Multichannel two-stage detection of signals

This paper deals with multichannel two-stage sequential detectors (MTSDs) based on different kinds of decision statistics. Explicit expressions are derived for the basic performance measures of such detectors: probability of false alarm, probability of detection, and average sample number (ASN). These characteristics of an MTSD depend on its main parameters: decision thresholds and durations of both stages. An efficient optimization method of MTSD parameters, which uses computer simulations to find decision statistics, is proposed. This technique is then applied to calculate parameters of various MTSDs with many channels (up to a few thousand) and to compare their performance with conventional detectors. Closed-form empirical formulas approximating the obtained measurement points are given. Results of computer simulations prove the high practical usefulness of the presented approach.