Estimating the Number of Sinusoids in Additive Sub-Gaussian Noise With Finite Measurements

Abstract

This paper considers the problem of estimating the number of sinusoidal signals in additive sub-Gaussian noise. We develop a novel non-asymptotic analysis of the eigenvalues of a Hermitian Toeplitz data matrix with finite noisy measurements. With this analysis, we propose a new threshold-based estimation algorithm which is guaranteed to correctly recover the true source number with high probability under certain conditions. The analysis is applicable to any independent sub-Gaussian additive noise. In particular, exact knowledge of the likelihood function is not needed and the noise terms may not be identically distributed. The theoretical claims are demonstrated by extensive numerical experiments.