  We study the statistical decision process of detecting the signal from a
`signal+noise' type matrix model with an additive Wigner noise. We propose a
hypothesis test based on the linear spectral statistics of the data matrix,
which does not depend on the distribution of the signal or the noise. The test
is optimal under the Gaussian noise if the signal-to-noise ratio is small, as
it minimizes the sum of the Type-I and Type-II errors. Under the non-Gaussian
noise, the test can be improved with an entrywise transformation to the data
matrix. We also introduce an algorithm that estimates the rank of the signal
when it is not known a priori.
