Two-dimensional direction-of-arrival estimation of coherently distributed noncircular signals via symmetric shift invariance

Abstract

In practical applications such as mobile communication, radar and sonar, the effect of angular spread on the source energy can no longer be ignored due to multipath phenomena. Therefore, a spatially distributed source model is more realistic than the point source mode in these complex cases. A lot of direction-of-arrival (DOA) estimation methods for distributed sources have been published. Whereas researches concentrated on the complex circular signal case, the noncircular property of signal can be employed to further improve the estimation performance, which has received extensive attention recently. To date, several low-complexity DOA estimation algorithms for two-dimensional (2D) coherently distributed (CD) noncircular sources have been proposed. However, all these algorithms need obtain the approximate shift invariance relationship between the sub-arrays by applying the one-order Taylor series approximation to the generalized steering vectors, which may introduce additional errors and affect the estimation accuracy. In this paper, a novel 2D DOA estimation algorithm based on the symmetric shift invariance relationship is proposed using the centro-symmetric three-dimensional (3D) linear arrays. Firstly, the extended array model is established by exploiting the noncircularity of the signal. Then, it is proved that the deterministic angular distribution function vector of the CD source has a symmetrical property for arbitrary centro-symmetric array, based on which the symmetric shift invariance relationships of extended generalized steering vectors are established in the three sub-arrays of 3D linear arrays. On the premise of such relationships, the center azimuth and elevation DOAs are obtained by the polynomial rooting method without spectral peak searching. Finally, the cost function implementing the parameter matching is constructed by the symmetric shift invariance relationship of the generalized steering vector of the whole array. Theoretical analysis and simulation experiment show that compared with the existing low-complexity algorithms, the proposed algorithm avoids the additional errors introduced by the Taylor series approximation, which allows it to achieve higher estimation accuracy with the small complexity cost. Moreover, the proposed algorithm can achieve omnidirectional angle estimation in the three-dimensional space.