Projection matrix method for shaped beam synthesis in phased arrays and reflectors

We present the projection matrix method for shaped beam synthesis in a general array of different size elements. The method relies on orthogonal projection of the desired far-field intensity vector onto the space spanned by the far-field intensity vectors of the array elements. It is found that for a uniform convergence of the solution, the far-field sample space must be extended beyond the coverage region; otherwise the projection matrix becomes ill conditioned. A general guideline for the far-field sample space is provided. The method, with necessary amendments, is then employed successfully for a reflector surface synthesis. The method is found to be several times faster than the gradient search method commonly used for beam synthesis. Numerical results for array and shaped reflector syntheses are shown and the advantages discussed.