A Design Method of Sparse Array with High Degrees of Freedom Based on Fourth-Order Cumulants

Fengtong Mei,Daming Wang,Yinsheng Wang,Weijia Cui,Chunxiao Jian,Xiaofei Zhang

doi:10.1155/2021/9915963

Fengtong Mei, Daming Wang + Show 4 more

Open Access

https://doi.org/10.1155/2021/9915963

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Abstract

Recently, the design of sparse linear array for direction of arrival (DOA) estimation of non-Gaussian signals has attracted considerable interest due to the fact that the fourth-order difference coarray offered by non-Gaussian significantly increases the aperture of a virtual linear array, which improves the performance of DOA estimation. In this paper, a super four-level nested array (S-FL-NA) configuration based on fourth-order cumulants (FOC) is proposed. The S-FL-NA consists of uniform linear arrays which have different interelement spacing. The proposed array configuration is designed based on interelement spacing, which, for a given number of sensors, is uniquely determined by a closed-form expression. We also derive the closed-form expression for the degrees of freedom (DOFs) of the proposed array. The optimal distribution of the number of sensors in each uniform linear array of the proposed array is given for an arbitrary number of sensors. Compared with the existing sparse arrays, the proposed array can provide a higher number of degrees of freedom and a larger physical array aperture. In addition, to improve the calculation speed of the fourth-order cumulant matrix, we simplify the FOC matrix by removing some redundancy. Numerical simulations are conducted to verify the superiority of the S-FL-NA over other sparse arrays.

Highlights

Direction-of-arrival (DOA) estimation is one of the important research fields in array signal processing [1,2,3,4,5,6]
A novel four-level nested array structure is proposed based on fourth-order cumulants (FOC), which is composed of four sparse ULAs. e proposed sparse array structure effectively utilizes the interelement spacings of the third and fourth sparse ULAs, which provides the largest aperture virtual uniform linear array compared to the existing array structures with a given number of sensors. e closed-form expressions for the physical sensor location and the virtual aperture are derived, and the optimal distribution of sensors to each of the sparse ULAs is given. en, to increase the calculation speed of the FOC matrix, we simplify the FOC matrix by removing some redundancy of that
The number of consecutive lags and physical apertures of five kinds of sparse array are compared, and multiple signal classification (MUSIC) spectra are simulated to show the number of distinguishable sources

Summary

Introduction

Direction-of-arrival (DOA) estimation is one of the important research fields in array signal processing [1,2,3,4,5,6]. An enhanced fourlevel nested array (E-FL-NA) is proposed [28] by adding two extra subarrays to the NA, achieving a higher number of the consecutive coarray lags than the aforementioned sparse arrays These array structures increase DOFs greatly, the inner structure of their virtual arrays has not been fully analyzed in the researches given above. A novel four-level nested array structure is proposed based on FOC, which is composed of four sparse ULAs. e proposed sparse array structure effectively utilizes the interelement spacings of the third and fourth sparse ULAs, which provides the largest aperture virtual uniform linear array compared to the existing array structures with a given number of sensors.

Cumulant-Based Fourth-Order Difference Coarray

The Proposed Four-Level Nested Array Structure

Simplified FOC Matrix for Low Complexity

Simulation Results

Conclusion