NTIA Report 86-207 Algorithms Used in ARROWS: Autodesign of Radio Relay Optimum Wideband Systems ,L.G. Hause u.s. DEPARTMENT OF COMMERCE Malcolm Baldrige, Secretary Alfred C. Sikes, Assistant Secretary for Communications and Informati·on October 1986 I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I TABLE OF CONTENTS Page LIST OF FIGURES . vi LIST OF TABLES . . .... viii 1. INTRODUCTION . . . . 1 1.1 What are the Algorithms and What Do They Do? . 2 1.2 Who Can Benefit from Using These Algorithms? 5 2. ALGORITHM A: REPEATER LINK EARTH GEOMETRY 6 2.1 Passive Repeater Considerations . . . . . . 6 2.2 Antennas . 7 2.3 Path Distances and Azimuths 9 2.4 Calculation of Map Crossings ..... 11 2.5 Earth Geometry Output Formats . . . . . . . 14 3. ALGORITHM B: PATH PROFILE DATA AND EFFECTIVE-EARTH RADIUS 19 3.1 Path Profile Parameter Definitions .... 20 3.2 Earth-Radius Factor ..... 20. 3.3 Profile Data Output Format . . . . . . . . 21 4. ALGORITHM C: PRIMARY ANTENNA HEIGHTS . 26 4.1 Calculating Minimum Antenna Heights For Both Ends 26 4.2 Calculating Minimum Antenna Height with One End Fixed 28 4.3 Recommended Antenna Heights Output Format ..... 28 5. ALGORITHM D: PATH PROFILES AND RAY TRACES . . . . . . . . 31 5.1 Terrain Profile and Ray Paths . 31 5.2 Path Geometry and Meteorological Information 40 5.3 Antenna Elevation Angle . 40 5.4 Effective Path Length . 41 5.5 Minimum Ray Path Terrain Clearance. . . 41 5.6 Antenna Heights Above Ground . 42 5.7 Mean Atmospheric Pressure on the Ray Path 42 5.8 Mean Path Height Above Ground .... 42 5.9 Mean Terrain Elevation .... 43 5.10 Standard Deviation of Terrain Elevations 43 iii 6. ALGORITHM E: SITE ANTENNA OR REFLECTOR LAYOUT 44 6.1 Plane Mirror Orientation 44 6.2 Projected Area 45 6.3 Shadowing 45 6.4 Layout Output Format 45 7. ALGORITHM F: REPEATER SITE LOSS AND ANTENNA GAIN 52 7.1 Terminal Site Antenna Gains 52 7.2 Site Loss for Double Antennas 53 7.3 Site Loss for a Single Mirror Configuration 53 7.4 Site Loss for Double Mirrors 54 7.3 Site Loss and Antenna Gain Output Format 56 8. ALGORITHM G: MEDIAN BASIC TRANSMISSION LOSS 58 8.1 Free-Space Basic Transmission Loss (Inverse Square Loss) 58. 8.2 Atmospheric Absorption 58 8.3 Median Basic Transmission Loss Output Format 64 9. ALGORITHM H: BASIC TRANSMISSION LOSS VARIABILITY 66 9.1 Path Attenuation Due to Rain 66 9.2 Dutton Rain Attenuation Model 66 9.3 Probability Modification Factor 66 9.4 Rain Attenuation Coefficient 70 9.5 Probability of a Particular Point Rain Rate Value 72 9.6 Rain Rate Distribution Confidence Bands 73 9.7 Path Rain Attenuation Probability Distribution 74 9.8 CCIR Rain Rate Zone Model 74 9.9 Radome Loss 79 9.10 Mu1tipath Fading Distribution 79 9.11 Variability Data Outputs 81 10. ALGORITHM I: LINK CARRIER-TO-NOISE RATIO PROBABILITY DISTRIBUTION 85 10.1 Path Carrier-To-Noise Ratio . 86 10.2 Carrier-To-Noise Output Format. . . . . ... 92 11. ALGORITHM J: ANALOG RADIO SYSTEM SINGLE-RECEIVER TRANSFER CHARACTERISTIC . . . . . . . . . . 98 11.1 Noise Sources . . 98 11.2 Thermal Noise Calculation .... . . 99 11.3 Equipment Intermodulation Noise Calculation .... 101 iv 11.4 Feeder Intermodulation Noise Calculation . 102 11.5 Radio System Transfer Characteristic for FM/FDM Links 108 12. ALGORITHM K: FM/FDM LINK PERFORMANCE . 111 12.1 Noise Limit Requirements for FM/FDM Links . 111 12.2 Long-Term Performance . 113 12.3 DCS Short-Term FM/FDM Noise Limits. . . 114 12.4 Calculating Link Performance and Link Performance Allocation 114 12.5 FM/FDM Link Performance Output Format . . .. . . 114 13. ALGORITHM L: PCM/TDM LINK PERFORMANCE . . .. . 116 13.1 Single Receiver Transfer Characteristlc for Digit"al Systems 117 13.2 Requirements for PCM/TDM Line-of-Sight Links from Draft MIL-STD-188-323 . . . . . . . . . . . . . 119 13.3 Calculating Predicted Outage Time in Terms of Error-Free Seconds . . . . . . . .. . . . . . . . 120 13.4 Alternative Kirk and Osterholz Digital Link Performance Calculations . . . . . . . . . . . . . . . 120 13.5 LOS Link Probability of Fade Outage and Unavailability Allocations . . . . . . . . . 120 13.6 Calculating LOS Link Probability of Fade Outage . 121 :L3,.7 Calculating Probability of Error-Free Data Block and Link Availability . . . . .. . 123 13.8 PCM/TDM Link Performance Output Format . 123 14. REFERENCES 126 v LIST OF FIGURES Page Figure 1. Geometry for calculating latitude for a given longitude. 12 Figure 2. Geometry for calculating longitude for a given latitude.. 12 Figure 3. Example link diagram 15 Figure 4. Minimum monthly mean values of surface refractivity normalized to mean sea level 22 Figure 5. Example terrain profiles 32 Figure 6. Example parabolic horn configuration 46 Figure 7. Example periscope antenna configuration 47 Figure 8. Example parabolic antenna configuration 48 Figure 9. Example single-mirror repeater site configuration 49 Figure 10. Example double-mirror repeater site configuration 50 F;~g~re 11. Example double-antenna repeater site configuration ,. 51 3 Figure 12. Contours of average absolute: humidity (gjm ) for a summer month 62 Figure 13. Mean temperature values, . 63 Figure 14. Rainfall climatic zones in the USA .. 69 Figure 15. Rain rate zones for North and South America 75 Figure 16. Rain rate zones for Europe, Africa and Western Asia 76 Figure 17. Rain rate zones for East Asia and Australia 77 Figure 18. Example rain-rate probability distributions 82 Figure 19. Example path rain attenuation distribution 83 Figure 20. Example mu1tipath attenuation distribution 84 Figure 21. Microwave waveguide attenuation 89 Figure 22. Example of a link received carrier-to-noise probability distribution . . .. . . . . . . . . . '. . . · . . . . 93 vi Figure 23. Waveguide velocity curves 104 Figure 24. Maxiumum distortion to signal ratio due to echo 107 Figure 25. Example FM/FDM single-receiver transfer characteristic 109 Figure 26. Example of a digital link single-receiver transfer characteristic . . . . . . . . . . . . . . . . . 118 vii .LIST OF TABLES Page Table 1. Earth Radii for Various Spheroids . 10 Table 2. Example Earth Geometry Data . 16 Table 3. Example of Profile Data . . . 23 Table 4. Example Recommended Antenna Height Data . 29 Table 5. Example Path Geometry and Meteorological Output . 36 Table 6. Example Repeater Site Gain and Antenna Gain Data Table 7. Oxygen Lines 61 Table 8. Water Vapor Lines . 64 Table 9. Example Median Basic Transmission Loss Output 65 Table 10. Rain Rate Input Data Sources For the Dutton Model . 68 Table 11. Storm Top Constant Values . 70 Table 12. Rainfall Intensity Exceeded (mm/h) - CCIR Rain Climatic Zones 78 Table 13. Example Output of Carrier-to-noise Ratio Data ..... -. . 94 Table 14. Example FM/FDM Single Receiver Transfer Characteristic Data 110 Table 15. Example FM/FDM Link Performance Data 115 Table 16. Example of Draft MIL-STD-188-323 Digital Link Performance Analysis . . .. . . 124 Table 17. Example of the Kirk and Osterholz (1976) Digital Link Performance Analysis . . . . . . . . . . . . . . . 125 viii ALGORITHMS USED IN ARROWS: AUTODESIGN OF RADIO RELAY QPTlMU~{ HIDEBAND ~YSTEMS L. G. Hause* This report describes the mathematical models used in the ARROWS programs. These programs, which run on a desktop computer, automate the calculations involved in the design of line-of-sight microwave radio relay links. The programs calculate, tabulate, and plot information about Earth geometry, terrain profiles, ray paths, repeater-reflector geometry, median basic transmission loss, variab1ility of loss, equipment effects, and link performance. Each model is selected on the basis of its acceptance within the communications industry and the size and type of data base supporting the model. The computer hardware and software configurations are designed to be convenient to operate and to give the design engineer immediate access to calculated results corresponding to changes in design parameters. The programs corresponding to these algorithms are designed to be used interactively by p~9rsons having no experience in .programming. The algorithms are applicable over a wide range of link parameters. The frequency range is from 1 GHz to 20 GHz. Path lengths should be less than 150 km. Key words: computer software; digital radio; microwave radio; passive repeater; radio link performance; radio relay 1. INTRODUCTION This report describes the algorithms used in the ARROWS program set. ARROWS is an acronym for Autodesign for Radio Repeater Qptimum Hideband ~stems. ARROWS is an automated, interactive set of desktop computer programs, that permit workers with moderate skill levels to perform the calculations necessary for the design of line-of-sight (LOS) microwave links for both FM/FDM and PCM/TDM systems. FM/FDM stands for "frequency modulation/frequency division multiplex" and PCM/TDM stands for "pulse code modulation/time division multiplex." Gathering and programming of these algorithms were sponsored by the *The author is with the Institute for Telecommunication Sciences, National Telecommunications and Information Administration, U.S. Department of Commerce, Boulder, CO 80303-3328. u.s. Arm~r Information Systems Engineering Support Activity, Ft. Huachuca, AZ. The programs are written in HPL language and are provided with documentation that permits them to be conveniently oper~ted, understood, modified, and updated. The primary use of the program set is the analysis of LOS links that may inc1\lde up to three repeater sites. These programs calculate the optimum antenna and reflector orientation values from the Earth geometry parameter values of the terminal and repeater sites. They also calculate the performance of the link based on the reflector size, antenna gains, and other equipment parameters. Both atmospheric and terrain parameters are taken into account. ARROWS programs are used to prepare either active or passive repeater designs. An example link is used to illustrate results produced by the ARROWS program set. These sites and paths exist in Europe, but equipment and communications channels attributed to them in the example do not exist. The sites were selected because their path and Earth geometry are typical, and the terrain-data set for these paths is conveniently available. The equipment selected to illustrate each path was not that which we felt was optimum for performance of the link, but that which we felt would illustrate the r.ange and diversity of the ARROWS programs. 1.1 What are the Algorithms and What Do They Do? The algorithms are given letter designations that correspond to the ARROWS individual subprogram letter designations as follows: A. Repeater Link Earth Geometry B. Path Profile Data and Effective Earth Radius C. Primary Antenna Heights D. Path Profiles and Ray Traces E. Site Antenna or Reflector Layout F. Repeater Site Loss and Antenna Gain G. Median Basic Transmission Loss H. Basic Transmission Loss Variability I. Link Carrier-to-noise Ratio probability Distribution J. Analog Radio System Single-receiver Transfer Characteristic K. FM/FDM Link Performance L. PCM/TDM Link Performance. 2