Robustness of the finite-length MMSE-DFE with respect to channel and second-order statistics estimation errors

The filters of the finite-length minimum mean-square error decision-feedback equalizer (MMSE-DFE) can be computed by assuming perfect knowledge of the channel impulse response and the input and noise second-order statistics. In practice, we estimate the unknown quantities and thus inevitable estimation errors arise. In this work, we model the estimation errors as small perturbations and we derive a second-order approximation to the excess MSE. Then, assuming that the input and noise SOS are perfectly known, we derive an expression for the mean excess MSE in terms of the channel estimation error covariance matrix. Analogous expressions involving the noise and input SOS estimation error covariance matrices appear on [1].