Cramer-Rao Bound for Blind Channel Estimators in Redundant Block Transmission Systems

In this paper, we derive the Cramér-Rao bound (CRB) for blind channel estimation in redundant block transmission systems, a lower bound for the mean squared error of any blind channel estimators. The derived CRB is valid for any full-rank linear redundant precoder, including both zero-padded (ZP) and cyclic-prefixed (CP) precoders. A simple form of CRBs for multiple complex parameters is also derived and presented which facilitates the CRB derivation of the problem of interest. A comparison is made between the derived CRBs and performances of existing subspace-based blind channel estimators for both CP and ZP systems. Numerical results show that there is still some room for performance improvement of blind channel estimators.