The spectrum sensing of the orthogonal frequency division multiplexing (OFDM) system in cognitive radio (CR) has always been challenging, especially for user terminals that utilize the full-duplex (FD) mode. We herein propose an advanced FD spectrum-sensing scheme that can be successfully performed even when severe self-interference is encountered from the user terminal. Based on the “classification-converted sensing” framework, the cyclostationary periodogram generated by OFDM pilots is exhibited in the form of images. These images are subsequently plugged into convolutional neural networks (CNNs) for classifications owing to the CNN's strength in image recognition. More importantly, to realize spectrum sensing against residual self-interference, noise pollution, and channel fading, we used adversarial training, where a CR-specific, modified training database was proposed. We analyzed the performances exhibited by the different architectures of the CNN and the different resolutions of the input image to balance the detection performance with computing capability. We proposed a design plan of the signal structure for the CR transmitting terminal that can fit into the proposed spectrum-sensing scheme while benefiting from its own transmission. The simulation results prove that our method has excellent sensing capability for the FD system; furthermore, our method achieves a higher detection accuracy than the conventional method.