A beam shaping algorithm based on inner-product operation for array-fed reflector satellite shaped-beam antennas

Since for array-fed reflector satellite shaped-beam antennas,traditional beam-shaping algorithms obtain their results simply by approximating the shaped beams to a limited number of samples in the desired patterns at the corresponding directions, which requires antenna designers to adjust the numbers and positions of those selected samples repeatedly before achieving satisfactory patterns and are always difficult to use in practice. Thus, this paper presents a new beam shaping algorithm based on inner-product operation, which instead minimizes the total error of the shaped beam from the desired pattern at almost all directions and therefore overcomes the limitation of those traditional methods. Moreover, the presented algorithm is also an analytical approach to achieve accurate results efficiently.