A Novel Nested Array Structure for DOA Based on CCM of Subarrays

Abstract

An innovative nested array structure that can notably increase the DOF and the linear arrays’ direction of arrival (DOA) estimated performance is proposed. For the conventional nested array, we vectorize the ACM’s output of the whole array and then remove the repeated rows to get a virtual array’s output. In contrast with classical nested arrays, the superiority of the new nested array is that it utilizes the combination of reverse ordering and conjugation of the inner uniform linear array (ULA) for one of the two subarrays and the sparse outer ULA for another to increase the array aperture. This means the outer sparse ULA’s sensor spacing is approximately the length of the entire inner ULA in the classical nested array structure. Yet, it is about twice the length in the new nested array structure. We generate one lengthy consecutive virtual uniform array excluding any redundant virtual sensors by vectorizing the two subarrays’ cross-correlation matrix (CCM), which is mentioned above. With the export signal of the virtual array and its conjugate form of it, an equivalent covariance matrix of full rank is constructed, which is called the Toeplitz matrix, to compensate for the rank lack of the virtual array’s ACM. For the sake of obtaining the DOA of input signals, the conventional DOA estimation method will be implemented on the ACM. The increase in outer sparse ULA’s sensor spacing ensures an increase in virtual array aperture in principle, which means it is capable of increasing the number of DOA estimations, which is called DOF, and optimizing the DOA estimated performance in contrast with the ULA and classical nested arrays. Results from trials certify the preponderance of the proposed structure in the aspect of DOF and the accuracy of DOA estimation.