Channel estimation using feedback

It is well known from the information theory literature that in the presence of a memoryless channel, as well as some channels with memory, the existence of feedback does not improve channel capacity, but can contribute dramatically to the simplification of the encoder and the decoder. In this paper, we focus on estimating the parameters of an unknown channel when a feedback link from the decoder to the encoder is given. We examine different types of channels and study the conditions under which feedback improves the estimation in the sense of the Cramer-Rao bound (CRB). We additionally find what is the best strategy for designing channel input signals and the channel parameter estimator of the receiver. By assuming a certain class of parametric models for the channel, we show that feedback is essential when some nuisance parameters of the model are unknown, but it is superfluous when there are no unknown nuisance parameters.