Local Detectors for High-Resolution Spectral Analysis: Algorithms and Performance

摘要

This paper develops local signal detection strategies for spectral resolution of frequencies of nearby tones. The problem of interest is to decide whether a received noise-corrupted and discrete signal is a single-frequency sinusoid or a double-frequency sinusoid. This paper presents an extension to M. Shahram and P. Milanfar (On the resolvability of sinusoids with nearby frequencies in the presence of noise, IEEE Trans. Signal Process., to appear, available at http://www.soe.ucsc.edu/milanfar) the case where the noise variance is unknown. A general signal model is considered where the frequencies, amplitudes, phases and also the level of the noise variance is unknown to the detector. We derive a fundamental trade-off between SNR and the minimum detectable difference between the frequencies of two tones, for any desired decision error rate. We also demonstrate that the algorithm, when implemented in a practical scenario, yields significantly better performance compared to the standard subspace-based methods like MUSIC. It is also observed that the performance for the case where the noise variance is unknown, is very close to that when the noise variance is known to the detector.