Modelagem Estocástica: Teoria, Formulação e Aplicações do Algoritmo LMS

Abstract

In this dissertation we present a research in aspects of stochastic modeling, convergence and applications of least mean square (LMS) algorithm, normalized least mean square (NLMS) algorithm and proportionate normalized least mean square (PNLMS) algorithm. Specifically, the aim is to address the LMS algorithm in your extension, defining his concepts, demonstrations of properties, algorithms and analysis of convergence, Learning Curve and Misadjustment of the algorithm in question. Within of the context of sensor networks and spatial filtering is evaluated the performance of the algorithms by the learning curve of the referred algorithms for arrangements of adaptive antennas. In the intrinsic context of the application in electrical engineering, in area of telecommunications that seek the best alternative and aims to optimize the process of transmission/reception to eliminate interference, and the least amount of elements in adaptive antenna arrays, which they are known as smart antenna, which aims to reach a signal noise ratio for small value, with appropriate number of elements. The performance of the LMS algorithm is evaluated in sensor networks that is characterized by an antenna array. Results of computer simulations for different scenarios of operation show that the algorithms have good numerical results of convergence to a suitable choice of the parameters related with the rate of learning that are associated with their average curves and the beamforming of the smart antenna array.