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University of Cincinnati UNIVERSITY OF CINCINNATI _____________ , 20 _____ I,______________________________________________, hereby submit this as part of the requirements for the degree of: ________________________________________________ in: ________________________________________________ It is entitled: ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ Approved by: ________________________ ________________________ ________________________ ________________________ ________________________ Digital Direction Finding System Design and Analysis A thesis submitted to the Division of Graduate Studies and Research of the University of Cincinnati in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE (M.S.) in the Department of Electrical & Computer Engineering and Computer Science of the College of Engineering 2003 by Huazhou Liu B.E., Xi’an Jiaotong University P. R. China, 2000 Committee Chair: Professor Howard Fan ABSTRACT Direction Finding (DF) system is used in many military and civilian operations such as surveillance, reconnaissance, and rescue, etc. In the past years, direction finding system is implemented usually using analog RF techniques such as Butler matrix and analog beamforming. Analog direction finding systems have drawbacks inherent from their analog properties such as expensive implementation, inflexibility to adjust or change functionality, intensive calibration procedures and etc. The digital technique relies on reconfigurable logic implementations. Thus it is more flexible and less expensive compared with its analog counterpart. In a digital direction finding system, all the received signals by array elements are sampled and digitized into digital format. They are processed by a high throughput digital processor. The whole system is much more reliable and accurate. Digital implementation of the direction finding system becomes practically exploitable in recently years. In this research work, we design a high throughput digital direction finding (DDF) system. It implements the digital Butler matrix to accomplish the direction finding task. Through theoretical timing error analysis, we then estimate the performance that the digital direction finding system can achieve. We also analyze how to choose the geometry of the antenna array, array size and so forth, based on theoretical and practical considerations. ACKNOWLEDGMENT I would like to express my sincerest gratitude to my advisor Dr. Howard Fan for his outstanding guidance, constant encouragement and patience. I wish to thank Dr. James Caffery, Shu Wang and Huiqin Yan for their valuable discussions and hard work in this project. Without their help, this thesis would have not been possible. I am thankful to Dr. Ali Minai for his time and helpful comments. I also wish to thank all of my friends and colleague in my lab for their help. Finally, I would like thank my parents for their love and supports over the years. And this work was funded in part by Nova Engineering, Cincinnati, OH, under U.S. Department of Defense Small Business Innovative Research (SBIR) contract. CONTENTS CONTENTS............................................................................................................................................ I LIST OF FIGURES ............................................................................................................................ III LIST OF TABLES ................................................................................................................................ V 1 INTRODUCTION ........................................................................................................................1 1.1 ANTENNA ARRAY...........................................................................................................................1 1.2 FUNDAMENTAL PARAMETERS OF ANTENNA ARRAY ......................................................................1 1.2.1 Radiation Pattern...................................................................................................................2 1.2.2 Array Factor ..........................................................................................................................2 1.2.3 Main Lobe..............................................................................................................................3 1.2.4 Side Lobes..............................................................................................................................3 1.2.5 Half -Power Beamwidth.........................................................................................................3 1.3 ARRAY GEOMETRY ........................................................................................................................3 1.3.1 Linear Array ..........................................................................................................................4 1.3.2 Circular Array .......................................................................................................................5 1.3.3 Hexagonal Array....................................................................................................................6 2 BEAMFORMING.........................................................................................................................8 2.1 ANALOG BEAMFORMING ................................................................................................................9 2.1.1 Analog Butler Matrix.............................................................................................................9 2.2 DIGITAL BEAMFORMING...............................................................................................................10 2.2.1 Description of DBF..............................................................................................................10 2.2.2 Time-domain Beamforming .................................................................................................12 2.2.3 Frequency-domain Beamforming ........................................................................................21 3 SYSTEM DESCRIPTION .........................................................................................................23 3.1 A/D SAMPLING AND SYNCHRONIZATION......................................................................................23 3.2 DIGITAL BUTLER MATRIX ............................................................................................................24 - i - 3.2.1 Narrow Band Butler Matrix.................................................................................................24 3.2.2 Wideband Butler Matrix ......................................................................................................25 3.2.3 Shading ................................................................................................................................27 3.2.4 Direction Finding Strategy ..................................................................................................28 4 ARRAY PARAMETER ANALYSIS ........................................................................................31 4.1 ANTENNA ARRAY SIZE CONSIDERATION......................................................................................31 4.1.1 Equal-spaced Linear Array..................................................................................................31 4.1.2 Uniform Circular Array.......................................................................................................37 4.2 UNIFORM CIRCULAR ARRAY WITH A CENTER ELEMENT ...............................................................48 4.3 HEXAGONAL ARRAY ....................................................................................................................50 5 TIMING ERROR ANAYSIS.....................................................................................................53 5.1 EQUAL-SPACED LINEAR ARRAY ...................................................................................................57 5.2 UNIFORM CIRCULAR ARRAY ........................................................................................................61 5.2.1 Four Element Uniform Circular Array Plus a Center Element ...........................................62 5.2.2 Four Element Uniform Circular Array................................................................................64 5.3 SIMULATION RESULTS..................................................................................................................66 5.3.1 Equal-spaced Linear Array..................................................................................................67 5.3.2 Four Element Uniform Circular Array Plus a Center Element ...........................................69 5.3.3 Four Element Uniform Circular Array................................................................................74 5.3.4 Overall System Simulations .................................................................................................77 6 CONCLUSION ...........................................................................................................................80 7 BIBLIOGRAPHY.......................................................................................................................81 - ii - LIST OF FIGURES FIGURE 1.1 RECTANGULAR RADIATION PATTERN......................................................................................2
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