Design of mutually incoherent arrays for DoA estimation via group-sparse reconstruction

A design metric is presented for optimization of antenna positions of mutually incoherent array layouts. The proposed metric is based on a generalized matched-filter response that coincides with the atom-selection criterion of Block-Orthogonal Matching Pursuit. An effective ambiguity function is derived that results from a weighted average of the ambiguity functions associated to each coherent set of Tx and Rx elements. The design involves a tractable constrained optimization of such ambiguity function, over hypothetical DoAs to identify the combined sidelobes, and over antenna positions, for a given number of Tx and Rx elements, spatial constraints and desired field-of-view. Applications include the design of arrays in any dimensions thanks to the versatility of group-sparse reconstruction, including MIMO arrays and near- or far-field models for DoA estimation. Several scenarios of automotive radar are considered for the application of the technique. The resulting incoherent apertures exhibit sidelobe cancellation and similar or even better performance than larger individual arrays.