Harmonic retrieval in the presence of non-circular Gaussian multiplicative noise: Performance bounds

We address the problem of harmonic retrieval in the presence of multiplicative and additive noise sources. In the new context of a complex-valued non-circular Gaussian multiplicative noise, we express the Cramér-Rao bound (CRB) as well as the asymptotic (large sample) CRB in closed form. Below a certain SNR threshold and/or when the number of samples is not large enough, the CRB becomes too optimistic and therefore we also derive the Barankin bound (BB). The new theoretical expressions for the CRB and BB are then used to study the behavior of the performance bound with respect to the signal parameters. We especially describe the region (in terms of SNR and number of samples) for which the CRB and the BB differ. Finally we compare the performance of the square-power-based frequency estimate, which is equivalent to the non-linear least-squares-based estimate, to these bounds.