Optimal Synthesis of Robust Beamformer Weights Exploiting Interval Analysis and Convex Optimization

• Published in: IEEE transactions on antennas and propagation Vol. 62; no. 7; pp. 3603 - 3612
• Main Authors: Rocca, Paolo, Anselmi, Nicola, Massa, Andrea
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Amplitude error tolerance; Amplitudes; antenna array design; Antenna arrays; Antenna radiation patterns; Antennas; Applied sciences; Arrays; convex programming; Deviation; Electromagnetism; Engineering Sciences; Exact sciences and technology; Indexes; interval analysis; interval arithmetic; Intervals; linear arrays; Mutual coupling; Optimization; Programming; Radiocommunications; Robustness; Sidelobes; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Tolerances; Transmission and modulation (techniques and equipments); Performance evaluation; Lateral lobe; linear arrays; Convex programming; antenna array design; Interval arithmetic; Beam forming; Optimal design; Fault tolerance; interval analysis; Signal processing; Numerical simulation; Linear antenna arrays; Radiated power; Antenna array; Amplitude error tolerance; Amplitude error tolera nce; convex programming; interval arithmetic; interval analys is
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2014.2318071

An approach for the optimal design of linear arrays in the presence of tolerances on the amplitude weights is presented. Starting from the knowledge of the maximum deviations from the nominal values of the amplitude coefficients of the beam-forming network (BFN), an analytical tool based on interval analysis (IA) and integrating a convex programming (CP) method is exploited to maximize the minimum peak value of the main beam of the radiated power pattern along the boresight direction, while fitting an arbitrary user-defined bound on the secondary lobes in a globally optimal fashion. In order to analyze the behavior of the proposed approach also assessing its effectiveness, a set of representative numerical examples regarding arrays of ideal and realistic radiating elements is reported where different sidelobe constraints, array configurations, and tolerance errors are considered.