Multi-dimensional model order selection

Abstract

Multi-dimensional model order selection (MOS) techniques achieve an improved accuracy, reliability, and robustness, since they consider all dimensions jointly during the estimation of parameters. Additionally, from fundamental identifiability results of multi-dimensional decompositions, it is known that the number of main components can be larger when compared to matrix-based decompositions. In this article, we show how to use tensor calculus to extend matrix-based MOS schemes and we also present our proposed multi-dimensional model order selection scheme based on the closed-form PARAFAC algorithm, which is only applicable to multidimensional data. In general, as shown by means of simulations, the Probability of correct Detection (PoD) of our proposed multi-dimensional MOS schemes is much better than the PoD of matrix-based schemes.

A multi-dimensional model order selection criterion with improved identifiability

“…We can see that the R-D RMT criterion can detect the true number of signals in both source number scenarios. While the R-D MDL/AIC/EFT criteria [9] can detect at most 4 sources, the R-D RMT identifiability is significantly higher. However, the performance of the R-D RMT with constant confidence level is not robust to the true number of signals.…”

“…One solution is to convert the measurement tensor to matrix form by r-mode matrix unfolding, and then employ one or a number of sets of r-mode (r = 1, · · · , R) eigenvalues for source enumeration [5,6,9]. This solution does not well exploit the inherent tensor structure of the measurement data, and as a result the identifiability is limited particularly when none of the dimension sizes is large enough.…”

“…Using Y (1) , the R-D RMT criterion can detect up to (P1 − 1) signals, while the R-D criterion in [9] can detect at most…”

“…The 1-D source enumerators mainly consist of the minimum description length (MDL) [2], Akaike information criterion (AIC) [3], exponential fitting test (EFT) [4][5][6] and random matrix theory (RMT) based criteria [7,8]. In [5,6,9], an R-D extension of the 1-D MDL/AIC/EFT criteria is proposed, in which all r-mode (r = 1, · · · , R) eigenvalues of the R-D measurement tensor Y Y Y ∈ C M 1 ×···×M R are calculated and combined to form global eigenvalues. As more information of eigenvalues can be employed for source enumeration, the R-D criteria is superior to the 1-D counterparts.…”

Multidimensional Sinusoidal Frequency Estimation Using Subspace and Projection Separation Approaches

“…with F being the number of sinusoids, which is assumed to be known a priori [13]. Here, α f is the unknown complex amplitude of f th tone, ω f,r ∈ (−π, π) is the unknown frequency of f th component in the rth dimension.…”