Suppression of Near- and Far-End Crosstalk by Linear Pre- and Post-Filtering

Full-duplex data communications over a multi-input/multi-output linear time-invariant channel is considered. The minimum mean square error (MMSE) linear equalizer is derived in the presence of both nearand far-end crosstalk and independent additive noise, assuming correlated data, and colored noise. The MMSE equalizer is completely specified in terms of the channel and crosstalk transfer functions by using a generalization of previous work due to Salz. Conditions are given under which the equalizer can completely eliminate both nearand far-end crosstalk and intersymbol interference. The MMSE transmitter filter, subject to a transmitted power constraint, is specified when the channel and crosstalk transfer functions a re bandlimited to the Nyquist frequency. Also considered is the design of MMSE transmitter and receiver filters when the data signals are arbitrary wide-sense stationary continuous or discrete-time signals, corresponding to the situation where the crosstalk is not phase-synchronous with the desired signal. For a particular two-input/two-output discrete-time channel model, we study the behavior of the MMSE, assuming FIR transmitter and receiver filters, as a function of how the matrix taps are allocated between these filters, and on timing phase. In this case, the jointly optimal transmitter and receiver filters a re obtained numerically using an iterative technique. For the channel model considered, the MSE is a very sensitive function of timing phase, but is nearly independent of how taps are allocated between the transmitter and receiver filters.