A multi-direction virtual array transformation algorithm for 2D DOA estimation

In this paper, a multi-direction virtual array transformation algorithm termed MVATA for two dimension (2D) direction of arrival (DOA) estimation is proposed. A kind of multi-direction rotation invariant virtual subarrays is firstly constructed. Secondly, by singular value decomposition (SVD) of the response matrix of the real array to signals from a sector, the interpolation matrices can be estimated and from which the real and virtual signal subspaces are further estimated. Thirdly, a rotational invariant factor matrix is derived from the real and virtual subspaces base on least squares. Subsequently, the azimuth and elevation can be solved through the rotational invariant factor matrix without spectral peak search. Theoretical calculation and time-consuming statistics show that the proposed MVATA has the advantage of computational complexity compared with the conventional interpolated methods. Moreover, the proposed MVATA can be applied to arbitrary structure array, and the estimated 2D angles can be paired automatically. Simulation results demonstrate the proposed MVATA possesses significantly accuracy improvement especially in low SNR and small snapshots.