Application of constrained optimization techniques to array pattern synthesis

Abstract

The paper presents two design methods for synthesizing antenna array patterns with an adjustable mainlobe width and minimum average sidelobe level. One method involves matching the array response to a desired response over the mainlobe width while minimizing the mean-square value of the array response over the sidelobe regions. The other method involves minimizing the mean-square error between a desired response and the response of the antenna array over a certain mainbeam width subject to a mean-square sidelobe constraint. Numerical techniques based on matrix factorization are proposed to reduce the computational complexity. Subsequently, a set of linear constraints are used to approximate the effect of the quadratic constraint. Numerical results show that the proposed techniques are very effective in the design of antenna pattern having an adjustable mainlobe width and minimum average sidelobe level.