Weight Selection for Pattern Control of Paraboloidal Reflector Antennas with Reconfigurable Rim Scattering

It has been recently 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 the unit-magnitude weights (i.e., weights which modify the phase of the scattered signals) 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. First, the optimal weights without any magnitude constraints are found. Afterwards, algorithms are developed for determining the unit-modulus weights with both quantized and unquantized phases. Further, it is shown that weights can be obtained that both cancel sidelobes while providing a constant main lobe gain. 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.