Underdetermined direction‐of‐arrival estimation using super nested array

Abstract

Among various sparse-arrays, super nested array (SNA) is found to be more attractive because it can achieve large degrees-of-freedom (DOFs) and alleviate the mutual coupling. This article address the problem of direction-of-arrival (DOA) estimation under underdetermined conditions based on the SNA. To tackle the underdetermined method, vectorising covariance matrix to obtain the large virtual array is developed to enlarge the DOFs and avoid phase ambiguity. However, the rank of vectorised covariance matrix equals to one, which fail to yield DOAs estimates, when multiple signals applied to the array. In order to circumvent this issue, the article first exploits the selective matrix to transform the disorder virtual array to an ordered one and remove the redundant element of the virtual array. Then reconstruct covariance matrix to overcome the low-rank problem. Exploiting the structure of SNA, the authors’ proposed method can achieve more target than conventional methods and reduce the mutual coupling when the number of source is larger than the number of antennas. Simulation results demonstrate the effectiveness of the authors’ proposed method.