Skip to main content
Log in

Pseudo-beam-Forming for Direction-of-Arrival Estimation with Difference Co-array of Co-prime Array

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

Abstract

This paper focuses on direction finding using a co-prime array from the view of a difference co-array. According to the corresponding relationship between the correlation lag and virtual element position of the difference co-array, from the correlation matrix of the co-prime array, the desired correlation units are extracted as single-snapshot data of the virtual co-array elements of the co-prime array and are then coherently accumulated into a pseudo-beam pattern. Because the difference co-array of a co-prime array consists of a group of contiguous virtual elements and multiple non-uniform virtual elements, this paper considers pseudo-beam-forming using only contiguous virtual elements, as in existing studies, and all of the virtual elements. Compared with the existing sub-beam multiplication method, pseudo-beam-forming reduces the negative effect from grating lobes and resolves more uncorrelated sources than the number of physical elements. Moreover, application of non-uniform virtual elements improves the resolvable source number, angle resolution and noise immunity, which are analyzed quantitatively based on the proposed distribution characteristic of virtual elements. Finally, to suppress side-lobe interference caused by the non-uniform virtual elements, we introduce and evaluate three coherence weighting factors, namely coherence factor (CF), phase coherence factor (PCF) and sign coherence factor (SCF), where CF is proved to be ineffective and SCF is optimal in suppression and computation performance.

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

Access this article

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
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

References

  1. K. Adhikari, J.R. Buck, K.E. Wage, Beamforming with extended co-prime sensor arrays, in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (Canada, 2013), pp 4183–4186

  2. K. Adhikari, J.R. Buck, K.E. Wage, Extending coprime sensor arrays to achieve the peak side lobe height of a full uniform linear array. EURASIP J. Adv. Signal Process. 148, 1–17 (2014)

    Google Scholar 

  3. G.S. Bloom, S.W. Golomb, Application of numbered undirected graphs. Proc. IEEE 65, 562–570 (1977)

    Article  Google Scholar 

  4. E. BouDaher, F. Ahmad, M.G. Amin, Sparse reconstruction for direction-of-arrival estimation using multi-frequency co-prime arrays. EURASIP J. Adv. Signal Process. 168, 1–11 (2014)

    Google Scholar 

  5. E. BouDaher, Y. Jia, F. Ahmad, M.G. Amin, Direction-of-arrival estimation using multi-frequency co-prime arrays, in 22nd European Signal Processing Conference (Portugal, 2014), pp 1034–1038

  6. E. BouDaher, Y. Jia, F. Ahmad, M.G. Amin, Multi-frequency co-prime arrays for high-resolution direction-of-arrival estimation. IEEE Trans. Signal Process. 63, 3797–3808 (2015)

    Article  MathSciNet  Google Scholar 

  7. D. Bush, N. Xiang, J.E. Summers, Experimental investigations on coprime microphone arrays for direction-of-arrival estimation. J. Acoust. Soc. Am. 136, 2214 (2014)

    Article  Google Scholar 

  8. D. Bush, N. Xiang, Broadband implementation of coprime linear microphone arrays for direction of arrival estimation. J. Acoust. Soc. Am. 138, 447–456 (2015)

    Article  Google Scholar 

  9. R.J. Burkholder, K.E. Browne, Coherence factor enhancement of through-wall radar images. IEEE Antennas Wirel. Propag. Lett. 9, 842–845 (2010)

    Article  Google Scholar 

  10. J. Camacho, M. Parrilla, C. Fritsch, Grating-lobes reduction by application of phase coherence factors, in 2009 IEEE International Ultrasonics Symposium (Italy, 2009), pp 341–344

  11. J. Camacho, M. Parrilla, C. Fritsch, Phase coherence imaging. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 56, 958–974 (2009)

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Y. Ma, B. Chen, M. Yang, Y. Wang, A novel ESPRIT-based algorithm for DOA estimation with distributed subarray antenna. Circuits Syst. Signal Process. 34, 2951–2972 (2015)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. P. Pal, P.P. Vaidyannathan, Coprime sampling and the MUSIC algorithm, in 2011 Digital Signal Processing and Signal Processing Education Meeting (Sedona, AZ, 2011), pp 289–294

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

    Article  MathSciNet  Google Scholar 

  18. Q. Shen, W. Liu, W. Cui, S. Wu, Y.D. Zhang, M.G. Amin, Low-complexity direction-of-arrival estimation based on wideband co-prime arrays. IEEE/ACM Trans. Audio Speech Lang. Process. 23, 1445–1456 (2015)

    Article  Google Scholar 

  19. P. Stoica, A. Nehorai, MUSIC, maximum likelihood, and Cramer–Rao bound. IEEE Trans. Acoust. Speech Signal Process. 37, 720–741 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  20. P. Stoica, A. Nehorai, MUSIC, maximum likelihood, and Cramer–Rao bound: further results and comparisons. IEEE Trans. Acoust. Speech Signal Process. 38, 2140–2150 (1990)

    Article  Google Scholar 

  21. Z. Tan, Y.C. Eldar, A. Nehorai, Direction of arrival estimation using co-prime arrays: a super resolution viewpoint. IEEE Trans. Signal Process 62, 5565–5576 (2014)

    Article  MathSciNet  Google Scholar 

  22. P.P. Vaidyannathan, P. Pal, Sparse sensing with co-prime samplers and arrays. IEEE Trans. Signal Process 59, 573–586 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. N. Xiang, D. Bush, J.E. Summers, Experimental validation of a coprime linear microphone array for high-resolution direction-of-arrival measurements. J. Acoust. Soc. Am. 137, 261–266 (2015)

    Article  Google Scholar 

  24. K. Yang, Z. Zhao, J. Liu, Q. Liu, Robust adaptive beamforming using an iterative FFT algorithm. Signal Process. 96, 253–260 (2014)

    Article  Google Scholar 

  25. J. Yang, G. Liao, J. Li, Robust adaptive beamforming in nested array. Signal Process. 114, 143–149 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their valuable comments. This work is supported financially by the National Natural Science Foundation of China under Grants 61501062, 41574136 and 41304117 and the Program of Sichuan Education Department under Grant 15ZB0082.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yong Jia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jia, Y., Chen, C., Zhong, X. et al. Pseudo-beam-Forming for Direction-of-Arrival Estimation with Difference Co-array of Co-prime Array. Circuits Syst Signal Process 37, 3862–3887 (2018). https://doi.org/10.1007/s00034-017-0741-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-017-0741-0

Keywords

Navigation