## Characterization and modeling of the channel and noise for broadband indoor Power Line Communication (PLC) networks.

##### Abstract

Power Line Communication (PLC) is an interesting approach in establishing last mile broadband
access especially in rural areas. PLC provides an already existing medium for broadband
internet connectivity as well as monitoring and control functions for both industrial
and indoor usage. PLC network is the most ubiquitous network in the world reaching every
home. However, it presents a channel that is inherently hostile in nature when used for
communication purposes. This hostility is due to the many problematic characteristics of
the PLC from a data communications’ perspective. They include multipath propagation
due to multiple reflections resulting from impedance mismatches and cable joints, as well as
the various types of noise inherent in the channel. Apart from wireless technologies, current
high data rate services such as high speed internet are provided through optical fibre links,
Ethernet, and VDSL (very-high-bit-rate digital subscriber line) technology. The deployment
of a wired network is costly and demands physical effort. The transmission of high frequency
signals over power lines, known as power line communications (PLC), plays an important
role in contributing towards global goals for broadband services inside the home and office.
In this thesis we aim to contribute to this ideal by presenting a powerline channel modeling
approach which describes a powerline network as a lattice structure. In a lattice structure, a
signal propagates from one end into a network of boundaries (branches) through numerous
paths characterized by different reflection/transmission properties. Due to theoretically infinite
number of reflections likely to be experienced by a propagating wave, we determine the
optimum number of paths required for meaningful contribution towards the overall signal
level at the receiver. The propagation parameters are obtained through measurements and
other model parameters are derived from deterministic power system. It is observed that the
notch positions in the transfer characteristics are associated with the branch lengths in the
network. Short branches will result in fewer notches in a fixed bandwidth as compared to
longer branches. Generally, the channel attenuation increase with network size in terms of
number of branches. The proposed model compares well with experimental data. This work
presents another alternative approach to model the transfer characteristics of power lines
for broadband power line communication. The model is developed by considering the power
line to be a two-wire transmission line and the theory of transverse electromagnetic (TEM)
wave propagation. The characteristic impedance and attenuation constant of the power line
are determined through measurements. These parameters are used in model simplification
and determination of other model parameters for typical indoor multi-tapped transmission
line system. The transfer function of the PLC channel is determined by considering the
branching sections as parallel resonant circuits (PRC) attached to the main line. The model
is evaluated through comparison with measured transfer characteristics of known topologies
and it is in good agreement with measurements. Apart from the harsh topology of power
line networks, the presence of electrical appliances further aggravates the channel conditions
by injecting various types of noises into the system. This thesis also discusses the process
of estimating powerline communication (PLC) asynchronous impulsive noise volatility by
studying the conditional variance of the noise time series residuals. In our approach, we use
the Generalized Autoregressive Conditional Heteroskedastic (GARCH) models on the basis
that in our observations, the noise time series residuals indicate heteroskedasticity. By performing
an ordinary least squares (OLS) regression of the noise data, the empirical results
show that the conditional variance process is highly persistent in the residuals. The variance
of the error terms are not uniform, in fact, the error terms are larger at some portions of
the data than at other time instances. Thus, PLC impulsive noise often exhibit volatility
clustering where the noise time series is comprised of periods of high volatility followed by
periods of high volatility and periods of low volatility followed by periods of low volatility.
The burstiness of PLC impulsive noise is therefore not spread randomly across the time
period, but instead has a degree of autocorrelation. This provides evidence of time-varying
conditional second order moment of the noise time series. Based on these properties, the
noise time series data is said to suffer from heteroskedasticity. GARCH models addresses the
deficiencies of common regression models such as Autoregressive Moving Average (ARMA)
which models the conditional expectation of a process given the past, but regards the past
conditional variances to be constant. In our approach, we predict the time-varying volatility
by using past time-varying variances in the error terms of the noise data series. Subsequent
variances are predicted as a weighted average of past squared residuals with declining weights
that never completely diminish. The parameter estimates of the model indicates a high degree
of persistence in conditional volatility of impulsive noise which is a strong evidence of
explosive volatility. Parameter estimation of linear regression models usually employs least
squares (LS) and maximum likelihood (ML) estimators. While maximum likelihood remains
one of the best estimators within the classical statistics paradigm to date, it is highly reliant
on the assumption about the joint probability distribution of the data for optimal results.
In our work, we use the Generalized Method of Moments (GMM) to address the deficiencies
of LS/ML in order to estimate the underlying data generating process (DGP). We use
GMM as a statistical technique that incorporate observed noise data with the information in
population moment conditions to determine estimates of unknown parameters of the underlying
model. Periodic impulsive noise (short-term) has been measured, deseasonalized and
modeled using GMM. The numerical results show that the model captures the noise process
accurately. Usually, the impulsive signals originates from connected loads in an electrical
power network can often be characterized as cyclostationary processes. A cyclostationary
process is described as a non-stationary process whose statistics exhibit periodic time variation,
and therefore can be described by virtue of its periodic order. The focus of this chapter
centres on the utilization of cyclic spectral analysis technique for identification and analysis
of the second-order periodicity (SOP) of time sequences like those which are generated by
electrical loads connected in the vicinity of a power line communications receiver. Analysis
of cyclic spectrum generally incorporates determining the random features besides the periodicity
of impulsive noise, through the determination of the spectral correlation density
(SCD). Its effectiveness on identifying and analysing cyclostationary noise is substantiated
in this work by processing data collected at indoor low voltage sites.