Preliminary shaped beam synthesis using the product function

A method of aiding the solution of shaped beam synthesis is proposed. A product of functions is created by choosing zero loci that are appropriate to the desired power pattern. The convergence results indicate that for shaped beam synthesis, the optimized product function may be a better starting point. The fact that the IFT (inverse Fourier transform) and the uniform array as initial iterates of a nonlinear optimization do not converge in the examples presented indicates the following hypothesis: the initial guess of an iterative method is best chosen if the constraints on the first guess and on the desired final solution are the same. For example, the IFT minimizes the mean squared error (MMSE); however, the desired solution is not related to an MMSE criterion and, therefore, does not converge as quickly as a more suitably chosen starting point