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Optimal Coprime Array: Properties, Optimization, and k-times extension

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Abstract

In this work, we attempt to solve the problem of achieving more consecutive degrees of freedom (DOF) in a coprime array for direction-of-arrival (DOA) estimation. Specifically, we propose a novel coprime array, which we term as optimal coprime array (OCA). OCA has attractive features in terms of achieving a large number of uniform DOF. Also, closed-form expression of the maximum uniform DOF for a specific number of sensors is available for the OCA, which is generally not found in the coprime arrays. Another advantage of the OCA is that it has less mutual coupling as a subarray of the OCA is translated. The properties of the OCA are analyzed considering two different situations. To increase the number of uniform DOF further, we extend it up to \({\varvec{k}}\)-times and prove that the proposed \({\varvec{k}}\)-times extended OCA (\({\varvec{k}}\)-OCA) works better than the existing \({\varvec{k}}\)-times extended coprime array in both attaining more consecutive DOF and reducing the mutual coupling effect. The \({\varvec{k}}\)-OCA achieves the maximum number of uniform DOF for a specified number of elements among all the existing coprime arrays. The simulation results show the effectiveness of the proposed OCA and the \({\varvec{k}}\)-OCA.

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Acknowledgements

Rajen Kumar Patra conveys deepest gratitude to Director, ITR, DRDO, for his support.

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Authors and Affiliations

  1. Radar Systems Group, Integrated Test Range, DRDO, Balasore, Odisha, 756025, India

    Rajen Kumar Patra

  2. Electronics and Electrical Communication Engineering, IIT Kharagpur, Kharagpur, West Bengal, 721302, India

    Anindya Sundar Dhar

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  1. Rajen Kumar Patra
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Correspondence to Rajen Kumar Patra.

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Patra, R.K., Dhar, A.S. Optimal Coprime Array: Properties, Optimization, and k-times extension. Circuits Syst Signal Process 42, 3770–3794 (2023). https://doi.org/10.1007/s00034-023-02292-8

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