Two-Dimensional Minimum Sensor Array: A New Perspective to Array Design

In this article, we design/propose a new class of planar arrays sparsely located on a two-dimensional (2-D) lattice to achieve the highest degrees of freedom (DOF) for a given number of sensors. We formulate an optimization problem to search for a hole-free 2-D sparse array with the fewest possible sensors. We convert this problem into a nonlinear binary problem by changing the variables, then into a binary linear programming problem, and solve it efficiently by employing branch and bound programming. Our results show that this optimal array outperforms alternative state-of-the-art 2-D array geometries in terms of a target resolution and direction of arrival (DOA) estimation accuracy given the number of sensors. Moreover, the proposed array outperforms other geometries in terms of the resolution probability of close targets and in the presence of mutual coupling.