Estimation of DOA for Noncircular Signals via Vandermonde Constrained Parallel Factor Analysis

Abstract

We provide a complete study on the direction-of-arrival (DOA) estimation of noncircular (NC) signals for uniform linear array (ULA) via Vandermonde constrained parallel factor (PARAFAC) analysis. By exploiting the noncircular property of the signals, we first construct an extended matrix which contains two times sampling number of the received signal. Then, taking the Vandermonde structure of the array manifold matrix into account, the extended matrix can be turned into a tensor model which admits the Vandermonde constrained PARAFAC decomposition. Based on this tensor model, an efficient linear algebra algorithm is applied to obtain the DOA estimation via utilizing the rotational invariance between two submatrices. Compared with some existing algorithms, the proposed method has a better DOA estimation performance. Meanwhile, the proposed method consistently has a higher estimation accuracy and a much lower computational complexity than the trilinear alternating least square- (TALS-) based PARAFAC algorithm. Finally, numerical examples are conducted to demonstrate the effectiveness of the proposed approach in terms of estimation accuracy and computational complexity.