A hybrid global-local optimization approach to phase-only array-pattern synthesis

Phased array magnitude/power-pattern synthesis is in general a nonconvex optimization problem which can exhibit a large number of local minima. This is often exacerbated by the addition of (nonconvex) magnitude constraints on the array weights. Practical large-scale design of such patterns requires both efficient local optimization to quickly identify candidate minima, and nonlocal (“global”) optimization to provide new starting points and evaluate the resulting minima to find a suitable, if not global, solution. Here we combine a very efficient constrained local formulation based on a weighted pattern-error metric with a parameterized heuristic method for generating initial array weights and a global method for searching over the parameter space. We additionally show that passband point-nulls, a common local-minima artifact, can be reliably detected early in the local optimization allowing for quick termination.