Source enumeration in large arrays using moments of eigenvalues and relatively few samples

This study presents a method based on minimum description length criterion to enumerate the incident waves impinging on a large array using a relatively small number of samples. The proposed scheme exploits the statistical properties of eigenvalues of the sample covariance matrix (SCM) of Gaussian processes. The authors use a number of moments of noise eigenvalues of the SCM in order to separate noise and signal subspaces more accurately. In particular, the authors assume a Marcenko-Pastur probability density function (pdf) for the eigenvalues of SCM associated with the noise subspace. We also use an enhanced noise variance estimator to reduce the bias leakage between the subspaces. Numerical simulations demonstrate that the proposed method estimates the true number of signals for large arrays and a relatively small number of snapshots. In particular, the proposed method requires less number of samples to achieve the same correct enumeration probability compared to the state-of-the-art methods. The authors evaluated the assumed pdf in order to justify the limitation and the behaviour of the proposed method for small number of snapshots and array sizes.