Design of Nonredundant Sparse Planar Arrays With Reduced Mutual Coupling

Most existing sparse planar arrays cannot fully realize their potential in terms of the degrees-of-freedom (DOFs) due to redundancies in their co-array generation. Meanwhile, the small interelement spacing in conventional planar arrays may cause serious mutual coupling effects. In this article, a series of designs for nonredundant sparse planar arrays in different application scenarios are proposed. They can obtain the maximum possible DOFs under the constraints of area and the number of array elements. We first present the rule for nonredundancy design for planar arrays, which is the basic criterion for the following optimization problems. According to generalized disjunctive programming, we establish systematic solutions for array designs by two mixed-integer linear programming optimization approaches. Then, three classes of nonredundant planar arrays are designed to achieve minimum area, predetermined area, and reduced mutual coupling, respectively. In particular, the nonredundant planar arrays with reduced mutual coupling can be designed to both avoid small interelement spacing and obtain the minimum area, which makes them more robust to mutual coupling conditions. Simulation results are provided to demonstrate the superiority of the proposed planar array configurations for direction-of-arrival estimation.