An efficient and simple algorithm for estimating the number of sources via ℓ0.55-norm

Recently, it has been proposed an empirical method for estimating the number of sources of signals impinging on multiple sensors, named norm-based (NB) algorithm. The algorithm computes the Euclidian norm of vectors whose elements are the normalized and nonlinearly scaled eigenvalues of the received signal covariance matrix, and the corresponding normalized indexes. Such norms are then used to discriminate the largest eigenvalues from the remaining ones, thus allowing for the estimation of the number of sources. In this paper we propose an improved norm-based (iNB) algorithm which uses the ℓ_0.55-norm as a means for classifying the eigenvalues. Differently from the NB, the iNB algorithm does not use the nonlinear scaling and does not need to set an additional empirical constant that is crucial to the proper operation of the NB algorithm. Comparisons are made with the estimators MDL (minimum description length) and AIC (Akaike information criterion), and with a recently-proposed estimator based on the random matrix theory (RMT). It is shown that the iNB algorithm can outperform one or more of these estimators in several situations, and that it always outperforms the NB algorithm.