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PREFACE
This book is a lineal descendant of an earlier Lenkurt publication, "Microwave Path EngineeringConsiderations 6000-8000 MC", which was originally published in 1960 and re-issued in a slightlyrevised edition in 1961. The purpose of that publication was to assemble in one volume, in a readilyusable and practical form, the basic information, principles, techniques and practices needed by anengineer engaged in the planning and engineering of line-of-sight paths for microwave communications
systems.
The present volume retains essentially the same purpose, in an expanded, enlarged, andmodernized version, reflecting the substantial changes which have taken place in the past decade. Amuch wider range of frequencies is covered, and new and extensive material is included onpropagation, diversity, and reliability calculations. Also much expanded is the material on noisepe;rformance and noise calculation methods, and new material has been added on towers, transmissionlines, and waveguides.
A preliminary edition of the present book was prepared in 1969 and a limited distribution made,with a view to obtaining comments and suggestions from the industry .Many valuable suggestions werereceived, most of which have been incorporated into the present edition to make it, we believe, amuch improved work. The efforts of those who were kind enough to review the preliminary edition
and send us their comments are gratefully acknowledged.
Although considerable effort has been made to eliminate errors, it is likely that some havesurvived, and we would appreciate having any of these called to our attention.
Robert F. WhiteSenior Staff EngineerSystems Engineering Department
Lenkurt Electric Co., Inc.San Carlos, CaliforniaJune, 1970
This third printing has been changed to Include changes to formulas in the text which wereoutlined In the second printing on page 119 under "An Important Post Script about propa-gatIon Calculations.'. That Information is also included for reference on page 119 of t h I s
printing.
T ABLE OF CONTENTS
SECTION
I INTRODUCTION
TITLE PAGE
II MICROW A YE FREQUENCY BANDS 2
ROUTE AND SITE SELECTIONIII 5
A. Order of Procedure 5
B. Sites 5
5The Requirements
Intermediate Repeater SitesSite Considerations. ..
55
c. Microwave Paths -General Appreciation Of Path Infillences 6
Description of Microwave Beam 6
67888
Influence of Terrain arid Obstructions. Influence of Weather. Influence of Rain and Fog at Higher Frequencies
Influence of Objects in Azimuth. Atmospheric Absorption.
D. Sources of Path Data 8
8Maps
2. Aerial Photography 11
11E. Path ProIJles
11I. Curvature
Scales 11
3. Equivalent Earth Profiles
174. Reflection Point Calculations
5. Preliminary Map Survey 18
18
18
18
21
21
21
21
UseofMaps Limitations. Cases of Incomplete Mapping. ., ..
Interference and Coordination-Preliminary ConsiderationsFrequency Band DivisionIntra-System Interference. External Interference.
226. The Field Survey
PAGETITLESECTION
Path ProfIles (Cont.
222424262626
Instrumentation. Things to be Avoided Methods of Operation' Records and Reports. Final Profiles. Path Coordinates, Azimuths and Distances
26F. Path Tests
27272727
Brief Description of the TestsInfonnation they ProvideEffects of K VariationsCost Considerations. ...
28OVERALL SYSTEM DESIGNIV
28A. Purpose of Section
28I. Final Objective for a System
282. Order of Presentation
28B. Interference and Frequency Coordination
28How Interference Occurs
2929
Interference MechanismsEffect on the System .
292. General Classifications
2929
Self Interference. .External Interference
303. Effect of Interference on Different Types of Signals
3031
Voice, Data, TelevisionTone Versus Pulse Interference
314. Calculations for Interference Effect
315. Satellite System Interference
33c. Propagation
33Variations in Signal Level due to Fading
33Comparison with Carrier Systems
ii
PAGETITLESECTION
c. Propagation (Cont,
332. Ground, Sky and Space Waves
33General Effects of Frequency
343. General Nature of Microwave Propagation
34Comparison with Light Waves
344. Free Space Attenuation
343434
Definition. Nature of Losses in Free Space
Free Space Formula. ..,
355. Terrain Effects
353538
Blocking, Cancellation of Out of Phase Signals
Nature of Obstruction Losses. Development of Fresnel Zone Radii. ..,
4)6. Atmospheric Effects
41424344444650
The Refractive Index. Illustrations of Refraction as Related to the M Profile
KFactors Weather Fronts. Rain Attenuation. Fog. Attenuation by Atmospheric Gases.
s7. Clearance Criteria
51
52
52
Normal Non-Reflective PathsReflective Terrain. ...Open, Rolling Terrain. ..
538. Delay Distortion
539. Fading
5510. Propagation Reliability and Diversity Considerations
5658
Diversity Arrangements. ...Reflective Path Diversity Spacings
591. Methods of Calculating the Probability of Outages due to propagation
596060
Non-Diversity Annual OutagesFrequency Diversity Improvement FactorCross Band Diversity Improvement Factor
iii
SECTION llTLE PAGE
c. Propagation (Cont.
Space Diversity Improvement Factor
Hybrid Diversity Improvement Factor
Correlation Coefficients. .
Multiline Systems. Non-Selective Fading. Other Treatments. ...
61
61
61
62
65
65
D, Noise Performance 65
Total Noise 66
6666666666
Thermal Noise. lntermodulation Noise. ...
Echo Distortion Noise. .Atmospheric and Man-Made NoiseMultiplex System Noise. ...
2. Noise Units 66
3. Determination of System Noise 67
68707171737373747478
Receiver Thermal Noise. ., ., .Practical Threshold. ...,Fade Margin ,...System Loading and its Effect on NoiseVoice Loading. , ., ," Mil ' t " L d '
lary oamg.,..,Composite Loading. ., ., ...Summing dB Powers. ,lntermodulation NoisePer Hop Total Noise. .., ...
784. System Noise Objectives
7979808081
CCIR/CCln' International CircuitsU.S.A. Public Telephone NetworksInctustrial Systems. " Mil .t "
S t1 ary ys ems. Television Transmission Systems
5. Noise Allowable for Small Percentages of Time 8}
81
82
82
82
82
CCIR/CCITT U.S.A. Public Telephone Networks
Industrial Systems. "Mil .t "
S t1 ary ys ems. Television Transmission. ...
iv
SECTION TITLE PAGE
v. EQUIPMENT 83
A. 83Radio Equipment
B. RF Combiners 83
c. Towers 84
D. Waveguide and Transmission Lines . 88
1. Rectangular Guide 89
2. Circular Guide 89
3. Elliptical Guide 89
90E. Antenna Systems
90I. Direct Radiating Antennas
90919191
Parabolic Antennas. High-Perforrnance or Shrouded Antennas
Cross-Band Parabolic Antennas. ...
Horn Reflector Antennas.
92Periscope Antenna Systems
99F Radomes
99G. Passive Repeaters
106H. Wire Line Entrance Links
CALCULA TIONS FOR A MICROW A YE SYSTEMS 107VI.
107A. Path Data Sheets
10B. System Reliability Estimates
1. Reliability with Respect to Multipath Fading 110
2. Reliability with Respect to Non-Selective Fading
3. Equipment Reliability Considerations
14
15
16
Equipment Availability CalculationsAvailability as a Parameter. ...What Alternatives?
4. Power Reliability Considerations
v
SECTION TITLE PAGE
c. 117Noise Performance Calculations
Microwave Noise 117
17
17
North American MethodCCIR Method. ...
2. Echo Distortion Noise
3. Multiplex Noise
184. Total Noise Estimates
North American MethodCCIR Method. ...
118118
APPENDIX I USEFUL FORMULAS AND EQUATIONS A
APPENDIX II USEFUL FORMULAS AND EQUATIONS IN METRIC FORM Bl
USEFUL T ABLES AND FIGURESAPPENDIX III c
vi
LIST OF TABLES
NUMBER TITLE PAGE
Microwave bands available to communications common carriers intheU.S.A.underPart2loftheFCCRules.
A2 Microwave bands available for private and local government micro-wave systems within the U.S.A. under various Parts of FCC Rules.(Not all bands are available to all types of users.) , 2
A3 Microwave bands available for TV Auxiliary Services within U .S.Aunder Part 74 of FCC Rules.
Microwave bands available for Federal Government Services withintheU.S.A.
A43
3AS Microwave bands per CCIR Recommendations
Microwave bands in Canada per Department of Communications System Plan 4A6
Multiplying factors which can be used to convert Fresnel Zone Radiicalculatedfor6.l75GHztootherbands.
Bl40
Multiplying factor for determining F n when F 41B2 is known
5c Excess attenuation due to atmospheric absorption
56Relationship between system reliability and outage timeD
69E Noise unit comparison chart
Standard CCIR 20 logl 0 6f/fch factors for top slot 71F
75G Summation or subtraction of non-coherent powers
80H Typical U.S.A. noise objectives
92I Antenna gains for estimating purposes
vii
LIST OF FIGURES
FIGURE TITLE PAGE
1 Diffraction vs. Refraction
2 Blocking and reflecting effects in the horizontal plane 9
3 Earth curvature for various values of K 13
Equivalent earth profile curves 14
5 Path profile example (flat earth) 15
6. Path profile example (curved earth) 16
7A-B Point of reflection on over-water microwave path 19-20
8 Overreach interference criteria 22
9 Adjacent section and junction or spur interference 22
10 The radar interference case 23
11 Interference coordination of paralleling systems . 23
12 31A method of screening microwave antennas when required on a radar site
13 Free space attenuation between Isotropic antennas 36
14 Behaviour of attenuation vs path clearance 37
IS 75 GHz)First Fresnel Zone radius (6, 39
16 Typical M profiles 45
17 Rain attenuation vs rainfall rate 47
18 Attenuation due to precipitation 48
19 Contours of constant path length for fixed outage time 49
20 Expected outage time in hours per year vs path length in miles forvarious areas of the United States. 50
21 Outage probability vs fade margin, for 6.7 GHz paths of various lengths 63
22 Outage probability vs path length, for a 6.7 GHz path with 40 dBfademargin 64
23A Receiver thermal noise 72
Typical receiver noise curve 76
viii
FIGURE nTLE PAGE
24 77Echo distortion noise
Approximate area required for guyed tower 85
25B Approximate area required for 3-leg shelf supported tower 86
8625C Approximate area required for 4-leg self supported tower
26 EIA wind loading zones in the U .S.A 87
27 A-D 94-97Periscope gain curves; 6'x8', 8'x12', 10'x15' and 12'x17' reflector
10128A Passive repeater gain chart
102Antenna-reflector efficiency culVes
Passive repeater gain correction when passive in near field 103
Double passive repeater efficiency curves 104
Microwave path data calculation sheet example 10829
ix
INTRODUCTION
This book is intended to assemble in onevolume, in a readily usable and practical form, acompendium of the best available information onthe planning and engineering of line-of-sight micro-wave paths for communications systems. The em-phasis is on techniques and practices, but a consid-erable amount of theoretical discussion is includedas an aid in understanding the various phenomenawhich are important in microwave transmission.
any microwave equipment designed for operationin the above bands, provided due account is takenof differences in RF components, transmissionlines, antennas, and propagation characteristics.
The use of frequency modulated microwaveradio systems is widely recognized as a flexible,reliable and economical means of providing point-to-point communications facilities. These radiosystems, when used with appropriate multiplexequipment, can carry from a few circuits up to alarge number of voice, telegraph and data circuits.They can also be arranged to carry additionalwide-band circuits for high-speed data, facsimile, orhigh-quality audio channels. Television is alsocarried by microwave radio, but, because of itswide baseband requirements, each video signal isusually carried on a separate radio channel.
Though the book will have its major value as ahandbook for communications engineers engaged inmicrowave path planning, it is sufficiently generalto be used by management people and by engineersin other fields, as an aid in understanding thecharacteristics of microwave communications sys-tems.
Many formulas, charts, and figures are scat-tered throughout the work. Lists of the charts andthe figures are included in the Table of Contents,and as an aid in day-to-day usage, selected formu-las, charts, and figures have also been duplicated inappendices at the end of the book.
Comparative cost studies usually prove amicrowave system to be the most economicalmeans for providing communication circuits wherethere are no existing cable or wire lines to beexpanded. Where there are severe terrain or weatherconditions to be overcome, the cost advantagebecomes several-fold. For temporary facilities, andother applications where installation time isseverely limited, the advantages of radio are ob-vious.
Throughout the text and in Appendices I andIII, all material involving units of length is develop-ed on the basis of feet and miles, the units incommon use throughout North America. In orderto make the book more useful to those who workin metric units, Appendix II provides metric ver-sions of those formulas and equations whichinvolve units of length. Also included in thisAppendix are some suggested ways in which certainof the charts and figures can be used with metersand kilometers rather than feet and miles.
In applications where expandability is import-ant, a microwave system can be installed initiallywith only a few carrier circuits. Then, as trafficincreases, the capacity can be expanded by theaddition of more channelizing equipment, or byparalleling radio equipment. Several radio channelscan be arranged to use the originally installedantennas, waveguides, supporting structures, build-ings and standby protection facilities.
The book covers FM microwave systemswhich operate in one of a number of frequencybands between approximately 2 GHz and 16 GHz.The discussion is general so that it can be applied to
MICROW A YE FREQUENCY BANDSII.
Most, if not all, microwave systems will besubject to regulation by the government of thecountry in which the system is to be located. Ingeneral, each country allocates specific bands offrequencies for specific services or for specificusers. Within the United States the Federal Com-munications Commission (FCC) is the controllingauthority for all systems except those operated byagenci~s of the Federal Government, the latterusually being placed in frequency bands separatefrom those controlled by FCC. In Canada, the
~
licensing body is the Department of Communica-tions. In many countries it I.is the Department ofPosts and Telegraphs, or some similar entity. Mostcountries, other than the United States, follow thefrequency allocations recommended by the Inter-national Radio Consultative Committee (CCIR).
Within the broad microwave portion of theradio frequency spectrum, the fixed allocations ineffect at the time of preparation of this manual(1970) are given in the following tables:
Microwave bands available to communications common carrier in the U.S.A.under Part 21 of the FCC Rules
Table AI
Table A2. Microwave bands available for private and local government microwave systemswithin the U.S.A. under various Parts of FCC Rules. (Not all bands are availableto all types of users.)
CENTERFREOGHz
ATT'N INdBAT
1.0 MILE
COMMENTS OREMISSION
LIMITATION
BANDNAME
RANGEGHz
1.85- 1.99
2.13-2.15&2.18 -2.20
2.45 -2.50
1.920
2.165
102.3
103.3
8,OOOF9
800F92 GHz
104.5
113.1
118.5
Shared
10,OOOF9
20,OOOF9
6GHz
12 GHz 12.7
2.475
6.725
12.450
TableA3 Microwave bands available for TV Auxiliary Services within U.S.A. under Part 74of FCC Rules.
ATT'N INdBAT
1.0 MILE
COMMENTS OREMISSION
LIMITATIONBANDNAME
2GHz
7 GHz
12 GHz
RANGEGHz
1.99-2.11
6.875- 7.125
12.7- 13.25
12.7- 12.95
CENTER
FREO
GHz
2.050
7.000
12.975
12.825
t Comm. Antenna Relay Service
2
6.575- 6.87512.2- ~
Table A4. Microwave bands available for FederalGovernment Services within U.S.A.
1974Table AS Microwave bands per CCIR Recommendations. Geneva
CENTERFREQGHz
REC
NO.
RANGEGHz
CAPACITY
CHANNELS
1.7- 1.9 1.808
2.000
ATT'N INdBAT
1.0 MILE
101.7
1.9- 2.1 102.6 60 & 120283-2
2.1- 2.3 2.203 103.5
102.21.7- 2.1 1.903600 to 1800
382-2 2.101
4.0035
103.0
108.6
1.9 -2.3
3.8 -4.2 t
3.950
6.175
108.5
383-1
3.7 -4.2 *t
5.925 -6.425 tt 112.4
113.2
113.8
1800 or equ iv
2700 or 1260384.2 6.43 -7.11~ 7.425 **
7.250-7.550 **
7.425- 7.725
7.550- 7.850
6.770
7.2757.125
7.400 114.060, 120, 300385
7.575 114.2
114.3-1
7.700
9608.200 -
7.725- 8.275 **
8.500 8.350 115.0
8.000 114.7 1800
960
386-1
10.7 -11.7 11.200 117.6387-2
t
tt*
**
Shared with Satellite-to-EarthShared with Earth-to-SatelliteAlternate for U.S.A.7.250 -7.300 GHz Reserved for Satellite-to-Earth7.975- 8.025 GHz Reserved for Earth-to-Satellite
3
Table A6. Microwave bands in Canada per Department of Communications Plan
INOTE' Assignments are given on the basis of use rather than type of user. Government
policy is that no frequency bands will be designated common carrier, etc., althoughin actual practice the common carrier would normally use those bands marked withasterisk, to obtain performance desired.
4
III. ROUTE AND SITE SELECTION
A. Order of Procedure a terminal must be the starting point on siteselection.
As a starting point, it is assumed that prelimi-nary facility planning (including operational re-quirements, traffic studies, expansion potential,reliability requirements and cost studies) has beencompleted to such a degree that the points to beserved have been fixed, and the required systemcapacity has been determined.
~~~~~t~ ~~~e!-.- Sit~
The choice of intermediate repeater sites isgreatly influenced by the nature of the terrainbetween sites. In preliminary planning it may beassumed that, in relatively flat areas, the pathlengths will average out bet~een 25 and 35 milesfor the frequency bands from 2 GHz through 8GHz, with extremes in either direction dependingupon terrain. In the 11 GHz and higher bands, thepattern of rainfall has a large bearing on pathlength. These factors will be covered in more detailunder subsection C. Microwave Paths.
Preliminary studies for site location canusually be made from maps and aerial photographsprepared by other agencies; however, the final siteselections must be made from field surveys, and theprofiles and notes thereby derived.
B. Sites
In all cases the sites should be as level aspossible. The need for leveling should be consideredas a part of the cost of preparing the site.
Terminal sites are more often than not loca-tions of existing structures or facility terminals, butthe intermediate sites are located with considerableemphasis on factors having to do with propagationover the intermediate paths, and possible interfer-ence from sources internal or external to thesystem. In some cases there may be problems in theuse of an existing building for a terminal radio site,even though common maintenance, facility layoutand economy tend to dictate such selection. If thebuilding is of adequate height to mount antennafixtures on the roof without fear of path blockageby other buildings, this will-be-anlaea1terminalpoint. The possibility off~tur~ ~g c9ns~u~-tion along the path must, of course, be taken. oconsideration. The mounting of antenna fixtures on
therioo1;-0~~~ayrequire irives1~ into the architectural ~ds tru ct \ifal---pra:Ii~Dii~min ewhether-thp;-structti'i~ ana the co-S[" ofbuilding modifiCattonsf:o-iCCOiiip100 ""fhe purposemust be conslaerea:-unrare-oe-casro-ns plans forfuture floor additions must be considered. It maybe desirable to add the steel for one or more floorsfor the future addition, and then ~astructure on top. This plan must include main:te-nance access to.Jbe-antennas-a~~-waye~uide. Such aplan should be worked out having in mind theviews of city officials who may require buildingfacing for the vacant floors for appearance reasons.
Since maintenance access is very important, anaccess road must be considered. In addition, theavailability of AC power of suitable voltage, andthe possibility that telephone facilities may beneeded, enter into the site selection.
The possibility of mterference, internal orexternal to the system, must be considered. Inter-nal interference may take the form of overreach,junction or adjacent section interference. Externalinterference may take the form of radar interfer-ence, interference from nearby radio systems ofsimilar fre:quency, or interference induced fromunfiltered lower frequency radio systems.
Site Considerations
There are a number of site considerationswhich must be investigated in the field survey, andthe accumulated data should be recorded forsubsequent use. Some of these are indicated in thefollowing paragraphs.
1.
Where additional height is required and build-ing structure is such as to reject all of the aboveconsiderations, a separate tower on the building lotor adjacent to it may be the solution. In any event,
A full description of each site by geographicalcoordinates, political ~ubdivisio~e~ ~~dsand physical -o15jeCts with which it cah beidentified. Geographical coordinates should becomputed to the nearest -second of l~and longituGe for the exact location recom-me-:miOO:rorfue tow;:-sj;;;uid this lo-;;aiion bechanged in later engineering work, the coor-dinates should be corrected accordingly.Note: This' degree of accuracy is requiredprimarily because it is specified in FCC Rules.
5
2. Any unusual weather conditions to be expec-ted in the area, including amount of snow andice accumulation, maximum expected windvelocity and range of temperatures.
representing the longitudinal center of the beam ormain lobe, particularly when discussing line-of-sightclearances. The microwave beam behaves much likea light beam insofar as atmospheric influences areconcerned, and is subject to certain other externalinfluences in a manner described in the followingdiscussion.
3. A description of the physical characteristics ofthe site, indicating the amount of levelingrequired, removal of rocks, trees or otherstructures, etc. Influence of Terrain and Obstructions
4, The relationship of the site to any commer-cial, military or private airport within severalmiles. It is very important to determine therelationship of the site to the orientation ofrunways where planes may be taking off orlanding. This information is needed to deter-mine compliance with government regulationson potential obstructions to air traffic.
The microwave beam is influenced by theintermediate terrain between stations and by ob-stacles. It tends to follow a straight line in azimuthunless intercepted by structures in or near the path.In traveling through the atmosphere it usuallyfollows a slightly curved path in the vertical plane,i.e. it is refracted vertically due to the variationwith height in the dielectric constant of the atmos-phere; generally slightly downward, so that theradio horizon is effectively extended. The amountof this refraction varies with time due to changes intemperature, pressure and relative humidity, whichcontrol the dielectric constant. This is illustrated inthe lower portion of Figure 1.
5. The mean sea level elevation of the site at therecommended tower location, and the effecton that elevation of any necessary leveling.
6. A full description or recommendation for anaccess road from the nearest improved road tothe proposed building location. At the point of grazing over an obstacle the
beam is diffracted. There is a very small shadowarea where some energy is redirected in a narrowand rapidly diminishing wedge toward total shad-ow. The angle enclosed by the wedge of diminish-ing energy behind the diffracting object, from fullsignal to full shadow, is extremely small. Thisphenomenon is illustrated in the upper portion ofFigure 1. T~-E~p~ poi~~o be stressed here, isthat when the centerline of the beam just grazes anobs~cle, there is a loss of energy reaching the farantenna. The loss may be from ~ to twentydecibels, depending on the type of surface overwhich the diffraction occurs. It has been shownexperimentally that a knife-edge diffraction ob-stacle will produce a loss of six decibels at grazing.A smooth surface, such as flat terrain or water ,which actually follows the earths contour, willproduce the maximum loss at grazing. Most ob-stacles normally found in the path will produce aloss somewhere between the above limits. Treestend to produce a loss close to six decibels. In orderto minimize diffraction losses, line-of-sight micro-wave paths are planned to have better than grazingclearance even under the most adverse atmosphericconditions.
There is a possibility that building coderestrictions may be involved. Such sites shouldbe avoided if practicable.
8. The nearest location where commerci~-tric power of suitable secondary o'f-aistribu-tion voltage may be obtained, and the nameand office location of the power company. Incountries or locations where public power isfurnished, similar information is required, butthe procedures for contact may be somewhatdifferent.
9. If telephone communication is desired, thenearest telephone facility should be indicatedtogether with the name of the company andthe type of service available.
10. Any other facts that can be determined at thetime of the survey which might bear on theproposed construction.
c. Microwave Paths -General Appreciationof Path Influences
1 Description of Microwave Beam Most physical objects in the line-of-sight willtend to block the beam, causing loss of signal at the
~ Deciduous trees which may cause rela-tlvely less loss in winter, can totally block the path
For simplicity, the following discussion willtreat the microwave beam in general as the line
6
in summer when the leaves are out. In all cases,trees should be considered as blocking when in thepath line, unless the beam has adequate clearanceover the trees.
The Fresnel zones are a s~ie~ of concentric~~ding t.he p~t.b. Th~Jjrst F-resI1elzone is the-~~~-~~ing PVP~ pn;nt fG~ whichthe sum of the distances from that point to the twoends of the path is exactly ~h~f~thlo~g~rtbJ1n-the---direct--e-!!d-to-end path. The nthFresnel zone is defined in .;ffiesame manner, exceptthat the difference is n half-wavelengths.
The beam can be reflected from relativelysmooth terrain and water surfaces, just as a lightbeam is reflected by a mirror. Since the wavelengthis very much longer than light waves, the criterionof smoothness is quite different. The criterion ofsmoothness is also quite different for very smallangles of incidence than it is for large angles. Thiscan be illustrated for visual light in the case of anasphalt highway. When viewed directly, the surfacelooks slightly rough and does not reflect light well;however, when viewed from a distance at a verysmall angle, it looks like a mirror or wet surface.
Since the cross-section of the Fresnel zones atany point along the path is a series of concentriccircles completely surrounding the path, it isimportant to note that clearance requirements,expressed in Fresnel zones, apply to the sides andabove as well as below the path. Formulas andgraphs for calculating Fresnel zone radii are given ina later section.
Influence of WeatherAn important concept in analyzing microwave
propagation effects, particularly those of diffrac-tion, refraction, reflection, and the effects ofterrain and obstructions, is that of the Fresnelzone. The first Fresnel zone radius is a kind of"rubber" unit, which is used to measure certaindistances (path clearances in particular) il1 terms oftheir effect at the frequency in question, ratherthan in terms of feet. The 2nd and higher orderFresnel zones are also very important under certainconditions, such as highly reflective paths.
Although a microwave beam is conventi9nallyshown as a line, the actual method of propagationis as a wave front, and the important portion of thewavefront involves a sizeable transverse area.
In order to ensure free space propagation it isessential that all potential obstructions along a pathare removed from the beam centerline by at least0.6 F 1 , where F 1 is the radius of the lst Fresnelzone at the point of the obstructions.
7
For this reason, it is necessary to provide pathclearance over intermediate objects which is some-what greater than line-of-sight. Because refractivebending varies in cycles daily and changes errat-ically at times, the clearance over the intermediateterrain must be adjusted to mini,mize the losses atthe extreme bending conditions. N ormally , asmentioned previously, the beam is bent downwardby ~tmospheric refraction so that the radio horizonis effectively extended. Nevertheless, at times theatmospheric conditions may be such that the beamis bent upward, effectively reducing the clearanceove'r terrain in the path. These phenomena andFresnel zones will be discussed more fully in a latersection.
path. While the microwave energy is concentratedin a fairly narrow beam, it tends to spread graduallyas it is propagated through the atmosphere. Thereare also minor lobes of the antenna which, althoughhaving much less power than the main lobe, aretransmitted in different directions. The corridor offree transmission required will run up to 230 feet atthe center of a 40 miles path at 4 GHz for example.However, the influence of objects in azimuth canrun well beyond this indication. Figure 2 illustratesthe case of objects in azimuth. The potentialproblem with off-path objects is reflections, andthese usually turn out to be from buildings. Energytraveling the longer reflection path lags behind themain beam. The most serious case is one ofmultiple reflections which might occur, for ex-ample, when a beam is transmitted down a streetwith tall buildings on both sides. In this case thedelay is likely to be so great as to cause delaydistortion in the baseband. A small round object isgenerally incapable of reflecting sufficient energy inone direction to cause trouble, as the reflectionbeam is diverse. However, a very large round objecthas been known to cause trouble. Such an objectwould be a large gas container or oil storage tank,running up to 150 feet and more in diameter.
Influence of Rain and Fog~ !:!i~~ :!~~e:E:c~~ --
At microwave frequencies up to the 6 and 8GHz bands, rain attenuation as such is not con-sidered sufficient to warrant special considerationin the design of the paths, except in very extremesituations. Under saturation rain conditions, a 30mile path migh t suffer only a few dB attenuation at6 GHz. Uniform fog conditions can be consideredin much the same light. However fog conditionsoften result from atmospheric conditions such astemperature inversion, or very still air, accom-panied by stratification; the former tends to negateclearances, and the latter causes severe refractive orreflective conditions, with unpredictable results. Inareas where these conditions prevail, shorter pathsand adequate clearances are recommended.I
~t!!:?:~~~i~ ~~f-Etlo~
Atmospheric absorption due to oxygen andwater vapor also exists. The magnitude of the effectis quite small at the lower frequencies (2-8 GHz),and is usually neglected. Even in the higher bandsthe effect is relatively small, but not entirelynegligible. Since the amount of attenuation fromthis phenomenon is directly proportional to pathlength, it is usually significant only on longer paths.A table of absorption attenuation as a function ofpath length and frequency band is given in sectionIV.C.
D. Sources of Path Data
1. Maps
Maps are the principal sources of basic data,both for office study which usually precedes thefield survey, and for the field survey itself. Thereare a number of types of maps which will bediscussed herein. Experience has shown that mapscovering a rather large area in the general territoryto be surveyed, represent good work and recordsheets which, when posted as the map surveyprogresses, illustrate the progress, generallocatiqns,angles and place names. A good map of this type is
At microwave frequencies of 11 and 12 GHzor above, rain attenuation can be very serious. Theamount of attenuation depends upon the rate ofrainfall, the size of the drops and the length ofexposure. Accordingly, in areas of heavy rainfallwhere extremely high reliability is required, shortmicrowave paths are recommended. It should benoted that the rate of rainfall to be considered isnot the annual total rainfall, but the instantaneousintensity at the time of occurrence. Thus, the westcoast areas of Oregon arid Washington in the UnitedStates, despite having frequent rain, are considerednot likely to experience serious rain attenuation at11 GHz for paths up to 30 miles, because the actualrate of rainfall at a given time is very low. For othercoastal areas the reverse is often true .
!!lt1.-u~n~e .!:!.~ OEj~~ ~ ~z.i!-n.E.~The influence of objects in azimuth is not
confined entirely to those which are directly in the
8
I L-"L-Reflecting
ObjectPartially
Blocking
Object-
ReflectingObject
Trans.Antenna
Rec.Antenna
Figure 2. Blocking and Reflecting Effects in the Horizontal Plane
the Aeronautical Chart, which is published for mostcountries where commercial and private air naviga-tion are the rule. In the United States they arepublished by the U.S. Coast and Geodetic Survey.In addition to showing large areas they show sometopography in very large contours, and the airnavigation routes. They may be ordered with theflight chart overlay which shows the establishedcommercial airways. The Coast and Geodetic Sur-vey publishes and distributes aeronautical charts ofthe United States, its Territories and Possessions.Charts of foreign areas are published by the USAFAeronautical Chart and Information Center(ACIC), and are sold to civil users by the Coast andGeodetic Survey. A catalog of aeronautical charts isavailable from one of the following field offices,which will also supply the aeronautical chartsdesired on a specific order. The catalog will besupplied free of charge. The charts are sold at theprices listed in the catalog. Exact payment mustaccompany the order .
The Aeronautical Charts cover large areas of astate, and often several states on one chart. For alarge part of the United States, they typically showelevations in contours of 500 or 1000 feet, andtherefore are not useful in actual plotting ofprofiles. They show airports, airways, major aerialobstructions and large topographical features suchas lakes and mountain ranges. If the terminallocations are plotted on the appropriate aero-nautical chart(s), and the intermediate charts (ifany) are spliced in, an overall view of the possibleroute is obtained. Generalizations can be madeconcerning features to be avoided and possibleareas of search. As the map survey proceeds, thepreferred and alternate sites arrived at by profilingfrom other maps ( discussed below) can be plottedusing the precise latitude and longitude of each.The composite chart then becomes a good overallworksheet and provides a quick check for thepossibility of overreach or other interference ( dis-cussed in a later section).
The basic maps from which office profiles canbe made are the topographic maps such as thosepublished by the U.S. Geological Survey. These areto be found in quadrangles of different sizesdepending upon the date of the survey and the areasurveyed. They also show different elevationcontour intervals in different areas, depending onthe area, date of survey and size of quadrangle.These contour intervals generally range from 2.5 to100 feet. Topographic maps in the United Statesbased on surveys made prior to 1920 have beenfound to contain spme errors both in elevations andlocations of topographic details. In the absence oflater surveys however, they can be used as a roughguide until specific field checks are made.
Chief, New York Field OfficeCoast and Geodetic SurveyRoom 1407 Federal Office Building90 Church Street, New York, N.Y. 10007
Mid-Continent Field DirectorCoast and Geodetic SurveyRoom 1436 Federal Building601 East 12th StreetKansas City, Mo. 64106
West Coast Field DirectorCoast and Geodetic SurveyRoom 121 Courthouse555 Battery StreetSan Francisco, Ca. 94111
Q
The Geological Survey has, for a number ofyears, been making surveys which will eventuallycover all of the United States and Puerto Rico. Thepublished maps covering the more recent surveysgenerally fall into one of the following sizes andscales:
The U.S.G.S. also maintains sales counters inWashington, D.C.; Denver, Colorado; Salt LakeCity, Utah; Sacramento, San Francisco, Menlo Parkand Los Angeles, California; and Anchorage,Juneau and Palmer, Alaska, where the maps can bepurchased in pers.on. The particular street addressesare subject to change from time to time, but canusually be found in the local telephone directory.There are also private agents who sell quadranglemaps at their own prices. Their names and addres-ses are listed in the state index circulars.
7-1/2 Minutes of latitude and longitude; Scale1:24,000 (1 inch = 2000 ft) or 1:31,680 (1inch = 1/2 mile).
15 Minutes of latitude and longitude; Scale1:62,500 (1 inch = approx. 1 mile). Accurate topographic maps are available for
many areas of Canada. All of Canada is covered bymaps published on the scales of 1:506,880 (1 inch= 8 miles) and 1:1,000,000 (1 inch = 15.783 miles).
Coverage on other large scales is not complete.Many areas are covered by maps published on thescales of 1:50,000 (1 inch = 0.79 miles), 1:63,360(1 inch = 1 mile), 1:126,720 (1 inch = 2 miles) and1:253,440 (1 inch = 4 miles). The indices of thesemaps and the maps themselves may be purchaseddirectly from:
30 Minutes of latitude and longitude; Scale1:125,000 (1 inch = approx. 2 miles).
1 Degree of latitude and 2 degrees of longi-tude; Scale 1:250,000 (1 inch = approx. 4
miles).
There is for each state and for Puerto Rico anindex circular showing all U.S.G.S. topographicmaps distributed. They show the quadrangle loca-tion, name, survey date and publisher (if other thanU.S.G.S.). There are also listed special maps andsheets with prices, map agents and Federal distribu-tion centers, addresses of map reference libraries,and detailed instructions for ordering topographicmaps.
Department of Energy , Mines and ResourcesSurveys and Mapping Branch615 Booth StreetOttawa, Ontario, Canada
They may also be purchased at local statio.ners, but this is not a reliable source.The index circulars are accompanied by a
folder describing the topographic maps. They arefurnished free on request and may be obtainedfrom one of the following offices:
Additional maps may be obtained from theDepartment of Mines, Lands and Forests, or De-partment of Natural Resources of the ProvincialGovernments in the appropriate provincial capitals.
Aeronautical charts for Canada on scales of 8miles to the inch and 16 miles to the inch, and airphotos may also be obtained from the Departmentof Energy, Mines and Resources, surveys andmapping branch.
For maps East of the Mississippi and Hawaii
u.s. Geological Survey -1200 South Eads StreetArlington, Virginia 22202
Map Information
For maps West of the Mississippi River, all ofLouisiana and Alaska Additional maps which may be useful are U.S.
Forestry Service maps, and strip maps of railroads,pipe lines, power companies and telephone com-panies.
u.s. Geological Survey -Map InformationRoom 15426 Federal Building1961 Stout StreetDenver, Colorado 80225 County highway maps published by the state
highway departments in the United States havebeen found to be useful in making the field surveys.They usually show man-made structures and areoften more up-to-date on road information, thanare many topographic maps. In addition, theyfrequently show some of ~he bench marks andoccasionally secondary level points. These must be
For Alaska they may also be obtained from
u.s. Geological Survey -Map InformationRoom 108 Skyline Building508 Second AvenueAnchorage, Alaska 99501
10
considered cautiously, as grades,culverts and poles
on which they may be located are subject to
change.
wave beam having a curvature of KR. The secondmethod of plotting is preferred, because it (1)permits investigation (and illustration) of the condi-tions for several values of K to be made on onechart, (2) eliminates the need for special earthcurvature graph paper, and (3) facilitates the taskof plotting the profile. It is convenient to plot theprofiles on regular 10 by 10 divisions to the inch,reproducible graph paper of the 11 by 17 inch or Bsize.
Comparable topographic mapping in othercountries of the world is usually available.
2. Aerial Photography
Aerial photography is often useful in roughterrain because it can show more of the details of aprominent terrain feature than a topographic map,and also shows trees and other obstructions. Anindex map showing all Government and militaryaerial photography in a given area can be obtainedby writing the Superintendent Of Documents,Washington D.C. 20402.
2. Scales
A horizontal scale of two miles to the inch hasbeen found to be very convenient. It permits pathsof up to 30 miles in length to be plotted on onesheet. For longer paths it is not difficult to trimand splice two sheets together with small pieces oftransparent tape on the reverse side. (It is suggestedthat pieces of tape not over 1.5 inches long to beused so that tape shrinkage will not ruin the charts.This precaution should also be made when splicingmaps together).
Aerial photography is also used in the pro-cess of preparing path profiles by the techniqueknown as photogrammetry .
Path ProfIlesE.
More than one vertical scale will be necessaryto cover all types of terrain. A basic elevation scaleof 100 feet to the inch has been found to be quiteconvenient for all cases where the changes inelevation along the path do not exceed 600 or 800feet. For paths in hilly country , a more compressedscale of 200 feet to the inch is convenient, and formountainous country, it may be necessary to use avertical scale of 500, or 1000 feet to the inch. Itshould be noted that if the distance scale isdoubled, the height scale should be quadrupled topreserve the proper relationship.
Mter tentative antenna sites have been selec-ted, and the relative elevation of the terrain ( andobstacles) between the sites has been determined, aprofile chart can be prepared. In some cases acomplete profile will be necessary ; in other casesonly the end sites and certain hills or ridges need tobe plotted.
The relative curvature of the earth and themicrowave beam is an important factor whenplotting a profile chart. Although the surface of theearth is curved, a beam of microwave energy tendsto travel in a straight line. However, the beam isnormally bent downward a slight amount byatmospheric refraction. The amount of bendingvaries with atmospheric conditions. The degree anddirection of bending can be conveniently definedby an equivalent earth radius factor, K. This factor,K, multiplied by the actual earth radius, R, is theradius of a fictitious earth curve. The curve isequivalent to the relative curvature of the micro-wave beam with respect to the curvature of theearth, that is, it is equal to the curvature of theactual earth minus the curvature of the actual beamof microwave energy .Any change in the amount ofbeam bending caused by atmospheric conditionscan then be expressed as a change in K. Thisrelative curvature can be shown graphically; eitheras a curved earth with radius KR and a straight linemicrowave beam, or as a flat earth with a micro-
Equivalent Earth PrQ!:!!~~3.
A path profile plotted on rectangular graphpaper with no earth curvature (as suggested above),and with the microwave beam drawn as a straightline between the antennas represents conditionswhen the beam has a curvature identical to t1:lat ofthe earth ( i.e. there is no relative change incurvature between the beam and the earth) and theequivalent earth radius, K, is equal to infinitty .Thisis one of the extreme conditions that must beinvestigated when making a study of the effect ofabnormal atmospheric conditions on microwavepropagation over a particular path. In order tocomplete a propagation study, it is necessary toshow the path of the beam (relative to the earth)for other expected values of K. In all cases, it is ofinterest to study the path under normal atmos-pheric conditions when K is equal to 4/3.
11
The curvature for various values of K can becalculated from the following relationship:
normally investigated. These curves, plotted to aconvenient scale, are shown in the full size versionof Figure 4 inserted loose in the back of the book.This figure can be used to make templates of plasticor cardboard, or it can be used as an underlay toprofiles that have been plotted on graph paper .When the final antenna heights have been selected,the path of the beam can be traced directly fromthe curves, as shown in Figure 5. Besides makingsure that the correct scales are used, one otherprecaution is necessary when using the curves inthis manner; it is necessary to keep the horizontallines of the profile chart parallel with the horizon-tal lines on the curves. This will automaticallyinsure that the correct portion of the curve is beingused. (The reduced version of Figure 4 on page 14is illustrative only).
dl d2h=L5K (1)
where h = the change in vertical distance from a
hori~ontal reference line, in feet
dl= the distance from a point to one end of
the path, in miles
d2 = the distance from the same point to theother end of the path, in miles
K the equivalent earth radius factor
For the K conditions of primary interest inpath analysis, Equation (1) takes the followingforms:
Where extremely large differences in elevationexist along the path, it may be more convenient toplot the profile with respect toa curved earth withradius KR and to use a straight line to represent themicrowave beam. The curves of Figure 4 can beused to establish a curved base-line, by inverting thecurves and tracing the curved line for the desiredvalue of K on 10 X 10 to the inch graph paper. Thecurved baseline is assigned an altitude which is thenearest hundred foot interval below the lowestaltitude required for the profile. The path profile isthen plotted above the baseline. A straight linedrawn between the proposed antenna locationsthen indicates the path of the microwave beam forthe chosen value of K.
h(K = 00) = 0(l-A)
dl d2
2 .B)h(K = 413) =
h(K = 213) = dl d:l-C:
h(K = 1) = .67 dl d2(I-D)
Contrary to a widely-held belief, it is notnecessary with either approach to locate the centerpoint of the path at the apex of the curve to"balance" it about the center. If the curves areaccurately constructed, the same results will beobtained whether the path is centered or offset;this characteristic of the parabolic arc can be shownmathematically as well as experimentally.
The forms I-B and l-C are particularly simple,useful, and easy to remember. Equation 1 and itsderivative forms are basic to all microwave pathengineering, and most transmission engineers im-mediately commit them to memory .
Figure 3 provides a graphical means of calcula-ting and plotting a section of a parabolic arc whichcan be used as a base-line for a curved earth profileplot, or (inverted) as a curved ray template to beused wi th a flat earth profile plot. The generatingequation is that of a parabola with its origin at theapex of the curve. The parameter d representsdistance from center, along the x axis, in miles,while h gives distance along the y axis, in feet, as afunction of the distance from the center ( origin)and the K factor being used.
Another very useful method is to constructthe curved baseline by calculation; this methodallows the use of any convenient scales and anyvalue of K. It also allows the use of millimeter-ruledpaper if desired, giving somewhat greater resolu-tion. In this method the "earth bulge" at a numberof points along the path is calculated by equation( 1) and is plotted above the bottom line of theprofile paper. A smooth parabolic curve is thendrawn through the points to provide the curvedbaseline for the profile. A value of K = 4/3 isusually chosen for such profiles, in which case the
Equivalent earth profile curves have beencalculated from the above formula for values of K
12
13
Figure 4. Equivalent Earth Profile Curves.(Example only; see Appendix for full-scale working template of Fig. 4 )
dld2equation reduces to h = ~. For K = 2/3 the
equation is h = dl d2 , and the earth bulge at anypoint is just double that at K = 4/3, making it
relatively easy to consider the effects of a changefrom K = 4/3 to K = 2/3.
adequate clearance at the lowest value of K, yethave the reflective ray blocked over the entirerange of K. In some cases this situation can beachieved by appropriate choices of antenna heightsso as to utilize terrain blocking, or to move thereflection point from water to a rough surface.
Figure 5 shows an example of a path profileon the flat earth basis. The curved beam paths aretraced with the aid of the curves of Figure 4 (notethat Figure 5 has been reduced in size; the originalwas on 10 X 10 to the inch graph paper). Figure 5illustrates a space diversity arrangement with 40'vertical separation of the diversity antennas. Clear-ance criteria for this path were at least 0.3F 1clearance at K = 2/3 for top-to-top antennas and atleast 0.6F 1 clearance at K = 1 for top-to-bottomantennas.
There is one other graphical analysis method,preferred by some engineers, which eliminates theneed for either curved baselines or curved raypaths. In this method the path terrain profile isplotted, on any convenient scale, on a flat earthbasis in a fashion similar to that shown in Figure 5.
The engineer then analyses the path to deter-mine the potential obstructing points, and for eachof these points makes a calculation of the earthcurvature at the point, using Equation ( 1) and alsoof the desired Fresnel zone clearance, using Equa-tion ( 4A) or Figure 15. The calculations must bemade using the particular set of criteria which areto be applied. For example, the clearance criterionmight be 0.6 F1 at K = 1.0.
Figure 6 shows an example of a profile plottedon a curved earth basis, using millimeter paper anda calculated curved baseline. This figure indicates apath with potential reflections from a water surfaceand also shows the analysis of the potentialblocking of the reflected ray under conditions of K= 4/3, K = 2/3 and K = 00. Figure 6 further
illustrates the fact that when antennas are atdifferent elevations with respect to the reflectingsurface, the reflection point moves along the pathas K varies. It is closest to the end with the lowerantenna at K = 00 (flat earth) and moves towardthe center of the path as K decreases. Such pathsare customarily analyzed by calculating the reflec-tion point for K = 00, K = 4/3 and K = 2/3, and in-vestigating the blocking or screening of the reflec-ted ray at each value, The ideal situation is to have
The sum of the calculated earth curvature andthe calculated desired Fresnel zone "clearance isadded to the elevation of the top of the obstruc-tion, and the point marked on the chart. Themicrowave beam, plotted as a straight line, mustclear this point. Similar calculations are made andsimilar points marked above each of the potentialobstructing points along the path. Tower heightsmust be determined so that a straight line betweenthe antenna locations clears all of the markedpoints. Where more than one set of criteria areapplied, as in the "heavy route" criteria described
14
on Page 51, separate calculations and separate
points must be marked for each set, over each
obstruction, and again all points must be cleared by
the line between antennas.
By the use of these charts, an approximate value ofn for each condition can be determined and thecorresponding values of d 1 calculated. These values,together with the calculated value for K = 00 canthen be used to plot the reflection point range onthe path profile, as shown in the example of Figure6.
A skilled transmission engineer can usuallyreduce the number of points for which calculationsneed to be made to a relative few. For example, inthe path of Figure 5 it is obvious that only fivepoints are potential obstructions.
Reflective path analysis can be carried outequally well and in somewhat simpler fashion usingthe flat earth, curved beam approach as depicted inFigure 5. With flat earth profiles, the reflectionpoints for the three significant values of K arecalculated and marked along the bottom line of theprofile. The appropriate curved beam template foreach of these values is then used to trace the beampath and determine whether the paths from an-tenna to reflective point are clear or obstructed.
Though this method at first glance appears tobe tedious, in practice it can be done very quicklyand easily for most paths. It has the great advantagethat any kind of rectilinear graph paper can beused, and that the most convenient scales can bechosen for each axis individually, since there is nointeracting effect between the two scales. Thismethod also provides a very useful means ofdouble-checking, at critical points, the clearances asdetermined by any of the other methods.
The nomograph solution provides accuracyadequate for most work. Where greater accuracy isdesired, the following relationships are useful :
4. Reflection Point Calculations
hl
dl
h2
dl =ct;When K = 00 (flat earth condition) there is a
very simple relationship between the antennaheights and the distances from the respective endsto the reflection point (in miles). The relationshipis:
For K = 2/3d2
After determining the approximate values of dland d2 by means of Figure 7 A, substitute them inthe above equation, together with hl and h2 .If thereflection point location is correct, the two sideswill be equal. If they are not equal, increase dl byasmall amount and decrease d2 by the same amount.If this change causes the inequality to increase,reverse the procedure. Continue by iteration until avalue is reached for which the two sides are equalor very closely so.
where hl is the elevation of the lower antenna andh2 the elevation of the higher antenna in feet abovethe reflecting surface, dl the distance in miles fromthe hl end to the reflecting point, and dl + d2 = Dthe path length in miles. This leads to the followingexpression :
d2
2
For K = 4/3
For K = 00
Use Figure 7B to determine the approxiplatevalues of dl and d2 then proceed as describedabove to determine a more exact value.
ILl
hl + h2
dl = nD, where n = (2A)
The small shaded area in the lower left:handcorner of each chart represents conditions forwhich the path would be below grazing, and a truereflection point would not exist.
For values of K other than infinity, and forunequal antenna elevations, the geometric relationinvolves cubic equations whose solution is some-what cumbersome. However, graphical solutionshave been worked out and are found in theliterature in several different forms. A nomographicsolution for the condition K = 2/3 is given in Figure7A, and a similar solution for K = 4/3 in Figure 7B.
The parameters X and y from Figure 7 canalso be used to de,termine the value of K for whichthe path would be at grazing clearance. For thiscondition the relation is given by the expression:
17
K= maximum, minimum and possible average length ofpath to be considered. This will depend to aconsiderable extent on the frequency band to beused, type of service to be assigned to the systemand the topography. Having made these determina-tions, it is suggested arcs be drawn representingthes~ values from the first terminal, and the areasbetween the arcs be searched for possible first sites.The search at this point will include the topo-graphic maps and any other maps or photographywhich can be searched for additional information.Having selected one or more possible sites for thefirst repeater point, preliminary profiles should bedrawn. These will furnish a check of the practica-bility of using the sites selected.
11.5 (X + y + 2 vxY>
They can also be used to determine the location ofthe reflection point for the grazing condition fromthe expression :
1n=
1 + V"Y7X
.The range of 0 to 3.0 for the Y parameter and0 to 2.0 for the X parameter on Figures 7 A and 7Bwill cover most situations where location of thereflection point is needed. For example, on a pathof 30 miles, a value of 3.0 forY would correspondto a height of 2700 feet above the reflecting surfacefor h2, and a value of 2.0 for X to a height of 1800feet above the surface for h1 .
Limitations
The ideal situation obtains when all of thetopographic maps for a given path can be assem bledon the same scale and spliced together accurately sothat a straight line can be drawn between theplotted adjacent sites. An accurate scale in miles isthen marked on the line and, following the lineover the contours, it is then possible to tabulate theelevations with their appropriate mileages. It isessential that the tabulated elevations and mileagesbe sufficient to fully describe the profile whenplotted. Where the line crosses a hilltop, it isreasonable to assume in the preliminary map studythat the ultimate height, unless specifically marked,is half the contour interval higher than the nearestlower contour line.
In some special situations it may be necessaryto calculate reflection points for paths where oneor both of these values are exceeded. Since thecharts are rectilinear and all of the lines are straight,it is relatively simple to extrapolate beyond thechart to determine an appropriate value for n. Theiterative process described above can be used toimprove the accuracy, if desired.
5.Preliminary Map Survey--
The preliminary map survey has for its objec-tive the planning of one or more routes whichmight appear to be possible between the terminalpoints given, based on available data, and theplotting of profiles which are necessarily prelimi-nary, for all of the indicated paths and alternatesdetermined from the study.
Qa~~ o!.1E-c~:n.!P~t~ l\i.ap]JJ!-1~
Where some maps in a given path are to adifferent scale than others, a useful technique is tosplice plai.n white paper to each map where thescale changes and project, by geographic coordi-nates, a known point or the next adjacent site sothat the proper line can be drawn on the availablemap. The tabulated data should then be plotted onthe type of profile desired. For the paths withincomplete topographic survey, it is desirable toplot the profile showing that portion of theelevations which is available. If the path appears tobe a good one in the field survey, the profile maybe completed from field data. The tentative regularand alternate sites should also be plotted bygeographic coordinates on the large scale map, toshow their relative position, and to assist in theinterference and frequency coordination study.
~ ~f .!!l~~
The prospects of arriving at the best possibleroute and sites are enhanced by the study of thegreatest numbers of alternate possibilities. It isrecommended that all available information bearingon the proposed route be first assembled. Largescale maps, such as the aeronautical charts, aresuggested for the beginning of the study, and forkeeping track of its progress and the site locations.
It is recommended that the terminal locationsbe first plotted on the aeronautical charts, if theseare available, or on a large scale map. At this pointit is advisable to make a determination of the
18
3.0
2.8
:j:)2.6~ ~w :1=:1
2.4 I:ttJ~
2.2
i:t:t
2.0
~
1.8
mt1.6
~
1.4
1.0
1"2
1
0.8
~0.6
~,m:t:0.4
++#
./ I~ .1~d2--1
d1(r/O)I.. 10 -.1 !
h1 < h2 h's in feet, d's in miles, I
TO USE: h1/ h2/ ICOMPuTE x = / 02 & y = / 02 +
Read 7/ from chart for Point X, y interpolating
if necessary.Calculate d1 = 7/ 0 & d2 = 0 -d10.2
f:f:j
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Point of Reflection On Over-Water Microwave PathFigure 7 A.
19
20
Interference and Coordination~~xE:i~arj ~~~d~~i~n~ - path should preferably be blocked by at least 1000feet when the overreach path is plotted on flatearth profile. Cases of less blocking should beanalyzed individually.One very important consideration in engineer-
ing microwave systems is the avoidance of interfer-ence. Such interference may occur within thesystem itself, or from external sources. Both ofthese possibilities can be eliminated or minimizedby good site selection when selecting the route, andby consideration of proper antennas and operatingfrequencies.
Spur or junction interference, and adjacentsection interference for systems using the so-calledtwo-frequency plan, are illustrated in Figure 9. Inall of these cases, far-end crosstalk is of concernbecause it is quantitatively dependent upon thediscrimination of the antennas at the junction, bothtransmitting and receiving. N ear-end crosstalk atthe junction may become important when there areseveral channels on the main route, as frequencytranslations can result in interference to an adjacentreceiver. The mechanisms of this type of interfer-ence are rather complex and need not be delineatedat this point. The criterion in both near-end andfar-end crosstalk is the signal-to-interference ratio,which is a function of antenna discrimination. Forexample, a periscope antenna arrangement wouldnot be used at a junction or on main routes usingthe two-frequency plan because it typically has arelatively low front-to-back ratio, and may havesome odd side lobes. On routes with only one radiochannel, or two channels in frequency diversityarrangement with maximum inter-channel freq-uency spacing, periscopes may often be used withhigh towers for economic reasons.
!r~~~cy- ~~d !!~i~oE
Operation of a microwave communicationssystem will generally be within one of the severalfrequency bands allocated for such services, aslisted in Section II. For two-way operation, as isgenerally required in such systems, each band isdivided in half, with the lower frequency halfidentified as "low band " and the other half as
"high band". At any given station all transmittersare normally on frequencies in one band and allreceivers in the other. Each path has a "TransmitHigh " station at one end and a "Transmit Low"
station at the other end. This arrangement mini-mizes near-end crosstalk. In some bands a differentarrangement is used.
It should be noted that radars can radiatesubstantial amounts of power in many of thecommonly used frequency bands, even though thefundamental radar frequency is much lower. Sup-pression filters are available for the radars in mostcountries, but the burden of making certain theyare installed may fall on the communications user.
External Interference
External interference cases were discussedsuperficially in (1) above, but require furtherclarification as to methods of approach and specificvalues. Radars typically radiate pulse energy , oftenin a 360 degree arc and at a very high energy level.Quite often the second or third harmonic, ifunfiltered, can have an effective radiated pulsepower in the order of +60 dBm (1 KW). As pointedout above, it is possible to determine whetherharmonic filters are installed, and if not, such filterscan usually be obtained. Experience in the UnitedStates indicates that the agency operating the radarwill usually install the filter if the necessity isestablished. There is another precaution recom-mended in the case of radar , in that, regardl~ss offrequency radiated, the input circuit of the micro-wave system should not see large amounts of peakpulse power. Input preselection filters for themicrowave system vary in the amount of discrimi-nation outside the pass band, but it is usually veryhigh. Nevertheless .it is possible to paralyze theinput converter in extreme cases. Therefore it isrecommended that the path from the radar to all
~!!-a.=§~~ll!-.- I.!:!:..t~f!!:!~~
Interference within the system may be classi-fied as overreach, adjacent section and spur inter-ference. Overreach interference is illustrated inFigure 8, in which only the frequencies in onedirection of transmission are represented. Thesituation in the opposite direction is identical. Theproblem is to avoid having frequency F 1 , transmit-ted from A, received at D at a substantial level,when there is a fade condition for the F1 signalreceived from C. The parameters which may beused to avoid this interference are; (a) a longeroverreach path as compared to the direct C-Dpath, (b) antenna discrimination against the over-reach path, and (c) earth blocking in the overreachpath. If the latter must be relied on, the overreach
21
microwave receivers within 50 miles be profiled atK = 00 and, if possible, substantial earth blocking be
arranged. In the unblocked case, it is recommendedthe path between radar and microwave receiver bein excess of ten miles, and the receiving antennadiscrimination be at least 30 dB. Figure 10 illus-trates the radar case.
In the case of paralleling or intersectingmicrowave systems the transmitter output power ofthe two systems is usually somewhat comparable,but where differences exist they must be taken intoaccount. Additional criteria for interference coor-dination involve the parameters of distance, an-tenna discrimination, receiver sensitivity and selec-tivity. Interference considerations are two-way inthis case, as the new system must not interfere withthe existing system. The paralleling system problemis illustrated in Figure 11. Profiles made forpossible earth blocking should be prepared for K =
Recommendation~
D" D " "20 L A-D#
Istance Iscrlm. = og-c:-o-- =
Antenna Discrim" ~
A-ntenna Discrim. ..e
Total*
*Total 50 dB or better
#F . d " . 20 L A-D
or oPPosite Irectlon og~
-dB
-dB
-dB
.dB
The Field Survey6,
The field survey is much more than the phraseimplies. Actual altimeter measurements, judgmentsof the actual terrain along each path and dataconcerning obstructions are recorded. The exis-tence of paralleling or intersecting foreign systemsand interference possibilities is indicated, and thevarious data concerning regular and alternate sitesare obtained. The preliminary profiles made fromthe map study become a tool for the fieldinvestigation, and these are supplemented, correc-ted, or actually replaced as a consequence of thefactual data obtained. In the absence of path tests,the information brought in from the field surveyconstitutes almost all of the factual data about theroute, from which judgments can be made whichwill determine the service performance of thesystem when installed.
Figure 8. Overreach Interference Criteria
~\
x
y
Instrumentation
The following instrumentation is recommen-ded, although all items may not be needed in allcases;
CODE
Regular Transmission Path
Interference Path
A, B, C, X Microwave Repeaters
NO
Not all interference paths are shown or identifiedThose shown are representative. A good pair of binoculars, 7 x 35 or 8 x
50, with coated lens. (Larger diametermagnification does not ordinarily im-prove the results).
Figure 9. Adjacent Section and Junction or SpurInterference Two precision altimeters of the proper
range for the terrain to be measured.
22
~'2.-
-i)~ ~) (F
-i)~ ~) (-F1F?
Computation for Unfiltered Radar
E.R.P.P. of 2nd or 3rd HarmonicGain Of Receiving Antenna
Requirements
+60
G
60+G
p
D
L
R
S
S/I dB
Harmonic Energy in Band -MessageTelevision
'.:undamental- Ten Miles + 30 dBAntenna Discrimination
NOTE
30dB45 dB
Path Loss Rad. 96.6 + 20 Log F +20 Log DAntenna Discriminator at 0< Degrees
Filter & Waveguide LossesRadar Harmonic Input (60+G.P-D-L)Computed Microwave Signal Input
Signal-to-lnterferenceRatio (S-R)
For on-site microwave terminals atradar locations, or locations lessthan ten.miles from a high poweredazimuth operated radar, obstructionblocking is desirable.
Figure i 0. The Radar Interference Case
23
Both may be of the portable type, or onemay be of the portable type and one therecording type. Care should be exercisedin considering these instruments. Eachprecision altimeter should be accom-panied by its own correction chart andan accurate thermometer. Suitable instru-ments may be obtained from one of the
following:
be considered. A very low antenna incombination with some intermediate ter-rain blocking may be possible. Where theantenna is actually on the flat terrain, avery low antenna can be selective,particularly i~ the lower frequencybands. Refer to the discussion underPROP AGA TION for further details.
Sites on high mountain ridges with low,flat terrain between. In high densitysystems, serious delay distortion mayresult. If it cannot be avoided by reselec-tion or terrain blocking, it may benecessary to locate one site on theintermediate low flats.
American Paulin System1524 Flower StreetLos Angeles, Calif. 90015
Wallace & Tiernan Inc.25 Main StreetBelleville, N.J. 07109
Sites near high power radar!A good hand level, and a pocket compass
Crossing of foreign system routes ofsimilar frequencies at small angles or withnear repeater stations.
A good theodolite is useful in someinstances to determine that an elevationmeasurement is on path. Visibility ofboth adjacent sites is necessary for suc-cess in such determination.
Obstructions near the line-of-sight whichmay reflect energy from the transmittersinto the receiving antennas. Paths along acity street between buildings are verybad.
Two-way portable radio (VHF) capableof shadow area reception at 30 miles.
In rugged coUntry , a precision mirror of6 inch to one foot dimension is a gooditem for "flashing" paths. Special signal-ing mirrors as developed for military useare particularly good.
Much can be done in the field search toeliminate propagation hazards which may affectservice.
~elh~~ f!.! Q~r~t~~
U.S.G.S. book or books showing estab-lished bench marks in area.
For running the profiles in the field (Altimetersurveys), it is desirable to have maps with accurateroad information and having a scale of about 1/2inch to the mile. In the U.S.A. the county highwaymaps serve this purpose very well. The maps for aparticular radio path should be spliced togetheraccurately, the radio sites specifically located and astraight line drawn between the sites. This line isthen scaled in miles. Consider when doing so thatthe maps are sometime stretched in printing. Thiscan be checked by using a scale across a number ofroad intersections to see if the mile points come upaccurately. The elevations shown at road intersec-tions should not be taken as accurate unless theyagree with established U.S.G.S. bench marks whichhave not been moved. The maps should be postedwith the location and elevation of establishedU.S.G.S. bench marks. They are then ready to beused as a guide in securing information for theprofile.
County highway maps (in U.S.A.) for thearea. Scale 1/2 inch = 1 mile.
Pertinent topographic map~, marked forthe preliminary profiles.
!.hi!-l~ ~ ~~oid~d-
There are several situations which should beavoided if practicable, particularly in the case ofhigh density systems with multiple RF channels.These are as follows:
Over-water paths and paths over low, flatterrain. Where they cannot be avoided,the high-low technique to place thereflection point over rough terrain should
24
The most accurate altimeter method of run-ning levels for the profile is known as the two-altimeter method. The process involves placingboth altimeters at the nearest bench mark andcalibrating them exactly alike. The altimeters arebased on the aneroid principle, so their readingswill vary , even when on a fixed bench mark. Thework should be done during stable weather condi-tions, and in the period from at least one hour aftersunrise to one hour before sunset. One altimeterremains at the bench mark throughout the measur-ing period. If this is a manually read instrument,readings of temperature and the altimeter should betaken each five minutes until the roving altimeterreturns. The readings of the two instruments shouldthen be compared. If the readings differ by as muchas five feet after temperature stabilization, thesurvey should be repeated after recalibration of theinstruments. The difference may be due to thehigher temperature in the car in which the rovingaltimeter is carried.
photography over the path by stereopticon tech-niques. The relative elevations are then determinedby stereopticon procedures. The accuracy is good,but the cost is relatively higher than the altimetersurvey method. In a case involving a fairly largenumber of profiles, and where new forces might berequired to handle the altimeter survey, thismethod might be investigated. It should be borne inmind however, that the field altimeter party bringsin a great deal more information than elevationdata, and such information is necessary in anyevent. A third method of profiling involves flyingover the path with equipment which measuresclearance (plane above terrain) using the radarprinciple. This is also relatively expensive and hascertain limitations.
In mountainous country where all of theintermediate terrain in a path is rough and tim-bered, a profile is of little value if adequateclearance can be determined by other means. Thiscan often be done by "flashing" the path. Itinvolves two parties, preferably equipped withtwo-way VF radio for communication. Lacking theradio, it is often possible to coordinate by time.The party carrying the mirror should pr-eferably beat the site opposite the direction from which thesun is shining, or two mirrors may be used; one ateach site. The mirror is to reflect a beam of lighttoward the far site. The aim must be very good.The stability of the mirror when held on the beamby hand will be such that the flashing effect isautomatic. To be effective, it is necessary for theflashing party to establish the exact direction to theopposite site, and to concentrate the flash alongthat line. One way of doing this is to drive stakes tomark the exact line and then, using the mirror ,focus the sun's rays along the line of stakes,gradually raising the beam until it is level with thedistant horizon. This process should be repeated atfrequent intervals until the far party is known tohave seen and identified the flashes. At the far sitethe flashes will appear very large. A transit set up atthe far site can be very useful, both for obsetvingthe flashes and obtaining accurate path bearings.The terrain clearance can be roughly establishedvisually, but not precisely. Any known ridges whichappear close to the line-of-sight should be checkedfor elevation at the critical point and adequateclearance established by computation.
If one recording instrument is used, it can beplaced at the bench mark and thereby save man-power. The principle of operation is the same aswith two manually read instruments.
The roving altimeter is used to measure theelevations along the path. A record is made of themileage at the measuring point, the temperature,the time, the trees and other obstructions, and anyterrain features of interest in preparing the profile.The roving altimeter should be used on the portionsof the path which are reasonably close to the benchmark. As many bench marks should be used as arenecessary to accurately survey all of the path onthis basis. The final measurement at the benchmark on each measuring trip provides a reasonablecheck on the data. The crew then moves to thenext bench mark and proceeds in the same way. Ifthere is only one bench mark near a path, it isdesirable to create secondary bench marks, usingthe same method as for measuring on the path.
Corrections ar~ made for temperature andapproximate relative humidity, using the instruc-tions in the handbooks furnished with the instru-ments. The computed elevations for the pointsmeasured are then determined. There should beenough points measured to. fully describe theprofile of the path, which is then prepared based onthe method selected for the office profiles. In checking path clearance by mirror flashing,
or by any optical or visual methods, account shouldbe taken of the fact that light rays have a slightlydifferent curvature than do radio rays. A nominal
Another method which has been used toobtain information for the profile involves aerial
25
value of K = 7/6 is usually taken as the "standard "
for light. Figure 4 includes a curve for this value ofK which can be used for evaluating clearancesdetermined by optical methods.
Path azimuths should be determined to thenearest tenth of a degree of arc and path distancesto the nearest tenth of a kilometer. In order toachieve the required accuracies it is necessary tocalculate the azimuths and the path distance fromthe coordinates of latitude and longitude at the twoends of the path. Because of the convergence ofmeridians, the azimuth at the two ends of the pathwill in general not be precisely 180° apart.
In most rugged terrain, and particularly inhigh mountain areas, the almost continuous andshifting wind currents tend to produce a thorough-ly fuixed atmosphere which does not supportatmospheric multipath fading of great depth. Insome cases it is possible to achieve high reliabilitywitpout diversity, or to use somewhat longer radiopaths than in lower terrain, without endangeringthe fade margins for which the equipment wasdesigned. However it should be noted that excep-tions exist, and that in some cases and somemountain areas atmospheric effects can cause deepatmospheric fading.
Two methods of calculation are in commonuse. The most common one is to use a computer tocalculate azimuths and distances by solving thegreat circle spherical triangle comprised of the twoend points and the north pole. The second, knownas the "inverse position method ", is adapted from acalculation method described in "Special Publica-tion No.8 -Formulas and Tables for the Compu-tation of Geodetic Position ", published by theCoast and Geodetic Survey. This method includesthe use of tables which take into account theoblateness of the earth. Because of this, the inverseposition method provides somewhat more accurateresults than the great circle method, unless thelatter includes a correction for non-sphericity.
!e~°!...~ R.!!.~ ~e.p-!!-rls
Information to be reported about the sites wascovered in subsection "B. Sites" as data to berecorded. For the paths and alternate paths, com-plete profiles carefully plotted with obstructionsand estimated antenna height requirements, shouldbe prepared, together with all facts or determina-tions with reference to possible interference. Inaddition, all pertinent supporting data, altimeterreadings, maps and bench mark information shouldbe furnished,
Although either method provides resultswhich are sufficiently accurate from a technicalviewpoint, a recently inaugurated program by oneFCC bureau (the Common Carrier bureau) uses theinverse position method, and it is therefore desira-ble that this method be used in calculations forapplications filed with that bureau. Included in theAppendix to this publication is a memorandumgiving a method of making azimuth and distancecalculations by the inverse position method, suit-able for hand calculations using a six-place loga-rithm table. The method detailed uses essentiallythe same format as that used in'the FCC computerprogram and should give identical results. Thememorand'um includes sufficient extracted datafrom Special Publication No.8 to be self-sufficientand not require use of the latter .
Final Profiles
The final profiles provide the basis for themicrowave system engineering, including the finalselection of paths, determination of final antennaelevations, selection of antenna sizes and configura-tions, and computation of the received signalstrengths, fade margins and the system noise to beexpected. The final profiles should reflect the finaldecisions on route, sites and antenna elevations.
Path Coordinates, AzimuthsaItdDisTallces F. Path Tests
After final selection of the precise locationsfor the tower or antennas, the latitude and longi-tude of each location should be very carefullydetermined. For systems under FCC jurisdiction,the rules require that the coordinates of theantenna or final radiating element be determined tothe nearest second. This requires very carefulscaling from the best available maps.
On line-of-sight microwave systems, path tests,when used, are made primarily for the analysis ofproblems related to the reflective characteristics ofthe path and, secondarily, to determine or providea cross-check on the path clearance. They are mostoften made on routes with very heavy communica-tions requirements or potential. Such routes typi-cally use heavy horn reflector antennas which
26
require changes in tower design when antennaelevations must be changed. To make such changesafter the route is placed in service would be costly.Path testing prior to construction of the systemhelps to avoid such a possibility. A further consid-eration affecting the decision whether or not pathtests are justified, is that 'large capacity microwavesystems utilizing multiple RF channels in parallel,are considerably more susceptible to the effects ofreflections than are systems using only a singleworking channel.
~~~~i~n ~~~ p.!.-°~c!-E:
By properly planning the height-loss runs, andby analysis of the results using a very accurateprofile, it is possible to determine the followinginformation about the path:
The location of reflection points in thepath.The value of K at the time of measure-ment.
The reflection coefficient.
This type of test is a short term process,normally performed during daytime periods whenatmospheric conditions are essentially normal andstable. It should not be confused with the type ofpath testing in which long term recordings are madeof the signal strength along a path. Such tests arecommon in tropo-scatter or other beyond line-of-sight systems, but are rarely used in line-of-sightwork. Long term fading characteristics, range of Kvariations to be encountered, and other things ofthat nature will not be normally determined in thisline-of-sight type of path test.
The antenna elevations where free spaceloss is just obtained.
The best antenna elevations to minimizeground reflection fading.
Path tests of this type require the utmostprecision in calibration of the equipment and inmeasuring the antenna heights.
Effects of K Variations
Accurate results can be obtained only whenthe value of K is stable. This can be expected overmost terrain only during fair weather and in thedaytime hours at least 1 to 2 hours after sunriseand before sunset. Changes in K during the height-loss runs would be reflected in incorrect values forall of the desired results listed above.
~~f .p~sc.E:p-t~n-o~ t!!.e .:!~~
In the most effective form, the tests involvetransmitting an unmodulated RF carrier over thepath between adjacent sites and measuring thereceived power at various combinations of antennaelevations. The receive power measurements arethen converted to path loss measurements, sincethe transmitted power and antenna gains areknown. A test series made with both antennasmoved in the same direction at the same rate, orwith one antenna fixed and the other moving, iscalled a "height-Ioss run ". The results are plottedwith path loss as ordinate against antenna eleva-tions as abscissa.
Cost Considerations
Path tests involve costly equipment and con-siderable manpo~er. For this reason, where singlechannel routes and light loading are involved,economics dictates reliance on the field accuracy ofother methods. Accurate profiling and good judg-ment will go a long way toward establishing a goodworking system.
27
IV. OVERALL SYSTEM DESIGN
A. Purpose of Section priority for consideration of each topic. For ex-ample, the first item listed below should beconsidered, and any problems resolved beforeproceeding to the next item, as any changesresulting from it could otherwise cause considerableduplication of effort. The order of priority is asfollows:
Given the fundamental plans and study re-suits, and the profiles, data and other informationobtained from the field investigation, the nextorder of procedure concerns the transmission engi-neering plans, calculations and design specifica-tions. Some of this work, such as planning, isactually accomplished prior to the route selection,work. After the field investigation is finished, thefinal calculations concerning antennas, interference,system and channel noise, distortion and propaga-tion reliability are made. If the final sites have notbeen selected from the field data at this point, thismust be done prior to much of the other work.Also at this point it may be important thatinformation about the final choice of sites be madeavailable to those responsible for obtaining thenecessary property, as failure to obtain one sitemay affect some of the other selections.
Interference and frequency coordination.
Propagation.
N oise and noise sources.
Distortion
Equipment.
The above order of priority , and in fact mostof the discussions in this section, are specificallyapplicable to high density systems involving multi-ple parallel RF channels over each path. Suchsystems often grow to the point where all, or nearlyall, of the available "channels in a full band are inuse over every path of the system. In suchsituations the interference potential, both intra-system and with other systems occupying the sameband, is very large.
1 Final Obje-~!i~e for a Syste~
The final objective for any microwave systemis that it provide the best distortion-free andinterference-free service continuity for the type ofservice to be assigned, and within the framework ofthe available economics.
Overall reliability or service continuity in-volves not only equipment failure rates and powerfailures, but also the propagation performance ofthe individual paths. This involves antenna sizes andelevations, frequency or space separations in diver-sity systems, path lengths and frequency-attenuation relationships. It also includes fadingmargins which, in addition to path parameters, areaffected by noise figure, transmitter power, andattenuation of waveguide and filter arrangements.
Microwave systems involving only one work-ing RF channel per path ( or one working and oneprotection channel) have the same kinds of prob-lems, but in most cases they have a much widerrange of practical solutions. The system designerhas a good deal more leeway in engineering suchsystems, even when they require the same degree ofreliability and performance as the more comp-licated systems.
B,
Distortion may occur in the radio path, butmore often it occurs due to poor return loss ofamplifier components, waveguide filters and anten-naB. Also the characteristics of switching devicesand/or combiners are involved.
Interference andFrequency Coordination
Radio system interference causing degradedtransmission may be introduced through antennas,waveguides, cabling, radiation or by spurious prod-ucts produced in the radio equipment itself. Inter-ference introduced into the cabling or in theequipment can be prevented by good installationpractices, including proper separation of high andlow level cabling, proper grounding practices,shielding where necessary, and good equipmentdesign and assembly. Interference introduced bycoupling between waveguides in the same station is
System noise is affected by the same thingswhich, in addition to interference, can have anadverse affect on overall system performance.
The presentation within this section isdesigned to provide an orderly discussion whichfollows, insofar as practicable, the design-related
28
usually produced by radiation from waveguide andfilter flanges which are not properly tightened, orwhich have been damaged and cannot be matedproperly. There are cases on record where interfer-ences of more than marginal character have existedfor long periods, but were undiscovered until aparticular critical service was assigned to the sys-tem.
periods, with serious effect on system noise. Inalmost all cases, noise in the baseband channels isanenctproduct ~rme"irItenerence-:-- ---
:
2. General Classifications
General classifications have been given broadlyas self interference and external interference. Eachof these broad categories can be broken down intoa number of different types for discussion pur-poses.
Because a radio system depends upon theatmospheric medium for transmission, it is subjectto interference from systems using the same me-dium. This includes not only other radio, radar andother devices, but also other parts of the samesystem. The interferences are broadly classified asexternal interference and self-interference. Thesewere briefly discussed in Section III and illustratedin Figures 8 and 11, which provide some measure-ment criteria for those concerned with selecting theroute. In this section it is the intent to discuss thesubject more analytically, and thereby provide asomewhat more thorough understanding of themechanisms involved. It is expected that this willbe of assistance in solving or judging marginal cases.
Self Interference
Self interference has been classified in termsof overreach interference as illustrated in Figure 8,adjacent section interference and junction interfer-ence, with the latter two cases illustrated in Figure9. Adjacent section interference also includes whatis sometimes' called same section interference. Theonly difference is the matter of whether thediscrimination is principally the front-to-back ratioof the receiving antenna or the transmitting anten-na. These cases were previously discussed becausethey involve the sites and radio paths.
Interference MechanismsThere are also possible cases of self interfer-
ence within the stations themselves. One of these isthe resllii of {'~ i",.. le~k f-rom ~ comm~supply. In the C.C.I.R. plan for 6 GHz common
carrler systems, eight channels of radio in eachdirection are recommended, each with a capacity ofl~?r~ -m~~~agp ~h~n~pl8.- The successfuloperation of this system requires very tight limitson -~ tole~e. A common carrier supplyis one way ~suring that all of the precisefrequency relationships are maintained within thesystem. If, on the other hand, through radiatingwaveguide flanges and/or leaking filter connections,the high level carrier supply is introduced into thewrong input circuit, a translated signal as well asthe regular signal can be introduced into thechannel, with certain degradation resulting. Also,because of the close relationships between' thechannels, there may be a tone translation whichresults in interference to an adjacent channel andeven to a third channel. \
The evaluation of interference can be complexand difficult because of the nature of the systemsinvolved, and the complex nature of the signals.The mechanisms are varied. In the simpler casesthey may be direct interference into the radioreceiver. In other cases they may be spuriousproducts or combinations of products which arriveat the receive input and produce a net resultantinterference into the receiver intermediate fre-quency section. The latter may be frequency trans-lations resulting from sum and difference productswithin the same system. In still other cases thereceiver may see an identical signal to the regularsignal, but which arrives later or earlier than the
regular signal.
!f~~ <!.!lih!. SJ~e.!!1
Interference can produce beats or noise prod-ucts in a radio receiver which have detrimentaleffects depending on the frequency, d~viation,channel separation and linearity of the r;eceivingmedium, as well as the nature of the interferingsignal. In some cases they combine with otherfrequencies in the system, including carrier sum anddifference frequencies, to produce interference in athird radio channel. These products may hold upautomatic gain control during critical fading
Externallnterference
The control of external interference dependsin part on coordination, control, and sometimescompromise on radio channel assignments through,in most cases, direct negotiation. The frequencyregulating body, such as the Federal Communica-
29
tions Commission in the United States, assigns thefrequency spectrum by services and licenses specificchannels within the designated bands. In most casesthe public service communications bands are as-signed in accordance with the recommendations ofthe Consultative Committee On InternationalRadio (C.C.I.R.); however, certain priorities andother special requirements are recognized. Thus inthe ~ GHz band, where transcontinental networkswere established in the United States prior toC.C.I.R. recommendations, a different plan is usedreq~iring a wider band. In the 2 GHz band and thebands between 6 and 11 GHz, the allocations usedin the United States differ considerably from thoseused by other nations, and channel assignmen ts areaccordingly different. For all plans, adjacent chan-nel discrimination within the immediate section isaided by cross-polarizing adjacent channels. Forsuch channels transmitted and received by the sameantennas, the discrimination is maximum; up to 20dB per antenna. Cross-polarization discriminationvaries widely at angles other than zero degreesbetween the interference signal and the desiredsignal. The pattern of variation is quite different fordifferent types of antennas and in many cases thediscrimination is actually negative when the angle is90 degrees. In dealing with cross-polarized interfer-ing signals, the calculations can be meaninglessunless the cross-polarization discrimination charac-teristic of the receiving antenna is known. Forexample, there is no generalized discriminationcurve for parabolic reflector antennas for any givenfrequency and, with a different feed, both thediscrimination curves and the cross-polarizationcurves will differ. For a particular case it isrecommended the manufacturer be requested tofurnish this information about the antenna beingused.
interfering signal power not to be exceeded, or notto be exceeded for more than some specifiedpercentage of time, at the input to the interfered-with receiver or, (2) as a value of 8/1 ratio where 8is the power of the desired signal at the receiverinput and I is the power of the undesired signal.For co-channel operation ( desired and undesiredsignals on the same frequency) typical objectivesfor the first type of criterion range from as low as-125 dBm to perhaps -100 dBm, and typicalvalues for the second type of criterion from ap-proximately 60 dB to 95 dB, depending upon anumber of factors.
Figures 10 and 11 illustrate the method ofcalculating S/I ratios for external interferences.Typical criteria for co-channel objectives are shownon the figures and are applicable where desired andundesired signals are closely held to a smallfrequency difference. For slightly larger frequencydifferences, where the interfering signal falls withinthe first order sidebands of a heavily loaded system,the criterion for satisfactory operation may becomemore stringent by as much as 25 to 30 dB.
For off-channel interference (between adja-cent channels for example) the criteria will besubstantially affected by the selectivity characteris-tics of the particular receiver involved. Most manu-facturers can provide curves or other data showingthe allowable levels for interfering signals as afunction of the frequency separation betweendesired and undesired signals. Tone translations canoccur when a frequency received in one channel,well out from the carrier frequency, is modulatedin a heterodyne repeater and radiated as a new tonein the next adjacent channel.
With antenna-reflector combinations (peri-scope antennas), angular discrimination up to about:t2 degrees will generally be about as good as thedish itself for a given polarization. For larger anglesand cross-polarized interference signals, precon-struction predictions would probably not be valid,due to the odd side lobe patterns from thereflector. Dual-polarized periscope antennas havebeen used with success in specialized cases. Gene-rally speaking, dual-polarized dishes are not asefficient as single polarized.
The effect of interference varies, not onlywith the nature of the interfering signal, but alsowith the nature of the desired signal.
~ oic~ Qa~a~ T!!!J~i~o~
Voice channel interference to voice channelsystems usually results in either intelligible cross-talk or burble, which is similar to what one mightexpect for voice frequency systems. All types ofinterference to data systems are generally capableof producing data errors. Interference to televisionsy~tems is usually readily detected and analyzed byobserving the video monitor and " A " oscilloscope.
The criteria established for external interfer-ence depend upon many factors, and to someextent are arbitrary .They are typically expressed inone of two ways; (1) as an absolute value of the
30
radiation that would otherwise interfere with themicrowave receiver. Also, because of the peak pulsepower of the radar, it is advisable to shield themicrowave antennas from the radar beam if prac-ticable. Figure 12 illustrates the case and providessome objectives. It will be noted that the receivingantenna at the far end of the microwave path willhave practically zero discrimination against theradar signal. Obviously, this violates the rule statedin ROUTE AND SITE SELECTION in connectionwith off-path radars. At this point it is necessary tolook at out-of-band losses of antennas, low freq-uency cut-off of waveguide, and preselection filtercharacteristics, for the fundamental. The harmonicfilters can usually be counted on for about 60 dBrejection. If the harmonic is normally in the regionof +60 dBm and the microwave transmitter has aone watt output, the in-band S/I ratio should be inthe region of 73 dB for a 6 GHz system using a 10foot transmitting antenna, the gain of which wouldbe about 43 dB.
Interference from voice systems or data systemsproduce typical overall patterns on the monitorwhich are easily recognized. Pulse interference,such as radar, produces scattered dashes on themonitor, which will be white on a black back-ground and black on a white background. On IFheterodyne microwave systems the point of inter-ference may be many miles away from the pointwhere monitoring equipment is normally available.The known history of the system, or visual inspec-tion of the route, may suggest where the interfer-ence is originating. In the final analysis, the systemcan be looped back at IF at different points,provided there is a return channel available, andmonitored at the transmitting point. For one-wayonly channels, a portable FM transmitter and avideo signal generator can be used at successivestations while the receiving terminal monitors. Thestandard window signal is best for interferenceanalysis.
Tone Versus Pulse Interference~~~!!!~ System Interference5.
Tone or beat interference is detrimental in thefrequency region in which it occurs, not onlybecause of the direct interference with the desiredsignal, but also because of the background noise itproduces, even at levels below the signal level. Pulseinterference, such as radar signals, may not benoticed in individual message channels when thepeak pulse power received is below the messagechannel level, because of the pulse spectrum distri-bution; however, when the interference peak pulsepower is above or equal to the message level, theinterference becomes intolerable. The breakoverpoint for data is usually somewhat lower, depen-ding upon the bandwidth and bit rate of the datasignal. For television, the breakover point is ap-proximately 15 dB below the equal level point. Toprovide fading margin, the approximate voice andtelevision limits are -30dB and -45dB respective-ly and, for data, except for voice channel data, it isrecommended the latter limit of -45dB be used.
Certain frequency bands are used on a sharedbasis both by terrestrial radio relay systems and
4. Calculations for Interference Effect
Figures 10 and 11 illustrate the off-path radarand the parallel systems case respectiv~ly, andindicate the calculations that are appropriate tothese exposures. There are, however, cases where itis necessary to terminate a microwave system on aradar site. In such cases, the microwave receiver isquite vulnerable to the radar transmitter signalsunless special precautions are taken. The radarshould be filtered for harmonics and spurious
31
earth-satellite systems. Because of the widely dif-fering parameters of the two systems, the potentialfor interference is high when earth stations andterrestrial radio relay systems in the same bands a:relocated anywhere near to each other. The potentialinterference radius around an earth station mayrange as high as several hundred miles, dependingon terrain factors and relative orientation.
channel shall not exceed -63 dBmOp (500 pWpO)for more than 20% of any month, and -43 dBmOp(50,000 pWpO) for more than 0.005% of anymonth. It is assumed that there are no more thantwo such sources of interference in any system.
The corresponding criteria for allowable inter-ferences from terrestrial radio relay transmittersinto earth station receivers are that the interferencein any voice channel shall not exceed -66 dBmOp(250 pWpO) for more than 20% of any month and-43 dBmOp (50,000 pWpO) for more than 0.01% ofany month. It is assumed that there are no morethan four sources contributing to the 20% value,and no more than three to the 0.01% value.
The present international commercial satelliteservice uses the 5.925-6.425 GHz band for trans-misf.ion from earth to satellite, and the 3.7-4.2GHz band for transmission from satellite to earth.Because of the enormous (by line-of-sight stan-dards ) effective radiated power of the up-linktransmission, the earth-station transmitters caninterfere with terrestrial system receivers in the 6GHz band to distances which can extend farbeyond the horizon. The earth station receivers aremuch more sensitive than those of a terrestrial relaysystem and they can be interfered with by even thelow-powered transmitters of terrestrial 4 GHzsystems well beyond the horizon.
Beyond-the-horizon operation in the form oftropo scatter has been in use for many years, andmuch work has been done on methods of calcula-ting path loss. This work is, however, primarilyconcerned with determining the average value andthe highest value of transmission loss to be expec-ted, with little or no concern about those periodswhen transmission loss drops to lower than normalvalues. But, in evaluating interference potentials,what is of concern is precisely the lowest value oftransmission loss over the undesired path, since thisresults in the highest level of interference. Theproblem is to calculate how strong the interferingsignal will be under supernormal propagation con-ditions, and for what percentage of the time suchstrong interference signal conditions can be expec-ted to occur.
Although there is little need for sophisticationin the calculations of microwave path losses withinthe horizon, the matter of path losses at rangesbeyond the horizon is much more complicated. Asa result, the problem of coordination betweenearth-satellite systems and terrestrial systems shar-ing the same bands is a rather complex considera-tion.
Within the United States, Part 25 of the FCCrules requires the earth station licensees or appli-cants to calculate coordination contours aroundeach earth station, and also to calculate interfer-ence levels for all stations within these areas. Afteran earth station has been established, any useroperating under Part 21 of the rules and desiring toestablish a microwave station in the 6, 4 or 2 GHzbands must, if the proposed station falls within thecoordination contours of an earth station, demon-strate to the Commission by suitable calculation,that the proposed station will neither interfere with(in the 4 GHz band), or be interfered with by (inthe 6 GHz band), the earth station. The procedurefor doing this may be quite complicated "as itinvolves calculation of expected path losses onbeyond-the-horizon paths.
This is a much more difficult task indeed, andis complicated by the fact that operational data hasnot been oriented in the past toward shedding anylight on this situation.
In recent years considerable work has beendone on the problem, by a number of organiza-tions. Much of the work is based on NBS TechnicalNote 101, Revised, January 1, 1967.
A COMSA T technical publication "Transmis-sion Loss Calculations For Interference Evaluationin the 4 Ghz and 6 Ghz Shared Frequency Bands",dated September 15, 1967, provides a somewhatsimplified method based on the NBS work (thelatter is very lengthy and somewhat abstruse so thatit is not easy to follow or apply ).The internationally established criteria, at the
present time (1969), for allowable interferences
from earth stations into terrestrial radio relay
receivers are that the interference in any voiceA considerable number of CCIR documents
deal with the coordination problem, for example:
32
diminishes much more rapidly with frequency, andis negligible in the microwave region. The inductionfield and secondary effects of the ground canusually be ignored, so that for the portion of thespectrum of interest here, there is only the directwave and the reflected wave, reflections from fixedobjects, or sky waves which are generally classifiedin this category although, theoretically at least,ref taction may be the proper category .I
therefore the velocity of propagation. The earthatmosphere is therefore the refracting medium thattends to make the radio horizon appear closer orfarther away. It also affects the path clearances inthe manner discussed in the section on SITE ANDROUTE SELECTJON. In the discussions following,it will be shown how it also affects other factors ofjudgment on the radio path.
4. Free Space Attenuation
Although the atmosphere and terrain overwhich a radio beam travels have a modifying effecton the loss in a radio path, there is, for a givenfrequency and distance, a characteristic loss. Thisloss increases with both distance and frequency. Itis known as the free space loss.
Because the path of a radio beam is oftenreferred to as line-of-sight, it is often thought of asa straight line in space from transmitting toreceiving antenna. The fact that it is neither a line,nor is the path straight, leads to the rather involvedexplanations of its behavior, which attempt to givean understanding of the fundamentals of pathpropagation essential to the solution of the prob-lems within each radio path.
Definition
Free space loss is defined as the loss thatwould obtain between two isotropic antennas infree space, where there are no ground influences orobstructions; in other words, where blocking, re-fraction, diffraction and absorption do not exist.An isotropic antenna is defined as one whichradiates or receives energy uniformly in all direc-tions. Although such an antenna is physicallyunrealizable, it provides a convenient referencepoint for calculations. Path loss charts for micro-wave tranmission are customarily prepared on thebasis of free space loss between isotropic antennas,and antenna gains are specified with respect to thegain of an isotropic antenna. These gains may beeasily applied to obtain the net loss from thewaveguide out at the transmitter to the waveguidein at the receiver. This is often referred to as thenet loss for the path.
Q°!!1E-~s~n ~.!!h- ~~ Y!! ~~
A microwave beam and a beam of ligh t aresimilar in that both consist of electromagneticenergy , the difference in their behavior beingprincipally due to the difference in frequency.Because a light beam is visible, it is easier to observeits behavior. So long as the similarities and differ-ences can be classified, the comparison is useful. Asa matter of fact, most of the characteristics ofmicrowaves can be visually demonstrated with lightwaves, and in a very small space.
A basic characteristic of electromagneticenergy is that it travels in a direction perpendicularto the plane of constant phase; i.e. if the beam wereinstantaneously cut at right angle to the directionof travel, a plane of uniform phase would obtain.If, on the other hand, the beam entered a mediumof non-uniform density and the lower portion ofthe beam traveled through the more dense portionof the medium, its velocity would be less than thatof the upper portion of the beam. The plane ofuniform phase would then change, and the beamwould bend downward. This is refraction, just as alight beam is refracted when it moves through aprism.
~a..!.~ ~f J::.~~s in y!!:!~ SE~e-
Radio energy is lost in space primarily becauseof the spreading of energy in the wave front as ittravels through space, in accordance with theinverse-square law. Only a small amount of theenergy which is radiated from the transmittingantenna actually reaches the receiving antenna. Theremainder is spread over areas of the wavefrontoutside the capture area of the receiving antenna.
~~ ~p~c!!.. ~!:>-~~l~The atmosphere surrounding the earth has the
non-uniform characteristics of temperature, pres-sure and relative humidity, which are the para-meters that determine the dielectric constant, and
The derivation of the formula for free spaceloss involves the isotropic radiator, from which theenergy is transmitted equally in all directions. If
34
Blocking, Cancellation ofQ~ §! !h~~~:! --
Where an obstacle is blocking, much dependsUpOh whether it is totally or partially blocking,whether the blocking is in the vertical or thehorizontal plane, and the shape and nature of theobstacle. The most serious of the secondary effectsis reflection from surfaces in or near the path,including the ground. The problem in such cases, isthat the reflected energy travels a separate andlonger route than the main beam, and usually is l:totdirectly in phase with it. The result is oftencancellation of the direct signal to an extentdependent on the relative powers of the direct andreflected signal, and the relative phase of the twosignals arriving at the receiving antenna.
one were to look instantaneously at the surface ofconstant phase at some point d distance from thesource, it would appear as a sphere of radius d. Ifone were to intercept the energy impinging on asmall portion of that surface with an area of A, theenergy intercepted would bear a relationship to thetotal energy from the source as A bears to the totalarea of the sphere, which is 41Td2 .This relationshiprepresents the loss between a point source and an
antenna whose "gain" in terms of A is equal to~
where A is wavelength. By appropriate substitutionsand converting d to miles and frequency in GHz asan inverse function of wavelength, the loss betweentwo isotropic antennas becomes:
A = 96.6 + 20 log10F + 20 log10D (3)
Nature of Obstruction Losseswhere A = free space attenuation between
isotropics, in dBF = frequency in GHzD = path distance, in miles
It may be useful to discuss the effect of somecommonly' experienced obstacles to illustrate thenature of obstruction losses. Trees for example,cause dispersion of energy and affect the verticalclearance. At grazing they look similar to a knifeedge in diffraction theory , and result in about a 6dB loss. When they become obstructions they arenormally considered to be totally blocking. Atclearances above grazing there are usually nosecondary effects of consequence above the pointof free space transmission.
For very short distances, such as between twopoints on the same tower, another formula isuseful, but is usually stated verbally rather thanmathematically. Simply stated, it is; for a distanceequal to one wavelength the loss is 22 dB, and eachtime the distance is doubled, another 6 dB is added.For example; at 6 GHz, one wavelength is 0.05meters and the loss for this distance is 22 dB. At0.1 meter, the loss is 28 dB and at 0.2 meter, theloss is 34 dB. This progression builds up rapidly andcan be used in connection with near-end crosstalkcalculations where the antennas are separated onthe tower. The two loss formulas can be shown toproduce identical results at a given distance. Figure13 is a set of curves showing free space losses atdifferent frequencies and distances.
The effect of man-made obstacles dependsentirely upon their shape and position, if micro-wave-transparent objects, which are few, are ig-nored. A large round container such as a gas storagereservoir , if partially in the path, causes bothdiffraction and dispersion as well as some blocking.It will also reflect a certain amount of energyoff-path, where the wrong receivers may be affec-ted to the point of serious interference. A morecommon object is a water tower, which mayproduce some of these effects at times whenrefractive conditions are such as to place the tankportion in the main beam.The effect of obstacles, both in and near
the path, and the terrain, has a bearing on the prop-agation of radio energy from one point to another ,even at microwave frequencies, where the groundwave does not enter into the calculations. 'rhenature of these effects depends upon many things,including the position, shape and height of obsta-cles, nature of the terrain, and whether the effectsof concern are primary or secondary effects.
Square or rectangular objects in the path o~near it can be very destructive from the transmis-sion standpoint, not only because of blockingeffects, but also because diffraction occurs over andaround them. The flat surfaces cause reflections.These are all, in effect, spurious signals and maycause both interference and signal cancellation. In
35
cities, where this usually occurs, reflected energyhas been known to mterfere with a receiver fromthe opposite direction, or after several reflections,cause delay distortion. Billboards are also goodreflectors. One particularly destructive type is themechanically rotating sign. This results in energybeing deflected in various directions as it rotates. Ina working system it can usually be identified bycomparing the rate of rotation with the rate ofinterference in the system.
reflection coefficient is the 180° phase shift whichtakes place for reflected energy at low angles. Thecurve marked R = -0.3 represents about the
common experience on many paths. It should bepointed out that the criterion of smoothness is notalways as obvious as it is, for instance, on water ora dry lake bed. The point is that within the"obstruction zone" the loss in signal dependssubstantially on the nature of the obstruction.
The curves of Figure 14 are illustrative only,and are not intended to be used for path losscalculation purposes, particularly in the obstructionzone. In situations where actual calculations ofsuch obstructed zone losses are required for aparticular path, it is recommended that themethods developed ill NBS Technical Note 101,Revised, or other equivalent methods be applied.
Figure 14 is an interesting set of curves whichillustrate the effect of the shape of an o bject overwhich a microwave beam passes. The curve markedR = 0 illustrates the knife edge diffraction case asshown in Figure 1. The curve marked R = -1.0
illustrates the smooth sphere diffraction case alsoshown in Figure 1. The significance of the negative
37
~e~e!?p-m~nl ~ !r~~I..J.~n!!:.- !!:.a~~ The first Fresnel zone at any point in the pathmay be calculated from the following formula:
Fl = 72o1N (4A)
where F 1 =
dl=
D
d2
f
~
First Fresnel zone radiusin feetDistance from one end ofpath to reflection point inmilesTotal length of path inmilesD-dlFrequency in GHz
Once again refer to Figure 14. The lowest antennaelevations which will produce cancellation of mainand reflected signals are indicated by the null belowFresnel zone 2. The locus of points along the pathwhere surfaces would produce the same conditiondescribes a larger ellipse, and its ellipsoid describesthe locus of all possible surfaces which wouldproduce second Fresnel zone cancellation. As illus-trated in Figure 14, the pattern of additive andcanceling Fresnel intervals increases with increasingpath clearance, but the differences keep gettingsmaller as the number increases. All of those whichproduce cancellation are even numbered zones. Ifthe value for the first Fresnel zone is known and itis desired to calculate the nth zone, where n is theFresnel zone number, then:
Refer again to Figure 14. The solid curverepresenting transmission losses when the reflectioncoefficient R is -1.0, is the type of curve to beexpected when path height-vs-loss tests are madeover flat, relatively smooth terrain such as dry lakebed, the salt flats of Utah or smooth water surface.The type of test represented is the typical path losstest, where transmitter and receiver are separatedby a normal path length with smooth terrainbetween. The curve is the result of a height-loss runas described under ROUTE AND SITE SELEC-TION. As the transmitting and receivng antennasare raised to the point where free space loss is justobtained, and then further, the received signalreaches a peak value. This is because the directsignal from the transmitting to the receiving an-tenna, and the ground-reflected energy are in phaseaddition at the receiving antenna. Since it is knownthat, for the very low angles of incidence typical of
microwave paths, there is a 180° phase delay (~) atthe reflection point, the total reflection path fiomtransmitting antenna to reflection point to receiv-
ing antenna must be 1/2 wavelength (~) longer than
the direct signal path. If this is true, there must alsobe a point where the direct and reflected signals arein phase opposition. This first occurs when thereflection path is one wavelength longer than thedirect signal path. With the 180° phase delay at thereflection point, the reflected signal is, in effect,one and one half wavelengths behind the dir~ctsignal at the receiving antenna, and in phaseopposition to the direct signal. The first point ofphase addition is the point where first Fresnel zoneclearance over the reflection point obtains. If animaginary line were drawn longitudinally on thepath from the transmitting antenna to the receivingantenna, such that a reflection surface at any pointon that line would produce first Fresnel zoneaddition, it would describe a very long, narrowellipse. If this ellipse were rotated about the mainbeam as an axis (using the straight beam philosophyand the center of the beam) it would describe anellipsoid of revolution, which is the locus of allpossible surfaces which would produce first Fresnelzone addition. The condition therefore applies toobjects at the side of the path as well as to groundreflections. The distance from the exact center ofthe main beam to the above line or surface is alsoknown as the first Fresnel zone radius. It will benoted that th~ reflection point need not be in themiddle of the path, but at any point which providesthe necessary geometric. rela.tions.
Fn = Fl V n (4B)
Or to calculate any Fresnel zone: directly
r;;d;--ii;:-ill
Fn = 72.1 V (4C)
Figure 15 is a curve which permits determination ofthe first Fresnel zone tor any point on a path ofgiven length for the center of the 5.925-6.425GHz band. This is sufficiently accurate for theentire band.
Table B1 lists multiplying factors to allowFigure 15 to be used for each of the othercommonly used bands. In each case the value 9f Fread from the scale is to be multiplied by the factorlisted for the band of interest. Also included is atable of square roots of integral numbers from 1
38
39
through 65 (Table B2), to facilitate calculation ofthe nth Fresnel zone radius when the Ist Fresnelzone radius is known. To calculate the nth zoneradius, simply multiply F 1 by the square root of n.
opposition, the loss can be very large, approachingcancellation. There are also some other effectswhich tend to distort the signals, and these arecovered in a later section.
At this point, the reader is :reminded that themicrowave beam travels as a wavefront of consider-able tranverse cross-section. Specular reflection ofsucb a wavefront requires a reflecting surface of acertain area,. rather than a single point. Thereceiving antenna collects reflected energy from thereflection surface from ahead, beyond and to thesides of the theoretical "reflection point". Whenthe terrain is perfectly flat and the reflection co-efficient is -1.0, it is possible to receive exactlyasmuch energy from the reflection path as from thedirect signal path. Under these conditions, whenthey are in phase addition, the summation signal atthe receiver will be 6 dB higher than would obtainwith free space loss, or without the ground in-fluence. When the two signals are in direct phase
Up to this. point the discussion has beenprincipally about a perfectly reflecting surface. Thisis not a common experience. Referring again toFigure 14, it will be noted that, as the reflectioncoefficient becomes less, the addition and cancella-tion effects diminish, so that for many pathsclearance is the principal concern. One very in-teresting point about the curves however, is thatregardless of the reflection coefficient, the eleva-tions where free space loss first occurs are such thatapproximately O.6F 1 clearance for the center ofthe beam obtains over the reflection point. Whenpath loss tests are made, the value of K at the timeof the test can be determined with this knowledgeand an accurate profile.
While, as mentioned above, many paths do notexhibit serious reflective characteristics, reflectivephenomena are not confined to totally flat areasand water surfaces. There are many areas withrolling hills that are devoid of trees and brush, orundulating valleys between high hills, which willcause serious reflections. Our common experiencewith light waves tends to inhibit our judgment as tothe criterion of smoothness, and also regarding thegeometry of the path itself. The judgment of suchareas by visual inspection alone is often inaccuratewith regard to three important parameters. Theseare; the criterion of smoothness for the frequencyto be used, the effective area of a possible reflectingsurface, and the angles of incidence and reflection.
Table Bl. Multiplying Factors Which Can BeUsed To Convert Fresnel ZoneRadii Calculated For 6.175 GHzTo Other Bands.
The reflection coefficient actually increasesmarkedly as the angle of incidence becomes verysmall. This can be illustrated by viewing an asphalthighway surface at a considerable distance. Thesurface appears like glass and actually reflects thesun at this very small angle of reflection. Yet whenviewed from directly overhead, the surface appearsquite rough at light frequencies. Since microwaveshave a very much longer wavelength than lightwaves, and the angles of incidence and reflectionare very small, the surface can be very muchrougher than the highway surface and still reflectvery well. For instance, wheat stubble, a uniformgrowing crop, and flat prairies, can be very goodreflectors at 2, 4 and 6 GHz. At 11 to 13 GHz thereflection coefficient appears to be somewhatreduced, probably because of the shorter wave-lengths.
40
tions. The variation in these limits morning andevening, are determined by local conditions. Forinstance, sunrise or sunset are quite different inmountainous terrain than they are at sea level, or inintermediate terrain. Between these daytime hours,for most areas, the refractive effect does notusually vary much from the K = 4/3 condition.During these daylight hours, rising convectioncurrents and winds tend to produce a homogene-nous atmosphere, in the sense that stratification inthe air does not exist, and the refractive gradientresulting from the normal pattern of pressure,temperature and relative humidity is fairly uniform.Because this is the only reasonably stable refractivecondition for any period, it is often referred to asstandard. It is also the basis for the start of pathanalysis in many instances, because beam bending isconsidered in relation to this reference standard.
There are at least two conditions whichproduce reflections quite similar to ground reflec-tions, and are often classified with ground reflec-tion phenomena. A growing crop such as alfalfaoften, on level irrigated land, tends to collect aheavy dew in the early morning. The resulting"surface" between wet vegetation and dry air, aspresented to microwaves, is highly reflective. Alsoin a fairly arid country where there is a smallstream in a valley, there is often, at times of stillair, a low ground fog. The upper surface of this fogrepresents an abrupt change in the dielectric con-stant and can be reflective.
6. Atmospheric Effects
The matter of establishing antenna elevationsto provide minimum fading would be relativelysimple were it not for atmospheric effects. Theantennas could easily be placed at elevations toprovide somewhere between fr~e space loss andfirst Fresnel zone clearance over the predominantsurface or obstruction, reflective or not, and thetransmission would be expected to remain stable.Unfortunately, the effective terrain clearancechanges, due to changes in the air dielectric, withconsequent changes in refractive bending. The radiobeam is almost never a precisely straight beam infact, which is to say that using our straight beamconcept, the condition for K = 1 is a rarity.
Actually the most stable atmospheric conditionexists, in most areas, during the daytime hoursfrom 1 to 2 hours after sunrise to 1 to 2 hoursbefore sunset, and during normal weather condi-
The Refractive Index
The radio refractive index of the atmosphere,n, is a number on the order of 1.0003, varyingbetween 1.0 (free space, above atmospheric in-fluence) and about 1.00045 at a maximum. Forgreater computational convenience, it is custotnaryto utilize a term N, called "radio refractivity",which is defined as:
N = (n-1) x 106 (5)
The "N" term would be zero in free space, and anumber on the order of 300 at the earth surface.
41
FigUre 16 is a group of M profiles representingspecific conditions which will be discussed in the
following paragraphs.
The radio refractivity of air for frequencies upto 30 GHz is given as:
N= 77.6~ + 3.73 x 105 ~ (6)T2 Illustrations of Refraction asReTatedtoth~-MProrue- -
where p is the total atmospheric pressure inmillibars, T is the absolute temperature in degreesKelVin, and e is the partial pressure of water vaporIin millibars. The p IT term is frequently referred toas the "dry term " and the elT2 term as the "wet
terIJl ".
Figure 16a illustrates the M profile represent-ing the "standard " condition, where K = 4/3 and
the slope of the profile is constant at 3.6 units perhundred feet.
By examination of Equation 6, it can readilybe seen that, while pressure and relative humidityare direct factors in the refractive index, tempera-ture as a function of N is the predominant factor.In the following discussion, the phenomenon oftemperature inversion is covered. It is easily seenwhy this phenomenon is of concern in connectionwith radio propagation.
If N decreases more rapidly than normal withincreasing altitude, the slope of the M curve issteeper, the value of K is greater than 4/3, and themicrowave beam follows the curvature of the earthmore closely. If the value of M becomes constantwith change in altitude, the microwave beamfollows the curvature of the earth exactly, and K isequal to infinity. This condition is representedgraphically by a vertical M profile, as shown forsuper-standard in Figure 16b. It would be repre-sented on a path profile by a flat earth and astraight line microwave beam. If conditions becomeeven more extreme, the M profile will have anegative slope, corresponding to a negative K, or a"concave earth " condition. An example of this
condition is the rare instance when an overreachinterference signal is recorded at a station, and yetthe overreach path is obstructed by several hundredfeet when the path profile is plotted on flat earth.
M Profiles
The discussion of atmospheric irregularities isoften aided by the use of another term or symbol,M, which is called the "modified " index of refrac-
tion. It is defined in terms of the radio refractiveindex and the mean sea level elevation. Thefollowing formula is applicable :
M = (n-1) x 106 + 4.8h 7)
When the slope of the M profile is greater thannormal, the refractive condition is referred to assuper-standard or earth flattening, since the radiohorizon distance is increased. When the slope of theM profile is less than normal, the refractive condi-tion is known as sub-standard or earth bulging. Thiscondition is reflected in Figure 16b.
where n
h
the radio refractive indexthe height above sea levelin hundreds of feet
~
In the normal atmosphere (where K = 4/3), Mincreases at a linear rate of about 3.6 units perhundred feet increase in altitude. When height isplotted as ordinate against M as abscissa, the plot iscalled an M profile. The slope of the M profiledetermines the degree of bending of the microwavebeam in relation to the earth.
In practice, linear profiles do not usuallyoccur except near the standard profile, becauseweather factors usually change the shape of the Mprofile as well as its slope.
For discussion purposes it might be somewhateasier to follow a simplified equation for M, whichresults from combining equations 4 and 6. Theterm N, which is the variable fraction of therefractive index, then becomes the parameteragainst which the modified index M and its profileare compared. The new equation becomes:
The effect of an abnormally high surfacetemperature, or increasing water vapor contentwith altitude, is shown in the M profile of Figure16c. Such a sub-standard surface condition willresult in curving the beam away from the earth, andthis is called inverse beam bending or earth bulging.The effect is similar to that from a linear M profileM = N + 4.8h (8)
42
the available data based on meteorological measure-ments is still of relatively limited value in deter-mining the values of K to be used in engineeringline-of-sight microwave paths.
with a slope less than normal ( earth bulging),except that it is concentrated near the surface ofthe earth.
A rise in temperature with increasing height,or a decrease in water vapor content, or both, willproduce the effect shown in Figure 16d. This is aslightly super-standard condition that will cause thebeam to follow the curvature of the earth moreclosely ( earth flattening).
Three K values are of particular interest in thisconnection;
(1) Minimum value to be expected over the path.This determines the degree of "earth bulging"and directly affects the requirements forantenna height. It also establishes the lowerend of the clearance range over which reflec-tive path analysis must be made, in the case ofpaths where reflections are expected.
When the changes in refractive index are mostsevere near the surface, the condition will be asshown in Figure 16e. This condition is known as asurface duct, because the beam ~l tend to staywithin the surface and the elevation limit a;depending on the slope of the M profile near thesurface. When the beam enters the duct at a smallangle, it is bent until it is horizontal, and thenturned downward by further bending.
(2) Maximum value to be expected over the path.This leads to greater than normal clearanceand is of significance primarily on reflectivepaths, where it establishes the upper end ofthe clearance range over which reflectiveanalysis must be made.
Figure 16f is the M profile of an elevated duct,the upper limit of which is formed by the upperlimit of the super-standard or inversion layer from ato b, and the lower limit by the sub-standard layerfrom b to c. Under these conditions, the beam willtend to remain within the duct limits from a to c,due to the bending toward the center of the duct.Concentration of radio energy within a duct willcause an increase in received signal when both thetransmitting and receiving antennas are within theduct. Obviously this effect cannot be relied on forsatisfactory propagation, because the conditionsproducing it are subject to change. The termstrapping, super-refraction and guided propagationare also employed to describe duct phenomena.
( 3) Median or "normal " value to be expected over
the path. Clearance under this conditionshould be at least sufficient to give free spacepropagation on non-reflective paths. Addi-tionally, on paths with significant reflections,the clearance under normal conditions shouldnot fall at or near an even fresnel zone.
Of these three values of K, only the medianvalue can be predicted with any degree of confi-dence from available meteorological data.
The minimum value chosen for K must, for ahighly reliable path, be an extreme value which willbe passed for only exceedingly small percentages ofthe time. Experience has indicated that, for actualmicrowave paths, the effective K over the entirepath reaches a very high or very low value for amuch smaller percentage of time than would beindicated by the distribution of K values as foundby meteorological measurements at single points.The most probable explanation is that the uhusualconditions causing these extreme values are un-likely to occur over more than a small part of thepath at any given instant. In any event, thecorrelation between limiting K values as found inpractice with those based on meteorological datahas been found to be very low, and the best guideto choice of K values to be used in path engineer-ing, is past history and experience in the field.
M profiles which are essentially linear aresignificant primarily because of their effect on pathclearance. The non-linear profiles, in addition toaffecting path clearances, also give rise to condi-tions leading to atmospheric multipath effects.
K Factors
The discussion of refractive effects as givenhere is principally for use as background informa-tion to aid in understanding the mechanisms andprinciples involved in the complex phenomenon ofpropagation through the atmosphere.
Despite the great amount of work which hasbeen done in collecting and analyzing data on thevariations with time of the refractive index, and itsgradient at many locations throughout the world,
43
The K factor corresponding to an atmospherewith a linear gradient of refractive index dn/dh canbe calculated by the equation:
There is also a seasonal pattern. The maximumvalues of K are usually greater in summer than inwinter, with the minimum values for summer andwinter running about the same. There is, therefore,a greater excursion of K in summer than in winter .This, together with its effect on the radio path, hasgiven rise to the generally prevalent feeling thatfading is a summer phenomenon. This is notexclusively true, as there are radio paths which fadein winter as well as summer, but in most areas thesummer fading is likely to be much more frequentand sometimes more severe.
1K= - (9A)
1 +~ .dn
ndh
where' a is the true radius of the earth, n the radiorefractive index, and dn/dh is the gradient of n withrespect to heigh t in the portion of the atmosphere.affecting the path.
Weather FrontsIn this equation, the variations of n itself are
too small to have significant effect, and n can betaken as 1.0003 for all practical purposes. Thisleaves dn/dh as the significant variable affecting thevalue of K.
It is more convenient to consider the gradientof N units instead of the gradient of n units, and,when dN/dh is substituted for dn/dh, with theappropriate correction factor of 10 -6, and the valueof 6370 kilometers for a and 1.0003 for n aresubstituted in (9A), the following equation isobtained:
157K = -..]~T(9B)
where dN/dh is the N gradient per kilometer.
Weather fronts moving through a particulararea during the hot summer months are usuallyaccompanied by sudden cooling in the loweratmosphere. The result is a rather abrupt change inthe air dielectric to a lower value, with a reductionin the n gradient and an increase in the value of K.This is a very temporary change. The value of Kchanges according to the storm condition while it isin progress, which may vary widely depending uponwhether saturation rain, high winds, hail, etc.,obtain. After the storm, the value of K usuallyreturns to something in the order of its normalvalue for the time of day and the area. The drop inbarometric pressure preceding a storm front bysome hours, is in itself not a large variant in thevalue of K, although it does affect the refractiveindex as such. Referring to Equation 6, it isestimated by the National Bureau Of Standards
77.6Pthat the "dry term " T accounts for at least
60% of the value of N .From (9B) it can be calculated that an Ngradient of -40 units per kilometer would give a Kof 4/3 (the so-called standard atmosphere), an Ngradient of -157 units per kilometer would give aK of infinity (super-normal refraction), and an Ngradient of about +79 units per kilometer wouldgive a K of 2/3 (sub-normal refraction).
Rain Attenuation
Attenuation of a microwave signal due torainfall or snow along the path, is present to somedegree at all microwave frequencies, but the effectis so s~all as to be insignificant, at least incomparison to the other types of fading, for thebands of 8 GHz and lower. But at higher fre-quencies, the excess attenuation due to rain in-creases rather rapidly and, in the bands above about10 GHz, i~ great enough to significantly affect pathlength criteria, except in areas of very light precipi-tatibn.
In addition to the linear variations in thegradient, there are periods of considerable non-linearity such ~s just after sundown, particularly incoastal areas. At that time the lower strata of air iscooling; the relative humidity is increasing, the ngradient is increasing, and the value of K increases.This pattern often holds until around midnight,after which the relatively warmer earth surface, andthe cooler air above it, appear to produce anirregular pattern in which values of K smaller thanthe daytime values are not unusual.
The degree of attenuation is a function of anumber of variables including the frequency band,size and shape of the drops, and the distribution of
44
values to the yearly outage times shown on Figure20, one can see that in the heavier rain areas, thesecond objective could not be met at all, and thefirst could be met only with very short paths. Inthe light rain areas such objectives might be metwith even relatively long paths.
rain (in terms of its instantaneous intensity) alongthe path. What is important is not the total amountof rain which falls over an extended period, butrather the maximum instantaneous intensity of fallwhich is reached at any given moment, and the sizeof the area over which the high intensity cellextends at that moment. Most available rainfallstatisFics cast little light on these matters and,consequently, are of only limited value in estima-ting the magnitude of rain attenuation effects.Figure 17 gives excess path loss in decibels per mileversl!s rainfall rate in inches per hour, for severalfrequency bands. It is based on the theoreticalwork of Ryde and Ryde. Figure 18, taken from aCCIR document, provides somewhat similar infor-mation in the form of excess path loss in decibelsper kilometer versus frequency in GHz, for anumber of rainfall rates. This figure also includescurves for attenuation in fog or cloud, which,though substantially lower than that of heavyrainfall, can nevertheless reach measureable valuesat the higher frequencies. Hathaway and Evans, inan article published in Communications and Elec-tronics, January, 1959, discussed both the theoreti-cal and practical aspects of the rain attenuationproblem and provided application data for the 11GHz band, applicable to the continental UnitedStates, which is still one of the best availablesources. Figure 19, , adapted from that article,
divides the U.S. into eight geographical areas inascending order of effect of rain attenuation, andFigure 20 gives the estimated outage time in hoursper year versus path length in miles for each area.The latter figure is based on 11 GHz paths with a40 dB fade margin. Figure 20 can be used for 13GHz by reducing the mileage figures on the pathlength scale by approximately 30%. Dropping thefade margin from 40 dB to 35 dB would increasethe expected outage time by approximately 25%,while increasing it from 40 dB to 45 dB woulddecrease the expected outage time by approxi-mately 15%.
On the other hand, there are certain types ofservice (for example, CATV relaying) in whichsomewhat lower reliabilities, 99.9% for example,are considered quite acceptable, and in such casesrelatively long paths may be practical, even in areaswith high rainfall.
Two things to bear in mind in connection withrain attenuation are that, (1) multipath fading doesnot occur during periods of heavy rainfall, so theentire path fade margin is available to combat therain attenuation, and (2) neither space diversity norin-band frequency diversity provide any improve-ment against rain attenuation.
One thing has been well established; thatcross-band frequency diversity, with one channel ina 6 GHz band and the other in an 11 or 12 GHzband, is entirely practical, even in the heaviest rainareas and for highest reliability requirements. Thereason is that, since multipath fading is unlikelyduring heavy rainstorms, the 6 GHz path can carrythe service during such periods without needing anydiversity protection. The degree of equipmentprotection is reduced slightly, but not by a signifi-cant amount.
Apart from the rain attenuation problem, the11 to 14 GHz bands have excellent characteristicsand, despite the rain limitation, they have provenvery useful in practice. They are lifesavers in areaswhere congestion has used up all available frequen-cies in the lower bands. In addition to theirusefulness in cross-band applications, they can beused for spur routes or very short paths in theheavy rain areas, and almost unrestrictedly in verylight rain areas. They are extremely valuable forhops into or in the vicinity of earth stations, sincethey avoid the coordination problems associatedwith the shared 4 and 6 GHz bands. In any givensituation, the effects of rain attenuation can bereduced by raising the fade margin, shortening thepaths, or both.
The degree of severity of the rain attenuationproblem, depends very critically on the degree ofreliability which is established as an objective.Present day reliability objectives for highest relia-bility systems are such as to require per pathreliabilities on the order of 99.99% to 99.9999%,depending on the number of hops involved. Thismeans that total outage objectives for a path mayrange from 0.01% to as little as 0.0001%. On anannual basis, 0.01% amounts to approximately 53rpinutes per year, while 0.0001% would amount toonly about 30 seconds per year. Comparing these
Fo~
When fog forms, either by nocturnal coolingof the ground or by the flow of warm air over cool
46
w-J
~(1:w0..
(I)-Jwcc
(3wO
z
(I)(I)O-J
II-<:I:0..
(I)(I)wuxw
Rain Attenuation vs. Rainfall Rate (Theoretical, after Ryde and Ryde)Figure 1 7.
47
-Attenuation in fog or cloud F, 0.032 gm/m3 (visibility greater than 600 meters)G, 0.32 gm/m3 (visibility about 120 meters)H, 2.3 gm/m3 (visibility about 30 meters)
* Attn -dB/mile = 1.61 x (Attn in dB/km)
Figure 18. Attenuation Due To Precipitation (after CCIR)
48
Reproduced by permission IEEE Transaction Paper No.58-1236 (Hathaway and Evans)I-~ -
CI
!I)a::)O:I:z 4
UJ~1--UJt:J«1--:)0
1
6040 45 5015 20 25
PATH LENGTH INMILES
30 359 106 7 8
Expected Outage Time In Hours Per Year vs. Path Length In Miles For Various Areasof the United States. (Based on 11 GHz paths with 40 dB fade margin; for 13 GHz paths,reduce path lengths by 30%. For 45 dB fade margin, decrease outage time by 15%; for35 dB fade margin, increase it by 25%.)
Figure 20,
L
~t~~~i~ ~L~-~IE.°!!p~e.!!~ G~s~ground, the total amount of water in the airremains substantially the same, but part of thewater condenses into minute droplets. Its contribu-tion to the refractive index is then substantially lessthan when it is in the form of vapor. The weathereffect normally accompanying a fog is very still air,and some temperature inversion. These are theconditions for a sub-standard surface layer with anM profile as in Figure 16c, The result is to reducethe effective beam clearance at all frequen..:ies and,in extreme cases, will put the system out of service.The term "earth bulging" is often applied to therefractive effect.
The principal gaseous absorption is by oxygenand water vapor. The attenuation due to oxygen isrelatively constant in the 2 GHz to 14 GHzfrequency range, and is slightly under 0.01 dB/mileat 2 GHz 'and slightly above at the 14 GHz end.Water vapor absorption, on the other hand, ishighly dependent on the frequency (as well as thedensity of water vapor). It is extremely low at 2GHz, on the order of 0.0002 dB/mile, and stillnegligible, on the order of 0.002 dB/mile, in the 8GHz range. But at about 14 GHz it is approxi-mately equal to the oxygen absorption, at about0.01 dB/mile, and at frequencies in the vicinity of20 GHz it is up to nearly 0.2 dB/mile. These dataare taken from NBS Monograph No.92, "RadioMeteorology", and Table C is also based on that
source.
Fog which occurs very close to the ground inthe early morning, usually in a valley immediatelyover a small stream, has quite another effect. In thiscase, the normal beam is in the clear, but thesurface at the fog layer is a smooth strata whichforms a good reflector of microwave energy.
50
the antennas high enough so that even undersubnormal refractive conditions there will still beadequate signal strength. Yet if the antenna heightsare greater than actually needed, there can be anunwarranted increase in system cost and -forpaths with significant ground reflections -anincrease in multipath and ground reflective fading.
Normal Non-Reflective Paths
Although there are some variations, there aretwo basic sets of clearance criteria which are
in common use in microwave communicationssystems. One is a "heavy route" set used for thosesystems with the most stringent reliability require-ments, the other a "light route" set used forsystems where some slight relaxation of the require-ments can be made. The following are typicalclearance criteria:
It is seen that the assumption of "free space"propagation through the atmosphere is reasonablywell justified for paths up to about 50 miles from 2through 8 GHz, or for paths up to about 20 milesfor 10 through 14 GHz, but for longer paths, thegaseous absorption loss should be taken intoconsideration. Unlike free-space loss, this loss isdirectly proportional to the length of the path. Thewater vapor absorption will change wit~ the densityof water vapor in the atmosphere, consequently thebands of 10 GHz and up, which have significantamounts of attenuation from this source, will varywith the vapor density.
At least 0.3F 1 at K = 2/3 and 1.0F 1 at K= 4/3, whichever is greater. In areas of
very difficult propagation, it may benecessary also to ensure a clearance ofat least grazing at K = 1/2. (For 2 GHz
paths above 36 miles, substitute 0.6F 1at K = 1.0).
Clearance Criteria Note that the evaluation should be carried outalong the entire path and not just at the center.Earth bulge and Fresnel zone radii vary in adifferent way along the path, and it often happensthat one criterion is controlling for obstacles nearthe center of the path and the other is controllingfor obstacles near one end of the path.
For practical calculation purposes, based onthe experience of many users, K is usually consid-ered to fall within a range from about infinity inthe supernormal direction (flat earth condition) toabout 2/3 in the subnormal direction, with normalor "standard atmosphere" being taken as K = 4/3.
For "Iight-route" systems with slightly
les~~r!~~~a-bility requirementsExcursions beyond these upper and lowerlimits do occur in some areas, but on rare occasionsand usually for quite small time intervals. Publisheddata based on point meteorological soundings showconsiderably higher percentages of time at theextreme ends, particularly in some difficult areas(hot, humid) such as the Gulf Coast, but practicalexperience indicates that the extreme values shownby such point measurements apply only to a smallarea and do not accurately represent what is likelyto happen along an entire path at a given instant.
At least O.6F + 10 feet at K = 1.0.
At points quite near the ends of the paths, theFresnel zones and earth bulge become vanishiQglysmall, but it is still necessary to maintain someminimum of perhaps 15 to 20 feet above allobstacles. ,
;The "heavy route" criteria are on the conser-
vative side except in the more difficult propagationareas, and undoubtedly in some cases will result ingreater heights than actually needed. But it isdifficult to predict accurately just what can happenon a given path under all conditions, and thesecriteria are well backed by experience. It should benoted, however, that even the heavy route criteria
The choice of clearance criteria for a micro-wave route or path is an important one, since it canprofoundly affect both the cost and the quality ofperformance. It is desirable on the one hand to get
51
moved in close to the low stations. The elevation ofthe antennas on the flats is quite low, and iscomputed to receive direct and not more than firstFresnel zone reflected energy most of the time. Thetransmit side works the same way, since the twotransmission directions are symmetrical geometri-cally. As the value of K changes, the reflectionpoint moves. As K becomes larger it moves towardthe low site, and when it becomes smaller it movestoward the high site. A principal objective is toestablish the low antenna elevation so that secondand higher order Fresnel zone energy , that mightotherwise reach the ~ow antenna (receiving side ), isblocked by tile curvature of the earth at anyexpected values of K except near infinity.
will not guarantee complete protection against therare and unpredictable "blackout" fading whichoccurs in some areas.
Note: A theory has been propo.s:ed recently atLenkurt which, if experience backs it up,might provide protection against some
( forms of "blackout" fading. The theoryi is based on an assump tion that even in
difficult propagation areas the extremegradients necessary to produce suchblackout situations are likely to occuronly very near the earth's surface. Someevidence seems to indicate that a layer ofperhaps lOO to 150 feet above the earth'ssurface might encompass most of thisdifficult area. The theory then suggeststhat in areas where this kind of propaga-tion anomaly is known to exist or mightbe expected, an additional criterion of atleast 150' clearance above the earth'ssurface, all along the path, for a K valueof 1.0 might be applied. Obviously onrelatively short paths with no otherclearance problems, this would require aconsiderable increase in tower heights,over those needed to meet the othercriteria.
Figure 7 can be used to locate the reflectionpoint for a given path under various values of K.However, for this special case, because of the smallvalue of x ( or h 1 ), it is advisable to deriveapproximations from the curve, and then use theiterative procedure described in the text to find theexact values of n for various K. The criticalparameters are the relative elevations h 1 and h2 ,path length, frequency and the size of the antennaaperture. By experimenting with Figure 7, thelimiting values for path geometry can be easilyestablished in a given case. The high-Iow techniqueis a good solution where applicaQle, if the operatingfrequencies are in the 2 or 4 GHz range. At 6 GHzand above, the smaller Fresnel intervals in relationto the sizes of antenna aperture required for goodtransmission, would render the scheme question-able at 6 and 7 GHz without other externalstructures, and impracticable at 11 to 13 GHz.
Reflective Terrain
For non-reflective paths it is necessary only toprovide sufficient clearance to ensure free-spacepropagation under normal conditions, and to meetminimum acceptable clearance under subnormalconditions. The same considerations apply to re-flective paths, but with the added requirement tostudy the path for supernormal conditions, at leastup to K = 00 in most cases.
The high-low technique can be used at allmicrowave frequencies if the reflection point,under all values of K, can be placed in roughnon-reflective terrain. It should be noted that underthis arrangement, the reflection point moves over aconsiderable distance with different values of K.For instance; a 30 mile path, with antennas at thesites at elevations of 10 feet and 1000 feet (relativeto the reflective surface), will have the reflectionpoint for K = 2/3 at 1.35 miles from the low site,but for K = 00 the point will be approximately 0.3miles from the low site. In many cases, advantagemay be taken of the existence of low ridges orother irregular obstacles. Figure 6 illustrates such acase.
As discussed in earlier sections, it is possible insome situations to choose sites and antenna heightsso as to provide screening or blocking of allpotential reflective paths. In other situations thismay not be possible. Where local conditions permit,the so-called high-Iow technique can be used toadvantage to minimize the effect of reflections.There are some variations in this plan, and somepitfalls. Basically, the plan involves one adjacentrepeater on a mountain ridge or very high point,and the other on a very low point, even on the flatsif such is the nature of the surface. The point is,that provided the difference in elevation is suffi-cient considering the length of each path, thereflection "point" (center of locus of reflection) is
Qp.!:..ll-!- ~0~~ .!~~ll-
In open terrain where a path may have treesand other obstacles at some points, and barren,
52
viewpoint, the principal precautions are avoidingexcessive waveguide lengths, and minimizing theamount and number of flexible waveguide sections.The latter have a tendency under the stresses ofinstallation or maintenance to produce mismatcheswhich, combined with slight mismatches at theantenna, will produce round trip echoes, causingdelay distortion.
rolling hills at others, the obstacles and high terrainshould be considered for clearance based on thecriteria indicated above. Additionally, the barrenhills should be considered as possible reflectors, anddeterminations made within the assumed limits ofK as to whether serious even zone reflections couldbe experienced. Frequently adjustments in antennaelevations can be made to eliminate such possibilitywithout seriously affecting terrain clearance at theassumed lower limit of K. There is an economy inconsidering the reflection possibility when originalantenna elevations are established, even thoughonly a small percentage of the cases considered mayturn out to be seriously reflective.
9I .Fading
The beam of microwave energy is not a singleline, but a wavefront extending for a considerabledistance about the center line. Since the index ofrefraction under normal atmospheric conditions islower at the top of the wave front and higher at thebottom, and since velocity is inversely proportionalto the index of refraction, the upper portion of thewavefront under such conditions will travel slightlyfaster, with the result that the wavefront as itmoves along the path will tend to have the toptilted more and more forward. Since the directionof beam travel is always perpendicular to thewave-front, the beam itself will be bent downward,thus increasing the apparent clearance. The amountof bending is actually very slight on a percentagebasis, but is sufficient to cause significant varia-tions.
8. Delay Distortion
Delay distortion may be caused by the radiopath, waveguide system or the radio equipment.The end product is noise distortion in the message,data or television channel assigned to the baseband.It can be particularly destructive of data serviceassigned to part of the baseband, when message ordata service is assigned to other parts of thebaseband, because of the cross-modulation noisepeaks that cause data errors.
In the propagation path, delay distortion iscaused by reflected energy which reaches thereceiving antenna, but is delayed by a number ofwavelengths as compared to the direct signal. Inthis case it is not the instantaneous phase, but theactual time delay, that causes the delay distortion.It can be detected by delay sweep instrumentation,and is measured in nanoseconds. The criticalamount of delay that can be tolerated withoutserious distortion depends upon the top frequencyof the baseband. As discussed under ROUTE ANDSITE SELECTION, the typical situations to avoidin order to minimize delay distortion in thepropagation path, are paths which are mountaintop to mountain top with low, flat terrain between,and paths that go through areas of tall buildings;particularly where the path aligns with the street.All paths which mlly result in terrain clearance ofF60 (60th Fresnel zone) or more over flat terrain,should be examined for possible delay distortion.Building reflections are difficult to coIll;pute inadvance, but situations which might indicate thispossibility should be avoided because of r~flectionfading and interference, as well as delay distortion.
Under certain atmospheric situations there canbe even greater than normal negative N gradients(supernormal, or "earth flattening" type), or othersin which the N gradients become less negative, oreven positive. In the latter situation the lower partof the wavefront will travel faster, and the beamwill be bent upward, reducing the apparent clear-ance. This is the subnormal, or "earth-bulging"
type.
Most of the time these gradients in the loweratmosphere are essentially linear .These linearvariations affect clearance, and are also importantwhen the path is reflective, but they do notproduce atmospheric multipath situations.
However, when non-linear gradients such asshown on c and d, and particularly e and; f ofFigure 16 occur, it is possible for multiple paths, inaddition to the direct path, to exist within theatmosphere itself, independent of any reflectingsurface.
These "kinks " in the atmosphere can occur
when conditions are such that stratified layers withdifferent gradients may lie on top of one another ,
Waveguide echoes are another source of delaydistortion. They result from impedance mismatchesor irregularities. From the systems engineering
53
much like a layer cake. The familiar smog-producing temperature inversion is an example.
tests, of 20 to 25 dB when 4 and 6 GHz CW testsignals are used. Two or more reflection surfaces ina path, which, under some combinations of antennaelevations and specific values of K, produce coin-cident even zone reflections, can cause even deeperfades.
These conditions typically are most likely tooccur on hot, still, humid wind-free nights whentemperature inversions are in. existence. Undernormal daytime conditions, temperature is greatestnear the ground and decreases with altitude, acorldition which leads to convection with the risingIair keeping the atmosphere well mixed. But atnight, radiation can cool the ground more rapidlyth6ill the air, and the temperature may then increasewith increasing altitude. This is a stable conditionand allows the stratifications to occur .Theseconditions can also happen in daytime, but aremuch less likely.
Growing crops such as alfalfa, can produceserious fading with early morning dew, especially ifon low, flat irrigated land. Wheat stubble (depend-ing partly on the planting orientation) and newwheat in the early growing period, provide insuffi-cient roughness to break up a reflection pattern. Alllow, flat areas, and rolling country without trees,heavy brush or obstacles, should be considered forground reflection possibilities when analyzing apath for the determination of antenna elevation,and for space diversity intervals. The combinationof ground reflection fading and atmospheric multi-path fading can be particularly severe.
When the appropriate conditions exist on apath, it is possible to get the so-called atmosphericmultipath, in which 2, 3, 4 or even many moredistinct signal paths may exist between transmitantenna and receive antenna. Under these condi-tions the received signal is the vector sum of thevarious components, all of which are varying inphase in a random manner, and usually in ampli-tude as well. In such a situation there will be shortintervals in which the various vectors will effec-tively cancel each other to produce a null. It is thisphenomenon, often accentuated by some groundreflection complications, which causes most of thefast, very deep fading experienced on many micro-wave links.
This brief and very sketchy discussion of avery complicated process is intended only to give ageneral familiarity with the phenomena causing thefading effects. Ordinarily in line-of-sight microwavework it is not necessary to calculate or measure theactual variations in the atmosphere or the index ofrefraction.
Insofar as the clearance portion is concerned,the accepted practice is to assume a range ofvariations based on documented experience, and toselect a set of clearance criteria appropriate to thetype of service and the area.Fading due to ground reflection phenomena is
not confined to water and perfectly smooth, flatsurfaces such as dry lake beds or salt flats, althoughsuch surfaces approach the classical reflectioncoefficient of -1, indicating a perfect reflector. Ourcommon experience will show that two differentsurfaces will reflect visible ligh t even though, whenexamined under a microscope, one is much rougherthan the other. Such is also the case with micro-wave energy , which will be reflected by differentsurfaces with somewhat different reflection coef-ficients. Moreover, tpe effective reflection coeffi-cient is affected by angle of incidence, and by thewavelength of the microwave energy .Additionally,from a quantitative standpoint, the effective area ofthe reflecting surface with just the right angle ofincidence, is a measure of the reflected energyreaching the receiving antenna. Experience hasshown that rolling prairie, such as that existing insome of the midwestern United States, can have afairly high reflection coefficient, and may producefades from one reflection surface, as shown by path
The treatment of multipath fading is alsobased largely on experience. This type of fading hasbeen found to follow distributions which aregenerally related to the well-known Rayleigh distri-bution. The latter or some modification is widelyused in estimating propagation reliability, and inestimating the improvements which are attainableby the use of suitable diversity methods.
It is generally agreed that multipath fadingtends to be greater on long paths than on shortones, and also to be somewhat greater at the higherfrequencies. The Rayleigh distribution is oftentaken as the limiting value for multipath fading online-of-sight paths with adequate clearance. Oneway of estimating reliability is to make a "worstcase" assumption that a path will have continuousRayleigh -distributed fading. This distribution has aslope of 10 dB per decade of percentage of time. Apath with this fading distribution would have 20 dB
54
however, th~t the Barnett and Vigants formulasgive results which are considerably more pessimistic( conservative) than similar formulas developed byJapanese investigators and reported in the litera-ture.
fades for 1.0% of the time, 30 dB fades for 0.1% ofthe time, and 40 dB fades for 0.01% of the time.Continuous Rayleigh-distributed fading is unlikelyto occur on most paths, and the assumption istherefore very much on the conservative side. Itdoes, however, allow some leeway for the effects ofcombinations of attenuation fading and multipathfading, which can be much worse than either onealone.
10. Propagation Reliability andDiversity Considerations
Table D provides a simple means of trans-lating a given system reliability percentage intoterms which are more easily related to experience.For example, the 99.99% value would corres-pond to about 53 minutes of outage time peryear, while the 99.9999% value would amount toonly about 32 seconds per year. The latter value istypical of per path objectives for the highestreliability systems.
The incidence of multipath fading varies notonly as a function of path length and frequency,but also as a function of climate and terrainconditions. In the most favorable areas, for ex-ample paths in dry windy mountainous areas, itmay be essentially non-existent. Hot, humid coastalareas typically have a high incidence of multipathfading, and inland temperate areas are somewherein between. Flat terrain along a path tends toincrease the probability of fading, while irregular orhilly terrain tends to reduce it. It was indicated in a previous section that
diversity techniques, when properly applied, canreduce the effects of multipath fading on line-of-sight systems to insignificance. Whether or not theconsiderable expense of providing diversity is justi-fied will depend very critically on the nature of thecommunications and the degree of outage which isacceptable.
Over the course of the years a number ofapproaches have been developed for calculating orestimating the distribution of deep fading for amicrowave path.
In a following section we develop methods ofcalculating the annual outage probability for aline-of-sight microwave path, as a function of thepertinent parameters and conditions of the path.
By providing adequate path clearance to essen-tially eliminate outages due to earth blocking(which diversity does not help in any event), andby providing fade margins of 40 dB or more, it ispossible to achieve per path propagation reliabili-ties, with respect to Rayleigh-distributed fading, onthe order of 99.99% or better without diversity.For many types of service this may be adequate.But for long systems, and particularly for systemscarrying data, it is almost mandatory to employdiversity if very high reliability is needed.
These methods are based on relatively newexperimental and theoretical results reported byW .T .Bamett, of Bell Telephone Laboratories, at anURSI meeting in Washington, D.C., in April, 1969,and by Arvids Vigants, also of Bell Laboratories, inseveral published papers. (See Page 119).
Barnett's work was in two parts. One de-scribed ways of calculating the outage due to fadingon a non-diversity path as a function of terrain,climate, path length, and fade margin. The othergave formulas for calculating the effective improve-ment achievable by frequency diversity, as a func-tion of the spacing interval and the frequency band.Vigants' work gave formulas for calculating theeffective improvement achievable by vertical spacediversity, as a function of the spacing in feet, thepath length, and the frequency.
A point of considerable significance in connec-tion with multipath fading, is that its potenti~ forcausing data errors is a function of the number ofinterruptions as well as total interruption time. Agreat many very short interruptions becau~e ofdeep multipath fades would be far worse than thesame total time if it were only a single interruption.As a result of this phenomenon, and the greatlyincreased use of systems for data as well as voice,diversity protection may be desirable even if thetotal time reliability objectives did not require it.Diversity reduces the number as well as the totaltime of the multipath propagation outages.
Since these studies were based on a relativelylimited number of paths, the generalization toother paths, other frequencies, and other areasinvolves some degree of risk. It may be noted,
55
I
Table D. Relationship Between System Reliability And Outage Time
OUTAGE TIME PER
I MONTH IYEAR I (A~-g-.)- I
OUTAGE
TIME
%
RELIABILITY
%DAY
(Avg.)
a
50
80
90
95
98
99
99.
99.
99.
99.
100
50
20
10
5
2
8760 hours
4380 hours
1752 hours
876 hours
438 hours
175 hours
88 hours
8.8 hours
53 minutes
5.3 minutes
32 seconds
720 hours
360 hours
144 hours
72 hours
36 hours
14 hours
7 hours
43 minutes
4.3 minutes
26 seconds
2.6 seconds
24 hours
12 hours
4.8 hours
2.4 hours
1.2 hours
29 minutes
14.4 minutes
1.44 minutes
8.6 seconds
0.86 seconds
0.086 seconds
0.1
0.01
0.001
0.0001
Qi~~~ ~~J~m-e-n..!S Vertical space diversity , applied on a perhop basis, with post-detection combiningor selection.For routes which have two or more parallel
working channels (for example, the TD2 or THmainline routes), the protection arrangements areof the so-called I-for-N or 2-for-N type, where oneprotection channel protects on a sectional basisagainst either equipment failures or selective fadingin anyone of several working channels. In effect,this is a form of frequency diversity, thoughconsiderably more efficient in usage of spectrumthan the straight frequency diversity arrangement,which requires two RF channels for each workingpath. There are at present no practical ways ofusing space diversity alone to provide both equip-ment and propagation protection on a multiplechannel switching section, consequently the I-for-Nor 2-for-N systems are the only available method ofhandling this situation.
Hybrid diversity, a special combinationof frequency and space diversity.
The frequency diversity arrangement providesfull and simple equipment redundancy, and has thegreat operational advantage of two complete end toend electrical paths, so that full testing can be donewithout interrupting service. Its disadvantage is thatit doubles the amount of spectrum required. Also itis sometimes\prohibited by the licensing authority;it is not, for example, available to industrial users inthe U.S.A.
The space diversity arrangement can alsoprovide full equipment redundancy (when auto-matically-switched hot standby transmitters areused), but does not provide a separate end to endoperational path. Because of the requirement foradditional antennas and waveguide, it is moreexpensive than the frequency diversity arrange-ment. However, it provides efficient spectrumusage, and extremely good diversity protection, inmany cases substantially greater than obtainablewith frequency div~rsity , particularly when thelatter is limited to small frequency spacing inter-vals.
For systems requiring only one working RFchannel, as typical of most industrial systems and agreat many of the military systems, the mostcommonly used basic protection methods are:
Frequency diversity, either in-band orcross-band, applied on a per hop basis,with post-detection combining or selec-tion.
56
9
99
999
9999
of correlation is high. For example; at a fademargin of 40 dB, diversity with 0.99 correlationwould improve the path reliability by a factor of100, from 99.99% to 99.9999%. At this same fademargin, diversity with 0.0 correlation would show acalculated improvement by a factor of 10,000! !
The somewhat specialized form of diversity,which we have called "hybrid diversity", consists ofan otherwise standard frequency diversity path, inwhich the two T-R pairs at one end of the path areseparated from each other, and connected toseparate antennas which are vertically spaced as inspace diversity .This arrangement provides a spacediversity effect in both directions; in one directionbecause the receivers are vertically spaced, and inthe other direction because the transmitters arevertically spaced. This arrangement combines theoperational advantages of frequency diversity withthe improved diversity protection (particularly onreflective or difficult paths) of space diversity. Ithas, of course, the same disadvantage as ordinaryfrequency diversity, in that it requires two RFfrequencies to obtain one working channel.
In order to estimateof a diversity system itmake some assumptioncorrelation coefficient,conditions.
Until fairly recently it has been a commonpractice to assume essentially zero correlation forfrequency diversity with spacings of 5% or more,and a correlation of around 0.8 for the morecommon spacing interval of 2%. Barnett's data,supported by that reported by others, indicatesthat the correlation is far higher and the diversityimprovement far less than would correspond tothese values.
Because of growing congestion in the micro-wave bands, the use of vertical space diversity hasincreased tremendously in the past few years. Thischange has come about largely as a result of itsdemonstrated effectiveness in long haul industrialsystems in the United States. Space diversity isparticularly effective against ground or water-reflective fading, and can even be arranged inparticular instances to provide "anti-correlated "
fading, in which a fade on one diversity half isaccompanied by an actual signal rise on the otherdiversity half. Space diversity is also quite effectiveagainst atmospheric multipath fading.
On the other hand, Vigants' data on spacediversity improvement indicates that the commonlyassumed 100 to 1 improvement, with a 40 dB fademargin and spacings of about 30 to 40 feet, is avalid and somewhat conservative assumption.
With 40 dB fade margins, the 100 to 1improvement indicated by this assumption is suffi-cient to provide estimated path reliabilities of99.9999%, even if there were continuous Rayleighfading on every path.
The amount of improvement against interfer-ence fading (an all-inclusive name for multipath orselective fading) which will be provided by diver-sity, depends on the distribution of the fading oneach diversity half, and on the degree of correlationbetween the two distributions. If each diversity halfhas Rayleigh-distributed fading, the correlationcoefficient between the two halves can be any valuefrom 0 to 1. A correlation coefficient of 0 wouldmean completely independent fading on the twohalves, and a correlation coefficient of 1.0 wouldmean that the two halves faded identically. Acoefficient of 0.0 corresponds to uncorrelated orindependent fading. It is often referred to as a"Rayleigh-squared " distribution, since, in this case,
the probability that both halves will simultaneouslyfade below a given level, is equal to the square ofthe probability that either half alone will fadebelow that level.
It should be noted that considerably lowerspace diversity correlation coefficients, with con-sequently much larger diversity improvements, havebeen reported in the literature. For example, aJapanese report to CCIR gave a semi-empiricalequation for space diversity correlation coefficientwhich produces coefficients on the order of 0.6 to0.7 for the spacings suggested in this document,and even lower coefficients for greater spacings.. Atthe 40 dB fade margin level, such correlationswould indicate diversity improvements in excess of
,1000 to 1; an order of magnitude greater th~ our
conservatively assumed value of 100 to 1.
In frequency diversity operation, band alloca-tions and frequency patterns are relatively rigid andthere is little freedom to choose or vary the amountof spacings. Typical diversity spacings in mostmicrowave bands are on the order of 2%, and evenless in some cases.
The diversity improvement at the higher fademargins is startlingly large for uncorrelated fading,and remains surprisingly good even when the degree
57
or calculate the leliabilityis necessary to know orabout the value of thefor the particular path
2.2 x 103 DFGHz x ht
t:.h2 = (10A)
path. Except in the case of symmetricalantenna heights, the spacings will be dif-ferent at the two ends of the path. Step F ,therefore, consists of repeating Steps Athrough D for the other direction oftransmission.
where ~h2=
Cautionary Note.
ht
diversity spacing at the h2end, in feet.height of the transmittingantenna, in feet, at the h}end, above a plane tan-gent to the earth at thepoint of reflection. (For"flat earth ", K = 00, this is
simply the elevationabove the reflection pointandht=h}.)frequency in GHzpath length in miles
=
Depending on the path configuration, theabove calculations can, at times, producespacings which are either very large or verysmall. In such cases the method maybecome impractical, and one would simplyrevert to choosing spacings adequate to
provide protection against atmosphericmultipath. Such arbitrary spacings willalmost always also provide a large measure
of protection against ground reflectedmultipath, or a combination of the two
types.
FGHz=D =
Step D: In most cases, the final spacing will be thatcalculated in Step C, but to ensure that itdoes not result in spacings which wouldgive more than a one-half wavelength pathdifference at K = 4/3, the following calcu-lation is also made using the same symbolsas in (10A)
11. Methods of Calculating theProbability of Outages dueto Propagation (See Page 119)
These methods are based on the previouslymentioned work of Barnett and Vigants. In thissection we will, for mathematical convenience, usefractional probability (per unit) rather than per-centage probability, and will deal with the "unavail-ability" or outage parameter, designated by thesymbol O. The "availability" parameter, for whichwe use the symbol A, is given by (1-0). "Reliabil-ity", in percent, as commonly used in microwavecircles, is given by 100A, or 100 (1-0).
(lOB)~h2 = 1.3 x 103 D
FGHz x ht
Note, however, that ht in this formula willnot be equal to hl, because of the earthcurvature.In order to determine this ht, it will benecessary to locate the reflection point forK = 4/3, by the methods described in an
earlier section. ht will then be equal to himinus the earth curvature corresponding tothe distance between the reflection pointand the hi end.
~°.E-Qi~~i~ !!:~~~ O~~!!!!
Let Undp be the non-diversity annual outageprobability for a given path.
d~
2
We start with a term r, defined by Barnett asfollows: .That is, htl = hi
where dl is the distance, in miles, from thehl end. (llA)
-actual fade probabilityr -Rayleigh fade probability (= lO-F/lOj
Step E The desired vertical spacing at the h2 endwill be the smaller of the two calculatedvalues of !::.h2 .
For the worst month
Step F: The above steps cover one direction oftransmission and give a calculated spacingbetween receive antennas at one end of the
rill = a x 10-5 x (£/4) x n3IlB)
59
Df
~r~~~~ I2!~r~tx. !!!1.p..r~~m~~Factor
~
aBaI;nett has defined two "frequency diversity
improvement factors", one for the 4 GHz commoncarrier band and another for the 6 GHz commoncarrier band. Those are experimental formulasderived by curve fitting of actual measured data inthe deep fade regions.F
path length in milesfrequency in GHz4: for very smooth terrain, includ-ing overwater,1: for average terrain, with someroughness,1/4: for mountainous, very rough, orvery dry .fade margin, to the "minimum ac-ceptable" point, in dB.
=
The formulas are :OV8r a year
"-¥l(14A)Ifd( 4) = 1/2 x
ryr = b x rm llC)
Ifd(6) = 1/4 x [ ¥ x lOF/lO (14B)b
is the frequency and ~f thediversity spacing, andis the fade margin in dB.
where f
1/2: Gulf coast or similar hot,humid areas,1/4: normal interior temperate ornorthern,1/8: mountainous or very dry
FBy combining the three equations and noting thatUndp is equal to the "actual fade probability" for agiven fade margin F, we can write
Unfortunately Barnett's data, though exten-sive, covers only these two bands, and there isnothing to indicate how to extend it to otherbands. Furthermore, his data at present covers onlypaths of average length (25 to 30 miles or so) anddo not indicate whether there is any distancedependency.(12)or
Undp=axbx 2.5 xlO-6xf The two formulas do indicate that a givenfrequency spacing in percent gives twice as muchimprovement at 4 GHz as at 6 GHz. This is astartling and unexpected phenomenon, and if thesame dependence continues on to the higher bandswould indicate progressively poorer diversity per-formance with increasing frequency.
x D3 X lO-F/lO
The product of the terrain and climate factors,a x b, in this equation, ranges from a maximum of4 x 1/2 = 2, for very smooth paths and hot, humidclimate, to a minimum of 1/4 x 1/8 = .031, formountainous or very rough, dry paths. This is arange of 64 to 1 in outages, between the worst andthe best situations. "Normal" or average paths,with some rouglmess would have a x b = .25,
halfway between the two extremes.
The method we will use here for calculatingthe outages for a system with diversity will be tocalculate separately the non-diversity outage for thepath, and a "diversity improvement factor", forwhich we will use the symbol I. The diversityoutage or fade probability will be given by:
Cross Band Diversity[nir~v!:m~~ !:a~~
Since Barnett's work doesn't cover this situa-tion, judgment must again be used. Experienceindicates that for 6/11 or 6.7/12.4 GHz cross-bandsituations, the diversity improvement is at least as.!!.!!!!P-= I (13)'div
60
good as that achieved by 4% in-band spacing at 6GHz. This corresponds to an improvement of 100to 1, assuming fade margins of 40 dB. Hence, with40 dB fade margins we can simply assume :
Correlation Coefficients
Although our calculations do not require thecorrelation coefficients, they are of some theoreti-cal interest. The correlation coefficient is related tothe improvement factors as follows:(15)Icbd = 100
(18)~~~ ~v~r~t~ ~E!~~~! ~<2!°!.-k2 = 1
IlOF/lO
Vigants has defined a "space diversity im-provement factor" which is a function of the pathlength, the frequency, the vertical spacing, and thefade margin. (He called it a 'fade reduction factor',but we will use the term 'improvement factor' to beconsistent with the similar term in Barnett's workon frequency diversity).
k2
I
where
F
is the correlation coefficientthe diversity improvement factor,andthe fade margin.
Note; All of the above formulas are valid only inthe situations where the calculated value of Iis at least 10. If the calculations indicate thatI is less than 10, the diversity improvementwill be somewhat better than shown by thecalculations. A further point; the formulasapply only to the deep fading regions, that is,fades of 20 dB or more. They cannot be usedto calculate the incidence of low level fading.
In a modified form,factor can be written as:
Vigants' improvement
7.0 x 10-5 X f x 82 X 10F/10
(16)Isd =
D
where f = frequency in GHzs vertical antenna spacing, in
feet, between centersD = path length in miles
F fade margin associated withthe second antenna. Thebarred F is introduced to coverthe situation where the fademargins are different on theupper and lower paths. In sucha case F will be taken as thelarger of the two fade marginsand will be used in ~culatingUnd for the path. F will betaken as the smaller and will beused in the ,calculation of Isd.
!!y.Erld J}~e~~ l~~~IE.e!!:.t ~~~r-
Example: To illustrate the method, consider a 30mile path with average terrain, with some rough-ness, in an inland temperate climate, operating at afrequency of 6.7 GHz with a fade margin of 40 dB.we will make calculations for this path withoutdiversity, with 2% frequency diversity, and with 40foot vertical space diversity.
Non-Diversity Case
Using (12), with the proper values for thevarious factors, we have
Undp = 1 x 1/4 x 1.25 x 10-6 x (6.7)1.5
X 303 x 10~4 = .0000148
Experience indicates that the improvement inhybrid diversity systems is mainly due to the spacediversity effect. Consequently, we assume that:
This would correspond to an A of .9999852, or a"reliability" of 99.99852%.
Frequency Diversity Case
(17)Ihybrid = IsdUsing (14C), we have
Ifd(7-8) =,1/8 x (.02) x 104 = 25and the improvement factor is calculated as if thepath were straight space diversity.
61
so that, substituting in (13), GHz, 15.4 for 6.2 GHz, 17.4 for 6.7 GHz, and 37.5for 11.2 GHz, and so on. The factor 10F/10 isequal to approximately .63 x 104 for a 38 dB fademargin, ,8 x 104 for a 39 dB fade margin, 1 x 104
for a 40dB fade margin, and so on. The factor 'is
simply the frequency diversity spacing, in per cent,divided by 100. By making up a few tables coveringthe pertinent range of parameters, the calculationscan be done ea:sily and quickly, using slide rule orlogarithms. Extreme precision in the calculations isnot warranted. Path lengths can be rounded to thenearest mile, and fade margins to nearest dB.
.0000148 = .00000059Ufdp = 25
Thus, the calculated "frequency diversity improve-ment" is 25 to 1, and the calculated reliability forfreq~ency diversity is 99.999941%. (If we had used(14B) instead of (14C), the calculated improvementfactor would have been 50, twice as great asshown).
Space Diversity CaseAs an aid in visualizing the relationships
between the various parameters and illustratingsome of the characteristics of the fading probabilitydistributions predicted by these theories and equa-tions, two charts are presented. In both cases afrequency of 6.7 GHz is assumed.
Using (16), we have
Isd = 7.0 x 10-5 X 6.7 x 1600 x 104 x fa
= 250Figure 21 shows the probability of outage vs.
fade margin for non-diversity paths of variouslengths, and for the same paths with 40' verticalspace diversity. The Rayleigh and the Rayleigh-square distributions are also given, for information.Also, Figure 21 is for an "average-average" path.That is, a x b = 1 x 1/4 = 0.25.
and substituting in (13), we have
.0000148 =.000000059Usdp = 250
A point of considerable interest, and onewhich differs significantly from some previoustheories, is that the slope of the fading probabilitydistribution for non-diversity paths in the deepfading region is the same as the Rayleigh slope, thatis, 10 dB per decade of probability, and that theslope of the simultaneous fading probability distri-bution for diversity paths in that region is the sameas the Rayleigh-squared slope, that is, 5 dB perdecade of probability.
Thus, the calculated "space diversity improvement"is 250 to 1, and the calculated reliabilitY for spacediversity is 99.9999941%:
The superiority of space diversity for thissituation is clearly evident, but it is important tonote that despite the 10 to 1 difference, thereliability associated with the frequency diversity isstill extremely high, and would be quite adequatefor very high reliability systems.
Figure 22 shows, for the same path andfrequency, the probability of outage vs. path lengthfor non-diversity with a 40 dB fade margin, and forthe same paths with a 40 dB fade margin and 40'vertical space diversity.
On the other hand, if the path were located inthe "worst case" propagation area, all of thecalculated outages would be increased by a factorof 8, which would put the frequency diversityreliability at 99.9995~%, perhaps slightly marginalfor ultra-high reliability systems.
~~t~~ §y~~~
Equations 11 through 18 provide a completeanalytical fading model which can easily be set upfor routine machine computation. It is also rela-tively easy to do the computations by hand. Handcomputation can be facilitated by preparing tablesof several of the factors. For example, the factor(f)I.5 is 2.82 for 2 GHz, 8 for 4 GHz, 11.2 for 5
The previous analysis applies only to diversitysystems of the 1 for 1 type, with the diversityapplied on a hop by hop basis. A more complexsituation exists with respect to propagation outagesin multiline systems. These systems have two ormore working RF channels and one (sometimes
62
63
10-3
6.7 GHz Path
40 dB Fade Margin
(After Vigants and Barnett)
@
m n~
j10-4
w<.9~f-:)Ou.O
~ 10-..JaJ~aJO[I:0..
i;t;;!,-I~;..,..,
1:$~
-
10-6
~~ :;;
#m
60
W:1-m
70 75
10-5 10 20 30 40
PATH LENGTH MILES
50
Figure 22. Outage Probability vs Path Length for a 6.7 GHz Path with 40 dB Fade Margin
64
another way, the "diversity improvement factors"for inter-hop combinations at a 40 dB fade marginwould be in the range of 10,000 to 1, so thatoutages attributable to an inter-hop combinationwould be considerably less than 1% of the outagesattributable to an intra-hop combination.
two) protection RF channel operating in parallelover the path, each on its own frequency. Theprotection channels, besides giving protectionagainst equipment failure, provide a form of fre-quency diversity protection against propagationfailure.
Thus, though there is a slight increase inoutage probability for the tandem arrangement, itis far too small to be of any significance and fromthe propagation point of view either system can betreated, analytica!ly, as if the diversity were on aper hop basis. In either case the total calculatedoutages for an N-hop system will simply be N timesthe calculated ~ingle hop outages. (In the case of'very high reliability systems, the possibility ofdiversity outages occurring at the same instant ontwo different hops is extremely small and so can be
neglected.)
The amount of diversity protection dependsamong other things on the frequency spacingbetween the closest spaced channels, and in thecase of fully equipped systems in the 4 or 6 GHzcommon carrier bands, adjacent channels may bese,parated by as little as 0.5% in frequency. con-sidering two such closely spaced channels as a"frequency diversity pair", it is clear that theprobability of simultaneous fading to thresholdcould be relatively high, that is, the fading highlycorrelated between the two channels.
The analysis of the complete propagationeffects in multiline systems, particularly thoseutilizing 2 protection channels and arranged withswitching sections comprising several hops in tan-dem, is too complex to be treated in this book.Comprehensive treatments can be found in theliterature.
~ °l!.-~e~~~ !a!:!i~ -
The diversity improvement factors apply onlyto fading which is caused by some sort of multiplepath conditions, since this sort of fading exhibitsfrequency and space selectivity .The improvementdoes not apply to those types of fading which arenon-selective. On well-engineered paths (adequateclearance and fade margins) outages due to suchnon-selective fading are very unlikely to occur, butwhen and if they do occur they can have asignificant effect on the overall availability becausethey tend to last much longer than multipath deepfades and because they receive no diversity im-provement. N o attempt has been made to includethem in the analytical models, since no adequateprediction methods are available for them and sincethey do not apply to the great majority of paths.
There is one aspect of the multiline situationwhich we can usefully treat. That aspect is theeffect on the diversity action which results fromswitching or combining only at the end of anumber of hops in tandem, rather than on everyhop. The difference between the two lies in the factthat in the tandem situation, outages can be causedby simultaneous inter-hop as well as simultaneousintra-hop fades to thresholds. For example, asimultaneous fade to threshold on Channel 1 ofHop A and Channel 2 of Hop B could cause anoutage in this situation, but not if the diversitywere applied on a per hop basis. If the same degreeof correlation existed for the deep fading oninter-hop combinations as on the intra-hop combi-nations, the outage with diversity applied end toend on an N-hop system would be N times that ofthe same system with diversity applied over eachhop. But in actuality the fading distributions oninter-hop combinations, even for adjacent hops,must be essentially independent (zero correlation)because each path at a given instant has a uniqueset of multipath condItions which cannot possiblybe the same as those of the other path. We thushave the situation that the fading for intra-hopcombinations is highly correlated (k2 in the rangeof .99 and higher) while the inter-hop combinationshave zero or at least very low correlations. Stated
Other Treatments
Several pertinent articles on reliability anddiversity have been published in recent years in theIEEE Transactions on Communications Te~hno-logy. Among them: February, 1966 -Barnett onreliability; December, 1966 -Abraham on reliabil-ity; August, 1967 -Makino and Morita on, spacediversity; February, 1968 -White on spacefdiver-sity; December, 1968- Vigants on space diversity.
D, Noise Performance
The noise, performance of a communicationssystem is one of the most significant parameters,with strong effects on many phases of system
engineering.
65
1 Total Noise Its magnitude is a complex function of the relativemagnitude of the delayed signal, its absolute delaywith respect to the main signal, the amount ofloading present, the width of the baseband, and therelative position of the channel in the baseband. Itis more significant the higher the channel fre-quency, the greater the echo amplitude and thegreater the delay. In high density systems with longwaveguide runs (or long IF cable runs), it isnecessary to maintain close control of impedancematching throughout (low VSWR of antennas,equipment, waveguide runs and all junctions) inorder to keep distortion to acceptably low levels.
The total noise in any derived channel iscomposed of noise contributions of several typesincluding; thermal, intermodulation, echo pathdistortion, interference, and noise from the multi-plex equipment.
Thermal Noise
Thermal noise is caused by random currentvariations in every portion of the electronic equip-ment and is present whether or not a modulatingsignal is being applied. One portion of the thermalnoise, often called intrinsic or idle noise, is thatgenerated in the transmitter and in the late stagesof the receiver. It is independent of receiver inputlevel, and is the limiting noise performance levelwhich could be measured between terminals underconditions of no modulating signal and a verystrong RF input signal.
Path reflections can, in some unusual cases,also produce echo signals with sufficiently longdelay as to cause significant path distortion. Such acondition could occur on a path with a relativelystrong reflection and an abnormally large amountof clearance, or as a result of a double bounce offone building to another building and thence to thedistant antenna. With good equipment design andproper system layout, path distortion noise can bekept to the very low levels needed to meet overallnoise objectives.
The more important portion of the thermalnoise includes noise generated by the antennaresistance, plus the noise generated in the front endcircuits of the receiver. This noise undergoesamplification within the receiver, along with theRF carrier, and as a result of the FM process thenoise at the output of the receiver will varyinversely with the RF carrier input level. For RFsignals above the FM improvement threshold (to bediscussed later), the thermal noise at the output ofthe receiver will decrease 1 dB for each 1 dBincrease in RF signal input, up to the point atwhich the intrinsic noise, unrelated to the RFcarrier, becomes controlling.
~t!E~~~i~ ~d-M~~~~ ~<2!S!
The contribution to system noise from atmos-pheric and most forms of man-made noise is verysmall at microwave frequencies and can be neglec-ted. However, interfering signals from other micro-wave systems, or from the spurious radiations ofhigh powered radars, can produce noise in amicrowave system. This form of noise must be keptto insignificant levels by proper equipment, systemsdesign and by appropriate coordination of fre-quency usage in any geographical area, as discussedin more detail elsewhere.Intermodulation Noise
Ml!!. t!pl~x -..'?!~~~ ~~e-Intermodulation noise is created whenever thecomplex modulating signal passes through any kindof non-linearity of phase or amplitude in thetransmission facility. It is present only when thesystem is being mod~lated, and increases with thelevel of the modulating signal. Such factors as thetotal number of active message channels, the levelof signaling and data tones, and the individualspeech levels, determine the level of the basebandsignal, or the baseband load on the system.
The multiplex system is also a source of noise,but its noise contribution is not affected by fading,so for any given configuration it is relatively fixed.The amount of noise contributed by the multiplexsystem under loaded conditions, is a characteristicof the equipment, and can be determined eitherfrom the manufacturer's specifications, or fromactual measurements on terminals connected back-to-back.
Echo Distortion Noise2.Noise Units
Echo distortion noise is a form of intermodu-lation noise which is created when delayed echosignals are present in the FM portion of the system.
The most commonly specified noise parameteris that of noise power in a voice channel. It is
66
defined and specified in a number of ways. Noisepower units in common use include: dBrncO = 10 log10 pWpO + 0.8 = dBaO +6.8
(19)= dBmOp +.90.8 = 88.3 SINdBrnc ( dB above reference noise, C-message
weighting. Reference noise is equivalent to a1,000 hertz tone at -90 dBm.)
The conditions for precision are a frequencyband of 300-3400 Hz, a square channel response,an ideal noise meter, and that the noise beessentially "white noise".
( dB above reference noise-adjusted, F1Aweighting. Reference noise adjusted isequivalent to a 1,000 hertz tone at -85dBm.) Note: The parameter "noise power ratio "
(NPR) has had wide usage as another wayof describing noise performance. But itcannot be considered as a "noise unit" inthe same sense as the other parameterslisted here, because its relationship tonoise in the derived channel is notconstant but depends on the relationshipbetween the noise loading ratio and thebandwidth ratio being used. For thisreason the use of NPR as a means ofspecifying noise performance is not rec-ommended since it often leads to con-fusion.
(picowatts of noise power, psophometri-cally weighted. 1.0 pWp is equivalent to a800 hertz tone at -90 dBm.)
dBmp (psophometrically weighted noise power indB, with respect to a power level equivalentto a 800 hertz tone at 0 dBm.)
(signal-to-noise ratio in dB, either unweight-ed or with a specified weighting.)
The first four units as defined above representabsolute values of noise. In order to make themmeaningful with respect to an actual circuit, it isnecessary to take into account the relative level atthe point of measurement. For measurements madeat a point of 0 relative level, the absolute andrelative values will be the same. Consequently, it iscustomary to express objectives and measurementsin equivalent noise power at a point of zero relativelevel (0 dBmO point), and to identify such objec-tives or measurements as dBrncO, dBaO, pWpO ordBmOp, respectively.
D~~e!~ination of System Noise3.
The receiver "front end " noise is of particular
significance in microwave system engineering be-cause of its effect on thresholds and fading margin,in addition to its effect on overall noise. Fortunate-ly, this type of noise and its effects in a derivedchannel are readily calculable from a knowledge ofcertain system parameters, including receiver noisefigure (F) in dB, receiver IF bandwidth in mega-hertz at the 3 dB points (BMHz), the per-channeldeviation (~f), the center frequency of the derivedchannel at the top of the baseband (fch), the effectof emphasis (if used), and the desired voice channelweighting characteristic.
The dBrnc is the present noise unit used in thetelephone industry in the United States. The dBa isno longer in general use in the telephone industry ,but is still common among industrial users. ThepWp and dBmp are international units based onCCIR recommendations. Table E shows the approx-imate relationships between these various noiseunits. Because of differences in weighting curves,the correlations are in some cases valid only for"white noise". The correlations shown, which arerounded off to integral values, are the ones inwidest use, though slightly differing correlations arealso found in the literature.
Note: The receiver noise figure F and thevarious equations for noise developed inthis and later sections are all based on theassumption that the noise temperature ofthe area in the field of view of theantenna is approximately 290Q Kelvin.This is a sufficiently accurate approx-imation for any microwave path betweentwo terrestrial points. But a differentapproach (using noise temperatures in-stead of noise figure) is needed forsituations where the antenna "sees" aregion of space with a much lower noise
In most practical cases the variations due tothe round-offs are unimportant, but where frac-tional dB 's are significan t ( in meeting guaranteedperformance requirements, for example), thefollowing correlations are more precise :
67
available fade margin in such a receiver is, there-fore, the difference in dB between the normalunfaded signal and the FM improvement threshold.The FM improvement threshold (TFM) can becalculated as:
temperature, such as an earth stationantenna looking up at a high angletoward a satellite. For such situations theformulas in this book will give correctresults if the noise figure Fas used here is
replaced byan "operationa{noise figure".ra + re
defmed as Fop = 10 log10 (~),
where T a is the noise temperature, indegrees Kelvin, associated with the an-tenna and T e the noise temperature ofthe equipment. For the case where Ta =290° Kelvin, Fop is identical to F.
TFM= 104 + 10 log10 BMHz + F(21)
This is the point at which the RF carrier-to-noiseratio (GIN) is equal to 10 dB. It is notable that theFM threshold is independent of baseband fre-quency, deviation, emphasis, etc., but the noise atthe FM threshold in a derived channel, which is afunction of these parameters, is indeterminate untilthese parameters are known or specified.
Receiver Thermal Noise
The starting point for receiver thermal noisecalculations is the thermal noise generated in theantenna resistance. For terrestrial microwave sys-tems with an assumed effective antenna noisetemperature of 290Q Kelvin, the antenna noisetransferred to the receiver has been calculated to be-174 dBm per cycle of bandwidth, or -114 dBmper megacycle of bandwidth. In a perfect receiverthis would be the only source of "front end" noise,but any actual receiver will itself contribute addi-tional noise, which will raise the equivalent noiseinput by the dB value of the receiver noise figure.Total equivalent noise input (N) in dBm can thenbe calculated as :
The choices for these other parameters, asnow reasonably well standardized by internationalusage, are such as to make the noise in a derivedchannel, at the FM threshold, fall approximately at,or slightly higher than, the level considered to bethe maximum tolerable noise for a telephonechannel in the public network. By present stan-dards, this maximum is considered to be 55 dBrncO(49 dBaO). In industrial systems, a value of 58dBrncO (52 dBaO) is commonly used as themaximum acceptable noise level.
The noise in a derived voice channel resultingfrom the receiver equivalent input noise can becalculated, for RF inputs above the FM threshold,as:
N= -114 + 10 log10 BMHz + F (20)
This is one kind of threshold, and is oftencalled "detection threshold", "absolute noise thres-hold" and similar expressions. It should be clearlyunderstood that, in an FM microwave system, thisthreshold does not represent a usable signal level.The true working threshold, often called the FMimprovement threshold or the FM breaking point,occurs when the power of the signal is approxi-mately 10 dB higher than the power of the noise.At this point the peaks of the signal begin .toexceed the peaks of the noise and FM quietingbegins. For input signals higher than this level, thethermal noise in a derived channel will decrease 1dB for each 1 dB increase in RF input level.
dBmcO = -c 48.1 + F 20 log10 /:),f/fch (22A)
dBaO =-c 54.1 + F 20 log10 llf/fch (22B)
S/NdB = C + 136.,
flat
F + 20 log10 t:.f/fch (22C)
pWpO(22D)
where cF
~
If the input signal drops below the FMthreshold, the noise in the derived channel risesquickly to an intolerable level. Consequently mostmicrowave receivers are arranged to mute when theinput level drops below this point. The maximum
6f
RF input power in dBm.receiver noise figure in dB,referred to the point at whichinput power is established.peak deviation of the channelfor a signal of test tone level.center frequency occupied bythe channel in the baseband.
=
fch =
68
69
In FM systems without emphasis, L;:.f has aconstant value, regardless of the baseband fre-quency occupied by the channel. In this case, theequations show that the noise will be higher in thehigher frequency channels, the increase being at 6dB per octave. Thus the thermal noise is worst inthe top channel, and that channel is typically usedfor system noise calculations-\
Sptp/Nrms = C -F + 118
(unweighted, unemphasized)
(22E)
Sptp/Nrms = C -.-F + 126.5
(EIA emphasis,EIA color weighting)
(22F)
In order to provide a more even distributionof noise across the baseband, emphasis networksj1!e often used to increase the deviation at thehigher frequencies and decrease it at the lowerfrequencies.
The latter formula is applicable to mosttelevision transmission in N orth America.
CCIR at this time (1970) has not yet standard-ized either emphasis or weighting for color TV. Formonochrome television, CCIR RecommendationNo.421-1 describes several different systems.Monochrome weighting network characteristics areincluded, and monochrome emphasis networkcharacteristics are given in Recommendation No.405. The following equation can be used tocalculate the video SIN ratio for the various CCIRmonochrome systems. The first constant term ineach equation represents the unemphasized, un-weighted SIN value, and the second constant termis the combined effect of weighting and emphasis.The equations also take account of the fact thatCCIR defines the "signal " to exclude the synchron-
izing pulses, unlike North American practices.
Most present day microwave systems aredesigned around the parameters recommended byCCIR for certain standard configurations. Forexample, per channel deviations of 200 kHz rms(282.8 kHz p~ak) are used for systems of 300,600or 960 voice channels, and per channel deviationsof 140 kHz rms (200 kHz peak) for systems of1200 and 1800 voice channel capacities. WhenCCIR emphasis is used, this deviation applies onlyto the channel at the crossover point of theemphasis curve; at 0.608 fmax, where fmax is thetop baseband frequency. Channels near the bottomof the baseband will have deviations approximately4 dB lower, and the channel at the very top of thebaseband, a deviation 4 dB higher than the refer-ence deviation.
Sp-p/Nrms = C F+A (220)
(CCIR monochrome emphasis and weighting)Even with emphasis, the thermal noise is
greatest in the top channel, consequently, it iscustomary to make calculations for that channelonly. Table F lists values for the 20 log10 ~f/fchfactors for the top measuring slot ( also standard-ized by CCIR) for the various channel configura-tions, both with and without emphasis.
nl19.5 + 13.7 (405lines, 3 MHz)115.7 + 17.3 (525lines, 4 MHz -
A = 112.8 + 16.2 (625 lines, 5 MHz)l l10.5 + 18.1 (625 lines, 6 MHz)
112.8 + 13.5 (819 lines, 5 MHz)
103.8 + 16.1 (819 lines, 10 MHz)
Japan)
The thermal noise parameter used in videoapplications is a broadband "signal-to-noise ratio"(SIN), which is defined as the ratio of the peak-to-peak signal to the rms thermal noise in the videobaseband. The ~IN ratio is dependent on thereceiver input level, the noise figure, the videobandwidth, the peak deviation, the de-emphasischaracteristics if used, and the weighting function.
Practical Threshold---
The "practical threshold ", or minimum ac-ceptable RF input level point, cannot be lower thanthe FM improvement threshold, but may be higherif it is established as an arbitrary value of noise inthe top channel. As an example, consider a 960channel system with CCIR deviation and emphasis,with a receiver noise figure of 10 dB and an IFbandwidth of 32 MHz. We can calculate the FMthreshold as TFM = -104 + 101og 32 + 10 = -78.9dBm. We can then use this level as the value of C in(22A) to calculate the derived channel noise level atthe FM threshold, for example :
The following formulas can be used to calcu-late the video SIN ratio in dB. They assume a peakdeviation of 4 MHz ( this is generally standardeverywhere) and a video bandwidth of 4.3 MHz.They would not be correct for other bandwidthsand deviations.
'71\
f Table F. Standard CCIR 20 loglO f::,.f/fch Factors For Top Slot
(-19.1' Lines corresponding to the limiting valuesestablished by the two types of threshold areshown on the figure. The FM threshold linescorrespond to four commonly used IF bandwidths.The 12 MHz IF is typical for systems limited to300 channels, the 22 MHz IF is typical for systemswith 300 to 600 channels and a 32 MHz IF istypical for systems with 600 channels or color TV.For systems of 960 channels through 1800 chan-nels, 40 MHz IF bandwidths are commonly used.
dBrncO = -(-78.9)= 59.9
48.1 + 10
If we are using a value of 55 dBrncO as themaximum allowable limit, it is evident that the"practical threshold" will be at an RF input whichis 4.9 dB above the FM threshold, or -74 dBm. Thisillustrates the point that the threshold may becontrolled either by the FM threshold or by thechannel noise, whichever requires the higher signal.
In order to meet overall noise objectives, mostmicrowave paths are engineered with normal signallevels chosen to limit receiver thermal noise toabout 14 to 16 dBrncO. Figure 23A shows that,with a 10 dB noise figure, this will dictate receiverinput levels of about -40 dBm for the 300 channelsystem, about -37 dBm for the 600 channel sys-tem, about -33 dBm for the 960 channel system,and about -28 dBm for the 1200 channel system.When very stringent noise objectives are required,receiver inputs up to 5 dB higher than the abovemay be essential.
!.a~e-M!!!~~
Fade margin is the dB difference between the"practical threshold " level and the normal signal
level. Most line-of-sight microwave systems areengineered with fade margins in the range of 35 to40 dB or more. The high normal signal levels areonly partly to provide protection against fading.Even if there were no fading, they would still beneeded, in most cases, to meet basic system noise
objectives.
~!-te!!:l-.!-~a~~ ~n~ i!s ~f!e~ ~n ~~i~Figure 23A shows characteristic curves of perchannel thermal noise for typical receiver configu-rations, as a function of RF input level. The curvesare calculated for a receiver with a noise figure of10 dB. They can be used for other values byshifting the input scale 1 dB upward for each dBincrease in noise figure above 10 dB, or 1 dBdownward for each dB of decrease in noise figure.
At the low end of the RF input range, thethermal noise is, the only significant noise source,but at the high end of the range, intermodulationnoise and intrinsic noise are significant contribu-tors, and provide a lower limit to the total noisecurve.
71
72
mance can be improved by increasing the perchannel deviation, but at the expense of worsenedintermodulation noise because increasing thedeviation increases the loading. The CCIR recom-mended parameters are well suited to systemscarrying principally public telephone traffic, butmay not be optimum for systems with highpercentages of the channels devoted to data.
The amount of intermodulation and intrinsicnoise is a characteristic of the equipment and canbe determined either from the manufacturer spec-ifications, or from actual measurements on systems;unlike receiver thermal noise, it is not readilycalculable from known system parameters. Theintermodulation noise is, however, a function ofthe system loading as well as equipment para-meters.
A slightly different loading formula is inwidespread use in the U.S.A. telephone industry.This loading, which was established by the BellSystem as a result of the latest available measure-ment data, is given -for multi-channel systems ofrelatively high capacity -by:
It is now standard practice to specify theloading capacity of a microwave system, and itsperformance, in terms of "white noise" loadingapplied to the used portion of the baseband at alevel chosen to make its peak values equivalent tothose of a multichannel telephone load.
p = (-16 + 10 log10N) dBmO (23C)~oic~~~~g-
Microwave systems are commonly designedand rated for the equivalent loads as established byCCIR and given by the following equations:
It represents 1 dB lighter loading than thecorresponding CCIR formula, and reflects a reduc-tion in talker volumes from previous values.
p = (-15 + 10 log10N) dBmO( when N = 240 or more )
(23A)
~Milil~ ~ ~~~g-
Standards currently in use or proposed by theDefense Communications Agency (DCA) for U.S.military systems specify an equivalent loading 5 dBhigher than CCIR, in order to allow essentiallyunrestricted use of data at relatively high levels.The corresponding formula is given by:
(-=1 + 4 log10N) dBmO(when N = 12 to 240)
(23B)p
pN
where equivalent noise loading powernumber of SSBSC channels
~
p = (-10 + 10 log10N) dBmO (23D)The expressions within the parentheses give theratio, in dB, of the equivalent noise load power totest tone power, and are often called "NoiseLoading Ratio" or NLR.
This means an equivalent loading power ap-proximately 3.2 times as great as that for CCIRloading. Thus, a 300 channel system with this typeof loading must be engineered essentially as if itwere a 960 channel system with CCIR loading.
The second equation reflects the fact thatthepeak-to-rms factor for the smaller number ofchannels is higher than that of white noise, so thata higher value of rms white noise power must beprovided, in this case, to obtain the same peakvalue as that of the voice channels. Beyond the 240channel point, the white noise and voice areconsidered to have the same peak factor, so thatthe rms values of the voice load and the equivalentwhite noise load are equal.
~°.!!lP-°~~ ~~~IL
Equations (23A) and (23B) given abovf, arebased on systems which are primarily used foivoicetransmission, though they include an allowance forsignaling tones and for a small percentage of theSSBSC channels to be used for telegraph or data
multiplex.The choices of per channel deviation, IFbandwidth, etc., are made to provide reasonablygood balance between thermal and intermodulationnoise at normal signal levels. Thermal noise perfor-
When relatively large numbers of the channelsare used for such data services, the calculation of
73
specified by the manufacturer, at the normal designloading of the system and for specified conditions.On a measurement basis, it can be determined bynoise loading measurements on terminals connectedback-to-back, with the RF received signal setsufficiently high so as to reduce front-end thermalnoise to insignificance. The resulting reading willthen give the equipment intermodulation plusintrinsic noise. If desired, the latter can be deter-mined by repeating the measurement with loadingremoved.
Echo distortion noise, as described earlier, is aform of intermodulation noise which is producedby delayed echo signals, created usually by acombination or combinations of impedance mis-matches in waveguides, antennas, and the equip-ment itself. It can also occur at IF, from cable andequipment mismatches and, more rarely, as a resultof long-delayed echoes in the path itself.
equivalent loading becomes more complex. Usualpractice is to calculate separately the equivalentwhite noise loading for the numbe~ of channelsused for voice, and the equivalent rms power indBmO of all the tones used for transmitting dataover the system, then to sum the two rms powerson a power additive basis to obtain an equivalenttotal white noise loading power and noise loadingratiio. This is justifiable because the peak to rmsIfactor for a composite signal consisting of a numberof tones, is closely equivalent to that of white noisewqen the number exceeds about 16 tones.
As an example, consider a 600 channel systemwith 500 channels devoted to voice, 40 channelscarrying data at a level of -12 dBmO per channel,and 60 channels, each carrying 20 submultiplexedtelegraph carriers at -21 dBmO per carrier. Theequivalent load of the voice is, from equation(23A), -15 + 10 log 500 = +12.0 dBmO; theequivalent load of the data is -12 + 10 log 40= + 4.0 dBmO, and the equivalent load of the tele-
graph carriers is -21 + 10 log 20 + 10 log 60= +9.8 dBmO.
The effects of echo distortion are a verycomplicated function of a number of things such asthe number of mismatches, the magnitudes of themismatches, the distance between them, the veloc-ity of propagation in the guide, the number ofchannels, the per channel deviation, the totalloading, the presence or absence of emphasis, etc.Because of the complexity, exact calculations arevery difficul t.
~u~~i~g!!:~ P~~e~
The curves of Figure 24 can be used tocalculate an approximate value of echo distortionnoise, for certain standard channel arrangements.To use the curves, it is necessary to know theequipment return loss, and to know ( or to assume )a composite value for the combined return losses ofantenna-plus-waveguide at the frequencies of in-terest. The latter are assumed to be lumped at theantenna location. As an example of the use of thechart in Figure 24, make the following assump-tions:
Table G provides a simple means of summing( or subtracting) non-coherent powers expressed indB form. Using this table, we can calculate that thesummation of the three loads of +12.0, +4.0 and+9.8 dBmO, determined in the preceding paragraph,is approximately +14.5 dBmO.
Since the equivalent noise loading for a 600channel system is only +12.8 dBmO, it is evidentthat the +14.5 dBmO load would be some 1.7 dBhigher than that of an equivalen~ 600 channel voicesystem. It would then be necessary to determinewhether the system could actually carry the extraload with an acceptable level of performance, andwithout exceeding bandwidth restrictions. If not,the load could be reduced by any of severalexpedients. One would be to lower the levels of thedata and the telegraph channels until the total rmspower of data tones occupying a SSBSC channeldoes not exceed -15 dBmO. Another would be toeliminate some of the voice channels. A thirdwould be to reduce the per-channel deviation,seeking a more optimum balance between thermaland intermodulation noise for the new conditions.It is beyond the scope of this work to discuss allthe ramifications associated with this problem.
Intermodulation N oise
A 960 channel system, in the 6 GHzband, with 100' of waveguide. Equip-ment return loss of 28 dB. Antenna-plus-waveguide return loss of 26 dB (equiva-lent to a VSWR of 1.1).
From the chart, the dBrncO constant for
960 channels at 100' is 70.5, and the loss
of 100' of waveguide at 6 GHz is
approximately 2 dB. Hence, the noise inthe top channel in dBrncO is equal to;
Equipment intermodulation noise is not adirectly calculable quantity .Its value is usually 70.5 28 26 4 = 12.5 dBrncO
74
Table G. Summation Or Subtraction Of Non-Coherent Powers.
This table can be used for summing the powersof two non-coherent signals expressed in dBform. It can also be used for power subtraction,
Col. 1 cor.2 Col.3
Pa -Pb Ps- Pa Ps- Pb
3.0103.1113.2153.3213.4293.5393.6513.7663.8844.0034.1244.2484.3744.5024.6324.7644.8985.0355.1735.3135.4555.5995.7455.8936.0426.1936.3466.5006.6566.8146.9737.377
7.7908.2108.6399.0749.515
9.96110.41411.33112.26613.21614.17015.13516.10817.08618.06819.05420.04325.01630.004
00
Pa and Pb represent two powers whosesummation is Ps: in all cases Pa is taken asthe larger of the two powers.
0.00.20.40.60.81.01.21.41.61.82.02.22.42.62.83.03.23.43.63.84.04.24.44.64.85.05.25.45.65.86.06.57.07.58.08.59.09.5
10.011.012.013.014.015.016.017.018.019.020.025.030.000
3.0102.9112.8152.7212.6292.5392.4512.3662.2842.2032.1242.0481.9741.9021.8321.7641.6981.6351.5731.5131.4551.3991.3451.2931.2421.1931.1461.1001.0561.0140.9730.8770.7900.7100.6390.5740.5150.4610.4140.3310.2660.2160.1700.1350.1080.0860.0680.054D.0430.0160.0040.000
To sum two powers, calculate Pa -Pb, locatethe resulting value in Column 1. then add thecorresponding value in Column 2 to Pato obtain Ps. the desired sum.
T o subtract one power from another, treatthe larger one as Ps and the smaller oneas Pa (if it is within 3 dB of Ps} or Pb(if it is more than 3 dB below Ps}.
In the first case, calculate Ps -Pa. locatethe resulting value in Column 2, thensubtract the corresponding value inColumn 3 from Ps to obtain Pb, thedesired remainder.
In the second case, calculate Ps -Pb, locatethe resulting value in Column 3, then subtractthe corresponding value in Column 2 fromPs to obtain Pa, the desired remainder.
When more than two powers are to be summedor subtracted, iteration can be used.
Example: Summation
To add + 10.0 dBmO to +8.7 dBmO
10.0-8.7=1.31.3 in Column 1 falls between 1.2 and1.4so the value from Column 2 is(2.45 + 2.37)/2 = 2.41.
So Ps = + 10.0 + 2.41 = + 12.41 dBmO
Example: Subtraction
To subtract -15.0 dBm from -10.0 dBmO-10.0- (-15.0) = 5, treating -10.0 as
Ps and -15.0 as Pb we locate 5 inColumn 3 as very near to 5.035, so wesubtract the corresponding value inColumn 2, 1.635, from -10.0 to obtain Pa,So Pa = -10.0- 1.635 = -11.6 (rounded),
75
'6c:...
00"0
wC/)
oz-Jwzz«I(..)a:wQ.
50
40
~80m10
-80 -70 -60 -50
RECIEVER INPUT IN dBm
-40 -30 -20
Figure 23B. Typical Receiver Noise Cprve. Top Slot Of 960 Channel System; 10 dB Noise Figure;200kHz Deviation; CCIR Emphasis, +14.8 dBmO Load.
76
From Table E, in a previous section, thiscan be found to be equivalent to 18picowatts, psophometrically weighted, ifthat noise unit is to be used. If emphasisis used, the noise will be 3 dB lower, or9.0pWpO.
~~ ~e.- ~~ J;j ~s~
If the level of intermodulation noise plusintrinsic noise for the top channel of a given systemat the desired loading is known (it usually must beobtained from the manufacturer), this noise andthe receiver thermal noise can be plotted on a chartarid added on a power basis, to construct an overallcurve showing loaded noise as a function of RFsignal level for the particular equipment and condi-tions. Figure 23B is an example of such a curve. Itshould be borne in mind that such a curve will bevalid only for the particular parameters and condi-tions on which it is based. Note also that Figure23B does not include echo distortion noise, whichmust be treated separately for each case. See laterexamples.
.It will be seen from the chart, that the echodist~rtion noise constants increase rapidly withguide length until a plateau is reached, beyondwhich they change very little as the guide getslonger. Because of the effect of waveguide attenua-tion in reducing the noise, for any given configura-tion there will be a peak point in the noise curve, atabout the knee of the curve, for which the noisewill be a maximum. For longer or shorter lengths itwill be less.
Return loss in dB can be calculated as
VSWR +120 log10 VSWR -1
The curve of Figure 23B is for a "baseband "
or remodulating type of equipment, and includesthe noise contributions of the FM modulator,demodulator and associated baseband equipment.In heterodyne systems these elements are notincluded with the radio equipment, so their loadednoise contributions must be determined separately,and added in as another contributor to the systemnoise. The radio portion of a heterodyne equip-ment will have the same thermal noise as anequivalent remodulating equipment, but its inter-modulation and intrinsic noise will be lower be-cause of the absence of remodulating and basebandequipment.
or taken from the following:
VSWR R.L. VSWR R.L. VSWR R.L.
1.02
1.03
1.04
1.05
1.06
40.1
36.634.1
32.2
30.7
1.07
1.08
1.09
1.10
1.12
29.4
28.3
27.3
26.4
24.9
1.15
1.20
1.25
1.30
1.40
23.0
20.819.0
17.8
15.4
4. System Noise Objectives
Note: The significant parameter in micro-wave systems work is return loss ratherthan VSWR. The continued use of VSWRin describing the impedance characteris-tics of microwave antennas, waveguidesand components is a holdover from thedays when the only available measure-ment technique, the slotted line, gaveresults directly in VSWR. With modernsweep generators and reflectometer tech-niques the measurement gives return lossdirectly, and it is somewhat pointless tofirst convert it to VSWR and then recon-vert it to return loSS. It would be simplerif ratings were simply stated in terms ofreturn loss rather than VSWR, by themanufacturers of microwave equipmentand components. Some companies havealready taken steps in this direction.
Because of the wide variety of communica-tions systems, and the many ways in which achannel can be used, there is no way to establish asimple and universal noise objective which wouldbe optimum for all systems. A very strong trade-offrelationship exists among system capacity, systemcosts, and system noise performance. Each com-munications user must, in some manner, evaluateand establish his own requirements in the light ofthese relationships. Choosing noise objectiveshigher than really needed can often cause aninordinately large increase in system cost, whilesetting them too low can seriously limit theusefulness and expandability of the system.
Since the noise power in a multi-hop system isapproximately equal to the power summation ofthe noise powers of the individual hops, the noise
78
objectives must, of course, include a distancefactor. Consequently, most noise objectives areestablished as proportional to the length of thesystem. This is a reasonable assumption for longsystems, since hop lengths tend to average out, butis difficult to apply to short systems, and particu-larly to those with short average hop lengths.
The CCIR/CCITT objectives were originallydeveloped for circuits over coaxial cables. It is nowrecognized that they are not well suited to micro-wave systems because of the "in any hour"requirement which, if strictly interpreted, couldmean the "worst hour" of the "worst month " ofthe "worst year". This has two significant disadvan-tages. One is that there is no practical way todetermine in advance ( and hardly any practical wayafter the fact) just what the relationship is betweenmean noise in the worst hour and mean noise undernormal conditions for any microwave system. Theother is that, even if there were such a way, itwould in many cases be economically grotesque toperhaps double the cost of the system to avoidallowing a relatively modest increase in noise duringa very few hours of the year .
The following paragraphs list some noiseobjectives in current use at the time of preparationof this manual. It should be borne in mind thatthese values are design objectives and not "stan-dards" or specification requirements, though theyare often interpreted in that way.
QcIR1C29!TT International Circuits
CCIR and CCITT establish hypothetical refer-ence circuits 2500 kilometers long, and relate theirnoise objectives to these reference circuits, or tosystems closely similar to them.
The subject has been under discussion forsome time, but as yet no changes have been agreedon. Most CCIR-conforming countries have adoptedan infdrmal and pragmatic approach, which is toassume that the mean noise in the worst hour willbe that corresponding to the noise with all hops inthe system faded by approximately 5 dB belowtheir normal free space level. This, of course,requires that in some cases, the hops be engineeredfor roughly 5 dB stronger signals than wouldotherwise be needed, but at least it establishes adefinable and measurable condition.
The basic design objective for a voice channelof the hypothetical reference circuit is 10,000pWpO mean noise power in any hol,lr, of which2,500 pWpO is allocated to the multiplex equip-ment and 7,500 pWpO to the transmission line(microwave system in this case). For systemsbetween 280 and 2500 kilometers in length, thenoise contributed by the line is considered propor-tional to length, i.e. 3 pWpO per kilometer.
The CCIR noise objectives assume that thesystem is loaded, either with traffic or with whitenoise, at the levels indicated by the appropriateCCIR loading formulas. In addition to the "meannoise in any hour" criterion, CCIR requires that thesame numerical value of noise, measured on a"one-minute-mean " basis, not be exceeded for
more than 20% of any month. This, too, isconventionally handled by a simulated fade of 5 dBbelow the median signal. This value is justified bythe fact that there is a difference of 5 dB betweenthe median (50%) level of a Rayleigh- distributedsignal and the 80% level, as well as by experimentaldata.
For real systems, the following somewhatmore complicated formulas are established:
Systems of50 to 840 kilometers; 3pWpOper kilometer plus 200pWpO.
Systems of 840 to 1670 kilometers,o 3pWpOper kilometer plus 400pWpOo
Systems of 1670 to 2500 kilometers; 3pWpOper kilometer plus 600pWpO.
CCIR does not attempt to define noise perfor-mance for systems shorter than 50 kilometers, sincesuch systems are not amenable to any pWpO perkilometer formula and must be treated as specialcases. The above formulas are for the noise contri-buted by the microwave or transmission systemonly, and do not include the multiplex noise. Thelatter must be added in to obtain total noise on thesystem.
~.~~ !u~l~ !.e!!::~~~ ~~'l!~
Noise objectives in the U.S.A. are not asrigidly or officially formulated as in the CCIR, andare subject to fairly frequent changes. Table H giveswhat we believe to be objectives commonly applied
79
time during which the receiver is below thepractical threshold (and usually muted) are bydefinition "propagation outages".
As presently stated (1970) these are spec-ifically identified as "worst hour" objectives. AnEIA ad hoc committee has recommended to DCAthat the "worst hour" statement be deleted and theobjectives specified and measured with all hopsfaded 3 dB below their normal calculated signallevel. The reasons are the same ones discussed inthe section on CCIR objectives.
This parameter thus establishes the bottomlimit of the fade margin range, and is closely tied inwith system reliability.
Line-of-sight microwave systems are invariablyengineered with very large fade margins, and oftenwith diversity protection, so that the percentages oftime during which anyone hop will be at, or below,threshold are very small. Consequently, it is un-likely that two hops of even a long system will besimultaneously below threshold. This means thatthe expected propagation outage time of a multi-hop system will be equal to the sum of theexpected propagation outage times of all theindividual hops. Consequently, only a single valueof maximum noise is used, regardless of the numberof hops, but the allowable time percentage duringwhich it can be experienced, does increase with thenumber of hops, and is approximately proportionalto system length.
Note that the military objectives apply withthe system loaded per Equation (23D), that is, -10dBmO equivalent noise loading per channel.
~e~~~~ T~an~mi~ion Systems
The random noise parameter used to specifynoise for television transmission, is the ratio of thepeak-to-peak video signal to the weighted rills noisein the band occupied by the television signal.Various objectives are in existence.
EIA Standard RS-250A recommends a weight-ed SIN ratio minimum of 59 dB for a single hopsystem, and a minimum of 56 dB for a multihopsystem. This is applicable for either color ormonochrome transmission. ~cI~cc!:!'T
CCIR Recommendation 421 lists, for the2500 kilometer hypothetical reference circuit, var-ious values ranging from 50 dB to 57 dB, dependingupon the system. This recommendation is formonochrome only. In general, systems engineeredto meet voice channel noise performance require-ments for 600 channels or more, will provideadequate noise performance for television trans-mission.
The CCIR objective for the 2500 kilometerhypothetical circuit, is that the one-minute meannoise power should not exceed 47,500 pWpO formore than 0.1% of any month, with proportion-ately smaller allowable percentages down to 280kilometers.
The same objective is applied to real circuitsfrom 280 to 2500 kilometers in length, but for realcircuits of any length up to 280 kilometers, a singlepercentage value of (280/2500) x 0.1%, or0.0112%, is specified.Note' The EIA and the CCIR definitions of SIN
differ by a factor of 3 dB, because EIAdefines the "signal " as the total video signal,
whereas CCIR defines it as the picturesignal, exclusive of synchronizing pulses.Other differences arise as a result of widelydiffering emphasis and weighting networks,so the EIA and CCIR SIN ratios cannot bedirectly compared.
Again, the CCIR objective is adapted fromolder objectives developed for cable systems, and isnot well suited for microwave systems. One reasonis that it is in terms of "one-minute mean noise",that is, noise integrated over a period of oneminute. This is reasonable for systems in Vfhichnoise changes are slow with respect to a minute,such as cable systems, but it is inappropriate for therapidly changing noise associated with deep fadingin a microwave system. Consequently it is adifficult parameter to predict and measure. Asecond objection is that this value of noise is notreally high enough to justify considering it a"mute" or "propagation outage" point, since thecircuits would be quite usable with 8 or 9 dBgreater noise.
5. Noise Allowable for SmallPercentages of Time
A second type of noise objective establishes amaximum allowable value of noise, beyond whichthe circuit is considered unusable. In a microwavesystem, this value of noise defines the "practicalthreshold " of the receivers, and those periods of
81
The allowable time percentage objectives de-pend on the type of system. For systems of thelong-haul type (specifically intertoll) an objectiveof 0.02% for a 4,000 miles system is applied, withproportionally shorter times for shorter systems.For systems of the short-haul type, an objective of0.02% for systems of any length up to about 200miles is used. Both types of objective are such as torequire, in general, some form of diversity to
protect against multipath fading.
No solution satisfactory to CCIR has yet beenfound to this problem, which is still under study byCCIR/CCITT. For further details of CCIR noiseobjectives, reference should be made to CCIRRecommendation No.395-1.
Note: CCIR Recommendation No.393-1, which applies only to the hypo-thetical reference circuit, has an addi-tional short term noise objective which isomitted completely from the objectivesin 395-1 for real systems.
!!-1~~~~~~~
The additional objective is that the noisepower on the 2500 kilometer referencecircuit should not exceed 1,000,000pWOunweighted (with an integrating time of5 ms) for more than 0.01% of anymonth.
The most commonly used value of maximumallowable noise in industrial systems is 52 dEaO.This corresponds to 58 dErncO, and thus allows 3dE higher noise before muting, than the currenttelephone objective described above. Until fairlyrecently, 52 dEaO was the objective of the tele-phone industry as well.
This value would correspond to 562,000pWpO of weighted noise power, or about57.5 dBrncO. Allowable time percentage objectives vary
rather widely, depending on the type of system andthe usage. Many industrial users have reliabilityobjectives no less stringent than those applied tolong haul telephone systems. Meeting such objec-tives will, in general, also require diversity toprotect against multipath fading.
It is a relatively easy parameter to pre-dict and measure, and is a satisfactoryvalue to be used as a muting or "propa-gation outage " point.
It thus appears that it would be a muchmore suitable CCIR noise parameter touse in real systems than the controversial47,500 pWpO parameter discussed above.
~MjJi1-aI;Y ~ 8-ls..te!!!S-
Current or proposed DCA standards state thatthe short term mean noise power, with an inte-grating time of 5 ms, on any 4 kHz (nominal)channel shall not exceed 316,000 pWpO for morethan an accumulated 2 minutes in any month ormore than 1 minute in any hour over any hop.
It is very similar in all respects, to theshort term allowable noise objectives asused in the USA and described in thefollowing two paragraphs.
316,000 pWpO is equivalent to 55 dBrncO or49 dBaO..
!:!:.~~ ~u~l~ !.e~~~~ ~~f.!!~Television Transmission
The maximum allowable noise level is pres-ently established at 55 dBrncO. It is to be measuredwith a short time constant meter ( on the order ofmilliseconds), and does represent the muting oroutage level, consequently it is a much morerealistic parameter than the comparable CCIR
objective.
EIA RS-250A suggests that a weighted SINratio of 33 dB be considered as the "outagethreshold " beyond which the noise will be unac-
ceptable. No time percentage is suggested. Acolor-weighted SIN ratio of 37 dB is also widelyused as a practical threshold for video.
82
EQUIPMENTv
ment for drop and insert along the route. Theheterodyne type is also preferable for systemscarrying color TV, if more than a few hops areinvolved.
It is obvious from the preceding discussionsthat there is a very close inter-relationship betweenthe characteristics of the various items of theequipment to be used, and the engineering choicesand performance parameters of the paths them-selves. Equipment of the baseband or remodulating
type is widely used for short haul or for distributivesystems in the telephone industry , and for eithershort or long haul industrial systems. The greatflexibility for drop and insert, plus maintenanceadvantages, are the determining factors. Hetero-dyne systems are inherently at a considerabledisadvantage in such applications.
Thus it is desirable, in fact almost essential,that the path survey engineers have enough advanceknowledge of the frequency bands to be considered( often only one, but in some cases more than one ),the kind of service, the number of channels (bothpresent and future) to be accommodated by thesystem, the kind of performance and reliabilitycriteria desired, and the pertinent parameters of themicrowave equipment to be used (for example,transmitter output power, receiver noise figure andbandwidth, per channel deviation etc.), to allow anintelligent approach to the problem of path engi-neering. Many choices are involved in path selec-tion, and choices made without a thorough know-ledge of all the pertinent circumstances may not bethe best ones.
Apart from the choice between heterodyne orremodulating equipments, some other primary con-siderations in the selection of the best radioequipment for a particular system include: (a)characteristic of the end-to-end baseband facility,including bandwidth, frequency response, loadingcapability, noise figure and noise performance; (b)the am,ount of radio gain available, as determinedby transmitter power output and receiver n<;>isecharacteristic; (c) operating frequency band, andrequired frequency spacing between radio channels,as determined by transmitter deviation, receiverselectivity and frequency stability; (d) primarypower requirements and options available; (h)supervisory functions available, including orderwire, alarms and controls; (f) equipment reliability,including availability of redundant versions such asfrequency diversity, I-for-N or 2-for-N multilineswitching, hot standby, or hot standby at trans-mitters and space diversity at receivers; and, (g)provisions for testing and maintenance.
A. Radio Equipment
Microwave systems can range from as little as5 or 10 miles to distances as long as 4,000 miles.Facility requirements can be relatively small, re-quiring structures and equipment for only a lightroute, or they may be very heavy, requiringmulti-channel, heavy route layout with sophistica-ted switching. They can be constructed for nomi-nally good service during certain limited hours ofthe day with considerable economy, or they can bebuilt for a very high quality of service on a 24 houra day, year-in and year-out basis. With the rapidly changing nature of the state
of the art, and the continuing development of newequipments and upgrading of old ones, specific dataon microwave equipment characteristics can be-come outdated in very short order. Consequentlywe have not included such data in this manual.Rather, the user or engineer should rely on up-to-date data obtained from the manufacturer.
Some systems are of a "through " type, with
all or almost all of the channels going end-to-end,while others require multiple access, with droppingand inserting of channels at most, if not all,repeater points. The latter is very typical inindustrial systems, in which long haul and shorthaul are almost always combined in a single radiochannel. B, RF Combiners
A variety of methods are used to combine atransmitter and receiver, or several transmitters andreceivers, for operation over a single antennasystem. These methods make use of waveguideswitches, hybrids, filters, phasors, isolators, circula-tors, and other devices that have a certain amountof inherent attenuation. This attenuation must beincluded when measuring transmitter power and
The two types of FM microwave equipment incommon use, are the IF heterodyne type and thebaseband, or remodulating, type. The IF hetero-dyne type, by eliminating demodulation and re-modulation steps at repeaters, contributes the leastamount of distortion, and is the preferred choicefor systems handling exclusively, or almost ex-clusively, long-haul traffic, with little or no require-
83
receiver sensitivity, or it must be taken intoaccount when calculating net path loss. Because ofthe wide variety of devices and possible combina-tions, it is necessary to rely on the manufacturerspecifications for attenuation data. These datashould clearly state the point at which transmitterpower and receiver sensitivity are specified andmeasured, and the loss of any device that is to bel~ated between this point and the antenna.
there are very strong incentives toward the use ofguyed towers, provided there is sufficient space toallow them.
Figures 25A, 25B and 25C show the requiredareas for various types of tower. Though thesedrawings are representative, other types of tower,particularly the large, heavy structures used withhigh-density systems, will have different base ar-rangements and area requirements. An examinationof the figures will show the large difference inground requirements. Where self-supported towerscannot be avoided, considerable study is warrantedin layout of a microwave system, to try to keep thepaths such that excessive heights are not required.
c Towers
Towers and tower problems have a significanteffect on many microwave path engineeringchoices. The microwave path engineer needs aconsiderable prior knowledge of the limitationswhich the characteristics of towers (and of an-tennas and waveguides as well) impose, and theresulting restrictions in his freedom of choice, inorder to be equipped to do his job properly.
There are several things which are frequentlyqueried in connection with towers, and with thequoting and furnishing of towers by a manufac-turer. Some of these are:
For example, the engineer must have a fairlyclear idea about how high he can economically gowith towers, before he can tell how long the pathscan be, or conversely, whether a given path can beachieved in one hop. From the material in previoussections, it is easy to calculate that a 30 mile pathon relatively flat terrain could call for towers onthe order of 250 feet at each end; if there were hillsor trees in the middle, this could easily go up to300', 350' or even more, in order to achieve thedesired clearances. These are not unreasonableheights for stations located in the country, or inareas where plots sufficiently large to allow guyedtowers exist. But, if a station is in a built-updowntown area, as end terminal stations often are,guyed towers are usually out of the question.Self-supported towers of such heights are extremelyexpensive, also require quite a bit of real estate forthe foundation, and often may be prohibited bylocal codes or other legal reasons. Another impor-tant consideration is the proximity to airports orair lanes, which brings in the possibility of govern-ment restrictions on permissible tower height.Some foreknowledge of the potential tower limita-tions is mandatory before the problem can beattacked knowledgeably.
Soil conditions.Wind loading.Local building codes and restrictions.
Unless accurate and specific information about soilcharacteristics (on the exact site of a proposedtower) are available, the quoted costs are almostinvariably based on "standard soil" as defined inEIA Standard RS-222A.
If it turns out that soil conditions are non-standard, for example very rocky and requiringdifficult excavation, or with low load bearingcapability requiring extra large bases, the additionalcost incurred because of such unusual conditions isusually stipulated to be billed to the customer. Insome unusual situations, this may amount to asizeable increase in tower cost.
Wind loading creates some misunderstandings,mainly in definitions. EIA Standard RS-222A onsteel towers, and its companion RS-195A onantennas, which are normally used in specifyingand determining wind loadings, contain recommen-dations and tables for different areas of thecountry. Figure 26 is a map of the U.S.A. dividedinto three loading zones. Zone A has a recommen-ded minimum of 30 lbs./sqft, Zone B 40 lbs./sqft,and Zone C 50 lbs./sqft. The latter is typical ofsoutheast coastal areas in the hurricane belt.
The two generic types of tower are guyed, andself-supporting. For very short towers there is notmuch cost difference, but as heights go up, the costof the self-supported types increase more or lessexponentially, while that of the guyed towers,which have a constant cross-section, increases moreor less linearly. So where high towers are required,
This wind loading is the "design " or "elastic
limit" wind loading, though neither of these termsis very satisfactory. The point is that this design
84
85
t /
H
p
1R1-
APPROXIMATE DIMENSIONS (Feet) APPROXIMATE DIMENSIONS (Feet)
Tower Height R w H Tower Height R p
255075
100125150175200225250275300325350
9.513.815.717.319.421.924.426.428.430.532.434.836.438.0
17.326.630.233.537.242.046.850.854.558.762.166.870.073.1
16.123.426.629.332.837.141.344.648.051.254.859.061.664.4
5075
100125150175200225250275300325350
15.417.820.522.825.427.930.633.235.838.140.842.644.5
21.825.328.932.235.939.543.346.950.653.857.660.064.0
(Shaded portion represents rupture area) (Shaded portion represents rupture area)
Figure 25B. Approximate Area Required for3-Leg Self Supported Tower.
Figure 25C. Approximate Area Required for4-Leg Self Supported Tower
8(j
loading is not associated with operational require-ments (tower twist and sway), so if a wind velocityof this magnitude exists, the tower might twist orsway enough to substantially degrade the signal,but it should return to normal, or very nearly so,when the wind stops.
deposit a large portion of their moisture contentnear the top. In such cases almost unbelievablequantities of ice can build up on antenna and towerstructures. In areas subject to icing, tower andantenna structures must be designed to carry theadditi9nal loading caused by the weight of the ice,plus added wind loading resulting from the in-creased surface areas.In addition to the "design " loading, which is
thej name-loading by which a tower is described,EIA specifies an operational loading for which thetwist and sway limits of the tower should notdegrade the signal by more than 10 dB. A table isincluded in RS-222A and RS-195A giving represen-tative values for allowable twist and sway forvarious beamwidths.
Local building codes within cities may imposemore severe restrictions on loading than those ofRIA.
Roof mounted towers are sometimes required.These, if of any great size, will require carefulevaluation of the structural adequacy of the build-ing to support the proposed tower .Please note carefully: The EIA operational
minimum loading is based on 20 lbs./sqft windload, regardless of what the design loadingmay be. If operational minimums higher than20 lbs./sqft are desired, it is necessary for theuser to call them out specifically so that thetower manufacturer can be asked to quote ona stronger tower, usually at a higher cost.
Within the United States, the F AA and FCCboth have complex regulations covering towerheights, depending on proximity to airports orairlanes. They also have requirements on painting,lighting, and in some cases, obstruction marking oftowers. Similar government entities in other coun-tries regulate tower heights and markings withintheir jurisdictions, usually in accordance with rec-ommendations of the ICAO (International CivilAviation Organization).
Wind loading increases as the square of theactual wind velocity .Expressed as a formula, p =KV2 , where p is the pressure in pounds per squarefoot, K is the wind conversion factor, and V is theactual wind velocity in miles per hour. EIArecommends the use of 0.004 as a nominal value ofK for pressures on the projected areas of flatsurfaces. Using this value for K, the approximatewind velocities corresponding to several commontower loadings are :
D. Waveguide and Transmission Lines
Waveguide and transmission line is importantnot only for its loss characteristics, which enterinto the path loss calculation, but also for thedegree of impedance matching attainable, becauseof the effect on echo distortion noise. The latterbecomes extremely important with high-densitysystems having long waveguide runs.
20 Ibs/sqft = 71.0 mph30 Ibs/sqft = 86.0 mph40 Ibs/sqft = 100.0 mph50 Ibs/sqft = 112.5 mph
The loading on a tower depends very criticallyon the sizes, shapes, locations and relative positionsof all the antennas, reflectors, waveguides and otherparaphernalia which are mounted on it. A veryimportant point is to review the possibility thatadditional paths or antennas may have to be addedin the future, since such considerations couldsignificantly affect the design of the initial tower.
In the 2 GHz bands coaxial cable is usuallyused, and, except for very short runs, it is usuallyof the air dielectric type. Typical sizes are 7/8 ",with an attenuation of about 2 dB/100', and1-5/8", at about 1.1 dB/100'. It is normallyordered in the exact lengths required, with factoryinstalled and sealed terminal connectors. When thelarger sized cable is used, it is desirable to reduce to7/8", with a suitable transition, for flexibility inconnecting to the radio equipment. In some casessimilar treatment may be needed at the antennaend, though generally the use of a rigid right-angleconnector will allow sufficient flexibility for an-tenna orientation.
A very important consideration in some areasis that of ice forming on towers and antennas. It isof particular significance in the case of mountain-top sites, especially those where moisture-ladenwinds may sweep up one side of the mountain and
88
to provide two polarizations at 4 GHz and twopolarizations at 6 GHz. But circular guide hascertain disadvantages. It is practical only forstraight runs, requires rather complicated and ex-tremely critical networks to make the transitionfrom rectangular to circular, and can have signifi-cant moding problems, when the guide is largeenough to support more than one mode for thefrequency range in use. Consequently, thoughcircular waveguide is available in seve~al differentsizes, and its low losses make it attractive, it isrecommended that it be used with considerablecaution.
The other bands use waveguide almost ex-clusively, one of three basic types; rigid rectangular ,rigid circular, and semi-flexible elliptical. The ellip-tical type is of continuous construction, while theother types come in sections with flanges. Shortsections of flexible waveguide are also used for theconnections to the antennas and to the equipment.In all cases it is desirable to keep the number andlength of flexible sections as small as possible, sincethey tend to have higher losses and poorer VSWRthan the main waveguide types.
R~tangular Gui~e1
3. Elliptical GuideRigid rectangular waveguide is the most com-monly used, with oxygen-free, high-conductivitycopper (OFHC) the recommended material. Thetypes and approximate characteristics are asfollows:
Semi-flexible elliptical waveguide is availablein sizes comparable to most of the standardrectangular guides, with attenuations differing verylittle from the rectangular equivalents. The distinc-tive feature of elliptical guide is that it can beprovided and installed as a single continuous run,with no intermediate flanges. When very carefullytransported and installed it can provide goodVSWR performance, but relatively small deforma-tions can introduce enough impedance mismatch toproduce severe echo distortion noise.
4 GHz band; WR 229 is standard for most instal-lations. It has a loss of approxi-mately 0.85 dB/100'.
6 GHz bands; WR137 is normally used. It has aloss of approximately 2.0 dB/100'.In cases where, due to high towers,a reduced transmission loss is re-quired, transitions can be suppliedfor use with WR159, which has aloss of about 1.4 dB/100'.
The most commonly used types and theirapproximate characteristics are as follows:
EW-37, approximately .85 dB/100'.
WRl12 is normally used. Attenua-tion is approximately 2.7 dB/I00'.
4 GHz band7-8 GHz
approximately 1.75 dB/100'.
6 GHz bands' EW-59,11 GHz WR90 is normally used. Attenua-tion is approximately 3.5 dB/I00'.
approximately 2.5 dB/100'.
7-8 GHz: EW-71,12-13 GHz; WR 75 is normally used. Attenua-tion is approximately 4.5 dB/I00'.
EW-107, approximately 3.7 dB/100'.
11 GHz bandFor the most critical applications, whereextremely low VSWR is required to meet stringentnoise performance specifications, special precisionwaveguide, manufactured to very tight tolerance, isrecommended.
EW-122, approximately 4.5 dB/100',
12-13 GHzbands:
2 Circular GuideIn all types of waveguide systems it is
desirable to keep the number of bends, twists, andflexible sections to a minimum. It is also vitallyimportant to use great care in installation, sinceeven very slight misalignments, dents, or introduc-tion of foreign material into the guides can createsevere discontinuities.
Circular waveguide has the lowest loss of all,and in addition, it can support two orthogonalpolarizations within the single guide. It is alsocapable of carrying more than one frequency bandin the same guide. For example, WC281 circularguide is normally used with horn reflector antennas
89
E. An tenna Systems where G
A
e
A
~
Highly directional antennas are used withpoint-to-point microwave systems. By focusing theradio energy into a narrow beam that can bedirected toward the receiving antenna, the transmit-ting antenna can increase the effective radiatedpower by several orders of magnitude over that of ano~-directional antenna. The receiving antennaalso, in a manner analogous to that of a telescope,can increase the effective received power by asiI11ilar amount.
gain over isotropic, in dBarea of antenna apertureantenna efficiencywavelength at operatingfrequency, in same units as A
The following paragraphs list some of themore c~mmonly used antennas or antenna systems,with some descriptive comments.
1 Direct Radiating Anten~as
Parabolic AntennasAlthough gaip is the primary characteristic,
there are other antenna characteristics which are ofimportance in communications systems. Antennabeam-width, side-lobe magnitudes, off-axis radia-tion and sensitivity patterns, and polarization dis-crimination are of great significance for frequencycoordination purposes. Impedance match (usuallyexpressed as VSWR, though return loss is a muchmore useful parameter) across the band to be usedis of great i~.portance in situations where echodistortion IS significant. Consequently, it is nolonger sufficient merely to select an antenna systemfor optimum gain efficiency.
This type of antenna consists of a parabolicdish, illuminated by a feed horn at its focus.Available in a wide variety of sizes, with diametersof 2', 4', 6', 8', 10' and sometimes 12' and 15' inmost frequency bands.
The simplest form is with single plane polar-ized feed, which can be either vertical (V) orhorizontal (H). Others have dual polarized feeds(DP), with separate V and H connections. DP'susually have a bit less gain than single polarized,because of the more complex feedhorns.
Nevertheless, it is basic that the antennasy~t~m must have enough gain so that the desirednet path loss between transmitter output andreceiver input is attained. The required antennagains are determined by a £~culation which in-volves a knowledge of the transmitter outputPQ}Y:~r ,Jixed losses of waveguides, circulators,hybrids, radomes, and any other items between thetransmitter and its antenna, and between thereceiver and its antenna, the unfaded path attenua-tion, and the receiver strength needed to give therequired noise performance and fade margin. Thecalculations are usually formalized and recorded ina "Path Data Sheet". An example is given inSection VI.
Off-beam discrimination is reasonably good,but front-to-back ratios on the order of 45 to 50dB maximum, are generally not adequate forback-to-back transmission ( or reception) of thesame frequency in both directions. Often availablewith special low VSWR feeds (on the order of 1.05to 1).
The gain efficiencies of most commerciallyavailable parabolic antennas are in the order of 55to 65%. With 55% efficiency, the gain of a parabolicantenna is given by:
G = 20 log10 B + 20 log10 F + 7.5(25)
where GFB
~
The gain of an antenna is expressed in dBrelative to the gain of an isotropic antenna, which isa theoretical omnidirectional antenna, with a gainwhich by definition would be 1, or O dB. At a givenoperating frequency, the gain of an antenna (eithertransmitting or receiving) is a function of theeffective area and is given by:
gain over isotropic, in dBfrequency in GHzparabola diameter in feet
Although this formula can be used for estimatingpurposes, actual gain should be determined fromthe manufacturer published specifications. In thehigher bands .(11 to 13 GHz particularly), and withcross-band and other complex feed horn systems,the efficiencies can often be considerably lowerthan given above, and actual gains may easily be 1to 2 dB lower than that given by equation (25).
10 log10 ( 41T A eli\ 2(24)
90
The half-power beamwidth of a parabolicantenna is given approximately by:
both directions. This is the primary reason for theiruse. Special feeds are usually required for very lowVSWR (1.05 to lor so) applications.
4> = 70/FB (26) Cross-Band Parabolic Antennas
These are parabolic antennas with feeds de-signed to permit operation in two widely separatedbands (for example, 6 and 11 GHz). Because of thevery complex and critical feed assemblies, theseantennas typically have somewhat reduced gain ( adB or so) and poorer VSWR than single-bandantennas. Problems have also been experiencedwith interaction between the two feed systems,since the 6 GHz waveguide can propagate spurious11 GHz modes. A commonly used method ofsolving the interaction problem is to insert in the 6GHz feed-line, at a point as close as possible to theantenna, a filter which attenuates the 11 GHzenergy while allowing the 6 GHz energy to passthrough essentially without loss.
where <1> =
FB
~
half-power beamwidth indegreesfrequency in GHzparabola diameter in feet
Side-lobes and front-to-back ratio are causedby imperfect illumination of the parabola, phaseerrors introduced by the feed, and irregularities inthe reflecting surface. Antenna patterns, usuallyavailable from the manufacturer, give the radiationin all directions on both principal planes relative tothe main beam. Such patterns are necessary forinterference studies.
In using such antenna patterns for interferencestudies, it should be kept in mind that it is not justthe response of the receiving antenna to theopposite polarization that is important. A transmit-ting antenna on one polarization will radiate poweron the other polarization as well, in accordancewith its cross-polarization pattern. If the transmit-ting antenna has poor cross polarization discrimina-tion at the angle looking toward a receiving antennawhich is oppositely polarized, no amount of dis-crimination at the latter will reduce the componentit receives from the cross radiation of the transmitantenna. Thus, in an interference analysis, one musttake as the polarization discrimination, the worstcombination of transmitter direct to receiver op-posite, or transmitter opposite to receiver direct.
Horn Reflector Antennas
The horn reflector (cornucopia) antenna has asection of a very large parabola, mounted at suchan angle that the energy from the feed horn issimultaneously focused and reflected at rightangles. The standard Bell System horn antenna isabout the equivalent of a 10' parabola insofar asgain is concerned. But it has much higher front-to-back ratios (on the order of 70 dB or more);sufficient to allow operation in two directions ( ormore) from a station on the same frequencies.
It has good VSWR characteristics, and, withsuitable coupling networks (which are quite com-plex), can be used for multiband operation on bothpolarizations. However, there are some modingproblems, particularly at the higher frequencies,which, if uncorrected, can cause severe distortion.
!:!i~~~f~rIE.aE..c~ <:?! ~h~~d~d-AE..t~~a~
These are similar to the common parabolictypes, except that they include a cylindrical built-out shield which helps to improve the front-to-backratio, and the wide-angle radiation discrimination. Disadvantages are that this antenna is ver'i big,
heavy ,and complex as to mounting, and quiteexpensive not only for the antenna itself, but for itseffect on mounting and tower costs. Almqst noflexibility in choice of sizes, though at least onesmaller size of horn reflector is currently available.
Shrouded antennas are usually available aseither single polarized or double polarized. Gainefficiency is usually sligh tly poorer than that of thesimple parabolas.
The following table can be used for prelimi-nary estimates of antenna gains in the variousbands. Final gains should be those guaranteed bythe manufacturers of the particular antenna to beused.
They are substantially bulkier, heavier, andmore expensive than the ordinary parabolas. How-ever, they can provide front-to-back ratios on theorder of 65 dB, sufficient in many cases, to allowback-to-back transmission of the same frequency in
91
2. Periscope Antenna Systems It is generally accepted, though with somedissenting opinions, that periscope antenna systemsdo not have particularly good off-beam discrimina-tion characteristics, and for this reason their use inhigh density systems and in very congested areasleaves something to be desired. Consequently, therehas been something of a trend toward increasedusage of direct radiating antennas, despite th eadded loss and echo distortion problems associatedwith the long waveguide runs, which they typicallyrequire.
In many cases, usually where considerableheight is required or waveguide runs are difficult tomake, a periscope antenna system is used. Itconsists of a parabolic radiator, generally at or nearground or building level, illuminating a reflector atthe top of the tower. Gain isa complex function ofthe antenna and reflector sizes and separation, thefrequency, and the geometric relationships.
A periscope system allows waveguide runs tobe kept short, thus reducing losses and improvingthe situation with respect to echo distortion, sincethe latter is a function of waveguide length as wellas impedance match. With suitable choices ofcombinations, and over certain ranges of separa-tions, antenna-reflector combinations can give netgains equal to, or even greater than, the gain of theparabola alone, thus in effect eliminating most ofthe losses due to waveguide.
In their most common configuration, peri-scope antenna systems have the illuminating dish atthe bottom of the tower, directly under thereflector. Assuming a horizontal 'path, the latterwill then be mounted so that its face makes anangle of 45°. with the horizontal. In some cases, forexample space diversity, physical relationships maydictate a "skewed " periscope arrangement, with the
dish moved off to one side, and sometimes forwardor backward along the path, with respect to thedistant end.For this reason the periscope system is often,
from the point of view of overall net gain, the mostefficient antenna system, particularly where hightowers are needed. The periscope system has hadvery wide usage in the bands from 6 GHz up, but itis relatively inefficient at 2 GHz, and has had verylittle usage at 4 GHz.
In such cases, the reflector will typically haveto be rotated around its vertical axis so that itsnormal no longer points directly along the path; thetilt angle in general will no longer be 45°, but willdepend on the actual configuration.
92
that of the curved reflectors, and it will be notedthat the lines for the curved reflectors are truncatedat that point in each case.
Calculations of the tilt, amount of rotationaway from the path, and the effect of the "skew"on the gain are somewhat complicated. Graphicalsolutions can be made using Lenkurt drawingEEH-20020, a copy of which is included in theAppendix section.
For the case of the curved reflectors, it will benoted that for each antenna-reflecOOr combinationthere is -to the right of the maximum point -abifurcated and shaded section bounded on the left
"by the (C.E.) line and on the right by the (C.R.)line. In this area to the right of the maximumpoint, the greater size of the rectangular reflectorcomes into play and results in a somewhat greatergain. In the case of small separations, the "corner"areas of the rectangular reflector are no longer aseffective, and may even become slightly detrimen-tal. Consequently we have, for conservatism,ignored the extra size of the rectangular reflector inthe area to the left of the maximum point, treatingthem the same as the elliptical.
In current practice, the reflectors used inperiscope systems may be rectangular , rectangularwith some or all of the corners truncated, orelliptical. The surface of the reflector may be flat,or it may be constructed so that it can be adjustedto have a curvature approximating that of a sectionof a large paraboloid, with the focus at the radiator.
A number of theoretical studies have beenpublished on periscope antenna system gains, andthese, together with experimental data and resultsfrom systems in practical use, provide the basis forgain curves commonly employed by microwavemanufacturers and users. It should be borne inmind that in all the studies a number of simplifyingassumptions had to be made to render the mathe-matical processes tractable. The results thereforecannot be regarded as exact.
When using the curves, the heavy solid linesshould be used. to the left of the maximum,whether the reflector is elliptical or rectangular. Tothe right of that point, the heavy solid line shouldbe used for elliptical reflectors, and the brokensolid line for fully rectangular reflectors. ReflectorsWith two corners clipped can be estimated betweenthe two lines, depending on the degree of clipping.Those with all four corners clipped can be treatedthe same as elliptical. At separations where a flatreflector exhibits greater gain it should, of course,be preferred to a curved reflector .
Curved reflectors provide somewhat greatergain than flat reflectors over most separationranges, and are believed to have somewhat betterdiscrimination characteristics. There are differencesof opinion about the merits of the curved reflec-tors, but Lenkurt's experience has been that whenthey are properly installed and aligned, and thecurving very carefully done, they perform aspredicted. Best results have been found to beobtained by carefully adjusting the curvature, priorto installation, to calculated values which will causethe reflector surface to closely approximate aparaboloidal section with its focus at the illumina-ting dish.
The gains as given by the charts are for thestandard periscope arrangement, with the reflectorat a 45° angle and located directly ( or nearly so )above the illuminating dish. In this case the projec-ted area of the reflector is equal to. 707 x (truearea) and is approximately square for the rec-tangular type and circular for the elliptical type.For skewed arrangements the projected shape willchange, and in some cases the projected area also.Moving the dish straight out to one side at a rightangle to the path leaves the projected area un-changed. A dish location forward from the reflectorincreases the projected area and a location back-ward from it decreases the projected area.
Figures 27A through 27D are charts of gain-vs-separation distance for various combinations ofantennas and reflectors. Each chart covers one ofthe standard reflector sizes, together with severalantenna sizes. Each chart covers three types ofreflectors. The heavy solid lines are for curvedelliptical reflectors (C.E.) and the broken solid liliesare for curved rectangular reflectors (C.R.), whilethe dashed lines are for flat elliptical reflectors(F .E.). In the case of the curved reflectors, thesurfaces are assumed to be adjusted to an accurateapproximation of a paraboloid with the focus atthe illuminating antenna. For small separationdistances the gain of the flat reflectors will exceed
Skewed shots also make it more unlikely thatthe correct parabolic curvature can be achieved.For all these reasons it is necessary to use consider-able caution when applying the curves of Figure 27to skewed arr{lngements, particularly those forcurved reflectors.
93
95
96
97
The charts are intended to represent the totalgain of the periscope system when the efficiency ofthe illuminating dish is 55%, but have been deratedby about 0.5 dB to allow for some of the variables.If antennas with gain efficiencies lower than 55%are used, a further derating should be made. Alsowhen radomes are used, the radome loss must bededucted from the overall gain, if it is notaccounted for in the fixed losses.
higher frequency means greater gain and greaterseparation, and a lower frequency means lower gainand lower separation ". To illustrate the point,consider a 10' antenna with a 12' x 17' reflector.Figure 2'JD indicates that such a combination willgive a gain of about 44.1 dB at a separationdistance of 450 to 500 feet, at 6.725 GHz. But at1.92 GHz the gain would be reduced to 44.1 -10.8 = 33.3 dB, and the separation distance would
by reduced to about 130 to 140 feet. Furthermore,at this relatively short separation distance, a ratherlarge curvature would be required on the reflectorface, a difficult mechanical problem. These factsindicate rather clearly why periscope systems areseldom used in the lower frequency bands.
The charts give directly the gain of theperiscope system in dBi ( dB with respect to anisotropic antenna) at 6.725 GHz, the center fre-quency of the 6.575 to 6.875 GHz industrial band,as a function of the separation distance betweenthe dish and the reflector. Thus for this band thecharts can be used directly. In the practical case the transmission engineer
usually knows the frequency band, the true separa-tion distance and the required gain for the antennasystem. The following example illustrates the pro-cedure:
In order to allow the charts to be used forother frequency bands, a table of correction factorsis provided covering the center frequencies of mostof the bands of interest. For each frequency, a gainfactor and a distance factor are given. Assume; Band, 7.437 GHz. Separation distance
280'. Required gain 41 dB. From thetables, the corresponding chart distancewill be 280 x .91 = 255' and the
corresponding chart gain will be 41- 0.9= 40.1 dB.
The use of the gain factors is straightforwardand self-evident. They are simply added algebrai-cally to the gains shown by the chart. For example,a chart gain reading of 38 dB would, at 1.92 GHz,give 38 -10.8 = 27.2 dB. Conversely, a true gain of27.2 dB at 1.92 GHz would correspond to anapparent (chart) gain of 27.2- (-10.8) = 38.0 dB.
One possible combination, from Figure27B, would be an 8' dish with an 8' x 12'reflector which could be either C.E. orC.R. Other combinations could also beused, for example, a 6' dish with a C.R.
reflector.
The use of the distance factor, however, is notquite so self-evident, and some care is needed tomake sure that it is properly used. The factors asgiven in the table are such that they are used asmultipliers when converting from the true distance(at some frequency other than 6.725) to the chartdistance, and as divisors when converting from thechart distance to the true distance. The reason forsetting it up this way is that the transmissionengineer normally will know the true distance andwill want to calculate the chart distance, and mostpeople find multiplication somewhat easier thandivision.
Though the chart presentation method usedhere is somewhat less simple to use than separatesets of charts for each band, it makes it possible tocover 12 frequency bands with only four chartsinstead of nearly fifty. Also the tables can be easilyextended to frequencies other than those shown.For a frequency of X GHz, the required distancef t .. 1 6.725 d th . f t .ac or IS simp y -'--- , an e gam ac or IS
X20 log10 6.725'
x
It is very important to recognize that the trueseparation distance at frequencies lower than 6.725GHz will be less than those shown on the charts,and the true separation distances at frequencieshigher than 6.725 GHz will be greater than thoseshown. The point is emphasized because there is anatural tendency to assume the opposite, becauseof the fact that the lower frequencies have longerwavelengths. A good mnemonic device is: " A
It is also a simple matter, using 2-decadesemi-logarithmic paper of the same type used inthese charts, to prepare a separate set of chartscovering any desired frequency band, by an overlayand tracing process. To facilitate this process, twosmall crosses are placed at appropriate spots oneach of the graphs. By calculation using the abovefactors, one can determine where the points cor-
98
required. In some cases it has been found expedientto place metal shields on the path side of theilluminating dish to cut down the direct signal.
responding to those crosses should fall on the newsheet and place a pair of dots at those points. Thetwo points are then overlaid exactly on the twocrosses and the various curves traced on the newsheet. F. Radomes
Horn reflector and shrouded types of antennasusually include integral radomes, whose losses aretaken into account in the manufacturer's publishedgain figures. Parabolic dish gains, however, usuallydo not include radome losses, and, if radomes areto be used, their losses must be ascertained ( fromthe manufacturer catalog) and added in with theother fixed losses. The amount of loss may varyfrom less than 0.5 dB for a typical unheatedradome at 6 GHz, to almost 2.0 dB for a typicalheated radome in the high frequency bands.
The gain-separation charts have been derivedfrom various published theoretical studies, andslightly modified toward the conservative side.They have been used successfully to calculate gainsfor systems in several -but not all -of the bandscovered in the tables. The charts are published herefor information only, and Lenkurt makes noguarantee of their accuracy.
It should be remembered that the require-ments on trueness of reflector face, and on allow-able deflections, become much more severe as thefrequency is increased, and are quite severe in thebands of 11 GHz and higher. Twist and swayrequirements at these higher frequencies also im-pose strong restraints on tower design.
Radomes also can be expected to degrade theVSWR as compared to that of the antenna withouta radome. This becomes very significant in situa-tionS .where very low VSWR's are needed to controlecho distortion. In some cases radomes have beenfound to create highly reflective "spikes" at parti-cular frequencies, and if these coincide with a usedRF channel frequency, the results can be a highdegree of distortion in that channel.
Sway requirements require special considera-tion in periscope systems, because the effects oftower sway (but not twist) are doubled as a resultof the reflection. Thus the sway tolerances aretwice as stringent as those of an equivalent directradiator. RS-195A provides a table with representa-tive values of twist and sway as a function ofantenna beamwidth, as well as a graph of antennaand reflector beamwidth as a function of antennaand reflector size and the frequency band. Thehalf-power beamwidth of an elliptical reflector isapproximately 60/FW degrees, and that of a rectan-gular reflector approximately 52/FW degrees,where F is the frequency in GHz and W is the widthin feet of the narrow dimension of the reflector.
G, Passive Repeaters
Where a direct microwave path cannot beestablished between two points because of somegeographical or man-made obstacle, it is sometimespossible to establish a path by way of a passiverepeater. The function of such a passive is as a"beam redirector" to pass the microwave beamaround or over something which would obstruct itsdirect path. A firm requirement is that there beradio "line-of-sight", with adequate clearances,between the passive and each of the end points.One potential problem with periscope systems
and, to a lesser extent, with passive repeaters, isthat of a "sneak" echo path existing between theilluminating dish and the distant end. Unless thisdirect path is thoroughly blocked by interveningterrain, some signal may get through directly,particularly under super-refractive conditions, and,if its magnitude is sufficient, can cause seriousintermodulation problems. The direct path will beshorter (usually by about the distance of theantenna-reflector separation) and it Will be a,"leading" instead of a "trailing" ech'o, but thedistortion effect is the same. Since echo signalswith long delays can cause significant intermodula-tion, even if they are 50 to 60 dB below the mainsignal, it is apparent that a good deal of blocking is
There are two general types of passive re-peaters in common use. One consists of twoparabolic antennas connected back-to-back througha short piece of waveguide. Because it is relativelyinefficient, this type of passive repeater is seldomused except on extremely short paths. The other,and more common type, is the flat "billboard"type metal reflector, which acts as a microwavemirror. With surfaces of adequate flatness it is closeto 100% efficient, as compared to about 55%efficiency for antennas. Furthermore, the passivereflector acts both as a receiving antenna and aretransmitting antenna, and its "gain " is therefore
applied twice.
99
Billboard passives fall into two basic configur-ations, depending on the geometric relationships. Ifthe site of the passive repeater is off to one side, orbehind one terminal, so that the included anglebetween the two paths at the reflector is less thanabout 130° (the smaller the angle the better), asingle billboard can be used. This is the mostcommon application.
where GFA
~
two-way gain in dBfrequency in GHzactual area of the passive insquare feetone-half of the included anglebetween the two paths at thepassive. (This last term ineffect converts A into its pro-jected or effective area).
~,
However, if the only available locationhappens to be more or less in line with the path, adouble billboard may be needed, consisting of tworeflectors usually fairly close together and geomet-rically arranged to reflect the beam at the properangles. Double billboards are applicable in situa-tions where the effective change in beam directionat the passive repeater is to be less than about 50° .
A useful formula for "rule of thumb" deter-mination of the approximate boundary of the nearzone for an antenna-reflector combination is:
2 B2T
d= ~ 2FB2 (28)=-
Billboard reflectors are available in a variety ofsizes, up to as large as 40' x 60'. They havetypically been used mainly at frequencies of6 GHzand higher. They can be used at lower frequencies,but because of the vastly increased gain at thehigher frequencies, and the fact that the added gainfactor appears twice for the billboards while theadded path loss factor appears only once, thebillboards are far more efficient at the higherfrequencies.
where d =
B
A
F
distance between antenna andreflector in feetdiameter of dish, or widestprojected dimension of the re-flector, whichever is larger, infeetwavelength in feetfrequency in GHz
~
Figure 28A gives the two-way free-space gainsof various sizes of passive as a function of fre-quency and the included horizontal angle.Passive repeater gain calculations are some-
what complicated. For single billboards, things aresimple if the billboard is in the far field of bothantennas. In such a case the antenna gains and thebillboard gains are independent and do not interactwith each other. Then we simply calculate a totalpath loss which is the sum of the two separate pathlosses, and from it subtract the sum of the twoantenna gains and the two-way gain of the reflec-tor, in order to arrive at the net end-to-end pathloss through the reflector.
When the passive is so close to one end that itis in the near-field of that antenna, as indicated byequation (28), the antenna and reflector gains areno longer independent, but react with each other insuch a way that the net gain would be reduced. Inthis case the above methods cannot be used, sincethey would give overly optimistic results.
One way of attacking the near-field situation,is to treat the antenna and the nearby passive in thesame fashion as a "periscope" antenna system. Inthis case, a "correction factor" is calculated, andapplied to the gain of the antenna, to obtain thenet gain of the periscope combination. Since thisgain is referred to the location of the reflector, the"path " in this method is simply that from the
reflector to the more distant end. The shorter pathsimply disappears from the calculation. Figure 28Bprovides curves for deriving a "periscope" correc-tion factor .
The following formula can be used to calcu-late the free-space, two-way gain of a single passivebillboard :
G = 22.2 + 40 log10F + 20 log10A(27)
+20 laglO cas cx:
100
2 FB2
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104
An alternative method of handling the near-field situation is provided by the curves of Figure28C, which are an adaptation from the curves ofFigure 28B. Figure 28C derives a gain reductionfactor which, when applied to the 2-way free-spacepassive gain, gives the equivalent net gain when theproblem is treated on a two-path basis. The bigadvantage of this approach is that it allows thepassive repeater to be shown in the same way ( as aseparate location) and treated in the same way onthe path calculation sheets, whether it is in the farfield or the near field.
From equation (27), free-space gain ofpassive is 105.0 dB.Assume free-space gain of 10' dishes is43.1 dB each.Waveguide and fixed losses omitted forsimplicity.From equation (28), or by inspection of1/K and Figure 28C it is apparent thatthe passive is in the near field of theclose-in antenna.
Calculation using Figure 28B
We find for the calculated values of l/Kand L, a correction factor of -1.8 dB.Using this in a "periscope" type formula,we find;
Closely spaced double passive repeaters areoften used in situations where the transfer angle isless than about 50 degrees. In such cases, thefree-space gain of the combination of the twopassives is equal to the 2-way free-space gain for theeffective area of the smaller of the two billboards(in most, but not all cases, they are made the samesize), minus a reduction in gain which can becalculated from the "double passive repeater effi-ciency curves" of Figure 28D. If the double passiveis close to one end of the path, near-field correctionmust also be applied.
Net Path Loss = 140.11.8) = 55.7 dB
43.1 (43.1
The quantity in brackets is the net gainof the periscope combination.
Calculation using Figure 28C
We find for the calculated values of llKand L a correction factor of -0.7 dB.Using this in a "two-path" formula, we
find;
Note that the parameters l/K and L in Figures28B and 28C are dimensionless. This means thatif the antenna and reflector dimensions are in feet,the separation distance must also be in feet.Any consistent set of units can be used.
Net Path Loss = 140.1 + 106.143.1 -(105.0 -0.7) = 55.7 dB
43.1-
The following example is included to illustratethe calculation procedures:
As seen, either method should give the sameresult, within the accuracy with which the chartscan be read.
Assume; 6 GHz band. 20' x 30' passive, with anincluded angle of 102°. 10' dishes at eachend of path. Short leg 0.5 miles. Long leg25 miles.
Although passives are extremely useful inmany cases, it should be remembered that theyhave their limitations. They are seldom practical inflat country, and even in hilly country, fairlyfavorable conditions are usually needed.
1TAd'~
3.14 x 0.984 x 0.5 x 5280o4 x 6 x 20 x 30 x COB 102 /2
~ 0.9
l/K= =
The effectiveness of a passive repeater is aninverse function of the product of the lengths ofthe two paths, rather than the sum of their lengthsas one might suppose. Thus it is highly desirable tokeep one of the paths very short. When highdensity systems with stringent noise performanceobjectives are involved, it is something of a rule ofthumb that the product of the two path lengths inmiles should not ~xceed about 30 (in the bands of
= D'~ = 10 I 3;14 o
y4a2 V4x20x30xcos102/2
~ 0.48
From equation (3), short leg attenuationis 106.1 dB;long leg attenuation is 140.1 dB.
105
6-8 GHz) or about 50 (in the bands of 11-13 GHz)unless extremely large passives can be used. This isby no means an absolute restriction, and each caseshould be considered on its own merits, taking intoaccount the system parameters and the requiredperformance. With low density systems, or systemswhere somewhat greater noise can be tolerated,products considerably in excess of these figures canbe acceptable.
in any passive application the possibility of suchreflections should be evaluated. Small passives withsmall included angles are particularly vulnerable tothis pro blem.
A slightlyOdifferent but related problem canoccur with passive repeaters which are essentially"in line" with the path (either double billboards orback-to-back parabola types). The potential echopath here is by diffraction of the direct signal, overor around the obstruction.When passives are used, it is often necessary
(though not always) to settle for somewhat lowersignal strengths than would be achieved if the sametotal path length could be spanned directly. In highdensity systems, where very strong signals may berequired, this may limit or prevent the use ofpassive repeaters in some applications.
H. Wire Line Entrance Links
In some circumstances it is possible to achievesubstantial economies or to solve otherwise diffi-cult problems by an arrangement in which themultiplex or terminal location and the actual radiosite are physically separated by some distance andare interconnected by wire line entrance links ofsome kind.
With very large passives, and particularly at 11GHz, the beamwidths may become so narrow as toraise problems in maintaining sufficient rigiditYunder all conditions, and there may even be apossibility that unusual atmospheric conditionsmay bend the reflected beam far enough to cause asignificant signal loss.
Such links are operated on a four-wire basis,with separate pairs or separate cables for the twodirections of transmission.
Entrance links operating at baseband usuallyutilize twin-conductor cables of the type used forvideo transmission. The range of distances may befrom a few hundred feet up to a mile or more,depending on a number of factors. Except for veryshort links, or small channel densities, equalizationand amplification are required for level and slopecoordination.
Nevertheless, the passive repeater, where thetopography permits, and where it is suitable inother respects for the particular application, can bea very useful and efficient tool. Its big advantage isthat it requires no maintenance, and thus can beused in spots which are too inaccessible or tooexpensive for an active repeater.
There appears to be no evidence of anytendency toward increased multipath fading be-cause of a passive in a path. In fact, a path brokeninto two segments by a passive repeater mightexperience less multipath fading than a direct pathof the same total length.
With heterodyne systems it is also possible toseparate the modems and the RF equipments, andoperate wire line entrance links at IF frequencies,over coaxial cables. Here, too, amplification andequalization may be required, , and the distancewhich can be spanned will be relatively limitedunless intermediate repeaters are used.
Although passive repeaters in themselves donot appear to contribute significant intermodula-tion noise, there are situations where sufficientsignal may be reflected from hillsides, terrain, oreven trees in the vicinity of the passive to create adelayed "echo" path with respect to the mainsignal. In some cases the result may be an in-tolerably high level of intermodulation noise. Thus,
Because of the many considerations involvedand the rather special nature of these applications,a full treatment of wire line entrance links isbeyond the scope of this book. However themicrowave engineer doing path transmission workneeds to be aware of these possibilities since theymay affect his choice of sites or methods.
106
VI. CALCULA TIONS FOR A MICROW A YE SYSTEM
A. to make reasonable estimates as to the amount andtypes of guide to be used; to be corrected later toreflect the ''as built" condition. The fixed losses,though they appear small in comparison to the pathattenuation, are vitally important to the system lossand gain equation, and must receive very carefulconsideration. Their importance can be understoodby recalling that an increase of 3 dB in the fixedlosses is equivalent to cutting the transmitter powerin half, or an increase of 6 dB in fixed losses is theequivalent of doubling the path length.
Path Data Sheets
The path data sheet provides a formalized wayof determining and recording all the parametersaffecting the overall transmission loss equation. It isa useful tool for preliminary work, as well as forrecording this and other pertinent data for futurereference.
A separate data sheet can be completed foreach path, or the data for a number of paths can becombined into a single running sheet. However, inthe latter case, the data and calculations are for theindividual paths and not for the overall system.
It is obvious that, in the system design state,the items from 10 on are not developed in theorder in which they appear in the data sheet. Infact, there are strong interactions between many ofthe items, and the actual selection usually involvesevaluating several different combinations to findthe one most suitable for the particular circum-stances.
Figure 29 is an example of a completed pathdata sheet. The following discussion of variousitems on the sheet is intended to illustrate some ofthe details of the system planning, as well as thecalculation methods.
The heading indicates that this is a one hopsystem, operating in the 5925-6425 MHz frequencyband, with a design capacity of 960 channels usingLenkurt 78A microwave and 46A multiplex.
Rather than discuss the remaining items inorder, we will discuss them in a sequence in whichthe transmission engineer might have developedthem, in a series of steps:
The data in Items 2, 3 and 4 we assume weredetermined during the path survey, which alsoproduced a path profile and other information,allowing the engineer to determine the towerheights shown in Item 5, based on the desiredclearance criteria, which we can assume to havebeen the "heavy route " criteria described in Sec-
tion IV.C, Part 7.
1. He ascertains that the fade margin he isrequired to provide, or desires to provide, is40 dB to the 55 dBrncO point. He enters thevalue of 55 dBrncO in the parentheses of Item30, to establish the practical threshold point.He also tentatively enters 40 dB in Item 31.This will be changed later to 39.9 dB as aresult of the final choices and calculations.From the disparity in tower heights at the two
ends, it appears either the path was non-symmetri-cal, or that the situation in Alpha was such that ahigh tower at that location was impractical.
2. He ascertains, from the manufacturer specifi-cations, or from a curve such as Figure 23A or23B, that the RF input required to give 55dBmcO in the top (worst) channel is -74dBm. He enters this value in Item 30.
Items 7 and 8 were determined by calculationfrom Items 2 and 3, and the path attenuation thencalculated by Equation (3), or read from Figure 13,and entered as Item 9.
3. By algebraically adding Item 31 to Item 30, hedetermines a tentative value of -34 dBm asthe received signal needed to give a 40 dB fademargin. However, he also ascertains from themanufacturer specifications that the recom-mended median receive signal level for 960channel operation is -33 dBm. Since thislatter value is higher than the -34 dBm hecalculated, he tentatively enters -33 dBm inItem 27. It will be changed later to -34.1dBm as a result of the final choices.
Items 10 through 15 record, separately foreach end of the path, the colle~tive dB losses in allitems of fixed loss appearing between the equip-ment connection flange and the antenn& connec-tion flange; plus the fixed loss of the radome if oneis used, and its loss is not already iniluded as partof the antenna gain figure.
In the system design stage, the exact wave-guide layout is usually not known, so it is necessary
107
108
Radome loss, Item 15, will of course dependon the type, as discussed elsewhere. The valueof 0.5 dB for an unheated radome is typical inthis band.
From the manufacturer specifications, hedetermines that the transmitter has a mini-mum output power of +28 dBm, and this isentered in Item 26.
4.
He adds up the fixed losses and enters them inItem 16; adds the 5.5 dB total fixed losses tothe 141.5 dB path attenuation of Item 9, andthen enters the result, 147.0 dB, in Item 17.
9.By subtracting Item 27 from Item 26 (algebra-ically) he determines a maximum allowablevalue of 61 dB for the net path loss, andtentatively enters 61 dB in Item 25.
5.
10. He now subtracts the tentative value of 61 dBof Item 25 from the 147.0 dB total losses ofItem 17, and obtains a value of 86.0 dB as atentative value of the required total gains;entering this value temporarily in Item 24.
By subtracting the tentative 61 dB in Item 25from the 141.5 dB in Item 9, he determinesthat the total antenna gains, minus the fixedlosses, must be at least 80.5 dB, in order toproduce the desired value of net path loss.
6.
He divides 86.0 by two to obtain a prelimi-nary value of 43.0 dB as the required antennagain at each end of the path. (It is usually,though not always, most economical to havethe antenna gains divided about equally.)
11At this point, if he has not already done so, hewill make a tentative selection of the type ofantenna systems to be used. If other consider-ations are not controlling, the choice willprobably be based on the best combination,considering gain-efficiency and economics.However, frequency congestion or other con-siderations might have precluded the use of aperiscope system, or dictated the choice ofsome specific antenna arrangements.
'7
12. He determines that a gain of 43.0 dB at 6175MHz will require at least a 10' parabolicantenna. In this case he enters the gain figureas taken from Table I, 43.0 dB, as the gain ofthe Alpha antenna in Item 23, and enters 10'in the Alpha column for Item 19.We assume in this case, that the choice is a
direct radiating parabola at Alpha, mounted atthe top of the tower, and a periscope antennasystem at Beta.
13, By subtracting this 43.0 dB from the tentative86.0 dB of Item 24, he finds that 43.0 dB gainwill be needed from the antenna system at theother end. From Figure 27, using the -0.7 dBgain factor and the 1.09 dB distance factor forthe 6.175 band, he determines that a 12' x 17'reflector would be needed to meet the 43.0dB true gain requirement.
8. Having chosen the antenna system, he mustthen make a reasonably close estimate of theamount of waveguide required, and all otherapplicable fixed loss items. In this case hechooses WR137 rigid waveguide, and entersthe estimated lengths in Item 10. He alsoenters estimated lengths of flexible guide, forconnecting to equipment and antenna, in Item11. He calculates waveguide losses, using 2.0dB per 100 feet for the rigid and 0.1 dB perfoot (a typical value) for the flex, and entersthe total waveguide losses in Item 12.
At an apparent (chart) distance of 230 x 1.09= 251', a 6' dish and either a C.R. or a C.E.reflector would give an apparent ( chart ) gainof about 44.5 dB, or a true gain at 6.175 GHzof 44.5 -0.7 = 43.8, somewhat better than
the o bjective .If the requirements were deemedabsolute, this would be his probable choice.However, in this case we assume that the engi-neer for some reason does not want to use thevery large and heavy 12' x 17' reflector. In-stead he examines the next lower size, a 10' x15', and determines that at the apparent dis-tance of 251' a 6' dish and a 10' x 15' C.E.reflector will give an apparent gain of about42.6 dB, or a true gain of 41.9 dB at 6.175GHz. After.entering this value in Item 23 andcarrying out the necessary calculations, he
"Connector loss", Item 13, is a catchall itemfor small losses associated with pressure win-dows, bends and flanges. The value of 0.5 dBper end shown here, is a safe, probablyconservative, estimate for most; waveguideruns. ,
In this case there are no circulators or hybridsexternal to the equipment, so no entry ismade in Item 14.
109
8760 hours long, and the most widely used way ofexpressing propagation reliability is in terms of theunavailability or outage ratio, considered over aperiod of a year. Since fading phenomena inmicrowave;~stems generally follow a yearly cycle,the statistics for <;>ne year can be expected to begenerally representative of those for any other year ,and this parameter is thus a good measure of longterm reliability. (In some cases it is also useful ordesirable to look at U on a short term basis, forexample, the worst month or the worst hour of theyear). Another easy-to-understand way of specify-ing reliability is by the number of hours ofdowntime or outage per year. Thus we have:
bility , even on a non-redundant basis. But in orderto meet the extraordinarily stringent objectivesimposed by the need for extremely high-reliabilitylong haul systems, some form of redundant orstandby equipment is required.
Frequency diversity systems or space diversitysystems with hot-standby transmitters each provideessentially 100% redundancy for the microwaveequipment, and 1-for-N or 2-for-N multiline sys-tems provide essentially 100% redundancy which isshared among the working channels.
Systems of this kind, with standby as well asworking channels operating continuously" andequipped with monitor, alarm, and automatictransfer facilities, provide the basic elements forultra-high reliability. Equally important in achiev-ing such reliability are the kind and quality of themaintenance given to the system. For example, an outage or downtime of .876
hours (about 53 minutes) per year would giveThese techniques for engineering and opera-
ting microwave systems to achieve extremely highreliabilities are well-known and well-developed, andthey can be applied with confidence based on thedemonstrated effectiveness of such techniques onexisting systems.
.8768760
= 10-4 = .0001u=
which corresponds to an annual "availability" A of.9999, or 99.99%; the term availability in reliabilityengineering circles has the same meaning as theterm 'reliability' as commonly used by microwaveengineers.
But the techniques of making a priori predic-tions of the reliability performance of proposednew systems have been less well-developed and haveplayed little part in the developments leading tohighly reliable systems. Most of these developedmethods have been empirical, as a result of accumu-lated experience.
As discussed in an earlier section, per hopreliability objectives of 99.9999% are notuncommon for modern long-haul systems. Thiswould require a value of U of .000001, correspond-ing to .00876 hours or about 32 seconds per year.Where these objectives include all sources of out-age, it means that equipment outages also must beheld to comparable levels.
Section IV-C-(ll) provided means for calcula-ting the probability of a propagation outage for amicrowave path, as a function of a number ofpertinent parameters. The calculations were deve-loped in terms of a parameter "0", called "unavail-ability", also referred to as the probability of
outage,
(Note: It is worth mentioning that al-though it has only recently been recog-nized, CCIR objectives for allowableshort term noise not to be exceeded forspecified very small percentages of time,do not include the effects of outages dueto equipment failure, but only the per-formance during those periods of timewhen the equipment is in operatingcondition. The problem of total reliabil-ity or availability has only recently comeunder study by CCIR and is in a prelimi-
nary stage.)
This unavailability parameter is simply theratio, defined over any given period of time, of theoutage, or "downtime" to the total, or "down-time" + "uptime". Thus;
Down-time:U = Down-time = -
Total-Time Down-time + Uptime
The most natural period of interest in connec-tion with microwave systems is the year, which is
112
Reliability engineering techniques have beendeveloped for calculating, a priori, the probabilityof successful operation of a component, unit, orsystem over any given time period, as a function ofthe number of components involved and theirfailure rates, the latter being assumed to beconstant with time ("Early failures" and wear-outfailures are excluded). Source data for failure ratesis usually some document such as MIL HDBK217-A, or some comparable industry data.
corresponding to an "availability" of 99.99%.Mathematically we could bring this up to the99.9999% level by reducing the MTTR to .01hours, that is, about 36 seconds, but in practice thisis an impossibility .In fact, when one considers thatmicrowave systems consist in general of a numberof unattended stations spac~d a considerable dis-tance apart, and that failures can occur at any hourof day or night, week-ends and holidays included, itseems highly optimistic even to assume a value aslow as one hour for the "mean time to repair",including travel time, time to diagnose the trouble,make repairs or change out units, and get thesystem back in service. Even two hours will be anoverly optimistic assumption in areas where re-peater sites are remote or difficult of access.
By starting with some basic source data, andmaking a number of assumptions, it is possible tocalculate for each unit or item of equipmentcomprising a microwave system a parameter "meantime between failures", abbreviated as MTBF ,usually expressed in hours. To the degree that thecalculated MTBF is valid, it represents the averageperiod of time the unit will operate without failure,considered over an indefinitely long period of time.(Actual field data on measured MTBF's are ofcourse much preferable, but are difficult to obtainwith high reliability equipments because failurerates are so low).
If one must assume a relatively long averagerepair time, such as an hour or more, the only wayto achieve an extremely low value of U is togreatly increase the denominator of the equations,the MTBF .
The relationship is very simple. In order to get anavailability of 99.9999% we must have a U of.000001, or 10-6 and the MTBF must be 1,000,000times the MTTR. If the repair time is 1 hour, theMTBF must be 1,000,000 hours, and if the repairtime is 2 hours, the MTBF must be 2,000,000hours.
If the MTBF of the total equipment compris-ing a microwave hop is known, and if anotherparameter called "mean time to repair", abbrevia-ted MTTR, is known or can be assumed, theequipment unavailability or outage ratio for thehop is given by:
These are truly staggering figures. Convertedto years, the MTBF of 2,000,000 hours means thaton the average there will be one failure on the hopevery 228 years. Surprisingly enough, it is possible,if certain requisites are met, to show calculated perhop MTBF's of this order of magnitude, by the useof redundancy in the form of 100% operationalstandby. The requisites are: high (but not astrono-mica!) basic reliability in the equipment comprisingeach side of the redundant pair; monitor, alarm andswitching facilities which detect and report anyfailures and automatically switch to the good side ifthe other side has failed; a sparing and maintenanceprogram which results in relatively quick repairs ofall "minor" or one-side failures, in order to keepthe time during which the path is operatingnon-redundantly as low as possible. (The "redun-dancy improvement factor", somewhat similar tothe diversity improvement factors, is essentially theratio of total time over a given period to thenon-redundant time during that period.)
(29)
In high reliability systems MTBF > > MTTR,and the following' approximation, which greatlysimplifies the mathematics, is quite accurate:
MTTRMTBFu= (30)
To illustrate, suppose that the MTBF of thehop equipment is 10,000 hours, that is, on theaverage a little less than one failure per year, andthat the MTTR, that is, the average period ofoutage after such a failure, is 1 nour. We then have:
1
10,000
u= = .0001
113
The following equation gives the calculatedMTBF of a fully redundant block (for example, aone-way frequency diversity hop) in terms of theMTBF of the total equipment comprising onecomplete side of the redundant block, and themean time to repair and restore a one-side failure:
!~ip--~~ ~v~il~b..!!i~ ~~c~~i~~
The calculations can be formally extended toprovide a means of calculating the availability for aredundant ~ock (in terms of its time complement,the unavailiibility or outage ratio U), as follows:
~
2Tl
T2
m
2 TI T2= M2m=
(31: Jr =(33)
where mM
TI
is the MTBF of the redundant blockis the MTBF of one complete sideis the mean time to repair andrestore a one-side failure.
where Or is the outage ratio for the redundantblockm, M and TI are as in (31) andT 2 is the mean time to repair and restorethe system after a both-side failure (anactual system outage).
As an example, consider a hop with redundantequipment having a one-side MTBF of M = 10,000hours, or 104 hours, and assume a value of 10hours for T 1. We then have:
T 2 is simply the mean time to get one or the otherside repaired and back in service, and thus is asomewhat complicated parameter .
108
20
= 5,000,000 hoursm= A calculation approach which is simple andconvenient mathematically is to assume each of thetwo one-side failures which cause the system outageis repaired independently, as if the other did notexist, and that the repair time for each is T 1 .Underthis assumption, it can be shown that:
as the MTBF of the redundant block.
The "redundancy improvement" is given by:
TIred =(32) T =-2 ? (34)
M2 TI
which in this case would be 10,000/20 or 500 to 1. giving
(Caution: This analysis excludes anyequipment outside the fully redundantportion, and also assumes that switchingis perfect and that there is no degree ofcommonality in the joining and splittingdevices. In practical situations theseother effects usually come into play andmay reduce the true overall MTBF by anorder of magnitude or more, below thatcalculated by the above equations. Theanalysis also is based on an assumptionthat failures on the two sides are randomand are completely independent and un-correlated, an assumption which may notalways be correct. For these and othersimilar reasons reliability calculations ofthis type should be viewed with consider-able caution).
( 33A)(-!Kf)
Although the above assumption is a convenientone, it is unrealistic when applied to real systems,where a true system outage generates much morepressure to make a quick repair and get the systemback in operation.
If, instead of a "robot repairman " assumptionas above, we consider a real life situation where themaintenance man will immediately be aware whena "both side" failure has occurred and will thenassess the situation and act to repair the side whichcan be restored in the shortest time, it can beshown that T2 can be derived from the following:
14
L
2TI TIur=M2 x 2
transmitters and one for receivers. In thiscase the calculations would be madeseparately for each of the redundantblocks, and the resulting Ur(transmit)and Ur(receive) added together to getUr(total) .
T32
.2 TI (35)T2 = T3
where T2 and TI are as defined in (33) andT 3 is the "mean time to repair and
restore one of the two one-sidefailures causing an outage ", using allavailable resources and maximumeffort to reduce travel time, but alsoassuming that the two failures oc-curred simultaneously or that at thetime of the second failure no starthad been made on repairing the firstfailure.
!v~~b.!!i!¥ ~s ~ ~ar-~e~~
Although the derivations of "availability"calculation methods (through the complementaryparameter unavailability or U) are formally andmathematically correct, there are some very seriousdrawbacks when one attempts to use this parameteras a measure of the reliability performance, withrespect to equipment, of a highly reliable redun-dant system.giving:
~~..kft ) =Ur = M2One basic requirement which must be met if
the U parameter is to be useful is that the period ofinterest must be sufficiently long as to provide areasonably good statistical sample of events ( eachindividual outage constituting an event).
T32
2 (T T -~)1 3 ~
M2
(33B)
(Note that if the "robot repairman " assumption is
made, T 3 becomes equal to T 1 and 33B reduces to33A, as it should).
In considering propagation outages, over aperiod of a year there might be perhaps two-thousand individual one-side events each lastingperhaps 3 or 4 seconds on the average ( one sidefade below threshold), and with appropriate diver-sity perhaps 10 individual both-side events eachlasting perhaps 2 seconds (both sides simultane-ously faded below threshold), giving an "annualoutage" of 20 seconds. Thus the period of a year islong enough to get a reasonable statistical sample,and calculated annual outages in this range couldexist on a real system so that the calculated valuescould be tested and measured in the field. So thecalculated U or the annual outage is a goodparameter in this case.
Carrying on with the previous example, as-sume M = 10,000 hours, T 1 = 10 hours, and furtherassume that T 3 = 3 hours.
The simple assumption of (33A) would give
( 10 ) 2 Or = 1Q4= 10-6 = .000001
or an "availability" of 99.9999%.
The "real life" assumption of (33B) wouldBut in the case of the equipment example
discussed above, an entirely different situationexists. The number of events is very small, and thelength of each event is very large. If the MTBF, ascalculated in the example, is 5,000,000 hours, therewill be on the average, over a sufficiently long time,about 1 failure every 570 years. Even if the hopwere to be operated for a thousand years, we wouldhave only a modest statistical sample of about 2"events". For periods shorter than a millenium, Uwould have little meaning, and for periods of a yearor even of the entire useful life of a microwave hop(15 to 20 years) it would have essentially nomeaning at all.
give32
2 (10 x 3 -2) 51 = 00000051
=lQ"S .108Ur=
or an availability of 99.999949%.
(Note: in a one-way frequency diversityhop there is only one redundant ,ljlock.But in a hot standby system, or a hotstandby transmitter-space diversity re-ceiver system, there are two separate andindependent redundant blocks, one for
115
and (37) by
R(8760) = 1 8760/m (37A)
Looking at it another way, if the mean timebetween failures is 570 years, we will have -on theaverage -one 570th of a failure every year.Mathematically if it takes 5 hours to repair one
failure, it will take 5¥0 hours to repair one 570th
of a failure. Five 570ths of an hour amount toabout 32 seconds, confirming the previously calcu-lated value of annual outage corresponding to thisexample.
For our previous example, with an m of5,000,000 hours, (37A) gives a probability of.99825, or 99.825%, that the hop will operatewithout failure for a period of a year, under theassumed conditions.
Though mathematically acceptable, fractionalfailures cannot exist in real life, and as a resultneither availability, unavailability, or annual outageis a suitable measure for equipment reliabilities inthis range. These quantities are useful and meaning-ful with respect to propagation reliability, but -asshown above -have little or no value with respectto equipment reliability. If one observed such anequipment over the course of a year, there wouldbe a very high probability of no outages at all. Butin any year in which an outage did occur, theunavailability would be extremely high and in factwould use up all the outages allowable for a 570year period. There is thus no way at all of checkingsuch calculations in the field.
This is perhaps the best way of expressingequipment reliability in such circumstances. Al-though neither the R parameter nor the m para-meter from which it is derived can be tested againstfield experience (because even the full expected lifeof the equipment is too short a time frame for it),the two quantities M and Tl in the expression (31)which gives the value of m are testable. Data takenover one hop for several years or over a number ofhops for one year on the number of one-sidefailures and the average time taken to repair themcan be directly checked against the calculatedestimates, and can be used in (31) and (37) insteadof the a priori calculated values. In this way anindirect check on the m and R parameters can bemade.What Alternatives?
The value of m as calculated from (31),preferably divided by 8760 to give the "mean timebetween failures, in years " is a good measure of
reliability for a redundant block.
It is clear also that propagation reliability andequipment reliability are completely different incharacter and should be treated separately ratherthan lumped together. Propagation reliability iswell and usefully described either by an availabilityparameter or by an annual outage parameter, butequipment reliability is not.
Another possibility is to use the followingequation to calculate the probability that theredundant block will operate without failure over aperiod of time t. The complete reliability parameter describing
such a hop would be in two parts, a "0" oravailability parameter for propagation and an "R"or probability of no outage for a year as theequipment parameter .
R(t) = e-t/m (36)
For a period of a year, this is 4. Power ReliabilityConsiderations
R(8760) = e-'-8760/m (37) The reliability of the power source supplyingthe equipment, is an extremely important factor inoverall reliability. Systems operating directly froma primary AC power source will be subject to anoutage whenever the power fails, even for a fewseconds. Even in areas with highly reliable primarypower, this is ordinarily not adequate to meetnormal system reliability standards. Consequently,
When m is very much greater than t, (36) is
accurately given by:
R(t) = 1 tim (36A)
116
obtain the total noise. Again, we use thecurves of Figure 23B. The intrinsic +intermod noise of 20 dBmcO or -70dBmOp can be converted to pWpO usingTable E, and is found to be 100 pWpO.
almost all microwave systems requiring high relia-bility are arranged with some provision for locallygenerated standby power, on a "no break" basis~The most satisfactory , and the most commonlyused method, is to operate the microwave equip-ment from a storage battery plant, which iscontinuously charged or "floated " to maintain it at
full capacity. The battery itself will take care of allshort outages, and a standby generating plant isprovided to switch on in case of longer outages.
The thermal noise is read for a receivelevel of -39.1 dBm instead of -34.1dBm, and is also found to be approxi-mately 20 dBmcO or 100 pWpO.
The total noise for the hop is then 200.0pWpO.
Noise Performance Calculationsc.
1. Microwave N oiseWe can again refer to Table E to find thatthis is 23.0 dBrncO; about 1.5 dB highernoise than calculated for the same systemusing the N orth American method.
Just as in the case of reliability, the startingpoint for system noise performance calculations isto ~alculate the noise for each individual hop, thenuse these results to calculate the system noise.
This serves to illustrate why systemsengineered using the CCIR approachoften must be provided with several dEhigher median signal levels, in order to beable to meet noise requirements under anassumed condition of a 5 dB fade. Theextra dB are often very expensive to
implement.
We will first calculate the noise performancefor the hop of Figure 29 by the N orth Americanmethod, then by the CCIR method as used inter-
nationally.
North American Method
In the N orth American method, the noiseis calculated for the condition of anunfaded signal and busy hour loading.From a curve such as Figure 23B (whichis appropriate for the particular equip-ment used in this example ), the totalnoise can be read directly as a functionof the received signal strength. In thiscase it is seen to be at approximately21.5 dBmcO for a received signal of-34.1 dBm. Or, one could read separatelythe intrinsic plus intermodulation noiseas 20 dBmcO and the terminal noise at-34.1 dBm input as 15 dBmcO, andcombine the two noises on a powerbasis to obtain 21.2 dBmcO, approxi-mately the same result, using Table G.
Although curves such as Figure 23B are usefuland simple to use, they are not essential to noisecalculations. An equally accurate calculation can bemade by calculating the thermal noise from theknown system parameters, using Equation (22),and adding in the intrinsic + intermodulation noise,which must be obtained from the manufacturer's
specifications.
In either the North American approach or theCCIR approach, the estimated microwave-contributed noise for a multihop system is obtainedby adding up the individual hop noises on a powerbasis. This is particularly easy to do when noises aregiven in pWpO, since they can be added directly.When the individual noises are expressed in dBmcOor dBaO, it is necessary to combine them two bytwo, using Table G, and continue the process untilall the powers have been included. If all hops havethe same noise power, the noise power of an N-hopsystem will be lO loglON dB higher than the perhop noise power, or N times the per hop power in
picowatts.
CCIR M ethod
In the CCIR method, it is commonpractice to; (1) show the intermodulationand thermal noises separately, (2) makethe thermal noise calculation With thesignal faded by approximately 5 dB, tosimulate the "any hour" requirement,and (3) show the noise values in pWpO,which can then be added directly to
Power addition of noise powers on a multihopsystem is based on two conditions; (1) that theequipment design is such that the odd-order inter-
117
modulation products, some of which tend to addon a voltage rather than a power basis, are verymuch lower than the even-order intermodulationproducts, and (2), that in very long systems,provisions are made to break up the basebandpattern at intervals of about 10 hops (mostcommonly by random supergroup and group inter-connections at the sectionalizing point in high-density telephone systems, or by similar intercon-nections or by filter sectionalizing in industrialsystems). If these conditions are met, it is con-sidered that the system noise will be essentiallypower additive. Note that if either of these twoconditions is not met, the assumption of poweraddition of multi-hop noise is not necessarilycorrect. Depending on the relative conditions, thepower in such cases can be expected to combine ona basis somewhere between power and voltageaddition.
Echo distortion noise is calculated for eachend of each path separately, and in multihopsystems, all of these noises are added on a poweradditive basis, to the other system noises.
3, ~~x Noise
This is normally simply taken from the manu-facturer specifications, and added in with the othersystem noise contributors. For illustrative purposes,consider a loaded multiplex noise contribution of23 dBrncO, or 200 pWpO per channel.
4 Total Noise Estimates
North American Method
21.0 dBrncO
10.0 dBnrcO
23.0 dBrncOFor illustrative purposes, assume a value of 28
dB equipment return loss, and a value of 26 dB forthe lumped waveguide-antenna return loss. Fromthis data, and a knowledge that the waveguide atAlpha is 100' long (approximately 2 dB loss), andthat at Beta is 25' long (approximately 0.5 dB loss),we can use Figure 24 to obtain an estimated valueof echo distortion noise.
Radio equipment noise,busy hour loadingEcho distortion noise,busy hour loadingMultiplex noise, busyhour loading
Total noise for complete trunk 25.3 dBrncO
This value is some 4.7 dB better thah theobjective given in Table H for 0 -50 mile intertolltrunks.
CCIR Method
Alpha: Equipment noise, busyhour loading ( 5 dB faded)Echo distortion noise
Total microwave noise
200.0 pWpO
Beta: 10.0 pWpO210.0 pWpO
Total
Noise = 70.5 -28 -26 -4= 12.5 dBrncO = 18.0 pWpONoise = 58.5- 28- 26 -1= 3.5 dBrncO = 2.2 pWpO
Noise= 13.0 dBrncO = 20.2 pWpO CCIR allowance for the microwave noise ( does
not include multiplex) would be approximately 3 x50 + 200 = 350 pWpO. (For paths less than 50kilometers, as this one just is, the noise allowance istreated as if the path were 50 kilometers. )
The 13.0 dBrncO is the estimated echo noisein the top channel of a system without emphasis. Ifthe emphasis is used, as it normally would be, theecho noise would be reduced by some 3 dB, toabout 10.0 dBnrcO. The calculated noise is approximately 2 dB
better than the objective.Adding the echo noise to the 21 dBrncO radio
equipment noise contribution, would increase thelatter by slightly less than 0.5 dB. Though such anincrease would be of little significance in a one-hopsystem, the accumulation of a number of suchcontributions in a long system would be significant.
In specifying, listing and calculating noisesfrom a great many sources, which are assumed tobe additive on a power basis, the picowatt is a veryconvenient noise unit, since the total noise issimply the arithmetic sum of the individual noises.
Echo noise can be reduced, dB for dB, byimproving either the equipment or the antennasystem return losses, and of course, the noise willincrease if the return losses decrease.
On the other hand, the logarithmic noise unitsare much more meaningful as to the actual effectsof noise changes, and a logarithmic form is the onlyconvenient form to use in system measurements
18
and maintenance. The North American approach isto use units in dB form for both purposes, simplytolerating the slight inconvenience in adding powersexpressed that way. The CCIR method generallyuses picowatts for specifications and calculations,
but reverts to some logarithmic form, such as thedBmOp, for measurements and maintenance usage.There are advantages and disadvantages to bothapproaches.
AN IMPORTANT POST SCRIPT ABOUT THE PROPAGATION CALCULATIONS
As stated on Page 55, the methods of calculating propagation outages used in thisbook are based on previously reported work by W. T. Barnett and Arvids Vigants ofBell Telephone Laboratories.
At the June, 1970 International Communications Conference in San FranciscoMr. Barnett gave an updating report on his work, based on the continuing study andanalysis which has gone ?n in the past year .Based on this further study, Barnettnow proposes a modification in the frequency term in the equation describingnon-diversity fading. The modification changes the frequency term in Equation(IIB) from (f/4)1 .5 to (f/4).
The effect of this modification is to make the calculated outage a linearlyincreasing rather than an exponentially increasing function of frequency. Outagescalculated according to the original equations, as used in this book, can bemultiplied by ( 4/f)° .5 to convert them to outages in accordance with the modified
formula. The value of this modifying factor is: 2 GHz 1.4; 4.0 GHz 1.0; 5.0 GHz0.9; 6.2 GHz 0.8; 6.7 GHz 0.77; 7.8 GHz 0.72; 8.7 GHz 0.68; 9.~ GHz 0.65; 11.2GHz 0.60; 12.4 GHz 0.57.
As can be seen, the maximum change resulting from the modification is limitedto about 40% difference in the calculated outage, and for the bands of most interest-those from 4GHz up -the outages calculated by the original methods are moreconservative (greater indicated outage) than the modified version. However, weconsidered it necesSary to modify the methods proposed with this printing.Consequently, the following changes have been made in the book itself:
In Equation (1IB) which appears on Page 59, the frequency term has been changedfrom (f/4)1 .5 to (f/4).
In Equation (12) which appears on Page 60 and again in Appendix Ion Page A2,the frequency term has been changed from f 1.5 to f, and the
constant factor from 1.25 to 2.5.In the metric version of Equation (12), which appears in Appendix II on Page B2,
the frequency term has been changed from f1.5 to f, and theconstant factor from 3.0 to 6.0.
It is emphasized that the experimental and theoretical studies are continuing, andother modifications may very well be reported at some future date.
NOTE:It is important to note that graphs, formulas and methods for calculating outagesthroughout the book are all for one way outage. To calculate two way outages it isnecessary to double the ,calculated multipath and equipment outages. Outages dueto rain or to non-selective fading do not have to be doubled since they occur simul-taneously in both directions of transmission.
119
APPEND IX IUSEFUL FORMULAS AND EQUATIONS
Text ReferencePage Number
Earth Curvature
dl xd2
1.5K
h= 12
h (K = 00) = 0 (lA) 12
dld2
2
h (K = 4/3) =lB) 12
lC)h (K = 2/3) = dl d2 12
h (K = 1) = .67 dl d2 (ID) 12
h in feet. d's in miles
Reflection Point Relations
hl
dl
dl hz
2-d-;
d2
2
For K = 4/3; (2C) 17
hl
dl
h2
="<1;
For K = 2/3;dl d2 (2B) 17
hldl =nD where n =~
h in feet, d and D in miles
For K = 00; (2A) 17
Path Attenuation
(3) 35AdB = 96.6 + 20 log10 FGHz + 20 log10 Dmiles
Fresnel Zones
lst zone ; (4A) 38I dl d2
F 1 = 72.1 V FQH;:D
(4C) 38nth zone; Fn= F]
F 1 in feet d and D in miles
At
Text ReferencePage Number
Fictitious Earth Radius
K=~
157+.
(9B) 44dNdh
~ is gradient in N units per kilometer
51Heavy-route, or highest reliability systems:
At least O.3F 1 at K = 2/3 and at least 1.0F 1 at K = 4/3,whichever requires the greater heights. (In areas ofvery difficult propagation, it may be necessary a1~o toensure a clearance of at least grazing at K = 1/2).
All criteria should be evaluated along entire path.
51Light-route, or medium reliability systems
At least 0.6Fl + 10 feet at K = 1.0
Vertical Diversity Spacing For Reflective ~aths
2.2 x 103 DFGHz x ht (10A) 596h2 = or
(see Text)
1.3 x 103 DFGHz x ht lOB) 59
h's in feet, D in miles
Fading Outages and Diversity hnprovement Factors
Undp=axbx 2.5xlO-6 xfxD3 xlO-F/lO (12) 60
~
I13) 60
A2
Text ReferencePage Number
Fading Outages and Diversity Improvement Factors (Continued)'
llf
fx lOF/lOIfd(4) = 1/2 x
(14A) 60
x lOF/lO (14B) 60
~f
f
x 10F 110Ifd(7-8) = 1/8 x (14C) 60
(140) 60
ICBD = 100(IS) 61
(16) 61
(17)Ihyb = ISD 61
k2 = (18) 61I
lOF/lO
Noise Threshold
N = -114 + 10 log10 B (IF) MHz + FdB(20) 68
FM Improvement Threshold
TFM = -104 + 10 log10 B (IF) MHz + FdB(21 68
Noise Units Correlation
69
(Precise: 67s -)
Nflat
A3
Text Reference~age Number
Thermal Noise In Derived Channel
t:.f
.O~
dBrncO = -C- 48.1 + FdB 20101 (22A) 68
~fdBaO = -C 54.1 + FdB 20 log10 fch (22B) 68
(22C) 68
(220) 68
Video Noise
(22E)~ .N (unwelghted, unemph) = C
rms
FdB + 118 70
(22F) 70FdB + 126.5~N (EIA, emph, EIA Color wtg) = Crms
Noise Loading
p= -15 + 10 log10N) dBmOCCIR when; N = 240 or more (23A) 73
(23B) 73p = (-1 + 41og1ON) dEmO when; N = 12 to 240CCIR
(23C) 73Bell p = (-16 + 10 log10N) dBmO
(23D) 73Military p= -10 + 10 log10N) dBmO
Parabola Gain
(24) 90EGdB = 10 log10 (41TAX2)
25) 90GdB = 20 log10Bft + 20 log10 FGHz + 7.5
A4
Text ReferencePage Number
3-dB Beamwidth
4> ~ r -' .for parabola (26) 9170
q, ~ r -~ , for elliptical reflector6099
524> ~ F W for rectangular reflector
.GHz ft
2-Way Free-Space Billboard Gain
(27) 100GdB = 22.2 + 40 log10 FGHz + 20 log10Asqft + 20 log10 cos 0:
Approximat~ear Zone Boundary
dft = 2 FGHz B2 ft (28) 100
AS
Text ReferencePage Number
~~~-~~(Metric )
ra-;-d;-Fl = 17.3VFGH;Ij"lst zone 38
Fn =Fl~nth zone 38
F in meters, d's and D in kilometers
Vertical Diversity Spacing for Reflective Path (Me~i~)
127 x D&2 = FGHz x ht , 59or
5975xD
FGHz x htl
d12
17
ht, = h 1 (See text) 59
h's in meters, d and D in kilometers
Fading Out~ges and Diversity (Metric )
x f x D3 X lO-F/lOUndp = a x b x 6.0 x 10-7 60
61
f fu GHz, s in meters
D in KMS, F in dB
The other equations in this section are unchanged
~arabola Gain (~
GdB = 20 log10 B + 20 log10 FGHz + 17.8 90
B is in meters
B2
1.2 x 10-3 x f x S2 X 10F/10
Text ReferencePage Number
3-dB Beamwidth (Metric )
for parabola 9122<1> ~ FGHz B
for elliptical reflector 9919<I> ~ FGHz B
for rectangular reflector 9916IP ~ FGHz W
<1> in degrees, B and W in meters
2-Way Free-Space Billboard Gain (Metric)
GdB = 42.9 + 40 log10 FGHz + 20 log10 A + 20 loglO cos cx:
A is in square meters
Approximate Near Zone Boundary (Metric )
dmtrs = 6.6FGHz B2
B is in meters
B3
Suggestions for use of Figures
kilometers, and subtracting 4.2 dB from the atten.uation reading.
Figure 3:Earth Curvature for Various Values of K.
The generating equation is Figure 15:The 1st Fresnel Zone radius chart can be used byconsidering the D and the d 's to be in kilometers,and dividing the value read on the F scale by 4.17to obtain F in meters.
d2
12.75 K
h=
The multiplying factors of Tables Bl and B2 canthen be applied to convert the readings for fre-quency bands other than 6.7 GHz, or for higherzones.
where h is in meters and d in kilometers.
If the distances on the d scale are considered torepresent kilometers rather than miles, the valueread on the "departure" scale must be multipliedby 0.118 to obtain h in meters. Figures 21 and 22:
Convert the distances shown in miles to kilometersby multiplying by 1.609. The charts can then beread directly.
Figure 4:Though the curves of Figure 4 were designed foruse with miles, feet, and 10-division-per-inch rec-tangular graph paper, with a basic scale of 1"horizontal = 2 miles, 1" vertical = 100', it turns out
that by good fortune they can also be used withkilometers, meters, and 10-division-per-centimeterpaper, with a basic scale of 1 cm horizontal = 1kilometer, 1 cm vertical = 7.5 meters, and also witha scale of 1 cm horizontal = 2 kilometers, 1 cmvertical = 30 meters.
Figure 24:The best way to use this chart is to convertwaveguide length in meters to feet by multiplyingby 3.28, then enter the chart with the reading infeet.
Figure 25:The dimensions shown in feet can be converted tometers by multiplying by 0.3048. Areas shown inacres can be converted to square meters by multi-plying by 4047.
A very slight error is incurred, amounting to aboutone part in 400 in the corresponding elevationreadings, but it is considerably lower than theaccuracy with which the charts themselves can beread so is inconsequential.
Figure 27:Since these charts are for specific sizes of standardreflectors and antennas dimensioned in feet, theycould not be directly used for metric-dimensionedreflectors and antennas.
Alternatives are use of the direct calculationmethods described in the text, using the metricversions of (lB), (lC) or (lD), as required, or touse ( 1) or the metric generating equation for Figure3 to construct metric templates with other scalevalues.
Figure 28A :This chart is also for specific sizes of reflectordimensioned in feet, and could not be used directlyfor metric-dimensioned reflectors.
Figure 7:The reflection point charts can be used directly
using
Figures 28B, C, D:These charts are dimensionless, and require onlythat all dimensions be in the same units.8.5h2
D2
8.5hlX = 2 and y =
D
Inverse Position Azimuth and Path Distance calcu-lations. The method produces distances in bothkilometers and feet, so can be used in either set ofunits.
where the h 's are in meters and the D 's inkilometers.
Figure 13:The free-space attenuation chart can be useddirectly by considering D to be the path length in
B4
APPENDIX IIIUSEFUL TABLES AND FIGURES
Table C. Excess Attenuation Due To AtmosphericAbsorption. P-51
PATHLENGTHMILES
20
40
60
80
100
Table D. Relationship Between System Reliability And Outage Time P-56
OUTAGE TIME PEROUTAGETIME
%RELIABILITY
0;0MONTH
(Avg.)DAY
(Avg,)YEAR
8760 hours
4380 hours
1752 hours
876 hours
438 hours
175 hours
88 hours
8.8 hours
53 minutes
5.3 minutes
32 seconds
720 hours
360 hours
144 hours
72 hours
36 hours
14 hours
7 hours
43 minutes
4.3 minutes
26 seconds
2.6 seconds
24 hours
12 hours
4.8 hours
2.4 hours
1.2 hours
29 minutes
14.4 minutes
1.44 minutes
8.6 seconds
0.86 seconds
0.086 seconds
0
50
80
90
95
98
99
99.'-
99.'
99.(
99.!:
100
50
20
10
5
2
0.1
0.01
0.001
0.0001
Cl
)
19
'!99
1999
P-92
*SEE NOTE ON PAGE 80
Table I. Antenna Gains for &timating Purposes
Plane Polarized Parabolic Antennas. (DP's, HP's and Cross-band somewhat lower)
Diameterin feet ";-;--;;;;:;12 GHz 13GHz
35.2
38.7
41.1
43.0
44.6
46.0
35.9
39.4
41.9
43.9
45.5
46.9
37.0
40.6
43.1
45.2
46.7
48.7
40.3
43.8
46.0
47.7
41.3
44.8
47.3
48.5
8X8 (Std)
6 (Circl
39.4
35.7
43.0
39.4
47.4
43.8
C2
P-69Table E. Noise Unit Comparison Chart.
dBaO pWpO I dBmOp S/NdB dBrncO IdBaO dBmOp I S/NdBdBrncO
a
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
pWpO
-6
-5
-4
-3
-2
-1
O
1.0
1.3
1.6
2.0
2.5
3.24.0
5.0
6.3
7.9
10.0
12.6
15.8
20.0
25.2
31.6
39.8
50.1
63.1
79.4
100
126
158200252
316
398501
631
794
1000
1259
1585
1995
-90 88-89 87-88 86-87 85-86 84-85 83-84 82-83 81-82 80-81 79-80 78-79 77-78 76-77 75-76 74-75 73-74 72-73 71-72 70-71 69-70 68-69 67-68 66-67 65-66 64-65 63-64 62-63 61-62 60-61 59-60 58-59 57-58 56-57 55
343536373839404142434445464748495051525354555657585960616263646566
28293031323334353637
.3839404142434445464748495051525354555657585960
2520
3162
3981
5012
6310
7943
10,000
12,500
15,850
19,950
25,200
31,620
39,810
50,120
63,100
79,430
100,000
125,900158,500
199,500
252,000
316,200
398,100501,200631,000
794,300
1,000,000
1,259,0001,585,000
1,995,000
2,520,000
3,162,000
3,981,000
-56-55-54-53-52-51-50-49-48-47-46-45-44-43-42-41-40-39-38-37-36-35-34-33-32-31-30-29-28-27-26-25-24
545352515049484746454443424140393837363534333231302928272625242322
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Table E shows the relationship between five commonly used units for expressing noisein a voice band channel. In the first four columns, the units represent weighted noise at apoint of zero relative level. In the fifth column the "S" represents a tone at zero relativelevel, and the "N" represents unweighted noise in a 3 kHz voice channel, therefore, SINis the dB ratio of test tone to noise.
The table is based on the following commonly used correlation formulas, which includesome sligpt round-offs for convenience. Correlations for Columns 2, 3 and 4 are valid forall types of noise. All other correlations are valid for white noise, but not necessarily forother types. ;
88 SINdBrncO = 1010910 pWpO = dBaO + 6 = dBmOp + 90
C3
I,;,,,,
C4
CS
C6
C7
FRESNEL ZONE NUMBERS ---1 2 3 4 5 6
wu«0..(/)wwI:(:L1.
2:aI:(:L1.m"0
-0.5 0
R = Reflection Coefficient
0.5 1.0CLEARANCE
1.5 2.0 2.5
FIRST FRESNEL ZONE
Figure 14. Behavior of Attenuation vs. Path Oearance for VariousTypes of Obstruction
C9
0-.!'f')
~
Ns11")r--.--.0-~
.=~~o
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L
ClO
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P;.48
*2~---m"0
(5
1-<!::>zw1-1-<!
60 ~o 10020 30 405 6 8 103 4FREQUENCY GHz
Attenuation in rainfall intensity of: A, 0.25 mm/hr (drizzle) -.01 in/hrB, 1.0 mm/hr (light rain) -.04 in/hrC, 4.0 mm/hr (moderate rain) -.16 in/hrD, 16 mm/hr (heavy rain) -.64 in/hrE, 100 mm/hr (very heavy rain) -4.0 in/hr
F, 0.032 gm/m3 (visibility greater than 600 meters)G, 0.32 gm/m3 (visibility about 120 meters)H, 2.3 gm/m3 (visibility about ~o meters)
Attenuation in fog or cloud:
*Attn dB/mile = 1.61 x (Attn in dB/km)
Figure 18. Attenuation Due To Precipitation (after CCIR)
C13
p-so
(/)0:::)OI
z
w~
1--W<:J<2:1--:)0
15 20 25
PATH LENGTH IN MILES
30 35 40 45 50 607 8 9 106
Expected Outage Time fu Hours Per Year vs. Path Length in Miles For Various Areasof the United States. (Based on 11 GHz paths with 40 dB fade margin ; for 13 GHzpaths, reduce path lengths by 30%. For 45 dB fade margin, d~crease outage time by15%; for 35 dB fade margin, increase it by 25%).
Figure 20.
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W~WUZ«I-t/)0
Systems Engineering Memorandum
This memorandum describes a method for makingaccurate calculations of the true azimuths, at eachend of a path, and the path distance, for microwavepaths whose end coordinates (latitudes and longi-tudes) are accurately known.
distance, a degree of accuracy more than adequatefor path calculation purposes. Also, since the FCC'sprogram takes the same approach, it should giveresults identical to that program, and thus avoidhaving them change the applied for azimuths anddistances.
The method is an adaptation from the "InversePosition Computation " on page 14 of "Special
Publication No.8", Coast and Geodetic Survey;Formulas and Tables for the Computation ofGeodetic Positions. Factors (log B and log A) fromcertain tables in that publication are used in thecomputation. The tables list these factors for everyminute of latitude from 00 to 72°, but this degreeof accuracy is not needed for these calculations.Following the FCC approach, we have extractedfrom the table only those values of log B and log Acorresponding to integral degrees of latitude from0° to 72°, and the necessary values are given in theattached Table "Extracts From Special PublicationNo.8," so the publication itself is not required.
Note that the log Am factor is ~ways negative, thecharacteristic in all cases being 8.
Calculations are best made using six-place logarithmtables, though five-place tables will give reasonablyaccurate results.
Since the method takes into account the oblatenessof the earth, it gives more precise values than anuncorrected great-circle calculation method. (Forpaths longer than about 75 miles, the great-circlemethod sho1,1ld be used.)
Two calculation work sheets are included, one ablank which can be used to make reproductions,and the other with a sample calculation to illustratethe method.
The listed values are log Am and log Em/Am. LogEm alone is not used in our computation, so it isnot listed in the table. The subscript 'm' indicatesthat the values are taken for the average latitude ofthe path, the nearest value listed in the table beingthe one selected.
NOTE: The method will fail when the two stationshave exactly the same longitude. In this case, onestation will have an azimuth of 00 and the other anazimuth of 180°. For the distance calculation, logSmeters will be equal to log I::.. qJsec minus log Amminus log Ern/Am. Also, when the two stationshave exactly the same latitude, angle w is equal to0° and need not be calculated.
The errors introduced by using these factors to thenearest degree, rather than to the nearest minute oflatitude, will not exceed a few seconds in azimuthand substantially less than a tenth of a mile in
C29
~~Then w = Smtrs 47;.97t:11"
log. .000621 add6:7.9.!37t?
/. ~77~7r,Calculate (slide rule adequate )
C ~ (sin rf>m) log Smiles
/3'!75")
28.77?Smiles~(~
-:?--.:. ~ ~
Use wand C to calculate azimuths from folloWing
table: 90° 00' 00"+~ /?//
3 ?4:tw:tcCase 1 Northern Hemisphere
Sta E north of Sta W
Az at W is 90° -w -CAz at E is 270° -w + C
7
/~O £ EAz at W =
Case 2 Northern HemisphereSta E south of Sta W
Az at W is 90° + w -CAz at E is 270° + w + C
xAz at E =
2700 00' 00"
:t w +(,Z 1? //
:tc + 374
,3~ ° ~ ~
~ miles 4Z2£ kmsCase 3 Southern HemisphereSta E north of Sta W
Az at W is 90° -w + C°AzatEis 270 -w-C
Path length
(1) Log Bm/Am & log Am from attached tab14for tabulated latitude nearest to <l>m.
<;;age 4 Southern HemisphereSta E south of Sta W
Az at W is 90° + w + CAz at E is 270° + w -C
C30
C3
Latitude
(degrees)Latitude(degrees)
Log Am Log Bm/ Am Log Am Log Bm/ Am
8.509727726725723719715711705698691682673663652641628615601586571555538520502483464444423402381359336313290267243218
8.509194169144118093066042
8.5090168.508990
965939913888862837812787762738714690667644621599578557536516496478459442425409393
00010203040506070809101112131415161718192021222324252627282930313233343536
.002949
.002949
.002946
.002941
.002935
.002927
.002917
.002906
.002893
.002878
.002861
.002843
.002823
.002801
.002778
.002753
.002726
.002698
.002669
.002638
.002606
.002572
.002537
.002501
.002463
.002424
.002384
.002343
.002301
.002258
.002214
.002169
.002123
.002077
.002029
.001981
.001933
37383940414243444546474849505152535455565758596061626364
6566676869707172
.001884
.001834
.001784
.001733
.001683
.001631
.001580
.001529
.001477
.001426
.001374
.001323
.001272
.001221
.001170
.001120
.001071
.001021
.000973
.000925
.000877
.000830
.000784
.000739
.000695
.000652
.000610
.000568
.000528
.000489
.000452
.000415
.000380
.000346
.000313
.000282
~
C32
