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This paper provides a comprehensive discussion about the characteristics of power line communication (PLC) channels related to its synchronization with the mains period. This fact constitutes an interesting and distinguishing feature of these kind of channels. Under the mains voltage presence, the behavior of some loads connected to the power network allows representing the transmission medium as a linear periodically time varying (LPTV) system. Some components in the received noise exhibit periodicity as well, in terms of impulsive waveforms synchronized with the mains period and other cyclostationary (CS) signals. This fact has been taken into account in the design of PLC systems, for instance by defining medium access control (MAC) frames synchronized with the mains period and by adapting the modulation to the cyclic signal-to-noise ratio (SNR) to improve the system performance. Hence, in PLC, it is of particular interest to describe the general relations of LPTV systems and CS signals when both have a common period, which is the purpose of this work. It is not aimed at providing new mathematical tools for the analysis of these cyclic signals and systems, which have been extensively developed over the last five decades, but to serve the readers of the PLC community more accessible mathematical relations that can be applied to the practical problems they have to face. A review of recent works dealing with the cyclic properties of PLC channels and transmission techniques aware of these strategies is included as well.

Cyclic Signals and Systems in Power Line Communications