Circuits, Systems, and Signal Processing

, Volume 38, Issue 4, pp 1889–1906 | Cite as

A Mixing Matrix Estimation Algorithm for the Time-Delayed Mixing Model of the Underdetermined Blind Source Separation Problem

  • Fang Ye
  • Jie Chen
  • Lipeng GaoEmail author
  • Wei Nie
  • Qian Sun
Short Paper


Considering the time-delayed mixing model of the underdetermined blind source separation problem, we propose a novel mixing matrix estimation algorithm in this paper. First, we introduce the short-time Fourier transform (STFT) to transform the mixed signals from the time domain to the time–frequency domain. Second, a neoteric transformation matrix is addressed to construct the linear clustering property of STFT coefficients. Then, a preeminent detection algorithm is raised to identify the single source points. After eliminating the low-energy points and outliers in the time–frequency domain, a potential function of clustering approach is put forward to cluster the single source points and obtain the clustering centers. Finally, the mixing matrix can be estimated through the derivation and calculation. The experimental results validate that the proposed algorithm not only accurately estimates the mixing matrix for the time-delayed mixing model of the underdetermined blind source separation problem but also has certain universality for different array structures. Therefore, both the effectiveness and superiority of the proposed algorithm have been verified.


Time-delayed mixing model Underdetermined blind source separation Mixing matrix estimation Single source points 



The paper is funded by the National Natural Science Foundation of China (No. 61701134), the Natural Science Foundation of Heilongjiang Province, China (No. F2017004), and the National Key Research and Development Program of China (No. 2016YFF0102806). Moreover, this work is supported by the Fundamental Research Funds for the Central Universities of China (Nos. HEUCFM180801, HEUCFM180802), and the Ph.D. Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities of China (No. HEUGIP201708).


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

Authors and Affiliations

  1. 1.College of Information and Communication EngineeringHarbin Engineering UniversityHarbinChina

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