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 $\varepsilon$. 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 $\varepsilon\to 0$.