对称旋转不变相干分布式非圆信号二维波达方向估计

在相干分布式非圆信号二维波达方向估计中,利用信号非圆特性可提升估计精度,但现有的低复杂度算法利用泰勒级数近似建立的旋转不变关系会引入额外误差.针对该问题,考虑中心对称的三维立体线阵,提出了一种基于对称旋转不变关系的二维波达方向估计算法.算法首先利用信号非圆特性建立了扩展阵列模型;然后证明了对于任意的中心对称阵列,相干分布源的确定性角信号分布函数矢量具有对称特性,利用此特性在三维立体线阵的三个子阵中分别建立了扩展广义方向矢量的对称旋转不变关系;基于此,通过无须搜索的多项式求根方式分别得到中心方位角和俯仰角估计;最后利用整个阵列广义方向矢量的对称旋转不变关系构造代价函数实现了参数匹配.理论分析和仿真实验表明,相比于现有的低复杂度算法,所提算法避免了泰勒级数近似引入的额外误差,以较小的复杂度代价获得了性能的较大提升.同时,所提算法能够实现三维空间全方位的角度估计.

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

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.