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Adaptive Beamforming with a Focal-Fed Offset Parabolic Reflect Or Antenna

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Adaptive Beamforming with a Focal-Fed Offset Parabolic Reflect Or Antenna Adaptive Beamforming With a Focal-Fed Offset Parabolic Reflect or Antenna by Jason Duggan A thesis submitted to the Department of Elect rid and Computer Engineering in conformity with the requirements for the degree of Master of Science (Engineering) Queen's University Kingston, Ontario, Canada April 1997 Copyright @ Jason Duggan, 1997 National Library BibliotMque nationale I*I ,Canada du Canada Acquisitions and Acquisitions et Bibliographic Senrices services bibliographiques The author has granted a non- L'auteur a accord6 melicence ncm exclusive licence dowing the National Lj'brary of Canada to %iblioth&penationale du Cimada de reproduce, loan, distn'bute or sell fepfoatuire, prkr, distn'buerou copies of Merthesis by any means vendre des copies & sa these & and in any form or format, making quelque &&re et sous qyelqy this thesis a-le to interested fore cpe ce soit pour mettre des persons. exemplaires de cette thba la disposition des persomes intCressks. The author retains ownership of the L'auteur conserve la propriet6 du copyright in Merthesis. Neither droit &auteur qUi prot&gesa th&se.Ni the thesis nor substantial extracts h these ni des extfaits substantiels & fiom it may be printed or otherwise cell& ne doivent &e imprimes ou reproduced with the &or's autrement~uitssansson permission. autorisation. Abstract The bandwidth and power restrictions on the communications system between a geostationary satellite and a mobile terminal are severe. Adaptive antenna array processing, which exploits the spatial distribution of the mobile users, is seen as one possible solution to these problems. Adaptive may processing allows the satellite to maximize the signal received from a desired user and null out the contributions of co-channel interfering users based on their distinct locations. The adaptive antenna Literature has used a linear or planar array structure on which to perform the may processing. The most common structure referred to is the uniform linear array (ULA) which is composed of a line of identical antenna elements spaced an equal distance apazt. Linear and planar array structures are more generally referred to as direct radiating arrays (DRA). On a geostationary satellite offset parabolic reflector antennas are the dominant antenna type. This is due to the reflector's high gain which is critical in a geostationary satellite to Earth Link. This thesis considers the use of an offset reflector with an may feed as a way of combining the high gain of the reflector with the spatial filtering ability of the antenna array. This type of antenna is referred to as a multiple beam antenna (MBA). The question is whether or not adaptive algorithms designed with the direct radiating array stmcture in mind will work on a multiple beam antenna. A signal model is developed which is general enough to encompass both the DRA structure and the MBA structure. The key quantity is the steering vector which describes the response of the antenna may to a plane wave arriving from a given angle. While the steering vector for a uniform linear may is analytically derivable with knowledge of the wavelength of the plane wave, and the spacing of the antenna elements, the steering vector for a MBA must be found numerically. One of the necessary steps to finding the steering vector of the MBA is the ability to determine the secondary field of each of the antenna elements. The theory of reflector antenna analysis is developed utilizing the physical optics approximation and the Fourier-Bessel method of solution. This theory is embodied in a computer program which is capable of generating the antema pattern of the reflector antenna with an array feed. This computer program is used to find the secondary field of each of the antenna elements. The program is also used to study some of the properties of offset parabolic reflectors including the effects of tapering of the feed's primary pattern and lateral displacements of the feed from the focal point. Using the principie of reciprocity and the secondary field of each of the antenna elements in the array the steering vector for the MBA is numericdyeduated. With the steering vector and the general signal model optimum minimum mean-squared error (MMSE) array processing is investigated demonstrating the ability of the MB A to perform adaptive beamforming. One of the conceptually simplest adaptive dgo- ri t hms, the Direct Matrix Inversion (DMI)algorithm is described and its performance on a MBA is demonstrated. A special class of adaptive algorithms called cyclic beamforming algorithms ase introduced. These algorithms exploit the inherent cyclostationarity in the desired user's signal to extract it in the presence of spectrally incoherent interference and noise. One of the highly desireable properties of these algorithms is that they do not require either a reference signd, or, knowledge of the directions of arrival of the users of the system. A particular cyclic bedorming algorithm, the Least Squares Self-coherence Restord (LS-SCORE)algorithm, is demonstrated to work on a MBA and its performance is studied. The conclusion of this thesis is that adaptive may processing can be performed by using the may as a feed to an offset parabolic reflector. Adaptive algorithms will work on the multiple beam antenna structure without any changes. Acknowledgements I would like to sincerely thank Dr. Peter J. McLane for his generous support and guidance throughout my graduate career. I would also like to thank Eric Amyotte of SPAR Aerospace for his time and patience in answering my many questions on my visits down to SPAR. I thank the the Telecommunications Research Institute of Ontario for their financial support and industry Canada, Communications Research Centre, Ottawa for their financial support and background material on cyclic beam- forming. Specifically, I would like to thank Chun Loo of CRC and Mark Rollins, formerly of CRC for their assistance. Thanks also goes to all of the staff in the TRIO office for their assistance, I would like to thank all the friends I have made during my time as a graduate student. In partidax I would like to thank Ken Gracie, Dave Young, Oguz Sunay, Dave Parrtnchych, Jean Au, Joubin Kaximi, Alex Seyoum, William Wan, Chris Tan aad Walid Ahmed. I thank them for their friendship, their support and for always being available to help me out when I needed it. I would like to thanlc my friends who not only supported me and gave me their friendship but also gave my a place to stay when I traveled back to Kingston to work on my thesis. Thank you to Jeniffer Sartor, Jason Pantarotto, Sarah Jones, Me1 Clancy, and Finola Shankar. To my family, thank you for your love, support and encouragement throughout my life. To Deirdre, thank you for your love and your belief in me. Table of Contents Abstract Acknowledgements Table of Contents List of Symbols xii 1 Introduction 1 1.1 Motivation ................................. 1 1.2 Literature Survey ............................. 4 1.2.1 Adaptive Ante~aArrays .................... 4 1.2.2 Adaptive Multiple Beam Antennas ............... 5 1.3 Contributions of Thesis .......................... 6 1.4 Presentation Outline ........................... 8 2 Beamforming Theory 10 2.1 Introduction ................................ LO 2.2 The Unlfom Linear Array ........................ 11 2.3 The Wideband Signal Model ....................... 13 2.4 The Narrowband Signal Model ...................... 14 2.5 Beamforming ............................... 19 2.6 Statistically Optimum Beamforming ................... 21 2.6.1 The Minimum MSE Solution ................... 21 2.7 An Example: Optimum Combining With A ULA ........... 23 2.8 Beadorrming With a Multiple Beam Antenna ............. 29 3 Offset Parabolic Reflector Antenna Analysis 30 3.1 Introduction ................................ 30 3.2 Geometry of the Offset Reflector ..................... 32 3.3 CoordinateSystems ............................ 35 3.4 Reflector Antenna Analysis ....................... 36 3.5 Derimtion of the Radiation Integral ................... 38 3.6 Solution of the Radiation Integral .................... 41 3.7 The Physical Optics Approximation ................... 41 3.8 Evaluation of the Radiation Integral .................. 42 3.9 The Fourier-Bessel Method ........................ 46 3.10 Summqof Fourier-Bessel Method ................... 49 3.11 Implementation and Verification ..................... 50 3.12 Properties of Offset Reflectors ...................... 57 3.12.1 Edge Taper, Aperture Efficiency and the Effect of the q Pasameter 57 3.12.2 Reflector Antenna Pattern Characteristics of Off-Focus Feeds .......................... 60 3.13 Extension to an Array Feed ....................... 66 3.14 Calculation of the Directivity ...................... 69 4 Beamforming With An Offset Parabolic Reflector Antenna 72 4 .1 Introduction and Overview ........................ 72 4.2 Beamforming With a Multiple Beam Antenna ............. 73 4.3 Optimum Combining With an Offset Reflector Antenna ........ 76 4.4 Adaptive Algorithms ........................... 84 4.5 Direct Matrix Inversion .......................... 85 4.6 Simulation of the Direct Matrix Inversion Algorithm ......... 86 4.7 Discussion ................................. 5 Cyclic Beamforming Algorithms on a Multiple Beam Antenna 5.1 Introduction and Overview ........................ 5.2 Cydostationary Signal Analysis ..................... 5.3 Cyclic Bhd Spatid Filtering Algorithms ................ 5.3.1 Cyclic Bhd Spatial Filtering Algorithms
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