International Journal of Antennas and Propagation

Volume 2019, Article ID 2131040, 8 pages

https://doi.org/10.1155/2019/2131040

## The Precompression Processing of LMS Algorithm in Noise Elimination

^{1}College of Weaponry Engineering, Naval University of Engineering, Wuhan 430033, China^{2}91278 Unit, Lvshunkou in DaLian 116000, China

Correspondence should be addressed to Chunsheng Lin; moc.361@hz_dna_scl

Received 2 June 2019; Revised 8 August 2019; Accepted 17 August 2019; Published 19 November 2019

Academic Editor: Francisco Falcone

Copyright © 2019 Pengfei Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this study, the authors propose a novel precompression processing (PCP) of the least mean squares (LMS) algorithm based on a regulator factor. The novelty of the PCP algorithm is that the compressed input signals vary from each other on different components at each iteration. The input signal of the improved LMS algorithm is precompressed based on the regulator factor. The precompressed input signal is not only related to the regulator factor *α* and the current value of the input signal at each iteration but also related to the amplitude of the input signal before this iteration. The improved algorithm can eliminate the influence of input signal mutation on the filter performance. In the numerical simulations, we compare the improved LMS algorithm and NLMS algorithm in the cases of normal input signal and input signal with mutation and the influence of different regulator factors on the noise elimination. Results show that the PCP algorithm has good noise elimination effect when the input signal changes abruptly and the regulator factor *α* = 0.01 can meet the requirements.

#### 1. Introduction

Adaptive filters are widely used in system identification, adaptive line spectrum enhancement, echo cancellation, and other fields [1–3]. In signal processing, researchers have been trying to pursue adaptive algorithms with fast convergence speed, good stability, and lower computational complexity. Because of its robustness, low computational complexity, and good convergence to steady-state signals, the least mean squares (LMS) algorithm has widely been used in adaptive filters.

Since the least mean squares (LMS) algorithm was proposed by Widrow and Hoff in 1960, there have been too many researches on variable step size and variable order of the LMS algorithm. In 1997, Gan proposed a new approach in adjusting the step size of the least mean squares (LMS) using the fuzzy logic technique, and the earlier work was extended by giving a complete design methodology and guidelines for developing a reliable and robust fuzzy step size LMS (FSS-LMS) algorithm [4]. In 1999, So proved that bias removal can be achieved by proper scaling of the optimal filter coefficients, and a modified least mean squares (LMS) algorithm is then developed for accurate system identification in noise [5]. And Keratiotis and Lind proposed an optimum time-varying step-size sequence for adaptive filters employing the least mean squares algorithm [6]. In 2013, Kang et al. proposed a new bias-compensated normalized least mean squares (NLMS) algorithm for parameter estimation with a noisy input. The algorithm is obtained from an approximated cost function based on the statistical properties of the input noise, and a condition checking constraint is involved to decide whether the weight coefficient vector must be updated [7]. In 2016, Huang et al. proposed a novel component-wise variable step-size (CVSS) diffusion distributed algorithm for estimating a specific parameter over sensor networks [8]. In 2018, Wu et al. proposed a multistage least mean squares (MLMS) algorithm based on polynomial fitting in time-varying systems [9].

The LMS algorithm has greatly been improved according to different applications. In noise elimination, the input signal sequence may mutate, the conventional LMS algorithm will be greatly affected in this case, and the impact of mutation signal on the filter cannot be eliminated, thus affecting the filtering effect. And the NLMS algorithm has good adaptability to local signal fluctuation, but it cannot judge the big mutation of an individual signal very well. The precompression processing (PCP) of the least mean squares (LMS) algorithm based on a regulator factor can reduce the effect of signal mutation on the noise filtering well. The simulation results show that regardless of the degree of signal mutation, the improved LMS algorithm can eliminate the impact of mutation, while other algorithms will be seriously affected by the mutation signal. And the improved LMS algorithm has good noise filtering effect compared with other algorithms. The advantages of the improved LMS algorithm eliminating the mutational signal are obvious.

#### 2. The LMS Algorithm

In 1960, Widrow and Hoff proposed the least mean squares (LMS) algorithm, which uses instantaneous values to estimate gradient vectors [11, 11]. The obvious advantage of the LMS is that the algorithm is simple, and it does not need to calculate the correlation matrix and inverse matrix. At the same time, it easily achieves stability and robustness because of which it is widely used [12, 13].

##### 2.1. The Main Rationale of the LMS Algorithm

The structure of the LMS adaptive filter is shown in Figure 1 [14].