Beampattern Synthesis for Linear and Planar Arrays With Antenna Selection by Convex Optimization

• Published in: IEEE transactions on antennas and propagation Vol. 58; no. 12; pp. 3923 - 3930
• Main Authors: Nai, Siew Eng, Ser, Wee, Yu, Zhu Liang, Chen, Huawei
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Antennas; Applied sciences; Array signal processing; Arrays; Beamforming; Conjugates; Convex analysis; Directive antennas; Exact sciences and technology; Linear antenna arrays; linear arrays; Mutual coupling; Optimization; planar arrays; Radiocommunications; Ripples; Robustness; Specifications; Studies; Synthesis; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Lateral lobe; Lower bound; Mutual coupling; Sparse array; Array signal processing; Iterative method; Specification; linear arrays; Planar antenna arrays; Convex programming; Non uniform distribution; Beam forming; Directive antenna; Simulation; directive antennas; Weight function; planar arrays; Robustness; Objective function; Plane antenna; Linear antenna arrays; Antenna array
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2010.2078446

A convex optimization based beampattern synthesis method with antenna selection is proposed for linear and planar arrays. Conjugate symmetric beamforming weights are used so that the upper and non-convex lower bound constraints on the beampattern can be convex. Thus, a mainlobe of an arbitrary beamwidth and response ripple can be obtained. This method can achieve completely arbitrary sidelobe levels. By minimizing a re-weighted objective function based on the magnitudes of the elements in the beamforming weight vector iteratively, the proposed method selects certain antennas in an array to satisfy the prescribed beampattern specifications precisely. Interestingly, a sparse array with fewer antennas (compared to other methods) is produced. This method can design non-uniformly spaced arrays with inter-element spacings larger than one half-wavelength, without the appearance of grating lobes in the resulting beampattern. Simulations are shown using arrays of up to a few hundred antennas to illustrate the practicality of the proposed method.