A system and method for broadband communications over power lines has a low-voltage transformer for the house connection unit and/or the electricity distribution inside the house. The system method allow for several parallel asynchronous data communications in different sub-channels with individual transmit power in each sub-channel. Sub-channel separation uses pass-band filters with high stop-band attenuation. High data rate in each sub-channel is achieved through the use of discrete wavelet multi-tone modulation. Coarse synchronization in each sub-channel and the optimization of the coefficients of the time-domain equalizer are carried out using a training sequence.