Low-Voltage PLC Noise Modelling

Abstract

This paper models the PLC impulsive noise using a linear superposition of univariate Gaussian distributions where the Bayes' theorem is used to find the posterior probabilities. The Gaussian mixture is formulated using discrete latent variables and modelled using two, three and four components in order to evaluate the effect of the number of components (Q). The parameters of the Gaussian mixture are then estimated using the maximum likelihood technique and the expectation-maximization algorithm. Regression analysis is proposed in order to solve the issue of singularity which is often present when the maximum likelihood approach is employed. The model is then validated through measurements where the impulsive noise is categorized into low, medium and highly impulsive depending on the amplitude of the indoor PLC noise. It is observed that as the number of components increases the performance of the Gaussian mixture model also increases as depicted by the correlation coefficient and RMSE. The χ 2 test indicates that the proposed model provides a better fit as the PLC noise amplitude increases. In addition, the shape of the impulsive noise PDF becomes more defined with higher Q values. A singularity case is also examined where the Gaussian mixture model also provides a good approximation of the measured data.

Variational Bayesian Learning for the Modelling of Indoor Broadband Powerline Communication Impulsive Noise

“…It was observed that as the number of components increases, the accuracy of the model also increases. Similar results were also found in [18] where the GM model which employed the ML estimation method to determine the optimal parameters was used to model the PLC impulsive noise. In this case, two, three, and four-component GM models were used, and the components that do not contribute to the GM were automatically pruned out as their mixture weights were reduced to zero.…”

“…Although the measured amplitude distribution for the Electronic Laboratory has a higher amplitude impulsive noise level and outliers, the two-component GM model is selected as the optimum model. In [18], it was also observed that when the PDF of the amplitude noise has outliers, the likelihood of the model changes minimally as the model complexity increases.…”

“…In [17], the bit error rate is modelled using the GM model where the parameters of the GM are estimated using the ML estimation approach. Further improvements on the same model are studied in [18], where the singularity problem present in the ML estimate is addressed, and the PLC impulsive noise is modelled using up to four components in the GM. Artificial neural network (which is a supervised learning approach) has been applied by [19] to detect the noise mixed with messages received in the orthogonal frequency division multiplexer to enhance the quality of noisy signals.…”

“…One problem with this procedure is the presence of singularities in the likelihood function, and as such the ML is strictly not well defined. This occurs where one of the component parameters has the same value as one of the data points thus assigning infinite density at the location of the data point [18,23]. Additionally, the ML framework is also known for its tendency to overfit data which becomes even worse for complicated models incorporating high-dimensional data [23].…”

“…Since the marginal log-likelihood log p(X) is independent of q(η), maximizing the lower bound is equal to minimizing the KL divergence which occurs when q(η) = p(X, η) and hence KL(q(η) || p(η | X)) = 0 [11]. Therefore, the main objective in variational Bayes is to minimise the KL divergence given by (18), which is equivalent to the maximization of the lower bound. As such, the lower bound will be as close as possible to the true posterior.…”