This paper presents a novel method for automatic modulation classification (AMC) for cognitive radio (CR) networks based on a simple classifier that is trained with high-order cumulant. The proposed method focuses on the statistical behavior of modulated signals and includes analog modulation and digital schemes, which received less attention in the literature. The effectiveness of the proposed method is demonstrated through simulation results using high-quality generated signals under different signal-to-noise ratios (SNRs) and channel conditions. The classification performance achieved by the proposed method is superior to that of the more complex deep learning methods, making it well-suited for deployment in end units of CR networks, particularly in military and emergency service applications. The proposed method offers a cost-effective, high-quality solution for AMC that meets the stringent requirements of these critical applications.