For the requirements of upper sidelobes suppression and lower null-fills of the base-station antennas' shaped beam,a fast iterative method for the synthesis of a pattern with specified levels of upper sidelobes and lower nulls is studied.Brent's method is used to iterate the extrema's positions with the specified levels of sidelobes and nulls of the power pattern's expression,the factorized expression of the pattern can be obtained according to final positions of zeros,and the coefficient of each term is th...