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Steady-State Performance Analysis of Quaternion-Valued Least Mean Square Adaptive Algorithm

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Communications, Signal Processing, and Systems (CSPS 2018)

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 517))

Abstract

The quaternion-valued least mean squares (QvLMS) adaptive algorithm has been proved valid for the adaptive filtering in quaternion domain. However, there have been few researches on its performance. This paper firstly deduces the energy conservation relation in quaternion domain and then analyzes the steady-state performance of QvLMS algorithm in stationary and non-stationary environment by using the quaternion energy conservation relation. The relevant expressions are deduced and then the step-size range which can guarantee the algorithm convergence is obtained. Simulation results demonstrate the rationality of the analysis.

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References

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61301228, 61501223 and the Fundamental Research Funds for the Central Universities under Grant 3132016331 and 3132016318.

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Authors and Affiliations

  1. Department of Information Science and Technology, Dalian Maritime University, Dalian, China

    Sen Li, Fengzhi Liu, Bin Lin & Rongxi He

  2. College of Computer Science and Technology, Nanjing Tech University, Nanjing, China

    Xiaomei Zhu

Authors
  1. Sen Li
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  2. Fengzhi Liu
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  3. Bin Lin
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  4. Rongxi He
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  5. Xiaomei Zhu
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Corresponding author

Correspondence to Sen Li .

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Editors and Affiliations

  1. Department of Electrical Engineering, University of Texas at Arlington, Arlington, TX, USA

    Qilian Liang

  2. School of Information and Communication Engineering, Dalian University of Technology, Dalian, China

    Xin Liu

  3. School of Information Science and Technology, Dalian Maritime University, Dalian, China

    Zhenyu Na

  4. College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin, China

    Wei Wang

  5. College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin, China

    Jiasong Mu

  6. College of Electronic and Communication Engineering, Tianjin Normal University, Tianjin, China

    Baoju Zhang

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Li, S., Liu, F., Lin, B., He, R., Zhu, X. (2020). Steady-State Performance Analysis of Quaternion-Valued Least Mean Square Adaptive Algorithm. In: Liang, Q., Liu, X., Na, Z., Wang, W., Mu, J., Zhang, B. (eds) Communications, Signal Processing, and Systems. CSPS 2018. Lecture Notes in Electrical Engineering, vol 517. Springer, Singapore. https://doi.org/10.1007/978-981-13-6508-9_28

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  • DOI: https://doi.org/10.1007/978-981-13-6508-9_28

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-6507-2

  • Online ISBN: 978-981-13-6508-9

  • eBook Packages: EngineeringEngineering (R0)

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