Data and channel estimators: a systematic classification

A taxonomy of algorithms in digital receivers is presented, including data, channel and joint estimators. The receiver is seen as an elaborate estimator, whose primary purpose is to estimate (or "detect") the data. In communications, the impulse response of the linear channel is normally seen as a nuisance parameter set. The optimal receiver is defined to be a MAP detector where the channel is either assumed to be perfectly known or, if statistically known, be removed by averaging. On the other hand, in channel estimation data are assumed to be known or removed by averaging. Finally, joint estimators, which are generally optimal data detectors only asymptotically, can be defined. All the estimators are initially defined to be of the block-type, but they can be approximated with recursive versions. The estimators are based on some statistical knowledge on the channel, for example on the first- or second-order statistics of the impulse response and noise. Adaptive estimators do not necessarily rely on this a priori knowledge, but they are approximations of the optimal estimators and explicitly or implicitly estimate also the statistics.