The objective of the proposed research is to design OFDM-AM systems with higher security by revealing a potential security issue though developing three learning-based attack methods to OFDM-AM systems and its corresponding defensive methods. Based on the principle of AM, channel state information (CSI) is inferred from the modulation type of each subcarrier without any prior knowledge of the desired transmission. With the inferred CSI, we develop three adversarial attacking methods by maximizing error rate, minimizing capacity, or maximizing outage probability. Simulation results show that the learning-based method can detect the modulation type of each subcarrier in high accuracy and then successfully infer the CSI range. Furthermore, simulations also demonstrate that the proposed attacks cause severe performance degradation of OFDM-AM systems (e.g., error rate, capacity) with fairly low power. On the other hand, the defensive methods targeting the proposed learning-based adversarial attacks are also considered. A coset quadrature amplitude modulation (coset-QAM) technique with coset selection matrix to improve the security of modulation types of OFDM-AM has been designed and found to be effective. Future research will focus on developing adversarial attacks on other field, e.g., MIMO and beamforming, and learning-based or traditional defensive methods to build the proposed high security wireless communication systems in 5G, 6G, and beyond.