Source Enumeration in Large Arrays Based on Moments of Eigenvalues in Sample Starved Conditions

This paper presents a scheme to enumerate the incident waves impinging on a high dimensional uniform linear array using relatively few samples. The approach is based on Minimum Description Length (MDL) criteria and statistical properties of eigenvalues of the Sample Covariance Matrix (SCM). We assume that several models, with each model representing a certain number of sources, will compete and MDL criterion will select the best model with the minimum model complexity and maximum model decision. Statistics of noise eigenvalue of SCM can be approximated by the distributional properties of the eigenvalues given by Marcenko-Pastur distribution in the signal-free SCM. In this paper we use random matrix theory to determine the statistical properties of the moments of noise eigenvalues of SCM to separate noise and signal eigenvalues. Numerical simulations are used to demonstrate the performance of proposed estimator compared with some other enumerators in sample starved regime.