Model Order Selection For Sum of Complex Exponentials

In this paper, we present a new method for estimating the number of terms in a sum of exponentially damped sinusoids embedded in white noise. In particular, we propose to combine the shift-invariance property of the Hankel matrix associated with the sum of exponentials with a constraint over its singular values to penalize small order estimations. In this way, we are taking into account not only the algebraic structure of the signal but also its statistical properties. This methodology significantly improves the estimation of the model order in comparison with the subspace-based methods, especially when a good separation between the noise and the signal subspace is not possible. We assess the performance of our technique by computing the correct order selection rate and by comparing it to previous results found in the literature.