An Improved Weight Selection Algorithm for Interference Mitigation in Paraboloidal Reflector Antennas with Reconfigurable Rim Scattering

With the explosion of proposed LEO satellite systems and constellation sizes, the potential benefits of spectrum sharing for satellite-based systems has increased tremendously. Our previous work has demonstrated that modifying the rim scattering of a paraboloidal reflector antenna using reconfigurable elements allows for interference cancellation [1], [2]. However, for dynamic spectrum sharing there is a need for algorithms with faster convergence and improved performance. Thus, in this work we develop improved algorithms for determining the weights of such a receiver system which could serve as the basis of a spectrum sharing approach. We begin this work by reviewing the unconstrained optimal weight values needed at each reconfigurable element for interference mitigation as well as the previously proposed approach for finding a unimodular solution. We then show that near-optimal unimodular weights can be found in closed form provided that the unconstrained optimal weight vector has an infinite norm that does not exceed unity. In such case, the near-optimal continuous phase unimodular weights can be determined with significantly lower complexity while still providing acceptable attenuation at the desired angles. Next, in order to find weights with discrete phase values (to simplify implementation), we transform the original problem using a penalty method and solve it by leveraging the Majorize-Minimization (MM) algorithm. It is shown that this algorithm converges significantly faster and provides deeper nulls than the previously proposed simulated annealing approach. Further, based on empirical results, we provide a simple criterion for the existence of unimodular weights which provide perfect nulls for all desired angles. Finally, we numerically demonstrate the convergence and gain values provided by the proposed algorithms are superior to previously proposed algorithms.