Earticle

Difference co-array can be constructed by using Khatri-Rao (KR) product, which can increase the degrees of freedom (DOF) significantly. Combined with fourth order cumulants, the KR product can be used to constructed fourth order difference co-array. The fourth order difference co-array of a four level nested array contains a uniform linear array (ULA), however, its second order difference co-array has missing holes, which may result in the ambiguity for DOA estimation. And the method based on KR product and fourth order cumulants has two main drawbacks. First it cannot be employed to Gaussian source signals. Second it needs a large number of snapshots. In this paper, a novel approach is proposed to construct a virtual ULA based on KR product and redundancy spacing of arrays for a four level nested array. Unlike the existing method based on KR product and fourth order cumulants, the new method only uses second order statistics. And compared to the method based on KR product and second order statistics, the new method achieves higher resolution. Numerical results are provided to demonstrate the effectiveness and superior performance of the proposed algorithm.

Herein, we estimate the direction of arrival (DOA) of non-Gaussian signals for nested arrays (NAs) by implementing the fourth-order difference co-array (FODC) and successive methods. In particular, considering the property of the fourth-order cumulant (FOC), we first construct the FODC of the NA, which can obtain O(N⁴) virtual elements using N physical sensors, whereas conventional FOC methods can only obtain O(N²) virtual elements. In addition, the closed-form expression of FODC is presented to verify the enhanced degrees of freedom (DOFs). Subsequently, we exploit the vectorized FOC (VFOC) matrix to match the FODC of the NA. Notably, the VFOC matrix is a single snapshot vector, and the initial DOA estimates can be obtained via the discrete Fourier transform method under the underdetermined correlation matrix condition, which utilizes the complete DOFs of the FODC. Finally, fine estimates are obtained through the spatial smoothing-Capon method with partial spectrum searching. Numerical simulation verifies the effectiveness and superiority of the proposed method.