Behavior of the LMS algorithm with hyperbolic secant cost
This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal the behavior of the proposed algorithm. The transient analysis is conducted based on a Taylor expansion approach and energy conservation (EC)...
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| Published in | Journal of the Franklin Institute Vol. 357; no. 3; pp. 1943 - 1960 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elmsford
Elsevier Ltd
01.02.2020
Elsevier Science Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0016-0032 1879-2693 0016-0032 |
| DOI | 10.1016/j.jfranklin.2019.12.040 |
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| Abstract | This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal the behavior of the proposed algorithm. The transient analysis is conducted based on a Taylor expansion approach and energy conservation (EC) relation expression. Following the results of transient state analysis of excess means square-error (EMSE), we achieve the steady-state EMSE and mean-square deviation (MSD) expressions of the proposed algorithm. Moreover, the sufficient condition for the stability convergence is given. Simulation results validate the theoretical analyses and demonstrate the enhanced performance of the proposed algorithm as compared with conventional LMS algorithm in the presence of white Gaussian noise (WGN) and uniform noise. |
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| AbstractList | This paper presents a new least mean square (LMS) algorithm with defining hyperbolic secant cost function. Then, the detailed analysis is conducted to reveal the behavior of the proposed algorithm. The transient analysis is conducted based on a Taylor expansion approach and energy conservation (EC) relation expression. Following the results of transient state analysis of excess means square-error (EMSE), we achieve the steady-state EMSE and mean-square deviation (MSD) expressions of the proposed algorithm. Moreover, the sufficient condition for the stability convergence is given. Simulation results validate the theoretical analyses and demonstrate the enhanced performance of the proposed algorithm as compared with conventional LMS algorithm in the presence of white Gaussian noise (WGN) and uniform noise. |
| Author | Zheng, Zongsheng Chen, Lihui Lu, Lu Yu, Yi Yang, Xiaomin |
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| SubjectTerms | Algorithms Computer simulation Cost analysis Cost function Energy conservation Error analysis Hyperbolic functions Mean square errors Noise Performance enhancement Random noise Stability analysis Taylor series Transient analysis |
| Title | Behavior of the LMS algorithm with hyperbolic secant cost |
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