### Abstract

Standard least mean square/fourth (LMS/F) is a classical adaptive algorithm that combined the advantages of both least mean square (LMS) and least mean fourth (LMF). The advantage of LMS is fast convergence speed while its shortcoming is suboptimal solution in low signal-to-noise ratio (SNR) environment. On the contrary, the advantage of LMF algorithm is robust in low SNR while its drawback is slow convergence speed in high SNR case. Many finite impulse response systems are modeled as sparse rather than traditionally dense. To take advantage of system sparsity, different sparse LMS algorithms with l_{p}-LMS and l_{0}-LMS have been proposed to improve adaptive identification performance. However, sparse LMS algorithms have the same drawback as standard LMS. Different from LMS filter, standard LMS/F filter can achieve better performance. Hence, the aim of this paper is to introduce sparse penalties to the LMS/F algorithm so that it can further improve identification performance. We propose two sparse LMS/F algorithms using two sparse constraints to improve adaptive identification performance. Two experiments are performed to show the effectiveness of the proposed algorithms by computer simulation. In the first experiment, the number of nonzero coefficients is changing, and the proposed algorithms can achieve better mean square deviation performance than sparse LMS algorithms. In the second experiment, the number of nonzero coefficient is fixed, and mean square deviation performance of sparse LMS/F algorithms is still better than that of sparse LMS algorithms.

Original language | English |
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Pages (from-to) | 1649-1658 |

Number of pages | 10 |

Journal | Wireless Communications and Mobile Computing |

Volume | 15 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2015 Aug 25 |

### Keywords

- adaptive system identification
- l<inf>0</inf>-norm LMS/F
- l<inf>p</inf>-norm LMS/F
- least mean fourth
- least mean square
- least mean square/fourth (LMS/F)
- sparse penalty

### ASJC Scopus subject areas

- Information Systems
- Computer Networks and Communications
- Electrical and Electronic Engineering

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## Cite this

*Wireless Communications and Mobile Computing*,

*15*(12), 1649-1658. https://doi.org/10.1002/wcm.2453