2-D direction finding using parallel nested arrays with full co-array aperture extension

Abstract Sparse arrays, such as nested arrays, are able to resolve more sources than sensors because their difference co-arrays can provide O ( L 2 ) degrees-of-freedom (DOFs) with L physical sensors. Most of the existing nested array direction-finding algorithms apply the spatial smoothing technique to realize this DOFs enhancement. One shortcoming of this type of methods is the efficient co-array aperture is reduced in processing the spatial smoothing, resulting in the DOFs are not fully utilized. In this paper, we propose a new approach using two parallel linear nested arrays to contribute full DOFs for two-dimensional direction-finding. To exploit the entire DOFs, we perform the vectorization of multiple fourth-order cumulant matrices and take the average of their co-array covariance matrices, instead of the spatial smoothing of the vectorization of the data covariance matrix. Based on a well-posed identification analysis, we show that the proposed approach can identify the number of sources approximately three times than the algorithms using the spatial smoothing technique. For example, for a two-level parallel nested array of 2 + 2 sensors in each subarray, the maximum number of sources that can be resolved by the proposed approach is 32, whereas, for most of the existing algorithms, the number reduces to 10.