Power line communications (PLC) is the central communications technology forthe realization of smart power grids. As the designated band for smart gridcommunications is the narrowband (NB) power line channel, NB-PLC has beenreceiving substantial attention in recent years. Narrowband power line channelsare characterized by cyclic short-term variations of the channel transferfunction (CTF) and strong noise with periodic statistics. In this work,modeling the CTF as a linear periodically time-varying filter and the noise asan additive cyclostationary Gaussian process, we derive the capacity ofdiscrete-time NB-PLC channels. As part of the capacity derivation, wecharacterize the capacity achieving transmission scheme, which leads to apractical code construction that approaches capacity. The capacity derived inthis work is numerically evaluated for several NB-PLC channel configurationstaken from previous works, and the results show that the optimal schemeachieves a substantial rate gain over a previously proposed ad-hoc scheme. Thisgain is due to optimally accounting for the periodic properties of the channeland the noise.
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