Bayesian information criterion for multidimensional sinusoidal order selection

Detecting the sinusoidal order is a prerequisite step for parametric multidimensional sinusoidal frequency estimation methods, whose applications range from radar and wireless communications to nuclear magnetic resonance spectroscopy. Although the Bayesian information criterion (BIC) has been commonly applied for model order selection, its application to sinusoidal order estimation is recent. By means of estimation of Fisher information matrix, we extend the 1-D BIC to multidimensional case for multidimensional sinusoidal order selection. The multidimensional BIC is shown in simulations to outperform the state-of-the-art algorithms in terms of probability of correct detection.