Optimal detection of a random multitone signal and its relation to bispectral analysis

Optimal detection of a multitone signal in Gaussian noise and its relation to bispectral analysis are addressed. Using hypothesis testing methods the optimal detector of a multitone signal with random phases and (known) harmonic relations is derived. It is shown that the optimal receiver consists of a power spectrum block, and a block which deals with the phase coupling. Under a low signal-to-noise ratio (SNR) assumption, this extra block is closely related to a processor based on the bispectral analysis. Thus, a detector which is based on a superposition of the output of the conventional noncoherent detector and the bispectrum estimate of the input signal is a suboptimal one, approaching optimal performance in the low SNR case