Estimation with non-ideal training information

We consider the problem of channel estimation when non-ideal training information (pilots) is available such as in Turbo equalization, where this information are probabilities about the transmitted symbols of varying reliability. We study how these probabilities can be incorporated into common estimation algorithms by observing the estimation error statistics. We consider the two cases that the probabilities are mapped to a hardor soft-estimate of the transmitted symbol. It turns out that neither of the two estimates yields always better estimation error variances. However, the channel estimator becomes biased with hard-estimates and we conclude that for the two estimations algorithms analyzed in this paper, soft-estimates are the better choice.