Obtaining Feasible Minimum Side Lobe Level for Narrow Beam Width Using Convex Optimization in Linear, Planar, and Random Antenna Arrays

Abstract

In many applications, the radiating elements of the used antenna may be configured in the form of a one-dimensional linear array, or two-dimensional planar array or even random array. In such applications, a simple optimization algorithm is highly needed to optimally determine the excitation amplitudes and phases of the array elements to maximize the system’s performance. This paper uses a convex optimization instead of other complex global stochastic optimizations to synthesize a linear, planar, and random array patterns under pre-specified constraint conditions. These constraints could be either fixed beam width with the lowest possible sidelobe levels or fixed sidelobe level with narrower possible beam width. Two approaches for array pattern optimization have been considered. The first one deals with the problem of obtaining a feasible minimum sidelobe level for a given beam width, while the second one tries to obtain a feasible minimum beam width pattern for a given sidelobe level. Both optimization approaches were applied to the linear, planar, and random arrays. Simulation results verified the effectiveness of both optimization approaches and for all considered array configurations.