Synthesis of Difference Patterns for 3-D Conformal Beam-Scanning Arrays With Asymmetric Radiation Aperture

Due to the asymmetry of the elements’ position distribution and polarization direction, it is a challenge to synthesize difference patterns with large slope and symmetric main-lobe on 3-D conformal beam-scanning arrays with asymmetric radiation aperture. In this article, an approach to synthesize the optimal difference patterns for 3-D conformal arrays with asymmetric radiation aperture is proposed. To determine the limitation region of the main-lobe and sidelobe for a 3-D conformal array, an initial difference pattern is generated by the joint multidimensional vector clustering method. Then, an auxiliary phase function is introduced to convert the nonconvex constraint of the symmetry of the difference beam into a convex one. Finally, an iterative convex optimization is applied to obtain the optimal difference pattern. The optimization progress is finished by extracting the vector field patterns of a simulated antenna element. Two design examples employing hemispherical conformal array (HCA) and conical conformal array (CCA) with asymmetric radiation aperture are implemented to demonstrate the effectiveness of the proposed method. Difference patterns with −20 dB sidelobe level (SLL) and large slope are obtained in both numerical and simulated results of the two design examples.