Detection of harmonic sets

We examine the detection problem of signals with narrowband, harmonically related components received by a passive sensor array. We investigate detector structures based on the Fourier method. The harmonic detector estimates the total signal power by combining the DFT coefficients from harmonic frequency bins. This power estimate is normalized by the estimated background noise power and then compared to a threshold. We investigate two harmonic detector structures: one that operates with coherent, correlated signals and the other with uncorrelated harmonic signals. We derive statistical laws governing both detector structures that facilitate setting a power threshold for a given probability of false alarm; and present upper- and lower-bounds for the probability of detection. The results developed and presented demonstrate the inherent advantage of the harmonic detector. At operating conditions characterized by low signal-to-noise power ratio values the harmonic detector exhibits enhanced detection performance by combining the estimated signal power from harmonic frequency bins. We generalize results from single-bin and harmonic detector structures and present them as special cases of a unifying framework.