Channel estimation using DFE is a similar process to a non-linear equalization process. In DFE (decision feed equalizer), equalization error bits/symbols between the feedforward tabs and feedback taps are calculated continuously. And equalizer's tap weights tap weights are updated correspondingly.
In plain language, the error between the received bits and known training bits is calculated, and tap weights are updated accordingly. The equalizer estimates the channel impulse response (CIR).
Once we find the channel impulse response or channel information, we can easily retrieve the original message signal from the noisy data.
In the communication process, the whole system is modeled as a linear time-invariant (LTI) system. And
y = h*x + n
where, y = received signal
x = transmitted signal
n = additive white Gaussian noise
[Read more about the Linear time-invariant (LTI) system and convolution process]