An improved two-dimensional direction-of-arrival estimation algorithm for l-shaped nested arrays with small sample sizes

In this paper, an improved two-dimensional (2-D) direction of arrival (DOA) estimation algorithm for L-shaped nested arrays is proposed. Unlike the approach for a classical nested array, which use the auto-correlation matrix (ACM) to increase the degrees of freedom (DOF), we utilize the cross-correlation matrix (CCM) of different sub-arrays to generate two long consecutive virtual arrays. These acquire a large number of DOF without redundant elements and eliminate noise effects. Furthermore, we reconstruct the CCM based on the singular value decomposition (SVD) operation in order to reduce the perturbation of noise for small numbers of samples. To cope with the matrix rank deficiency of the virtual arrays, we construct the full rank equivalent covariance matrices by using the output and its conjugate vector of virtual arrays. The unitary estimation of signal parameters via rotational invariance technique (ESPRIT) is then performed on the covariance matrices to obtain the DOA of incident signals with low computational complexity. Finally, angle pairing is achieved by deriving the equivalent signal vector of the virtual arrays using the estimated angles. Numerical simulation results show that the proposed algorithm not only provides more accurate 2-D DOA estimation performance with low complexity, but also achieves angle estimation for small numbers of samples compared to existing similar methods.