Sum and difference beam-pattern synthesis with side lobe control

This paper considers the synthesis of sum and difference beam patterns for a planar array of antenna elements to be used as a tracking antenna. The patterns are synthesized using an optimization such that the directivity of the sum pattern is maximized subject to prescribed sum and difference pattern side-lobe levels. A significant result is that the sum and difference patterns are synthesized with the same set of complex weights. Beam pattern results are presented for a given prescribed side-lobe level with and without beam scanning. In addition, it is of interest to maximize the slope of the difference pattern at boresight since the slope is directly related to tracking accuracy. Accordingly, various difference patterns are presented and the maximum slope determined. The parameters considered include side-lobe level, scan angle, directivity, and difference pattern slope