Cramer Rao bounds for channel estimation with symbol a priori information

In this paper we derive the Cramer-Rao bound (CRB) for the estimation of a multiple-input multiple-output (MIMO) channel when a given a priori information about the transmitted sequence is available. This approach also enables to compute the non-data-aided (NDA) bound, i.e. the CRB when the receiver only knows the symbol constellation. We explore various scenarios, including the case of a deterministic channel and the case of a random channel. Numerical evaluations of the CRB-based bounds are presented for different channels. In particular, the influence of the symbol-constellation size is highlighted. Finally, the performance of an estimator based on the expectation-maximization algorithm is shown to be very close to the proposed bounds.