A class of widely linear complex-valued adaptive filtering algorithms
Author(s)
Xia, Yili
Type
Thesis
Abstract
A large class of signals encountered in communications, biomedical engineering, renewable
energy and power systems are conveniently processed in the complex domain C, where traditional
adaptive signal processing in C is regarded as a straightforward extension of the
corresponding algorithms in the real domain R. However, recent advances in widely linear
modelling and augmented complex statistics show the suboptimality of such an assumption.
In this work, based on the widely linear model, a class of linear and nonlinear adaptive
filtering algorithms have been derived to process the generality of complex-valued signals
(both second order circular and noncircular) in both noise-free and noisy environments,
and their usefulness in real-world applications is demonstrated through case studies.
The focus of this thesis is on the use of augmented second order statistics and widely
linear modelling. The so called Augmented Complex Least Mean Square (ACLMS) algorithm
has already been extended from the standard CLMS algorithm to perform optimum
mean square error(MSE) type of adaptive estimation for the generality of complex-valued
signals and has been shown to outperform the CLMS algorithm, however, a theoretical
understanding of its performance is still missing. To this end, this thesis first addresses
this issue in terms of both convergence analysis and steady state analysis. Next, based on
the generalised framework introduced by the derivation of the ACLMS algorithm, a class
of widely linear adaptive algorithms have been introduced; these include the Regularised
Normalised ACLMS (RNACLMS) algorithm, the Augmented Affine Projection algorithm
(AAPA) for linear Finite Impulse Response (FIR) adaptive filters, and also in the context
of reservoir computing, for the recently introduced random state space based Echo
State Networks (ESNs). Furthermore, the widely linear model has been introduced in the
context of distributed networks, where the individual adaptive filters share information
with their neighbours to achieve a cooperative estimation. The enhanced performances
of the widely linear algorithms are illustrated in renewable energy and power system applications,
in particular, for the prediction of wind profiles and frequency estimation of
unbalanced three-phase power systems.
energy and power systems are conveniently processed in the complex domain C, where traditional
adaptive signal processing in C is regarded as a straightforward extension of the
corresponding algorithms in the real domain R. However, recent advances in widely linear
modelling and augmented complex statistics show the suboptimality of such an assumption.
In this work, based on the widely linear model, a class of linear and nonlinear adaptive
filtering algorithms have been derived to process the generality of complex-valued signals
(both second order circular and noncircular) in both noise-free and noisy environments,
and their usefulness in real-world applications is demonstrated through case studies.
The focus of this thesis is on the use of augmented second order statistics and widely
linear modelling. The so called Augmented Complex Least Mean Square (ACLMS) algorithm
has already been extended from the standard CLMS algorithm to perform optimum
mean square error(MSE) type of adaptive estimation for the generality of complex-valued
signals and has been shown to outperform the CLMS algorithm, however, a theoretical
understanding of its performance is still missing. To this end, this thesis first addresses
this issue in terms of both convergence analysis and steady state analysis. Next, based on
the generalised framework introduced by the derivation of the ACLMS algorithm, a class
of widely linear adaptive algorithms have been introduced; these include the Regularised
Normalised ACLMS (RNACLMS) algorithm, the Augmented Affine Projection algorithm
(AAPA) for linear Finite Impulse Response (FIR) adaptive filters, and also in the context
of reservoir computing, for the recently introduced random state space based Echo
State Networks (ESNs). Furthermore, the widely linear model has been introduced in the
context of distributed networks, where the individual adaptive filters share information
with their neighbours to achieve a cooperative estimation. The enhanced performances
of the widely linear algorithms are illustrated in renewable energy and power system applications,
in particular, for the prediction of wind profiles and frequency estimation of
unbalanced three-phase power systems.
Date Issued
2011
Date Awarded
2011-11
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Mandic, Danilo
Sponsor
European Commission and EPSRC
Creator
Xia, Yili
Publisher Department
Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)