On the equalizability of nonlinear/time-varying multiuser channels

We attack the problem of perfect equalizability of multiuser channels, in which the usual linear time-invariant assumption is dismissed. In the linear, time-invariant case, the condition for perfect equalizability is plain and expressed in terms of the column rank of the channel´s transfer matrix. Using the module-theoretic approach developed by M. Fliess (see System and Control Letters, vol.15, p.391-6, 1990; Linear Algebra and its Application, no.203-204, p.429-42, 1994; Forum Math, vol.2, p.212-32, 1990), in which the transfer matrix of a time-varying channel as well as the rank of a nonlinear channel are clearly defined, we show how the condition obtained in the linear time-invariant case naturally extends to the time-varying and the nonlinear cases