Multiple signal detection using the Benjamini-Hochberg procedure

Abstract

We treat the detection problem for multiple signals embedded in noisy observations from a sensor array as a multiple hypothesis test based on log-likelihood ratios. To control the global level of the multiple test, we apply the false discovery rate (FDR) criterion proposed by Benjamini and Hochberg. The power of this multiple test has been investigated through narrow band simulations in previous studies. Here we extend the proposed method to broadband signals. Unlike the narrow band case where the test statistics are characterized by F-distribution, in the broadband case the test statistics have no closed form distribution function. We apply the bootstrap technique to overcome this difficulty. Simulations show that the FDR-controlling procedure always provides more powerful results than the FWE controlling procedure. Furthermore, the reliability of the proposed test is not affected by the gain in power