and Mf as the

Barnett model may be written as follows:

P

m

M /10

(1 - exp {-ln2/10 f }) (4-3)

Q 2 x 10-9 over mountains

Q 5.1 x 10-9

average terrain

Q 3.7 x 10-7(l/h)0.5 over water and coastal areas

h = average path height above ground in meters. d > 50.

Of all models for multipath fading, the Barnett and Morita models have

the largest data bases and seem to us to have been more carefully thought

out and checked than any other models. For these two reasons they have

been selected for inclusion in the automated digital· system engineering

model.

36
To convert the average fraction of time below a given level P during m

the worst fading month to the fraction of time below a given level during an

average year, Py ' the method described by vigants (1975) is recommended.

This procedure is given by the equation:

Py = P (9T + 160) x 10-3

moo(O<T <25) (4-4)

where T is the mean annual temperature in degrees Celsius (e) on the ray o

path.

Figure 4-3 shows the estimated time variability of basic transmission

loss due to multipath alone and rain attenuation alone. This figure is the

format of the main output of Program No.4. From this presentation, the

relative importance of multipath and rain attenuation fading with respect to

each 'other is quickly apparent. Table 4-1 is an example of the tabular

format for showing much the same infonnation as Figure 4-3. This format is

the most convenient type for transmitting the information needed for manual

entry into Program No.5.

To calculate the time below a given level referenced to the long-term

median due to rain attenuation, the Rice-Holmberg (R-H) model will be used

(Rice and Holmberg, 1973). The techniques and refinements of the R-H model

developed for Europe (Dutton, et al., 1974) and for the united States

(Dutton, 1977) will be used in the model. The Rice-Holmberg algorithm is

as follows:

The R-H model determines the number of hours in an average year of

rainy t-minute periods, Tt(R), for which a surface rain rate, R, in mm/hr is

expected to be exceeded. The value Tt(R) is given in the R-H model (continuing their notation) as

Tt(R) Tltqlt(R) + T2tq 2t(R) hrs,

where

qlt(R) = eXP(-R/Rlt),

q2t(R) 0.35 exp(-0.453074R/R2t}

+ 0.65 exp (-2.S57143R/R2t},

TIt SM/Rlt hrs,

(4-5)

(4-6)

(4-7)

(4-S)

T2t (1-B)M/R2t hrs, (4-9)

where M is the recorded station average annual precipitation in millimeters and f3 is the ratio of "thunderstorm rain", Ml , to M for a year.

37
158

168

178

IIi iii iii

8/25/78 Project No. 78-9-99 1m

+ Calculated Median ------Multipath

TNI18IIi88ion LOll =153.3 dB Rain

"

"-,

"

,

"-

"

,

,

"

,

,

",

,

"

"-',,-

Path Length <Geo> =114. 55 kat

Carrier Frequency =8. 2ft GHz

Vertical Polarization

218 ~~~...L.....-.II.---~"","",,"-,-.....a..-..-.Ir--.....w..LI-lr...L-ol-..Io---L----l"""""""""""""'''''''''''''-''~''''''''''''~---''''''''''''''''''''''''''''''~''''''''''

8.9 is 8.1 III B.BBI a..l a._I illll11

Fraction of TiDle, P, Below Level

Terroin type =mountains RadOllf8 L088 per Antenna =1. 6 dB

Avg. Annual Tamp. = 20 OC Mean Annual Rainfall = B9H mm

No. of Rainy Dayslyr. =111

Thunderstorm Ratio B=lIS

Multipath and Rain Loss Variability

for the Path from FELDBERG

Tower 0 to LANGERKOPF Towe~l

Figure 4-3. Example basic transmission loss variability distributions.

38
Table 4-1. Example of Tabular Output of Path Loss Variability Information

MUltipath and Rain Loss Variability_

for the FELDBERG, LANGERKOPF Link

8/25/78 Project No. 78-9-99 DRW

Transmitter: FEL 0

Receiver: LK F 1

Path Length - G.e.D. (krn) =

Frequency (GHz) =

Vertical Polarization

Median Transmission Loss (dB) =

Avg annual Temperature (C) =

No. Rainy Days/Year =

Annual Precipitation (rom) =

Thunderstorm ratio: Beta =

Terrain factor (mountains =

Rain attenuation curve:

114. 55

8.20

153.27

20

III

800

0.15

0.25

Tr ansmis sion

loss (dB)

173 .. 3

178.3

183. 3

188.3

193.3

198. 3

203.3

208.3

213.3

Loss below

r-1 e d ian ( dB )

20.0

25.0

30.0

35.0

40.0

45.0

50.0

55.0

60.0

Fraction of time, P,

Loss is exceeded

3.64E-04

2.11E-04

1.49E-04

1. 02 E- 04

6.25E-05

3.23E-05

1. 32 E- 05

3. 99 E- 06

8.22E-07

Multipath equation:

Multipath coefficient, K = 0.02589

P = K*[1-exp(-ln2/X)], where X = 10+(O.1*M)

and M = Number of dB below median loss.

(Program Version: 25Aug78)

39
R1t = A1

+B1 in tC1 exp [~~~o]+ t~lO } mm/hr,

Al = 1 + 65.67864 exp(-SM/8766) mrn/hr,

B1 = 13.457 exp(-SM/8766) mrn/hr,

C1 = 0.00704709132,

R2t = (l-S)M rom/hr. 24D[0.165+0.776 exp (-120/t) + A exp (-B/t) ]

(4-10)

(4-11)

(4-12)

(4-13)

(4-14)

(4-16)

(4-15)

Here D = D(O.Ol) is the number of .days during an average year in which

precipitation exceeded 0.01 inches of recorded precipitation, and

B = 1443.95 In [8.26136 (36~.25 -0.940823>]

A = exp (B/1440)

8.26136

We are interested in rain rate events of very short duration and therefore chose t = 1. The value of D for Europe is found by using

D = 0.07651M - 83.632S + 62.523. (4-17)

The unknowns inthe'equations 4-5 through 4-17 are S, M, and D. Many of

these values are"obtained from Figures 4-4 through 4-10. The figures show

values of Sand M for Europe, the united States and roughly estimated values

for the remainder of the world. For parts of the world other than the u.s.

and Europe, a value for M can be obt'ained from The Times Atlas of the World

(1975) plate 4. For parts of the world other than the u.S. and Europe,

D= 1 +M/8 orD = ,365 (4-18)

whichever is less. For most of the world,. measured statistics are not available for D necessitating the approximations provided 'by eqs. 4-17 and 4-18.

A special map of annual rainfall throughout the world is often needed

when using Program No.4. This large map is provided in the computer

operators manual since the model is very sensitive to this parameter. The

world maps should only be used outside the united States and Europe.

Figure 4-11 is an example output of the point rain rate distribution.

This computer output is useful to the engineer evaluating a long path

traversing mor,~ t.hp.n one raihfall value region. The fraction of time, P,

that a given rain rate is exceeded on this graph is obtained from the

equation:

40
Scoies

km e:c:E:L:S

o 100 lOG 300 400 sao

M;. F9

o 100 200 300 400 500

Figure 4-4. Annual'precipitation, N, in millimeters, for an

average year in Europe.

//

I

I

.4-1894 J
N

SCales

m EL::eL:E3

o ,00 lOG 300 400

Mi. E9 E3 i ,

o 100 200 500 400 500

Figure 4-5. Mean annual thunderstorm ratio, (3, for Europe. (Dashed contours

indicate regions of sparse data.) 'F'f1546 I
w

Scales

km= ..... Ijijij4

o 500

Ml F3 Fa . I

o 100 200 300 400 500

Figure 4-6. The estimated number of :rainy days, 0, for an

average year in Europe.

'.74 -29-76]
<It ..22

082

_461~ HAWAII

t.:.~~..1.00 • 31~

&

Figure 4-7. 30-year mean annual precipitation, M, in millimeters,

for the U.S.A.
U1

II

, ,

I /

J t &M. 7~ q 0

, ,e:;;t' __ 0

C41.162 184 ~c=.

HAWAII.087~{J2 ~.

Figure 4-8. Mean annual thunderstorm ratio, a, for the U.S.A.
(j)

I / is I

! (3=.,/ /

11~ 7~ v

· I c:7 \

lob \ ~o '130 .. L'. \ 0

I 110 / __

Figure 4-9. 30-year annual number of days,.D, with precipitation

greater than 0.25 rom for the U.S.A.
20'

50'

60'

__--et 10'

10'

:c

s:

,.,'WJt;... .., I' 10'

...... ,:.).," , I 10'

~~~~~+--H----+---+t---+---+---1f-----I:.:rn¥t;;;';.;H~~~~--+--+--#t---+l-h~~~~~~~~ 30'

0.1

I':!\. ·....r·. ··i ~<l':'" ":':':':':':'421 20'

LONGITUDE

90' lOS' 120° 135' 150' 165° EAST J800 WEST 165°, ISO° 135° 120° 105° 90° 75° 60° 45° 30° IsolEST 0' EAST IS' 30' 45' ..,-- iii i i tit , i -r- f Iiiii' so- 75'

20'

30'

90'60'

40'~---+- I \gl li&I I / I I \ 1{'<iJT:/ I 1 .-Is .......L::: 140'

SOOI I """" I 7'1 ,~~) L V ISO'

Figure 4-10. Mean annual thunderstorm ratio, S, for the world.

30°' 'q..l7'···~=-q·; I: +--- I I' If·~''JIIt; \I~ Y - I

60' I I. D. j~ 160'

40'

I -

700 ~-""+~:-- •.~- r-- - 0.01 - 1.... 70'

...:.'. :.....: I':r __ ~~~,...,., r ~~ -!'I'""'" ...... 3~ ~~ ~KI -.-

~.

........:..... ~'"""' •••.:. ---.-C':7.'h-.

' .. :'. - I·.... >: r0~_3 ...

90°60° 750 90° 105° 120° 135° 150° 165" EAST 1800 WEST 1650 lSO° 135° 1200 1050 90° 75° 60° 45° 300 15° WEST ()O EAST 15° 30° 45° 6010'

50'

60'

10'__

~_----I

1)'~-r--~~=-jl----:t---t--r-r--r-t-=:::t~~±1~~~PtT7tB~~~---:-+-~~.~~

20,1 I __ ..L.:: ~~~l"\J t.: 1 1 r I I I \ \ \\)Y,1.~/I'. II I \

w lO'r~~·~~~~"+--t--\+-t-~--+--LJ~

~~:3 10'~1 1"1'__ "·:fi_l\o;~·".F"io:: -I I' i 1l I'

-....J
1.&1 I._I

26Jun78 Project No. 9tm4 1lIi

1.1 l81 1..1

Fraction of Ti.., p. pr -Year,

that G Given Rain Rate i. Exceeded

1· ~--- --.... .....-a---.... --a

19 1.5

lit

(I)• 18

...,

o

c

....

o

.f,)

c

.....

o

CMean AmJal Rainfall =••

No. of Rainy Daye/yr. =111

Thunderetor8 Ratio B== L15

Point Rain Rate Time Distribution'

for the Path from FELDBERG

Tower 0 to LANGERKOPF Tower 1

Figure 4-11. Example point rain rate distribution.

48
P = Tt (R)/8766. (4-19)

The layer of water formed on an antenna weather cover during a rain

storm produces a few'dB of attenuation (Hogg et al., 1977, pp. 1579).

The amount of· attenuation depends on several factors:

1. Rain rate

2 • Wind direction r

3. Condition of the radome surface; i.e., roughness, weathering,

composition, etc.

4. The shape of the radome, i.e., flat or curved.

5. The microwave frequency.

Measurements produced 4 to 8 dB attenuation at 20 GHz and 3 to 6 dB at

'II GHz (Hogg et al., 1977). An equation for estimating radome attenuation,

~, for each antenna is:

= 0.2 f 5<f<50 GHz (4-20)

where f is the carrier frequency in GHz and is the wet radome

attenuation in dB.

This estimate is for a ,parabolic antenna with a flat weather cover.

CCIR (1974a) shows the calculation of attenuation per unit path length

due to rain as a function of radio frequency and rain rate. It has become

clear that the polarization of the radio wave is also an important variable

(Hogg, et al., 1977, pp. 1577-1578). The relationship between rain attenuation, YH,v for spherical raindrops, and rain rate and frequency may be expressed as follows:

a,

YH,v = ~,VR dB/kIn ,(4-21)

where K and" a, are functions of frequency andR is the rain rate in mm/hr

(CCIR , 1974a, pp. 71).

a, = -0.0059 f +1.265 5<'f<50 GHz (4-22)

(4-23)

These expressions for a, and K are obtained from measured values (Lin, 1977,

pp. 1597) and (CCIR, 1974a, pp. 77) f is the carrier frequency in GHz.

( )

(-0.0059 f + 1.265)

= f ~9~·5 5<f<50 GHz

Using the experimental results on attenuation polarization dependence

described by Hogg, et a1. (1977):

Y

H = ..(f1

;04.5 x R)

for horizontal polarization and

(-0.0059 f + 1.265)

49

(4-24)
( 4 0.34

Yv = 0.8 + f-2.9 5<£<50 GHz (4-25)

for vertical polarization.

If the rain rate along a path were uniform, the total path attenuation, AR, would be equal to plus the length of the path, d, times YH,v.

High rain rates are not uniformly distributed along paths longer than a

few hundred meters, therefore an expression is required to relate point rain

rate to path rate. A simple expression for the ratio of path rate, ~A' to

point rate, R, is' given in Lin '(1977) and it has been checked against

measured data,

~A 2636 --= R>10 rnm/hr. R 2636 + d (R - 6.2)

To calculate total path attenuation due to rain,

AR = +

YH,Vd 2636

R>lO mm/hr. 2636 + d (R - 6.2)

(4-26 )

(4-27 )

The variability of path loss due to rain attenuation is plotted using

the graphical format shown in Figure 4-3. The basic transmission loss,

~, shown for rain in this figure is approximately equal to the median basic

transmission loss added to the rain attenuation, ARo

50
PROGRAM NO.5, LINK EQUIPMENT GAIN

In order to assess adequately the performance ofa microwave link, it

is necessary to calculate the time availability distribution of received

signal level, RSL, at each end of the· link. To calculate this distribution, information on the following considerations is required:

1. Median basic transmission loss across the path.

2. Variability of the transmission loss.

3. Antenna gains.

4. Transmitter power output.

5. Transmission line loss.

6. Diplexer and power splitter losses.

7. Type and configuration of the diversity and combining system.

8. Equipment and support systems reliability.

Calculation of equipment and support system reliability is generally

considered separately from the other seven components. Usually a given

amount of allotted outage time is assigned to equipment and support

systems failure and approximately the same amount of time is assigned

to anomalies associated with the propagation p.ath. Progralu No. 5 calculates the time availability of RSL assuming uninterrupted equipment

and support system service. A simplified flow diagram of the Link

Equipment·Gain program is presented in Figure 5-1.

Basic transmission loss and its variability is calculated in

programs 3 and 4.

Antenna gains for parabolic antennas may be supplied to the program

either by direct entry or by entering carrier frequency and aperture diameter.

To calculate antenna gain, G,- we use the equation from MIL-HDBK-4l6 (1977),

page 4-194:

G

where

(5-1)

n aperture efficiency (usually 0.55),

D diameter; A = wavelength (in the same units).

Equation 5-1 may be rewritten for n = 0.55, f in GHz and Din meters

to give:

G 20 log 7.772 Df dB.

51

(5-2)
5-1

EQUIPMENT

GAIN

HOUSEKEEPING

CALCULATE

MEDIAN

RSL

5-7

coMBiNE

MULTIPATH AND RAIN

LOSS VARIABILITIES

5-8

PLOT 2) END

OR END

?

1) PLOT

5-18

PLOT DISTRIBUTI"ONS

5-11

LOAD

PROGRAM

6

5-12

END

Figure 5-1. Link equipment gain.

52
Transmitter power output is entered in dB above a milliwatt (dBm).

(One Watt is equal to +30 dBm.) Transmission line loss values may be entered

directly or values may be calculated from line lengths and from graphs provided in the Andrew Systems Catalog (1978) (Figure 5-2).

Diplexer losses should be entered when they are applicable (applicabi.lity depends upon where receiver and transmitter power measurement

reference points are located in the system).

Calculation of vertical space diversity improvement, I , (with switch

as

cOmbining) is based on the model provided by Vigants (1975) pp. 110-112.

If we let T be the time that the signal from the main antenna remains

m

below a given signal level and if we let T be the simultaneous time that

s

the signal from both antennas is below L, then I is defined as T IT . as m s

From Vigants' (1975) model,

where

I

as

2

0.001213 fdS x 10

(G -G + Mf ) s m

10 , s<20

Lvi >20

f

(5-3)

G the median RSL from the main antenna in dBm

m

G the median RSL from the secondary antenna in dBm

s

f the carrier frequency in GHz

s = the vertical separation of antennas in meters,

center-to-center

d the path length in kilometers

Mf the fading depth below the median RSL

For calculating frequency diversity improvement, I of ' we also use the model

given in Vigants (1975):

where

If1- f 2 1<0.5

M >20 f

(5-4)

f l and f 2 are the carrier frequencies in GHz.

53
Reproduced by permission of ANDREW Corp.

en

w

ex:

fW

S

8...

ex:

W

a..

m."

!

z

o

i=

c(

:;)

z'W

...

6.0

-."" -;':--

1.5 2

•..._'L'.,

3 4 5 6 7 8 9 10

::::

;

::: '" : ,

-~-

.. ,+~

.. , , ,,,- . ..-.

_.. _ ..--,..

- .....

!'--'

."---

:-"---''''

,. ,--.'

'..•-.

-- '," .,---

1

f--' ,,,.. ,,

'-T'-

.

i ::'

.

!

...---. ""..•-. ~: ,::

.--... ,,,:'-

---",,--

-- ---:..,:

15 20

Attenuation curves based on:

VSWR 1.0

Ambient Temperature 24°C (75° F)

High-Conductivity Copper

FREQUENCY IN GIGAHERTZ

Figure 5-2. Microwave waveguide attenuation.

54
The value of I calculated in equations 5-2 and 5-4 is valid only if

o

the diversity signal is at each instant the stronger of the two received

signals. If switching only occurs when the receiver off-line has a

signal level which exceeds the on-line receiver signal by some threshold

power ratio, B, in dB, the actual diversity improvement is I where:

(5-5)

The efficiency factor, n

d is,given by:

55

tions, we assume that for frequency diversity the difference in carrier

frequency values is negligibly small in terms of the effects on median

signal level and variability. The distributions can be combined by

simply adding the times below a given level because, in general, multipath

fading does not occur at the same time as rain attenuation fading.

sity (Figure 5-3), the multipath variability with diversity must be calculated using the diversity improvement factor, I. Diversity is only an aid

for decreasing the effect of multipath fading. The distributions of the

rain signal level and the diversity improved multipath signal are combined

in the same manner as they were in the nondiversity case. In our calculan

d

2 ( 10B/10 + 10-B/10 ) -1 (5-6)

For example if B = 6 dB, nd = 0.47. Such threshold power ratios for

switching are often built into combiner configurations to prevent excessive switching.

Table 5-1 is a sample summary of the link and equipment parameters

used to calculate RSL.. This sununary is one of the two output formats

from Program No.5. Figure 5-3 is a sample of the time availability

distribution output format. The RSL distribution without diversity

(Figure 5-3) is obtained by combining RSL variability due to rain

attenuation with the variability due to multipath without diversity. The

combining of.variability distributions is done by adding the fraction of

time below a:Biven level due to multipath to the fraction of time below

the same level due to rain. To obtain the RSL distribution with diver-
Table 5-1. Sample Summary of Basic Link and Equipment Gain Parameters

Basic };lath and ECluipnlerlt Gain f'aran:eters for the Link

f rOBl ft'BLDBER'G tc LA1\jGERKOPlt- (Shee t 1)

(18Ju178 flroject l~O. 9103504 IfHli)

Input P'arameter 'rransmit ter Rece iver

Primary Secor.dary

LKF~

1

4 9 18' 4. 00 .. N

'7 50 '47 .OO"E

6 02 .00

23 48'13.55"

11 41'

105.00 90.00'

PARABOLIC PARABOLIC

47.36 47.36

3.66 3.66

EW8S' EW8S

10.50 10.50

120.00 115.00

12.60 12.08

1.20 1.00

= l'-'EL

= 0

= 50 14'33.00"N

- 8 29'49.00"E

( Ill) = 6 88 • 8 0

=204 18' 1.69"

=192 15'

(rn)= 120.00

= PARABOLIC

(dBi)= 47.36

(m)= 3.66

= EW8S

(dB/lOOm) = 10.50

(m)= 135.00

,< dB) = 14 • 18

(dB)= 1.00

Latitude

Longitude

'}iower Base E lev. above f4bL

Azimuth from 'True North

Azimuth from Magnetic North

Antenna Height above Ground

Antenna Type

Antenna Gain

Antenna Diameter

f'eeder 'rype

Feeder Loss

fleecier Length

'rotal Line Loss

Circulator/Diplexer Loss

Site Designator

Tower NUITlber

111

0\
Table 5-1. Sample Summary of Basic Link and Equipment Gain Parameters

Basic Path and Equipment Gain Parameters for the Link

f r·om FELDBERG to LANGERKOPF (Shee t 2)

Path Length

Polar i zation .

Primary Carrier Frequency

Receiver Front-End Type

Receiver Front-End Location

Diversity Configuration

Detection Combiner 'rype

corr:b iner 'fype

11ransrr.i t ter Power

Median Basic Transmission Loss . \. . Prlmary Recelver r..ledl.an l~SL

Secondary Receiver l"ledian RSL

Vertical Antenna Separation

Difference in Median RSL

Diversity Efficiency ~Iactor

(km) =

=

(GrlZ);=

=

=

=

=

=

(dtiITi) =

(dB )=

(dBm.) =

(dilm) =

(In) =

(dB)=

=

114.55

Ver tical

8.20

PREAt·lP20DB

ANTEl~NA

DUAL SPACE

PRE DE'fEC

~'iAX RATIO

43.00

153.27

- 30. 73

- 30 .73

15.UO

0.00

1.00

-~--~~~~----~~~~-~~--~---~------

Received Signal Level Curve:

Received Signal

Level:RSL (dbm)

-50.7

-5.5. 7

-60.7

-65.7

-70.7

-75.7

--SO.7

-85.7

-90.7

RSL Belc\-j

£vIed'ian (dd)

20.0

25.0

30.0

35.0

40.0

45.0

50.0

55.0

60.0

SpaCE Diversity

Improvement

2 • O·

6.2

19.5

61.8

195.4

617.9

1954 • 0

61 79 .2

19540.5

57

r'ract ion of time,

P, below RSL

6 .3·3"E-=O·4-·

:2.38£-04

1.52E-04

1. 02£"04

6.'25£-05

3.23E-05

1.32E-05

3.99E-06

8.22.t;-07
0 Without Diversity

With Diversity

-3~

18Ju178 Project No. 9103504 THH

+ Calculated Median

RSL =-317 dB

-4B

e. 1 l at Be B~l ~~Bl

Fraction of Time, P, Below Level

Path Length (Gem =114.55 km

Dual Space Diversity

Transmitter Power =43.~0 dBm

Primary Median RSL =-30. 73 dBm

Secondary Median RSL =-30.73 dBm

-SB

r-t

o -78 c.

tn

.,...

(J)

-0

(J)

>

0a; -sa

o

Q)

0.::

....-4·

<D

>

(J)

-I

Antenna Gain (dBi)

Line &E9uip Loss (dB)

Fre9uency (GHz)

Polarization

Transmitter Primary Receiver

47.36 47.36

15.18 13.80

8.20

Horizontal

Secondary Receiver

47.36

12.03

8.2~

Horizontal

Combined Multipath and Rain Loss Variability

for the Path from FELDBERG

Tower 0 to LANGERKOPF Tower 1

Figure 5-3. Time availability of received level

58
PROGRAM NO.6, LINK PERFORMANCE CALCULATIONS

The purpose of the link performance program is to calculate the

reliability and quality of a line-af-sight link used in either an analog

or digital system. Performance must be evaluated for both long- and

short-term services. For analog systems, long-term service quality is

primarily a function of" equipment quality and median signal level. This

service quality is conveniently calculated using the computer (see Figure

6-1). For practical digital systems transferring data at rates less than

50 Mb/s, the long-term service quality is primarily a function of equipment quality. The median signal level required for optimum digital system

quality is many dB less than that required for optimum analog quality (Bell

Telephone Labs, 1970, pp. 553-554). This characteristic of digital systems

with their nonmultiplicative noise build-up makes it unnecessary to calculate

the long-term, high signal level quality of such systems. Short-term reliabili.ty and quality of both analog and digital systems are dependent on

the propagation characteristics of the radio path. Calculation of shortterm radio propagation reliability for a given value of signal quality

is easily done using the desk-top computer system and is indicated in

Figure 6-1.

Noise calculations for analog systems have not changed significantly

in the past several years and the model presented here is much the. same

as the one used in MIL-HDBK-4l6 (1977).

To obtain an overall summary tabulation having link performance compared to applicable standards, the following steps are necessary:

1. Calculate standards requirements for FM-FDM links.

2. Obtain standards requirements for digital links.

3. Calculate the FM-FDM link, worst-channel receiver transfer

characteristic (signal-to-noise ratio as a function of receivedsignal-level, p). Thermal noise, equipment intermodulation

r

distortion and feeder echo distortion must be calculated first

to obtain the receiver transfer characteristic.

4. Calculate the digital link receiver transfer characteristic

(bit-error-rate as a function of P ).

r

59
CALCULATE RSL

DISTRIBUTIONS

AND fADE MARGIN

INPUT DCS

NOISE REQUIREMENTS

CALCULATE RSL

DISTRIBUTION

CALCULATE LONGTERM THERMAL

NOISE

CALCULATE FEEDER

INTERMODULATI ON

NOISE

CALCULATE ·LINK

NOISE ALLOWANCE

CALCULATE

EQUIPMENT

INTERMODULATI ON

NOISE

0'

o

DETERMINE LONGTERM TOTAL NOISE

PERFORMANCE

CALCULATE SHORTTERM TOTAL NOISE

PERFORMANCE

CALCULATE ANNUAL

AVAILABILITY

COHPARENOISE

ALLOWANCE WITH

TOTAL NOISE

PERFORMANCE

COMPARE SHORTTERM NOISE ALLOCATION

WITH PREDICTION

COMPARE CALCULATED

"AND ALLOWABLE

OUTAGE TIME VALUES

Figure6-l. Link performance evaluation.
5. Calculate the outage time at the minimum allowable, shortterm, signal quality level by comparing corresponding signal

quality values from the receiver transfer characteristic

with fraction of time values from the RSL time distribution

(calculated in Program 5) using RSL as the comparison

parameter.

6. Tabulate input variables, results from steps 1, 2, and 5

and other important information about the link.

Each of these steps will be discussed in the order shown above.

Defense Communications System (DCS) Noise Req'uirements forFM-FDM Si'stem

Link Design:

On the basis of a hypothetical reference circuit, MIL-STD-188-300 (1971)

in paragraph 4.3.3.1.2 allocates a maximum of 3.33 pWpO/km median noise

level in the noisiest voice channel due to radio equipment and propagation.

This value translates to approximately 3.2 pWO/km (flat weighting). In

order to provide a design objective this value was selected as a standard

of analog link quality comparison for Program No.6. The 3.2 pWO/km

value seems to be' ;consistent with CCIR (1974b) and industry standards for

high performance links (Broadhage and Hormuth, 1968, page 22). Most of

this noise allocation is assigned to equipment noise since thermal noise

is a small component at the median signal level. Median path length in

te~restrial LOS microwave systems is approximately 35 km. Because of equipment noise predominance and the 35 km average distance, we can allocate an

average of 112 pwe of noise in the worst channel per link. For a specific

combination of paths, a different link noise allowance may be calculated:

P

NA

where

3.2

n

i n

L:

i 1

d.

1 (6-1)

P"NA is the noise allowance per "link in pWO.

d. is a path length in km.

1

n is the number of paths.

P

NA 112 pWO is the default value of noise allowance

per link.

61
It should not be cause for alarm if an individual link's median

noise level does not fall within its assigned noise allowance since it

is the summation of the median noise values which is important. (See

Program No.7.)

For short-term performance considerations, the maximum allowable

flat weighted noise is 500,000 pWO in the worst channel (MIL-STD-l88-300,

1971, p. 48). 500,000 pWO corresponds to a value of signal-to-noise ratio

in the worst channel equal to 33 dB.

The signal-to-noise ratio is allowed to fall below 33 dB for no more

than 10 minutes per year (approximately 2 min during the worst month, MILHDBK-4l6, 1977, p. 4-261) which is equivalent to an average availability of

0.99998 of the year.

DCS Short-Term Requirements for a Digital System Link Design:

MIL-STD-188-322 (1976) states that for LOS digital microwave systems:

"It is a design objective to have a 30 dB minimum fade margin on

all paths. All radio links are required to have a lninimum annual

path availability of 0.99995 for maintaining a bit error rate of

5 x 10-9 for operation below 10 GHz. All radio links are also

required to have a minimum annual path availability of 0.99998 for

maintaining a bit error rate of 1 x 10-2 ."

These availability values are the short-term requirements for digital

systems. Long-term or median path performance (for error rates substan-

-9 tially less than 5 x 10 ) are not meaningful since such low error rates

are generally a function of equipment performance, not path performance.

Long-Term (Median) Thermal Noise Calculation:

For purposes of system noise calculations, thermal noise is defined

as noise from all sources in a channel when there is no modulated signal

present on any of the channels in the microwave system. By this definition, thermal noise includes atmospheric and cosmic noise, and all

intrinsic and thermal noise produced in the equipment when no modulation

is present. Thermal noise is measured in a channel with all modulation

removed from all channels of the system.

The signal-to-ther~al noise ratio in an FDM-FM system is related to

path loss variability. As the path loss on a hop becomes low, i.e., the

62
received signal level becomes high, the thermal noise is relatively quite

low. As received signal level decreases toward FM threshold, the thermal

noise becomes higher. Signal-to-thermal noise ratio, S/N

t , in a voice

channel is proportional to received signal level, P , or carrier-to-noise r

ratio C/N. In the region above FM threshold, SiN may be expressed in

t

several forms:

SiN = P + 20 log -10 log (kTb x 103 ) -F

t r f c m

(6-2)

P

r

~F 3

+ 20 log f -PF - LF - 10 10g(kTbc x 10 ) -F

m

(6-3)

~F BrF S/Nt = C/N + 20 log f -PF - LF + 10 log b

m c

of BrF

C/N + 20 log f + 10 log b

m c

(6-4)

(6-5)

BIF

LF

2 (~F + f )

m

( <Sf) (antilog PF\ (antilog LF\ ln 1,u..,

20) 20 J ~ilL..

-10 + 10 log n in dB.

(6-6)

IC_-l\ \ u- I J

(6-8)

~F is the peak carrier deviation in kHz

of is the rms per channel deviation in kHz

S/N

t

is the voice-channel-signal-to-thermal-noise ratio in dB

P is the received carrier level in dBm, r

C/N is the predetection carrier-to-noise ratio in dB and N is

the receiver front end thermal noise power in the same

units as Pr

PF is the baseband signal peak factor of 13.5 dB

LF is the RMS noise load factor in dB

b is the usable voice channel bandwidth taken to be 3.100 kHz

c

BrF is the receiver rF bandwidth in kHz

f is the highest modulating frequency in the baseband in kHz

m

F is the receiver noise figure in dB

k is Boltzman's constant, 1.3804 x 10-20 millijoules/degree K

T is the antenna temperature taken to be 290 degrees K, and

n is the number of voice channels in the baseband.

63
(6-9)

The value of P at which thermal noise threshold, P (TH), occurs is given r r

by the equation:

Pr(TH) = 30 + 10 log (kTBIF x 103) + F.

The value of P at which FM threshold occurs, P (FMTH), is:

r r

P (FMTH) = 10 + P (TH). r r (6-10)

The terms on the right-hand side of equations 6-2 and 6-3 with the

exception of P may be calculated for a given set of equipment param- r

eters. This then becomes a constant - a figure of merit - and as P

r

is allowed to vary, the voice channel signal~to-thermal-noiseratio

varies in proportion. Using this information, a receiver thermal noise

transfer characteristic or "quieting curve" may be constructed, where

its slope is uniquely determined by any of the above equations for

conditions above FM threshold.

Equipment Intermodulation Noise Calculation:

Equipment. intermodulation noise, for the purpose of system noise

calculations, is defined as the total noise from all sources produced

as a result of the presence of a modulated signal in the system except

feeder echo noise. Intermodulation noise is measured in a channel with

all modulation removed from the channel being measured, and with all

remaining channels loaded with actual traffic or with an equivalent amount

of white (randomly-distributed) noise over a specific bandwidth. The

intermodulation noise power in the channel is then equal to the measured

total noise with modulation present, less the measured thermal noise with

no modulation present.

The values of noise power ratio (NPR) in the channel having the

worst signal-to-noise ratio must be obtained from either equipment

performance specifications or carefully controlled tests. The specific

loading conditions and received signal level (RSL) must be known for each

NPR value. Of particular importance, is the NPR value corresponding to

the optimum RSL for a particular microwave radio.

If information is not available, an NPR value of 55 dB obtainable

using new, quality equipment ···is probably the highest value that can be

64
assumed for the initial estimate. A pre-emphasis improvement of 4 dB in

the worst channel is usually assumed included in this NPR value.

The above discussions hold for remodulating (baseband) radios. If

the designer is concerned with heterodyne repeaters, the above measurements become very difficult to make and the designer has to rely on

manufacturers' specifications. Alternatively, a 4 dB improvement in NPR

(Lenkurt Electric Co., 1970) over the remodulating radio may be assumed.

For example, if a 55 dB NPR is assumed for theremodulating radio, a 59 dB

NPR would be used for a similar quality heterodyne unit.

Allocation of calculated noise is difficult particularly for mixed

systems on a hop; i.e., a remodulating transmitter at one end and a

heterodyne repeater receiver at the other end. Very little information

exists on the noise contribution of the individual components or even

that of the transmitter and receiver separately. For an engineering

estimate, the equipment intermodulation noise may be allocated in equal

parts to the transmitter side and the receiver side.

The noise power ratio can now be converted to an equivalent noise

channel signal-to-equipment intermodulation noise ratio, SiNe, and additionally to .equipment intermodulation noise, Ne:

SiNe

Ne

NPR + 10 log (Bb/bc) - LF dB (6-11)

antilog 90 - SiNe pWO (6-12) 10

f - f (6-13) m

where

f the upper baseband frequency (kHz). m

f~ the lower baseband frequency (kHz).

b the nominal voice channel bandwidth, 3.100 kHz.

c

LF the RMS load factor in dB (see eq. 6-8).

In these noise calculations flat-weighted noise will be used for ease

in hand~ing. If the designer desires to use other noise weightings,appropriate factors may be included at the conclusion of the design procedure.

65
Feeder Intermodulation Noise Calculation:

If a transmission line many wavelengths long is mismatched at both

the generator and load ends, its frequency-phase response is linear with

a small sinusoidal ripple, and this leads to reflected waves in the line

that cause distortion of an FM signal. This type of distortion is more

conveniently considered as being caused by an echo signal generated in a

mismatched line, which results in intermodulation distortion. Significant

levels of this type of intermodulation noise are reached when the waveguide

lengths exceed approximately 20 meters per individual antenna, or 30 meters

total per hop (MIL-HDB~-416, 1977, p. 4-284).

The feeder intermodulation noise is also considered to be independent of path loss or signal level variations and is therefore another

component of the time invariant nonlinear noise power.

Feeder intermodulation noise, Nf , may be approximated given transmission line lengths, velocity of propagation in the lines, transmission

system component VSWR's or return losses, transmission line losses and

directional losses. The calculations are performed separately for each

end of a hop; i.e., transmitter and receiver, and the results are

summed to determine the total hop contribution.

To calculate Nf in the worst channel, the echo delay time is first

calculated. Determine echo delay time, T, from the transmission line

length, L, and the percent velocity of propagation, (% v), obtained

(6-14) -2 (% v x 10 ) mise

V are:

from Figure 6-2 using:

T = 2L/V Sf where V

Reasonable default values for

V 0.65 (3 x 108 )

V 0.75 (3 x 108 )

for elliptical waveguide and

for rectangular waveguide.

The echo delay time is then converted to radian delay, 8

o

e = 2nf T x 103 (6-15) o m

where f is the highest modulating frequency in the baseband. The

m

echo power, r, relative to the signal power causing it is given by the

expression:

(MIL-HDBK-416, 1977,

pp. 4-286, 4-389)

(6-16)

66
courtesy of Dre John Osepchuk (MIL-HDBK-416, 1977).

VELOCITY OF. PROPAGATION FOR ELLIPTICAL IAVEGUIDE

15 20

.... £113%

f '/·i.:

..1.. : .. j., .. . 1. ..I...: .~!.. i :

.,. ~._ ...L .~..~L_. __ ..L .. __ .L-l__._...- j .•

;

;

.... ··.'d.. ......... -~..... ~.

40a.- ~-------~--~.......-~-~---------------II 10

90

>-

t::

80 -'

>""

w

u

w

w 70 0:

...

lAo

0

=

w

u

G: 60 W

0-

50

FREQUENCY IN GIGAHERTZ

VELOCITY OF PROPAGATION FOR RECTANGULAR WAVEGUIDE

90

80

>-

....

u0

w

-' 70 >

.'"u

c

w'"

G: 68 ....

lAo

0

....

z

w

U

G:

w 50 0-

40

30

15 20

FREQUENCY IN GIGAHERTZ

Figure 6-2. Waveguide velocity curves.

67
where r = the number of dB that the echo is down from the signal

power

RL

a

the transmission line loss in dB.

the return loss (dB) at the interface between the transmission line and either the transmitter or receiver

(whichever case is applicable).

the return loss (dB) at the interface between the transmission line and the antenna.

This model assumes that all discontinuities are negligible with respect

to the ones at these interfaces in the intermediate section of the

transmission line between the transmitter or receiver and the antenna.

If pa.rameters other than return loss are provided such as the

VSWR or the voltage reflection coefficient, p, they can be converted to

return loss, RL, using the following expressions:

p

RL

VSWR - 1

VSWR + 1

20 log (lip).

(6-17)

(6-18)

The power in the echo cannot totally be considered as distortion

power, D, unless the echo delay is large. To obtain the value of SiD,

a "parameter An must be det~rmined:

or alternatively,

A

LF

of x 10 20

f

m

(6-19 )

A

of

f

m

(6-20)

(The variables in the equations for A have been defined earlier in

this section. See equation (7-8) to calculate LF.)

S Using parameter A and 8

0 , (0 - r) can now be obtained from Figure 6-3)

A good approximation (developed by the authors) for - r can be obtained

from the equations:

1 Fl (A,8) = 7.17 - 8.23 In A + 40 log e

F2 (A) 9.421 - 54.84A + 113.2A2 - 88.5A3+ 31.52A4

- 4.239A5

S where D r equals the greater of Fl and F2 •

68

(6-21)

(6-22)
1.0 10

69

Maximum distortion to signal ratio, due to echo.

0.1

MAXI!r1U!-1 MODULATING FREQ (RADIS) X ECHO DELAY TIME (S)

Figure 6-3.

~..:.:::.: ::+~I:'A a 0 6 -~. - A: 0 4~:t:.:: ::~ ..::1::= ~::: ~'1--++-'H'+'.....,.•..-f _ ••" __ '__'~"".''''.--&-4,'''''''''''''''_'.--:--;.. _.. - . :. . ~:..- .::::..:.. ., ,+~;:; :::: .::t-_. .. . '-.+--.~'-I-.++-+-.+-lI-+-+-"""'+--·+-+-_-4._I.:_-""-."'",-~-,,'--+-.,-i-I'-I
The calculation of echo attenuation (separately for transmitter and

receiver) outlined above can now be converted to voice channel noise.

To do this, the total echo attenuation, r, is added to the (SiD - r)

value obtained from Figure 6-3.

This results in the signal-to-distortion ratio, SiD which must be

corrected for the ratio of baseband to voice channel bandwidth and for

the RMS load factor. In equation form, the voice channel signal to

feeder echo noise ratio becomes:

Bb SINf = SiD + 10 log - LF dB.

c

The conversion to flat-weighted noise is as follows:

. 90 - SiN antllog f pWO.

10

The foregoing feeder echo noise calculations are performed separately

for each end of a hop by arbitrarily designating one end the transmitter and the other end the receiver. At the conclusion, these two

noise results are summed together to give a total hop feeder echo

noise contribution.

(6-23)

(6-24)

The sum of the total feeder echo noise and equipment intermodulation noise in this design will be called the time invariant nonlinear

noise since these noise components do not depend on path loss variability.

This total noise component is normally the dominant contribution forrelatively high signal levels near the long-term median.

The effect of using a linear adder or maximal ratio combiner is to

decrease the time invariant nonlinear noise (Ne + Nf ) in all channels

by a factor of 1/2. This combiner improvement, I , is approximately c

3 dB or 0 dB depending on the combiner type.

Pre-Emphasis/De-Emphasis:

As a result of the linear frequency modulation process, channel

noise power increases with baseband frequency so that the higher channels

have smaller signal-to-noise ratios than the lower ones. To compensate

for this effect in most radio-relay systems, pre-emphasis is applied.

Pre-emphasis means that before frequency modulation is accomplished in

70
the transmitter the level of the upper part of the baseband is increased

while the level of the lower part is decreased. This is done in a manner

such that the mean total baseband power is the same as it was before

pre-emphasis was applied. The result is that noise in the channels is

redistributed so that the S/NT in the worst channel is improved at the

expense of the better channels. In the worst channel, pre-emphasis/

de-emphasis improvement, I is approximately 4 dB if the CCIR network is

p

used (EIA Standard,1972, pp. 30-34).

Receiver Transfer Characteristic for FM-FDM Systems:

The receiver transfer characteristic is one of the outputs of Program No. 6 (Figure 6-4). The receiver transfer characteristic is called

the quieting curve when feeder echo noise is not included in its calculation. This transfer curve is a good indication of the link dynamic

performance characteristics. It is essentially a plot of worst voice

channel signal-to-noise in decibels as a function of received signal

level. The receiver transfer characteristic is limited at the upper end

(high received signal levels) by the equipment intermodulation noise, and

at the lower end by the FM improvement threshold.

The available dynamic range for linear system performance is that

portion of tqe unity-slope straight line between the FM improvement threshold and the. line intersection with the S/(Ne

+ Nf ) ·

Performance below the FM improvement threshold can be approximated

by a line with a slope of 4 (4 dB decrease in signal-to-noise ratio for

each 1 dB decrease in received signal level) at SiN values lower than

that corresponding to the FM improvement threshold.

The equation for the receiver transfer characteristic includes

feeder echo noise as well as thermal noise and equipment noise. For performance above FM threshold, worst channel signal-to-noise ratio, SiN , is

w

given by the equation:

SiN = 90 - 10 log N

w w

where N is the noise in the worst channel

w

N

w =(antilog (-Ip/lO) (NT) + antilog (-Ip/IO) (Ne

+ Nf ) ·

See equation 6-10 to calculate the value of P at which FM threshold

r

occurs.

71

(6-25)

(6-26)
-88 -78 .. F>5B -.

Single Receiver Input Power, RSL

......

']Jt

(..)

&

=-28 ......... -1.

FM/FD~ Equipment Transfer Characteristic

For the Link from FELDBERG Tower 0

To LANGERKOPF Tower 1

Figure 6-4. Example of a worst channel FM-FDMreceiver

transfer characteristic.

72
Receiver Transfer Characteristic for Digital Systems:

Although the bit-error-rate; BER, threshold will vary for various

types of digital receivers, the shape of the transfer characteristic

will generally remain the same in the presence of Gaussian noise (Bell

Telephone Labs., 1970, p. 629). The equation for the receiver transfer

characteristic is:

(6-27)

where the constant, k , may be determined from the BER threshold using a

o

successive approximation method described in a book by G.E. Forsythe, et al.,

(1977 pp. 161-165). Figure 6-5 is an example of a digital receiver transfer

characteristic.

primarily due to rain attenuation, one more important piece of information

is desirable. This information is how often the calculated short-term

outage RSL level will occur. will it occur twice per year or once every

two years, etc? As desirable as this information would be, a reasonably reliable model is not available in the literature at this time.

Lin (1977) p. 1589, does, however, point out that the annual outage

time of a radio route is statistically more stable than that ofa radio

link which indicates that this type of information is not so important

as it first appears to be.

All that remains to be done on the link analysis is to tabulate the

link performance summary. Table 6-1 is an example of this summary.

73
-88 . -78

Single Receiver Input Power, RSL (dBm)

( 21Ju178 Project No. 91B3584 1lII)

Data Trane.i88ionRate =12. 6iJ Mb/.

Type of Sy8t.. =Three-Level Partial Reeponee

Carrier Frequency = a. 2m GHz

lxlr7 BER Threehold (-71·6)·

18 8

18-1

18-2

18-3

18-4

I.JJ

CD

cD 18-5

-i->

0

0:::

18-6 to

t.

(.

lLJ 18-7

-a.>

.r-t

CD 18-8

18-9

la-18

-9H

PCM-TDM E9uipment Transfer Characteristic

For the Link from FELDBERG Tower

To LANGERKOPF Towar 1

Figure 6-5. Example of a digital receiver transfer

characteristic.

74
Table 6-1. Example of the Lir1llc Performance Sunnary

(21Ju178 Project No. 9103504 THH)

Design Summary for the FM/FDM Link

from FELDBERG to LANGERKOPF (Sheet 1)

ANTENNA

FM/FDf\t

114.55

Vertical

20

94

1"2

321

r·1ountains

800

0.25

100

20DBPREAlriP

DU.AL SPACE

PRE DETEC

[·1A X RA'f 10

=

=

•

=

=

=

=

=

=

=

(nlo,) =

(km) =

(C)=

(kPa)=

(gm/cu. m) =

Above Ground (m)=

Input Parameters:

System 'l"ype

Path Length

Polarization

Mean Path Temperature

Mean Path Pressure

Absolute Humidi ty

Average Path He ight

Terrain Type

Mean Annual Rainfall

Mean Thunderstorm Ratio

Annual No. of Rainy Days

Re'ce iver r"ront-End Type

Receiver Front-End Location

Diversity Configuration

Combiner Location

Combiner r.r·ype

-..J

U'1
Table 6-1. Example of the Link Performance Swmnary(con't)

Design Sumn,ary for the l"M/FDM Link

from FELDBERG' to LAi~GERKOPF (Sheet 2)

Input Parameter 'l'ransmi tter Receiver

Primary Secondary

47.36

3.66

E~a5

10. 50

110.00

11. 55

1.00

0.61

1.06

30.71

1.06

30. 71

i"':\ t~f~ t~· L11.. 1C

LKi'-

1

4 9 18' 4. 0 0 "1~

7 50'41.0Q"E

6 02 .00

2348'13.55·

11 41'

105. 00 90 • 00

47.36

3.66

E.J85

10.50

125.00

13.13

1.00

0.61

1.06

30.71

1.06

30.71

fJAHAdurJI:

,47.36

3.66

EW8S

10.50

140.00

14.70

1.00

0.61

1.0"

30.71

1.0b

30.71

==

=

:=

=

= i'EL

= 0

= 50 14'33.00"N

= 8 29'49.00"E

(-m) = 688.80

=204 18' 1.69"

=192 IS'

(til) = 120. (;0

= PA Hl\B{JI..Ie

.. (n,) =

(d8)=

(cB)-

({Bi )::.

(dU/100 Il') =.

(.n) =

(n.) =

(dB)=

Antenna Diameter

Feeder 'l.'ype

feec3er Loss

I:'eeaer Leng tl'i

'lotal Line Less

Circulator/Diplexer. Loss

FeederVelocity Ratio

VSwR at Antenna

Return Loss at Antenna

\iSwl~ at Rad io

Return Loss at Radio

Site Designator

Tower ~umber

Latitude

I..ong itude

rrower ijase Elev • above t\lSL

Az inlu ttl from 'l:r ue ..,or th

AziJnutn frolf~ .r·~agnetic· ·North

Antenna Height abcve Ground

~ntenna 'l')'pe

Antennc;. l;ain

'-J

0\
Table 6-1. Example of the Link Performance Suimnary (can't)

Design Summary for the FM/FDM Link

from FELDBERG to LANGERKOPF (Sheet 3)

.....,J

......

Para'met~r

Primary Carrier Frequency

Secondary Carrier Frequency

Transmitter Power

Transmitter Antenna Gain

Primary Receiver Antenna Gain

Second Receiver Antenna Gain

Transmitter Line Loss

Primqr:Y.Receiver Line Loss

Se,cond Receiver Li·ne·Loss

Me:dianBasicTrans. Loss

Expected Median RSL - Recv P

Expected Median RSL - Reo" ·S

(GHz)=

(GHz )=

(dBm) =

(dBi) =

(dBi)=

(dBi)=

(dB)=

(.dB)=

(dB)=

(dB)=

(dBm) =

(dam) =

V·alue

8.20

43.00

47.36

47.36

47.36

14.70

13.13

11.55

-29.89

-29. 89
Table 6-1. Example of the Link Performance Summary (con't)

Design SUmRiary for the FM/FDM Link

from FELDBERG to LAN:GER·KOPF (Sheet 4)

(X)

Parameter

Is Pre & De-Emphasis Used?

Number of 3.1 kHz Channels

Receiver IF 3dB Bandwidth

Equipment NPR

Peak Carrier Deviation

RMS per Cha nnel Dev iation

Receiver Noise Figure

l·'M Threshold

Baseband Signal Peak Factor

m'lS Noise Load Factor

Voice Ch.annel· Bandwidth

Highest 1*100. Freq. in BD

Thermal Noise at l.fed'ian RSL

Feeder Echo Noise

Equip~ent Noise

Total Long-TermN oise

Long Ternl Noise Allowance

Desired Availability

Calculated Availability

F ader~1ar9in

=

(kHz) =

(dB)=

(kHz)=

(kHz) =

(dB)=

(dBm) =

(dB)=

(dB)=

(kHz)=

(kHz)=

(pWO) =

(pWO) =

(pW'O) ==

(pWO)=

(pWO):

=

=

(dB) =

Value

Yes

'600

20000.00

56.00

7330.03

200.00·

10.00

-80.97

13.5

17.78

3.1

2660.00

14. 03·

0.13

179.70

95. 71

112.00

0.99998

0.99995

45.52
Table 6-1. Example of the Link Performance Summary (con't)

Design Summary for the PCM/TDfwl Link

from l"ELDBERG to LANGERKOPF (Sheet 4, alternate printout for digital systems)

..oJ

\0

Parameter

Data Transmission'Rate

RSLat BER Threshold

BER at BERThreshold

Desired Availability

at BER

Calcul~ted 'Availabi,lit,y.

at BER

Fade Margin

Value

'(fttb/-s),= 12 .60

(dam) = -71.00

= 1.00E-07

= 0'.99995

= 1.OOE-09

= O.9~99,90

'1.0'0E-09

(dB)= 39.81'
PROGRAM NO.7, ·SYSTEM PERFORMANCE

The main purpose of the System Performance Program is to provide in

tabular form a summary showing long- and short-term system performance

for a number of tandem links. The flow diagram for the system performance evaluation model is presented in Figure 7-1.

Tables 7-1 and 7-2 are example tabulations for an FM/FDM and a

digital system, respectively. The tabulations can be used as an aid in

deciding which links should have their requirements relaxed or tightened.

By means of this iterative process, an optimum design may then be calculated. Tables 7-1 and 7-2 are for links going in one direction from one

end of the system to the other. Obviously, a pair of tables is required

for each system. One table is needed for links from east to west and the

other from west to east. The allocated system noise is obtained by

multiplying 3.2 pWO and the total length of the system in kilometers (see

eq.6-l). Computed system availability is obtained by multiplying the

values of availability for each path. Allocated system outage time is

obtained by dividing the system length by the average path length (35 km)

and multiplying that ratio and the allowable link outage time, 0.00002,

(MIL-STD-l88-322, Table 1). This outage time subtracted from 1 gives

the allocated system availability.

80
SUM

ESTIMATED

LINK NONAVAILABILITY

VALUES

COMPARE

SUMS

SU" LINK

NONAVAILABILITY

ALLOWANCES

NO

SUH

EST IHATED

LtNK NONAVAILABiliTY

VALUES

COHPARE

SUMS

SUM LINK

NONAVAILAB,LITY

ALLOWANCES

SUM

LONG-TERM

LINK NOISE

VALUES

COMPARE

SUMS

SUH LINK

LONG-TERM

NOISE

ALLOWANCES

(X)

I-'

TABULATE INPUTS, S,,"S,

DifFERENCE BETWEEN

ALLOCATION AND PREDICTION.

ALSO PRINT TOTAL SYSTEM

PERFORMANCE.

Figure 7-1. System performance evaluation.
(X)

I\.)

Table 7-1. Example FM/FDM System Performance Table

Performance Prediction for the FEL-RHNFM/FDfwt System

(26Sep78 project No. 9103504 LGH)

Path Fade Computed Allocated Computed Allocated

Link Freq. Leng th Margin Noise Noise Avail. Avail.

(GHz) (km) (dB) (pWO) (pWO)

FEL-LKF 8.2015 114 .55 45.52 96 112 0.999952 0.999980

LKF-RIIN 8. 7500 57.60 44.10 lSI 112 0.999960 0.999980

----- ------ System Values: '172.15 247 551 0.999912 0.999902
(X)

w

Table 7-2. Example Digital System Performance Table

Performance Prediction for the FEL-RltN Dig i tal System

(26Sep78 Project No. 9103504 LGH)

Path Fade Computed Allocated

Link F.req. Length ~'arg in Avail. Avail.

(GHz) (km) (dB)

FEL-LKF 8.2015 114.55 45.52 0.999952 0.999980

LKF-RHN 8.7500 57.60 44.10 0.999960 0.999980

--- ------ System Values: 172.15 0.999912 0.999902
8. RECOMMENDATIONS

The seven microwave system design programs described in this report go

far in reducing the cost of designing a microwave line-of-sight system but

there are many other labor intensive tasks which would be done better and

at less cost than they are now done by using interactively programmed desktop computers. Some of these. tasks are listed below:

1. Design of passive repeater systems.

2. Design of obstacle diffraction paths.

3. Reading of detailed map profiles onto disc memory by using the

map following, reading and digitizing capabilities of modern

microprocessor controlled plotters.

In addition to the design ofOsystems, record keeping capabilities of

desk-top computer systems are very efficient in the use of time and space

since, in many instances, an ordinary notebook full of flexible discs can

hold more information than a file cabinet. The indices and contents of

discs can conveniently and quickly be displayed or produced in hard copy.

These discs are readily kept current. Such things as site layout and

tower stress diagrams can be stored as well as daily site or system logs

and maintenance records. These concepts are practical provided that

interactive programs are developed which guide the user and are convenient

to operate. It is recommended that these capabilities be considered and

compared with present on-site record keeping methods.

The seven programs that have been developed can be much improved in

the light of continued user experience and new improvements in the models

on which they are based. It is reco~ended that a continuing effort be

made to improve the programs and that periodically the models themselves

be carefully re-examined as a result of improvements reported in the open

literature. This statement is particularly true of the rain attenuation,

multipath, and digital link and system performance models which are in a

state of rapid development.

84
9. . REFERENCES

Andrew Corp, (1978), Antenna Systems, Catalog 30, 151.

The American Ephemeris and Nautical Almanac for the Year 1975 (1973),

Nautical Almanac Office u.S. Naval Observatory, Superintendent of

Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Barrlett, W.T. (1972), MultipathPropagation at 4, 6, and 11 Bell

System Tech. J., Vol-51, No.2, 321-361, Feb.

Bell Telephone Laboratories (1970), Transmission Systems for Communications(Western Electric Company, Inc., Winston-Salem, N.C.).

Brodhage, H., and W. Hormuth (1968), 7th Ed., Planning and Engineering of

Radio Relay Links, (Siemens Aktiengsellschaft, Munich, Germany).

CCIR, (1974a), Doc. Vol 5, Geneva, Switzerland.

CCIR, (1974b}, Doc. Vol 9~ Rec. 395-1, Geneva, Switzerland.

Dutton, E.J., H.T. Dougherty, and R.F. Martin, Jr. (1974), Prediction of

European rainfall and link performance coefficients at 8 to 30 GHz,

Technical Report No. ACC-ACO-16~74, AD!A-000804.

Dutton, E.J.(1977), Precipitation variability in the U.S.A. for microwave

terrestrial system design, OT/ITS, OT Report 77-134.

EIA, Electronic Industries Association (1972), Standard Microwave Transmission Systems" EIA Std. RS-252-A, (Electronics Ind. Assoc., Engineering

Dept., 2001 Eye Street, N.W., Washington, D.C. 20006).

Forsythe, G.E., M.A. Malcolm, and C.B. Moler (1977), Computer Methods for

Mathematical Computations, Prentice-Hall, Inc., Englewood Cliffs,

NJ 07632.

Hogg, D.C., A.J. Giger, A.C. Longton, and E.E. Muller (1977), The Influence

of rain on design of ll-GHz terrestrial radio relay~ Bell System

Tech. J., Vol 56, No.9.

ITT, International Telephone and Telegraph Corporation (1975), Reference

Data for Radio Engineers, H.P. Westman, ed., 6th edition (Howard W. Sams

and Co., New York, N.Y.)~

Kamela, Czeslaw (1964), Dynamic Geodesy, Vol-I, (The Scientific Publications Foreign Cooperation Center of the Central Institute for

Scientific, Technical and Economic Information, Warsaw, Poland).

Lenkurt Electric Company (1970), Engineering Considerations for Microwave

Communications Systems, (GTE Lenkurt Dept. C134, San Carlos,

California 94070) .

85
Liebe, H.J. and G.G. Gimmestad (1978), Calculation of clear air EHF

refractivity, Radio Science, Vol 13, No.2, March-April 1978.

Lin, S.H. (1977), Nationwide long-term rain rate statistics and empirical

calculation ofll GHz microwave rain attenuation, Bell System Tech.

J., Vol-56, No.9.

List, R.J. (1951), Smithsonian Meteorologica~ Tables, 6th Ed., (Smithsonian Institution, Washington, D.C.).

MIL-HDBK-416, Department of Defense (1977), Design Handbook for Line-ofSight Microwave Communications System.

MIL-STD-188-300, Department of Defense (1971), Standards for Long Haul

Communications - System Design Standards Applicable to the Defense

Communications Systems.

MIL-STD-188-322, Department of Defense (1976) ,Subsystem Design/Engineering

and Equipment Technical Design Standards for Long Haul Line-of-Sight

(LOS) Digital Microwave Radio Transmission.

Morita, Kazuo (1970), Prediction of Rayleigh fading occurrence probability

of line-of-sight microwave links, Review of the Electrical Commun.

Laboratory, Vol l8~ Nos. 11-12, 810-822.

Morris, D.E., C.J. Christopher, G.W. Chance, D.B. Barney (1976), Third

Generation Programmable Calculator has computer-like capabilities,

Hewlett-Packard Journal, Vol 27, No. 10.

Rice, P.L. and N.R. Holmberg (1973), Cumulative Time Statistics of surfacepoint rainfall rates, IEEE Trans. on Corom., Vol. COM-21, No. 10.

The Times Atlas of the World (1975), (Comprehensive Edition), Times Books in

collaboration with John Bartholomew & Son Lim-1-ted, Edinburg, Scotland.

Vigants, A. (1975), Space-Diversity Engineering, Bell Systems Tech. J.,

Vol-54, No.1, 103-142.

86
FORM OT.29 (3-73)

BIBLIOGRAPHIC DATA SHEET

u.s. OEPARTMENi OF COMMERCE OFFIC E OF TEL ECO\itMUNICA 'f.IONS

1. PUBLICATION OR REPORT NO

I NTIA Report 79-18

2. Govtt Accession No. 3. Recipient ts Accession· No.

4. TITLE AND SUBTITLE

Automated digital system engineering model

7. AUTHOR(S)

L.G. Hause and D.R. Wortendyke

8. PERFORMING O~GANIZATION NAME AND ADDRESS Department of Commerce

National Telecommunications and Information Administration, Institute for Telecommunication Sciences

Boulder, CO 80303

11. Sponsoring Organization Name and Address

U.S. Army Communications - Electronics Engineering

Installation Agency

Fort Huachuca, AZ 85613

14. SUPPLEMENTARY NOTES

S. Publication Date

I'-1arch 1979

6. Performing Organization Code

NTIA/ITS

9. Project/Task/Work Unit No.

9101905

to. Contract/Grant No.

CCC-PO-8-77

12. Type of Report and Period Covered

NTIA Report

13.

is. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a si~nificant

bibliography ot literature survey, mentioo it here.)

This report describes a desk-top computer system and mathematical models which were

used in seven of its progams. These programs make key calculations in the design

of line-of-sight microwave systems. The models have the following ranges; bit

rates up to 50 Mbits/s, carrier frequencies from 1 to 40 GHz, and path distances

up to 150 km. The programs calculate, tabulate and plot information about earth

geometry, path profiles and ray paths, median basic transmission loss, path-loss

variability ,equipment gain, link performarfce, and system performance. Models

were chosen based on their wideness of acceptance and the size and type of data

base substantiating the model. Any design engineer using this model can have

immediate access to calculated results corresponding to changes in design para~­

eters. The reasons for this capability are that the programs are written for use

in an interactive mode and the programs can be used by people with no experience

in programming.

16." Key works (Alphabetical order, separated by semico1.ons)

Line-of-sight microwave, computer program, earth geometry, path profiles, basic

transmission loss, digital systems, micromave link performance, multipath fading,

rain attenuation

17. AVAILABILITY STATEMENT

[Xl UNLIMITED.

o FOR OFFICIAL DISTRIBUTION.

18. Sec uri ty Class (1his report)

Unclassified

19. Security Cla.ss (This page)

Unclass"ified

20. Number of pa.ges

98

21. Price:

L'SCOMM-OC 29716-P73

U. S. GOVERNMENT PRINTING OFFICE 1979 - 679-223/388 Reg. 8