Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs

Eweda, Eweda; Bershad, N.J.; Bermudez, J.C.M.

doi:10.1109/tsp.2018.2860552

Cited by 31 publications

(19 citation statements)

References 20 publications

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“…The adaptive filtering algorithm is defined as a filter algorithm capable of adjusting and tracking its own parameters, without knowing the statistical properties of input signals and noises [21][22].…”

Section: Adaptive Filtering Algorithmmentioning

confidence: 99%

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

Yang¹

2020

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Currently, many adaptive filtering algorithms are available for the non-Gaussian environment, namely, least mean square (LMS) algorithm, recursive least square (RLS) algorithm, least mean fourth (LMF) algorithm, and subspace minimum norm (SMN) algorithm. Most of them can converge to the steady-state, but face various constraints in the presence of alpha (α)-stable noises. To solve the problem, this paper aims to develop an adaptive filtering algorithm for non-Gaussian signals in α-stable distribution, drawing on the merits of existing adaptive filtering algorithms. Firstly, the authors introduced the theory of α-stable distribution, the central limit theorem and fractional lower-order statistics (FLOS). Next, two classic adaptive filtering algorithms, RLS and LMS, were summarized, and compared through tests. On this basis, the FLOS-SMN algorithm was designed in the light of the features of the LMS and the SMN, which applies to the filtering of non-Gaussian signals in αstable distribution. Finally, the proposed algorithm was proved as faster, more stable and more adaptable than the traditional method.

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Section: Adaptive Filtering Algorithmmentioning

confidence: 99%

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

Yang¹

2020

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“…But in most of the wireless channel simulation, the channel gain doesn't follow Gaussian distribution. Many system design and simulation need to consider Non-Gaussian noise [5], [6], [7]. Thus many literatures have investigated how to generate colored Non-Gaussian noise.…”

Section: Motivationmentioning

confidence: 99%

Non-Gaussian Colored Noise Generation for Wireless Channel Simulation with Particle Swarm Optimizer

Dai

Abbasi

2020

2020 14th European Conference on Antennas and Propagation (EuCAP)

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Random Variable (RV) with different Probability Density Function (PDF) and Power Spectral Density (PSD) is a critical component for simulation of different wireless channel fading profile. To get a specific PSD for simulation of different multi-path scenario, the usual method is to pass a white noise through a filter with the required shape. But the filtering process will cause the change of random variable's PDF unless the input noise follows Gaussian Distribution. In this paper, a Particle Swarm Optimization (PSO) based method to generate Non-Gaussian noise by a pre-distortion filter and Inverse Transform Sampling (ITS) that meets both the requirement of PSD and PDF is described. As the solution is based on filtering, after the filter weight is found using PSO, the simulation could be carried out in a real-time manner compared to block-based methods. The numerical simulation confirms that it can generate the required PDF and more than 90% similar to the required PSD.

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“…The observation noise z k (n) is assumed to be zero-mean white Gaussian with variance σ 2 z,k . In nonstationary environment, the optimal parameter vector w (n) is modeled as a random walk process [2], [12]:…”

Section: Problem Formulation and Dlmsmentioning

confidence: 99%

“…Therefore, the theoretical analyzes of LMS-type algorithms with cyclostationary white Gaussian inputs attracted substantial research interests as in [6]- [10]. More recently, the stochastic behaviors of the LMS and NLMS algorithms for cyclostationary white non-Gaussian input has been presented in [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Diffusion LMS for Cyclostationary White Non-Gaussian Inputs

Wei

Chen

2019

IEEE Access

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This paper studies the transient behavior of the diffusion least-mean-square (LMS) algorithm over the single-task network for the non-stationary system using diverse types of cyclostationary white non-Gaussian inputs for an individual node. The analytical models of the recursive mean-weight-error vector and mean-square-deviation are derived for the system with random walk varying parameters and the white random process with periodically deterministic time-varying input variance. In addition, the approximated steady-state mean-square-deviation of the diffusion LMS is presented for the slow varying input variance. Monte Carlo simulations show excellent agreement with the theoretical prediction of mean-square-deviation validating the accuracy of derived analytical models and the tracking ability for non-stationary system and cyclostationary inputs simultaneously.INDEX TERMS Diffusion LMS, cyclostationary white non-Gaussian processes, adaptive network, tracking analysis.

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Stochastic Analysis of the LMS and NLMS Algorithms for Cyclostationary White Gaussian and Non-Gaussian Inputs

Cited by 31 publications

References 20 publications

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

Non-Gaussian Colored Noise Generation for Wireless Channel Simulation with Particle Swarm Optimizer

Performance Analysis of Diffusion LMS for Cyclostationary White Non-Gaussian Inputs

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