Bayesian and deterministic CRBs for semi-blind channel estimation in SIMO single carrier cyclic prefix systems

Traditionally, the performance of different semi-blind channel estimation algorithms has been assessed and compared to a certain lower bound. One of these famous lower bounds that has been extensively used in the literature is the Cramer Rao Bound (CRB). Depending on how we treat the symbols and the channel, different versions of CRB have been derived. There are two possible cases on how to treat the symbols and/or the channel namely, deterministic unknowns or random. Moreover, the symbols are either jointly estimated with the channel or eliminated. In other words, we have six different cases to be handled. In this paper we present the CRBs that exist in the literature and fit to some of these cases and derive the others in the context of SIMO single carrier cyclic prefix systems (SC-CP). On the top of that we present a unified framework that permits to derive all versions of CRBs in a concrete manner. All the derived CRBs are validated numerically by conducting limited Monte-Carlo simulations.