Noncircular DOA estimation algorithm via propagator method and euler transformation

We mainly consider the direction of arrival (DOA) estimation of noncircular (NC) signal for uniform linear array in this paper. A computationally efficient noncircular real-valued DOA Estimation algorithm based on Euler transformation and propagator method (NC-Euler-PM) is proposed. The proposed algorithm, which avoids spectral peak searching process and eigenvalue decomposition, can achieve closed-form solution of DOAs by utilizing the rotational invariance (RI) property. In this work, the key idea is to construct a real-valued extended array output via Euler transformation, thus the arithmetic of the proposed algorithm is converted from complex field to real field. The proposed NC-Euler-PM algorithm has a lower computational complexity than that of NC-RI-PM algorithm, NC-ESPRIT algorithm and Improved NC-RI-PM algorithm. The angle estimation performance of the proposed algorithm is better than that of the conventional PM algorithm and close to that of Improved NC-RI-PM algorithm. Particularly, due to the extended real-valued propagator matrix in the proposed algorithm, the proposed NC-Euler-PM algorithm has better angle estimation performance than Improved NC-RI-PM algorithm in lower signal-to-noise ratio (SNR). The maximum number of signals estimated by the proposed algorithm is two times of that of the conventional PM algorithm by exploiting the non-circularity. The estimation error and Cramer-Rao bound (CRB) of noncircular signals for uniform linear array are also derived. Simulation results are presented to demonstrate the effectiveness of the proposed algorithm.