Equalization with Part-Time Help

We consider relay-assisted equalization where a half-duplex relay forwards a signal to a receiver in attempt to aid in the task of equalization. All channels are assumed to be frequency selective, and therefore they contribute intersymbol interference (ISI). We first consider the case of a naive amplify-and-forward protocol where the relay forwards a scaled version of its received (and ISI-corrupted) signal. We then consider an equalize-and-forward protocol where the equalizer attempts to perform linear equalization before forwarding its signal. We show that a relay can indeed provide considerable benefit in the task of equalization even when only providing "part-time help", and we demonstrate the performance of the two schemes with simulations.