Source Enumeration Via MDL Criterion Based on Linear Shrinkage Estimation of Noise Subspace Covariance Matrix

Numerous methodologies have been investigated for source enumeration in sample-starving environments. For those having their root in the framework of random matrix theory, the involved distribution of the sample eigenvalues is required. Instead of relying on the eigenvalue distribution, this work devises a linear shrinkage based minimum description length (LS-MDL) criterion by utilizing the identity covariance matrix structure of noise subspace components. With linear shrinkage and Gaussian assumption of the observations, an accurate estimator for the covariance matrix of the noise subspace components is derived. The eigenvalues obtained from the estimator turn out to be a linear function of the corresponding sample eigenvalues, enabling the LS-MDL criterion to accurately detect the source number without incurring significantly additional computational load. Furthermore, the strong consistency of the LS-MDL criterion for m, n -> infinity and m/n -> c is an element of (0, infinity) is proved, where m and n are the antenna number and snapshot number, respectively. Simulation results are included for illustrating the effectiveness of the proposed criterion.