Exact expectation analysis of the deficient-length LMS algorithm

Nonstationary environments are ubiquitous in communications and acoustic systems. The ability to track their dynamics is one of the most desirable features of adaptive processing algorithms. The designers of these algorithms employ guidelines derived from stochastic analyses to adjust user-defined parameters to maximize performance or avoid stability issues. It is therefore important that analyzes of adaptive processing algorithms take into account the built-in sophisticated learning capabilities. This work presents a comprehensive model of the performance of the least mean square algorithm, operating under Markovian time-varying channels. Our advanced analysis considers both transient and steady-state regimes. Furthermore, in our analysis, the popular independence assumption is not adopted, resulting in a stochastic model which is accurate even when: (i) the step size is not infinitesimally small; or (ii) when the unknown system presents a high nonstationary degree. In addition, our evaluation is also able to provide a deterministic theoretical step-size sequence that optimizes algorithmic performance, as well as an accurate step size upper bound that guarantees algorithm stability. Computer simulations performed are in accordance with our theoretical predictions.

An Exact Expectation Model for the LMS Tracking Abilities

This paper offers a hybrid analytical and estimation based technique to determine the photovoltaic (PV) system parameter in a systematic way. The new model formulation is based on the datasheet parameters under standard test condition and normal operating cell temperature environment, forming the analytical approach's foundation. The estimation part is based on the adaptive filtering algorithm, which shows superiority in estimated parameters compared to existing techniques applied in the photovoltaic system. The proposed approach is made available for a single diode PV model and scaled up aggregated model in extracting the model parameters of two real PV modules in the market, representing the exact <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> - <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> characteristics of the manufacturer datasheet. A rigorous comparative analysis is carried out between two adaptive and two optimization based estimations for performance evaluation and recommendation purposes. 

A Novel Adaptive Filtering Algorithm Based Parameter Estimation Technique for Photovoltaic System

This paper provides a detailed overview of active impulsive noise control (AINC) technology of α-stable distribution noise. The second-order moment of the non-Gaussian impulsive noise does not exist, so the adaptive algorithms based on second-order statistics would lead to poor noise reduction performance. On account of this defect, a series of AINC algorithms have been proposed over the past 25 years. In this paper, we briefly classified the AINC algorithms into the classic algorithms and the expanded algorithms depending on different criteria, and both the classic AINC algorithms and the expanded AINC algorithms are further divided. Afterward, we introduced the principles and characteristics of different AINC algorithms and listed the weights update formulas of those algorithms. Finally, the computational complexity comparisons of common AINC algorithms and further recommendations are given, and a brief review about the experimental testing of AINC systems is provided in order to assist related scholars to carry out AINC researches more conveniently.

Review on Active Noise Control Technology for α-Stable Distribution Impulsive Noise

Due to the inherent feedback feature of adaptive filtering algorithms, a comprehensive theoretical understanding of their learning process is still challenging. In order to make the mathematics tractable, most stochastic analyses adopt simplifications. One of these is the independence assumption, which presumes statistical independence between adaptive weights and input signal samples. Furthermore, the additive noise is usually assumed to be white, although it may not be the case in practice. This paper advances a novel theoretical model of the least-mean-square adaptive filter that, under the independence assumption, does not presume a white noise signal. Additionally, a theoretical result is established which implies that the stability properties of such an adaptive filter are not influenced by noise coloring. Such a result does not employ the above-mentioned assumptions, i.e., it is valid for both colored noise and non-infinitesimally small step size values. An optimal step-size sequence that minimizes the mean-square deviation and takes into account the stochastic coupling of the excitation data and adaptive weights is proposed. It is noteworthy that such a design does not induce divergence in practice and does not assume, for the first time, a white measurement noise. The theoretical contributions are confirmed by simulations.

Advances on the analysis of the LMS algorithm with a colored measurement noise

The choice of a fixed step size in adaptive filtering algorithms implies a conflict between the convergence rate and the steady-state performance. In order to address this tradeoff more effectively, variable step-size schemes have been proposed. The efficiency evaluation of such techniques requires comparisons of the resulting step-size values with theoretical optimum values obtained from a statistical analysis of the adaptive algorithm convergence. The analysis generally employs statistical approximations, the most critical being the assumption of independence between the input signal and the filter coefficients. In this letter, it is argued that such a comparison can be misleading because the supposedly optimal step-size sequence sometimes induces divergence in the initial phase of learning. This occurs most often when the input signal is colored and/or heavy tailed. This instability trend can be explained by a convergence analysis that does not employ the independence hypothesis. In addition, the use of this exact analysis implies an optimal step-size sequence that can be significantly different from that obtained with standard analysis methods. This approach can be used to improve the design process of variable step-size adaptive filtering algorithms.

Exact Expectation Evaluation and Design of Variable Step-Size Adaptive Algorithms

The adjustable weights of adaptive filtering algorithms are usually assumed to obey a Gaussian distribution. This is somewhat natural under maximal-entropy considerations, since most analyses in the open literature only take into account first-and second-order statistics. This work investigates the third-order statistical feature known as skewness of the least mean square parameters distribution. Two theoretical analyses for skewness estimation are proposed: i ) one that employs the independence assumption, which states that the excitation data is statistically independent from the adaptive weights; ii ) one derived from the exact expectation analysis, a method that is able to predict the learning capabilities of the least mean square algorithm even when the step size is not infinitesimally small. This brief shows that the skewness of the adaptive weights distribution may present a large deviation from the common Gaussian assumption, especially in the first phase of the learning. Furthermore, it is also demonstrated that the skewness may grow without limit even when adaptive weights present convergence in both average and mean square behaviors.

Filipe Igreja

Papers

Exact Expectation Evaluation and Design of Variable Step-Size Adaptive Algorithms

An Exact Expectation Model for the LMS Tracking Abilities

On the Skewness of the LMS Adaptive Weights

Analysis of the least mean squares algorithm with reusing coefficient vector