A multi-dimensional model order selection criterion with improved identifiability

A novel R-dimensional (R ≥ 3) model order selection (MOS) criterion is proposed for estimating the number of sources embedded in noise. By extending the classical r-mode matrix unfolding of a Rth-order measurement tensor to multi-mode matrix unfolding, (2^R-1 - 1) unfolded matrices are obtained. To maximize the identifiability, the unfolded matrix whose number of rows is closest to that of the columns is chosen. Meanwhile, as the so-obtained unfolded matrix is of large size, a sequence of nested hypothesis tests on its associated eigenvalues is utilized for MOS in the framework of the random matrix theory. The maximum number of sources the proposed enumerator able to identify is on the order of the square root of the product of all dimension sizes, whereas the identifiability of existing criteria is limited to the maximum dimension size minus one. Numerical results are included to illustrate the performance of the proposed enumerator.