Skip to main content
SpringerLink
Log in

Unfolded Coprime Transformed Nested Arrays for Increased DOF and Negligible Mutual Coupling

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this work, we propose the unfolded versions of the coprime transformed nested array (CTNA), which exploits the sum difference coarray (SDCA). We know that the CTNA has attractive properties in achieving more degrees of freedom (DOF) in direction-of-arrival estimation. However, the mutual coupling of the CTNA cannot be neglected. Here, we present the unfolded versions of the CNTA, specifically UCTNA-I (Unfolded CTNA) and UCTNA-II, which are obtained by flipping two different subarrays of the CTNA. The proposed configurations significantly reduce the mutual coupling of the CTNA without compromising the DOF it achieves. Vectorized conjugate augmented MUSIC algorithm is used to explore the SDCA of the array. The detailed properties of the arrays with the weight functions are provided in the paper. The optimization of the arrays is also carried out. Simulations are performed to prove the superiority of the proposed arrays by comparing them with the other existing arrays.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data Availability

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

References

  1. R. Cao, S. Liu, Z. Mao, Y. Huang, Doubly-Toeplitz-based Interpolation for joint DoA-Range estimation using coprime FDA, in 2021 IEEE Radar Conference (RadarConf21) (2021), pp. 1–6

  2. Z. Chen, Y. Ding, S. Ren, Z. Chen, A novel nested configuration based on the difference and sum co-array concept. Sensors 18(9), 2988 (2018)

    Article  Google Scholar 

  3. Z. Fu, P. Chargé, Y. Wang, Rearranged coprime array to increase degrees of freedom and reduce mutual coupling. Signal Process. 183, 108038 (2021)

    Article  Google Scholar 

  4. L.C. Godara, Application of antenna arrays to mobile communications, part II: beam-forming and direction-of-arrival considerations. Proc. IEEE. 85(8), 1195–1245 (1997)

    Article  Google Scholar 

  5. E. Holzman, Introduction to direction-of-arrival estimation (chen, Z.; 2010) [reviews and abstracts]. IEEE Antennas Propag. Mag. 53(1), 110–111 (2011)

    Article  Google Scholar 

  6. L. Jin, Q.Y. Yin, Space-time DOA matrix method. Acta Electron. Sin. 28(6), 8–12 (2000)

    Google Scholar 

  7. C.L. Liu, P.P. Vaidyanathan, Remarks on the spatial smoothing step in coarray MUSIC. IEEE Signal Process Lett. 22(9), 1438–1442 (2015)

    Article  Google Scholar 

  8. C.L. Liu, P.P. Vaidyanathan, Super nested arrays: linear sparse arrays with reduced mutual coupling-Part I: fundamentals. IEEE Trans. Signal Process. 64(15), 3997–4012 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. C.L. Liu, P.P. Vaidyanathan, Maximally economic sparse arrays and cantor arrays, in IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP). Curacao (2017). pp. 1–5 https://doi.org/10.1109/CAMSAP.2017.8313139

  10. J. Liu, Y. Zhang, Y. Lu, S. Ren, S. Cao, Augmented nested arrays with enhanced DOF and reduced mutual coupling. IEEE Trans. Signal Process. 65(21), 5549–5563 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Liu, Z. Mao, Y.D. Zhang, Y. Huang, Rank minimization-based Toeplitz reconstruction for DoA estimation using coprime array. IEEE Commun. Lett. 25(7), 2265–2269 (2021)

    Article  Google Scholar 

  12. J. Ma, S. Zhong, Z. Peng, W. Gao, W. Wang, X. Wang, Coprime transformed nested array with enhanced DOFs and reduced mutual coupling based on the difference and sum coarray. Electronics 11(5), 823 (2022)

    Article  Google Scholar 

  13. Z. Mao, S. Liu, Y.D. Zhang, L. Han, Y. Huang, Joint DoA-Range estimation using Space-Frequency virtual difference coarray. IEEE Trans. Signal Process. 70, 2576–2592 (2022)

    Article  MathSciNet  Google Scholar 

  14. A.T. Moffet, Minimum-redundancy linear arrays. IEEE Trans. Antennas Propag. 16(2), 172–175 (1968)

    Article  Google Scholar 

  15. P. Pal, P.P. Vaidyanathan, Nested arrays: a novel approach to array processing with enhanced degrees of freedom. IEEE Trans. Signal Process. 58(8), 4167–4181 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. P. Pal, P.P. Vaidyanathan, Coprime sampling and the MUSIC algorithm, in 2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE) (IEEE, 2011), pp. 289–294

  17. R.K. Patra, A.S. Dhar, A special coprime array configuration for increased degrees of freedom. Digit. Signal Process. 122, 103369 (2022)

    Article  Google Scholar 

  18. Z. Peng, Y. Ding, S. Ren, X. Wang, Extended transformed nested arrays for DOA estimation of non-circular sources. IEEE Access 8, 162350–162362 (2020)

    Article  Google Scholar 

  19. Z. Peng, Y. Ding, S. Ren, W. Wang, W. Gu, Supplementary coprime array with enhanced DOFs exploiting hole filling strategy based on the difference and sum coarray. Digit. Signal Process. 121, 103325 (2022)

    Article  Google Scholar 

  20. Z. Peng, Y. Ding, S. Ren, H. Wu, W. Wang, Coprime nested arrays for DOA estimation: exploiting the nesting property of coprime array. IEEE Signal Process Lett. 29, 444–448 (2022)

    Article  Google Scholar 

  21. S. Qin, Y.D. Zhang, M.G. Amin, Generalized coprime array configurations for direction-of-arrival estimation. IEEE Trans. Signal Process. 63(6), 1377–1390 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. A. Raza, W. Liu, Q. Shen, Thinned coprime array for second-order difference co-array generation with reduced mutual coupling. IEEE Trans. Signal Process. 67(8), 2052–2065 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  23. R. Roy, T. Kailath, ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 37(7), 984–995 (1989)

    Article  MATH  Google Scholar 

  24. R. Schmidt, Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34(3), 276–280 (1986)

    Article  MathSciNet  Google Scholar 

  25. T.J. Shan, M. Wax, T. Kailath, On spatial smoothing for direction-of-arrival estimation of coherent signals. IEEE Trans. Acoust. Speech Signal Process. 33(4), 806–811 (1985)

    Article  Google Scholar 

  26. Z. Shan, T.S. Yum, A conjugate augmented approach to direction-of-arrival estimation. IEEE Trans. Signal Process. 53(11), 4104–4109 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  27. J. Shi, G. Hu, X. Zhang, H. Zhou, Generalized nested array: optimization for degrees of freedom and mutual coupling. IEEE Commun. Lett. 22(6), 1208–1211 (2018)

    Article  Google Scholar 

  28. W. Si, F. Zeng, C. Zhang, Z. Peng, Improved coprime arrays with reduced mutual coupling based on the concept of difference and sum coarray. IEEE Access 7, 66251–66262 (2019)

    Article  Google Scholar 

  29. P.P. Vaidyanathan, P. Pal, Sparse sensing with co-prime samplers and arrays. IEEE Trans. Signal Process. 59(2), 573–586 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  30. X. Wang, Z. Chen, S. Ren, S. Cao, DOA estimation based on the difference and sum coarray for coprime arrays. Digit. Signal Process. 69, 22–31 (2017)

    Article  Google Scholar 

  31. Y. Wang, W. Wu, X. Zhang, W. Zheng, Transformed nested array designed for DOA estimation of non-circular signals: reduced sum-difference co-array redundancy perspective. IEEE Commun. Lett. 24(6), 1262–1265 (2020)

    Article  Google Scholar 

  32. P. Zhao, G. Hu, Z. Qu, L. Wang, Enhanced nested array configuration with hole-free co-array and increasing degrees of freedom for DOA estimation. IEEE Commun. Lett. 23(12), 2224–2228 (2019)

    Article  Google Scholar 

  33. P. Zhao, K. Wang, G. Hu, L. Wan, Underdetermined DOA estimation using unfold coprime array from the perspective of sum-difference co-array. IEEE Access 7, 168557–168564 (2019)

    Article  Google Scholar 

  34. Z. Zheng, W.Q. Wang, Y. Kong, Y.D. Zhang, M.I.S.C. Array, A new sparse array design achieving increased degrees of freedom and reduced mutual coupling effect. IEEE Trans. Signal Process. 67(7), 1728–1741 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  35. W. Zheng, X. Zhang, Y. Wang, J. Shen, B. Champagne, Padded coprime arrays for improved DOA estimation: Exploiting hole representation and filling strategies. IEEE Trans. Signal Process. 68, 4597–4611 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  36. W. Zheng, X. Zhang, Y. Wang, M. Zhou, Q. Wu, Extended coprime array configuration generating large-scale antenna co-array in massive MIMO system. IEEE Trans. Veh. Technol. 68(8), 7841–7853 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

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

Author information

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

Authors
  1. Rajen Kumar Patra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anindya Sundar Dhar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rajen Kumar Patra.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Patra, R.K., Dhar, A.S. Unfolded Coprime Transformed Nested Arrays for Increased DOF and Negligible Mutual Coupling. Circuits Syst Signal Process 42, 7275–7296 (2023). https://doi.org/10.1007/s00034-023-02438-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-023-02438-8

Keywords

Search

Navigation