Minimax-maxmini algorithm: a new approach to optimization of the thinned antenna arrays

The motivation for the thinned arrays is to reduce the array cost and mutual coupling effects while achieving desired array specifications. The main concern in the design of thinned arrays is to find an optimal set of element spacings to meet array specifications assuming uniform current for practical convenience. Since the array factor of the thinned array is a nonlinear function of element spacing and there are an infinite number of combinations of element locations, the problem of optimizing the array pattern with respect to the element locations becomes nonlinear and complex. Thus, it is not easy to design the optimal pattern analytically. The pattern optimization is even more difficult when the array is scanned off the array normal. A novel method called the minimax-maxmini algorithm is proposed to achieve uniform sidelobe in the sense of a Dolph-Chebyshev array pattern. A class of efficient approaches to minimax-maxmini optimization of the thinned array pattern with respect to the sidelobe are presented. The minimax-maxmini optimization is solved iteratively by the revised simplex method in linear programming. In this approach, the level of the higher sidelobes is reduced by sacrificing the level of the lower sidelobes so that the overall sidelobe level is lowered with all the sidelobes equalized to almost the same level. It is shown that the proposed algorithm with adaptive goal programming performs better than the conventional minimax algorithm. The thinned arrays which are robust in terms of the sidelobe level within a certain scanning range are discussed. Computer simulation results are also presented.<>