Direction of Arrival (DOA) Estimation Using Kronecker Subspace

This paper proceeds directions of arrival (DOA) estimation by a linear array. These years, some algorithms, e.g. Khatri-Rao approach, Nested array, Dynamic array have been proposed for estimating more DOAs than sensors. These algorithms can merely estimate uncorrelated sources. For Khatri-Rao approach, this is due to the fact that Khatri-Rao product discard the non-diagonal entries of the correlation matrix in opposed to Kronecker product. In this article, an algorithm named as Direction of Arrival (DOA) Estimation using Kronecker Subspace is proposed to solve more correlated sources than sensors via some properties of vectorization operator and Kronecker product. The simulations in different scenarios are presented considering various numbers of frames and correlation values, here. These verify our mathematical analysis. Furthermore, Cramer-Rao bound (CRB) which is a crucial criterion to estimate, is under investigating for DOA problem. Although, CRB for DOA estimation has been proposed before, it is applicable only for fewer sources than sensors. In this paper, CRB for more sources than sensor is derived by extending the dimensions with using both real and imaginary parts of the parameters. This bound is compared to the error of the presented algorithm. The simulations show that the error of the presented algorithm is merely 7 dB far from the CRB.