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The Generalized Compressed Nested Array for the Construction of Fourth-order Difference Co-array

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Abstract

In the present study, the generalized compressed nested array (GCNA) is proposed to improve the fourth-order cumulant-based direction of arrival (DOA) estimation performance when the small-scale array is deployed. The main objective of this study is to demonstrate that the new-formed array can form the sum co-array, which is close to the nested array, by a few sensors. Meanwhile, it is found that the difference co-array of its sum co-array or the fourth-order difference co-array (FODC) of GCNA is hole-free so that it can achieve a long consecutive virtual array. Obtained results show that for less than 12 sensors, GCNA can achieve the longest consecutive virtual array when the comparison is made with conventional FODC-based sparse arrays. It is inferred that for a small-scale sensor array, the GCNA can acquire more degrees of freedom (DOFs) for DOA estimation than other sparse arrays. In order to evaluate the performance of the proposed sparse array, numerous simulations are carried out to compare the number of resolved sources and estimation accuracy of different sparse arrays. Accordingly, it is concluded that the proposed GCNA outperforms conventional representative sparse arrays.

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Data availability statement

The data used to support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work was sponsored by National Natural Science Foundation of China under Grants 61901371, 61901372 and 51974250. This work was also supported in part by the Natural Science Basic Research Program of Shaanxi under Grants 2020JQ-600 and 2020JQ-599, and in part by the Youth Science and Technology Nova Project in Shaanxi Province under grant 2020KJXX-018.

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Authors and Affiliations

  1. School of Electronics Engineering, Xi’an Shiyou University, Xi’an, 710065, China

    Bo Dang

  2. School of Information Science and Technology, Northwest University, Xi’an, 710127, China

    Yan Zhou

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  1. Bo Dang
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  2. Yan Zhou
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Correspondence to Yan Zhou.

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Dang, B., Zhou, Y. The Generalized Compressed Nested Array for the Construction of Fourth-order Difference Co-array. Circuits Syst Signal Process 40, 6340–6353 (2021). https://doi.org/10.1007/s00034-021-01769-8

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