A Novel Designed Sparse Array for Noncircular Sources with High Degree of Freedom

Hindawi Mathematical Problems in Engineering Volume 2019, Article ID 1264715, 10 pages https://doi.org/10.1155/2019/1264715 Research Article A Novel Designed Sparse Array for Noncircular Sources with High Degree of Freedom Yan-kui Zhang,1 Hai-yun Xu ,1 Da-ming Wang,1 Bin Ba ,1 and Si-yao Li2 1 2 National Digital Switching System Engineering and Technology Research Center, Zhengzhou 450002, China Communication NCO Academy, Army Engineering University, Nanjing 210000, China Correspondence should be addressed to Hai-yun Xu; Received 1 September 2018; Revised 8 December 2018; Accepted 26 December 2018; Published 29 January 2019 Academic Editor: Raffaele Solimene Copyright © 2019 Yan-kui Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The existing coprime array is mainly applicable to circular sources, while the virtual array degree of freedom (DOF) for noncircular sources is enhanced limitedly. In order to perfect the array DOF and the direction of arrival (DOA) estimation accuracy, a high degree of freedom sparse array design method for noncircular sources is put forward. Firstly, the method takes the advantages of the characteristic of the noncircular sources to expand the array manifold and then explores and solves the location distribution of the physical array sensors on the basis of the virtual array model with the help of the searching approach. The array configuration can obtain the longest continuous virtual array. The comparisons between the proposed array configuration and the common array configurations are advanced. The simulation experiments show that the sparse array presented in this paper can effectively increase the continuous virtual array aperture of noncircular sources, improve the array DOF and DOA estimation accuracy, and achieve the purpose of better estimation of multiple DOAs in underdetermined conditions. 1. Introduction Direction of arrival (DOA) estimation is one of the main research topics in array signal processing. It is widely used in radar, sonar, radio astronomy, and so on [1, 2]. The traditional DOA estimation algorithms are mainly based on the uniform array, and the 𝑀 array sensors can achieve at most 𝑀 − 1 effective estimation of the azimuths [3, 4]. The number of target sources needed to be located is sometimes greater than the number of array sensors, that is, underdetermined condition. In order to improve the array degree of freedom (DOF) and realize the effective estimation of multiple sources in undetermined condition, in recent years, many sparse array structures have been proposed by experts and scholars. With the new sparse arrays, the apertures of arrays can be effectively extended, and the array DOFs and estimation accuracy could be improved [5, 6]. Typical sparse arrays include the minimum redundancy array (MRA), the minimum hole array (MHA), the nested array, and the coprime array [7]. MRAs and MHAs are the ideal array configurations for circular sources; the optimal virtual array can be achieved [8, 9]. The nested array consists of a nonsparse uniform array and a sparse uniform array, which ensures a higher array DOF and continuous virtual array [10, 11]. The coprime array is composed of two uniform sparse arrays with larger array sensor spacing and a high array DOF, and the nested array is a special type of coprime array [12, 13]. The general structure of the coprime array and the solutions to basic DOA estimation are given in [14, 15]. The authors of [16, 17] propose improved coprime arrays and use the spatial smoothing algorithm for the virtual array to improve the estimation precision. In [18, 19], a coprime array with displaced subarrays (CADiS) structure is exploited. This coprime array configuration greatly expands the array aperture, improves the array DOF, and increases estimation accuracy. On the basis of the CADiS configuration, [20] summarizes the general configuration of coprime array with multiperiod subarrays (CAMpS) and proves that the CADiS is a special form of CAMpS. A kind of shifted coprime array (SCA) is proposed in [21], which further improves the virtual array aperture of CADiS configuration. The sparse array configurations mentioned above are mainly focused on the DOA estimation of circular sources, and there is no open research on the sparse configurations designed for noncircular sources. 2 Mathematical Problems in Engineering A noncircular source is a special transmission signal. Compared with a circular source, a noncircular source has more useful information. One of the most important features is that the ellipse covariance of noncircular sources is not zero. Therefore, this characteristic can be used to improve the array DOF and the DOA estimation accuracy. A DOA estimation method based on symmetric shift invariance array for noncircular sources is presented in [22], which enhances the array DOF by using the noncircular characteristic. Some DOA estimation methods for noncircular sources are listed in document [23–27]. These methods extend the array aperture by using the noncircular characteristics of sources and advance the array DOF and estimation accuracy. The DOA estimation methods mentioned above for the noncircular sources are all based on the array configuration of circular sources, and the array DOF and estimation accuracy are improved by using the characteristic that the ellipse covariance is not zero, but the use of this characteristic is not sufficient. In order to further increase the array DOF of noncircular sources and improve the accuracy of DOA estimation, a novel high DOF sparse array design approach for noncircular sources is presented in this paper. In this configuration, the virtual array model is constructed by using the characteristics of noncircular sources. Then the maximum continuous virtual array structure of noncircular sources is given by search method on the basis of difference. At last, the typical DOA estimation methods under this model are given. The validity of the method is proven by simulation experiments. The main contributions of this paper are as follows. (1) A novel designed sparse array for noncircular sources (SANC) with high DOF is proposed, which effectively extends the continuous virtual array aperture and improves the DOA estimation accuracy. (2) The design method and flow chart of the SANC configuration are given in this paper. The comparison between the array configuration proposed and the common array configurations is given, and typical DOA estimation methods under this array configurations are introduced. (3) A virtual array model is constructed, and the CramerRao lower bound (CRLB) is derived under the proposed model, effectively proving that the proposed array configuration not only can realize the effective estimation in overdetermined conditions but also (...truncated)