ii Summary ThematerialpresentedinthisthesisistheresultofthePh.D.activitycarried on between January 2009 and December 2012 at the Ph.D. school in Infor- mation Engineering of the University of Trieste. After a brief introduction on the involved topics, the final objective of this thesis is that of presenting the original results, consisting in the development of power pattern synthesis algorithms for arbitrary antenna arrays including, in particular, arrays for satellite applications. Since the earlier satellite missions of last century, satellite communication systems have received growing attention due to the opportunities they offer and their greater flexibility with respect to alternative solutions adopting other media, such as, for example, fiber optic cables. The enormous spread of satellites, for both military and civilian applications, has been achieved thanks to the experienced technological progress, which has allowed an in- crease of satellite capacities. The need of constantly increasing the capacity of commercial communications satellites resulted in the continuing evolution of the antenna systems onboard the satellites. The business environment has driven the architecture of satellites’ systems towards more efficiency and cost consciousness while at the same time, providing flexible access to a growing diversity of services and customers. Antennas that provide a multiplicity of frequency reuse coverage beams through either spatial or polarization iso- lation have been developed, resulting in the evolution of satellite antennas from a simple omnidirectional dipole to multiple-beam, dual-polarized con- figurations with frequency reuse between the beams for increased capacity. These requirements translate into high-gain, high-efficiency antennas with low side-lobe levels and excellent polarization purity. Moreover, since new requirements are often determined after the satellite is operational, antennas adjustable to produce a wide variety of radiation patterns have become pop- ular. These are the so-called multiple-beam antennas, which can adjust their iii iv radiationcoverageareasaccordingtonewdemands. Multiple-beamantennas are currently being used for direct-broadcast satellites, personal communi- cation satellites, military communication satellites, and high-speed Internet applications. High-gain multiple-beam antenna systems usually take one of three generic forms: lens, reflector or direct radiating array. Thus, arrays of antennas can be used in multiple-beam systems either to feed other types of antennas, or directly as radiating structures. Thematerialofthisthesisismainlyrelatedtothesynthesisalgorithmsfor antenna arrays. In particular, many analytical and numerical techniques for thepowerpatternsynthesisofantennaarrayshavebeencarefullystudiedand analyzed. Some of them are suitable only for linear or rectangular arrays, the others for arrays of more complicated geometries. Furthermore, it is extremely important, for power synthesis techniques in satellite applications, to be able to consider additional constraints. These typically are the phase- only reconfigurability of the radiated beams, the control of the cross-polar patterns, which allows the polarization re-use and/or the control of the cross- polarinterference, thedynamicrangeratioreductionwhichcomportssimpler feeding networks and lower mutual coupling between array elements, and the near-fieldreduction, whichallowstotakeintoaccounttheantennasoperating environment. A numerical iterative algorithm has been developed during the Ph.D. school in Information Engineering, suitable for arrays of arbitrary geometry, thus including sparse and conformal arrays, which are often used in satel- lite applications. The algorithm allows to solve the power pattern synthesis problem, which is an inherently non linear problem. The solution is achieved using the alternating projections algorithm, which is a numerical iterative technique for finding a point of the intersection between two sets. It will be seen that the projections method has previously already been applied to problems of image processing and also in the antenna pattern synthesis. However, the results and the computational burden are strongly related to the projection operators, which in turn, strictly depend on the definition of the adopted distance, thus on the definition of the sets adopted in the formulation of the problem. Thus, the main originality of the developed al- gorithmsconsistsinanextremelyadvantageousdefinitionofthesetsinvolved in the solving scheme, which, along with the adopted distance, allow an easy evaluation of the projection operators and thus a simple solving procedure. The thesis is organized as follows. Chapter 1 introduces the satellite an- v tennas, analyzing some solutions adopted in the past. Particular attention is devotedtomultiple-beamantennas(MBAs)andinparticulartoarraysofan- tennas, which can constitute the feeding system of reflector MBAs, or which can be used as direct radiating antennas themselves. Chapter 2 presents ana- lytical and numerical methods of power pattern synthesis for antenna arrays proposedintheliterature. First, theclassicalanalyticalmethods, suitablefor linear arrays of equally spaced elements are presented. Then, numerical iter- ative methods are analyzed. Attention is devoted to both deterministic and stochastic algorithms. A section is dedicated to the near-field constraint, due to its importance in practical real applications. In fact, taking into account the effect of the antenna operating environment is of fundamental impor- tance: obstacles or mounting platforms, as well as other electronic devices located in proximity of the antenna, may strongly degrade the radiated far- field pattern. Then, Chapter 3 presents the developed algorithm. Precisely, the evolution is described from a synthesis algorithm suitable for arbitrary phase-only reconfigurable arrays to a powerful algorithm for phase-only an- tenna arrays, including several additional constraints, such as the dynamic range ratio reduction, the cross-polar pattern synthesis and the near-field reduction. Moreover, in its final form, the algorithm also allows to minimize the power radiated in the side-lobe regions of both the co- and cross-polar patterns and the electric energy stored in the near-field region of interest. Numerical results validating the effectiveness of the proposed algorithm are presented in Chapter 4 and the conclusions are summarized in Chapter 5. Finally, the appendix mathematically describes the classical alternating pro- jections method and the genetic algorithms, which have been used as global optimization algorithms for comparison purposes. vi Contents Contents vii 1 Literature review 1 1.1 Satellite antennas . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Historical Background . . . . . . . . . . . . . . . . . . 3 1.1.2 Multiple-beam antennas . . . . . . . . . . . . . . . . . 8 2 Satellite arrays of antennas 17 2.1 Synthesis of antenna arrays . . . . . . . . . . . . . . . . . . . 17 2.1.1 Radiated Near-Field . . . . . . . . . . . . . . . . . . . 22 3 The developed algorithms 27 3.1 Alternating projection approach . . . . . . . . . . . . . . . . . 27 3.2 Power synthesis for phase-only reconfigurable arrays . . . . . . 29 3.2.1 The solving procedure . . . . . . . . . . . . . . . . . . 30 3.2.2 The projection operators . . . . . . . . . . . . . . . . . 33 3.3 The Dynamic Range Ratio constraint . . . . . . . . . . . . . . 36 3.3.1 The solving procedure . . . . . . . . . . . . . . . . . . 36 3.4 Cross-polar pattern synthesis . . . . . . . . . . . . . . . . . . 38 3.4.1 The solving procedure . . . . . . . . . . . . . . . . . . 39 3.5 Near-field constraint . . . . . . . . . . . . . . . . . . . . . . . 42 3.5.1 The projection operators . . . . . . . . . . . . . . . . . 43 3.5.2 Power minimization . . . . . . . . . . . . . . . . . . . . 45 4 Numerical examples 49 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Co-polar pattern synthesis . . . . . . . . . . . . . . . . . . . . 50 4.3 Comparison with different approaches . . . . . . . . . . . . . . 52 vii viii CONTENTS 4.4 Cross-polar pattern synthesis . . . . . . . . . . . . . . . . . . 55 4.4.1 Side-lobes power reduction . . . . . . . . . . . . . . . . 59 4.5 Reduction of the near-field amplitude . . . . . . . . . . . . . . 61 4.5.1 Non constant near-field constraint . . . . . . . . . . . . 69 4.6 Complete 3D example . . . . . . . . . . . . . . . . . . . . . . 76 5 Conclusion 87 5.1 Summary of contributions . . . . . . . . . . . . . . . . . . . . 87 A Appendix 91 A.1 The alternating projections method . . . . . . . . . . . . . . . 91 A.1.1 Method of projections onto convex sets . . . . . . . . . 92 A.1.2 Method of projections onto non-convex sets . . . . . . 94 A.2 Genetic algorithms . . . . . . . . . . . . . . . . . . . . . . . . 95 Bibliography 99 Chapter 1 Literature review This chapter gives a brief overview on satellite antennas, with special focus on satellite antenna arrays. The first part of the chapter roughly introduces the basic concepts of satellite antennas, with focus on the main problems arising in the design of onboard antennas. Examples of antennas used as onboard antennas since the earlier satellite missions are provided. Particular attention is devoted to multi-beam antennas, which are widely employed in modern satellites and which include array of antennas. 1.1 Satellite antennas In its first two decades, international commercial satellite communication evolved from a single satellite connecting western Europe with the US to a system linking most countries of the world through several satellites, carry- ing about two thirds of international telephonic traffic. During this period the capacity of a geostationary communications satellite increased from 240 channels in INTELSAT I (“Early Bird” launched in 1965) to over 33000 equivalent voice channels in INTELSAT VI series of satellites, launched in 1989. The need to constantly increase the capacity of commercial communi- cations satellites resulted in the continuing evolution of the antenna system onboard the satellite [1]. Cables were viewed as complimentary and satellites were used from the beginning to restore cable services in case of cable breaks. Today we enjoy instantaneous high quality telephone service to most parts of the world and 1 2 Literature review have the benefit of real-time televised news and other events from all over the globe. The perception of these services has changed from technological marvel to a commonplace everyday commodity. Satellitesarenottheonlycommunicationtechnologygrowntomeetthese needs. There are two major long-haul information transport media, satellites and optical fiber cables, which in some cases may compete, in other cases may complement each other. Terrestrial optical fiber cable networks have penetrated most major metropolitan centers in the United States and even across the Atlantic and Pacific. Intercontinental fiber optic communications are a reality. However, geographic features are no barrier to communication via satellite. Even accepting the probability that optical fiber may one day appear in every home and business in the United States, several decades may pass before it happens and it is unlikely to happen at all in many parts of the world due to geographical barriers such as mountains and large uninhabited areas that the fiber optics cables would be required to traverse. The ease of transporting and erecting small satellite terminals will create a ready and growing market in these areas [2]. The business environment has driven the architecture of satellites’ sys- tems towards more efficiency and cost consciousness while at the same time, providing flexible access to a growing diversity of services and customers. Antennas that provide a multiplicity of frequency reuse coverage beams througheitherspatialorpolarizationisolationhavebeendeveloped, resulting in the evolution of satellite antennas from a simple omnidirectional dipole to multiple-beam, dual-polarized configurations with frequency reuse between thebeamsforincreasedcapacity. Theradiationpatternsofsatelliteantennas can be depicted as a footprint on the earth, which contains all earth stations that communicate with the satellite. Outside this footprint, the pattern should fall off to a negligible level as fast as possible to permit multiple reuse of the same frequency band in other beams and to avoid interference with othersystems. Thesizeofthefootprintmayrangefromearthcoverage(a17◦ solid angle encompassing the entire earth disk visible from synchronous alti- tude), to shaped beams that are perhaps covering a continent or a region, to pencil beams, perhaps as small as a 1◦ solid angle. Orthogonal polarizations arefrequentlyusedtoobtainfrequencyreuseandbeam-to-beamisolation. In terms of antenna technology, these radiation pattern requirements translate into high-gain, high-efficiency antennas with low side-lobe levels and excel- lent polarization purity [2]. Better cost effectiveness is a must in order to