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Circuits, Systems, and Signal Processing

, Volume 37, Issue 9, pp 3862–3887 | Cite as

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

  • Yong Jia
  • Chuan Chen
  • Xiaoling Zhong
  • Yong Guo
Article

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.

Keywords

Co-prime array Pseudo-beam-forming Difference co-array Side-lobe suppression Coherence weighting factor 

Notes

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.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Yong Jia
    • 1
  • Chuan Chen
    • 1
  • Xiaoling Zhong
    • 1
  • Yong Guo
    • 1
  1. 1.College of Information Science and TechnologyChengdu University of TechnologyChengduChina

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