  We consider a statistical problem of detection of a signal with unknown
energy in a multi-channel system, observed in a Gaussian noise. We assume that
the signal can appear in the $k$-th channel with a known small prior
probability $\bar{\pi}_k$. Using noisy observations from all channels we would
like to detect whether the signal is presented in one of the channels or we
observe pure noise. In our work we describe and compare statistical properties
of maximum posterior probability test and optimal Bayes test. In particular,
for these tests we obtain limiting distributions of test statistics and define
sets of their non-detectable signals.
