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

Abstract

Abstract-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 pointnulls, a common local-minima artifact, can be reliably detected early in the local optimization allowing for quick termination.

Acceleration of Gradient-Based Algorithms for Array Antenna Synthesis With Far-Field or Near-Field Constraints

“…Nevertheless, the generalized intersection approach, with improved convergence [13], also employs a gradient-based algorithm in one of its projectors [14], [15]. In addition, local search algorithms are sometimes used along with global search algorithms, obtaining the so-called hybrid algorithms, which perform local searches in certain regions to refine the results provided by the global search [16], [17].…”

Transmit and receive circular array pattern synthesis for radar applications

“…Unlike linear arrays, circular arrays can also be used to synthesize omnidirectional patterns in azimuth, allowing for ubiquitous-radar [8] operation. Heuristic approaches exist to generate sector and omnidirectional patterns, and we use these to initialize a phase-only patternsynthesis algorithm adapted from [9] to optimize the patterns, potentially including transmit nulling. These techniques will be illustrated through example designs on a 31 element array.…”