Efficient Circular Flat-Top Pattern Synthesis With Circular Planar Array via Dimensionality Reduction

A novel method is presented to efficiently synthesize circular flat-top patterns with circular planar arrays, employing dimensionality reduction techniques. Considering the symmetry of the circular planar array geometry, we define the distance from each element to the array geometric center as the independent variable, then expand the excitation distribution using the even-order polynomials of a single Chebyshev polynomials. With the help of such polynomial expansion, we can synthesize pattern by solving polynomial coefficients instead of directly solving array excitation distribution, significantly reducing the number of optimization variables by over 98% compared with the number of array elements, which effectively converts a high-dimensional problem into a more manageable low-dimensional one. Two synthesis examples involving circular planar arrays with equispaced and nonequispaced elements are conducted to validate the effectiveness and advantages of our proposed method.