A Convex Optimization-based Approach for Sidelobe Level Suppression and Null Control in Antenna Arrays by Displacing a Minimum Number of Elements

This paper introduces two methods for peak sidelobe level (PSLL) reduction and null steering in the pattern of linear arrays using position control. While most research on this topic uses stochastic optimization techniques, here convex optimization and the off-grid compressive sensing framework were used to accomplish the required goals. For the first method, the problem of minimizing the PSLL and forming prescribed nulls in the pattern of linear arrays by controlling the elements' positions is cast as a convex optimization problem with the help of first-order Taylor approximation. For the second method, the goals are achieved by perturbing the locations of as few array elements as possible. Towards this end, the problem of forming prescribed nulls in the pattern of non-uniformly spaced linear arrays for a predefined PSLL by elements' position control is formulated as a sparse recovery problem within the off-grid compressive sensing framework. Simulations were performed to evaluate the efficacy of the proposed methods, and the results were compared to results obtained using stochastic optimization techniques.