Abstract: To overcome the grid mismatch issue and enhance the performance of beam patterns, a sparse reconfigurable linear array design method based on reweighted atomic norm minimization is proposed. This method formulates the sparse reconfigurable linear array design problem as multiple measurement vectors sparse optimization model. It solves for the element positions and element excitations of the sparse reconfigurable linear array by the reweighted atomic norm minimization. Unlike conventional compressed sensing-based methods, this approach leverages atomic norm theory to establish a gridless sparse optimization model that jointly optimizes the number, positions, and excitations of array elements. As a result, it can overcome the grid mismatch problem and enhance the matching accuracy of the array beam pattern. Simulation experiments demonstrate that compared to compressed sensing methods, the reweighted atomic norm minimization method can design sparse reconfigurable linear arrays with an order of magnitude higher beam matching accuracy.