Nonparametric estimation of signal amplitude in white Gaussian noise

We assume that a transmitted signal is of the form S(t)f(t), where f(t) is a known function vanishing at some points of the observation interval and S(t) is a function of a known smoothness class. The signal is transmitted over a communication channel with additive white Gaussian noise of small intensity E >. For this model, we construct an estimator for S(t) which is optimal with respect to the rate of convergence of the risk to zero as E > -> 0.