In this paper, we propose a quantization approach, as an alternative of sparsification, to curb the growth of the radial basis function structure in kernel adaptive filtering. The basic idea behind this method is to quantize and hence compress the input (or feature) space. Different from sparsification, the new approach uses the “redundant” data to update the coefficient of the closest center. In particular, a quantized kernel least mean square (QKLMS) algorithm is developed, which is based on a simple online vector quantization method. The analytical study of the mean square convergence has been carried out. The energy conservation relation for QKLMS is established, and on this basis we arrive at a sufficient condition for mean square convergence, and a lower and upper bound on the theoretical value of the steady-state excess mean square error. Static function estimation and short-term chaotic time-series prediction examples are presented to demonstrate the excellent performance.

Quantized Kernel Least Mean Square Algorithm

Rapid industrialization and its automation on the globe demands increased generation of electrical energy with more reliability and quality. Renewable energy (RE) sources are considered as a green form of energy and extensively used as an alternative source of energy for conventional energy sources to meet the increased demand for electrical power. However, these sources, when integrated to the utility grid, pose challenges in maintaining the power quality (PQ) and stability of the power system network. This is due to the unpredictable and variable nature of generation by these sources. The distributed flexible AC transmission system (DFACTS) devices such as distributed static compensator (DSTATCOM) and dynamic voltage restorer (DVR) play an active role in mitigating PQ issues associated with RE penetration. The performance of DFACTS devices is mostly dependent on the type of control algorithms employed for switching of these devices. This paper presents a comprehensive review of various conventional and adaptive algorithms used to control DFACTS devices for improvement of power quality in utility grids with RE penetration. This review intends to provide a summary of the design, experimental hardware, performance and feasibility aspects of these algorithms reported in the literature. More than 170 research publications are critically reviewed, classified, and listed for quick reference for the advantage of engineers and academician working in this area.

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Comprehensive Review of Distributed FACTS Control Algorithms for Power Quality Enhancement in Utility Grid With Renewable Energy Penetration

Adaptive system identification ASI problems have attracted both academic and industrial attentions for a long time. As one of the classical approaches for ASI, performance of least mean square LMS is unstable in low signal-to-noise ratio SNR region. On the contrary, least mean fourth LMF algorithm is difficult to implement in practical system because of its high computational complexity in high SNR region, and hence it is usually neglected by researchers. In this paper, we propose an effective approach to identify unknown system adaptively by using combined LMS and LMF algorithms in different SNR regions. Experiment-based parameter selection is established to optimize the performance as well as to keep the low computational complexity. Copyright © 2013 John Wiley & Sons, Ltd.

Adaptive system identification using robust LMS/F algorithm

An adaptive channel equalizer using self-adaptation bacterial foraging optimization

Robust adaptive algorithms for underwater acoustic channel estimation and their performance analysis

Channel equalization using simplified least mean-fourth algorithm

In digital communication, adaptive channel equalization techniques underpin the successful provision of high speed and reliable data transmission over severely-dispersive channels, e.g. wireless and mobile ones. In a real world that is largely dominated by non- Gaussian interference signals, adaptive equalizers relying heavily on the LMS are bound to yield suboptimal performances. This work addresses this sub-optimality issue by proposing a new adaptive equalizer which judiciously combines the power of the least- mean fourth (IMF) algorithm to better tackle non-Gaussian environments, and the capability of the power-of-two quantizer (PTQ) to greatly reduce the IMF's high computational load. This combination endows the proposed algorithm with a capability of tracking fast-changing channels. A performance analysis of the proposed adaptive channel equalizer, based on a new linear approximation of the PTQ, is also presented. Extensive simulation testing of the proposed adaptive equalizer corroborates very well the theoretical findings predicted by the analysis of the linearized LMF- PTQ algorithm.

Adaptive channel equalization: A simplified approach using the quantized-LMF algorithm

The time-varying least-mean-fourth-based channel equalization method is an automated procedure that provides an adaptive equalizer in a CDMA receiver. Equalizer filter coefficients are estimated using a least-mean-fourth (LMF) error calculation based on a training set of symbols sent by the transmitter. When the LMF error calculation is combined with a power-of-two quantization (PTQ) process, superior receiver performance is achieved in a time-varying CDMA channel operating in non-Gaussian noise environments.

Time-varying least-mean-fourth-based channel equalization method and system

High speed and reliable data transmission over a variety of communication channels, including wireless and mobile radio channels, has been rendered possible through the use of adaptive equalization. In practice, adaptive equalizers rely heavily on the use of the least-mean square (LMS) algorithm which performs sub-optimally in the real world that is largely dominated by non-Gaussian interference signals. This paper proposes a new adaptive equalizer which relies on the judicious combination of the least-mean fourth (LMF) algorithm, which ensures a better performance in a non-Gaussian environment, and the power-of-two quantizer (PTQ) which reduces the high computational load brought about by the LMF and hence renders the proposed low-complexity equalizer capable of tracking fast-changing channels. This paper also presents a performance analysis of the proposed adaptive equalizer, based on a new linear approximation of the PTQ. Finally, the extensive simulation carried out here using the quantized LMF corroborates very well the theoretical predictions provided by the analysis of the linearized proposed algorithm.

Adaptive equalizer based on a power-of-two-quantized-LMF algorithm

Adaptive equalization is undoubtedly one of the cornerstones of digital communication as it allows for fast and reliable data transmission over practical channels that are non-ideal and that are plagued with serious problems such as signal dispersion and non-Gaussian interferences. In such cases, the performance of the well-known least-mean square (LMS) algorithm or that of any of its variants remains sub-optimal at best. As a remedy to this, the least-mean fourth (LMF) algorithm was later proposed but its high computational load was found to be a constraining factor in its practical implementation, particularly for real-time applications. Inspired from a previous work done on the LMS [1], we recently proposed a new algorithm [2], termed LMF-PTQ, combining the power of the LMF with the implementational advantages of the power-of-two quantization scheme. In this work, we demonstrate, through an extensive simulation study, the effectiveness of our proposed LMF-PTQ algorithm in the equalization of a time-varying channel in a CDMA system which suffers from both signal dispersion and non-Gaussian disturbances. The results obtained so far are very encouraging and provide us with ample enthusiasm to investigate the proposed algorithm further.

Musa U. Otaru

Papers

Channel equalization using simplified least mean-fourth algorithm

Adaptive channel equalization: A simplified approach using the quantized-LMF algorithm

Time-varying least-mean-fourth-based channel equalization method and system

Adaptive equalizer based on a power-of-two-quantized-LMF algorithm

Equalization of time-varying channels using the quantized least mean-fourth algorithm