Blind fractionally-spaced equalization of noisy FIR channels: adaptive and optimal solutions

Blind Fractionally Space (FS) equalizers only require output samples taken at rates higher than the symbol rate to estimate the channel or the equalizer. Methods for finding FIR zero forcing equalizers directly from the observations are described and adaptive versions are developed. In contrast, most current methods require channel estimation as a first step to estimating the equalizer. For the noisy channel, the FIR equalizer is shown to be minimum mean-square error. FS equalizers are not unique, thereby allowing optimum zero-forcing parametric FIR or nonparametric IIR equalizers to be derived such that in addition to being zero-forcing, they also minimize the noise power at the output. These optimum equalizers do not depend on the input distribution and are also valid for deterministic inputs. Finally, if the additive noise is white, they do not depend on the SNR.