Computational methods for antenna pattern synthesis

Some general numerical methods for antenna pattern synthesis, with and without constraints, are developed. Particular cases considered are 1) field pattern specified in amplitude and phase, 2) field pattern specified in amplitude only, and 3) these two cases with a constraint on the source norm. Both the source and the field are discretized at the beginning, and the methods of finite dimensional vector spaces are used for the computations. The theory is general, but is applied only to point sources arbitrarily distributed in a plane, and to pattern synthesis in this plane. Some numerical examples are given for ten sources approximately equispaced on one-half of an ellipse, with the desired field pattern chosen to be the csc pattern in the first quadrant.