The error rate performance of a previously developed reduced complexity channel estimator, known as the generalized least mean squares (GLMS) algorithm, is investigated in conjunction with a minimum-mean-square-error (MMSE) decision feedback equalizer (DFE). The channel estimator is based on the theory of polynomial prediction and Taylor series expansion of the underlying channel model in time domain. It is a simplification of a previously developed generalized recursive least squares (GRLS) estimator, achieved by replacing the online recursive computation of the 'intermediate' matrix by an offline pre-computed matrix. Similar to the GRLS estimator, it is able to operate in Rayleigh or Rician fading environment without reconfiguration of the state transition matrix to accommodate the non-random mean components. Simulation results show that it is able to offer a trade-off between reduced complexity channel estimation and good system performance.