k-Level Extended Sparse Array Design for Direction-of-Arrival Estimation

Sparse arrays based on the concept of a sum-difference coarray (SDCA) have increased degrees of freedom and enlarged effective array aperture compared to those only considering a difference coarray. Nevertheless, there still exist a number of overlapping virtual sensors between the difference coarray and the sum coarray, yielding high coarray redundancy. In this paper, we propose a k-level extended sparse array configuration consisting of one sparse subarray with k-level expansion and one uniform linear subarray. By systematically analyzing the inherent structure of the k-level extended sparse array, the closed-form expressions for sensor locations, uniform DOF and coarray redundancy ratio (CARR) are derived. Moreover, with the utilization of a k-level extended strategy, the proposed array remains a hole-free property and achieves low coarray redundancy. According to the proposed sparse array, the spatial and temporal information of the incident sources are jointly exploited for underdetermined direction-of-arrival estimation. The theoretical propositions are proven and numerical simulations are performed to demonstrate the superior performance of the proposed array.

Automated summary

This paper introduces a sparse array configuration based on the concept of sum-difference coarray (SDCA), and derives mathematical expressions for sensor locations, uniform degrees of freedom (DOF), and coarray redundancy ratio (CARR) by analyzing the inherent structure of the sparse array. The proposed array utilizes the spatial and temporal information of the incident sources for direction-of-arrival estimation, achieving superior performance.