Abstract
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.
Highlights
As an important field of array signal processing, direction of arrival (DOA) estimation has been applied in a wide range of applications such as wireless communications, sonar, radar, and acoustic localization [1,2,3]
Considering that the virtual arrays extend the dimension of the equivalent covariance matrix, which need a lot of calculations, the unitary transformation is performed on equivalent covariance matrix to reduce the computational complexity of the proposed algorithm
Two criteria for assessing the performance of the DOA estimation algorithm are the probability of resolution and the root mean square error (RMSE)
Summary
As an important field of array signal processing, direction of arrival (DOA) estimation has been applied in a wide range of applications such as wireless communications, sonar, radar, and acoustic localization [1,2,3]. Considering the properties of several CCMs with the same signal subspace, a subspace-based algorithm without singular value decomposition (SVD) or EVD has been proposed to obtain the azimuth and elevation angles [26]. [28] has presented a 2-D DOA estimation algorithm for closely spaced sources, which performs SVD on two matrices constructed by CCMs to estimate the azimuth and elevation angles. [39] has proposed an algorithm for L-shaped nested arrays, which constructs several CCMs with different time lags and performs a signal subspace joint diagonalization technique (SSJD) to estimate the azimuth and elevation angles simultaneously. We propose an improved algorithm for L-shaped nested arrays in order to estimate the azimuth and elevation angles with a small number of snapshots. The notation N denotes an N × N exchange matrix with ones on its anti-diagonal and zeros elsewhere
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