Synthesis of Large Ultra-Wideband Rotationally Symmetric Sparse Circular Arrays

Abstract

The paper introduces an effective method for synthesising large wideband rotationally symmetric sparse circular arrays. Initially, the approach involves incorporating several concentric auxiliary rings within the circular aperture comprised of rotationally symmetrical folds. The array elements are then distributed solely over these rings, thereby avoiding ineffective optimisation within each fold. Furthermore, an initial spacing is established and extended along the concentric rings to quickly establish the initial distribution of the uniform array. Subsequently, the optimisation process involves refining the element positions and numbers by imposing various constraints on factors such as the spacing increment between adjacent rings, the polar angle between adjacent elements on each ring, and the initial polar angle among adjacent elements, which significantly enhances optimisation efficiency. By utilising the peak sidelobe level in wide-angle scanning as the fitness function, the synthesis problem is transformed into an optimisation conundrum, which is addressed using the covariance matrix adaptation evolutionary strategy (CMA-ES). Finally, a series of numerical examples is presented to demonstrate the effectiveness and benefits of the proposed synthesis method.