Adaptive weighted least squares algorithm for Volterra signal modeling

Published versio

Blind identification of bilinear systems

Journal ArticleAbstract-This paper is concerned with the blind identification of a class of bilinear systems excited by non-Gaussian higher order white noise. The matrix of coefficients of mixed input-output terms of the bilinear system model is assumed to be triangular in this work. Under the additional assumption that the system output is corrupted by Gaussian measurement noise, we derive an exact parameter estimation procedure based on the output cumulants of orders up to four. Results of the simulation experiments presented in the paper demonstrate the validity and usefulness of our approach

Nonlinear system identification using deterministic multilevel sequences

Bu çalışmada sınırlı doğrusalsızlık derecesine sahip Volterra süzgeçleri için yeni bir gösterilim geliştirilmektedir. Bu gösterilim kullanılarak Volterra süzgeçleri için kesin bir tanılama yöntemi sunulmaktadır. Bu yeni yöntem, giriş işareti olarak farklı seviyelere sahip impulslardan oluşan gerekirci diziler kullanmaktadır. Yeni tanılama yöntemi doğrusal, zamanla-değişmez sistemlerdeki birim impuls cevabının doğrusal olmayan sistemlere başarılı bir uyarlaması olarak düşünülebilir. Çalışmada sunulan tanılama yöntemi kesindir; böylece gözlem gürültüsü olmadığında Volterra çekirdeklerini hatasız kestirmektedir. Bilgisayar benzetimleriyle tanılama yönteminin literatürde yakın zamanda sunulmuş olan yöntemlerden daha iyi kestirim sonuçları verdiği gösterilmiştir.Anahtar Kelimeler: Doğrusal olmayan sistem tanılama, Volterra süzgeçleri.In this paper we develop a new representation for the finite-order Volterra filters. This representation introduces a novel partitioning of the Volterra kernels.Using this representation, we formulate a novel exact identification method for Volterra filters, which uses deterministic sequences consisting of impulses with distinct levels. The identification method might be considered as a successful extension of the impulse response of the linear, time-invariant systems to the realm of nonlinear systems. The developed method indeed includes identification using the unit impulse response as a subcase when the system under consideration is a linear system. Our identification method is exact; hence, it calculates the exact Volterra kernels in the absence of noise for very short length input sequences. Our method calculates each Volterra kernel individually. The kernel estimates are not utilized in the calculation of further kernel estimates. This property hinders error propagation among kernel estimates. Our method calculates directly the Volterra kernels, instead of calculating first some intermediary representation such as the Wiener kernels, which do not have any directly interpretable results. Our method does not introduce and identify any kernels which are redundant for the regular Volterra filter. We demonstrate with simulations that the identification algorithm can produce better parameter estimates than some most recent algorithms in the literature. Keywords: Nonlinear system identification, Volterra filters

Contribuição ao estudo do impacto das não linearidades nos sistemas de telecomunicações

Doutoramento em Engenharia ElectrotécnicaEsta tese insere-se na área de Electrónica de Rádio Frequência e Microondas e visa o desenvolvimento de ferramentas que permitam a melhor compreensão e análise do impacto da distorção não linear produzida em amplificadores de potência no desempenho de um sistema de telecomunicações sem fios. Devido à crescente complexidade dos amplificadores a simulação baseada em representações de circuito equivalente tornou-se extremamente pesada do ponto de vista computacional. Assim têm surgido várias técnicas de simulação de sistemas baseadas em modelos comportamentais, ou seja, que tentam aproximar a resposta do sistema a um sinal de entrada, independentemente dos elementos físicos que implementam o circuito. Neste trabalho foram estudadas as principais técnicas de modelação comportamental existentes assim como as principais características de um amplificador de potência que o modelo comportamental deve ser capaz de prever. Uma nova formulação de um modelo comportamental baseado na série de Volterra é apresentada em conjunto com o método de extracção ortogonal dos seus coeficientes. A principal vantagem deste novo método de extracção é permitir a determinação independente de cada valor coeficiente na série, garantindo-se deste modo um modelo com uma capacidade de aproximação óptima. A determinação dos coeficientes na série de modo independente é conseguida com base na reorganização dos termos da série e na identificação ortogonal de cada componente de saída. Adicionalmente, a identificação das componentes de saída de uma não linearidade é ainda utilizada na definição de uma métrica que permite avaliar de modo simples qual é a degradação imposta à qualidade do sinal ao ser passado num amplificador não linear. Esta métrica contabiliza simultaneamente a degradação imposta pelo ruído e pela distorção.This thesis is related to the RF and Microwave Electronics field and the main goal of this thesis is to develop tools that can contribute to understand and analyse the impact of nonlinear distortion generated by power amplifiers on wireless communication systems. Due to the growing complexity of amplifiers, equivalent circuit based simulations become a heavy computational task due to the large number of nonlinear elements to account for. So, several system simulation techniques have been proposed based on behavioural modelling, that is, models that can approximate the system’s response to a given input signal regardless of the physical circuit implementation description. In this thesis, the most important behavioural modelling techniques have been studied as well as the main power amplifier characteristics that the behavioural model should account for. A new formulation of a Volterra series based behavioural model is presented as well as the corresponding coefficient orthogonal extraction procedure. The main advantage of this new extraction method is to allow the independent determination of the exact value of each coefficient, guaranteeing this way an optimum approximation condition. The exact coefficient determination is achieved by reorganizing the series terms to reach independent subsets and by identifying separately each of systems’ output components. In addition, nonlinearity output component separation is also used to define a Figure of Merit that allows the simple evaluation of signal quality degradation when passed through a nonlinear amplifier. This Figure takes into account simultaneously the impact of noise and distortion.FCTFS

Nonlinear System Identification Using Gaussian Inputs

This paper is concerned with the identification of nonlinear systems represented by Volterra expansions and driven by stationary, zero mean Gaussian inputs, with arbitrary spectra that are not necessarily white. Procedures for the computation of the Volterra kernels both in the time as well as in the frequency domain are developed based on crosscumulant information. The derived kernels are optimal in the mean squared error sense for noncausal systems. Order recursive procedures based on minimum mean squared error reduction are derived. More general input output representations that result when the Volterra kernels are expanded in a given orthogonal base are also considered. © 1995 IEE