Do we need Channel estimation prior to (time domain DFE or linear) adaptative equalization in single tone transmission? If we are to transmit a single tone signal over a channel impaired by inter symbol interference and awgn, and if the equalization is adaptative (LMS/RLS track) and is done in time domain by LE (linear equalizer) or DFE, do we need to compute the channel impulse response first or the equalizer simply track channel changes when it computes it coefficients ?
Linear Equalizer: Depdends on the type, but no, generally you just estimate an optimal inverse ("optimal" according to the specific metric of linear equalizer type) of the channel impulse response and apply that.
Decision-Feedback Equalizer: No. The way the channel equalization is computed is literally in the name.