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

We focus on harmonic retrieval in multiplicative and additive noise. At low SNR, Maximum-Likelihood based estimate does not reach the Cramer-Rao bound. Actually, at low SNR, the Cramer-Rao bound is not a tight bound anymore and has to be replaced with the so-called Barankin bound which is tighter but more complicate. In this paper, we derive the Barankin bound when the multiplicative noise is complex-valued and non-circular. We observe that the Barankin bound is much more greater than the Cramer-Rao bound, especially when the multiplicative noise is not non-circular enough.