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 near- and 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 near- and 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 are 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 are 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.