Joint 2-D DOA Estimation via Sparse L-shaped Array

In this paper, we address the problem of estimating the two-dimensional (2-D) directions of arrival (DOA) of multiple signals, by means of a sparse L-shaped array. The array consists of one uniform linear array (ULA) and one sparse linear array (SLA). The shift-invariance property of the ULA is used to estimate the elevation angles with low computational burden. The signal subspace is constructed by the cross-covariance matrix (CCM) of the received data without implementing eigendecomposition. The source waveforms are then obtained by the estimated elevation angles, which together with each sensor of the SLA, considered as a linear regression model, is used to estimate the azimuth angle by the modified total least squares (MTLS) technique. Our new algorithm yields correct parameter pairs without requiring the computationally expensive pairing operation, and therefore, has at least two advantages over the previous L-shaped array based algorithms: less computational load and better performance due to the use of SLA and CCM. Expressions for the asymptotic mean-squared error (MSE) of the 2-D DOA estimates are derived. Simulation results show that our method provides accurate and consistent 2-D DOA estimation results that could not be obtained by the existing methods with comparable computational complexity.