Search for Costas arrays via sparse representation

Costas arrays are mainly known as a certain type of optimized time-frequency coding pattern for sonar and radar. In order to fulfill the need for effective computational approaches to find Costas arrays, in this paper, we propose a sparse formulation of the Costas array search problem. The new sparse representation can pave the way for using an extensive number of methods offered by the sparse signal recovery literature. It is further shown that Costas arrays can be obtained using an equivalent quadratic program with linear constraints. A numerical approach is devised and used to illustrate the performance of the proposed formulations.