A method on amplitude-weighted array technology is proposed based on an analytical formula in which the radiation amplitudes of array elements are evaluated analytically by a random symmetrical far-field radiation pattern. Using this formula, any desired spatial radiation pattern in the far field could be built by applying the analytical solutions of radiation amplitudes of array elements. To check the validity of this formula as well as the proposed technique, an annular intensity distribution as target far-field pattern is designed, and the respective radiation amplitude of array elements are determined by solving the formula analytically. The available far-field pattern is calculated by applying these solutions and then compared with the target far-field pattern. The theoretical results show the capabilities of the analytical derivation as well as the proposed technique in forming specific radiation patterns.