Improved spectral analysis of nearby tones using local detectors

This paper concerns the problem of resolvability power in the frequency domain. The canonical case of interest is to distinguish whether the received noise-corrupted signal is a single-frequency sinusoid or a two-frequency sinusoid, where the amplitudes, phases and frequencies are unknown to the receiver. Using a model-based hypothesis testing approach, we quantify a measure of attainable resolution between sinusoids with nearby frequencies, in the presence of noise. An explicit relationship is derived for the minimum detectable difference between the frequencies of two tones, for any particular false alarm and detection rate, and at a given SNR. An associated algorithm is proposed that produces significantly better performance compared to the standard subspace-based methods like MUSIC and can be effectively used in practice as a postprocessing step for the existing spectral estimation methods.