Systems and methods for off-diagonal MIMO precoders are described. At least one embodiment includes a method for precoding data for transmission in a discrete multi-tone (DMT) xDSL system to cancel self-induced far end crosstalk (self-FEXT) comprising: learning characteristics associated with a plurality of N users within the xDSL system to determine an initial off-diagonal multiple input multiple output (MIMO) precoder (ODMP) for a given tone frequency; and converging towards an optimum ODMP from the initial ODMP in order to cancel downstream self-FEXT for the plurality of N users, wherein the ODMP is represented as a zero diagonal matrix with only off-diagonal terms, and wherein the converging towards the optimum ODMP comprises: maximizing the channel capacity for the plurality of N users for the given tone frequency; and minimizing an increase in transmit power of the xDSL system relative to an original transmit power where a precoder is not active.