Precoding mitigates or removes interference signals (especially
crosstalk) among multiple users with interconnected transmitters in vectored DSL systems and the like. Efficient implementation is provided of the
R matrix in RQ factorization that characterizes multi-user downstream vector channels (such as DMT VDSL one-sided or two-sided transmission channels). A set of precoder coefficients can vary with each tone used by each user and depend upon the encoding order of users selected for each tone. In adaptive operation, the coefficients of the R and Q matrices can be updated when changes occur to the transmission environment. Variable modulo arithmetic mitigates the power-enhancement problem, and the base of
modular arithmetic also can vary with each user within a single precoder for a
single tone. The user order of preceding need not be the same on each tone, and the
modular arithmetic progression may thus also be different on each tone because multi-user situations create an unusual situation for
precoding in that the modulo arithmetic used for each user can be different (thus imposing a larger power increase) and because digital duplexed or synchronized DMT systems can separately implement a precoder for each tone. Further, the
precoding process terminates each DMT symbol, after
processing up to the total number of users. An optional
dither signal, known to both
transmitter and
receiver, can be added at the transmit side and removed at the
receiver side to smooth the
precoding process and ensure that aberrations in the transmitted
constellation size and characteristics are consistent despite any unusual variations in the feedback
signal that exits the feedback filter matrix G before being subtracted from the user
signal of interest. Some embodiments use a “subtraction only” mode while other embodiments use a
dither signal and / or modulo arithmetic, though embodiments of the present invention do not require use of identical constellations by both
transmitter and
receiver.