An alternative approach to impulsive noise characterisation and statistical modelling for broadband powerline communication networks.

Abstract

Research into the modelling of powerline communication impulsive noise – which exhibits unpredictable behaviour in its time domain characteristics of amplitude, inter-arrival time, and service time - is still in progress. As a result, in order to propose an appropriate mitigation strategy to address the interference generated by powerline communication impulsive noise, an appropriate characterization of its time domain parameters is crucial. Given the complex structure of the powerline communication network that includes a heavy wiring system, the models proposed for the various noise characteristics are stochastic in nature. In this work, extensive noise measurements were carried out over various indoor networks in the School of Engineering, University of KwaZulu-Natal, Durban, South Africa. The measurements were conducted at the following sites: the Computer Laboratory, the Machines Laboratory, the Electronic Laboratory, the Second-year Laboratory, the Post-graduate office, as well as at an adjacent apartment. This campaign was undertaken to adequately capture the behaviour of powerline communication noise, which varies randomly depending on location, time, and the devices linked to the electrical network. To begin with, the amplitude distribution of the powerline communication impulsive noise was examined. The Gaussian mixture model was used to analyse the amplitude distribution of powerline communication noise, which is essential in estimating the level of noise reaching the receiver. Gaussian mixture models are commonly employed in modelling the powerline communication impulsive noise amplitude distribution. However, the weights of the Gaussian mixture components are derived using statistical distributions, with the most common models employing the Bernoulli and Poisson distributions. These models, however, have been found to be insufficient in describing powerline communication noise. This thesis contributes to the modelling of the amplitude distribution of powerline communication impulsive noise by using unsupervised learning to determine the parameters of the Gaussian mixture. Regression analysis is also proposed to solve the issue of singularity in the likelihood function of this model as well as to determine the optimum number of Gaussian components. Further analysis of the amplitude distribution is performed using a fully Bayesian treatment referred to as the Variational Bayesian model, where the parameters of the Gaussian mixture model are assumed to be random variables, such that prior distributions over the parameters are introduced. Moreover, the optimal number of components is determined from the measurement data through the Variational Bayesian criterion. This ensures that improved accuracy due to the increased number of components in modelling the powerline communication impulsive noise amplitude distribution is eliminated thus reducing the model complexity while adequately describing the data. The variational-expectation algorithm, analogous to the expectation-maximisation algorithm employed in the Gaussian mixture model, is used to determine the model parameters. Measurements have shown that the powerline communication impulsive noise can be modelled as a superposition of several exponential distributions. Consequently, most of the research models proposed for modelling the inter-arrival and service time distribution are based on the Markov chain. There is still no defined method of evaluating the number of states, with existing models employing various curve-fitting techniques to find the optimum model for the measurement data. This work provides an alternative approach based on the queueing theory technique, where the impulsive noise occurrence in the powerline communication channel is modelled as an Erlangian queue. A straightforward method for obtaining the optimum number of exponential phases by employing the mean and the variance of the Erlang-k distribution is presented. The proposed model assumes that the impulsive noise passes through k arrival stages before entering the powerline communication network and another k service stages before leaving the powerline communication network. In all of the measurement data under consideration, impulsive noise events are observed to achieve steady-state in the inter-arrival and service time distributions. In this work, the measurements indicate that the powerline communication noise can occur as a single-impulse noise or a burst-impulse noise. The burst-impulse noise is caused by the overlap of three or more high-amplitude single-impulse noise events that occur successively in an impulse train. The amplitude of the noise, as well as the interarrival and service time distribution, vary depending on the location and time. As a result, the impulsive noise is categorised as low, medium, or highly impulsive, depending on the noise levels. The probability density function of the noise amplitude exhibits heavy tails comparable to the Gaussian mixtures. The performance of the maximum likelihood estimate and the Variational Bayesian model in finding the parameters of the Gaussian mixture are validated through measurements, where the maximum likelihood estimate yields better accuracy. However, cases of singularity are encountered in addition to an increase in performance as the number of impulsive noise components is increased. Therefore, the implementation of the Variational Bayesian approach in modelling the parameters of the Gaussian mixture enables the determination of the appropriate number of Gaussian mixture components and no singularity case is found. Although the Variational Bayesian model provides a good generalization to the measured data, the maximum likelihood technique gives better accuracy since the Variational Bayesian model provides an approximate solution, as it is based on maximising the lower bound. Both models are observed to have a high level of significance as well as a good correlation to the measured data and thus either can be used in modelling the amplitude distribution of the powerline communication noise. In modelling the inter-arrival and service time distributions, the Erlang-k distribution is observed to be more appropriate for modelling the burst-impulse noise events with a high level of significance to the measured data. The exponential distribution, which is a special case of the Erlang-k distribution, is determined to be appropriate in estimating the inter-arrival time of the single-impulse noise events, indicating high variance in the measurement data. The models proposed in this thesis can be used as simulation tools to assist the development of physical layers of powerline communication systems.