Harmonic retrieval in non-circular complex-valued multiplicative noise: Cramer-Rao bound

We address the problem of harmonic retrieval in the presence of multiplicative and additive noise. We derive the finite-sample Cramer Rao bound (CRB) as well as the asymptotic (large sample) CRB when the multiplicative noise is complex-valued and noncircular. These bounds are then analyzed with respect to the signal parameters. Finally, we prove that the square-power based frequency estimate, which is equivalent to the so-called nonlinear least square estimate, is asymptotically efficient when the multiplicative noise is white.