Least square method for optimum thinned antenna arrays

The objective in thinned array design is to synthesize an optimum beam pattern whose performance is comparable to that of the filled array while satisfying given design specifications. A variety of optimization methods may be used such as least squares, perturbation, and dynamic programming. In this paper, a weighted least square approach is proposed to find an optimum beam pattern in a Dolph-Chebyshev sense. The square of the error between a thinned array pattern and a desired pattern is minimized in such a way that some sections of the array visual range are emphasized more than other ones to find an optimum beam pattern. It is shown that an exponential weighting function is appropriate for achieving a uniform sidelobe. Also, it is found that the minimum mean square error does not necessarily yield an optimum beam pattern based on convergence characteristics.