A Tensor-Based Approach to L-Shaped Arrays Processing With Enhanced Degrees of Freedom

A new tensor-based approach, which is capable of significantly increasing the degrees of freedom (DOF) of an L-shaped array consisting of two orthogonal uniform linear arrays (ULAs), is proposed. By dividing each ULA into some overlapping subarrays and then combining their received signals into a data tensor, a new cross-correlation tensor between the two data tensors from the two ULAs is built. Analyses show that such a cross-correlation tensor can be transformed into an equivalent received data matrix of a virtual uniform rectangular array (URA). Under the constraint of a fixed actual number of physical sensors, the optimal number of the subarrays is found by maximizing the DOF of the URA. It is shown that a virtual URA with approximately $0.34{{(M+1)}^{2}}$ DOF can be obtained from an L-shaped array with $2M$ physical sensors. To exploit the increased DOF for the two dimensional (2-D) DOA estimation without the multidimensional search, a parallel factor (PARAFAC) model of the URA is provided so that the PARAFAC decomposition can be utilized to do the 2-D DOA estimation effectively. Simulation results demonstrate that the proposed method can yield a better estimation performance and resolve more sources than some computationally efficient methods reported in literature.