## 1 Introduction  
Automatic retransmission request (ARQ) strategy is a key technique to reduce the energy consumption of cooperative communication. Reducing the number of signal retransmissions has been the focus of scholars [1]. Due to the increase in the number of nodes, cooperative communication is used to share data in clustered networks. However, the energy provided by the communication system is limited, so low-energy consumption communication techniques have become the focus of scholars' research today [2]. In the signal-forwarding phase of cooperative communication, the cooperative automatic retransmission request (CARQ) strategy can improve the probability of successful signal transmission, but the existing methods consume too much energy. It has been found that an excessive number of retransmissions is the direct cause of energy consumption [3]. The method to reduce the number of retransmissions is an important re-investigation direction for low-power cooperative communication. Scholars have been working on the study of automatic retransmission request strategies. Following the rise of wireless communication, [PERSON] first proposed the framework of automatic retransmission request protocol for cooperative communication in cooperative ARQ [4]. The protocol added an answer mechanism for the destination node, and the two-way communication model provided a classical research model for subsequent studies. Thereafter, [PERSON] designed a relay model with three nodes forwarding signals based on this model [5]. The new model of relay forwarding signals solves the problem that direct communication cannot transmit information, and the relay model of signal forwarding by three nodes is a classical model of cooperative communication, which has attracted the attention of communication engineering scholars. [PERSON] introduced the ARQ model in the study of cooperative communication and CARQ techniques gained importance in multi-user network applications due to the retransmission signals that improved the stability of the network [6]. Although the early studies used the CARQ model with packet and random coding, the transmission delay of the system was reduced and the technology of communication engineering was improved. [PERSON] was the first scholar to introduce cooperative communication into wireless communication networks [7], the connectivity of cooperative communication has improved the stability of wireless communication networks, and cooperative communication accelerated the development of wireless networks. To improve the bandwidth of LAN communication, [PERSON] proposed a CARQ strategy for channel packet transmission [8]. The strategy solves the inefficiency of multi-link communication with packet retransmission. However, the disadvantage of the strategy is that it consumes a lot of energy as a cost. [PERSON] proposed an improved CARQ strategy based on two-hop switching [9]. The strategy shortens the distance of the communication link and the communication BER is improved. However, the probability of interruption of the communication process increases due to irregular switching time. [PERSON] designed the CARQ adaptive control method with adjustable power and delay [10]. The method improves the power allocation control parameters and the communication time of the network nodes is extended. Additionally, the life cycle and stability of CARQ are improved because the power parameters are also adjustable. As the number of communication nodes increases, the method is discarded due to the increase in the regulated parameters as well. At the same time, the hardware memory capacity required to control the method is increased. [PERSON] integrated queuing theory into the amplify and forward CARQ strategy [11]. The method improves the throughput of the system and the efficiency of communication transmission is enhanced. However, due to the long computation time of the queuing theory algorithm, the algorithm cannot be applied to large-scale networks.