Cumulants-Based Toeplitz Matrices Reconstruction Method for 2-D Coherent DOA Estimation

Abstract

In this paper, a new high-resolution approach called fourth-order cumulants-based Toeplitz matrices reconstruction (FOC-TMR) method, is presented for two-dimensional (2-D) direction-of-arrival (DOA) estimation of incident narrowband coherent signals. The angle estimation problem is addressed by arranging the cumulants elements of received signals from two parallel uniform linear arrays (ULAs) to two Toeplitz matrices. In Gaussian noise cases, it is shown that the ranks of the two Toeplitz matrices equal the number of the incoming waves and are independent of their coherency. Therefore, with eigen decomposition of the Toeplitz-based generalized DOA matrix, the closed-form, automatically paired 2-D angle parameters can be estimated properly from its large eigenvalues and corresponding eigenvectors, respectively. In the condition of two closely spaced coherent signals in both 2-D angles, simulation results show that, in comparison with the fourth-order cumulants-based forward spatial smoothing (FOC-FSS) method, the proposed algorithm has lower computational complexity and yields better estimation performance in terms of maximum probability of success (MPS), maximum root mean square error (MRMSE) of incoming signals in both white noise and color Gaussian noise situations, especially, in low signal-to-noise ratio (SNR) and small number of snapshots conditions.

Efficient method of two-dimensional DOA estimation for coherent signals

“…As for two N × N dimension Toeplitz matrices, the maximum number of signals that can be distinguished is N−1 by the proposed FOC-ITMR method. Assume that the number of each subarray in [26] is 2 M + 1, the FOC-TMR method can distinguish M signals. According to the parameters set in [25], the FOC-FSS method can tell the same number of signals as [26].…”

“…Assume that the number of each subarray in [26] is 2 M + 1, the FOC-TMR method can distinguish M signals. According to the parameters set in [25], the FOC-FSS method can tell the same number of signals as [26]. In other words, based on the same array configuration and the same number of sensors, the proposed algorithm has twice larger array aperture than the a b Fig.…”

“…Therefore, the proposed algorithm can not only resolve more signals than the compared method in [26] but also achieve better estimation performance.…”

“…In [25], the FOC-FSS approach has been presented to remedy rank deficiency problem. In [26], the FOC-TMR method is presented to obtain source location by reconstructing two Toeplitz matrices.…”

Two-dimensional DOA estimation of coherent sources using two parallel uniform linear arrays

“…Xia et al [15] have proposed a polynomial root-finding-based method for 2-D DOA estimation by using two parallel uniform linear arrays (ULAs), which has less computational burden. Some decorrelation algorithms are proposed in [16][17][18] to achieve 2-D DOA estimation by utilizing two parallel ULAs. However, the limitation of the abovementioned algorithms is that the estimation performance cannot be satisfactory due to the fact that the structure of the array is not being fully exploited.…”