An Information Theoretic Approach to Source Enumeration in Array Signal Processing

In this paper, a new information theoretic algorithm is proposed for signal enumeration in array processing. The approach is based on predictive description length (PDL) that is defined as the length of a predictive code for the set of observations. We assume that several models, with each model representing a certain number of sources, will compete. The PDL criterion is computed for the candidate models and is minimized over all models to select the best model and to determine the number of signals. In the proposed method, the correlation matrix is decomposed into two orthogonal components in the signal and noise subspaces. The maximum likelihood (ML) estimates of the angles-of-arrival are used to find the projection of the sample correlation matrix onto the signal and noise subspaces. The summation of the ML estimates of these matrices is the ML estimate of the correlation matrix. This method can detect both coherent and noncoherent signals. The proposed method can be used online and can be applied to time-varying systems and target tracking.