Multi-frequency Array Beam-forming
Iakovlev S., Moran W., Evans RJ.
In this paper, we address the problem of optimal beam-forming for an antenna array generating beams at multiple frequencies simultaneously. The key challenge here is to perform automatic current allocation among antenna elements, which is a hard combinatorial problem. We formulate it mathematically and propose a fast algorithm that solves it using available optimisation tools. We also derive conditions under which the unconstrained beam-forming problem can be solved exactly. The conditions lead to several uncertainty principles for the antenna design. The developed algorithm is tested in numerical simulations and its performance is demonstrated.