Decoupled two-dimensional direction of arrival estimation of single distributed source by vectoring differential phases

In practical applications such as radar, sonar, and mobile communications, transmitted signals are often affected by the scattering and reflection phenomena, which causes the signal energy received by the antenna array to be distributed into a certain space. In this case, a distributed source model will be more applicable. In general, the distributed sources have been classified as coherently distributed (CD) source and incoherently distributed (ID) source, which prove to be suitable for the cases of slowly time-varying and rapidly time-varying channels, respectively. In this paper, we consider the two-dimensional direction of arrival (DOA) estimation of distributed sources (including CD source or ID source). Specifically, uniform circular array (UCA) is widely used because of its ability to measure full azimuth angle and high resolution. However, the existing estimation algorithms all require spectral peak searching and the eigenvalue decomposition, which can bring a large computational complexity. To solve this problem, a decoupled rapid two-dimensional DOA estimation algorithm is proposed based on vectoring differential phases considering the two cases of single CD source and ID source. Firstly, based on spatial frequency approximation model, it is proved that none of differential phases between the received signals of different sensors in the UCA is affected by angle spread parameters when there is only a single distributed source. Under the premise of such a property, the central DOAs can be decoupled through obtaining the differential phases. Next, we can obtain the phase angles of strictly upper triangular elements in the sample covariance matrix, which correspond to differential phases between different sensors. Finally, by vectoring these differential phases, the central azimuth and elevation DOAs are estimated in the closed form from a least-squared problem, where the spectral peak searching and eigenvalue decomposition can be avoided, hence the computational complexity is reduced greatly. Theoretical analysis and simulation results show that the proposed algorithm has higher estimation accuracy and does not require prior information about the distribution of angular signals. With both low computational complexity and low hardware complexity, the proposed algorithm is beneficial to the engineering practice of array direction finding in complex environment.