We consider the problem of discriminating a legitimate transmitter from an impersonating attacker in an underwater acoustic network under a physical layer security framework. In particular, we utilize features of the underwater acoustic channel such as the number of taps, the delay spread, and the received power. In the absence of a reliable statistical model of the underwater channel, we turn to a machine learning technique to extract the feature statistics and utilize them to distinguish between legitimate and fake transmissions. Numerical results show how, using only four channel features as input of either a neural network or an autoencoder, we achieve a good trade off between false alarm and detection rates. Moreover, cooperative techniques fusing soft decision statistics from multiple trusted nodes further outperform the discrimination capability of each separate node. Data from a sea trial carried out in Israeli eastern Mediterranean waters demonstrate the applicability of our approach.