On the relation between geometrical distance and channel statistics in in-home PLC networks

The concept of coverage in power line communications (PLC) is more difficult to be defined than in wireless systems. The main reason is that the PLC signal is conveyed by electrical wires and the wires follow an unpredictable path. We refer to the signal path length, and to the distance between the transmitter and receiver outlets as electrical distance and geometrical distance, respectively. The behaviour of the PLC channel is clearly a function of the electrical distance and it is reasonable to assume that the higher the geometrical distance, the higher the electrical distance. In this work, we focus on the PLC channel in in-home networks, and we discuss whether the statistics of the channel depends on the geometrical distance. We study the average channel gain, the root-mean-square delay spread, and the channel delay as a function of the geometrical distance. Furthermore, we address coverage, that we define in terms of maximum achievable rate as a function of the distance in the presence of additive colored Gaussian noise. We provide the linear relation between the metrics and the distance and the results are based on an experimental measurement campaign that we carried out in Italy, where we collected more than 1300 channel responses in multiple premises. Finally we propose a channel classification that is based on the geometrical distance.