## 1 Introduction  
The recognition of modulation type in an unknown signal holds significant importance as it provides essential insights into its structure, origin, and properties. Automatic modulation classification serves various purposes, including spectrum surveillance and management, interference identification, military threat evaluation, electronic countermeasures, source identification, and numerous others. For instance, identifying the modulation type of an intercepted signal allows for more efficient jamming by focusing available resources on vital signal parameters. This is particularly relevant in wireless communications, where different services follow established modulation standards. Modulation recognition is a crucial aspect of signal processing, entailing the determination of a signal's modulation mode without prior knowledge. M-ary quadrature amplitude modulation (MQAM) is a widely used digital modulation technology employed in satellite communication and cable networks due to its commendable spectrum efficiency and robust interference resistance. The lack of prior information, such as signal parameters at the receiving end, can make it hard to figure out the modulation order of the QAM signal in non-cooperative communication situations, especially when the signal-to-noise ratio (SNR) is low [1]. Digital modulation identification algorithms can be categorized into two main groups: maximum likelihood hypothesis-based methods rooted in decision theory and statistical pattern recognition techniques relying on feature extraction [2; 3]. These techniques are particularly valuable in uncooperative channel environments, and pattern recognition algorithms are often preferred in practical applications due to the absence of prior knowledge about received modulation signals [4]. Higher-order constellation (HOC)-based techniques are well-known pattern recognition methods that perform well at classifying digital modulation signals when the signal-to-noise ratio (SNR) is low. However, they might not work well for classifying higher-order MQAM modulation formats [5]. The constellation diagram varies between different modulation signal types and serves as a robust signature. Researchers have employed algorithms that utilize constellation diagram to identify the order of MQAM [6; 7; 8; 9]. It is possible to recognize modulation in MQAM signals by putting together the constellation diagram using clustering algorithms [10]. The subtractive clustering (SC) algorithm constitutes a significant focus in the field of MQAM signal constellation reconstruction [11]. This algorithm considers each data point as a potential cluster center and calculates it based on the density index of the signal's data points. [PERSON] et al. [12] predefined the optimal clustering radius for MQAM signals and employed the SC algorithm to reconstruct the MQAM signal's constellation diagram. However, this approach demands significant computational resources and exhibits poor clustering performance in low signal-to-noise ratio conditions. [PERSON] et al. [13] extracted characteristic parameters from the signal's constellation diagram using the SC algorithm and compared them with those from the standard constellation diagram to figure out what kind of modulation it was. However, the method showed limited noise resilience and lacked a standardized approach for selecting clustering radii. To improve the accuracy of clustering center coordinates within the signal's constellation diagram, some studies integrate the fuzzy c-means (FCM) algorithm for secondary clustering. FCM is a clustering algorithm that assesses the degree to which each data point belongs to a specific cluster through a membership relationship [14; 15]. However, FCM is sensitive to the values that are chosen at the start for the cluster centers, and its results often get stuck in local optima, making it harder to find the globally optimal clustering centers.