## 1 Introduction  
In the modern era of digital interconnectedness, wireless communication systems are pivotal in forging effective channels that link individuals, devices, and data across vast distances [1, 2]. These systems, dependent on the transmission and reception of signals, are critical for seamless communication. Initially, the field of wireless communication was characterized by a restricted suite of modulation schemes and a cooperative nature, where entities engaged in communication mutually agreed on the schemes to be employed. This era did not demand signal recognition at the receiving end. As wireless communication systems have progressed, expanding in diversity and intricacy, the implementation of multiple modulation schemes has become commonplace. This development underscores the need for precise classification of these varied schemes, a task skillfully managed by automatic modulation classification (AMC) [3, 4]. AMC has an integral role in non-cooperative communication scenarios, acting as a link between signal detection and demodulation. Here, non-cooperative communication refers to instances where an external party gains access to a communication system with no prior approval from the original communicating parties, without affecting their ongoing communication. AMC's utility spans military and civilian sectors. In military applications, it is instrumental in identifying and analyzing electromagnetic signals, which can reveal the functionalities of enemy electronics and assess their threat levels. Moreover, AMC processes this intelligence, bolstering reconnaissance efforts. In civilian applications, AMC's ability to distinguish between modulation schemes is fundamental to efficient device communication and vital for smart, efficient, and reliable systems. A clear example is in smart home ecosystems, where wireless communication integrates smart appliances and security systems. Through AMC, these devices can discern and accurately process communication signals, ensuring secure data transmission and operational reliability. In situations where many parameters of the transmitted data and receiver are not known, such as signal power, carrier frequency, and phase offset, automatic modulation classification is a challenging task [5]. Traditional methods can be broadly grouped into two categories: likelihood theory-based AMC (LB-AMC) [6; 7; 8] and feature-based AMC (FB-AMC) [9; 10; 11]. The pivotal concept underlying the LB-AMC method involves establishing a likelihood function based on the statistical attributes of the signal model. This determines an optimal discrimination threshold. By evaluating the signal's likelihood ratio against the threshold, a modulation scheme can be identified. LB-AMC has been shown to achieve optimal performance in Bayesian estimation, as it minimizes the probability of erroneous classification. Nevertheless, its elevated computational complexity poses a challenge to its practical adoption, as it may not satisfy the requirements of real-time processing and a low cost. Notably, when the parameters remain unknown, the recognition accuracy may be significantly affected. Currently, the FB-AMC method has emerged as the predominant approach. Its main principle is to select suitable features and carry out feature extraction from the received signal. Subsequently, a trained classifier classifies the extracted feature information. In comparison with LB-AMC, its algorithm complexity is significantly diminished. In particular, it can be perceived as a mapping relationship from the signal space to the feature space. It morphs a high-dimensional signal space into a lower-dimensional feature space, simplifying calculations. Additionally, the features extracted from the received signal can exhibit differences between diverse modulation schemes. The features should be precise to achieve superior recognition performance. Selection of excellent statistical features is paramount for FB-AMC.