An MSE Lower Bound for Parametric and Nonparametric Channel Estimation

This paper compares parametric and nonparametric channel estimation methods in a multipath environment. For both methods, the MSE on the received symbol pulse is shown to consist of a modeling error term and an estimation error term. We lower bound the latter term by computing the associated Cramer-Rao bounds. We point out that the MSE can be minimized by a proper selection of the number of parameters to be estimated. In addition, we present simulation results from practical estimators that confirm our theoretical analysis. Our numerical results indicate that the parametric method outperforms the nonparametric approach.