Recent insights in the Bayesian and deterministic CRB for blind SIMO channel estimation

The performance of channel estimation is often assessed by deriving the proper Cramér-Rao Bound (CRB). Depending on how to treat the symbols and the channel, we have previously derived different versions of CRB. Specifically, we have dealt with the cases where the symbols and/or the channel are assumed to be either deterministic unknowns or random. Moreover, the symbols have been considered to be either jointly estimated with the channel or marginalized. All in all, we have derived six different versions of Bayesian and deterministic CRBs. However, we have shown that many of these CRBs are too optimistic in the sense that they are not strict enough to be attained by any deterministic or Bayesian estimator. In this paper we propose modified versions of those loose CRBs in the context of SIMO FIR system that are valid at least in the moderate and high SNR regimes. The analytical formulas for the lower bounds introduced are validated by some Monte-Carlo simulations.