Consistency of Detection of the Number of Signals using Multiple Hypothesis Tests

We study a multiple hypothesis test for detecting signals embedded in noisy observations of a sensor array. The global level of the multiple test is controlled by the false discovery rate (FDR) criterion recently suggested by Benjamini and Hochberg. In previous studies, the suggested procedure has shown promising results on both simulated and real data. Here we carefully examine the consistency property of the multiple test procedure. Applying the asymptotic properties of maximum likelihood (ML) estimation, we prove strong consistency under a mild condition on signal and noise eigenvalues. This condition enables us to find the minimum SNR to ensure consistency. Our analysis is further confirmed by numerical experiments conducted under low SNRs and closely located signal sources.