Component-wise conditionally unbiased bayesian parameter estimation: general concept and applications to Kalman filtering and LMMSE channel estimation

Bayesian parameter estimation techniques such as Linear Minimum Mean Squared Error (LMMSE) often lead to useful MSE reduction, but they also introduce a bias. In this paper, we introduce the concept of Component-Wise Conditionally Unbiased (CWCU) Bayesian parameter estimation, in which unbiasedness is forced for one parameter at a time. This concept had already been introduced in symbol detection a decade ago, where it led to unbiased LMMSE receivers and in which case global CU corresponds to Zero-Forcing. The more general introduction of the CWCU concept is motivated by LMMSE channel estimation, for which the implications of the concept are illustrated in various ways, including the effect on error probability in Maximum Likelihood Sequence Detection (MLSD), reprecussion for blind channel estimation etc. Motivated by the channel tracking application, we also introduce CWCU Kalman filtering.