Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1982 Atmospheric anisotrophy and its effect on the delay power spectra of tropospheric scatter radio signals Hosny Mohammed Ibrahim Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Electrical and Electronics Commons Recommended Citation Ibrahim, Hosny Mohammed, "Atmospheric anisotrophy and its effect on the delay power spectra of tropospheric scatter radio signals " (1982). Retrospective Theses and Dissertations. 7507. https://lib.dr.iastate.edu/rtd/7507 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. 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Universi^ Microrilms International 300 N. Zeeb Road Ann Arbor, Ml 48106 8224225 Ibrahim, Hosny Mohammed ATMOSPHERIC ANISOTROPY AND ITS EFFECT ON THE DELAY POWER SPECTRA OF TROPOSPHERIC SCATTER RADIO SIGNALS Iowa State Urmersity PkD. 1982 University Microfilms IntSrnâtiOnQ,! 300 X. Zeeb Road.Ann Arbor.MI 48106 PLEASE NOTE: In all cases this material has been filmed in the best possible way from the available copy. Problems encountered with this document have been identified here with a check mark V 1. Glossy photographs or pages 2. Colored illustrations, paper or print 3. Photographs with dark background 4. Illustrations are poor copy 5. Pages with black marks, not original copy. 6. Print shows through as there is text on both sides of page_ 7. Indistinct, broken or small print on several pages t/^ 8. Print exceeds mairgin requirements 9. Tightly bound copy with print lost in spine 10. Computer printout pages with indistinct print_ 11. Page(s) lacking when material received, and not available from school or author. 12. Page(s) seem to be missing in numbering only as text follows. 13. Two pages numbered . Text follows. 14. Curiing and wrinkled pages 15. Other University Microfilms International Atmospheric anisotropy and its effect on the delay power spectra of tropospheric scatter radio signals by Hosny Mohammed Ibrahim A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major: Electrical Engineering Approved: Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. f'ià/ar Department Signature was redacted for privacy. Iowa State University Ames, Iowa 1982 ii TABLE OF CONTENTS Page DEDICATION iv I. GENERAL INTRODUCTION 1 II. REVIEW OF TROPOSPHERIC BEYOND-THE-HORIZON PROPAGATION AND THE RAKE SYSTEM 4 A. Introduction 4 B. Scattering Theory 5 1. The correlation function 7 2. The structure function 8 3. The spectral density function 8 C. Reflection Theory 14 D. The RAKE System 16 E. Anisotropic Spectral Densities 20 III. A SIMPLIFIED MODEL FOR EXTRACTING THE ANISOTROPY COEFFICIENT FROM THE DOPPLER SPECTRUM 23 A. Introduction 23 B. Development of the Simplified Model 24 1- Crawford model 24 2. Birkemeier's anisotropic model 28 3. Developing the simplified model 30 C. Experimental Verification of the Simplified Model 34 1. The isotropic component of the argument a,- 34 2. The crosspath wind speed 40 3. The coefficient Bj 41 4. Illustrative examples 46 IV. THE EFFECT OF ANISOTROPY ON THE DELAY POWER SPECTRA AND MULTIPATH SPREAD OF TROPOSCATTER SIGNALS 62 A. Introduction 62 i i i B. The Description and Calculations of Delay Power Spectra Based on an Anisotropic Model 63 1. Bello's model for calculating the delay power spectra 65 2. Delay power spectra based on an anisotropic model 67 C. Anisotropy Profiles and Their Effect on the Delay Power Spectrum 69 1. Linear increase of anisotropy with delay 70 2. Exponential increase of anisotropy with delay 71 3. One elevated layer 71 4. Two-layer model 72 D. The Effect of Anisotropy on Intermodulation Distortion and Error Probability of Binary Communication Systems 78 1. Intermodulation distortion 79 2. Effect of anisotropy on the error rate of a binary communication system 81 E. Measurement of the Multipath Characteristics 88 V. CONCLUSION . 97 VI. BIBLIOGRAPHY 100 VII. ACKNOWLEDGMENTS 103 VIII. APPENDIX A: PARAMETERS OF THE ISU-UW TROPOSCATTER LINK 104 IX. APPENDIX B: WATFIV COMPUTER PROGRAM FOR CALCULATING THE DISTRIBUTION OF THE DIFFERENTIAL ISOTROPIC SCATTERED POWER VS CROSSPATH DISTANCE 114 X. APPENDIX C: WATFIV COMPUTER PROGRAM FOR CALCULATING THE DELAY POWER SPECTRUM BASED ON AN ANISOTROPIC SCATTERING MODEL 129 iv DEDICATION TO NAGWA AND THE MEMORY OF MY FATHER 1 I. GENERAL INTRODUCTION The effect of the anisotropy of the scattering in the atmosphere on the multipath spread of the forward scattered signals is studied in this thesis. It is found that the shape of the delay power spectra and its corresponding statistics are very dependent on the profile of the average anisotropy coefficient.. Several theoretical profiles and their corresponding delay power spectra have been studied. The corresponding effect on the bit error rate (BER) of binary communication systems is also presented. Several different propagation theories have been proposed for interpreting signals received on transhorizon radio paths. Prominent among these are: 1) the "reflection from stratified layers" model developed by Friis^aJ_. [1], and 2) the "scattering from isotropic turbulence" model developed by Booker-Gordon [2] and Tatarski [3]. However, atmospheric turbulence always contains large scale components which are far from being isotropic, while reflection by layers is dominant only when there are temperature inversions. Thus, interpreting transhorizon signals on the basis of an anisotropic turbulence model is more representative of the true nature of the atmosphere. In addition, the degree of anisotropy is very closely related to the dynamic stability of the atmosphere [4]. Birkemeier [4] has indicated that the degree of anisotropy affects the multipath spread of the forward scattered signals. Bello et aT_. [5-7] have developed a mathematical model based on the statistics of the delay power spectra. They have shown that the multipath spread is a basic parameter that affects the irreducible bit 2 error rate, produced by frequency selective fading. Data taken from the Iowa State University - University of Wisconsin RAKE radar system are used in the present study. This system operates over a 406 km path at 940 MHz. The RAKE receiver effectively splits the common volume into time delay shells. The system uses a pseudorandom code modulation of 5 or 10 MHz which provides a delay resolution of 0.2 or 0-1 microseconds. A microprocessor based data acquisition and analysis system, designed for the tropospheric project calculates the Doppler spectra of each time delay shell. These spectra are further processed to extract the anisotropy coefficient and its variation with height. Direct measurements of atmospheric anisotropy have not been attempted due to the difficulties associated with measuring small scale refractivity fluctuations in three dimensions simultaneously in time and space. This thesis utilizes a simple model that is capable of characterizing the anisotropy of the scattering process. The model combines the "reflection by layer" theory and a "scattering by anisotropic turbulence" model developed by Birkemeier et [8] The simplified model offers definite advantages for the process of extracting the anisotropy coefficient from the Doppler frequency distribution of the received signals. Chapter II presents an overview of the theories of the troposcatter propagation; both the reflection theory and turbulence theory are reviewed together with the anisotropic correlation functions and their corresponding spectra. The forward scatter radar geometry and the coordinate system of the RAKE receiver are also presented. Chapter III 3 presents the simplified Gaussian shaped anisotropic model. A computer program is developed to calculate the theoretical received power as a function of the cross-path position of the scatterers for the different time delay shells of the RAKE receiver.