Improving signal subspace estimation and source number detection in the context of spatially correlated noises

This paper addresses the issue of Orthogonal Techniques for Blind Source Separation of periodic signals when the mixtures are corrupted with spatially correlated noises. The noise covariance matrix is assumed to be unknown. This problem is of major interest with experimental signals. We first remind that Principal Components Analysis (PCA) cannot provide a correct estimate of the signal subspace in this situation. We then decide to compute the spectral matrices using delayed blocks to eliminate the noise influence. We show that two of these delayed spectral matrices are enough to get the unnoisy spectral matrix. We also introduce a new source number detector which exploits the eigenvectors of a delayed matrix to estimate the signal subspace dimension. Simulation results show that the signal subspace estimation is improved and the source number detector is more efficient in this situation than the usual AIC and MDL criteria.