On the use of Cramer-Rao-like bounds in the presence of random nuisance parameters

We focus on the use of Cramer-Rao-like bounds for the estimation of a deterministic parameter in the presence of random nuisance parameters. As a working example, we consider the problem of estimating the carrier frequency offset affecting a linearly modulated waveform received through a Rician fading channel. We calculate the relevant Cramer-Rao bound (CRB) and also a set of Cramer-Rao-like bounds proposed in the literature, among which we mention the hybrid CRB, the modified CRB and the Miller-Chang (1978) bound. An extension of the latter bound is also provided. The relative merits of these bounds are discussed, both in terms of their tightness and ease of calculation. A few useful inequalities involving the above bounds are also established