# Optimization and compensation techniques for modern reflector antenna designs

TABLE OF CONTENTS 1 Introduction 1 1.1 Background 1 1.2 Outline of Dissertation 7 2 Computational Methods 10 2.1 Introduction 10 2.2 Particle Swarm Optimization 11 2.2.1 Single-Objective PSO 11 2.2.2 Multi-Objective PSO 14 2.3 Diffraction Synthesis Techniques 16 2.3.1 PO/PTD Diffraction Analysis 16 2.3.2 PO/PTD Diffraction Synthesis Technique 17 2.3.3 GO/PO Dual-Reflector Shaping Technique 21 3 Application of PSO in Antenna Designs 23 3.1 Introduction 23 3.2 PSO for Array Feed Designs 23 3.2.1 Introduction 23 3.2.2 A 2-Dimensional 16-Element Array Antenna for Remote Sensing Application 24 3.2.3 Pattern Synthesis of a 5x5 Array Antenna 29 3.3 PSO for Shaped Reflector Designs 34 iv

3.3.1 Introduction 34 3.3.2 A Shaped Multi-Beam Reflector Antenna for DBS Com munications 35 3.3.3 Single-Objective Results 35 3.3.4 Multi-Objective Results 41 4 Reflector Surface Distortion Compensation Techniques 45 4.1 Introduction 45 4.2 Array Feeds for Reflector Surface Distortion Compensation .... 46 4.2.1 Introduction 46 4.2.2 Conjugate Field Matching Method 46 4.2.3 The PSO Method 52 4.3 Shaped Subreflectors for Reflector Surface Distortion Compensation 55 4.3.1 Introduction 55 4.3.2 Shaped Subreflector Compensation Technique Using PSO . 56 4.3.3 A Comparison with Simplex 62 4.4 Sub-Reflectarrays for Reflector Surface Distortion Compensation . 64 4.4.1 Introduction 64 4.4.2 Concept of Sub-Reflectarray Compensation 65 4.4.3 Implementation of Sub-Reflectarray Compensation .... 67 4.4.4 A Comparison with Array Feed and Shaped Subreflector Compensation Techniques 86 5 Other Compensation Techniques for Reflector Antenna Designs 90 v

5.1 Introduction 90 5.2 Twin-Horn Feed for Azimuth Displacement Compensation .... 91 5.2.1 Introduction 91 5.2.2 Back-to-Back Reflector Antenna Configuration 93 5.2.3 Integrated Twin-Horn Feed Design 96 5.2.4 Simulated Pattern of the 3.5-m Reflector Antenna 104 5.3 Beam Squint Compensation Technique 106 5.3.1 Introduction 106 5.3.2 The Simple Formula I l l 5.3.3 Simulation Results of Three Representative Examples . . . 115 5.3.4 Potential Applications 126 5.4 Sub-Reflect arrays for Spherical Aberration Compensation 128 5.4.1 Introduction 128 5.4.2 Compensation of a 35.5-m Spherical Reflector Antenna . . 129 5.4.3 Compensation of a 1.5-m Breadboard Spherical Reflector Antenna 136 6 Conclusion and Suggestions for Future Work 141 6.1 Conclusion 141 6.2 Suggestions for Future Work 145 A Boundary Conditions for PSO 147 A.l Introduction 147 A.2 Various Boundary Conditions 148 vi

A.3 Simulation Results of Benchmark Functions 152 A.4 A 2-Dimensional 16-Element Array Antenna for Remote Sensing Application 158 A.5 Summary 159 B List of Abbreviations 161 References 163 vn

LI ST OF FI GURES 1.1 A schematic diagram of the topics presented in this dissertation. ... 8 2.1 Illustration of the PSO algorithm 12 2.2 A flowchart of the parallel PSO algorithm 13 2.3 A conceptual sketch of a Pareto front of two fitness objectives 16 2.4 (a) Parameterization of the antenna system, (b) Incorporation of opti mization algorithms into the PO/PTD diffraction synthesis 18 3.1 Configuration of a 2-dimensional 16-element array antenna for remote sensing application. Only 3 independent amplitudes are needed for optimization due to the symmetry of the problem 25 3.2 (a) Convergence curves of the 2-dimensional 16-element array antenna design, (b) Average gbest value of 5 independent runs 26 3.3 Far-field pattern of the optimized 2-dimensional 16-element array antenna. 26 3.4 Pareto front of the 2-dimensional 16-element array antenna using d- MOPSO 28 3.5 Far-field patterns of three representative Pareto optimal designs of the 2-dimensional 16-element array antenna 28 3.6 Design envelope for a 5x5 array antenna 29 3.7 Configuration of a 5x5 array antenna for pattern synthesis. Only 8 in dependent amplitudes are needed for optimization due to the symmetry of the problem 30 3.8 Far-field pattern of the optimized 5x5 array design using Eq. (3.7). . . 31 viii

3.9 Optimized array amplitudes of a 5x5 array antenna using Eq. (3.7). . . 31 3.10 Convergence curves of the 5x5 array antenna design using Eq. (3.7). . 32 3.11 Far-field pattern of the optimized 5x5 array design using Eq. (3.8). . . 33 3.12 Optimized array amplitudes of a 5x5 array antenna using Eq. (3.8). . . 33 3.13 Convergence curves of the 5x5 array antenna design using Eq. (3.8). . 34 3.14 A shaped multi-beam reflector antenna for DBS reception from three satellites, a = b = 15 A, F = 30 A, H = 19.167 A. The operating frequency is 12.5 GHz 36 3.15 Far-field patterns of the parabolic reflector antenna. The directivities of Feeds 1, 2, and 3 are 36.27 dB, 38.56 dB, and 36.27 dB, respectively. 40 3.16 Far-field patterns of the shaped reflector antenna design 3. The di rectivities of Feeds 1, 2, and 3 are 36.78 dB, 36.81 dB, and 36.78 dB, respectively 40 3.17 Convergence curves of the shaped multi-beam reflector antenna design. It can be clearly observed that seeding with the original paraboloid provides a good guidance to the entire swarm 41 3.18 (a) Deviation of the shaped reflector from the original paraboloid, (b) Four line cuts of the deviation of the shaped reflector 41 3.19 Pareto front of the shaped multi-beam reflector antenna using d-MOPSO. 42 3.20 Far-field patterns of two representative Pareto optimal designs 43 3.21 (a) Swarm trajectories in the objective space throughout the optimiza tion process, (b) A close-up view of the swarm trajectories, (c) Pareto fronts after 100, 200, 500, and 1000 iterations 44 IX

4.1 (a) Geometry of a distorted 1.68-m reflector antenna operating at 8.45 GHz. D = 1.68 m, F = 1.832 m, and H = 1.45 m. (b) An analytical description of the reflector surface distortion, the maximum peak-to- center deviation is 11 mm 48 4.2 Far-field patterns of the 1.68-m reflector antenna without and with sur face distortions. Directivities are 42.51 dB and 39.11 dB, respectively. A directivity loss of 3.40 dB is observed 49 4.3 Far-field patterns of the distorted reflector antenna compensated by the 19-element array feed obtained using (a) Maximum Directivity method and (b) Sidelobe Control method. Simulated directivities are 41.23 dB and 41.22 dB, respectively. Sidelobe levels are -22.46 dB and -26.46 dB, respectively 50 4.4 Excitation coefficients of the 19-element array feed obtained using (a) Maximum Directivity method and (b) Sidelobe Control method. ... 51 4.5 Layout of the 19-element array feed for the compensation of reflector surface distortions 52 4.6 Convergence curves of the optimization of the 19-element array feed. An optimal design is found after the 520t/l iteration 53 4.7 Excitation coefficients of the 19-element array feed obtained using PSO. 53 4.8 Far-field pattern of the distorted reflector antenna compensated by the 19-element array feed obtained using PSO. The simulated directivity is 41.29 dB, and the sidelobe level is -23.35 dB 54 4.9 Geometry of the 25-m Gregorian reflector antenna for ARISE project. 58 4.10 An analytical description of the reflector surface distortion. The maxi mum peak-to-center deviation is 3 mm (0.22 A at 22 GHz) 58 x

4.11 Far-field patterns of the 25-m Gregorian reflector antenna without and with surface distortions. Directivities are 74.31 dB and 72.95 dB, re spectively. A directivity loss of 1.36 dB is observed 59 4.12 Convergence curves of the shaped subreflector for reflector surface dis tortion compensation. It can be clearly observed that seeding with the original ellipsoid provides a good guidance for the entire swarm 60 4.13 Deviation of the shaped subreflector for reflector surface distortion com pensation using PSO 61 4.14 Far-field pattern of the shaped subreflector for reflector surface distor tion compensation using PSO. The directivity after compensation is 74.27 dB 61 4.15 Deviation of the shaped subreflector for reflector surface distortion com pensation using Simplex 63 4.16 Far-field pattern of the shaped subreflector for reflector surface distor tion compensation using Simplex. The directivity after compensation is 74.26 dB 63 4.17 Concept of the sub-reflectarray compensation 66 4.18 Geometry of a 20-m offset parabolic reflector antenna 67 4.19 An analytical description of the reflector surface distortion. The maxi mum peak-to-center deviation is 9 mm (0.3 A at 10 GHz) 68 4.20 Far-field patterns of the 20-m offset parabolic reflector antenna without and with surface distortions. Directivities are 65.47 dB and 62.15 dB, respectively 68 XI

4.21 Ray trajectories in plane S at (a) 1.0 m and (b) 0.5 m away from point F in Figure 4.18. The dashed line represents the optical rim of the sub- reflectarray. Note that the sub-reflectarray size in (a) is larger than that in (b) 70 4.22 Geometry of the sub-reflectarray with phase controlling patches. ... 72 4.23 (a) Normalized amplitude distribution (in dB) and (b) phase shift (in degrees) of the sub-reflectarray obtained using the Maximum Directiv ity CFM method 75 4.24 Far-field pattern compensated with the sub-reflectarray with ideal am plitude and phase excitations obtained using CFM. The directivity is 65.10 dB, and the sidelobe level is -17.93 dB 75 4.25 Normalized actual amplitude distribution (in dB) of the sub-reflectarray illuminated by a cos9^) type feed with -10 dB feed taper 76 4.26 Far-field pattern compensated using the sub-reflectarray compensation technique. The directivity is 64.74 dB, and the sidelobe level is -17.15 dB 76 4.27 Compensated far-field patterns using sub-reflectarray with a random phase variation of (a) ±10° and (b) ±20°. The directivities are 64.69 dB and 64.56 dB, respectively 78 4.28 Phase shift of the sub-reflectarray from a side view. It shows a contin uous distribution covering the 300° phase swing with incremental steps of a few degrees 79 4.29 Phase shift of the sub-reflectarray after quantization using a uniform phase shift of (a) 20 steps, (b) 12 steps, (c) 8 steps, and (d) 6 steps. . 80 xn

4.30 Compensated far-field patterns using a quantized phase shift shown in Figure 4.29: (a) 20 steps, (b) 12 steps, (c) 8 steps, and (d) 6 steps. The compensated directivities are 64.70 dB, 64.65 dB, 64.53 dB, and 64.36 dB, respectively 81 4.31 Measured eight-step non-uniform phase shift of variable size patches. . 82 4.32 Quantized phase shift of the sub-reflectarray using the eight-step non uniform phase shift in Figure 4.31. Only five phase steps are actually used after quantization 82 4.33 Compensated far-field pattern using the quantized phase shift shown in Figure 4.32. The compensated directivity is 59.41 dB 83 4.34 Adjusted eight-step non-uniform phase shift of variable size patches. . 84 4.35 Quantized phase shift of the sub-reflectarray using the adjusted eight- step non-uniform phase shift in Figure 4.34. All eight phase steps are used after quantization 84 4.36 Compensated far-field pattern using the quantized phase shift shown in Figure 4.35. The compensated directivity is 64.55 dB 85 4.37 Compensated directivities versus the reference phase values of every 10° shift. A 0.5 dB difference is observed 85 4.38 Far-field pattern compensated using the array feed compensation tech nique. The directivity is 65.08 dB, and the sidelobe level is -19.63 dB. 86 4.39 (a) Normalized amplitude (in dB) and (b) phase (in degrees) excitations of the array feed for reflector surface distortion compensation 87 4.40 Far-field pattern compensated using the shaped subreflector compen sation technique. The directivity is 64.85 dB, and the sidelobe level is -15.55 dB 88 xm

4.41 Deviation (in mm) of the shaped subreflector for reflector surface dis tortion compensation 88 5.1 Conceptual illustration of the next generation OSVW measurement mission. An azimuth displacement of 0.5° exists between transmit ting and receiving events due to the high spinning rate and high orbit altitude of the antenna 92 5.2 A novel back-to-back reflector antenna structure on a spinning platform for remote sensing applications 94 5.3 Geometry of the 3.5-m parabolic reflector with secondary mirror. ... 95 5.4 (a) HFSS models of the single conical corrugated horn and the inte grated twin-horn feeds, (b) Detailed dimensions of the HFSS model. The diameter of the horn is 66.2 mm, and the center-to-center spacing is 37.4 mm 97 5.5 Single conical corrugated horn mounted in the UCLA spherical near- field measurement facility. The feed is linearly polarized in the elevation direction 98 5.6 Simulated return loss of the single conical corrugated horn compared with the measured return loss of the adapter and the feed. The center frequency is 13.4 GHz, and the required bandwidth is less than 20 MHz. 99 5.7 Comparison between the simulated (solid line) and measured (dashed line) normalized far-field patterns of the single conical corrugated horn in the 0 = 0°, 45°, and 90° cuts 100 5.8 The integrated twin-horn feed mounted in the UCLA spherical near- field measurement facility. The feed is linearly polarized in the elevation direction 101 xiv

5.9 Simulated and measured S parameters of the integrated twin-horn feed. The center frequency is 13.4 GHz, and the required bandwidth is less than 20 MHz 102 5.10 Comparison between the simulated (solid line) and measured (dashed line) normalized far-field patterns of the integrated twin-horn feed in the 0 = 0°, 45°, and 90° cuts 103 5.11 Holographic images of the field over the aperture of the integrated twin- horn feed: (a) co-polarized and (b) cross-polarized fields. The excited field in the adjacent horn is below -30 dB 104 5.12 The feed system consists of two pairs of Ku-band Tx/Rx scatterometers, a C-band scatterometer, and an X-band radiometer. The Ku-band feeds are linearly polarized in the elevation direction 105 5.13 Simulated far-field patterns of the 3.5-m reflector antenna through the beam peaks of the (a) transmitting feed and (b) receiving feed. The simulated directivities are 50.68 dB and 49.01 dB, respectively, and the beam separation is 0.49° 105 5.14 Beam squint in a single offset parabolic reflector antenna with an on- focus circularly polarized feed. The tilt angle of the feed is 9Q. The observer is looking in the direction of wave propagation 107 5.15 Beam squint in a single offset parabolic reflector antenna with an off- focus circularly polarized feed. The tilt angle of the feed is 9Q. The observer is looking in the direction of wave propagation 107 5.16 A feed displacement along the yj axis can effectively correct the linear phase shift across the reflector aperture 112 xv

5.17 Geometry of a 1.68-m single offset parabolic reflector antenna. The tilt angle of the RCP feed is 43.18° 116 5.18 (a) Simulated far-field pattern of the 1.68-m offset parabolic reflector antenna operating at 8.45 GHz. The pattern is cut through its bore- sight, (b) A close-up view. The simulated squint angle 9s = 0.0604°. . 117 5.19 Plots of the x-component of the simulated near-field in a 2x2 m aperture plane: (a) normalized amplitude in dB scale, (b) phase in degrees, and (c) a line cut of phase through x = 0. The dashed line represents the projected aperture boundary 118 5.20 Plots of the y-component of the simulated near-field in a 2x2 m aperture plane: (a) normalized amplitude in dB scale, (b) phase in degrees, and (c) a line cut of phase through x = 0. The dashed line represents the projected aperture boundary 119 5.21 (a) Simulated far-field pattern of the 1.68-m reflector antenna compen sated by the feed displacement of -2.34 mm. The pattern is cut through its boresight. (b) A close-up view. No squint angle is observed 120 5.22 Line cuts of the simulated phase distribution in the 2x2 m aperture plane after the feed displacement compensation: (a) x-component and (b) y-component 120 5.23 Geometry of an offset Cassegrain reflector antenna 121 5.24 (a) Simulated far-field pattern of the suboptimal offset Cassegrain re flector antenna. The pattern is cut through its boresight. (b) A close-up view. The simulated squint angle 8s = —0.0053° 122 xvi

5.25 (a) Simulated far-field pattern of the suboptimal offset Cassegrain re flector antenna compensated by the feed displacement of —0.0287 A. The pattern is cut through its boresight. (b) A close-up view. No squint angle is observed 122 5.26 Geometry of an axially symmetric Cassegrain reflector antenna. Only half of the Cassegrain reflector is plotted. The feed is displaced by 10 A in the 0 = 0° plane 124 5.27 (a) Far-field pattern of the axially symmetric Cassegrain reflector an tenna with a laterally displaced feed. The pattern is cut through the beam maximum in the * = 0° cut {9 = -0.7918°), which is 61.934 dB. (b) A close-up view. No squint angle is observed 125 5.29 (a) Far-field pattern of the axially symmetric Cassegrain reflector an tenna with an off-focus feed compensated by feed displacement. The optimal feed displacement is —0.00676 A. The pattern is cut through the beam maximum in the 4> = 0° cut {0 = —0.7918°), which is 62.331 dB. (b) A close-up view. No squint angle is observed 126 5.30 Geometry of a 35.5-m spherical reflector antenna. O denotes the center of the sphere, and F denotes its paraxial focal region. The effective illuminated aperture is 28 m in diameter 130 xvii *

*5.31 Uncompensated far-field pattern of the 35.5-m spherical reflector an tenna. The simulated directivity is 66.15 dB. In contrast, a parabolic reflector antenna with the same 28-m effective aperture would produce a nice pencil-beam with directivity of 79.48 dB and half-power beamwidth of 0.02° 130 5.32 Far-field patterns of the 28-m parabolic reflector antenna for no scan and 4° scan cases. The directivities are 79.48 dB and 67.92 dB, respec tively. A huge scan loss of 11.56 dB is-observed 131 5.33 (a) Ray tracing of a bundle of parallel rays incident on the 35.5-m spherical reflector within the 28-m effective aperture, (b) The location and geometrical configuration of the compensation sub-refiectarray. . . 132 5.34 Extracted phase information using the Sidelobe Control CFM method. Note that the path delay from the primary feed to each sub-refiectarray element is included 134 5.35 A 4° (200 beamwidths) scanned beam is achieved by rotating the feed system, including the primary feed and the compensating sub-refiectarray, about the center of curvature of the spherical reflector by 4° 134 5.36 Compensated far-field patterns using the 0.3-m compensating sub-refiectarray. The simulated directivities are 78.81 dB for no scan case, and 78.59 dB for 4° (200 beamwidths) scan case. The near-in sidelobe levels are -19.71 dB and -17.85 dB, respectively 135 5.37 PO currents on the spherical reflector for (a) no scan case and (b) 4° scan case. The 28-m effective illuminated aperture is shifted toward the edge to achieve the scanned beam 136 xvm *

*5.38 Geometry of a 1.5-m breadboard spherical reflector antenna. O denotes the center of the sphere, and F denotes its paraxial focal region. The effective illuminated aperture is 1.3 m in diameter 137 5.39 Uncompensated far-field pattern of the 1.5-m spherical reflector an tenna. The simulated directivity is 42.98 dB. A parabolic reflector an tenna with 1.3-m effective aperture would produce a nice-pencil beam with directivity of 52.83 dB 137 5.40 (a) Ray tracing of a bundle of parallel rays incident on the 1.5-m spher ical reflector within the 1.3-m effective aperture, (b) The location and geometrical configuration of the compensating sub-reflectarray 138 5.41 Compensated far-field patterns using the 0.1-m compensating sub-reflectarray. The simulated directivities are 52.93 dB for no scan case, and 52.63 dB for 4° (10 beamwidths) scan case. The near-in sidelobe levels are -20.91 dB and -19.72 dB, respectively 139 A.l Positions visited by one of the particles in different solution spaces: (a) x,y € [—10,10] and (b) x,y 6 [—1,19]. The white square shows the boundary of the solution space 148 A.2 Summary of various boundary conditions in PSO 149 A.3 Six different boundary conditions for a 2-dimensional problem. P' and v1 represent the modified position and velocity, respectively, after the errant particle is treated by boundary conditions 150 A.4 Plots of 2-dimensional (a) Rosenbrock and (b) Rastigrin functions. White squares show different solution spaces investigated in different types of problem sets, and the five-pointed star indicates the position of the global minimum 153 xix *

*A.5 The average gbest values of 50 simulations versus (a) the number of iterations and (b) the number of evaluations for Type I 30-dimensional Rastigrin function 154 A.6 The average gbest values of 50 simulations versus the number of evalu ations for Type I problem set. (a) 3-D Rosenbrock function, (b) 30-D Rosenbrock function, (c) 3-D Rastigrin function, (d) 30-D Rastigrin function 155 A.7 The average gbest values of 50 simulations versus the number of evalu ations for Type II problem set. (a) 3-D Rosenbrock function, (b) 30-D Rosenbrock function, (c) 3-D Rastigrin function, (d) 30-D Rastigrin function 156 A.8 The average gbest values of 50 simulations versus the number of evalu ations for Type III problem set. (a) 3-D Rosenbrock function, (b) 30-D Rosenbrock function, (c) 3-D Rastigrin function, (d) 30-D Rastigrin function 157 A.9 Optimization of a 2-dimensional 16-element array antenna for remote sensing. The average gbest value of 5 simulations versus (a) the number of iterations and (b) the number of evaluations 159 xx *

*LI ST OF TABLES 3.1 Requirements for the far-field pat t ern of a 5x5 array ant enna 29 3.2 Expansion coefficients of the modified Jacobi polynomials for reflector surfaces with elliptical (circular) boundaries 37 3.3 Closed-form expressions of the expansion coefficients of the modified Ja cobi polynomials for offset parabolic reflectors with elliptical (circular) boundaries. All other terms are zero 38 3.4 Directivity of a shaped multi-beam reflector ant enna for simultaneous DBS reception from three satellites 39 4.1 Geometrical configuration of t he 25-m Gregorian reflector antenna for ARISE project. The operating frequency is 22 GHz 57 4.2 Expansion coefficients of the modified Jacobi polynomials for the ellip soidal subreflector surface with elliptical boundary 60 5.1 Simulation and measurement results of the single conical corrugated horn. 100 5.2 Simulation and measurement results of the integrated twin-horn feed. . 103 5.3 Simulation results of the 3.5-m reflector antenna 106 5.4 Beam squint compensation for reflector antennas with circularly polar ized feeds I l l xxi *

*ACKNOWLEDGMENTS I would like to express my sincere gratitude to my advisor, Professor Yahya Rahmat-Samii, for his invaluable support, encouragement, and guidance through out this research and my graduate studies at UCLA. I would also like to thank Professors Nathaniel Grossman, Tatsuo Itoh, and Yuanxun Ethan Wang for serv ing on my doctoral committee and reviewing this manuscript. I would like to thank my colleagues in the UCLA ARAM Laboratory for their constructive advices when helping me with the technical details. I would also like to thank Dr. Imbriale of Jet Propulsion Laboratory for the fruitful discussions on Chapter 4.4. Lastly, my special thanks to my wife, my parents, and my family. Without their unwavering support and encouragement through all of my pursuits over the years, this work would have never been accomplished. xxn *

*VITA Sept. 27, 1978 Born in Suzhou, Jiangsu, China 2001 B.S. in Electrical Engineering Southeast University Nanjing, Jiangsu, China 2001 - 2004 Research Assistant State Key Laboratory of Millimeter Waves Southeast University Nanjing, Jiangsu, China 2004 M.S. in Electrical Engineering Southeast University Nanjing, Jiangsu, China 2004 - 2009 Graduate Student Researcher Electrical Engineering Department University of California, Los Angeles Los Angeles, California, USA 2006 - 2008 Teaching Assistant Electrical Engineering Department University of California, Los Angeles Los Angeles, California, USA xxni *

*PUBLICATIONS AND PRESENTATIONS W. Dou and S. Xu, "Numerical analysis of waveguide discontinuity based on the weak forms of the Helmholtz equations," Journal of Electromagnetic Waves and Applications, no. 10, pp. 1295-1303, 2004. W. A. Imbriale, Y. Rahrnat-Samii, H. Rajagopalan, S. Xu, and V. Jamnejad, "Microelectromechanical Systems (MEMS) actuated wave front correcting sub- reflector: distortion compensation for large reflector antennas," in 8th Annual NASA Earth Science Technology Conference (ESTC2008), June 2008. Y. Rahmat-Samii, N. Jin, and S. Xu, "Particle swarm optimization (PSO) in electromagnetics: let the bees design your antennas," in 22nd Annual Review of Progress in Applied Computational Electromagnetics, March 2006, pp. 1-9. S. Xu and Y. Rahmat-Samii, "Multi-objective particle swarm optimization for high performance array and reflector antennas," in Proceedings of 2006 IEEE An tennas and Propagation Society International Symposium, July 2006, pp. 3293- 3296. S. Xu and Y. Rahmat-Samii, "Various boundary conditions in particle swarm op timization: a comparative study," in 2006 USNC/URSI National Radio Science Meeting, July 2006. S. Xu, Y. Rahmat-Samii, and D. Gies, "Shaped-reflector antenna designs using particle swarm optimization: an example of a direct-broadcast satellite antenna," xxiv *

*Microwave and Optical Technology Letters, vol. 48, no. 7, pp. 1341-1347, July 2006. S. Xu and Y. Rahmat-Samii, "Boundary conditions in particle swarm optimiza tion revisited," IEEE Transactions on Antennas and Propagation, vol. 55, no. 3, pp. 760-765, March 2007. S. Xu, H. Rajagopalan, Y. Rahmat-Samii, and W. A. Imbriale, "A novel reflector surface distortion compensating technique using a sub-reflectarray," in Proceed ings of 2007 IEEE Antennas and Propagation Society International Symposium, June 2007, pp. 5315-5318. S. Xu and Y. Rahmat-Samii, "Sub-reflectarrays for main reflector surface distor tion compensations," in 2007 USNC/URSI National Radio Science Meeting, July 2007. S. Xu and Y. Rahmat-Samii, "Sub-reflectarrays for spherical aberration compen sation: concept and simulations," in Proceedings of 2008 IEEE Antennas and Propagation Society International Symposium, July 2008, pp. 1-4. S. Xu and Y. Rahmat-Samii, "A compensated spherical reflector antenna using sub-reflectarrays," Microwave and Optical Technology Letters, vol. 51, no. 2, pp. 577-582, February 2009. S. Xu, Y. Rahmat-Samii, and W. A. Imbriale, "Subreflectarrays for reflector sur face distortion compensation," IEEE Transactions on Antennas and Propagation, xxv *

*vol. 57, no. 2, pp. 364-372, February 2009. S. Xu, S. F. Razavi, and Y. Rahmat-Samii, "A transmit/receive twin-horn feed for spinning remote sensing reflector antennas," Microwave and Optical Technology Letters, to be published. S. Xu and Y. Rahmat-Samii, "A novel beam squint compensation technique for circularly polarized conic-section reflector antennas," IEEE Transactions on Antennas and Propagation, to be published. xxvi *

*ABSTRACT OF THE DISSERTATION Optimization and Compensation Techniques for Modern Reflector Antenna Designs by Shenheng Xu Doctor of Philosophy in Electrical Engineering University of California, Los Angeles, 2009 Professor Yahya Rahmat-Samii, Chair Advanced reflector antenna applications demand more sophisticated design tech niques to meet the ever-increasingly stringent requirements on antenna perfor mances. With the access to previously unimaginable computational resources, the particle swarm optimization (PSO), a global stochastic evolutionary algo rithm, provides a new methodology for the diffraction synthesis techniques for reflector antenna designs, where the optimization kernel is crucial to effectively and efficiently explore the complicated antenna parameters for an optimal solu tion. In this dissertation, PSO is successfully applied to array feed optimizations and shaped reflector designs. In particular, the reflector surface distortion com pensation is extensively investigated. Empowered by the PSO engine, array feed and shaped subreflector compensation techniques are revisited. A novel sub- reflectarray compensation technique is proposed, which presents some remark able advantages compared with other approaches. Three other compensation techniques for reflector antenna designs, an integrated twin-horn feed for azimuth displacement compensation, beam squint compensation, and sub-refiectarrays for spherical aberration compensation, are discussed as well. xxvii *

*CHAPTER 1 Introduction 1.1 Background A reflector antenna consists of one or more reflecting surfaces and a feed system. Typically equipped with a large antenna aperture in terms of wavelength, this type of antenna can provide several favorable features, such as high directivity, high radiation efficiency, low sidelobe levels, and has been widely used in radar systems, satellite communications, deep-space telemetry, and radio astronomy [1], [2], [3]. In recent years, advanced spaceborne applications have imposed more strin gent requirements on reflector antennas. For instance, high beam efficiency is required to achieve the necessary contrast for the scene brightness variation in radiometry applications [3]; while in multi-beam or contoured-beam antenna de signs, the radiation energy needs to spread out to better fit the shape of the desired coverage region [4], [5], [6]. Moreover, to meet the great challenge of ever-increasing reflector size and limited space and weight in spaceborne applica tions, deployable reflector antennas such as mesh reflector antennas [7], [8] and inflatable membrane antennas [9], [10] have been proposed due to their inherent advantages of being lightweight, small in size before deployment, and acceptable production cost. Reflector surface distortions are [11], [12], however, inevitable due to the thermal effects in the outer space environment, and become more 1 *

*prominent because of the ever-increasing operating frequencies and the intrin sic nature of the delicate materials and manufacturing technologies utilized in these applications. Therefore, the compensation of reflector surface distortions is necessary to overcome the resultant performance degradation [13], [6], [14]. In order to produce the required radiation characteristics, one may employ an array feed to illuminate a parabolic reflector [13], [15]. By controlling the amplitude, phase, or both, of individual array element [16], [17], [18], [19], [20], [21], various array designs have been obtained for a variety of purposes. The optimization of the array excitation is, in nature, nonlinear and highly multi modal. Different optimization techniques have been extensively studied in lit erature. Gradient-based methods, such as the steepest ascent method [16], the Simplex method [17], and the BFGS quasi-Newton algorithm [18], work well for a small number of parameters, but require the computation of derivatives, and tend to be trapped in local optima. Evolutionary algorithms, such as simulated an nealing [19] and genetic algorithms (GA's) [18], [20], [22], are capable of searching for the global optimum in a stochastic way, but the iterative calculations require more computational time. On the contrary, one may want to keep the feed system as simple as possible, in extreme scenario, a single feed, but utilize a shaped reflector, a shaped subre- flector, or both, to achieve a desired radiation pattern. Geometrical optics (GO) based techniques [23], [24] are originally used to achieve arbitrary amplitude and phase distribution at the aperture plane. However, the computed pattern of a GO-synthesized reflector antenna may significantly deviate from the ultimately desired pattern since no diffraction effects are included in computation[6], [25]. To overcome the limitation of GO synthesis, diffraction synthesis techniques are proposed based on the concept of reflector surface expansion and coefficient op- 2 *

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Abstract:
Advanced reflector antenna applications demand more sophisticated design techniques to meet the ever-increasingly stringent requirements on antenna performances. With the access to previously unimaginable computational resources, the particle swarm optimization (PSO), a global stochastic evolutionary algorithm, provides a new methodology for the diffraction synthesis techniques for reflector antenna designs, where the optimization kernel is crucial to effectively and efficiently explore the complicated antenna parameters for an optimal solution. In this dissertation, PSO is successfully applied to array feed optimizations and shaped reflector designs. In particular, the reflector surface distortion compensation is extensively investigated. Empowered by the PSO engine, array feed and shaped sub-reflector compensation techniques are revisited. A novel sub-reflectarray compensation technique is proposed, which presents some remarkable advantages compared with other approaches. Three other compensation techniques for reflector antenna designs. an integrated twin-horn feed for azimuth displacement compensation, beam squint compensation, and sub-reflectarrays for spherical aberration compensation, are discussed as well.
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