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

The filters constituting the minimum mean square error decision-feedback equalizer (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 channel and SOS, and inevitable estimation errors arise. We model estimation errors as small perturbations, i.e., of order /spl epsiv/, with /spl epsiv/ a sufficiently small positive number, and we study the behavior of the MMSE-DFE under mismatch by performing a first-order perturbation analysis. We prove that the excess MSE induced by O(/spl epsiv/) estimation errors is O(/spl epsiv//sup 2/), uncovering important robustness properties associated with the MMSE-DFE.