Enhance Degrees of Freedom for Coprime Array Using OptSpace Algorithm

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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Rearranged coprime array to increase degrees of freedom and reduce mutual coupling

Signal Processing ◽

10.1016/j.sigpro.2021.108038 ◽

2021 ◽

Vol 183 ◽

pp. 108038

Author(s):

Zhe Fu ◽

Pascal Chargé ◽

Yide Wang

Keyword(s):

Degrees Of Freedom ◽

Mutual Coupling ◽

Coprime Array

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2-D DOA estimation method based on coprime array MIMO radar

EURASIP Journal on Advances in Signal Processing ◽

10.1186/s13634-021-00783-x ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Fei Zhang ◽

Zijing Zhang ◽

Aisuo Jin ◽

Chuantang Ji ◽

Yi Wang

Keyword(s):

Degrees Of Freedom ◽

Estimation Method ◽

Doa Estimation ◽

Mimo Radar ◽

Estimation Methods ◽

Estimation Accuracy ◽

Multiple Sources ◽

Source Estimation ◽

Array Aperture ◽

Coprime Array

AbstractAiming at the problem that traditional direction of arrival (DOA) estimation methods cannot handle multiple sources with high accuracy while increasing the degrees of freedom (DOF), a new method for 2-D DOA estimation based on coprime array MIMO radar (SA-MIMO-CA) is proposed. First of all, in order to ensure the accuracy of multi-source estimation when the number of elements is finite, a new coprime array model based on MIMO (MIMO-CA) is proposed. This method is based on a new MIMO array-based co-prime array model (MIMO-CA), which improves the accuracy of multi-source estimation when the number of array elements is limited, and obtains a larger array aperture with a smaller number of array elements, and improves the estimation accuracy of 2-D DOA. Finally, the effectiveness and reliability of the proposed SM-MIMO-CA method in improving the DOF of array and DOA accuracy are verified by experiments.

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DOA Estimation Based on Sum-Difference Coarray with Virtual Array Interpolation Concept

10.21203/rs.3.rs-463699/v1 ◽

2021 ◽

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

Abstract The 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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Improved 2D Coprime Array Structure with the Difference and Sum Coarray Concept

Electronics ◽

10.3390/electronics9020273 ◽

2020 ◽

Vol 9 (2) ◽

pp. 273

Author(s):

Guiyu Wang ◽

Zesong Fei ◽

Shiwei Ren ◽

Xiaoran Li

Keyword(s):

Closed Form ◽

Degrees Of Freedom ◽

Spatial Information ◽

Temporal Information ◽

Direction Of Arrival Estimation ◽

One Dimensional ◽

Sparse Arrays ◽

Array Structure ◽

The Difference ◽

Coprime Array

Recently, the difference and sum (diff-sum) coarray has attracted much attention in one-dimensional direction-of-arrival estimation for its high degrees-of-freedom (DOFs). In this paper, we utilize both the spatial information and the temporal information to construct the diff-sum coarray for planar sparse arrays. The diff-sum coarray contains both the difference coarray and the sum coarray, which provides much higher DOFs than the difference coarray alone. We take a planar coprime array consisting of two uniform square subarrays as the array model. To fully use the aperture-extending ability of the diff-sum coarray, we propose two novel configurations to improve the planar coprime array. The first configuration compresses the inter-element spacing of one subarray and results in a larger consecutive area in the coarray. The second configuration rearranges the two subarrays and introduces a proper separation between them, which can significantly reduce the redundancy of the diff-sum coarray and increase the DOFs. Besides, we derive the closed-form expressions of the central consecutive ranges in the coarrays of the proposed array configurations. Simulations verify the superiority of the proposed array configurations.

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Direction-of-Arrival Estimation for Coprime Array Using Compressive Sensing Based Array Interpolation

International Journal of Antennas and Propagation ◽

10.1155/2017/6425067 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Aihua Liu ◽

Qiang Yang ◽

Xin Zhang ◽

Weibo Deng

Keyword(s):

Covariance Matrix ◽

Degrees Of Freedom ◽

Linear Array ◽

Estimation Method ◽

Direction Of Arrival ◽

Doa Estimation ◽

Interpolation Algorithm ◽

Estimation Performance ◽

Sample Covariance ◽

Coprime Array

A method of direction-of-arrival (DOA) estimation using array interpolation is proposed in this paper to increase the number of resolvable sources and improve the DOA estimation performance for coprime array configuration with holes in its virtual array. The virtual symmetric nonuniform linear array (VSNLA) of coprime array signal model is introduced, with the conventional MUSIC with spatial smoothing algorithm (SS-MUSIC) applied on the continuous lags in the VSNLA; the degrees of freedom (DoFs) for DOA estimation are obviously not fully exploited. To effectively utilize the extent of DoFs offered by the coarray configuration, a compressing sensing based array interpolation algorithm is proposed. The compressing sensing technique is used to obtain the coarse initial DOA estimation, and a modified iterative initial DOA estimation based interpolation algorithm (IMCA-AI) is then utilized to obtain the final DOA estimation, which maps the sample covariance matrix of the VSNLA to the covariance matrix of a filled virtual symmetric uniform linear array (VSULA) with the same aperture size. The proposed DOA estimation method can efficiently improve the DOA estimation performance. The numerical simulations are provided to demonstrate the effectiveness of the proposed method.

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