The least mean square (LMS) algorithm is widely expected to operate near the corresponding Wiener filter solution. An exception to this popular perception occurs when the algorithm is used to adapt a transversal equalizer in the presence of additive narrowband interference. The steady-state LMS equalizer behavior does not correspond to that of the fixed Wiener equalizer: the mean of its weights is different from the Wiener weights, and its mean squared error (MSE) performance may be significantly better than the Wiener performance. The contributions of this study serve to better understand this so-called non-Wiener phenomenon of the LMS and normalized LMS adaptive transversal equalizers. The first contribution is the analysis of the mean of the LMS weights in steady state, assuming a large interference-to-signal ratio (ISR). The analysis is based on the Butterweck expansion of the weight update equation. The equalization problem is transformed to an equivalent interference estimation problem to make the analysis of the Butterweck expansion tractable. The analytical results are valid for all step-sizes. Simulation results are included to support the analytical results and show that the analytical results predict the simulation results very well, over a wide range of ISR. The second contribution is the new MSE estimator based on the expression for the mean of the LMS equalizer weight vector. The new estimator shows vast improvement over the Reuter-Zeidler MSE estimator. For the development of the new MSE estimator, the transfer function approximation of the LMS algorithm is generalized for the steady-state analysis of the LMS algorithm. This generalization also revealed the cause of the breakdown of the MSE estimators when the interference is not strong, as the assumption that the variation of the weight vector around its mean is small relative to the mean of the weight vector itself. Both the expression for the mean of the weight vector and for the MSE estimator are analyzed for the LMS algorithm at first. The results are then extended to the normalized LMS algorithm by the simple means of adaptation step-size redefinition. / Ph. D.

Submitted by Cristiane Chim (cristiane.chim@ucpel.edu.br) on 2018-05-08T17:34:22Z No. of bitstreams: 1 Vagner Guidotti Furtado (1).pdf: 2942442 bytes, checksum: a43c18ecb28456284d4b6c622f11210d (MD5) / Made available in DSpace on 2018-05-08T17:34:22Z (GMT). No. of bitstreams: 1 Vagner Guidotti Furtado (1).pdf: 2942442 bytes, checksum: a43c18ecb28456284d4b6c622f11210d (MD5) Previous issue date: 2017-12-07 / The division operation in digital systems has its relevance because it is a necessary function in several applications, such as general purpose processors, digital signal processors and microcontrollers. The digital divider circuit is of great architectural complexity and may occupy a considerable area in the design of an integrated circuit, and as a consequence may have a great influence on the static and dynamic power dissipation of the circuit as a whole. In relation to the application of dividing circuits in circuits of the Digital Signal Processing (DSP) area, adaptive filters have a particular appeal, especially when using algorithms that perform a normalization in the input signals. In view of the above, this work focuses on the proposition of algorithms, techniques for reducing energy consumption and logical area, proposition and implementation of efficient dividing circuit architectures for use in adaptive filters. The Newton-Raphson and Goldschmidt iterative dividing circuits both operating at fixed-point were specifically addressed. The results of the synthesis of the implemented architectures of the divisors with the proposed algorithms and techniques showed considerable reduction of power and logical area of the circuits. In particular, the dividing circuits were applied in adaptive filter architectures based on the NLMS (Normalized least Mean Square) algorithm, seeking to add to these filters, characteristics of good convergence speed, combined with the improvement in energy efficiency. The adaptive filters implemented are used in the case study of harmonic cancellation on electrocardiogram signals / A operação de divisão em sistemas digitais tem sua relevância por se tratar de uma função necessária em diversas aplicações, tais como processadores de propósito geral, processadores digitais de sinais e microcontroladores. O circuito divisor digital é de grande complexidade arquitetural, podendo ocupar uma área considerável no projeto de um circuito integrado, e por consequência pode ter uma grande influência na dissipação de potência estática e dinâmica do circuito como um todo. Em relação à aplicação de circuitos divisores em circuitos da área DSP (Digital Signal Processing), os filtros adaptativos têm um particular apelo, principalmente quando são utilizados algoritmos que realizam uma normalização nos sinais de entrada. Diante do exposto, este trabalho foca na proposição de algoritmos, técnicas de redução de consumo de energia e área lógica, proposição e implementação de arquiteturas de circuitos divisores eficientes para utilização em filtros adaptativos. Foram abordados em específico os circuitos divisores iterativos Newton-Raphson e Goldschmidt ambos operando em ponto-fixo. Os resultados da síntese das arquiteturas implementadas dos divisores com os algoritmos e técnicas propostas mostraram considerável redução de potência e área lógica dos circuitos. Em particular, os circuitos divisores foram aplicados em arquiteturas de filtros adaptativos baseadas no algoritmo NLMS (Normalized least Mean Square), buscando agregar a esses filtros, características de boa velocidade de convergência, aliada à melhoria na eficiência energética. Os filtros adaptativos implementados são utilizados no estudo de caso de cancelamento de harmônicas em sinais de eletrocardiograma (ECG)

Made available in DSpace on 2016-08-17T14:52:41Z (GMT). No. of bitstreams: 1 Dissertacao-WilanderTestonePereiraSilva.pdf: 3903191 bytes, checksum: b91ff906a27937df64d75b330c6ea137 (MD5) Previous issue date: 2016-03-11 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / 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. / Nesta dissertação de mestrado apresenta-se uma investigação em aspectos de modelagem estocástica, convergência e aplicações dos algoritmos de mínimos quadrados médio (LMS), mínimos quadrados médio normalizado (NLMS) e mínimos quadrados médio normalizado proporcional (PNLMS). Particularmente, aborda-se o Algoritmo LMS em sua extensão, definindo conceitos, demonstrações de propriedades, algoritmos e análise de convergência, Curva de Aprendizagem e Desajuste do referido algoritmo. Dentro do contexto de redes de sensores e filtragem espacial avalia-se o desempenho dos algoritmos por meio da curva de aprendizagem dos referidos algoritmos para os arranjos de antenas adaptativas. No contexto intrínseco da aplicação em engenharia elétrica, isto é, na área de telecomunicações procura-se a melhor alternativa e almeja-se a otimização do processo de transmissão/recepção para eliminar interferências e a menor quantidade de elementos em arranjos de antenas adaptativas, que são conhecidas como antenas inteligentes, e que tem como objetivo atingir uma relação Sinal Ruído para valor pequeno, com número adequado de elementos. O desempenho do algoritmo LMS é avaliado em redes de sensores que é caracterizada por um arranjo de antenas. Resultados de simulações computacionais para diferentes cenários de operação mostram que os algoritmos apresentam bons resultados numéricos de convergência para uma escolha adequada dos parâmetros relacionados com a taxa de aprendizagem que são associadas com suas curvas médias e com a conformação de feixes do arranjo em antenas inteligentes.