Generalized Non-Redundant Sparse Array Designs

We present novel generalized non-redundant sparse array design strategies that achieve the highest possible number of degrees-of-freedom (DOFs) for direction-of-arrival (DOA) estimation. These array designs offer difference co-arrays that do not contain any lag redundancies except the unavoidable redundancies at lag zero. We first develop a co-array-based zero-redundancy design rule which serves as a baseline for constructing these non-redundant arrays, and a large-aperture naive structured non-redundant sparse array is presented. We then develop a systematized design framework based on disjunctive programming to obtain non-redundant sparse array structures with a minimum array aperture, resulting in minimum hole arrays. The disjunctive programming framework is then extended to an equivalent mixed-integer linear programming problem. As a result, given the same number of physical sensors, the design framework provides a difference co-array with the maximum number of correlation lags and resolves more sources than existing sparse array structures. The non-redundant sparse array design is further generalized in two new directions, respectively achieving an arbitrary array aperture and reducing mutual coupling effects. Among the several new sparse array designs obtained from such generalizations, the hybrid non-redundant sparse array design simultaneously achieves the highest number of DOFs, meets a desired array aperture requirement, and reduces mutual coupling effects. Structured matrix completion methods are employed to interpolate the missing lags in the resulting difference co-arrays, thereby enabling high-resolution gridless DOA estimation with improved performance. Simulation results demonstrate the superiority of the generalized non-redundant sparse array design strategies over existing sparse array structures