Optimization and Hole Interpolation of 2-D Sparse Arrays for Accurate Direction-of-Arrival Estimation

This paper presents a method to optimize 2-D sparse array configurations along with a technique to interpolate holes to accurately estimate the direction of arrival (DOA). Conventional 2-D sparse arrays are often defined using a closed-form representation and have the property that they can create hole-free difference co-arrays that can estimate DOAs of incident signals that outnumber the physical elements. However, this property restricts the array configuration to a limited structure and results in a significant mutual coupling effect between consecutive sensors. In this paper, we introduce an optimization-based method for designing 2-D sparse arrays that enhances flexibility of array configuration as well as DOA estimation accuracy. We also propose a method to interpolate holes in 2-D co-arrays by nuclear norm minimization (NNM) that permits holes and to extend array aperture to further enhance DOA estimation accuracy. The performance of the proposed optimum arrays is evaluated through numerical examples.