Second-order statistics versus HOS for the estimation of harmonics in additive and multiplicative noise

Second-order statistics (SOS) have been widely used for the detection and estimation of coherent sinusoids in additive wide-band noise. This paper addresses the detection and estimation of harmonics which have been corrupted by both multiplicative and additive noise, HOS are useful in estimating harmonics of zero mean amplitude where SOS generally fail. The paper analyses and compares the performance of SOS and HOS when the harmonic has both coherent and non-coherent powers. We determine thresholds on the coherent-to-non-coherent sine wave power ratio which delimitate the regions of optimality of SOS and HOS. Gaussian as well as non-Gaussian noise sources are studied.