Comparison of Some Cost Functions for Automatic Equalization

Automatic equalization for digital systems often has as its immediate goal the minimization of some cost function that depends explicitly on the values of intersymbol interference, and thus implicitly on the tap settings. For ease of implementation it is often desirable to slightly modify the conventional distortion measures. A theoretical comparison of several such criteria, some of which are of the peak distortion variety and some of which are of the mean-square class, is made. With one exception, the tap settings that minimize the modified mean-square criteria yield to first-order identical values for the conventional quadratic cost function. All the analogous peak distortion criteria result in zero forcing of sample values, provided that the binary eye is open. Some comments about automatic equalization that are of a tutorial nature are also made.