An Efficient Method for Sparse Linear Array Sensor Placement to Achieve Maximum Degrees of Freedom

Compared to the uniform linear array (ULA), the sparse linear array (SLA) has many advantages such as a greater degrees of freedom (DOF), a higher resolution, and robustness against mutual coupling. The optimal placement of elements to achieve the maximum DOF in SLA has been an old problem in array signal processing. Finding the optimum placement is limited to an exhaustive computer search as yet. Therefore, some familiar SLAs (such as `nested' and `coprime' arrays) have been suggested to improve DOF although none of them necessarily can achieve the maximum DOF with a certain number of sensors. In this paper, first we have proposed a novel hole-free SLA that yields the minimum number of sensors (MSA) for the desired DOF. The optimization problem associated with such an array is a nonlinear binary optimization problem. Then, the problem is transformed into a binary linear programming (BLP) problem which could be solved exactly. Using the proposed method, a fast and efficient solution to the minimum redundancy array(MRA) is found. Finally, the simulation results show that the proposed array has a higher DOF compared to the other competitive methods for a given number of sensors, which is the maximum possible DOF. This can lead to a better target resolution and DOA estimation.