A flexible statistical framework for the characterization and modelling of noise in powerline communication channels.

Abstract

One communication medium that has received a lot of interest in recent years is the power line channel, especially for the delivery of broadband content. This channel has been traditionally used to carry electrical power only. But with the recent advancements in digital signal processing, it is now possible to realize communications through the power grid, both in narrowband and broadband. The use of the power line network for telecommunication purposes constitutes what is referred to as powerline carrier communications or simply powerline communications (PLC). The biggest incentive for PLC technology use is the fact that the power line network is already in place, which greatly reduces the communication network set up cost, since no new cabling layout is required. PLC technology is widely applied in home networking, broadband internet provision and smart grid solutions. However, the PLC channel presents a very hostile communication environment. And as such, no consideration has been made in the design of traditional power line network to accommodate communication services. Of all the PLC channel impairments which include frequency-dependent attenuation, frequency selectivity, multipath and noise, noise is the biggest threat to communication signals. This noise manifests itself in form of coloured background noise, narrowband interference and impulsive noise. A thorough understanding of this noise distribution is therefore crucial for the design of a reliable and high performing PLC system. A proper understanding of the noise characteristics in the PLC channel can only be realized through noise measurements in live power networks, and then analyzing and modeling the noise appropriately. Moreover, the noise scenario in power line networks is very complex and therefore cannot be modeled through mere analytical methods. Additionally, most of the models that have been proposed for the PLC noise previously are mere adaptations of the measured noise to some existing impulsive noise models. These earlier modeling approaches are also rigid and model the noise via a fixed set of parameters. In the introductory work in this thesis, a study of orthogonal frequency division multiplexing (OFDM) as the modulation of choice for PLC systems is presented. A thorough survey of the salient features of this modulation scheme that make it the perfect candidate for PLC modulation needs is presented. In the end, a performance analysis study on the impact of impulsive noise on an OFDM based binary phase shift keying (BPSK) system is done. This study differs from earlier ones in that its focus is on how the elementary parameters that define the impulsive noise affect the system, a departure from the usual norm of considering the overall noise distribution. This study

focuses on the impact of interarrival times (IAT), pulse amplitudes as well as pulse widths, among other parameters. In the first part of the main work in this thesis, results of an intensive noise measurement campaign for indoor low voltage power line noise carried out in various power line networks, in the Department of Electrical, Electronic and Computer Engineering buildings at the University of KwaZulu-Natal, Howard campus are presented. The noise measurements are carried out in both time and frequency domains. Next, the noise measurements are then analyzed and modeled using two very flexible data modeling tools; nonparametric kernel density estimators and parametric alpha stable (α-stable) distributions. The kernel method’s ability to overcome all the shortcomings of the primitive histogram method makes it very attractive. In this method, the noise data structure is derived straight from the data itself, with no prior assumptions or restrictions on the data structure, thus effectively overcoming the rigidity associated with previous noise models for power line channels. As such, it results in density estimates that “hug” the measured density as much as possible. The models obtained using the kernel methods are therefore better than any parametric equivalent; something that can always be proven through goodness of fit tests. These models therefore form an excellent reference for parametric modeling of the power line noise. This work forms the author’s first main contribution to PLC research. As a demonstration of the kernel models suitability to act as a reference, parametric models of the noise distribution using the alpha stable (α-stable) distribution are also developed. This distribution is chosen due to its flexibility and ability to capture impulsiveness (long-tailed behaviour), such as the one found in power line noise. Stable distributions are characterized by long/fat tails than those of the Gaussian distribution, and that is the main reason why they are preferable here since the noise characteritics obtained in the kernel technique show visible long/heavy tailed behavior. A parameter estimation technique that is based on quantiles and another on the empirical characteristic function are employed in the extraction of the four parameters that define the characteristic function of the α-stable distribution. The application of the α-stable distribution in other signal processing problems has often been over-simplied by considering the symmetric alpha stable distribution, but in this thesis, the general α-stable distribution is used to model the power line noise. This is necessary so as to ensure that no features of the noise distribution are missed. All the models obtained are validated through error analysis and Chi-square fitness tests. This work forms the author’s second main contribution to PLC research. The author’s last contribution in this thesis is the development of an algorithm for the synthesis of the power line as a Levy stable stochastic process. The algorithm developed is then used to generate the PLC noise process for a

random number of alpha stable noise samples using the alpha stable noise parameters obtained in the parametric modeling using stable distributions. This algorithm is generalized for all admissible values of alpha stable noise parameters and therefore results for a Levy stable Gaussian process are also presented for the same number of random noise samples for comparison purposes.