School of Electronic and Information Engineering, Tianjin University, Tianjin 300072, China.
Sensors (Basel). 2013 Jan 7;13(1):746-57. doi: 10.3390/s130100746.
In this paper, a novel direction of arrival (DOA) estimation algorithm called the Toeplitz fourth order cumulants multiple signal classification method (TFOC-MUSIC) algorithm is proposed through combining a fast MUSIC-like algorithm termed the modified fourth order cumulants MUSIC (MFOC-MUSIC) algorithm and Toeplitz approximation. In the proposed algorithm, the redundant information in the cumulants is removed. Besides, the computational complexity is reduced due to the decreased dimension of the fourth-order cumulants matrix, which is equal to the number of the virtual array elements. That is, the effective array aperture of a physical array remains unchanged. However, due to finite sampling snapshots, there exists an estimation error of the reduced-rank FOC matrix and thus the capacity of DOA estimation degrades. In order to improve the estimation performance, Toeplitz approximation is introduced to recover the Toeplitz structure of the reduced-dimension FOC matrix just like the ideal one which has the Toeplitz structure possessing optimal estimated results. The theoretical formulas of the proposed algorithm are derived, and the simulations results are presented. From the simulations, in comparison with the MFOC-MUSIC algorithm, it is concluded that the TFOC-MUSIC algorithm yields an excellent performance in both spatially-white noise and in spatially-color noise environments.
本文提出了一种新的到达角（DOA）估计算法，称为 Toeplitz 四阶累积量多重信号分类方法（TFOC-MUSIC）算法，该算法通过结合一种称为修正四阶累积量 MUSIC（MFOC-MUSIC）算法的快速 MUSIC 类算法和 Toeplitz 逼近来实现。在提出的算法中，去除了累积量中的冗余信息。此外，由于四阶累积量矩阵的维数减少，计算复杂度降低，该维数等于虚拟阵元的数量。也就是说，物理阵元的有效阵元孔径保持不变。然而，由于有限的采样快照，存在降秩 FOC 矩阵的估计误差，因此 DOA 估计的能力会降低。为了提高估计性能，引入了 Toeplitz 逼近来恢复降维 FOC 矩阵的 Toeplitz 结构，就像具有最优估计结果的理想 Toeplitz 结构一样。推导了该算法的理论公式，并给出了仿真结果。从仿真结果可以看出，与 MFOC-MUSIC 算法相比，TFOC-MUSIC 算法在空间白噪声和空间色噪声环境下都具有优异的性能。
