  Source number detection is a critical problem in array signal processing.
Conventional model-driven methods e.g., Akaikes information criterion (AIC) and
minimum description length (MDL), suffer from severe performance degradation
when the number of snapshots is small or the signal-to-noise ratio (SNR) is
low. In this paper, we exploit the model-aided based deep neural network (DNN)
to estimate the source number. Specifically, we first propose the eigenvalue
based regression network (ERNet) and classification network (ECNet) to estimate
the number of non-coherent sources, where the eigenvalues of the received
signal covariance matrix and the source number are used as the input and the
supervise label of the networks, respectively. Then, we extend the ERNet and
ECNet for estimating the number of coherent sources, where the forward-backward
spatial smoothing (FBSS) scheme is adopted to improve the performance of ERNet
and ECNet. Numerical results demonstrate the outstanding performance of ERNet
and ECNet over the conventional AIC and MDL methods as well as their excellent
generalization capability, which also shows their great potentials for
practical applications.
