Open and Closed-Loop Weight Selection for Pattern Control of Paraboloidal Reflector Antennas with Reconfigurable Rim Scattering

It has been demonstrated that modifying the rim scattering of a paraboloidal reflector antenna through the use of reconfigurable elements along the rim facilitates sidelobe modification including cancelling sidelobes. In this work we investigate techniques for determining unit-modulus weights (i.e., weights which modify the phase of the scattered electric field) to accomplish sidelobe cancellation at arbitrary angles from the reflector axis. Specifically, it is shown that despite the large search space and the non-convexity of the cost function, weights can be found with reasonable complexity which provide significant cancellation capability. It is demonstrated that this can be done using open-loop (i.e., with pattern knowledge), closed-loop (without pattern knowledge), or hybrid (with inexact pattern knowledge) techniques. Initially, we examine the use of unconstrained weights. A primary finding is that sufficiently deep nulls are possible with essentially no change in the main lobe with practical (binary or quaternary) phase-only weights. The initial algorithms require a knowledge of the antenna pattern (what we term an ``open-loop'' approach). However, since perfect knowledge of the pattern is not typically available, we also develop closed-loop approaches which require no knowledge of the antenna pattern. It is found that these closed-loop approaches provide similar performance. We demonstrate the time-varying performance of closed-loop approaches by simulating an interfering source which moves across the field of view of the antenna. Finally, we leverage the advantages of both open-loop and closed-loop approaches in a hybrid technique that exploits inexact knowledge of the pattern by seeding a closed-loop optimization with an open-loop solution as its starting point.