We consider an aeronautical ad-hoc network relying on aeroplanes operating in the presence of a spoofer. The aggregated signal received by the terrestrial base station is considered as 'clean' or 'normal', if the legitimate aeroplanes transmit their signals and there is no spoofing attack. By contrast, the received signal is considered as 'spurious' or 'abnormal' in the face of a spoofing signal. An autoencoder (AE) is trained to learn the characteristics/features from a training dataset, which contains only normal samples associated with no spoofing attacks. The AE takes original samples as its input samples and reconstructs them at its output. Based on the trained AE, we define the detection thresholds of our spoofing discovery algorithm. To be more specific, contrasting the output of the AE against its input will provide us with a measure of geometric waveform similarity/dissimilarity in terms of the peaks of curves. To quantify the similarity between unknown testing samples and the given training samples (including normal samples), we first propose a so-called deviation-based algorithm. Furthermore, we estimate the angle of arrival (AoA) from each legitimate aeroplane and propose a so-called AoA-based algorithm. Then based on a sophisticated amalgamation of these two algorithms, we form our final detection algorithm for distinguishing the spurious abnormal samples from normal samples under a strict testing condition. In conclusion, our numerical results show that the AE improves the trade-off between the correct spoofing detection rate and the false alarm rate as long as the detection thresholds are carefully selected.