Optimization of pre- and post-filters in the presence of near- and far-end crosstalk

Full-duplex data communications are considered over a linear, time-invariant, multi-input/multi-output channel. For both the continuous- and discrete-time cases, optimal multi-input/multi-output transmitter and receiver filters are derived using the minimum mean-square-error (MSE) criterion, with a power constraint on the transmitted signal, in the presence of both near- and far-end crosstalk. The discrete-time problem is solved for two different filter models: arbitrary linear (IIR) (infinite-complexity) and fixed-order (FIR) filters. In addition, the optimal transmitter and receiver filters are derived for the case in which the transmitted signal is a pulse-amplitude-modulated data signal. For a particular two-input/two-output channel model in the FIR case, the behavior of the MSE as a function of the allocation of matrix taps between transmitter and receiver filters and of timing phase is studied. 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.