By dispersive channel I take it that you mean that the phase velocity c of the propagating waves constituting the signal varies significantly across the frequency band of the signal.

The effect of dispersion is to cause energy in the signal to travel with frequency-dependent "group velocities" cg(f), where cg(f) =dw/dk , where w is the angular frequency w = 2*PI*f, k is the wavenumber, k=w/c(f), and c(f) is a frequency-dependent phase speed for signal propagation.

For a single propagation path (not considering a multi-path channel), and for a narrowband signal pulse of time duration Dt and bandwidth Df=1/Dt,  the effect of dispersion is to broaden the pulse in time at a distant receiver, on the order of:

Dt(R) = Dt + R  |cg(fc+Dt/2) - cg(fc-Dt/2)|

where R is the propagation distance between communication nodes, source and receiver.

The broadening of pulses generally causes signal self interference at the receiver because the energy of one pulse overlaps somewhat with the energy of another at the receiver. Modelling the effects of dispersion in this respect means modelling the signal self interference that comes from the pulse-width widening in time at the receiver. The signal self interference increases with increasing propagation distance R.

In multi-path propagation, you may have different dispersion characteristics (different group velocities) for each path. 

Ronald

 Thank you Dr.Ronald for the explanation on the dispersive channel.