Abstract
Recently, direction of arrival (DOA) estimation for non-circular (NC) sources has attracted great attention in array signal processing since NC signals can provide more information to generate the virtual difference and sum (diff-sum) coarray. In this paper, we propose a generalized vectorized noncircular MUSIC (GVNCM) method, which can solve the underdetermined DOA estimation problem when the difference coarray and the sum coarray are discontinuous. Based on the GVNCM algorithm, an extended transformed nested array strategy is proposed by splitting the dense subarray of transformed nested array (TNA) into several parts and shifting them to the right to reduce the redundant elements between the difference coarray and the sum coarray. Following this strategy, two novel array configurations are developed. The analytical expressions of the new structures and the consecutive range of their diff-sum coarrays are provided. The two proposed arrays can achieve higher degrees of freedom and maximum number of detectable signals compared with TNA. In order to evaluate the underdetermined DOA estimation performance of NC signals, we derive the corresponding expression of Cramer-Rao bound. The effectiveness of the proposed arrays is verified through numerical simulations.
Highlights
Direction of arrival (DOA) estimation is an important topic in array signal processing field and plays a critical role in many applications such as radar, sonar, wireless communication and navigation [1]–[6]
We introduce an extended transformed nested array (ETNA) strategy, which displaces some elements in the dense subarray of TNA to the right to increase the aperture of diff-sum coarray
These six array configurations can achieve high DOFs as they are all designed for the DOA estimation of non-circular sources
Summary
Direction of arrival (DOA) estimation is an important topic in array signal processing field and plays a critical role in many applications such as radar, sonar, wireless communication and navigation [1]–[6]. In [22], the authors translated the two subarrays of NA separately and proposed a new sparse array called improved nested arrays with sum-difference coarray (INAwSDCA). We improve VNCM method and propose a generalized vectorized noncircular MUSIC (GVNCM) algorithm which can deal with the case that diff-sum coarray has a long consecutive range but the difference and the sum coarray are discontinuous. We introduce an extended transformed nested array (ETNA) strategy, which displaces some elements in the dense subarray of TNA to the right to increase the aperture of diff-sum coarray. The extended transformed nested array strategy and two proposed array structures, i.e., TwETNA and ThETNA, are elaborated in Section III with analytical expressions of the continuous diff-sum coarray range. In denotes n × n identity matrix. 0n and 0m×n are zero matrices with dimension n × n and m × n, respectively
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