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.

Powerline communication (PLC) noise is the main cause of reduced performance and reliability of the communication channel. The major source of these noise bursts, which distort and degrade the communication signal, is the arbitrary plugging in and unplugging of electric devices from the electrical network. It is therefore important to perform statistical modelling of the PLC noise characteristics to enable the development and optimisation of reliable PLC systems. This paper presents the Variational Bayesian (VB) Gaussian Mixture (GM) modelling of the amplitude distribution of the indoor broadband PLC noise. In the proposed model, a fully Bayesian treatment is employed where the parameters of the GM model are assumed to be random variables. Consequently, prior distributions over the parameters are introduced. The VB criterion is used to determine the optimal number of components where the Bayesian information criterion emerges as a limiting case. To find the parameters of the GM components, the variational-expectation maximisation algorithm is employed. Measurements from different indoor PLC environments are then used to validate the model. Thereafter, performance analysis is carried out, and the VB framework is compared to the Maximum Likelihood (ML) estimate method. It is observed that while the ML model performs better when the amplitude distribution contains multiple peaks, the VB framework offers high accuracy and good generalization to the measured data and is thus effective in modelling the amplitude distribution of the PLC noise.

No abstract