Complex constrained CRB and its application to semi-blind MIMO and OFDM channel estimation

We derive an expression for the Cramer-Rao lower bound (CRB) on the covariance of unbiased estimators of a constrained complex parameter vector and demonstrate key applications of the theory. In the first part, motivated by the result in A. van den Bos et al. (1994) we introduce an important extension to the set of constraints on the complex parameters. This extension then leads to a simple expression for the complex constrained CRB similar to the result in P. Stoica et al. (1998). This CRB framework is employed in the context of estimation of a wireless channel matrix H. We demonstrate that the channel estimation error lower bound is directly proportional to the number of unconstrained parameters in H. The usefulness of these results is illustrated by their application to two different estimation problems arising in wireless communications. The first is whitening-rotation based semi-blind MIMO channel estimation and the second pertains to time versus frequency domain channel estimation in OFDM systems.