Improved generalized-proportionate stepsize LMS algorithms and performance analysis

This paper analyzes the performance of the GP-NLMS algorithm, revealing the nature of its fast convergence as well as its deficiency of inducing bigger steady state error. Based on the analysis, a class of improved Generalized-Proportionate Stepsize LMS (GPS-LMS) algorithms are proposed. With an efficient switching mechanism, the new algorithms can dynamically switch between the GP-NLMS and conventional LMS-type algorithms to achieve fast initial convergence and tracking speed and low steady state error. Computer simulations verified the superior performance of the proposed algorithms. © 2006 IEEE.published_or_final_versio

Digital signal processing algorithms and structures for adaptive line enhancing

Imperial Users onl

Structures and Algorithms for Two-Dimensional Adaptive Signal Processing

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOpe

Adaptive signal processing algorithms for noncircular complex data

The complex domain provides a natural processing framework for a large class of signals encountered in communications, radar, biomedical engineering and renewable energy. Statistical signal processing in C has traditionally been viewed as a straightforward extension of the corresponding algorithms in the real domain R, however, recent developments in augmented complex statistics show that, in general, this leads to under-modelling. This direct treatment of complex-valued signals has led to advances in so called widely linear modelling and the introduction of a generalised framework for the differentiability of both analytic and non-analytic complex and quaternion functions. In this thesis, supervised and blind complex adaptive algorithms capable of processing the generality of complex and quaternion signals (both circular and noncircular) in both noise-free and noisy environments are developed; their usefulness in real-world applications is demonstrated through case studies. The focus of this thesis is on the use of augmented statistics and widely linear modelling. The standard complex least mean square (CLMS) algorithm is extended to perform optimally for the generality of complex-valued signals, and is shown to outperform the CLMS algorithm. Next, extraction of latent complex-valued signals from large mixtures is addressed. This is achieved by developing several classes of complex blind source extraction algorithms based on fundamental signal properties such as smoothness, predictability and degree of Gaussianity, with the analysis of the existence and uniqueness of the solutions also provided. These algorithms are shown to facilitate real-time applications, such as those in brain computer interfacing (BCI). Due to their modified cost functions and the widely linear mixing model, this class of algorithms perform well in both noise-free and noisy environments. Next, based on a widely linear quaternion model, the FastICA algorithm is extended to the quaternion domain to provide separation of the generality of quaternion signals. The enhanced performances of the widely linear algorithms are illustrated in renewable energy and biomedical applications, in particular, for the prediction of wind profiles and extraction of artifacts from EEG recordings

Tree-Structured Nonlinear Adaptive Signal Processing

In communication systems, nonlinear adaptive filtering has become increasingly popular in a variety of applications such as channel equalization, echo cancellation and speech coding. However, existing nonlinear adaptive filters such as polynomial (truncated Volterra series) filters and multilayer perceptrons suffer from a number of problems. First, although high Order polynomials can approximate complex nonlinearities, they also train very slowly. Second, there is no systematic and efficient way to select their structure. As for multilayer perceptrons, they have a very complicated structure and train extremely slowly Motivated by the success of classification and regression trees on difficult nonlinear and nonparametfic problems, we propose the idea of a tree-structured piecewise linear adaptive filter. In the proposed method each node in a tree is associated with a linear filter restricted to a polygonal domain, and this is done in such a way that each pruned subtree is associated with a piecewise linear filter. A training sequence is used to adaptively update the filter coefficients and domains at each node, and to select the best pruned subtree and the corresponding piecewise linear filter. The tree structured approach offers several advantages. First, it makes use of standard linear adaptive filtering techniques at each node to find the corresponding Conditional linear filter. Second, it allows for efficient selection of the subtree and the corresponding piecewise linear filter of appropriate complexity. Overall, the approach is computationally efficient and conceptually simple. The tree-structured piecewise linear adaptive filter bears some similarity to classification and regression trees. But it is actually quite different from a classification and regression tree. Here the terminal nodes are not just assigned a region and a class label or a regression value, but rather represent: a linear filter with restricted domain, It is also different in that classification and regression trees are determined in a batch mode offline, whereas the tree-structured adaptive filter is determined recursively in real-time. We first develop the specific structure of a tree-structured piecewise linear adaptive filter and derive a stochastic gradient-based training algorithm. We then carry out a rigorous convergence analysis of the proposed training algorithm for the tree-structured filter. Here we show the mean-square convergence of the adaptively trained tree-structured piecewise linear filter to the optimal tree-structured piecewise linear filter. Same new techniques are developed for analyzing stochastic gradient algorithms with fixed gains and (nonstandard) dependent data. Finally, numerical experiments are performed to show the computational and performance advantages of the tree-structured piecewise linear filter over linear and polynomial filters for equalization of high frequency channels with severe intersymbol interference, echo cancellation in telephone networks and predictive coding of speech signals

Spontaneous and explicit estimation of time delays in the absence/presence of multipath propagation.

by Hing-cheung So.Thesis (Ph.D.)--Chinese University of Hong Kong, 1995.Includes bibliographical references (leaves 133-141).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Time Delay Estimation (TDE) and its Applications --- p.1Chapter 1.2 --- Goal of the Work --- p.6Chapter 1.3 --- Thesis Outline --- p.9Chapter 2 --- Adaptive Methods for TDE --- p.10Chapter 2.1 --- Problem Description --- p.11Chapter 2.2 --- The Least Mean Square Time Delay Estimator (LMSTDE) --- p.11Chapter 2.2.1 --- Bias and Variance --- p.14Chapter 2.2.2 --- Probability of Occurrence of False Peak Weight --- p.16Chapter 2.2.3 --- Some Modifications of the LMSTDE --- p.17Chapter 2.3 --- The Adaptive Digital Delay-Lock Discriminator (ADDLD) --- p.18Chapter 2.4 --- Summary --- p.20Chapter 3 --- The Explicit Time Delay Estimator (ETDE) --- p.22Chapter 3.1 --- Derivation and Analysis of the ETDE --- p.23Chapter 3.1.1 --- The ETDE system --- p.23Chapter 3.1.2 --- Performance Surface --- p.26Chapter 3.1.3 --- Static Behaviour --- p.28Chapter 3.1.4 --- Dynamic Behaviour --- p.30Chapter 3.2 --- Performance Comparisons --- p.32Chapter 3.2.1 --- With the LMSTDE --- p.32Chapter 3.2.2 --- With the CATDE --- p.34Chapter 3.2.3 --- With the CRLB --- p.35Chapter 3.3 --- Simulation Results --- p.38Chapter 3.3.1 --- Corroboration of the ETDE Performance --- p.38Chapter 3.3.2 --- Comparative Studies --- p.44Chapter 3.4 --- Summary --- p.48Chapter 4 --- An Improvement to the ETDE --- p.49Chapter 4.1 --- Delay Modeling Error of the ETDE --- p.49Chapter 4.2 --- The Explicit Time Delay and Gain Estimator (ETDGE) --- p.52Chapter 4.3 --- Performance Analysis --- p.55Chapter 4.4 --- Simulation Results --- p.57Chapter 4.5 --- Summary --- p.61Chapter 5 --- TDE in the Presence of Multipath Propagation --- p.62Chapter 5.1 --- The Multipath TDE problem --- p.63Chapter 5.2 --- TDE with Multipath Cancellation (MCTDE) --- p.64Chapter 5.2.1 --- Structure and Algorithm --- p.64Chapter 5.2.2 --- Convergence Dynamics --- p.67Chapter 5.2.3 --- The Generalized Multipath Cancellator --- p.70Chapter 5.2.4 --- Effects of Additive Noises --- p.73Chapter 5.2.5 --- Simulation Results --- p.74Chapter 5.3 --- TDE with Multipath Equalization (METDE) --- p.86Chapter 5.3.1 --- The Two-Step Algorithm --- p.86Chapter 5.3.2 --- Performance of the METDE --- p.89Chapter 5.3.3 --- Simulation Results --- p.93Chapter 5.4 --- Summary --- p.101Chapter 6 --- Conclusions and Suggestions for Future Research --- p.102Chapter 6.1 --- Conclusions --- p.102Chapter 6.2 --- Suggestions for Future Research --- p.104Appendices --- p.106Chapter A --- Derivation of (3.20) --- p.106Chapter B --- Derivation of (3.29) --- p.110Chapter C --- Derivation of (4.14) --- p.111Chapter D --- Derivation of (4.15) --- p.113Chapter E --- Derivation of (5.21) --- p.115Chapter F --- Proof of unstablity of A°(z) --- p.116Chapter G --- Derivation of (5.34)-(5.35) --- p.118Chapter H --- Derivation of variance of αs11(k) and Δs11(k) --- p.120Chapter I --- Derivation of (5.40) --- p.123Chapter J --- Derivation of time constant of αΔ11(k) --- p.124Chapter K --- Derivation of (5.63)-(5.66) --- p.125Chapter L --- Derivation of (5.68)-(5.72) --- p.129References --- p.13