Optimal cyclic statistics for the estimation of harmonics in multiplicative and additive noise

The problem of detection and estimation of harmonics in multiplicative and additive noise is addressed. The problem may be solved using (i) the cyclic mean if the harmonic amplitude is not zero mean or (ii) the cyclic variance if the harmonic amplitude is zero mean. Solution (ii) may be used when the amplitude of the harmonic is not zero mean while solution (i) fails in the case of zero mean harmonic amplitudes. The paper answers the following questions: given a multiplicative and additive noisy environment, which solution is optimal? The paper determines thresholds on the coherent to non-coherent sine powers ratio which delimitate the regions of optimality of the two solutions. Comparison with higher-order cyclic statistics is presented. Gaussian as well as non-Gaussian noise sources are studied