Simple and Efficient Algorithm for Improving the MDL Estimator of the Number of Sources

We propose a simple algorithm for improving the MDL (minimum description length) estimator of the number of sources of signals impinging on multiple sensors. The algorithm is based on the norms 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 used to discriminate the largest eigenvalues from the remaining ones, thus allowing for the estimation of the number of sources. The MDL estimate is used as the input data of the algorithm. Numerical results unveil that the so-called norm-based improved MDL (iMDL) algorithm can achieve performances that are better than those achieved by the MDL estimator alone. Comparisons are also made with the well-known AIC (Akaike information criterion) estimator and with a recently-proposed estimator based on the random matrix theory (RMT). It is shown that our algorithm can also outperform the AIC and the RMT-based estimator in some situations.