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

The finite-length minimum mean square error decision-feedback equalizer (MMSE-DFE) is an efficient structure mitigating intersymbol interference (ISI) introduced by practically all communication channels at high-enough symbol rates. The filters constituting the MMSE-DFE, as well as related performance measures, can be computed by assuming perfect knowledge of the channel impulse response and the input and noise second-order statistics (SOS). In practice, we estimate the unknown quantities, and thus, inevitable estimation errors arise. We model the estimation errors as small perturbations, and we derive a second-order approximation to the excess MSE. Furthermore, we derive second-order approximations to the mean excess MSE in terms of the parameter estimation error covariance matrices and simple and informative bounds, revealing the factors that govern the behavior of MMSE-DFE under mismatch. Simulations confirm that the derived second-order approximations provide accurate estimates of the MMSE-DFE performance degradation due to mismatch.