A special coprime array configuration for increased degrees of freedom

In this paper, the mutual information between the received signals and the source in the coprime linear array is investigated. In Shannon’s information theory, the mutual information is used to quantify the reduction in the priori uncertainty of the transmitted message. Similarly, the spatial information in the coprime array is the mutual information between direction of arrival (DOA), source amplitude, and received signals. Such information content is composed of two parts. The first part is DOA information, and the second one is scattering information. In a single source scenario, we derive the theoretical expression and its asymptotic upper bound of DOA information. The corresponding expression of scattering information is also formulated theoretically. Besides, the application of spatial information is discussed. We can obtain the optimal array configuration by maximizing the DOA information of the coprime array. Similarly, the information is also used to quantify the performance difference between the coprime array and uniform array. In addition, the entropy error is employed to evaluate the estimation performance based on spatial information. Numerical simulation of the information content confirms our theoretical analysis. The results in this paper have important guiding significance for the design of the coprime array in the actual environment.

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Increasing Utilization of Redundant Virtual Array for DOA Estimation Based on Coprime Array

Mathematical Problems in Engineering ◽

10.1155/2020/8830416 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Chenghong Zhan ◽

Guoping Hu ◽

Zixin Zhang ◽

Ziang Feng

Keyword(s):

Parameter Estimation ◽

High Precision ◽

Degrees Of Freedom ◽

Doa Estimation ◽

Far Field ◽

Virtual Array ◽

Previous Algorithm ◽

Array Structure ◽

Simulation Results ◽

Coprime Array

In this paper, we initiated a method to estimate the direction of arrival (DOA) of far-field, narrowband, and incoherent targets using coprime array. First, we proposed a coprime array structure and analysed the distribution of difference coarray (DCA). The degrees of freedom (DOF) of the proposed coprime array became clearer by referring to the DCA conception. However, previous algorithm only uses the continuous virtual array, which causes the virtual array elements in the repeated position being abandoned. Therefore, the paper analyses the distribution of virtual array based on DCA conception and averages the receiving signal on these redundant virtual array elements to increase the utilization of receiving data. As a result, the algorithm has high precision in parameter estimation. Simulation results have shown the superiority of the proposed algorithm.

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DOA estimation based on sum–difference coarray with virtual array interpolation concept

EURASIP Journal on Advances in Signal Processing ◽

10.1186/s13634-021-00782-y ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Yarong Ding ◽

Shiwei Ren ◽

Weijiang Wang ◽

Chengbo Xue

Keyword(s):

Numerical Simulation ◽

Degrees Of Freedom ◽

Doa Estimation ◽

Superior Performance ◽

Norm Minimization ◽

Atomic Norm ◽

Virtual Array ◽

Simulation Results ◽

The Difference ◽

Coprime Array

AbstractThe sum–difference coarray is the union of difference coarray and the sum coarray, which is capable to obtain a higher number of degrees of freedom (DOF) than the difference coarray. However, this method fails to use all information provided by the coprime array because of the existence of holes. In this paper, we introduce the virtual array interpolation into the sum–difference coarray domain. After interpolating the virtual array, we estimate the DOA by reconstructing the covariance matrix to resolve an atomic norm minimization problem in a gridless way. The proposed method is gridless and can effectively utilize the DOF of a larger virtual array. Numerical simulation results verify the effectiveness and the superior performance of the proposed algorithm.

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Algorithm to Estimate Direction of Arrival with Interpolated Array Elements for Coprime Array Holes

Mathematical Problems in Engineering ◽

10.1155/2020/1429628 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Guicai Yu

Keyword(s):

Degrees Of Freedom ◽

Signal To Noise Ratio ◽

Direction Of Arrival ◽

Array Element ◽

Regular Pattern ◽

Minimum Number ◽

Virtual Array ◽

Novel Method ◽

Coprime Arrays ◽

Coprime Array

A novel method for adding antennas in the coprime arrays is introduced in this study, in order to solve the problem of the reduced degree of freedom of the array in the hole-existing coprime arrays. The minimum number of antennas interpolated in the algorithm maximizes the available degrees of freedom of virtual arrays, and the number of interpolated antennas does not change the original aperture size of the coprime arrays. With the proposed algorithm, the estimate of the direction of arrival is more accurate for a given signal-to-noise ratio. The scheme first finds the regular pattern of hole positions in virtual array elements, and then, according to the regular pattern, the position of the hole of the partial virtual array element is interpolated with the array element antenna at the position of the corresponding coprime arrays. The holes of the virtual array element are filled, giving virtual uniform continuous array elements with maximum degrees of freedom. We use the ESPRIT, and the simulation results show that the proposed algorithm improves the accuracy and resolution of estimates of the direction of arrival.

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Enhance Degrees of Freedom for Coprime Array Using OptSpace Algorithm

IEEE Access ◽

10.1109/access.2019.2903106 ◽

2019 ◽

Vol 7 ◽

pp. 32672-32680 ◽

Cited By ~ 7

Author(s):

Qianpeng Xie ◽

Xiaoyi Pan ◽

Shunping Xiao

Keyword(s):

Degrees Of Freedom ◽

Coprime Array

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

Mathematical Problems in Engineering ◽

10.1155/2019/1264715 ◽

2019 ◽

Vol 2019 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Yan-kui Zhang ◽

Hai-yun Xu ◽

Da-ming Wang ◽

Bin Ba ◽

Si-yao Li

Keyword(s):

Design Method ◽

Doa Estimation ◽

Degree Of Freedom ◽

Estimation Accuracy ◽

Sparse Array ◽

Array Configuration ◽

Virtual Array ◽

Array Aperture ◽

Coprime Array ◽

High Degree

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.

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