###### Abstract  
Modulation awareness and cooperative transmissions have individually received a significant amount of research in the scholarly literature. However, a limited number of works are principally concerned with the combination of the two topics, and they are restricted to frequency-flat wireless channels. In this study, we propose a new modulation awareness method applicable to dual-hop amplify-and-forward cooperative broadcasts. The suggested method is built on the creation of theoretical representations of cross-correlation functions of the received signals. We conceptually prove that a family of modulation types generates spikes for certain cross-correlation functions, while others do not. We create a numerous layer hypothesis evaluation for the purpose of making judgments centered on this attribute. The suggested method has a number of benefits, such as the ability to operate on both frequency-flat and frequency-selective channels, as well as the absence of the necessity of channel awareness or noise power. Computer simulations analyze the performance of the proposed method, which delivers adequate awareness performance in a variety of operational scenarios. modulation awareness; cooperative broadcasts; fading channels 2022225441  
Herein lies the significance of AMA algorithms at receivers, since they have to know the kind of modulations used in order to decode the supplied data. Adaptive modulation is adopted in a number of current wireless technologies, such as cellular systems, microwave transmissions, satellites and wireless local area networks [7; 8]. The likelihood-based (LB) and feature-based (FB) approaches are the most often used in the field of AMA [9; 10]. In general, LB techniques tackle AMA issues using probability theories and hypothesis models. Even though LB AMA techniques reach the highest level of precision, they are computationally intensive and may be prohibitively costly in reality. To compensate for this limitation, FB AMA techniques exploit signal characteristics, such as higher order statistics and cyclostationarity to discriminate between modulation types [11; 12; 13; 14]. Similarly, cooperative communications have sparked substantial attention in research and industry because of their superior performance characteristics such as system capacity and transmission range, including the simplicity with which they may be implemented [15; 16; 17; 18]. The fundamental notion is driven by the fact that, in a wireless context, the signal sent by a source to a destination is also heard by other endpoints, which are frequently known as relays. The signals captured by the relays are recycled and sent to their destination. The destination subsequently integrates the messages from the source and the relays, resulting in spatial variety by leveraging numerous reception of the same data at different stations and transmission channels. Extensive work has been made in information theoretic analysis of various cooperative systems to estimate feasible rates, capacity limitations and the diversity-multiplexing trade-off as well as data detection and channel estimation (e.g., [19; 20; 21; 22; 23; 24]). Despite the importance of these findings, more work must be done before they can be put into practice. One of the primary concerns with cooperative systems is determining how to perform AMA in the context of multiple transmissions of the source and relays. Only two studies, to the best of our knowledge, have tackled the AMA issue for cooperative systems [10; 25]. Nevertheless, they are restricted to frequency-flat fading channels and the decode-and-forward (DF) approach in their communication protocols. The most important contributions and discoveries made by this research are described in the following aspects. * We develop a new AMA method for amplify-and-forward (AF) dual-hop cooperative systems over frequency-selective fading channels.