(None) = RL-2000 REPORT NO. FAA-RD-75-32 IMPROVED SIDELOBE SUPPRESSION MODE PERFORMANCE OF ATCRBS WITH VARIOUS ANTENNAS Dipak L. Sengupta Jovan Zatkalik Chen-To Tai FEBRUARY 1975 INTERIM REPORT DOCUMENT IS AVAILABLE TO THE PUBLIC THROUGH THE NATIONAL TECHNICAL INFORMATION SERVICE, SPRINGFIELD, VIRGINIA 22161 Prepared for U.S. DEPARTrMENT OF TRANSPORTATION FEDERAL AVIATION ADMINISTRATION Systems Research and Development Service Washington DC 20591

NOTICE This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use t hereo f. ~............ _, ti, ~ NOTICE I 'The United States Government does not endorse products or manufacturers. Trade or manufacturers | names appear herein solely because they are considered essential to the object of this report.

Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. FAA-RD-75-32 4. Title and Subtitle 5. Report Date IMPROVED SIDELOBE SUPPRESSION MODE February 1975 PERFORMANCE OF ATCRBS WITH VARIOUS 6. Performing Organization Code ANTENNAS 8. Performing Organization Report No. 7. Authorss) Dipak L. Sengupta, Jovan Zatkalik, and Chen-To Tai* DOT-TC-FAA754 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) The University of Michigan FA519/R5119 College of Engineering 11. Contract or Grant No. Dept. of Electrical and Computer Engineering DOT-TSC-717 Radiation Laboratory Radiation Laboratory 13. Type of Report and Period Covered Ann Arbor MT 48105 12. Sponsoring Agency Name and Address Interim Repo rt U.S. Department of Transportation July 1973-June 1974 Federal Aviation Administration July 197 -Systems Research and Development Service 14. Sponsoring Agency Code Washington DC 20591 15. SupplementaryNotes U.S. Department of Transportation Under contract to: Transportation Systems Center *Under contract toKendall Square Cambridge MA 02142 16. Abstract The ISLS mode performance of terminal and enroute ATCRBS using existing and various improved antennas in the presence of perfectly dielectric flat ground are investigated theoretically. Necessary analytical expressions for various quantities characterizing the system performance have been derived. A computer program has been developed for the computation and tabulation of these quantities as functions of the elevation angle of the observation point for different combinations of heights of the directional and omnidirectional antennas. For each antenna combination results are given for the following seven quantities: the P1 and P2 pulse intensities, the pulse ratio P1/P2, the mainbeam killing and sidelobe punch-through zones in space, the effective azimuth beamwidth, the number of replies and the coverage diagram. Short discussions of results are given wherever appropriate. 17. Key Words 18. Distribution Statement Improved Sidelobe Suppression, DOCUMENT IS AVAILABLE TO THE PUBLIC ATCRBS, Sidelobe, Vertical THROUGH THE NATIONAL TECHNICAL Lobing, Main Beam Killing VIGIA22161 " Lobing, Main Beam Killing INFORMATION SERVICE, SPRINGFIELD, VIRGINIA 22161 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price Unclassified Unclassified 168 D 1.8 Form DOT F 1700.7 (8-72) Reproduction of completed page authorized

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Preface This report investigates theoretically the ISLS mode performance of ATCRBS using the existing and various improved beacon antennas in terminal and enroute configurations. The beacon antennas are assumed to be located above a perfectly dielectric flat ground having a relative dielectric constant of 3. The report is a preliminary attempt to theoretically evaluate the performance of each antenna so that the improvements of ATCRBS performance, if any, may be properly assessed. On the basis of the present study it has been found that unless the relative phase between the directional and omnidirectional antennas is properly adjusted the ISLS mode performance of ATCRBS can be considerably worse than that for the SLS mode. We are pleased to acknowledge the benefit of several discussions with Mr. Frank LaRussa and Dr. Rudy Kalafus of DOT/TSC, Cambridge. We also acknowledge the valuable counsel and suggestions of Professor Ralph E. Hiatt. We wish to acknowledge with thanks the work of Dr. Mohammed Hidayet and Mr. Min Han who prepared the computer programming for this report. iii

TABLE OF CONTENTS Section Page 1 INTRODUCTION 1 1. 1 Preliminary Remarks 1 1. 2 Functional Characteristics of Interrogation Schemes 1 1. 3 Outline of the Report 5 1.4 Basic Assumptions 6 2 BASIC THEORETICAL FORMULATIONS 8 2. 1 Definition of the Problem 8 2.2 The Intensities of P1 and P2 Pulses 9 2. 3 Physical Implications of the Maximum and Minimum Envelope Functions 14 2.4 The Pulse Ratio 14 2. 5 Effective Azimuth Beamwidth and Number of Replies 15 2.6 Coverage Diagram 19 3 FREE SPACE PATTERNS OF THE TEST ANTENNAS 21 3. 1 Antennas Under Study 21 3. 2 Analytical Expressions for the Free Space Elevation Plane Patterns of Various Antennas 21 3. 2. 1 Westinghouse Array Antenna 21 3. 2. 2 Texas Instruments Reflector Antenna 22 3. 2. 3 Hazeltine Open Array Antenna 23 3. 2. 4 Existing Hog-Trough Antenna 24 3. 2.5 Hazeltine E-Scan Antenna 25 3. 2.6 Enroute Texas Instruments Fix Antenna 26 3. 2.7 Enroute NADIF Fix Antennas 27 3.3 Summary of the Important System Parameters 29 4 NUMERICAL RESULTS AND DISCUSSION 31 4. 1 The Computer Program 31 4. 2 Numerical Results for Terminal Installations 32 4. 2. 1 Westinghouse Array Antenna 32 4. 2.2 Texas Instruments Reflector Antenna 38 4. 2. 3 Hazeltine Open Array Antenna 42 4. 2. 4 Existing Hog-Trough Antenna 48 4. 2. 5 Hazeltine E-Scan Antenna 72 4. 3 Numerical Results for Enroute Installations 81 4. 3. 1 Westinghouse Array Antenna 81 4. 3. 2 Texas Instruments Reflector Antenna 86 4. 3. 3 Existing Hog-Trough Antenna 93 4. 3.4 Texas Instruments Fix Antenna 105 v

Table of Contents (cont'd) 4. 3. 5 NADIF Fix I Antenna 115 4.3.6 NADIF Fix II Antenna 122 4. 3.7 NADIF Fix Im Antenna 129 5 GENERAL DISCUSSION 139 5.1 Summary of Important Results 139 5. 2 SLS Mode Results 141 5. 3 Comparison of ISLS and SLS Mode Performance 142 5. 4 General Discussion of ISLS Mode Results 142 6 REFERENCES 145 APPENDIX A: Computer Program for IBM-360, Model 67 146 APPENDIX B: Report of Inventions 155 vi

LIST OF ILLUSTRATIONS Figure Page 1 ATCRBS interrogation signal format on mode 3/A. 2 2 Geometry of the interrogator, multipath source and aircraft. 3 3 SLS and ISLS signals received by the transponder. 4 4 Schematic arrangement of the antennas and the excitation of the P1 pulse radiation. 8 5 Schematic representation of the two-element array radiating the P1 pulse. 10 6 Pl(8)MAX, Pi()MIN and P2(8) as functions of 0. 33 7 Normalized pulse ratio envelopes as functions of 0. 34 8 Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the Westinghouse array antenna. 36 9 Effective azimuth beamwidths as functions of the angle from the horizon for the Westinghouse array antenna. 37 10 Number of replies as functions of angle from the horizon. 39 11 Coverage diagram for the Westinghouse array antenna. 40 12 Pl(9)MAX, P1(e)MIN and P2(0) as functions of 0. 41 MAX' MIN 13 Normalized pulse ratio envelopes as functions of 0. 43 14 Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the Texas Instruments reflecting antenna. 44 15 Effective azimuth beamwidths as functions of the angle from the horizon for the Texas Instruments reflector antenna. 45 16 Number of replies as functions of angle from the horizon. 46 17 Coverage diagram for the Texas Instruments reflector antenna. 47 18a 1Pi()MAx, P1() MIN and P2(0) as functions of 0. 49 18b P1(0)MAx' P1()MIN and P2(0) as functions of 0. 50 MAX' MIN 19a Normalized pulse ratio envelopes as functions of 0. 51 19b Normalized pulse ratio envelopes as functions of 0. 52 20a Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the Hazeltine open array. 53 20b Mainbeam killing and sidelobe punch-through zones as functions of 0 for the Hazeltine open array. 54 vii

List of Illustrations (cont'd) Figure Page 21a Effective beamwidths as functions of angle from the horizon for the Hazeltine open array. 55 21b Effective azimuth beamwidths as functions of angle from the horizon for the Hazeltine open array. 56 22 Number of replies as functions of angle from the horizon. 57 23 Coverage diagram for the Hazeltine open array. 58 24a P MA P1(O) MIN and P2(9) as functions of 0. 60 24b Pl(e)MAX, P1(O) and P2(0) as functions of 0. 61 24c PI(e)MAX, P1(e)Mi and P2(0) as functions of 0. 62 MAX' MIN 24d Pl(O)MAX, P1(O)MIN and P2(9) as functions of 0. 63 25a Normalized pulse ratio envelopes as functions of 0. 64 25b Normalized pulse ratio envelopes as functions of 0. 65 25c Normalized pulse ratio envelopes as functions of 0. 66 25d Normalized pulse ratio envelopes as functions of 0. 67 26a Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the existing hog-trough antenna. 68 26b Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the existing hog-trough antenna. 69 27 Effective azimuth beamwidths as functions of the angle from the horizon for the existing hog-trough antenna. 70 28 Number of replies as functions of angle from the horizon. 71 29a Coverage diagram at the maximum envelope for the existing hog-trough antenna. 73 29b Coverage diagram on expanded scale at the maximum envelope for the existing hog-trough antenna. 74 29c Coverage diagram at the minimum envelope for the existing hogtrough antenna. 75 29d Coverage diagram on expanded scale at the minimum envelope for the existing hog-trough antenna. 76 30 Pi(e)MAX, PI(e)MIN and P2(0) as functions of 0. 77 31 Normalized pulse ratio envelopes as functions of 0. 78 32 Number of replies as functions of angle from the horizon. 79 33 Coverage diagram for the Hazeltine E-scan antenna. 80 viii

List of Illustrations (cont'd) Figure Page 34 P1(0)MAX, P1(e)MN and P2(e) as functions of 0. 82 35 Normalized pulse ratio envelopes as functions of 0. 83 36 Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the Westinghouse array antenna. 84 37 Effective azimuth beamwidths as functions of the angle from the horizon for Westinghouse array antenna. 85 38 Number of replies as functions of angle from the horizon. 87 39 Coverage diagram for the Westinghouse array. 88 40 Pl(0)MAX, P1(0)MIN and P2(0) as functions of 0. 89 41 Normalized pulse ratio envelopes as functions of 0. 90 42 Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the Texas Instruments reflector antenna. 91 43 Effective azimuth beamwidths as functions of the angle from the horizon for the Texas Instruments reflector antenna. 92 44 Number of replies as functions of angle from the horizon. 94 45 Coverage diagram for the Texas Instruments reflector antenna. 95 46a Pl(e)MAX, P1(e)MN and P2(9) as functions of 9. 96 46b P1(0)MAX Pl()MIN and P2(0) as functions of 0. 97 46c P(e)MAX P1(e)MN and P2(0) as functions of 0. 98 MAX' MIN 46d Pl(O) MAX P1(e)MIN and P2(0) as functions of 0. 99 47a Normalized pulse ratio envelopes as functions of 0. 100 47b Normalized pulse ratio envelopes as functions of 0. 101 47c Normalized pulse ratio envelopes as functions of 0. 102 47d Normalized pulse ratio envelopes as functions of 0. 103 48 Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the existing hog-trough antenna. 104 49 Effective azimuth beamwidths as functions of the angle from the horizon for the existing hog-trough antenna. 106 50 Number of replies as functions of angle from the horizon. 107 51a Coverage diagram of the maximum envelope for the existing hogtrough antenna. 108 51b Coverage diagram on expanded scale of the maximum envelope for the existing hog-trough antenna. 109 ix

List of Illustrations (cont'd) Figure Page 51c Coverage diagram of the minimum envelope for the existing hog-trough antenna. 110 51d Coverage diagram on expanded scale of the minimum envelope for the existing hog-trough antenna. 111 52 Pl(O)MAX P1()MIN and P2(e) as functions of 0. 112 53 Normalized pulse ratio envelopes as functions of 0. 113 54 Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the Texas Instruments Fix antenna. 114 55 Effective azimuth beamwidths as functions of the angle from the horizon for the Texas Instruments Fix antenna. 116 56 Number of replies as functions of angle from the horizon. 117 57 Coverage diagram for the Texas Instruments Fix antenna. 118 58 P1(8)MAX P1(8)MIN and P2(8) as functions of 0. 119 MAX' MIN 59 Normalized pulse ratio envelopes as functions of 0. 120 60 Mainbeam killing and sidelobe punch-through zones as functions of nominal pulse ratio for the NADIF Fix I antenna. 121 61 Effective azimuth beamwidths as functions of the angle from the horizon for the NADIF Fix I antenna. 123 62 Number of replies as functions of angle from the horizon. 124 63 Coverage diagram for NADIF Fix I, I and III antennas. 125 64 Pl(8)MAX, P1(8)MIN and P2(8) as functions of 8. 126 65 Normalized pulse ratio envelopes as functions of 8. 127 66 Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for NADIF Fix II antenna. 128 67 Effective azimuth beamwidths as functions of angle from the horizon for NADIF Fix II antenna. 130 68 Number of replies as functions of angle from the horizon. 131 69 Pl(0)MAX' P1()MIN and P2(0) as functions of 8. 132 MAX' MIN 70 Normalized pulse ratio envelopes as functions of 0. 133 71a Mainbeam killing zones as functions of nominal pulse ratio for NADIF Fix III antenna. 134 71b Sidelobe punch-through zones as functions of the nominal pulse ratio for NADIF Fix III antenna. 135 72 Effective azimuth beamwidths as functions of the angle from the horizon for the NADIF Fix III antenna. 136 x

List of Illustrations (cont'd) Figure Page 73 Number of replies as functions of angle from the horizon. 138 A-1 Flow diagram for the main program. 146 xi

LIST OF TABLES Table Page 1 Excitation coefficients of the elements of the Westinghouse array antenna. 22 2 Sampled values of the pattern function for the Texas Instruments reflector antenna. 23 3 Sampled values of the pattern function for the Hazeltine open array antenna. 24 4 Sampled values of the pattern function for the existing hog-trough antenna. 25 5 Sampled values of the pattern function for the Hazeltine E-scan antenna. 26 6 Sampled values of the pattern function for the enroute Texas Instruments Fix antenna. 27 7 Sampled values of the pattern function for the enroute NADIF Fix antennas 28 8 Some important parameters of the antenna systems. 30 9 Summary of the ISLS maximum envelope mode performance criteria of ATCRBS. 140 10 Summary of the ISLS minimum envelope mode performance criteria of ATCRBS. 140 11 Summary of the performance criteria of ATCRBS operating in the SLS mode. 141 xii

1. INTRODUCTION 1. 1 Preliminary Remarks This is the second Technical Report on Contract DOT-TSC-717 entitled "Volumetric Study in Support of ATCRBS". The effects of ground on the improved interrogator sidelobe suppression (ISLS) mode performance of ATCRBS using various antennas are theoretically investigated in the present report. A similar investigation of the SLS mode performance of ATCRBS has been reported in our first Technical Report [1]. The results obtained in [l] will be used frequently in the present study and, in fact, the present report should be studied in the context of [1]. 1. 2 Functional Characteristics of Interrogation Schemes The basic principles of different interrogation schemes used in ATCRBS are discussed in detail in the open literature [2 - 6]. Here we mention only those aspects which are appropriate for the present investigation. The ground interrogator of ATCRBS has a number of interrogation modes to accommodate its various uses [5]. Each interrogation consists of a pair of 0. 8ps wide pulses (Pl, P3) transmitted at 1030 MHz by the directional antenna of the beacon. An additional pulse (P2 pulse) is transmitted 2ps after the initial P1 pulse from the interogator equipped with sidelobe suppression system (SLS). The P2 pulse is transmitted by the omnidirectional antenna of the beacon. The ATCRBS interrogation signal format on mode 3/A, assigned to common ATC, is shown in Fig. 1. Ordinarily this interrogation signal is transmitted by the ground interrogator antenna system equipped with sidelobe suppression system (SLS). The pulse P2 is transmitted in order to suppress the aircraft responses to the signals received via the sidelobes of the directional antenna of the beacon. The effective radiated power of the P2 pulse is designed to be greater than that of any (P1 pulse) radiated via the sidelobe of the directional antenna. The aircraft transponder is designed not to respond if P2 > P1. When the transponder detects a 1

PI P3 0.8 + 0.1/js P2 2 2!0.15s-.a 8~0.2 s FIG. 1: ATCRBS interrogation signal format on mode 3/A. sidelobe interrogation, it is inhibited for a period of 35 + 10 ps, during which time a received interrogation cannot elicit a reply. The radiated power level of P2 is nominally set at 18 dB below the peak level of the directional beam radiating the P1 and P3 pulses. In order to accommodate reasonable manufacturing tolerances, the U. S. National Standard designates that a transponder shall be inhibited with high probability whenever the amplitude of the P2 pulse exceeds that of the P1 pulse and shall respond with high probability whenever the amplitude of P1 exceeds that of P2 by 9dB or more. The SLS scheme works satisfactorily in the absence of multipath sources on ground between the interrogator and the transponder. However, if the main beam of the antenna illuminates a large reflection surface, e. g., a hill, building, hangar, etc., which in turn reflects the transmitted energy at a level sufficient to trigger the transponder in an aircraft not in the main beam of the antenna, a false target indication will occur. 2

Consider a situation shown in Fig. 2 where the aircraft is receiving a direct signal as well as a strong signal reflected by a multipath source. The direct and MULTIPATH SOURCE / \ / \ REFLECTED \ / <DIRECT \ AIRCRAFT INTERROGATOR ANTENNA PATTERNS FIG. 2: Geometry of the interrogator, multipath source and an aircraft. the reflected SLS signals arriving at the aircraft is shown in Fig. 3a. The direct signal is a sidelobe interrogation received from the interrogator. The main beam interrogation signal is received at a time delayed by T via the reflected path. If the direct signal is recognized as a side-lobe interrogation the transponder will be suppressed for at least 25ps (35t10 0s) and if T < 25 s then the reflected main beam interrogation will not elicit a reply from the transponder. Frequently it happens that P1 pulse amplitude received by the direct path is not of sufficient amplitude to be recognized by the transponder. In such cases the direct path 3

DIRECT REFLECTED RECEIVER THRESHOLD (a) SLS signal (a) SLS signal PI P3 P2 DIRECT REFLECTED (b) ISLS signal FIG. 3: SLS and ISLS signals received by the transponder. 4

interrogation does not cause suppression and the reflected interrogation elicits a reply, thereby giving a false target indication. To increase the probability of direct path suppression, a fraction of the P1 pulse energy is radiated from the omnidirectional antenna. This increases the range at which the direct path interrogation will reliably suppress the transponder. This technique is termed the improved sidelobe suppression (ISLS). Figure 3 b shows the interrogation signal at the transponder corresponding to Fig. 2 in the ISLS case. The typical P1 pulse amplitude in the omni pattern is 18dB below the peak main beam P1 pulse, i.e., equivalent to the P2 pulse. The ISLS direct signal in Fig. 3 b will now be recognized by the transponder as a sidelobe suppression signal and the transponder reply will be suppressed for at least 25ps and if T < 25ts the multipath signal will not elicit any reply. Since ISLS increases the total number of sidelobe suppressions that occurs, it reduces by a small amount the probability of reply to valid interrogation. 1.3 Outline of the Report The purpose of the present report is to investigate theoretically the effects of ground on the improved sidelobe suppression mode of operation of the ATCRBS for nine different interrogator antennas and for various combinations of heights of directional and omnidirectional antennas located above a flat infinite ground. The basic theoretical formulations of various quantities of interest are given in Section 2. The quantities of interest are the intensities of the radiated pulses at a far field point where a transponder is located, the received pulse ratio at the transponder, the potential main beam killing and sidelobe punch-through zones in space, the effective azimuth beamwidth of the interrogator directional antenna, the effective number of replies elicited from the transponder and the coverage diagram appropriate for the beacon system. The various antennas along with their free space patterns are discussed in detail in [1i. For simplicity of computation approximate analytical expressions have been developed for the free space radiation patterns of all the test antennas. Since they have been discussed elsewhere, we only quote the appropriate expressions in Section 3. 5

Numerical results and discussion of pertinent quantities are given in Section 4. A general discussion of the results along with our conclusions are given in Section 5. The computer program used for obtaining the numerical results is given in Appendix A. 1.4 Basic Assumptions It is appropriate to give here the basic assumptions and approximations on which the present investigation is based. These should be noted when applying the results to an actual system. The theoretical formulations used make the following assumptions and approximations: 1.4. 1 The directional and omnidirectional interrogator antennas have definite phase centers located at different heights above ground. The displacement between the two antennas can take place in both the vertical and horizontal directions. 1.4. 2 For most of the antennas, the free space directional and omnidirectional elevation plane patterns are ideally matched with the exceptions of the NADIF Fix antenna with the Westinghouse omni and the NADIF Fix antenna with the existing small omni (called the NADIF Fix II and the NADIF Fix mI antennas, respectively). 1.4.3 The elevation plane antenna pattern profile at different azimuth sections is the same. This implies that the elevation pattern profile in the region of the azimuthal sidelobe is of the same shape as in the region of the main beam. Consequently, if f(O) is the elevation plane pattern profile in the plane of symmetry of the main beam, then Lf(0) will be the elevation plane pattern profile of the azimuthal sidelobe, where L is the sidelobe level relative to the maximum of the main beam (note that 0 < L < 1). 1.4.4 The nominal or 3 dB beamwidths of the azimuthal plane patterns of the directional antennas are independent of the elevation angle. For small 6

elevation angles (say 0 < 5 ), this assumption is quite acceptable. The azimuthal plane patterns of the directional antennas are assumed to be given by universal Gaussian curves. 1.4.5 For the purpose of radiating the P1 pulse, equal amounts of P1 pulse power are fed into the directional and omnidirectional antennas. To radiate the P2 pulse an amount of P2 pulse power equal to that of the P1 pulse is fed into the omnidirectional antenna. 1.4. 6 The horizontal displacements between the phase centers of the directional and omnidirectional antennas are assumed to be such that the P1 pulses radiated by them arrive at the transponder either in phase or out of phase with each other. The former is referred to as the maximum envelope case and the latter the minimum envelope case. 1.4.7 For most of the antennas the elevation plane patterns are available. For the purpose of computational simplicity we have developed approximate analytical expressions for the elevation plane patterns of all the antennas. 1.4. 8 The ground is assumed to be flat and a pure dielectric with permittivity e = 3. 1.4.9 The main beam killing takes place whenever the P1 and P2 pulse amplitudes at the transponder satisfy the relation P (dB) - P2(dB) < 9dB. 1.4.10 In the azimuthal sidelobe region, sidelobe punch-through occurs whenever the P1 and P2 pulses at the transponder satisfy the relation P 1 (dB) - P2(dB) > 0. 7

2. BASIC THEORETICAL FORMULATIONS 2. 1 Definition of the Problem Let us consider the general case of the ISLS mode of operation where the directional and omnidirectional antennas of the beacon are at different heights and are displaced in the horizontal direction. Figure 4 represents the disposition of antennas and the excitations for the case of P1 pulse radiation. Generally, both I I L a~x — z ---~ I I I I I I B I FIG. 4: Schematic arrangement of the antennas and the excitation of the P1 pulse radiation. 8

antennas are excited with different power and the relative phase of excitation is dependent on the difference in the cable lengths. Let the points A and B in Fig. 4 represent the phase centers of the directional and omnidirectional antennas respectively. The main task is to calculate the intensities of P1 and P2 pulses at the transponder point produced by the antenna system shown in Fig. 4. The ground is assumed to be flat and a pure dielectric with relative dielectric constant e = 3. r For the radiation of the P1 pulse the excitation of the antennas is as shown in Fig. 4. For the radiation of the P2 pulse only the omnidirectional antenna is excited with an appropriate amount of power. 2.2 The Intensities of P1 and P2 Pulses Let the complex free space elevation plane pattern of the directional antenna with respect to the point A (Fig.4) be represented by fd(O)eJ d(O), where fd(0) and 5d(O) are the amplitude and phase patterns, respectively, of the antenna in free space. It can be shown [1] that the corresponding patterns of the antenna in the presence of ground and with respect to the same point A are given by Fd(0) ={[fd()] +2p()fd( )fd(O )cos L2dsin 0 +^d(0) - d(-] + [p(0)fd(0)] 2} (1) fd(0) sin d(e) +P()fd(-O) sinLd(-0) - 2HIdsin 0 d d(0) cos d(O)+ p(0)fd(-O)cos[$d(-0) - 23Hdsin j (2) where: the complex pattern in the presence of ground is represented as Fd(0)exp jd(0), 13 = 27r/X is the free space propagation constant, p(O) is the reflection coefficient of ground for vertical polarization [1] and is given by p() = 3 sin 0 - 2 + sin20 a) 3sin0+V2+sin 0 Eq. (2a) assumes that the ground is a perfect dielectric with dielectric constant 3 and is flat. Further discussion of p(0) is given in [1]. 9

Similarly, if f0(W) and $0(O) are the free space amplitude and phase patterns of the omnidirectional antenna with respect to point B (Fig. 4), the corresponding patterns in the presence of ground are given by the following: F (0) = {[0()] 2+2p(O)fo(O)fo(-cos [2 sin+O() -(-0)] + [p()f (-)J 2 1/ (3) of(6) sin[d(O)] +p(6)fo(-) sin[0(-0) - 2jH0sin o] *0(o) = arctan f (0) cos p^e(0)p(e) fo(-0) cos 0(-0) - 2Hosin 0 (4) In the ISLS mode of operation, the P1 pulse is radiated by a two-element array, with different element,ptterns, different excitation coefficients and with disposition of elements as represented in Fig. 5. The excitations of the elements z 4 I I I I I EXCITATION Fo ()ej* () B EXCITATION, Fd (8g)eJd(8) AR M(R,8) -x R........ —.,, X A FIG. 5: Schematic representation of the two-element array radiating the P1 pulse. 10

A and B are proportional to Eqs. (1) - (2) and (3) - (4) respectively and are as shown in Fig. 5. From Fig. 5 it can be shown that the electric field produced by the array at a far field point M(R, 0) is given by the expression W Gd jd(eo) -j0R 3Fw0G0 Oe)-j3(R-AR)-] R d R 0 (5) where the origin of the coordinates are assumed to be located at A, Wd, Gd are the excitation power and maximum gain of the directional antenna, W0, Go are the excitation power and maximum gain of the omnidirectional antenna for P1 pulse, T is the phase difference in excitation caused by the difference in the cable length, etc. AR is the path difference, as shown in Fig. 5, and is given by AR = Ax cos 0 +Az sin 0, (5a) where it is assumed that the point M is located such that its azimuth angle is zero. Equation (5) can be written in the following form: E() = Ae jRFd(F() e d0)e0) +qF(0)exp[^(0+AR + ) (6) where 30WG A = R (7) R q= WdGd (8) The constant q determines the level of the PI pulse radiated through the omni antenna. With Go, Gd given, this level can be adjusted to the proper value by adjusting the powers Wd, W0. In free space, if it is assumed that the elevation plane patterns 11

of the two antennas are identical, the quantity 1/q gives the ratio of P1 pulse radiated by the directional antenna to the PI pulse radiated by the omnidirectional antenna. Normally 1/q is taken to be 18dB. The voltage intensity of the P1 pulse at the far field point is proportional to the amplitude of the expression given by Eq. (6) and is given by P1(O)ISLS = IE I s A {[2Fd(I )F ()cos S(0) + rqF(, (9) where (0)= 0(0) - 0 (e) - PAR - a, (10) AR = Ax cos O +Az sin e Az =H -Hd Equation (9) gives the desired expression for the P1 pulse at the transponder for the ISLS mode of operation of the beacon. For further analysis it is convenient to use an alternate form of P1(0) SLS. Assume that the excitation ISLSj powers of the directional antennas are the same for ISLS as well as SLS cases. It is known [1] that the voltage intensity of the P1 pulse in SLS mode is given by 30WG JVd(O) -j6} R P ( )SLS t FeR Fd e (11) which can be obtained from Eq. (9) with q = 0. In both ISLS and SLS modes of operation the P2 pulse is radiated by the omnidirectional antenna only. If the excitation power of the omni antenna when the P2 pulse is radiated is W2 (in both modes) then we obtain the following expression for the voltage intensity of the P2 pulse at the far field point: = 30W2G0 j0 () -jf3R A F(0) P2(0) R F0(e) e e K F0 (12) 12

i (13) where KO = W (13) We shall call the constant K0 the nominal ratio of the P1 to P2 pulse. With Gd and GO given, this ratio can be adjusted to the proper value by adjusting the powers Wd and W2. Normally K0 is taken to be equal to 18dB. With the help of Eqs. (11) and (12), the expression for the P1(O)ISLS as given by Eq. (9) is transformed into Pi()ISLS {[P1()SL] +2qKo0P (0)SLS 2(0)cos (e) + 0Ko 2} (14) Equation (14) is the new, alternate expression for P1()SLS. It gives the relation between the intensity of the P1 pulse in the ISLS mode of operation, and the intensity of the same pulse in SLS mode of operation. From Eq. (14) it is evident that SLS mode can be theoretically treated as a special case of ISLS mode with the factor q equal to zero. The value of the constant qK0 can be found from Eqs. (8) and (9) and is given by qK0 = jW0W2 (15) which means that qK0 is equal to the square root of the ratio of the excitation powers of the omnidirectional antenna radiating the P1(0) pulse in ISLS mode and the P2(0) pulse. These two powers are commonly equal (qK0 = 1), but for the purpose of further analysis we shall take them to be different, i.e., qK0 1. Let us investigate the behavior of the P1()i) as a function of the horizontal displacement Ax of the two antennas. The functions Fd(0) and F (0) are independent of Ax. In Eqs. (9) and (14), the only function which depends on Ax is S(0), as defined in Eq. (10). In a given situation, the factor cos (0) will lie between +1 and -1. Thus in the ISLS mode the P1(O) pulse amplitude will lie between a maximum envelope function P1(0)MAX and a minimum envelope function P1(e)MIN. These two envelope functions are given by MIN 13

Pi() MAX = A[Fd() +qF0(O] = PI(e)SLS+qKO P2(0) (16) Pi() = A[Fd()-qF(O)] = P(0)SL qKoP2(e).(17) The two envelope functtons defined by Eqs. (16) and (17) are used to obtain the Pl(O)ISLS pulses as functions of the elevation angle 0. The physical implications of the envelope functions are given in the next section. 2.3 Physical Implications of the Maximum and Minimum Envelope Functions In the previous section we have said that the received P1 pulse amplitude lies between a maximum and a minimum envelope function. It is appropriate here to give a discussion on the physical implications of these functions. Basically the maximum level is attained when the P 1 pulses from the directional and omnidirectional antennas appear in phase at the transponder. The minimum level is obtained when they appear out of phase. The RF phase difference between the two P1 pulses is given by Eq. (10). In an ideal case ipd(0) = b0(0), i.e., the elevation plane phase patterns of the antennas are identical Even if they are not identical, it is reasonable to assume that ~d(O) -(0) is a constant over a range of interest in 0, i.e., for 0 < 0 < 10. Within this range sin 0 is a very small quantity and cos 0- 1. Thus one can approximate Eq. (10) by v(e) - (c- Ax-r- ), (18) where c = ~'d()- 0() - constant. It is now conceivable that by properly choosing r, one can adjust (0O) = 0 or 7r which will then yield the two envelope functions. In a practical situation this can be obtained by introducing the appropriate amount of phase difference between the two antennas. 2.4 The Pulse Ratio From Eqs. (9) and (12) the following expression is obtained for the pulse ratio at a point located within the azimuthal main beam of the antenna: (2 1/19) P2(SS) K()ISLS F 2(0o + 2 (19) P2(0) "ISLS-'t 0-^ 0' ^ F 0(> 14

where K(9) is the ratio P1(O)/P2(0) in the SLS mode of operation and is given SLS by [1]: Fd(0) SLS OF 0(2) K(O)SLS = K0 F (-) (20) In addition to the true pulse ratio function K() SLS we introduce here the concept of envelopes of pulse ratio functions KMAX()ISLS and KIN()ISLS having the same meanings as discussed in the case of the P1(0) function. Thus using Eqs. (18) and (19) with cos (0),= 1, we obtain the following expressions for the pulse ratio envelopes: KF (0) = MAX ISLS OLFO(0) SLS+q (21) F (0) K () K d K()(22) MI ISLS ocd wiin an ai l sidloe of If the far field point is located within an azimuthal sidelobe of the interrogator directional antenna, then the received pulse ratio can be obtained by the same expressions given above (Eqs. 18 - 22) provided their right hand sides are multiplied by the quantity L which represents the sidelobe level compared to the main beam amplitude (note: in general 0< L < 1). With the known pulse ratio functions, the main beam killing and false target zones in space can be obtained in the same manner as in the SLS case [1]. In the present ISLS case there will be zones corresponding to each envelop of the pulse ratio. In general for given threshold levels of the receiver, the main beam killing zones will be more serious at the minimum envelopes and the sidelobe punchthrough zones would be more serious at the maximum envelopes. 2.5 Effective Azimuth Beamwidth and Number of Replies So far we have investigated the various field intensity functions in a vertical plane passing through the plane of symmetry of the azimuthal plane pattern of the 15

directional antenna of the beacon. In the present section we investigate the behavior of these functions with respect to the variation of the azimuth angle. It should be noted that the effective azimuth beamwidth and the number of replies elicited from a transponder depend on the azimuthal plane pattern of the directional antenna of the interrogator. Suppose that the three dimensional pattern of the directional antenna in the presence of ground can be expressed by Fs (, a) = Fd()nd(a) (23) where F d(0) is the elevation plane pattern of the antenna above ground as given in Eq. (1), and n(d(a) is the azimuthal plane pattern of the same antenna normalized such that r7d(0) =. (24) For the omnidirectional antenna we shall take the ideal rotationally symmetric azimuthal plane pattern r0(a) = 1, and hence the three dimensional pattern of the omnidirectional antenna located above ground is Fso(0,,a) = F(0), (25) where F (0) is given by Eq. (3). Applying the same procedure as in Section 2. 2, we can obtain an expression for the P1 pulse as a function of 9 and a. After introducing Fd(, a) instead of Fd(e), and (0,a) instead of (0) in Eq. (9), we obtain P(9, 'ISLS = A[F(0)d(t)] +2qFd(0)nd(a)FQ(0) cos (0,a)+ [qFo)] 2T (26) where 9(0,a) can be obtained from g(0) in Eq. (10) by taking the path difference Axcos c instead of Ax. The alternate expression corresponding to Eq. (14) is 16

Pl( O)ISLS Pl( )SLS nd(a) +2qKOP l(0)SLS nd(P2 (0) cos (0, a) + [qKP2( 2}/ (27) We again introduce the envelope functions P1(0, a)MAX and P1(, a)MIN which correspond to cos (0,a) = +1 and -1 respectively in Eqs. (36) and (27). We then have the following two general expressions for the pulse envelopes: Pi(0,a)MAX = A[Fd(e)fld(a) +qF0(e)] = Pl(e)SLSfd(a) +qK0P2(0),(28) The effective azimuth beamwidth aeff is defined as eff aeff = 2a, (30) where a1 is the positive solution of the equation P1(, a)SLS = aP2 (), (31) where a is the threshold of the transponder logic, which is nominally 9dB. For the two envelope cases the corresponding beamwidths are 2a 1MA and 2a1MIN which correspond to Eqs. (28) and (29) respectively. alMAX and alMIN are the positive solutions of the following two equations: Pl(O)SLSld(lMAX) +qKOP2(0) = aP2(0), (32) P1 SLSd (MIN )-qKoP2(0) =aP2(0) (33) As in [1i the azimuthal plane pattern of the directional antenna is taken to be the universal Gaussian function and is given by f7d(a) = exp -1.39(a/0)2, (34) where a is the total half-power beamwidth of the pattern. 17

After using Eqs. (34), (32) and (33) and some algebraic manipulations, we obtain the following: FK () - 20 log(a- Kq) 1/2 a () = 2 1 SLS 0 q)(35) iMAX ' 12. 0735 1 rK (8)L -20 log(a +qK0)1/2 a (9) = 2a 1 SLS f1 (36) iMIN() 20L 12.0735 136 where K i()SLS is the dB ratio of P1(0) to P2(0) pulses in the SLS mode of operation, i.e., Pi(e)SLS F() FK Fd(9) K (9) 20 log=20 log (SLS = 2 P2() = 2010 F )(37) For the SLS case [l] we have, from Eq. (35) or (36), with qK0 = 0, K 1(0)SLS- 20 log a 1/2 Ceff() = 2a0L 12.0735 j (38) Comparing Eq. (38) with Eqs. (35) and (36), we notice that the effect of ISLS mode of operation on the effective azimuth beamwidth is equivalent to a change in the threshold level for the SLS mode of operation by an amount tqK0. The number of replies corresponding to the two envelope functions are f. N () = A (9), (39) MAX ) "1MAX f, MIN( Q1MIN( ' (40) where f. is the pulse repetition rate and 2 is the angular scanning speed in deg/sec. 1 Typical values of f and p are f. = 350 pulses/sec = - 90~/sec for terminal installation, - = 36~/sec for enroute installation. 18

The number of replies from the SLS mode of operation has been discussed in [1] and is given below for comparison: f. N(e) = (6) (41) SLS = 2eff As explained in [l], the effective azimuth beamwidth and number of replies have practical meanings for relatively close targets such that the replies from them in the absence of SLS or ISLS mode of operation could be obtained in an azimuth angle range wider than the conventional 3 dB beamwidth azimuth range. 2.6 Coverage Diagram The maximum range of a beacon system is a statistical quantity depending on the acceptable probability of detection and the tolerable probability of "false alarm". For the purpose of the present analysis we shall adopt the following convention which appears to be appropriate for practical purposes: Let R0 denote the maximum free space range of a beacon system in the SLS mode for some given and convenient probabilities of detection and false alarm. Suppose that this range R0 is given to us as a parameter. Then all unknown constants in the various field intensity expressions discussed in earlier sections (e. g., the excitation power, minimum detectable signal, etc.) can be expressed in terms of this parameter. If P 1(0) min denotes the minimum detectable ISLS P1(6) pulse at the transponder point, then it can be shown from Eq. (9) that the corresponding range is given by (30W G) 1)/2 1 R()ISLS l()d()] +2qFd(0)F0(0)cos () + qF()2, (42) ISLS (4ind ) where the range R is now expressed as a function of the elevation angle 0. The maximum free space range in SLS mode is evidently given by (30W G d 1/2 0 P1() (43) min 19

where Pl(0). refers to the minimum detectable P1 pulse in the SLS mode. min Combining Eqs. (42) and (43) we obtain the following expression for the range: IRSLS= R o{[Fd) +2qFd(O)FQ(e)cos C() + [qF (o)I2 (44) where we have assumed that the minimum detectable P1 pulse amplitudes are the same in both ISLS and SLS modes of operation. Eq. (44) is the desired expression for the coverage diagram in ISLS mode of operation. After introducing the envelope functions we obtain the following two range equations appropriate for the maximum and minimum envelopes: R (6o)R [F -) +qF (Oil R() qR F () (45) MAX = 0 = SLS 0+O0( R (0INe) R Fd(e) qF()1 =R(e) S-qR F (oF0(e) (46 MIN OVd J SLS ' (46) where R(0) is the range at an angle 0 in the SLS mode of operation. All curves SLS which represent the true coverage diagrams in ISLS mode will always lie between the two envelope curves given in Eqs. (45) and (46). Typical values of R are R = 40 nautical miles for terminal stations and R0 = 200 nautical miles for enroute stations. 20

3. FREE SPACE PATTERNS OF THE TEST ANTENNAS In the previous chapter we have discussed theoretically the methods of obtaining the various quantities characterizing the ISLS mode performance of ATCRBS. To obtain quantitative results for any of these quantities the free space patterns of the interrogator antennas must be available. Detailed discussions of the analytical expressions for the free space patterns of various test antennas used in the present investigation have been given in [l] and will not be repeated. For completeness of the report and for quick reference we give here the final expressions for the free space patterns of the antennas. 3.1 Antennas Under Study 1].l Performance of the beacon system using nine different antennas are studied in the present investigation. These are the Westinghouse array antenna [7]. Texas Instruments reflector antenna [9n the existing "hogtrough" antenna [o], Hazeltine E-scan antenna [11], enroute Texas Instruments Instruments Fix antenna (TI Fix Antenna) [8] enroute NADIF Fix with Texas Instruments omni antenna (NADIF Fix I) [8], enroute NADIF Fix with Westinghouse omni antenna (NADIF Fix II) [7], and enroute NADIF Fix with existing small omni antenna (NADIF Fix 1I) [io]. All these antennas are described in the references cited. The method of obtaining analytical expressions to approximate the given elevation plane patterns of all nine antennas mentioned above is discussed in [1]. In the following sections we quote the expressions appropriate for each antenna without giving their derivations. 3.2 Analytical Expressions for the Free Space Elevation Plane Patterns of Various Antennas [ 1 3.2.1 Westinghouse Array Antenna. The free space elevation plane pattern of the directional antenna is given by 1 sin (cos e)cos sin0) F ) 15.86 2c2s 5.42014+ ancos(npdsine+~, (47) d 15.t86 cos e 4 n=1 nl where the coefficients a and ~n are given in Table 1. n n 21

TABLE 1: EXCITATION COEFFICIENTS OF THE ELEMENTS OF THE WESTINGHOUSE ARRAY ANTENNA Element No. Amplitude a Phase in deg. n n n 7 0. 8108 -91.27 6 0.6346 -47.04 5 0.2644 -151.88 4 1. 1086 -64.65 3 0.4554 13.02 2 1.7039 -135.06 1 4.3738 -64.85 0 5.4201 00.00 It should be noted that the array has seven more elements numbered from -1 to -7 whose excitation may be obtained from Table 1 with a = a and _n = -. -n n -n n A plot of fd(6) vs. O may be found in [l]. The free space azimuthal pattern of the directional antenna is given by rd(c) = exp [-1.39(a2. 25)2], (48) where a is in-degrees. The free space elevation and azimuthal plane patterns of the omnidirectional antenna are given by the following: f0(0) = fd(0) as given by Eq. (47) (49) no() = 1 3.2.2 Texas Instruments Reflector Antenna. The free space elevation plane pattern of the antenna is given by n=10 sin [r sin0O fd() e= f (e ) L.084 (50) = - d. n rsin 1 n n=-2 1 L0.07846 The coefficients f (6 ) and 0 in Eq. (50) are given in Table 2. d n n 1 22

TABLE 2: SAMPLED VALUES OF THE PATTERN FUNCTION FOR THE TEXAS INSTRUMENTS REFLECTOR ANTENNA n -2 -1 0 1 2 3 4 5 6 7 8 9 10 eo n -9.0 -4. 5 0.0 4.5 9.0 13.6 18.3 23. 1 28. 1 32.3 38.9 44.5 51.3 f (e ) d n 1 0.084 0.080 0.500 1.000 0.800 0. 860 0.790 0.860 0. 960 0. 540 0. 230 0. 120 0.060 A plot of fd(0) vs. 0 as given by Eq. (50) can be found in [1]. The free space azimuthal plane pattern of the antenna is given by rid(a) = exp -1. 39(a/2. 36)2] (51) where a is in degrees. The free space elevation and azimuthal plane patterns of the omnidirectional antenna are given by the following: f0(e) = fd(e) as given by Eq. (50) o0(a) = 1 (52) 3.2.3. Hazeltine Open Array Antenna. The free space elevation plane pattern of the antenna is given by 3 fd(e) =n 1fd1(en) i 'r sin80 - sin O - Xr.. 2250 (53) 23

where 6 and fd (0 ) are given in Table 3. n dL n 1 TABLE 3: SAMPLED VALUES OF THE PATTERN FUNCTION FOR THE HAZELTINE OPEN ARRAY ANTENNA n 0 1 2 3 n 0.00 13.0 26.75 42.40 f (e) 0. 500 1.000 0. 885 0.530 A plot of fd(6) vs. e as given by Eq. (53) may be found in [1]. The free space azimuthal plane pattern of the antenna is given by nd(a) = exp [-1.39(a/2. 30)2 (54) where a is in degrees. The free space elevation and azimuthal plane patterns of the omnidirectional antenna are given by f0(0) = fd(e) as given by Eq. (53) 0 (a) = 1 } (55) 3.2.4 Existing Hog-Trough Antenna. The free space elevation plane pattern of the directional antenna is given by n=+2 f(0)= - n=-2 r sine f ( n) 10.47767 d1 n. sine ~ 1 LO. 47767 - (56) where 8 and fd (0) are given in Table 4. n 1 24

TABLE 4: SAMPLED VALUES OF THE PATTERN FUNCTION FOR THE EXISTING HOG-TROUGH ANTENNA no f (6 ) n d1 n -2 -72.80 0.084 -1 -28.55 0. 510 0 0.00 0. 966 1 28.55 0.780 2 72.80 0.045 A plot of fd(e) vs. 0, as given by Eq. (56), may be found in [1]. The free space azimuthal plane pattern of the directional antenna is given by rd(0) = exp [-1. 39(a/2.27)2], (57) where a is in degrees. The free space elevation and azimuthal plane patterns of the omnidirectional antenna are given by f0 () =fd(O) as given by Eq. (56) 1 0 d (58) 0(a) = 1 J 3.2.5 Hazeltine E-Scan Antenna. The free space elevation plane pattern of the directional antenna is given by n=6 s r sin L 1 f = E f (o. 11942 - i (59) n=-3 1 n -Lo"942 -n where 6 and fd (6 ) are given in Table 5. n d n A plot ok fd(0) vs. 0, as given by Eq. (59) may be found in [i]. The free space azimuthal plane pattern of the directional antenna is given by frd(a) = exp [-1. 39(a/2. 33)2] (60) where a is in degrees. 25

TABLE 5: SAMPLED VALUES OF THE PATTERN FUNCTION FOR THE HAZELTINE E-SCAN ANTENNA n 0 f (e) n d n -3 -21.00 0. 079 -2 -13.80 0.072 -1 -6.85 0. 030 0 0.00 0. 530 1 6.85 0.915 2 13.80 0.945 3 2.100 0. 845 4 28.55 0.845 5 36.70 0.315 6 45.80 0. 034 The free space elevation and azimuthal plane patterns of the omnidirectional antenna are given by f0(0) = fd(0) as given by Eq. (59) (61) r(o() = 1. 70((a)= 3.2.6 Enroute Texas Instruments Fix Antenna. The free space elevation plane pattern of the directional antenna is given by n=12 sin r sine - fd(= d (O ) L0583 n] (62) n=-2 ( 1 [ 0. 0583 where 0 and fd ( ) are given in Table 6. n d n A plot ok fd(0) vs. 0, as given by Eq. (62) may be found in [1]. The free d space azimuthal plane pattern of the directional antenna is given by?d(a) = exp[-1.39(a/1. 5)2] (63) where a is in degrees. 26

TABLE 6: SAMPLED VALUES OF THE PATTERN FUNCTION FOR THE ENROUTE TEXAS INSTRUMENTS FIX ANTENNA n f (e ) n d n -2 -6.70 0.010 -1 -3.33 0.039 0 0.00 0.561 1 3.33 0.990 2 6.70 0.482 3 10.10 0.450 4 13.50 0.435 5 17.00 0.420 6 20.50 0.355 7 24.10 0.417 8 27.80 0.342 9 31.65 0.350 10 35.70 0. 334 11 39.90 0.240 12 44.40 0. 120 The free space elevation and azimuthal plane patterns of the omnidirectional antenna are given by f0(0) = fd(0) as given by Eq. 62), ( (64) r?0(0) = 1 J 3.2.7 Enroute NADIF Fix Antennas (NADIF Fix I, II and I). The three enroute NADIF Fix antennas use the same directional antenna but different omnidirectional antennas. The equivalent vertical apertures of the NADIF Fix directional antennas are taken to be the same as that of the enroute Texas Instruments Fix antenna. Consequently the free space elevation plane patterns of the NADIF Fix directional antennas are given by Eq. (62) where the coefficients n and fd (0 ) n d n are given in Table 7. A plot of fd(e) vs. 0, as given by Eq. (62) with coefficients of Table 7, may be found in [1]. The free space azimuthal plane patterns of NADIF Fix directional antennas are given by 27

r(a) - exp [-1.39(a/1.53)2] (65) where a is in degrees. TABLE 7: SAMPLED VALUES OF THE PATTERN FUNCTION FOR THE ENROUTE NADIF FIX ANTENNAS n -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 0 n -6.70 -3.33 0.00 3.33 6.70 10. 10 13.50 17.00 20. 50 24.50 27.80 31.65 35.70 39.90 44.40 f (0) d n 1 0.010 0.094 0.635 0. 990 0.530 0. 542 0. 515 0.515 0. 430 0.465 0.437 0. 302 0. 302 0.217 0. 153 The free space elevation and azimuthal plane patterns of the NADIF Fix I omnidirectional antenna are given by f0(0) = fd(0) given by Eq. (62) with coefficients in Table 7,. (66) no(a) = 1 J The free space elevation and azimuthal plane patterns of NADIF Fix II antenna are given by f (0) = fd(0) of the Westinghouse array antenna as given by Eq. (47), (67) 0(a) = 1 28

The free space elevation and azimuthal plane patterns of NADIF Fix II antenna are given by f (8) = fd(0) of the existing hog-trough antenna, as given by Eq. (56) (68). (68) rO(a) 1 Notice that the elevation plane patterns of the directional and omnidirectional antennas of NADIF Fix II and III antennas are not identical. 3.3 Summary of the Important System Parameters The ISLS mode performance of the ATCRBS using all the antennas, discussed in the previous sections, are investigated in the present study. In each case the appropriate antenna pattern functions are used to obtain the desired performance parameters discussed in Section 2. In addition to the pattern functions, the following parameters characterize each system studied: Hd is the height of the phase center of the directional antenna expressed in feet, H0 is the height of the phase center of the omnidirectional antenna expressed in feet, K0 is the nominal pulse ratio in dB, usually taken to be 18dB, 1/q is the nominal ratio between the P1 pulse amplitudes radiated by the directional and omnidirectional antennas in free space, usually 1/q = 18dB. 0 is the total azimuthal half-power beamwidth of the directional antenna, expressed in degrees, a is the field gradient at the horizon and is defined to be the rate of decay g of the field in dB per 1~ below the horizon, X is the free space wavelength, X = 11.464 inches at f = 1. 03 GHz, f. is the pulse repetition frequency, f2 is the scanning rate in degrees per second. 29

The various antenna systems to be studied, along with the important parameters characterizing each system are shown in Table 8. TABLE 8: SOME IMPORTANT PARAMETERS OF THE ANTENNA SYSTEMS Antenna Type Hd H0 0 a KO or q fi 10 g Westinghouse Array 34 42 2.25 2.5 18 360 90 3 Texas Inst. Reflector 34 43 2.36 3.4 18 360 90 Hazeltine Open Array 33 37 2. 30 1.6 18 360 90 s Existing Hog-Trough 41 43 2. 27 0.37 18 360 90 H Hazeltine E-Scan 16 16 2.33 2.4 18 360 90 Westinghouse Array 82 90 2.25 2.5 18 360 36 Texas Inst. Reflector 82 91 2.36 3.4 18 360 36 o Existing Hog-Trough 108 110 2.27 0.37 18 360 36 g Texas Instruments Fix 92 112 2.2 5.0 18 360 36 NADIF I 92 112 1.53 5.0 18 360 36 X NADIF Fix I 92 111 1.53 5.0 18 360 36 NADIF Fix II 92 111 1.53 5.0 18 360 36 NADIF Fix III 92 110 1.53 5.0 18 360 36 All the terminal antennas, except the Hazeltine open array and the E-scan antennas, are mounted on a 27-foot tower. The Hazeltine antenna is mounted on a 17-foot tower. All the enroute antennas are mounted on a 75-foot tower. 30

4. NUMERICAL RESULTS AND DISCUSSION In the present chapter we give the numerical results obtained for the various quantities of interest characterizing the performance of the ATCRBS using different antennas. Short discussions of results are given wherever appropriate. 4.1 The Computer Program A computer program has been developed to obtain numerical and/or graphical results for the various quantities described in Section 2. The program is capable of handling simultaneous the SLS and ISLS mode of performance of the ATCRBS using the different test antennas discussed in Section 3. For the ISLS mode of operation, the computer output consists of the following: 4.1.1 free space elevation plane patterns of various ATCRBS antennas (tabulated numerical results), 4.1.2 Pl()MAX, Pi(e)MN and P2(0) in dB as functions of the elevation angle 0 (graphical). 4.1.3 pulse ratios KMAX(0)SL = Pl(e)MA P2(e), KMN()SLS = P1()MIN/P2(0) in dB as functions of 0, normalized to the free space nominal value K (= 18dB) (graphical), 4.1.4 effective azimuth beamwidths a MAX(e) and a MIN(0) as functions of 0 (tabulated), 4.1.5 number of replies NMAX(0) and NMN (0) as functions of 0 (graphical). From the above results, the main beam killing and sidelobe punch-through zones and the coverage diagram for each antenna system are prepared using the methods described in [i]. The program can handle arbitrary combinations of Hd and H, arbitrary nominal pulse ratios K and 1/q, any values of f and Q for any chosen range of the elevation angle 0. The complete program is given in Appendix A. 31

4.2. Numerical Results for Terminal Installations In this section numerical results are given for the terminal ATCRBS using different antenna systems. The method of obtainining some of the diagrams is described in more detail only for the Westinghouse antenna which is considered first. Since the same procedure is used to obtain the results for other antennas, the discussion of the method will not be repeated for the other systems. 4.2. 1 Westinghouse Array Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are, respectively, Hd = 34' and H = 42'. The vertical aperture of each antenna is 8'. The free space elevation plane patterns of the directional and omnidirectional antennas are assumed to be identical. Figure 6 shows P1(0)MAX, P1(0)MIN and P2(0) in dB as functions of 0, MAX' MIN where the zero dB level is adjusted to coincide with the maximum P1(0) level in the free space case. The corresponding free space curves (for q = 0) are also shown in Fig. 6 for comparison. Note that the two free space level curves are displaced from each other by the nominal pulse ratio of 18dB. Observe that for the SLS case q = 0 and the P1(e) curve for the same antenna would lie between the SLS Pl(MA) and Pi1()MN curves shown in Fig. 6. (See also [1].) For the value MAX MIN of q used here it is found from Fig. 6 that the lobing structures of P((e)MA and P1(e)MN are approximately the same and are displaced from each other by a certain amount. The amount of this displacement depends on the parameter q and the elevation plane pattern of the omnidirectional antenna in the presence of ground. The lobing structure of the P2(0) curve is different from the two P1(e) curves. The oscillations in the curves are found to be less than 1 dB fore 0- 30 and for 0 > 50 the P2 curve assumes the free space value, and P1(e)MA and P1(e)MIN curves assume their respective saturation values above and below the free space value. Figure 7 shows the envelopes of the pulse ratio KMAX(0)ISLS and KMIN(e)ISLS as functions of e and normalized to the nominal free space value K0 (= 18dB). Observe that the maximum envelope curve lies above the minimum 32

- -FREE SPACE LEVELS C) S. o 0 IMAX MIN "I' V 1.00 2.00 3i00 1Loo S.00 RNGLE FROM HORIZON QEGREES WESTINGHOUSE ANTENNA FREOQ = 1030. 000 MHZ ELEVv: DIREC. 34.00 OMNI. I2.00' P1/P2= 18.00 OB P1 DIRu/OMN*= 18.00 08. FIG. 6: P1(O)MAXJ P1(O)MIN and P2(O) as functions of 0. 33

0 Cl 9-4 SIDELOBE PUNCH THROUGH,THRESHOLD FOR Ko=18dB 013 C0 a I I I I I MIN I I I I I MAIN BEAM KILLING I THRESHOLD FOR Ko 18dB 1 7 —, - +, - - - - - - - - - - - -- or c. 1.00 2.00 3.00 RNGLE FROM HORIZON DEGREES 4.00 5.00 WESTINGHOUSE RNTENNR FREQ.= 1030.000 MHZ ELEV.: DIREC. 34.00' OMNI. 42.00' P1 DIR./OMN.= 18.00 DB. FIG. 7: Normalized pulse ratio envelopes as functions of 6. 34

envelope curve. As a result, the maximum and minimum values of K MAX()ISLS are larger than those of KMIN(0) SLS. This implies that the main beam killing would be more serious at the minima of KMIN(0)ISLS and the sidelobe punch-through would be more serious at the maxima of K MAX(0)iSL. For 0 > 4 the oscillations MAX ISLS in the pulse ratio curves may be considered to be negligible. The main beam killing and sidelobe punch-through zones for the antenna are obtained from the normalized pulse ratio curves shown in Fig. 7. The main beam killing zones in space are those regions in space where the pulse ratio falls below a given threshold level a [ij For a pulse ratio curve normalized to the nominal free space value KO0 the main beam killing threshold occurs at (a - K0) dB. Thus with a = 9dB and Ko 19 dB, the main beam killing threshold occurs at (9- 18) = -9dB as shown in Fig. 7. The sidelobe punch-through zones in space are those regions in space where the pulse ratio rises above the sidelobe punch-through threshold level b [1]. For a pulse ratio curve normalized to the nominal free space value of K dB, if the azimuth sidelobe level of the antenna is -L dB, the sidelobe punch-through threshold level occurs at (b+L-K )dB. With b 0 OdB, L = 25 dB and K = 18 dB, the sidelobe punch-through threshold level occurs at (0 +25 - 18) = 7 dB, as shown in Fig. 7. Figure 8 shows the potential main beam killing and sidelobe punch-through zones as functions of the nominal pulse ratio K0. These zones have been obtained from Fig. 7 with a = 9dB, b = 0dB and L = -25 dB. It should be noticed that in Fig. 8 there are two sets of zones corresponding to the two pulse envelope ratio curves shown in Fig. 7. Observe that the main beam killing zones for the maximum envelope ratio lie within those for the minimum envelope ratio whereas the sidelobe punch-through zones for the maximum envelope ratio lie outside those of the minimum envelope ratio. As can be seen from Fig. 8, for K = 18dB there are two main beam killing zones and two sidelobe punch-through zones for the range 0 < 0 < 3~. Figure 9 shows the effective azimuth beamwidths aMAX (e), a1MIN(0) as functions of 0 for the threshold level a = 9dB and nominal pulse ratio Ko = 18dB. 35

MAINSEAM IKILLNG 7.oNES 3,a. I (n (D. W0 Z S 2 0 W. LL. U.j, (D Z4 lz I %.F v - ItA Da - lu 0 5 RATIO 1% 0 5 S's - US of t4OMINAL pjLSE 'h zones as junctio 34111,,d.1dolobe Punc"..ttiroug nua. lid:= am killm for tbe Wes e grra-Y =te gdB., - 18.00 dB, a::O -FIG. 8. Mainbe pulse ratiO the novainal - 1030 b&lizl pIDUtiOM"' R = 421., f - 25 dB. b 0- 0 d13.0 L = "' 36

u) wL 6 LU \MAX z 5 r 3 ID IMIN H- 3 w 2 LULL LL LLJ 0 1 2 3 4 5 ANGLE FROM HORIZON IN DEGREES FIG. 9: Effective azimuth beamwidths as functions of the angle from the horizon for the Westinghouse array antenna. H = 34', H = 42', f = 1030 MHz, nominal pulse ratio K = 18dB, P1 DIt/OMNI = 8 dB. 37

For 0,3 the effective beamwidths assume constant values of about 4.6~ and 2.20 at the maximum and minimum envelope cases respectively. In the SLS mode of operation with the same antenna the free space constant value of the effective azimuth beamwidth is about 3. 9. Figure 10 shows the number of replies NMAX(), NMIN(0) as functions of 6. MAX MIN These have been obtained by using Eqs. (39) and (40) with f. = 360 pulses/sec and = 90 deg/sec (15 rpm). Since the number of replies is an integer, Fig. 10 is obtained by taking the first integer which is less than or equal to the solution of Eq. (39) or (40). It is found from Fig. 10 that at any angle 0 the number of replies is larger for the maximum envelope case. Both NMAX(O) and N (0) are oscillating MAX MIN functions of 0. For the antenna considered in Fig. 10 the numbers of replies assume constant values for > 3. 5. The saturation values of N and N are found MAX MIN to be about 18 and 7 respectively. It should be noted that the saturation value of the number of replies is about 15 for the same antenna in the SLS case [i]. Figure 11 shows the coverage diagram for the antenna normalized to the maximum free space range of 40 nautical miles. The diagram has been prepared with the conventional 4/3 radius of the earth to take into account the normal refraction at the lower atmosphere. Equations (45) and (46) have been used to obtain the ranges as functions of 0. As shown in Fig. 11, for the maximum envelope case the maximum range of 50. 5 nautical miles occurs at 0 - 0. 4 and the minimum range of 14 nautical miles occurs at 0-0. 90. The corresponding ranges for the minimum envelope case are 40 nautical miles at 0 -- 0. 4 and 7 nautical miles at - 0. 9, respectively. For comparison the SLS mode free space coverage diagram for the same antenna is also shown in Fig. 11. 4.2.2 Texas Instruments Reflector Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are, respectively, Hd = 34' and H0 = 43'. The free space elevation plane patterns of the directional and omhidirectional antennas are assumed to be identical. Figure 12 shows P1() MAXO P1(e)MIN and P2(0) in dB as functions of 9, where the 0 dB level is adjusted to coincide with the maximum P1()SLS level in the 38

0 Cl =*. ~l 8" MAX I rj r r - - r I r I I I r L i, r i 1 1 1 r I I r n r1 r'.... r I I L r I I I I I I I I I I J I I 1.00 2.00 3.00 4.00 5.00 RNGLE FROM HORIZON DEGREES WESTINGHOUSE RNTENNR FREQ.= 1030.000 MHZ ELEV.: DIREC. 34.00' OMNI. 42.00' P1/P2= 18.00 OB P1 OIR./OMN.= 18.00 DB. FIG. 10: Number of replies as functions of angle from the horizon. 39

800 60*r5d 40 300 25 20I 1816, 140 1 20,0e88 50T 1 i I I I I I ~I I I 1 1 95 1 7.5 - 0 tI I 32 0j- 4 82 1 2A4 2 2 6 4 4 48 5 6 6 d ' 59 D 50 0,50 1) 50 0 5 0 0. 0 5 0 . 50

- — FREE SPACE LEVELS PI.00 1.00 2.00 3.00 4.00 5.00 ANGLE FROM HKORIZON DEGREES TEXRS INSTR. RNTENNA FREQ.= 1030.000 MHZ ELEV.: DIREC. 34*00' OMNI. 43.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 OB. FIG. 12: Pe.)MA,% Pl(e) MIN and P2(e) as functions of e. 41

free space case. The corresponding free space curves (for q = 0) are also shown in Fig. 12 for comparison. The oscillations in the curves may be considered to be negligible for > 4. 5. The general behavior of the curves is similar to Fig. 6 for the Westinghouse antenna. Figure 13 shows the maximum and minimum envleope pulse ratios as functions of 0 and normalized to the nominal free space value K (= 18dB). The oscillatory nature of the curves may be considered negligible for 0 > 4. 5~ The main beam killing and sidelobe punch-through zones as functions of nominal pulse ratio are shown in Fig. 14. For K = 18dB there is one main beam killing zone and two sidelobe punch-through zones within the range of 0 shown in Fig. 14. Figure 15 shows the effective azimuth beamwidths alMAX(0), a1MIN(0) as functions of 0 for the threshold level a = 9dB and the nominal pulse ratio K 18dB. For 0 > 4.50 the curves assume constant values given by lMAX 4.80 and a1MIN - 2. 30. In the SLS mode of operation with the same antenna, the free space value of the effective azimuth beamwidth is about 4. Figure 16 shows the number of replies NMA(0), N (0) as functions of 0. MAX MIN For 0 > 4. 50 NMX(0) -- 19 and NM 7. For the same antenna the saturation MAX MIN value of the number of replies is about 16 in the SLS case [1]. Figure 17 shows the coverage diagram for the antenna normalized to the free space maximum range of 40 nautical miles. As shown in Fig. 17 for the maximum envelope case the maximum range of about 44 nautical miles occurs at 0 -- 0. 4 and the minimum range of about 6 nautical miles occurs at 0 -0. 7. The corresponding ranges for the minimum envelope case are about 34 and 3 nautical miles respectively. 4.2.3 Hazeltine Open Array Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are, respectively, H = 33' and H = 37'. The vertical aperture of the antenna is 4' and it is assumed that the free space elevation plane patterns of the directional and omnidirectional antennas are identical. 42

-4 -0~ 0IC 0 - I oMAX MI I' I 4r I 1 *I I TX I AN1 0 P1i4 1.OM. 1 8.0NB 1: g l a / I: I I i ig~ 1 \ i ~ I V 3 II I I I I Fl OR./M. 180 OB FIG. 13Nomlzdplertoevlpsafucinof0 43

3 MAIBE.AM KILLING ZONES 2.; 2 SIDEUBE PUNCH-THROUGH ZONES 1.6.6 0.4 MAX F0I 0.1 2 t3 14 NOMpNAL PULSE RAOO Ko IN DS FIG. 14: iainbeam klling aNd sidelobe punchthrough zones as a unctlons os G the nominal plse ratio for the Texas iustrunents reflecting an. tenna. Hd = 34', H0 — 43', f = 1030 MHz, pU DIR/OMRI = 18.O0 dB, l9dB B3 = riHo L = -25 dB. & - dB, 3 = dB,,AA 4*1*

6 MAX w i. 4 i / MIN.==3 N.... 0 1 2 3 4 5 ANGLE FROM HORIZON IN DEGREES FIG. 15: Effective azimuth beamwidths as functions of the angle from the horizon for the Texas Instruments reflector antenna. H = 34', H = 43', f = 1030 MHz, nominal pulse ratio K = 18dB, 1 DIR/OMNI = 18dB. 45

0 - 8 0 -- 0_ LJ CZ MAX IIFL I r r I I L I I MIN r- i- r -1 L I.I_ L L r I' L I I I I I I, I I I r I I I I r U I (Ir I I 1.00 2.00 3.00 4.00. 00 RNGLE FROM HORIZON DEGREES TEXRS INSTR. RNTENNR FREQ.= 1030.000 MHZ ELEV.: OIREC. 34.00' OMNI. 43.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 DB. FIG. 16: Number of replies as functions of angle from the horizon. 46

80d' 60d5d' 40" 30 0 2e' 2p 1~'1 04 14 le2 I " d 109.5 9" 8.5 9' 7T*5 A I. I I. —I. —, I.. -I-. I I -. - I. - A — A - A. -r % I I I I I I I I I I I I I a. -.4 \1 k II I/ I/ I I/ I/ I A I/V 40, 36 32, H w w 0 tn% -- I I I I — V- t-l — I A I- I/ -- I- / I - V 1- 1 /I I - - I/ A -A A y I — I - X- t — I 1\ -- Y / I A/ V/ I I k I A v A __v I- 11/1"I I-V I — --- -.. I. I. N i - I - I I 1. -A I I -N.; / A A I/ v I/ I A I \1 Al I / 1/1- A A A.T- -1 I i — A I v I /I 11 i I V 17 T 1 1 1 7' 17' t 7" t t,, 1 1, 4 6",, - I A v v I/ v Y I/ I y a,! I I 9 41 1 1 - 9 4 4 1 - /I V 11 A / I v A /I, I I.-I I I - I" — I z I 1.111 11 I I z lr —. I ---- 11-A A A 1-1 A A/ I 1/1... I. - - I, j I i i f i I.;.- .. - - _74- 1 - V — - I-/-I V — I I --- I M!1/ -1/ VU T r —Ir 1/..... -. I. -2 - I - I I I... I. ---- -.- - - - - - -I I L i 1EV '1 A/W17 i - -'it - 1 -+ 6, 1 4 I -,WL / vj9a-? -1 -. I - i I mfe-Gf N'T 1 V j I. I i 71 - ' —4 i '-..~-~ - 1 --- JLA#6 ".% 9- -T I Uz XL MIYAA A' Ai /rKk -L I I I.,o,' I - -- -.... -1. I. z I -W m r I t I.. I.. -. — 21 t - - / I --- - I - i -1 I -\!\I )T yY V/V V P-Irl - --.. I- - -. -1 /Lmd —l: 460 -.4 z CD' IL 16 - F- i!-P -i! —.,Ooo i ft - 7' 1 A li 1 A 74 - - -71 - -17' W 'MI ,, " - - - c - - -- FR SPAC.................. "now 4.50 60 0.50 50 J\I- - -V-/WY/ I/I! A I z I z I z i v lot; I- L-to -.... I 1., --- "., Z I., I Z L I. I ". I-. A I.- I. - ---- - - - --— r A-el -F -- it&\ II2V2L I Z1AJ2I21IK - i. I U i a I I I I I I - r. I.,.. - - - - I I - -w% p - a OKlQ%- - d - I I / A //r/,v A 1-1-1 - I I I -1 I/ J - v -I- I / I Z Ll - I ---- li- '. -. -. ir 0,I 1/1/ /,Y/A/ Y IA~//AX >[l-2.t. vr- -__ WOW,vIly, " ", -: L PIL -a:= 0-0,- Y —7=': -- n- JI W~-= I I I I I I I I I I I I I I I a I I I I I I I- I I I I _ I I _ I mmrmvw - - - - v -. - -, - I. 4 - I I I I I I I 9 I, I I i I 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 SLANT RANGE IN NAUTICAL MILES [G. 17: Coverage diagram for the Texas Instruments reflector antenna. H d = 34', Ho 43',1 f = 1030 F1 MHz

Figure 18 a shows P1(O)MAX' P1()MMIN and P2(e) pulses as functions of 0 where the 0dB level is adjusted to coincide with the maximum of P 1()SLS level in the free space case. Due to the small field gradient (a = 8dB/5 ) of the ang tenna, the oscillations of the patterns in Fig. 18 a are not so quickly damped out as in the case of the previous two antennas. For this reason, Pl(0)MA P1(0)MIN and P2(0) curves in the extended region 5~ <9 < 10~ are shown in Fig. 18 b. For 0 > 10~ the oscillations in the curves are negligible. The pulse ratios as functions of 0 are shown in Figs. 19 a and 19 b for 0 < < 5~ and 5~ < 0 < 10~ respectively. The main beam killing and sidelobe punch-through zones as functions of nominal pulse ratio are shown in Figs. 20 a and 20 b. For Ko = 18dB there are four main beam killing zones and four sidelobe punch-through zones for the range of 0 values shown. Figures 21 a and b show the effective azimuth beamwidths as functions of 0 for 0 < 0 < 50 and 5~ < 0 < 100. The oscillations in the curves continue up to 0 10~ and beyond 0 = 10~ they assume their respective saturation values. The saturation values for the maximum and minimum envelope cases are about 4.7 and 2.0 respectively. In the SLS mode of operation with the same antenna, the free space value of the effective azimuth beamwidth is about 4. The number of replies as functions of 0 are shown in Fig. 22 for the range 0 < 0 < 50. The saturation values of NMAX(0) 19 and NMIN(0) -'8, which occur for 0 > 100. For the same antenna operating in the SLS mode, the free space value of the number of replies is 16. The coverage diagram normalized to the free space maximum range of 40 nautical miles is shown in Fig. 23. As shown in Fig. 23 for the maximum envelope case, the maximum range of about 44 nautical miles occurs at 0 0. 4 and the minimum range of about 8 nautical miles occurs at 0 ~ 0. 80. The corresponding ranges for the minimum envleope case are 34 nautical miles and 5 nautical miles respectively. 4. 2. 4. The Existing Hog-Trough Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are 41' and 43' respectively. The vertical aperture of each 48

-. --- FREE SPACE LEVELS 0 -j0 cf) I' clu 94, 0.1 LOO6,0 LO10 3.-00 COO0 5.00 RNGLE FROM HORIZON DEGREES H1RZELTINt. RNTENNR FREQ*= 1030.000 MHZ EbLEW: DIREC. 33.00' OMNI. 37.00' Pl/P2= 18.00 06 Pl DIR.IOMN.= 18.00 08. FIG. 18 a: P1(e) Mr P1(e) ANand P2(e) as functions of 0. 49

~ 10.-* — FREE SPACE LEVELS 9.00 HR.MaLUl'NE PNTENNR F REQ. = t030.000O MHZ tLEV.: D!REC. 33.00' OM NI. 37.00 ' Pl/P2= 18.00 DS PI D IR./ON = ais Of 0 FIG. 18 b:- Pi(Oe)MAX Pl() MIN and P2(0) as functions of 8. 50

MAX r8. -J ~8 1 -cnI cn \I II I I I, I a tI I ' MIN I i I I V 1 I..I I.00 ~.00 00 3.00..00 5.00 RNGLE FROM HORIZON DEGREES HAZELTINE RNTENNR FREQ.= 1030.000 MHZ iLE V. DIREC. 33.00' OMNI. 37.00' P1 DIR./OMN.= 18.00 DB. FIG. 19 a: Normalized pulse ratio envelopes as functions of 0. 51

MAX ' / 'K%/1~,00 RNGLE FROM HORIZON DEGREES HRZELTINE RNTENNR FREQ.= 1030,000 MHZ fLEV.: DIREC. 33.00' OMNI. 37.00' P1 DIR./OMN.= 18.00 DB. FIG. 19 b: Normalized pulse ratio envelopes as functions of 0. 52

MAINBEAM KILUNG ZONES 9 SIDELOBE PUNCH-THROUGH ZONES w 1.6 1.4 z 0.2 N O 1.0 -0 0.2 10 II 12 13 14 15 16 17 18 19 20 NOMINAL PULSE RATIO Ko IN DB FIG. 20 a: Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the Hazeltine open array. Hd =33', H = 37',. f = 1030 MHz, P1DIR/OMNI- 18dB, a = 9dB, b = -25dB. 53

MAINSEAM KILLING ZONE-S / sOtBo PUNCH'-THROUGH Zo NES miN I en MIa w z_.. 3 2 12 9 ~j 8 4.* I8 t9 to ISE RAW IN zones as functionsOf NOMINAL 33',ough -, -o30 MHz, FIG 20b: MaNOemkln and stalelobe Ipunchl-thrug ' -_100M, ~ 0 33, L 0.25dB. 8 [or the Haeltine oper array. bd L. -FIG. 2dBfoo, e a -- 9 dB, p I DIm/ J ol = I8 54

6 I M z 4 3 2 I& U. 0 I 2 3 4 5 ANGLE ABOVE HORIZON IN DE ES FIG. 21 a: Effective beamwidths as functions of angle from the horizon for the Hazeltine open array. H 34', H 37', f = 1030 MHz, nominal pulse ratio K = 18dB, P1 DIR/Oi -NI 18dB. 55

6 MAX 0S I 4 a MIN, I mI I I 2 / IL 5 6 7 8 9 10 ANGLE ABOVE HORIZON IN DEGREES FIG. 21 b: Effective azimuth beamwidths as functions of angle from the horizon for the Hazeltine open array. H " 34', H = 37', f = 1030 MHz, nominal pulse ratio K = 18dBP1 DIR/OINI = 18dB. 56

MAX n MIN I., I I. I I L e I I I I r i i L I L I I I I I I I I t I I 1 1 e I I I - I s.00 1t6V.: oIFC.- 33.3t./OMNT4. = i.o00 Pt/P22: p18. m P1 DoR / t8r FIG. 22: Number of replies as functions of angle from the horizon. 57

8d' 60*5d' 4Oe 30' 25w I I I I I I 2ew le 160, 140 I I I I 120 10 id'090 0 8.50 8 r. ILL ILL IL IL (I) c I2 (2I LL 2r 36 I —./~~*-* —:-*-00 - 0 - 0 13.50 0.~ 50 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 SLANT RANGE IN NAUTICAL MILES FIG. 23: Coverage diagram for the Hazeltine open array. Hd 33'I, Ho= 37',j f = 1030 MHz. d0

antenna is about 2' and it is assumed that the free space elevation plane patterns of the directional and omnidirectional antennas are identical. Figure 24 a shows the Pl(O)MAX, P1() MIN, and P2(0) pulses as functions of 6 in the range 0 < 0 < 5, where the 0 dB level is adjusted to coincide with the maximum of the Pl(6)SLS level in the free space case. Because of the small field gradient of the antenna (a = 0. 5 dB/5 ) the lobing structure in Pl(O)MAX, g MAX P 1(e)MiN and P2(0) are much more pronounced in the present case. The oscillations MIN in the curves are found to be appreciable for values of 6 up to about 20. Figs. 24 b through d show the variations of the respective pulses for three more regions of 0, 5~ < < 10~, 10~ < 0< 150 and 15~ < 0 < 20~ Figures 25 a through 25 d show the pulse ratios as functions of 0 for four different ranges of 0. Here also the oscillations in the curve persist for 0 values up to about 20~. Figures 26 a and 26 b show the main beam killing and sidelobe punch-through zones as functions of the nominal pulse ratio. It is anticipated that these zones exist for this antenna beyond the 0 values shown in Fig. 26. If desired, they may be obtained from the corresponding pulse ratio curves for the ranges of 0 shown in Figs. 26 a and b. There are seven main beam killing zones and eight sidelobe punchthrough zones for K = 18 dB. Figure 27 shows the effective beamwidths as functions of 0 for the range 0 < 0< 5~. It is anticipated that the effective beamwidths would fluctuate for 0 values up to about 20. For 6 > 20~, clMAX(6), 4. 8~ and a MIN(0)% 2 5. For 1MAX 1MIN the same antenna operating in the SLS mode [1] the free space value of the effective azimuth beamwidth is about 3.750, which occurs at 0 > 20~. Figure 28 shows the number of replies NMAX(0) and NMIN(0) as functions of 0. For 0 > 20, NAX () v 19 and IN () ' 9. For the same antenna the saturation value of the number of replies in the SLS mode is about 15. 59

0 Co.-.-. -FREE SPACE LEVELS 0.00 - -- - -- 1.00 2.00 3.00 4.00 5.00 ANGLE FROM HORIZON DEGREES EXISTING RNTENNA TILTED RNGLE= 0.0 D ELEV., DIREC. 41.00' OMNI. 43.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 DB. FIG. 24 a; Pl(e)MAX, P1(0)MIN and P2(0) as functions of 0. MAX' MIN 60

-.- -.FREE SPACE LEVELS 4-J Cn c31 c.j US 1~cc. '.4 DIcc 0. C. C 0).Pi MAX MIN 0 EXISTING RNTENNR ELEV.: DIBiEC, 41 Pl/P2= 18.00 BB P1 T ILTED RNGLE= 0. 0 D.600' OMNI. t43.00' DIR./QMN.= 18.00 CB. FIG. 24 b: Pl(6) MX$ Pl(O) MN and P2(0) as functions of 9. 61

0 C3 ~~ 11 Mi —. —.FREE SPACE LEVELS P2 i.OC 11.00 12.00 13.00 14.00 15.00 RNGLE FROM HORIZON DEGREES EXISTING RNTENNA TILTED RNGLE= 0.0 0 ELEV.: DIREC. 41. 0' OMNI. 43.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 DB. FIG. 24 c: P1(e)MX, P1(e)MIN and P2(8) as functions of e. MAX' MIN 62

MAX r / I 938 I..p MIN - -*- FREE SPACE LEVELS P2 V-4 8 0-. rV-4. I EXISTING RNTENNR FREQ.= 1030.000 MHZ ELEV.: DOIREC. 41.00' OMNI. 43.00' P1/P2= 18.00 DB PI OIR./OMN.= 18.00 OB. FIG. 24 d: P(e))MAX, PI(O)MIN and P2(9) as functions of 0. 63

0 0 I. CY EXISTING ANTENNA TILTED RNGLE= 0.0 D ELEV.: DIBEC. 41.00' OMNI. 43.00' P1 DIR./OMN.= 18.00 DB. FIG. 25' a: Normalized pulse ratio envelopes as functions of 0. 64

(Di~ Qr C, 8 C\JS 1 1 I CL L - I r L., c' I I\ E t; IL ICD I I, I,1 t t L, 'I I ELEV., DIREC. 41.00' MN. 43. 00 ' 0 1 C If - I MIN '5.00 6.00 7.00 8.00 9.00 10.00 RNCLE FROM HORIZON DEGREES EXISTING RNTENNR TILTED RNGLE= 0.0 B ELEV.: Dt1EC. 41.00' OMNI. 13.00' P1 DIR./OMN.t 18.00 DB. FIG. 25 b: Normalized pulse ratio envelopes as functions of 0. 65

MAX MIN a % \% I V 'II 'II 'II V 00o 13.00 111.00 15.00 IORIZON DEGREES INR FFIEQO= 1030.000 MHZ 4111.00 OMNIs 113.00' l8.00 OB. EXISTING RNTEN ELEV.: DIREC. P1 DIR./OMN.= FIG. 25 c: Normalized pulse ratio envelopes as functions of 0. 66

0 0 MAX MIN I I I, I I l I II EXISTING RNTENNR TILTED RNGLE= 00 D ELEV.: DIREC. 41.00' OMNI. 43.00' P1 DIR./OMN.= 18.00 DB. FIG. 25 d: Normalized pulse ratio envelopes as functions of 0. 67

MAINBEAM KILLING ZONES / SIDELOBE PUNCH-THROUGH ZONES._ \ la ---------— _.__._____ IdI CD I 8 ' MAX a I 1.6 - Z 0 1.4 0 1.2 0 LU.j (D 0.8 0.6 0.4 0.2 10 II 12 13 14 15 16 17 18 19 20 NOMINAL PULSE RATIO Ko IN DB FIG. 26 a: Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the existing hog-trough antenna. H = 41', H =43', f = 1030 MHz, P1DIR/OMNI = 18dB, a = 9dB, b=dOdB, L -25dB. 68

z a M. u.!i NOMINAL PULSE RATIO Ko IN DB FIG. 26 b: Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the existing hog-trough antenna. H d, H = 43', f = 1030 MHz, P1 DIR/OMNi = 18dB, a = 9dB, b = OdB, L = -25dB. 69

6 i) w i z 4MIN I. L gD 33 w 12 L0 1 2 3 4 5 ANGLE FROM HORIZON IN DEGREES FIG. 27: Effective azimuth beamwidths as functions of the angle from the horizon for the existing hog-trough antenna. H 41', H = 43', f = 1030 MHz, nominal pulse ratio Ko = 18dB, Pl DIR/ONI = 18dB. 70

o) ~o 0 I I I f f f f I I f' r r r r r rr I, I r r' r r r r r r r r r r r r r r r r r tr r L r1 f Il f I fiL M r r r r rr r r'r or r r r r r r r A I rr r t P/P2 18.00 DB P1 DI.MN.= 18.00 DB. r r i i 1I 1 r A CblOO 1.00 20000.00 3.00 4.00 5.00 RNGLE FROM HORIZON DEGREES EXISTING RNTENNR TILTED RNGLE= 0.0 D ELEV.: DIREC. 41.00 OMNI. 43.00' P1/P2= 18.00 0DB P DIR./OMN.= 18.00 DB. FIG. 28: Number of replies as functions uf angle from the horizon. 71

Figures 29 a and 29 b show the coverage diagram for the antenna normalized to the free space maximum range of 40 nautical miles. As shown in Fig. 29(a) for the maximum envelope case, the maximum range of 81 nautical miles occurs at e0 0. 4 and the minimum range of 5 nautical miles occurs at 0 ^0.8~. The corresponding ranges for the minimum envelope case are 62 and 2 nautical miles respectively. 4.2. 5. Hazeltine E-Scan Antenna. This is a special beacon antenna with coincident phase centers of the directional and omnidirectional antennas. The heights of the two phase centers are Hd = H0 = 16' The vertical aperture of each antenna is 8' and it is assumed that their elevation plane patterns are identical. Figure 30 shows the P1() P()MIN and P2(8) pulses as functions of 0 where the 0 dB level is adjusted to coincide with the maximum P1(0LS) level in the SL S free space case. As can be seen from Fig. 30, the lobing structures of the curves are identical for the present antenna. As a result, the pulse ratio curves are constants with respect to 6 and the normalized values are approximately +1. 19dB and -1. 19dB respectively, as shown in Fig. 31. There is no main beam killing or sidelobe punch-through region for this antenna. The effective azimuth beamwidths a MAX(0) and a1MIN(0) are constants with respect to 0. These are MAX(0),4.75 and a1MIN(6) ~2~. The number of replies NMAX (), NM (0) as functions of 0 are MAX MIN shown in Fig. 32. They are constants with N MAX() = 19 and N MN() = 8. For MAX MIN the same antenna the number of replies is 16 in the SLS mode [1]. The coverage diagram for the antenna is shown in Fig. 33. As shown in the figure, for the maximum envelope case, the maximum range of about 4. 5 nautical miles occurs at 0 0. 9 and the minimum range of about 1.4 nautical miles occurs at 6 ~ 1. 7. The corresponding ranges for the minimum envelope case are 36 nautical miles and about 1. 2 nautical miles respectively. 72

I1 -LUJ LU u. z I O I-1rIil Z: 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0O 5.5' s5.0* 4.5* 4.0C 7.0~ 3.5* 2.5' 2.0o 1.5~ 1.0 0.5* 0 20 0 S 40 50 60 0 80 90 100 o SLANT RANGE IN NAUTICAL MILES FIG. 29 a: Coverage diagram at the maximum envelope for the existing hog-trough antenna. Hd =41' H = 43, f= 1030 MHz. 73 ).o0

80* 60r5d 40' 300 25 20 le 16 a l lI t.I.I I. I.1.1L a I 1 1.0 0 0 0a 1 2 -10 10 95 8.50 -. 4C 36 32 w w 0 0 z f), 0 z ~-12 w m E I I rt --- — - - Ei -r ~, E-I o 4 8 12 1 0 24 2 2 36 4 4 48 5 6 6 SLAN RANE INNAUTCAL ILE - 66. 5'p - 60 -5-50 -50 -4.50 0 - 4 -3.5 0 - 30 - 2.5' -Pe - 1.5" - 10 - 0.50 - 0 0 c FIG. 29 b: Coverage diagram on expanded scale at the maximum envelope for the existing hoe ~-trough antenna. H = 41's Ho= 43'8 f = 1030 MHz. d0

90 *7.0o 85 80 75 70 65 60 55 6.0~ 5.5~,4.5 4.0' 50 ILun I-. b 45 3.50 40 35 30.3.0* 2.5' 2.0' 25 20 I.S' 15 1.O0 10 o.5' 5 0 0- - - - tar O 10 20 30 40 0 0 70 80 ou SLANT RANGE IN NAUTICAL MILES FIG. 29 c: Coverage diagram at the minimum envelope for the existing hog-trough antenna. H = 41' H = 43', f = 1030 MHz. d 75

8O' 60d5d' 40' 30' 25' 200 18 I6F 14' 1.,,-.1 I -- L I 1- a -l w 1 2 1.10 1095*9 8.50 8, 0 1. I I - -7.5 m WWMR6 44 -40 *2tr - I.E -. - / I LfiLLL/ \ / I I/ l/V717A1 - i --- -- i! i IV I A VTI1A7Fq -9 i 1 -J — l. -11 a 1 - I iILy /ILL-I Ii/V77 I \ENLOIOE 16F1 A A A 7 7T7VI F 01 3 ~ w w U0 IUkfROGE ' A i. h/ //V xir IA/L I1'/ V-I,4 i. f., -. I.. - III -I - - - A / i/ I - -A -1 t - mI -. I -1 I — p "Ilzlq-t?I% pk --- — z I XKIAIIL7 1-714 6" I I-E Jt A — F -I & I I I I I I. I, PA. I e I,, 4- 1,1 44!. A. I.-.., 6 I.Z- 1 I '{ /IlY Y/VY /1 /1//-l I, E --- - - m - - PO 0000I -— abbe 4: 6.5' 450 3'5 30 ISD 0.0 I. I - 1... 1.. I -- I 11 I J, t -,an - 7. I.. I. I.... - - - - - - - - - ---- I -.11 1 ---' I 0 H-1 om Z F-1 w m,V6 - — T RI VYV -- - - - --....-. - - I I a I j- Ariz --. -. - -- JL~ fC-T7 -1 I I 11 M V a i II -T J-..,. - -W a JA/ AlXLIL/J A AidI~-k-Kt A -Fr. -., -1...-I.. I.. - - - - - - --- e-' —~ -- 9 F a /r VI --- - --............... er -, -1........I --- -1 / /T/,V 'I-,' 'I' 2 -'I 8- / 0- 1= II.,. - ,mEp;&, = I I I I I I I I I I I I I I I I I., T, I I I I~. I I I I I I I I I I I --— T I I I i - I -- I — - I I I I - — I I I -1 -- -. - - - I- I -- -- - - I - -- - -- -.-. - I — I - I I -1 - I I - I I I — r I I 9 9 - A - - I I 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 SLANT RANGE IN NAUTICAL MILES Coverage diagram on expanded scale at the minimum envelope for the existing hog-trough antenna. H =41' Ho 43,f =lO030QMHz. d '0 FIG. 29 d:

8 NW4 -- FREE SPACE LEVELS Pi MIN N% CL4 4 0 z (1: I I 1.00 2100 RNGLE FBOM HOR -- - I 3"00 W.00 sloo JZON DEGREES RNTs FREQ*= 1030.000 MHZ l6wOO" OMN14 l6wOO" PI DIRt/OMN*= 18.00 oBs HRZELTINE ESCRN ELEV.: OIREC* Fl/P2= l8wOO DB FIG. 30: Pl(O)m,, MIN and P2 (0) as functions of 0. 77

0 N J-p a: 0 --J Z.9 '.4. MAX '/ MIN '/ _ _ IM..... m, -,'of V.00 1.00 RNGLE I 1 2.00 3.00 FROM HORIZON DEGREES -.00 Ii. 00 S.OI $.00 HRZELTINE ESCRN RNT. FREQ.= 1030.000 MHZ ELEV.: DIREC. 16.00' OMNI. 16.00' PI DIR./OMN.= 18.00 DB. FIG. 31: Normalized pulse ratio envelopes as functions of 8. 78

8 em-4 0 UI MAX MIN.0 4 i a i IL 0 1.00 a:00 3.00 RN~GLE FROM HORIZON DEGREES Ii. 00 5.00 HRZELTINE ESORN RNT. FREQ.= 1030.000 MHZ ELEV.v DIFREC, 16.600' OMNI. 16.00' P1/P2= 18.00 DB PI1 DIR,/OMN,.= 18.00 DB. FIG. 32: Number of replies as functions of angle from the horizon. 79

300 eo5Cr 40e I It - I 30O0 25w' 20 IlB 16' 1 4 1 1 I I 1 1 20 1.0 I009500 go.50 0 7 5 0t -- - -- - 00 O U-. _ / / )..4 w 171 - 6.50 - 6 0 - 5.50 -50 -4.5 0 -4* -3.50 - 3 0 - 2.50 -2 0 -1.5 0 -10 - O.e 1100.- 0.50 0 4 8 12 1 20 24 28 3 3i 40 44 48 52 56 60 SLANT RANGJE IN NAUTICAL MILES FIG. 33: Coverage diagram for the Hazeltine E-scan antenna. H= 26' Ho= 26', f = 1030 MHz.

4.3 Numerical Results for Enroute Installations In this section numerical results are given for the performance of enroute ATCRBS using different antenna systems. In general, all the enroute antenna systems are mounted on a 75' tower. The scanning rate of the enroute antenna is 6 rpm, i.e., Q = 36 /sec. 4. 3. 1. Westinghouse Array Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are, respectively, Hd = 82' and Ho = 90'. The vertical aperture of each antenna is 8'. The free space elevation plane patterns of the directional and omnidirectional antennas are assumed to be identical. Figure 34 shows P1(0MAX' P1(0)MN and P2(0) pulses as functions of 0 where the zero dB level has been adjusted to coincide with the maximum of the P1(o)SL level in the free space case. The corresponding free space curves (for SLS q = 0) are also shown in Fig. 34 for comparison. As compared with the terminal installation with the same antenna (Fig. 6 ), in the enroute case the number of lobings within the same range of 0 is much greater. This is because of the greater height of the antenna used in the enroute installation. However, the oscillations in the patterns become negligible for 0 > 4. 5 as in the terminal case. Figure 35 shows the envelopes of the normalized pulse ratio KMAX (0)ISL MAX ISLS and K N (0)SS as functions of 0. The oscillations in the curves become negliMIN ISJLS gible for > 3~. Figure 36 shows the main beam killing and sidelobe punch-through zones as functions of nominal pulse ratio. For KO = 18dB (a - 9dB, b = OdB) there are five main beam killing zones and four sidelobe punch-through zones within the range of 0 shown in Fig. 36. Comparing Figs. 36 and 8, it is found that the number of both zones is increased by increasing the antenna height in the enroute case. Figure 37 shows the effective azimuth beamwidths aMAX(0), a1MIN(0) as functions of 0 for the threshold level a = 9dB and nominal pulse ratio K = 18dB. 0 For 0 > 5~, iMAX(0) 4. 7~ and a1MIN() ^ 2.20. The corresponding value of the azimuth beamwidth in the SLS case is about 3. 9. 81

8 < l -.-.. FREE SPACE LEVELS OPI MIN.P2 &8 4.00 t.00 s5oo WEST INGHOUSE ELEV.: DIREC. P1/P2= 18.0 O0 RNTENNR FREQ.= 1030.000 MHZ 8 2.a00' o ONI 9.00 DB PI DIRw/OMN,,= 1800 D8, 'zU- 34: p i(O)MAX' PI(eMI and P2(0) as functions of 0. MIN 82

011 CU 0 cJ,-4 \ TV y -MI I MIN I It II I1 X, I0 I I l, I 0 1.00 2.00 300 4. 00 S. 00 RNGLE FROM HORIZON DEGREES WESTTNGHOUSE RNTENNR FREQ = 1030.000 MHZ ELEV.: DIREC. 82.00 ' OMNT. 90.00' P1 3IR./OMN.= 18.00 OB. FIG. 35: Normalized pulse ratio envelopes as functions of 0. 83

3 MAINBEAM KILLING ZONES 2.1 SIDELOIBE PUN CH... THROUGH'ZONES 10 4 MAX 3 14 1 6 17 1 9 2 N O M I N L P U L E R A I O K 0MNID F1G 3 6 M..e~ k ll n n i d l b u.. t.. u g —o n e s as-f n-tin —o th0o ~ us ai o h e t g ~ r a n e~ ~ 8 ' % =LL ~ ~ 0 3x1 1.a d B0 -2 d.M Z D R O N %J -2

6 MAX C) 5 OL 0 z 4 LJ m MIN I 3 I — C) 0 I 2 3 4 5 ANGLE FROM HORIZON IN DEGREES FIG. 37: Effective azimuth beamwidths as functions of the angle from the horizon for Westinghouse array antenna. H = 82', H = 90', f = 1030 MHz, nominal pulse ratio K = 18dB, P1DIR/OMNP= 18dB. 85

Figure 38 gives the number of replies NMAX(0), NMIN() as functions of 0. For 0 > 30 the number of replies assume constant values N MAX () ^ 37, N (0) "' 17. For the same antenna, the saturation value of the number of replies in the SLS case is about 31. For 0 < 30, NMAX () varies between 50 and 20 and NMIN(0) varies between 36 and 0. Figure 39 shows the coverage diagram for the antenna normalized to the free space maximum range of 200 nautical miles. As shown in Fig. 38 for the maximum envelops case, the maximum range of 251 nautical miles occurs at 0 ' 0. 18~ and the minimum range of 50 nautical miles occurs at 90 0. 3. The corresponding ranges for the minimum envelope case are 192 and 28 nautical miles respectively. 4.3.2. Texas Instruments Reflector Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are, respectively, Hd = 82' and H0 = 91'. The free space elevation patterns of the directional and omnidirectional antennas are assumed identical. Figure 40 shows P1(0)MAX, Pi(0)MIN and P2(0) as functions of 0, where the 0 dB level is adjusted to coincide with the maximum P 1()SLS level in the free space case. The corresponding free space curves (for q = 0) are also shown in Fig. 40 for comparison. The oscillations in the curves may be considered negligible for 0 > 4. 5~. Figure 41 shows the normalized maximum and minimum envelope pulse ratios as functions of 0. The oscillations in the curves for 0 > 4. 5 may be considered to be negligible. Figure 42 shows the main beam killing and sidelobe punch-through zones as functions of the nominal pulse ratio. For K = 18 dB (a = 9dB, b = 0), there are six main beam killing zones and four sidelobe punch-through zones within the range of 0 shown. Figure 43 shows the effective azimuth beamwidths MA^X(0), a1MIN (0) as functions of 0 for the threshold level a = 9dB and nominal pulse ratio K - 1. 8dB. For 0 > 4. 5~, a (0) 4. 7~ and aMiN (e), 1. 9. The corresponding beamw idth is about 3. in the SLS mode. width is about 3. 90 in the SLS mode. 86

0. co (0 -J LLJ cc MAX MIN F, I L ILg I I r L 81 100 1.00 2.00 3.00 &. 00 S: 00 FR4GLE~ FR~OM HOR~IZON DtEGREES WESTINGHOULSEI FNTENNR FREQ.= 1.030.O0u M1HELEV.: DIFREC. 82.OO' OMNI. 9O9OO' ePi/P= i8.OO DB PI D1FR./Or1N.= tS.OO0 B FIG. 38: Number of replies as functions of angle from the horizon. 87

4" 60*b 120 110 100 90 80 j — uj 7( uJ UUO 6 in 0o Z O tI 3.0e 2.5' 2.0' I 3 0 i0 5 0 1.5~ 1.0~ 40 30 20 00 10 0 I I I 240 260 28u *vV FIG. 3: C IIN NAUTICAL MILES, =1030 MHz. diagram for the Westinghouse array. Hd 82' O' 0 FIG. 39: Coverage diagr 0

8 * —.. — FREE SPACE LEVELS MIN (n8 ZN r- i -=. Q ' 7. cr..: P2 -, -- ----.-. - - 1.00 2.00 3.00 '.00 S.00 RNGLE FROM HORIZON DEGREES TEXRS INSTR. RNTENNR FREQ.= 1030.000 MHZ ELEV.: DIREC. 82.00' OMNI. 91.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 B8. FIG. 40: P(1() P()MN and P2(0) as functions of 0. MAX' MIN 89

0 c] MAX I;!,$ W i '-il 11; i,1 1, /I I II I ' I A M '.00 1.00 2.00 3.00 '.00 5.00 RNGLE FROM HORIZON DEGREES TEXRS INSTR. RNTENNR FREQ.= 1030.000 MHZ ELEV.: DIREC. 82.00' OMNI. 91.00' P1 DIR./OMN.= 18.00 DB. FIG. 41: Normalized pulse ratio envelopes as functions of 0. 90

MAWBEAM KLING ZONES 8 1.81l s MIN i~r.6 F -- MAX i.4 8 1.6 <! ~I; e 0.8L 0 0.6 0.8 0.2 10 11 12 13 14 15 16 17 18 19 20 NOMINAL PULSE RATIO Ko IN DB FIG. 42: Mainbeam ling and sidelobe punch-through zonesf the nminal pulse ratio for the Texas instruments rfetratna no18' 1' '00~~z Pi DIR/OMNI = 1dB, a = dB, b =OdB, L = -25dB. A1 91

6 1 5 mC LW IMIN I —4 3: >2 U) LU LL. 0 I 2 3 4 5 ANGLE FROM HORIZON IN DEGREES FIG. 43: Effective azimuth beamwidths as functions of the angle from the horizon for the Texas Instruments reflector antenna. H. 82', H - 91', f = 1030 MHz, nominal pulse ratio K = 18dB, i1DIR/O9NI = 18dB. 92

Figure 44 shows the number of replies NMAX (), N MN(9) as functions of e. For 0 > 3~ the numbers of replies assume essentially constant values NMAX (0) —, 39, NMN (0) ^ 16. For the same antenna in the SLS mode, the saturaMAX MIN tion value of the number of replies is about 32 and occurs for 0 > 3~ For 0 < 3 N (0) varies between 51 and 22 and N MN() varies between 39 and 0. MAX MIN Figure 45 shows the coverage diagram for the antenna where the maximum free space range is adjusted to 200 nautical miles. As can be seen from Fig. 45, for the maximum envelope case the maximum range of 220 nautical miles occurs at 0, 0. 18~ and the minimum range of 52 nautical miles occurs at 0 0. 3. The corresponding ranges for the minimum envelope case are 172 and 28 nautical miles respectively. 4.3.3. Existing Hog-Trough Antenna The heights above ground of the phase centers of the directional and omnidirectional antennas are, respectively, Hd = 108' and Ho = 110'. The free space elevation plane pattern of the directional and omnidirectional antennas are assumed to be identical. Figure 46 a shows the variation of Pl()MAX, P1()MN and P2(9) as functions of 0 in the range 0 < 0 _ 5~, with the 0 dB level adjusted to coincide with the maximum P l(0)SL in the free space case. Because of the small field gradient SLS (a = 0. 5dB/5~0) of the antennas, the number of lobings in the patterns is quite large. In fact, the oscillations in the curves are found to persist for values of 0 up to about 20~. Figures 46 b through d show the variations of the respective pulses for three more ranges of 0, 5~ < 0 10~, 10~ < 0 150 and 15 < 0 < 200. Figures 47 a through d give the variations of the pulse ratios as functions of e for four ranges of 0 within 0 < 0 9 200. The oscillations are found to be appreciable for 0 values up to 20. Figure 48 gives the main beam killing zones and sidelobe punch-through zones as functions of the nominal pulse ratio. As expected, compared to the terminal case within the same range of 0, the number of zones is increased in th enroute case. With the range 0 < 0 < 30, there are 5 main beam killing 93

8 Cc ( N). MAX LL-8 C 0 Lu m 0 L4); r rql rl!1 L i J i I I it i I I L / r rl II r1 I i r n n 1 n i, I II tII1II II L t I- r I I, i i i I i I I ii ir Lr - - - i j |,,,, j i,,, u L ~ i l; 1 1 11 11 U I I 1 I I1 II 11 IIAi It I I t I D0 1.00 2.00 3.00 4.00 S.00 RNGLE FROM HORIZON DEGREES TEXRS INSTR. RNTENNR FREQ.= 1030.000 MHZ ELEV.: DIREC. 82.00' OMNI. 91.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 DB. FIG. 44: Number of replies as functions of angle from the horizon. oa 94

wL LU LA. LU. 0 c, z co U/) 01 D 0 9-. z X - 0i w -- 3.00 -.2.5' 2.00 - '100 120 140 60 10200 22 24 26 28 30 SLANT RANGE IN NAUTICAL MILES028 FI. 5: Co er ge di gr m for the Te-vas Instrum ents reflector ant n a R 821, H 9 f 10 0 M z

0 -.-. —.. FREE SPACE LEVELS EXISTING RNTENNR TILTED RNGLE= 0. 0 D ELEV.: DIBEC. 108.00' OMNI. 110.00' P1/P2= 18.00 DB P1 DJR./OMN.= 18.00 DB. FIG. 46 a: Pi(O)MAX, Pi(0)MIN and P2(e) as functions of 0. MAX' MIN 96

Cb 0 0 Ir -ft.. —. -- FREE Sp4CE v, s pi 01 — j C( I I - —.. " Cj CL. c, EL Pil - &a j tj 4 / um, - law 4 a FIG. 46 b: pl(O) IV 4 CZ I I AIAX-l PI(O) 18. L)O ATIIV all dP2(0) as funct. Ion's Of 0. 0,0 0 0,00 I 080 (P7 ut

0 ~b C> #A PI - -- -- FREE SPACE LEVELS MAX c) * i An f IMIN: I "\J ti-^.. P2 -;10.0}S ~50 m1 2.00 1. 14 iIRn —M Nt- --- ~ --- INGLE F4c:lOM H ZON andCEES 1 a ns V of FIG. 46 c: Pl(0) MAX PKe)^ and P2 (0) as functis of0 -J"MIN in f0 98

Ct CS *,. I MIN -- —. FREE SPACE LEVELS P2 14 - EXISTING RNTENNA TILTED RNGLE= 0.0 0 ELEV.: DIREC. 108.00' OMNI. 110.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 DB. FIG. 46 d: P1()MAX P1()MN and P2(8) as functions of 0. MAX' MIN 99

cQ C, w -9 N V 8 t k | I ' l i; i i i If j j ' ANGLE FROM HORIZON DEGREES ' l 5 EXISTING RNTENNR TILTED RNGLE- 0.0 D 4:r ra 1 P I 013 IIU/t N 800 GB. FIG. 47 a: Normalized pulse ratio envelopes as functions of, 100

C%I cc.. II C~ ItIANl 061 i f Ij.50 I 10 07.00 8.00 9.00 00 RNGLE FROM HOL9IZQN DEGREES EXISTING RNTENNfl TILTED RNGLE= 0.0 U ELEV.: EUI9EC. 108.100', QMNJ* 110.00'1 Pi l1819./MNO= 18.00 UE5. FIG. 47 b: Normalized pulse ratio envelopes as functions of 0. 101

DFI 0-4 MAX., 0 -IS 11.00 102.a00 13'.00 14. 00 15.00 ANGLE FTRQM H0I12QN DYEGREES EXISTING RNTENNR TILTEQ RNGLE= 0.0 9 ELEV.: 1YIBEC. 108.00' IG!MN I. 110.00' P1 Th8./QHN.= 18.00 YEB. FIG. 47 c: Normalized pulse ratio envelopes as functions of e. 102

0,g. Cl CD d, M CD C\J ' MAX C/ 0t -J '- I —. t- iit 15.00 16.00 17.00 18.00 19.00 20.00 ANGLE FROM HORIZON DEGREES EXISTING RNTENNfl TILTED ANGLE= 0.0 B ELEV.: DIREC. 108.00' OMNJI. 110.00' PI DIR./OMN.= 18.00 DB. FIG. 47 d: Normalizedpulse ratio envelopes as functions of 0. 103

MAINBEAM KILLING ZONES SIDELOBE PUNCHTHROUGH ZONES \ -~ - 3 2.6 ------- 2.04 S 1.6 8 ' 1.4 -".6 0 0.2. 0.6 FIG 48: Mainbea lnds L 25dB. U1.0 M AX <~ 0.8 --— ' SJ V-S

zones and 12 sidelobe punch-through zones for K = 18dB, a = 9dB and b = OdB. If desired, zones for 0 > 3 may be obtained from the corresponding pulse ratios. Figure 49 gives the effective beamwidths MAX (0), a MN() as functions 1MAX 1MIN of e in the range 0 < e < 5. The saturated values of the beamwidths are aMAX(0) 4. 80 and aMIN(0) '2. 40, and they occur for 0> 200. The corresponding value of the effective beamwidth for the same antenna in the SLS mode is about 4.0~. Figure 50 gives the number of replies NMAX(0) and NMIN () as functions MAX MIN of 0, for four different ranges of e in 0 < e < 20~. For e > 200, N (0e) 38 MAX and N (Mi) - 18. For the same antenna the saturation vajue of the number of replies which occurs at e > 20~ is about 32. For 0 < 20, NM (0) varies between MJAX 47 and 0, and NMN () varies between 33 and 0. MIN Figures 51 a and 51 b show the coverage diagram for the antenna where the maximum free space range in the SLS case is adjusted to 200 nautical miles. It can been seen from Fig. 51 a that for the maximum envelope case the maximum range of 408 nautical miles occurs at 08 0. 18 and the minimum range of 22 nautical miles occurs at 08 0. 3. The corresponding ranges for the minimum envelope case are found to be 321 and 19 nautical miles respectively. 4.3.4. Texas Instruments Fix Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are Hd = 92' and Ho = 112' respectively. The free space elevation plane patterns of the directional and omnidirectional antennas are assumed to be identical. Figure 52 shows P1(8)MAX, P1(0)MIN and P2(0) as functions of 8, where the OdB level is adjusted to coincide with the maximum of P(8)SLS level in the SLS free space case. The corresponding free space curves (q = 0) are also shown in Fig. 52 for comparison. The oscillations in the curves may be considered to be negligible for 0> 3. Figure 54 shows the main beam killing and sidelobe punch-through zones as functions of the pulse ratio for K = 18 dB (a. 9dB, b = OdB). There are three main beam killing zones and three sidelobe punch-through zones within the range of 0 shown. 105

5 U) LU (/ L& 1 -I I IM F: I 2 3 4 5 ANGLE FROM HORIZON IN DEGREES FIG. 49: Effective azimuth beamwidths as functions of the angle from the horizon for the existing hog-trough antenna. H = 108', H = 110', f = 1030 MHz, nominal pulse ratio K = 18dB, P1 DI/OMNI = dB. L30 106

MAX I II i 11 if 1 11 II Ii II II II II 5.00 EXISTING ANTENNA TILTED ANGLE= 0.0 D ELEV.: DJREC. 108.00' OMNI. 110.00' P1/P2= 18.00 DB P1 DJR./0MN.= 18.00 DB. FIG. 50: Number of replies as functions of angle from the horizon. 107

350 300 25" 20~ 9.5~ 450 425 400 3i,5 350 325 300 275 Iu 250 LL U0 225 0 Z " 200 0 - 175 Z - 150 I 0 UJ: 125 '85' 7.50 5.00 4.00 3.50 3.0' 2.5' 100 75 50 25 0 0 40 80 120 160 200 240 280 320 360 400 440 SLANT RANGE IN NAUTICAL MILES FIG. 51 a: Coverage diagram of the maximum envelope for the existing hog-trough antenna. Hd =108', H = O1', f = 1030 MHz. d ~ 108

40 -3.5' 60W' 120 100 90 3.0~ 2.5~ 2.0~ 80 It 7 UJ I. Iz C t z r 0 1.5' 60 50 1.0~ 40 30 20 0o 10 260 i I I I I -- 0 20O FIG. WO~o I - 120 140 160 60 0 10 MILES 8x~igbgtough antenna - ndedscae ofthemaxium nvelope for the eitn FI.51 b: Coverage diagram on expa 030 Mleofth mz mm FIG. It i = 110',f10.11~

20" 450 Y.. 9., 425 8. 400 -"8.( 375 1,"7.: R II~350 /i_-" 7.( 325 6 -300 -.( 275 — 5..' I- f 250 cjI" u_ 0 225 4 4.5' z < 200:,D 4.0 0 ' 175 Z,-3.5 150 3.0" I uJ ' 125 2.5" 100 2.0" 75 51.5 50 25:l:::;:S, _______l-,,,~_~_p___ --- —- O.5' 0 0 8 2 6-2i 00 0 40 80 120 I0 200 240 280 320 360 400 440 SLANT RANGE IN NAUTICAL MILES FIG. 51 c: Coverage diagram of the minimum envelope for the existing hog-trough antenna. Hd = 108'0 Ho = 110', f= 1030MHz. 110 50 50 )o o) )~ 0

3.5* 120 3.0e loo100 90 80 w 7( ui I. UL 0 6::) 0 z 4< 5 m 3 2: Wz I — ~D,2.5* 2.0~ 3 1.5*,0 50 1.0~ 40 30 20 10 00 20 7~ 6~0 8 ~00 20 \40 ~ o 200 220~ 240 20 2s v 200 2 o IN NAUTICAL M.LES existing og-trough 3 20SLAT RN~e nim-m nvelope for the FIG. 1d: overae digramon expanded scale of the miia m antenna. Hld = 108 H 0

8,p=4 t -*-*-FREE SPACE LEVELS PI MAX MIN F,2 1.00 2.00 3.00 4.00 5.00 RNGLE FROM HORIZON DEGREES TEXRS FIX RNTENNR FREQ.= 1030.000 MHZ ELEV.: OIREC. 92.00' OMNI. 112.00' P1/P2= 18.00 OB P1 DIR./OMN.= 18.00 OB. FIG. 52: Pl()MAX. P1(0)(MIN and P2(0) as functions of 0. MAX' MIN 112

8 rAl 8 0n. 6 -4 08 MIN I I. 00 1.00 2.00 3.00 1.00 5.00 ANGLE FROM HORIZON DEGREES TEXRS FIX ANTENNR FREQ.= 1030.000 MHZ ELEV.: DIREC. 92.00' OMNI. 112.00' PI DIR./OMN.= 18.00 DB. FIG. 53: Normalized pulse ratio envelopes as functions of 0. 113

3 - 2.8 MAINBEAM KILLING ZONES 2.6 2.4 2.2 2.0 20 MAX MIN 1.8 I1.6 SIDELOBE z PUNCH-THROUGH 1.4 ZONES Z N o 1.2 9 1.0 - j 0.8 ------- z MIN 0.6 0.4 0.2 10 II 12 13 14 15 16 17 18 19 20 NOMINAL PULSE RATIO Ko IN DB FIG. 54: Mainbeam killing and sidelobe punch-through zones as functions of the nominal pulse ratio for the Texas Instruments Fix antenna. Hd = 92', H0 = 112', f = 1030 MHz, P1 DIR/OMNI = 18dB, a = 9dB, b = UdB, L = -25dB. 114

The effective beamwidths alMAX(0),' aMIN (0) as functions of 0 are shown in Fig. 55. The beamwidths are obtained for KO = 18dB and a = 9dB. For 0 > 2.5~, MAX (0) ', 3. 1~ and a MIN(0) 1.4~. The corresponding SLS mode value of the 1MAX 1MIN effective beamwidth for the same antenna is about 2.6~. The number of replies N MX(0), NMN(0) as functions of 0 are shown in MAX MIN Fig. 56. For 0>2.50, N (0), 24, NMN(0) 11. For 0 < 2. 5, NM (0) MAX ' MIN ' MAX varies between 33 and 0, N M (0) varies between 25 and 0. For the same antenna, MIN the saturation value of the number of replies in the SLS mode is about 20. Figure 57 shows the coverage diagram for the antenna where the maximum free space range in the SLS case is adjusted to 200 nautical miles. It can be seen From Fig. 57 that for the maximum envelope case the maximum range of 250 nautical miles occurs at 0 0. 18 and the minimum range of 50 nautical miles occurs at 0 -0. 3. The corresponding ranges for the minimum envelope case are found to be 200 and 15 nautical miles, respectively. 4. 3.5 NADIF Fix I Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are Hd = 92' and Ho = 112' respectively. The system uses the Texas Instruments omnidirectional antenna. The free space elevation plane patterns of the directional and omnidirectional antennas are assumed to be identical. Figure 58 shows Pl(0)MAX, P1(0)MN and P2(O) as functions of 0 where the MAX' MIN OdB level is adjusted to coincide with the maximum P1(0) level in the free space case. For 0 > 3~ the oscillations in the curves may be considered to be negligible. Figure 59 shows the normalized maximum and minimum envelope pulse ratios as functions of 0. For 0 > 2. 5 the oscillations in the curves may be considered negligible. Figure 60 shows the main beam killing and sidelobe punch-through zones as functions of the nominal pulse ratio. For K = 18dB, a = 9dB and b = 0 dB, there are 3 main beam killing zones and 2 sidelobe punch-through zones in the range of 0 shown. 115

0 W3 5 -Z 4 4 MAX co tL i MIN > 2 U0 I 2 3 4 5 ANGLE FROM HORIZON IN DEGREES FIG. 55: Effective azimuth beamwidths as functions of the angle from the horizon for the Texas Instruments Fix antenna. H = 92', H = 112', f = 1030 MHz, nominal pulse ratio K0 = 18dB, P1 DIa=/OMNI= 8 dB. 116

MAX MIN rL I r a I-j - i L - - - -U IU TEXRS FIX ANTENNA FREQ.= 1030.000 MHZ ELEV.: DIREC. 92.00' OMNI. 112.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 DB. FIG. 56: Number of replies as functions of angle from the horizon. 117

600*45 300 250 20" 150 120 11I 100 90 8* 750 70 6.5 60 1 u*** g - I I I I I I I I I 5.50 50 450 40 -- - 1 - M l — I I i - II I 1 1. I I I I uj LLU LU. 0 z Li, 03& 0 z I0L 12 0 11 0 100 9 0 80 70 I60 5 0 I40 30 20 10 G I _ — II i I i 62P W*, --- o - P - I, IT, Aame II.,4.. lp - IC m F "A1 I 1 I -AI I — A..'j U1 U A-. / -NI 0 i loo, 7.1 P:> 1.I I-.1 i It I I. >0 tt; I I. i I 10#1 I 0 1 I I I I vg::: i 11 11 I I I 11-1 I I i..Z: I I I.I —,. I I I I I. d I ro I i e I p t.< 11-0 I el 1-11...O 000,-e 0 0-1-0 117 - mom_= - - - 0 ;;D IL I I'M ---- FR 00000 e-010, 'NN 1.50" 1.00 m 14 -I.J.-. 4-50M -1 -m — 21 6- -.-A. 11 I I I _- -AL 1 1 1 -,-I.. I I I I - ---L-AM - I 1% i U0 FIG. 57: 40 60 80 100 120 140 160 180 200 220 240 260 280 300 SLANT RANGE IN NAUTICAL MILES Coverage diagram for the Texas Instruments Fix antenna: Hd = 108', H0= 112', f = 1030 MHz.

8 0; - %-4 Ce,-. -. -FREE SPACE LEVELS Pi MAX MIN 6 I-' t — Cj z cc 1.00 2.00 3.00 14.00 5.00 ANGLE FROM HORIZON DEGREES NADIF FIXI ANTENNA FREQG= 1030.000 MHZ ELEV.: DIREC. 92.00' OMNI. 112.00' P1/P2= 18.00 OB P1 OIR./OMN.= 18.00 OB. FIG. 58: Pl(O)ML,%i Pl'o6MIN and P2(0) as functions of 0. 119

0 Na. W4 0 0 (~j..8 o-c 0-4 a-! I I 'l I I 0 0 *-4 ) I II 'I II I I - 0 -A CY + i i i i I 1r.00 1.00 2.00 3.00 ANGLE FROM HORIZON DEGREES 1.00 5.00 NRDIF FIX1 RNTENNR FREQ.= 1030. ELEV.: DIREC. 92.00' OMNI. P1 DIR./OMN.= 18.00 DB. 000 MHZ 112.00' FIG. 59: Normalized pulse ratio envelopes as functions of 0. 120

I MAINBEAM KILLING ZONES 3 2.8 2.6 2.4 -MIN 2.2 2.0' MAX 1.8 J SIDELOBE W 1.6 - PUNCH-THROUGH I. iJ ZONES z 1.4 -Z 1.2 --- -.o, d U. 0.8 MAX -- = 0.6- E 0. 4 0.2 - 10 11 12 13 14 15 16 17 18 19 20 NOMINAL PULSE RATIO Ko IN DB FIG. 60: Mainbeam killing and sidelobe punch-through zones as functions of nominal pulse ratio for NADIF Fix I antenna. H = 92', H = 112', f = 1030 MHz, P1 DIR/OMNI = 18dB, a = 9dB,b = OdB, L = -25dB. 121

The effective beamwidth alMAX(0), a1MIN(0) as functions of 0 for the threshold level a = 9dB and nominal pulse ratio K = 18 dB are shown in Fig. 61. For 0 > 2.5~ a X(0) 3. 1~ and a1MIN(0) - 1. 40. The corresponding SLS mode value of the effective beamwidth for the same antenna is about 2. 6~. The number of replies N MAX(), NMIN(0) as functions of 0 are shown in Fig. 62. For > 2. 5~, NMAX(0) -24 and MIN(0) -10. For 0 < 2. 50, NM (0) varies between 35 and 0, N MIN(0) varies between 27 and 0. The saturation value of the number of replies is about 20 for the same antenna in the SLS case. Figure 63 shows the coverage diagram for the antenna where the maximum free space range in the SLS case is adjusted to be 200 nautical miles. It can be seen from the figure that for the maximum envelope case the maximum range of 280 nautical miles occurs at 0 0. 18 and the minimum range of 50 nautical miles occurs at 09~ 0. 3. The corresponding ranges for the minimum envelope case are 220 and 15 nautical miles respectively. 4.3.6. NADIF Fix II Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are Hd = 92' and Ho = 111' respectively. It uses the same directional antenna as NADIF Fix I. The omnidirectional antenna used is the Westinghouse omni. Thus the free space elevation plane patterns of the two antennas are not identical. Figure 64 shows Pi(0)MAX~ P1(0)Mi and P2(0) as functions of 0 where MAX' MIN the 0dB level is adjusted to coincide with the maximum P1(0)SLS level in the free space case. For 0 > 3~ the oscillations in the curves may be neglected. Figure 65 shows the normalized maximum and minimum envelope pulse ratios as functions of 0. For 0 > 2. 5 the oscillations in the curves may be considered negligible. Figure 66 shows the main beam killing and sidelobe punch-through zones as functions of the nominal pulse ratio. For KO = 18dB, a = 9dB and b = 0dB, there are 1 main beam killing zone and 3 sidelobe punch-through zones in the range of 0 shown. 122

6 w w $ 5 0 Z IMAX | 4 nI t MIN I.IAL,- I I I I 2 3 4 5 ANGLE FROM HORIZON IN DEGREES FIG. 61: Effective azimuth beamwidths as functions of the angle from the horizon for the NADIF Fix I antenna. Hd = 92', H = 112', f = 1030 MHz, nominal pulse ratio K = 18dB, P1 DIR/OJNI = 18dB. 123

C o o* MAX MIN n / III i I rL n n rI i J L Lr C i I gi ILI I 1.00 2.00 3.00 1.00 5.00 ANGLE FROM HORIZON DEGREES NRDIF FIX1 ANTENNR FREQ.= 1030.000 MHZ ELEV.: DIREC. 92.00' OMNI. 112.00' P1/P2= 18.00 DB P1 DIR./OMN.= 18.00 DB. FIG. 62: Number of replies as functions of angle from the horizon. 124

40 -3.5" 12 0 II 0 100 9 0 3.00 - 2.50 2.0 0 80 I I w 7 w UU0 V) 0 z 4 I -4 tn. w:3 w 0 z 0 ui x ro 1.5* 60 5 0 1.011 40 30 20 Io0 10 0 I I i - 100 4uv g. 46. - I -— L --- --- - 160 V -L-1 I I - 3014M 120 14 own --- 60 so 100 AUTICAL MILES 40 SLANT RANGE I N N 14 = 92t If:= 10 30 M14 z - d III antennas - Coverage diagram for NADIF Fix L 1-1, an FIG. 6 3 -.

8 -. — FREE SPACE LEVELS Pi MAX. -11%. Ift-ft MIN cnc CL' C\I. z cc.OO 1.00 2.00 3.00 LL.00 5. 00 RNGLE FROM HORIZON DEGREES NROIF FIX2 FINTENNR FREQ*= 1030.00 MHZ ELEV.: DIREC, 92.00' OMNI. 111.600' P1/P2= 18.00 OB PI OIR./OMN.= 18.00 DB. FIG. 64: PlI(e) MAXI P1l(e) MIN and P2(e) as functions of e. 126

MAX 0_ c:3.J -J oCr) =: 0 9-. S - MIN I.00 1.00 2.00 3.00 4.00 5.00 RNGLE FROM HORIZON DEGREES NROIF FIX2 RNTENNR FREQ.= 1030.00 MHZ ELEV.: DIREC. 92.00' OMNI. 111.00' P1 DIR./OMN.= 18.00 DB. FIG. 65: Normalized pulse ratio envelopes as functions of 0. 127

2.1 MAINBEAM KILLING ZONES SiDELOBE o INCrW-THROUGH 0 20d Cw 1.8ZOE uo 1.6 z 1.4 0 1 CZ 0O.6 0.2 102 I 1 3 1 5 16 17 18 19 2 NOMINAL ULSE RATIO K. IN DB FIG 66 Manbam iI~ngand 'sidelobe punch-thrOugrh zones as- f 21noti=flS of the 66 noinbal pulsen rai for NADIF Fix II antenna. H 92' H0 2B =1030 MHz, Pi. DIR/O~1da9B AdL2d 128

The effective azimuth beam widths aMAX(8), a1MIN (e) as functions of 0 for the threshold level a = 9dB and nominal pulse ratio KO = 18dB are shown in Fig. 67. For 0>2.5, MAX) ( 3, aM (e) - 1~ The number of replies NMAX(e), N MiN(e) as functions of e are shown in Fig. 68. For e > 2. 5, N MAX(e) 22, N MIN() does not assume a constant value in the range of e shown in Fig. 68. For e < 2. 50, N MAX() varies between 36 and 0. NMIN () is found to vary between 28 and 0. The saturation value of the number of replies is about 17 for the same antenna operating in the SLS mode. The coverage diagram of the antenna is the same as the NADIF Fix I, and is given by Fig. 63. 4.3.7. NADIF Fix III Antenna. The heights above ground of the phase centers of the directional and omnidirectional antennas are Hd = 92' and Ho = 110', respectively. It uses the existing small aperture omnidirectional antenna. The free space elevation plane patterns of the directional and omnidirectional antennas are not identical. Figure 69 shows P1(0)MAX' P1(e)MIN and P2(0) as functions of 8, where the 0dB level is adjusted to coincide with the maximum P ()SLS level in the free space case. For 0 > 2. 50, the oscillations in the Pl()AX P1(0)MIN may be neglected. However, due to the small vertical aperture of the omni antenna, the fluctuations in the P2(0) pulse are appreciable throughout the range of e shown. Figure 70 shows the normalized maximum and minimum envelop pulse ratios as functions of 0. The oscillations in the curves persist throughout the range of 0 shown in Fig. 70. Figures 71 a and b show the main beam killing and sidelobe punch-through zones as functions of the nominal pulse ratio. For KO = 18dB, a = 9dB and b = OdB, there are 10 main beam killing zones and 12 sidelobe punch-through zones in the range of 0 The effective azimuth beamwidths aiMAX(8), aMiN(8) as functions of 0 for the threshold level a = 9dB and the nominal pulse ratio KO = 18dB are shown in Fig. 72. For 0 > 10~, CrA () -, 3. 5~ and ai(0N),-2.2~. The corresponding SLS MAX 1MIN mode saturation value of the effective beamwidth for the same antenna is about 3. 10. 129

O, o 4.0 w I t MAX z I3.0 <[ D 1 ' A MIN 2.0 CJ w 1.0 LL Li. 0.0 1.0 2.0 3.0 4.0 5.0 ANGLE FROM HORIZON IN DEGREES FIG. 67: Effective azimuth beamwidths as functions of angle from the horizon for NADIF Fix II antenna. H = 92', H = 110', f = 1030 MHz, nominal pulse ratio K0 = 18B, P1 DIOMNI = 18dB. 130

8 -F MAX 'I 8 0,. -i aLJ cr 1IN r. I rL ro L1I i L ' L Lr Lr l -- L I - L I U II II - - ~ *W ~. uu.0 4. O0 5.00 ANGLE FROM HORIZON DEGREES NROIF FIX2 RNTENNR FREQ.= 1030.00 MHZ ELEV.: DIREC. 92.00' OMNI. 111.00' P1/P2= 18.00 OB P1 DIR./OMN.= 18.00 08. FIG. 68: Number of replies as functions of angle from the horizon. 131

- -.. FREE SPACE LEVELS 0 1.00 2.00 3.00 4.00 5.00 RNGLE FROM HORIZON DEGREES NRDIF FIX3 RNTENNR FREQ.= 1030.00 MHZ ELEV.: DIREC. 92.00' OMNI. 110.00' P1/P2= 18.00 OB P1 DIR./OMN.= 18.00 DB. FIG. 69: P1()M, P1(O)MN and P2(O) as functions of 0. MAX' MIN 132

8 S W-4 0 0 C'J i N0.4 MAX LI ~! qt VI I '1' -J X: cc z.a '-.4 -i (In MIN 'I 8 IN NRDIF FIX3 RNTENNR FREQO= 1030.00 MHZ ELEV.: OIFREC. 92.00' OMNIs '110.00' PI DIR.,/OMN.,= 18.00 08. FIG. 70: Normalized pulse ratio envelopes as functions of e. 133

MAINBEAM KILLING MIN ZONES ' 2.8 A XMAX ~-N 2.0;= --- ------ 2 1.6 2.4 2.0 - -2 ~ I0.8 3 1,... 1.6 o 1.4 10 11 12 13 14 15 16 17 18 19 20 NOMINAL PULSE RATIO Ko IN DB FIG. 71 a: Mainbeam killing zones as functions of nominal pulse ratio for NADIF Fix III antenna. Hd = 92, Ho 110', f = 1030 MHz, P1 DIR/OMNI = 18dB, a = 9dB, b = OdB, L = -25dB. 134

MAX 3 SIDELOBE PUNCHTHROUGH ZONES MIlN 2.8 - 2.6 - 2.4 - 2.2k 4=-w -1 c Mft - 2.0 - 1.81 - CM z z 0 N 0 2 0 z I.6 e"lo I.4! c -1 12 - I. 10 llw - - I 0.8 - vW.v. 0.6 0.4 0.2 I I p I I a In 10 II 12 13 14 15 16 17 18 19 20 NOMINAL PULSE RATIO Ko IN DB FIG. 71 b: Sidelobe punch-through zones as functions of the nominal pulse ratio for NADIF Fix m antenna. H = 92', H = 110', f = 1030 MHz, P 1 DIR/OMNI - 18dB, a = 9< B, b L = -25dB. 135

6. 5.0 L. z 4.0 w/ 3.0 II MIN wL 2.0 w LI. LL 1.0 0.0 1.0 2.0 3.0 4.0 5.0 ANGLE FROM HORIZON IN DEGREES FIG. 72: Effective azimuth beamwidths as functions of the angle from the horizon for the NADIF Fix III antenna. H = 92', H = 110', f = 1030 MHz, nominal pulse ratio K = 18dB, F 1 DI/O'NI = 18dB. 136

Figure 73 shows the number of replies NMAX(e), NMIN(0) as functions of 0. The number of replies does not assume constant values within the range of & shown in Fig. 73. For 0> 10~, NMA(0) - 28 and N MN(0) ^-17. The correspondMAX\ MIN ing saturation value of the number of replies is about 24 for the same antenna operating in the SLS mode. The coverage diagram for the antenna is the same as NADIF Fix I and II, and is shown in Fig. 63. 137

0 8r MAX MIN (f)8 LLJ =; i-iN -4 uJ cr II II II I I I I I I 1.00 2.00 3.00 ANGLE FROM HORIZON DEGREES NRDIF FIX3 ANTENNR FREQ.= 1030.00 MHZ ELEV.: DIREC. 92.00' OMNI. 110.00' P1/P2= 18.00 DB P1 OIR./OMN.= 18.00 DB. FIG. 73: Number of replies as functions of angle from the horizon. 138

5. GENERAL DISCUSSION Detailed numerical results for the ISLS mode performance of ATCRBS using different antenna systems have been given in Section 4. In the present section we give a short discussion of some of the selected results. 5. 1 Summary of Important Results The ISLS mode results given in the previous chapter have been divided into two main groups: one corresponds to the maximum pulse envelope case, and the other to the minimum pulse envelope case. The occurrence of either case depends mainly on the phase relationship between the directional and omnidirectional antennas (see Section 2). Some of the selected important parameters characterizing the overal ISLS mode performance of the ATCRBS in these two cases are shown in Tables 9 and 10, respectively. The tables have been prepared so that the various antenna systems involved may be compared with each other on the basis of different performance criteria. The various symbols used in Tables 9 and 10 are explained as follows: N, is the number of main beam killing zones in CP< 6 < 50 for nominal MB pulse ratio K 3 18dB and the threshold level a = 9dB, 1/q = 18dB, N is the number of sidelobe punch-through zones in 00 < 6 < 50 for SL nominal pulse ratio KO = 18 dB, threshold level b = OdB, sidelobe level L = -25 dB and 1/q = 18 dB, N is the maximum number of replies in 0 < 6 < 50, max - - N. is the minimum number of replies in 0 < 6 < 50, min - - N is the number of replies in free space, R is the maximum range in nautical miles for ATCRBS in the presence max of ground, R. is the minimum range in nautical miles for ATCRBS in the presence mm of ground, R0 is the maximum SLS mode range in nautical miles for the ATCRBS in free space. 139

TABLE 9: SUMMARY OF THE ISLS MAXIMUM ENVELOPE MODE PERFORMANCE CRITERIA OF ATCRBS Antenna Type N N N N N R R R MB SL max max min Westinghouse Array 0 2 24 18 9 50.5 40 14: Texas Inst. Reflector 0 2 25 19 11 44 40 6 i Hazeltine Open Array 0 4 24 19 8 44 40 8 ~ Existing Hog-Trough 1 7 26 19 0 81 40 5 Hazeltine E-Scan 19 19 45 40 14 Westinghouse Array 0 5 49 37 20 251 200 50 Texas Inst. Reflector 0 4 50 39 21 220 200 52 Existing Hog-Trough 2 20 47 38 0 408 200 22 o Texas Fix Reflector 1 3 33 24 0 250 200 50 NADIF Fix I 2 2 35 24 0 280 200 50 NADIF Fix II 1 3 36 22 0 280 200 50 NADIF Fix I 2 12 36 28 0 280 200 50 TABLE 10: SUMMARY OF THE ISLS MINIMUM ENVELOPE MODE PERFORMANCE CRITERIA OF ATCRBS Antenna Type N S N N N R R R MB SL max f min max 0 min Westinghouse Array 2 2 18 7 0 40 40 7 c Texas Inst. Reflector 2 2 18 7 0 34 40 3 g Hazeltine Open Array 4 3 17 8 0 34 40 5 a Existing Hog-Trough 5 7 20 9 0 62 40 2 / Hazeltine E-Scan 8 8 36 40 12 Westinghouse Array 5 4 36 17 0 192 200 28 Texas Inst. Reflector 6 4 38 16 0 172 200 28 Existing Hog-Trough 16 13 33 18 0 321 200 18 8 Texas Fix Reflector 3 3 25 11 0 200 200 15 0 4 NADIF Fix I 3 2 26 10 0 220 203 15 X NADIF Fix II 3 3 28 0 220 200 15 NADIF Fix III 8 12 29 17 0 220 200 15 From Tables 9 and 10 it is found that in general, the maximum envelope ISLS mode performance of ATCRBS using any antenna system is superior to the minimum envelope ISLS mode performance. Basically the reason for this is that the received pulse ratio within the main beam region is always larger for the 140

maximum envelope case at all angles. However, in the maximum envelope case the sidelobe punch-through occurs more frequently. For all the antennas considered, it is found that the operation in the maximum envelope considerably reduces the main beam killing zones in space. As discussed in Section 2, modes operating in the maximum or the minimum envelopes may be obtained by properly adjusting the phase difference between the directional and omnidirectional antennas. From the results given in Tables 9 and 1Q it may be concluded that in almost all cases it is more advantageous to operate in the maximum envelope level, which can be obtained by using the appropriate amount of phase delay between the directional and omnidirectional antenna when radiating the P1 pulses. 5.2 SLS Mode Results Detailed results of the SLS mode performance of ATCRBS using various antenna systems have been discussed in [1]. For the purpose of comparing the performance of ATCRBS in ISLS and SLS modes we give some selected results of the SLS mode performance in Table 11. TABLE 11: SUMMARY OF THE PERFORMANCE CRITERIA OF ATCRBS OPERATING IN THE SLS MODE Antenna Type N NS N Nf N R R0 R MB SL max f min max 0 min - Westinghouse Array 1 2 23 15 0 45 40 10.5 c Texas Inst. Reflector 0 2 23 16 3 39.3 40 11 G Hazeltine Open Array 2 4 23 15 0 39.3 40 4.1 E Existing Hog-Trough 6 6 23 15 0 76 40 4. 8 Hazeltine E-Scan 0 0 16 41 200 13 Westinghouse Array 0 4 45 32 6 223.4 200 41.4 Texas Inst. Reflector 0 4 45 32 8 196.4 200 38.7. Existing Hog-Trough 10 19 43 30 0 368.4 200 16. 8 o Texas Instruments Fix 3 3 30 20 0 232 200 30 -A ntennna X NADIF Fix I Antena 3 3 32 20 0 252 200 30 NADIF Fix I 2 4 33 20 0 252 200 30 NADIF Fix II 3 13 33 20 0 252 200 30 141

5.3 Comparison of ISLS and SLS Mode Performance On comparing the results given in Tables 9, 10 and 11, it is found that in general, the quality of SLS mode performance of ATCRBS falls between those of the maximum and minimum envelope cases of the ISLS mode, the maximum envelope mode performance being superior. From the results obtained in the present investigation, it appears that during the ISLS mode of operation it would be advantageous to adjust the relative phase of the directional and omnidirectional antennas such that the system operates at the maximum pulse envelope. The phase adjustment necessary to achieve the maximum in the ISLS P1 pulse envelope might be made by monitoring the signal received by a sensor suitably placed to be in the far field of the two antenna system and at a height equivalent to an elevation angle corresponding to the first maximum in the P1 pulse lobing pattern. 5.4 General Discussion of ISLS Mode Results Except for the existing hog-trough and Hazeltine open array antennas, it is found that the lobings in the elevation plane patterns of all other antennas in the presence of ground take place mostly in the region e < 50. For 0 > 5~ the patterns above ground become essentially similar to the corresponding free space patterns; in this region of space the Pl(O) MAX and P1()MIN levels occur slightly above and below the free space SLS mode P1(O) pulse intensity level. The lobings in the patterns are attributed to the fact that the free space elevation plane patterns have large field gradients below the horizon as well as the fact that for vertical polarization the reflection coefficient is a rapidly decreasing function of 6 in the region of interest. The lobings in the region 0 < 2. 5 are found to be most critical. The lobings in the patterns continue up to 0 " 200 for the existing hog-trough antenna and up to 0 e 100 for the Hazeltine open array antenna. The reason for this is that these two antennas have small field gradients. As shown in Table 8, the field gradients associated with them are 0.37dB/10 and 1.6dB/10 respectively. The pulse ratio curves show that for most antennas only the first and sometimes the second minima could cause the appearance of mainbeam killing zones if 142

the value of the nominal pulse ratio K0 is not too small (i.e., K0 > 12 dB, say). Also, only the first and sometimes the second maxima are responsible for sidelobe punch-through zones if K0 is not too large (i.e., KO < 18dB, say). In the case of the hog-trough and Hazeltine open array antennas the first few maxima and minima would be responsible for the creation of the main beam killing and sidelobe punchthrough zones. In general, it has been found that for a given antenna system, the main beam killing zones become a more serious problem when the system operates in the minimum pulse ratio envelope. The behavior of the oscillations in the coverage diagrams as functions of 6 for the different antennas appears to be similar to that of the lobings in the elevation plane patterns of the antennas. For most of the antennas the coverage diagrams oscillate appreciably for 00 < O < 50, for 0 > 50 the oscillations become negligible and the ranges of the beacon for the maximum and minimum envelope cases are slightly above and below the free space SLS mode range. For the existing hogtrough and Hazeltine open array antennas the oscillations persist up to 6,%25 and 0 - 10~ respectively. On the basis of the present investigation it is found that with 25 dB sidelobe level in the azimuth plane pattern of the antenna the most important parameter characterizing the performance of an antenna is its field gradient in the vertical plane pattern of the antenna below the horizon. Of the antennas studied, the existing hog-trough and the Hazeltine open array antennas have the smallest field gradients; thus the overall performance of these two antennas is poorer than the others. The Hazeltine open array performs better than the existing hog-trough antenna because of its higher field gradient. Judging from the criteria of Tables 9 and 10, the Westinghouse array,antenna, the Texas Instruments reflector antenna and the Hazeltine E-scan antenna all promise to have superior performance. It is seen that the performance characteristics of the first two antennas are much the same. Tables 9 and 10 show the distinct advantage of having the phase centers of the directional and omnidirectional antennas coincident as does the Hazeltine E-scan antenna. For the enroute system, it is seen that the performance of the Westinghouse array and the Texas Instruments reflector antennas 143

is generally equal and superior to other enroute systems, especially when judged on the basis of main beam killings, sidelobe punch-throughs and the number of replies. NADIF Fix III results shown in Tables 9 and 10 show the existence of a large number of sidelobe punch-through zones. This is attributed to the use of the existing small aperture omni antenna which has a small field gradient. This indicates that for satisfactory performance, both the directional and omnidirectional antennas should have large field gradients. 144

6. REFERENCES [1] J. Zatkalik, D. L. Sengupta and C-T Tai, "SLS Mode Pefformance of ATCRBS with Various Antennas", Technical Report 1, Contract DOT-TSC-17, The University of Michigan Radiation Laboratory Report 012539-1-T, July 1974. [2] A. Ashley, C. F. Phillips and A.A. Simolunas, "System Capability of Air Traffic Control Radar Beacon System", Department of Transportation, Air Traffic Control Advisory Committee Report, Vol. 2, pp. 287-300, 1969. [3] N.K. Shaw and A.A. Simolunas, "System capability of air traffic control radar beacon system", Proc. IEEE, Vol. 58, No. 3, 399-407, 1970. [4] A. Ashley and J. S. Perry, "Beacons", Chapter 38, in Radar Handbook, ed. M. Skolnik, McGraw-Hill Book Co., New York, pp. 38-1 - 38-33, 1970. [5] "U. S. national standard for the IFF Mark X (SIF)/air traffic control beacon system characteristics", Amendment 1, October 10, 1968 (obtainable from Federal Aviation Administration, Washington, D.C.). [6] P.R. Drouilhet, "The development of the ATC radar beacon system: past, present, and future", IEEE Trans. on Communications, Vol. Com-21, No. 5, 408-421, 1973. [7] B.M. Poteat, W.B. Evans, A.W. Markusan, K.W. Connor, K.F. Horenkamp, D. Davis and D.R. Logan, "ATCRBS Antenna Modification Kit: Phase I", Westinghouse Defense and Electronic Systems Center, Systems Development Division, Baltimore, Maryland, July 25, 1973. [8] P.N. Richardson, "Air Traffic Control Radar Beacon System (ATCRBS) Phase I Final Engineering Report, Report No. UI-855511-F, Texas Instruments, Inc., Dallas, Texas, 1973. [9J V. Mazzola, P.W. Hannan, E.M. Newman and P. Kendrick, "ATCRBS Antenna Modification Kit, Phase I", Engineering Report No. 10991, Hazeltine Corporation, Greenlawn, New York, 1973. 0i] Frank LaRussa, Private communication, 1973. [1] R.J. Giannini, J.H. Gutman and P.W. Hannan, "A cylindrical phased-array antenna for ATC interrogation", Microwave Journal, Vol. 16, No. 10, 46-49, 1973. 145

APPENDIX A COMPUTER PROGRAM FOR IBM-360, MODEL 67 READ AP. THMIN, THMAX, NTH. H. HI, BETA. DBYOM. ALFZ. GEE PRINT H. HI. P1P2. DBYOM. NTH. BETA.. — ---- TH = THMIN CALCULATION of BW1. BW2.[ - - CALCU LAION of PH. PHI CALCULATION of FP. FP1 CALCULATION of FISLS1. FISLS2 - — '........ I:TH +DTHI A CALCULATION OF DISLS1. DISLS2 | CALCULATION of RISLS1. RISLS2 I CALCULATION of ALFK. ALFK1. ALFK21 CALCULATION of NSLS. NISLS1. NISLS2 PRINT. TH. PHD1. FP. FISLS1. FISLS2. ALFK. ALFK1. ALFK2 PRINT. TH. FPD. DISLS1. DISLS2. RSLS. RISLS1. RISLS2 NSLS. NISLS1. NISLS2 _, PLOT. FPD. DISLS1. DISLS2. RSLS. RISLS1. RISLS2. NSLS. NISLS1. NISLS2. by SPLOT through Calcomp plotter Yes TH < THMAX No - TH EN p FIG. A-1: Flow diagram for the main program. 146

List of Some of the Symbols Used ABS = Absolute value ALFK = a eff()SLS ALFK1 = a (0) max ALFK2 = a. (0) mm ALOG10 = Log 10 BETA = j3 DISLS1 = 20 log 10 (FISLS1) DISLS2 = 20 log 10 (FISLS2) DR = 7x/180.0 DTH = (THMAX - THMIN)/(NTH-1) FISLS1 = P1 max(e) FISLS2 = P1 min(0) FP = P1(O)SLS for H FPD = 20 log 10 (FP) FP1 = P1(O)SLS for H1. FPD1 = 20 log 10 (FP1) NSLS = N(O)SLS NISLS1 = N (0) max NISLS2 = N. (0) mm PH = Fd(O) PHD = 20 log 10 PH PHDI = 20 log 10 PHI PHI = Fd(-O) PI = T REF = p(O) RISL1 = DISLS1 - FPD1 RISLS2 = DISLS2 - FPD1 RSLS = PFD - FPD1 SIN1 = specified for each antenna SQRT = Square root TH = 147

MAIN PROGRAM C *** PROGRAM TO ANALlIZE THE PERFORMANCE i)F BEACON SYSTEMS *** C C C C. C C c C C PI C C CI C C C. *** INPUT QUANTITIES AP ANTENNA TYPYE; 1 WESTINGHOUSE AN4TENNA 2 TEXAS INST.IU'ENTS ANTEN114NA 3 HAZELTINE ANTENNA 4 E XI STI N ANTE NNA 5 NADIF FIXi ANTENNA 6 TEXAS FIX ANTENNA 7 -IAZFLT1INE ESCAIN ANTENNA Tl MAX UPPER L'IMI-!T FOR ELEVATIO'J A4'GLE IN PATTERkN CALCULATION THMIN LOWERk LIMIT FOR ELEVATION ANGLE IN PATTERN CALCULATIO'N BETA TILTED ANGLE NTH NUMBERk OF POINTS BETWEEN H1CRIZONTAL AND THMAX -g ELEVATION OF DIRECTIONAL ANTENNA Hil ELEVATInN; iF OMNIr)IRECTIOINAL ANERNNA P1P2 RATIO OF P1 PULSE TO P2 '3ULSE AMPLITUDES IN )B 3BYOM RATIO OF THE PORTION OF PI PULSE RADIATED BY THE DIRkECT IiNAL ANTENNA Ti THAT RADIATED 3Y THE OMNIDIPECTIOrNAL ANTENNA FGR ISLS CASE ALFZ NOM4INAL BEAMWIDTH GEE CCNSTANT RELATED TO THE SPEED iF ROTATIO-N INTEGER AP DATA A /4.3738,1.7039,3.4554t,1.1036b,.2644,0.634690.8108/ 1).004,3.08r,.530,1.000,0~.330,90.360, 0.790, C. 860,3. 960,0. 540, 23. 233,0. 120,0. 060,2*i.O, 33).5C 1, 1. 030,.3.885, ).530, 110. 0, 40. 084, 0. 51 0. 9569,0.780,0.045,910*0.3i 50.0190.0394,0. 635,C.99,0'.53 0. 542,).515,O.515,O.43l,0.4t5,3.437, 63.'32790.3329).21"790. 153, 70. 01,. 039t.5619. 995,.482,p.451,.435,.42,.355,t.417,.342,.35,9.334 8,0.24,p. 12,v 9).079,i,.0'72,3).03,).53,0.915,O1.945,i:.845,0O.845,3.315,0.034,5*0.0/ lEAD( 5,200) t.PT-iMI- NT-$MAX,NTHH,-4l,BETAPIP2,,DBYOM, ALFZ, GEE IF (NTH.GT.4 1 ) N4TH=401 1= (T-iMAX.GT.90.0) THMAX=90.0 ** PERATIN3 FREQUENCY F-=1030.0 MHZ F=103).3 P1 =3. 14159265 DR=0.017't53292 PP1= -36.*0 Po 2=0. 0 RAT1=-15.30 RA TZ=1.5.030 Ni PMIN =000 NO PM''AK =0 33:ONST=4. * PI* F/1 808. 0 PlP 2= ABS (D VP2) DBYOM=AfgS (CBYOM) ~ISL S= 1. 0/C 1 0. O"'',1 OD YOM/20. 0) BWI=2-.32 1./ (1.0**( (P P2-DBYOM)/20. 0)) BW2=7. 6ft-8Wi Sri 1=20.0*4ALO 03 Bc 41) BW2=20. )*ALOG1O (BW2 ) )TH=( THMAX-THMI Nj) /( NTH-1) IR IT E (6,p2 12 ) GO TO (1,92,t3,4,t596 7 ), AP 148

main program (cont'd) ARITE (6,2011 BETA WRITE (7,201) BETA '4S=7 B=2. * 4*F/1 1808.O GO TO 8 2 WAITE (b,202) BETA WRITE (79202) BETA NS=13 K1=3 SI N1=0.07846 GJ TO 8 3 WRITE (5,203) BETA WRITE (7,203) BETA NS=4 SI N1=0. 22495 50 TO 8 f, WRITE (5,204) SETA WUITE (79204) 3ETA NS=S K1=3 SIN1=0.47767 GO TO 8 5 WRITE (6,205) BETA 4JRITE (79205) BETA NS=15 K1=3 SIN1=0.0583 GO TO 8 6 WRITE (6,206) BETA WRITE (7,206) BETA '4=15 <1=3 SINi=0.0583 GO TO 8 7 WrIRITE (5,207) BETA WRITE (7,2027) BETA K1 =4 SI N1=0. 11942 8 dRITE (6208) HHIP1P2,)BYtIM WR IT E (7 9209) H, HlI, Pl P2, DOBYOM, P 1P29 NTH A~ = 12. O*Hr HI=12.3*Hl )O 14 N=1,NTH TH=TH?" f4+( N-1)*DTH THETA=TH*DR SI NTH= SIN( THETA) SQRT1=S3RT(2. SlNTH**2) REF=(3.*1-SINTH- S' T)/(3.*SINTH+S T1) TS=(TH-B6TA)*DP SINTB=SIN(,rR) COST B=COS (TB) TC=( TH+BETA)*DR S JNTC=SI4 ( TC) COSTC=COS ( TC) IF (AP.EQ.1) 3O TO 11 C ***FREE SPACE PATTERN FOR ALL EXPECT WESTI1GHOUSE ARG1=SINTB/SINi AR GN=SI1'TC /SI'4 I 149

main program (cont'd) PH=0.0 PH 1=0. 0 DO 10 K=1,NS AiR%=P * ( ARG1-K+Kl) IF (ABS(ARG).LE.O.0349) GO37 TO 9 PH=lPH+C (K,pAP)*S IN (ARG)/ARG 3)J TO 101 9 PH=PH+C(K, AP) 1 01 ARGM=PIt-(Kl-K-APGN) IF (ABS(ARGM).LE.0.03491 GO7 TO 102 lPH1=PH1+C(K, AP)*S IN(ARGM )/ARGM 3.0 TO 10 102 PHl=PHl+C(KAP) 10 CONTINUE GO TO 13 C ***FREE SPACE PATTEIN FOR WESTINGHOUSE U1:OSTHI=COS (THETA) MARG2=P I*COST3/2. ARG3=PI*S INT 8/2.0 P-IL=SI N(ARG2)*COS(ARG3 )/COSTB AR2=PI2-,CDSTC/2.0 AR3=PI*S INTC/2.3 'lHX=SI N(AR 2) *COS(AR3) /COSTC lPH=PHZ'5.4 201 PI 1=5. 4201*PHX D3 12 K= 1iNS A RG4 =Ml P I 4B*8*S I NT B AlGL=Kl'~PI*B'SI NT' PH=PH+2.*PHZ*-A(K)"-C2-S(ARG4*)R*-C(KA~1)) P.-il=P-i1*2.*O-iX*A(K),!COS(DR=C(K,PAP)-ARGL) 12 )-NTINUFEL PH=PH/ 15.686 P-Il1=PHlI15.686 13 IF (AFBS(PH).LE..0O16O35) GO37 TO 103 PHD=20.0*AIOG1O CABS (PH)) 33J TO 104 103 PHD=-36.00 1 04 I F (ABSP-il1). LE.3.016035 ) GO TO 105 11HD 1=2 0. O*ALOIS 1CC( A3 S ( PH 1) GO TO0 13 6 105 P-iDl=-36.00 106 IF (H.LE.0) GO Ti 14 E TA=PHl0~REF/ PH A IG 5= CON ST *ri S[ \J TH F P= PH*,S QRT C1.+ ET A*2 +2.*ET A*COS (AR G5) I IF (FP.LE.O0.016035) GO TO 107 FPD=20.3*ALOG1IOC(FP) GO TO fOb 107 FPD=-36.0 1)9 IF (Hl.LE.D.O) GOL TO 14 A RG6 =CON ST*H I *SI N TH FP 1= P H*S ~ T ( 1. + E TA!**-2+ 2. *E TA OC0S( A R36)) IF (FP1.LE.0.01!5035) GO TO 109 F`PD1=20.0*AL0:1O(FP1) FlPD2=FP01-PIlP2 IF (FP02.LE.-36.00) FPD2=-36.00 GJ TO 110 109 FPD1=-3b.0 FPD2=FP)lI 113 FISLSI=FP+QISLSt-FP1 150

main program (cont'd) = I SL S2=FP-QI SL S* FP1 I F (ABS( FISL S1).$-E.0.016035) GO TO Ill DI SLS1=20.0*ALOG10 (ABS (FISLS1)) G'O TO 112 Ill DISLSI=-36.0 112 IF (ABS(FISLS2).LE.O.O16O35) GO TO 113 DISLS2=20.O*&L]G1O0 ABS(FISLS2)) GO TO 114 113 DISLS2=-36.0 114 RSLS=FPr)-FPD1 RI S I 5=D I SLS 1-F PD1 U SI SL 2=DI S LS 2-F PD 1 IF (THETA.EQ0.0.O) GO TO 121 ALFK=(RSLS+PIP2-9.)/12.0735 ALFK 1=CR SL 5+P 1:2-fBW1)/ 12.0735 ALFK2=(RSLS+PlP2-F.W2 )/12.0735 IF (ALFK.LE.O.O) `30 TO 115 ALFK=2.*AL FZ*S:)RT(CALFK) 30 TO 11b 115 ALFK=O.0 116 IF(ALFK1.LE.0.0) GO TO 117 ALFK 1=2.t-ALFZ4'SQRT( ALFK1) GO TO 118 117 ALFK1=O.0 118 IF (ALFK2.LE.O.O) GO TO0 119 ALFK2=2.*ALFZ*SQT( ALFK2) 370 TO 120 119 ALFK2=O.O 123 NSIS=ALFK*G-EE NI SLS;I=ALFK14'GEE 'JISL S2=AL-FK2*GEE GO TO 122 121 ALFK=0.0 ALFK1=O.0 ALFK2=0. 0 '4SLS=0 NI 5151=) 14dI L S2=0 I?? 4RIRTEC$.210) THPHDPIHD1,FPtFISLS1,zI SLS2,ALFKALFKI,~IFK2 WRITE (79211) THFPD2,FPD 9,DISLSIDISLS2,.RSLSR IS.SlR ISLS2, 1lJSLS9,NISLS1tNISLS2 lIs CONTINUE 200 r-OPMAT (lXI1,2F6.2913,P/,2FI0.4,/,3F10.4,t/,2Fl3.4) 231 FORMAT ('"WESTI1JGHJUSE ANTENNA TILTED ANI-vE=',F4.j1, DEG') 2 02 FORMAT ('TEXAS INSTR. ANTENNA T I L TED AJGLE=',F4.1,' DEG') 203 F)R.MAT C 'HAZALTINE ANTENNA TILTED ANGLE=',F4.1,' DEG') 2 ) f FO0RM AT (',EXIST ING ANTENNA T IL T ED A4GLE=',rF4.I1, )=%' ) 205:ORMAT ('NADIF FIX1 ANTIENNA TILTED ANGLE= I,9F4.It1,' DEG') 206 FORMIAT (T EXA S F IX A4 TE NNA TILTED ANSLE=',F4.1,' DEG') 207 FORMAT ('HAZALTINE: ESCAN ANT. T IL T ED A4GL E= I F4. 1, I DEG') 208 F)RMAT ('CELEVATION OF DIRECTIONAL ANTENNA = ',FID.fit' FEET it I///q'ELEV'A,T1ON OF OMNIDIRECT1rY4AL ATEN'JA= ',FIO.4,' FEET ', 2/I//v'RATI)3 OF PULSE S PI /PI =',F6.2,i' 08',v 2/,//9'P1 THRU O1P~EC. %NT./P1 THRU OMNI. ANT. ( ISLS) =# F6.2,' DB'f 2///94X,' ANGLE FROM' O5X,' FREE S PACE PATTERN J',6X, 'P A T T E R N ',I 3' A 3 ) V E IS R 0 U N D'.7Xt'E'- F F E C T I V E B E A M W I1 ~ 4'1DT H ',/,4X,' HORIZON ',3XAS)VE H)1.'t3X,'3EILJW -IR.'#3X, 5'PI. PULSE SLS',v4X#' Pl ISLS MAX',94X,' P1 ISLS MIN',p3X,'ISLS CASE',7XIP 61ISLS M-AX',t7X,'ISLS MIN',/) 209 FORMAT ('ELEV.: DIR EC.' FS.29,'''',4Xt '0M'I.',tF8.2,'''"lip/I 151

main program (cont'd) 1I'P/P2=',F6.2, ' DB P1 DIR./OMN.='-,F6.2,' DB., /, 1' P1/P2=',F6.2 ' DB.' /, 1' ',/ 1 ANGLE FROM HORIZON DEGREES', / 2' P AND P2 PATTEPNS SLS (DB)',/, 3'P1 AND P2 DATTEc%4S ISLS (D8)',/, 4' ISLS NORMALIZED P1/P2 (DB) ',/, 5'NUMBER OF REPLIES',/, 5 I4,/, 7'3EG =ROM HOR', X,'P2 DB',7X,' Pl SLS DB',3X, 'P1MAK ISLS',2X, B'PlMIN ISLS',2X,'RSLS DB',5X,'RISLS MAX',3X,'RISLS MIN',2X, 9'NO OF REP SLS', 2Xt'NISLS MAX',2X, e'ISLS MIN',/) 210 FORMAT (4X,F9.4, IX,E12.4,lX,E12.4,lX,E12.4,4X,E12,4,3X,E12.4,2X, 1E12.4, 3X, E12.4, 3X,E 12.4) 211 FORMAT (6E12.,7X,I3,9X,I3,8X, I3) 212 FORMAT ('1') STOP END 152

Program for Graphical Output SPLOT )I ME NSION X(401),9X1(800),9X2(800) vX3 (800) DIME NS ION Y1I(401) tY2(401), Y3(4011IiY4( 401) tY5(401),vY6(401),Y7(401) RE AL IJR1tN P2, NRP3 DIMENS!JD4 NQ1(800), 42(8:03)vR3( 800)' DI ME Ns ION T1(1O),T2(1')),T3(15bT4(10),,T5(10) )IMENS1JN XPRI,'r(10),YPRNT1(10),YPRNT2(10),YPRNT3(1),gYPRNT4(1o,)) RE AD (5, 21, E0l=500 ) ( TI( I ), I 1I 10) READ (5921) (T2(1)91=lv,1O) READ ( 5,924) ( T3( I), =I=,14) READ (5921) (T4 (I b!=I1,10) READ (5,21) (T5(1),I~1,1O) READ (5t21) ( XPR1I"T( I ),1=1 t8) READ (5,P21) (YPRN'Ll(I1),I=1,8J 1EAD (5,p2l) ( YPPNT2(I),1I=1 98) READ (5t21) (YPPNT3( I),I =1, 9) R EAD (5,21) (YPP.NT4(I),I=1,98) READ (5,*22) N MI=1 M12 = 1 M3=1 D3 3 I=1,N READ (5,23) X (I ) Yl ( I ),Y2( I )tY3 (I )9Y4( I ),Y5( I),Y6( I, tY7( I) 1q,'NRI,rNNP2,NNR3 IF(I.NE.1) GO TO) 100 NRL1(1) =NNRl N1:t2( 1) =NNR 2 NR3 ( 1 ) = INR3 XL( 1)=X( I) X2(1)=X( I) X3 (1)=X( I) 100 I F ( ( \ t. ~1.E ZN1~l)AV(.EN GO TO 1 4L=M1+1 Xl(MI1)=(X(I)+X(I-1))/2.0 ML=MI+1 Xl (Ml) =X1 C '-1) NRI(M1) =NNP1 I IF C(,N'R2.cEQ.'JR2 I2))..ANO.C I.NE.N));o TO 2 42 =M2+ 1 XZ(M2)=(X(I)4X(I-1))/2.0 NR2,2 )=NJR2(~42-1) M2=M2+1 X2( M2)=X2( l-;l) NR2 (M42 )=NN4R2 2 F ( (NNR3. EC. NR3 (M3)).AND.(I.NE.N) I GOTOD3 M13=M3+1 X3 ( M3) =(X ( I) 4X ( I-I ) )/2.0 4J 3( M_3o=NR3( M3-1 M.3= 3+ 1 X3 ( 143) =X3 C PM3-1) 'JR 3( M3) )=NNP3 3 CONT INUE' 'Z.ALL PLT(X (2)9Yl( 2),\4-19X( 2) Y2( 2) tN-IP. 0.,. vOPX PRI NT(I) lYPRNTI1(lhTl (1 ) T2 (1 ) T4(1) lv(PRNT2(1),TI( 1),T2(l1),PT3(l1)) %A LL PLT(X (2),Y5, (2) gri-I,0.0.0 O0,,0)v,0.0, 0,XPR INr (1I )t YP;ZNT3( 2), lTl(1), T2( 1),T5(l1)) CA LL PLTr(X Q )vY52 VpN-1,X 2,Y (,c2,'J - 1,.o, 0.o 9 OiXP~kTJ( 1) 1Y'IRNT3( 1), Tl( 1), T2(l ) v T3 (5 ) 153

SPLOT (cont'd) CALL PLrT(X1('1),NIC"'' 1 ), Ml,3.0, 0.0,,0.0,30,0,XPR INT( 1) tYPRNT4( 1) CALL PLT(X2( ),1 2( 1),"2tX3( 1),NR3( 1),M3,90. O,O.OP,0,XPR INT (I), lYPRNT4(1) 9TI (),T2 (1 ),T3 (1) 21 FORMAT(l0A4) 2? FOR.MAT ( 14,/ 23 FORMAT (8El12.4, 7X,13,9X 13,8X,I13) 24 FJRMAT t14A4) 500 STlP SUBROJT1INE PLT(X1,YlNl,X2,Y2,NJ2,X3,Y3,4J3,XPIRIN'T,YP.RINTT1,r2,T3) )IMEJSIrN XiU3rOD),X2(80D)),X3(800) DIlMENSION Yl(!oCC),,Y2C8300),Y3(300) DIMENS13N4 X)~.I\1T(1C),YPRINT(10),Tl( JO),T2(10),T3(10) CALL PLTXMX(10.nl) C ~L LPS>-LE( 5.0,1. 0,XMTN,DXX[,Nl,l,X2,N2,lX3,N3,1) CALL PSCALE(b.0, 1.3,'MINDY,YiNl, 1,Y2,N42,1,Y3,N3,1I '- LL PLTOF S(XMIt~,OX,YMIIN,DY,3.3,3.0) CALL ')AXIS(?.0,,3.t.',X':ZlIT,-'3C,5.O,0.0,XNIN,DX,1.0) CALL PAXIS(3.O,3.DYPRINT,33,6.O,90.D9,YMINDY, 1.0) C4.LL PLTREC IF (Nl.EQ.O) G3 TO 1 1 IF (N2.EQ.0) '10 TO 2 CALL PDSHLN(X2iY2'-,N2, 1,0.1, 1.0) 2 I= (N2.FQ.0) GO TO 3 C ALL P CTRL. J,( X3, Y3 413, 1,1I. 0) 3 CL=PSY-'lLN(0.15 3D),'ALL PSYlO19(5. 25-CL/2.,12.0,0. 15,T1 0.0,40) CALL PS01B(C.25-L2.~.,0152.04):ALL PLTE~4D RETURN END * * ******t*****t ********* 154

APPENDIX B REPORT OF INVENTIONS A diligent review of the work performed under this contract has revealed no new innovation, discovery, improvement or invention. 155

I