Underdetermined two-dimensional angles parameters estimation for incoherent distributed sources based on an L-shaped array

This paper proposes a localization algorithm based on an L-shaped array for estimating the two-dimensional (2-D) directions-of-arrival (DOAs) of incoherently distributed (ID) sources in the underdetermined case. To begin with, the generalized array manifold (GAM) model is established based on the first-order Taylor series approximation. The raw received data is split into frames that be processed through delay cross-correlation operation to construct the virtual received data. Then, the covariance matrix of the virtual data is calculated, followed by eigenvalue decomposition to obtain the signal and noise subspaces. The 2-D central DOAs estimation is achieved by two one-dimensional (1-D) spectral searching, exploiting the generalized shift-invariance property and the reduced-rank principle. Finally, the 2-D central DOAs are matched by finding the minimum value of an optimization function, utilizing the property that the noise and signal subspaces are orthogonal to each other. Simulation results demonstrate that the proposed algorithm achieves high accuracy in the central DOAs estimation without requiring any prior information about the angular distribution.