Source Number Estimation and Effective Channel Order Determination Based on Higher-Order Tensors

  • Yuan Xie
  • Kan Xie
  • Shengli XieEmail author
Short Paper


Source number estimation is an essential task in underdetermined convolutive blind source separation, and effective channel order determination is also a challenging issue. For solving the two problems, the classical methods are based on information theoretic criteria. However, these are prone to the underestimation and overestimation of the number of sources in the underdetermined case. To compensate for this shortcoming, in this paper we propose two algorithms based on higher-order tensors. First, an improved algorithm is presented to estimate the number of sources. By transforming the tensor into a matrix, the eigenvalues of the resultant matrices are used to estimate the number of sources. Additionally, we employ higher-order tensors to detect the effective channel order and confirm the relationship between the number of sources and the effective channel order in the convolutive mixture model. Finally, a series of simulation experiments demonstrate that the proposed algorithms have an advantage over the conventional methods.


Source number estimation Effective channel order determination Information theoretic criteria Higher-order tensors 



The authors would like to thank the anonymous reviewers for their insightful comments and helpful critiques of the manuscript that helped improve this paper. This work was partially supported by the National Natural Science Foundation of China (Grants 501170112, 501180011, 503160116, 61773128, 61673126, U1701261). Additionally, this work was partially supported by the Postdoctoral Science Foundation of China (2018M643022). Natural Science Foundation of Hebei province (E2016106018).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AutomationGuangdong University of TechnologyGuangzhouChina
  2. 2.Guangdong Key Laboratory of IoT Information ProcessingGuangzhouChina
  3. 3.Key Laboratory of Ministry of EducationGuangzhouChina
  4. 4.State Key Laboratory of Precision Electronic Manufacturing Technology and EquipmentGuangzhouChina

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