  Power line communications (PLC) is the central communications technology for
the realization of smart power grids. As the designated band for smart grid
communications is the narrowband (NB) power line channel, NB-PLC has been
receiving substantial attention in recent years. Narrowband power line channels
are characterized by cyclic short-term variations of the channel transfer
function (CTF) and strong noise with periodic statistics. In this work,
modeling the CTF as a linear periodically time-varying filter and the noise as
an additive cyclostationary Gaussian process, we derive the capacity of
discrete-time NB-PLC channels. As part of the capacity derivation, we
characterize the capacity achieving transmission scheme, which leads to a
practical code construction that approaches capacity. The capacity derived in
this work is numerically evaluated for several NB-PLC channel configurations
taken from previous works, and the results show that the optimal scheme
achieves a substantial rate gain over a previously proposed ad-hoc scheme. This
gain is due to optimally accounting for the periodic properties of the channel
and the noise.
