  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.
