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

In this paper, we focus on the use of Cramer-Rao-like bounds for the estima tion of a deterministic parameter in the presence of random nuisance parame ters. As a working example, me consider the problem of estimating the carri er frequency offset affecting a linearly modulated waveform received throug h a Rician fading channel. We calculate the relevant Cramer-Rao bound (CRB) and also a set of Cramer-Rao-like bounds recently proposed in the literatu re, among which we mention the hybrid CRB, the modified CRB and the Miller- Chang bound. An extension of the latter bound is also provided. The relativ e merits of these bounds are discussed, both in terms of their tightness an d ease of calculation. A few useful inequalities involving the above bounds are also established