Detection of weak signals in high-dimensional complex-valued data

This paper considers the problem of detecting a few signals in high-dimensional complex-valued Gaussian data satisfying Johnstone's [On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist.29 (2001) 295–327] spiked covariance model. We focus on the difficult case where signals are weak in the sense that the sizes of the corresponding covariance spikes are below the phase transition threshold studied in Baik et al. [Phase transition of the largest eigenvalue for non-null complex sample covariance matrices, Ann. Probab.33 (2005) 1643–1697