## 2 Theoretical Study
### Optimal Relay Node Selection
Within the packet, the node with the largest link quality is defined as the best relay node and a link quality based maximum competition approach is determined. The designed relay competition rules are as follows. During the broadcast of the signal by the source node of the cooperative communication, the surrounding nodes establish a communication link with the source node and the quality of the communication link is influenced by the link length [26], all nodes establish a  
Figure 1: Diagram of cooperative communication two-phase communication work. communication link with the destination node and the channel quality is defined by the minimum disruption probability. Additionally, the two-channel communication quality is the smallest value of the two aforementioned links [27]. The definition \(q_{i}\) represents the channel quality of the \(i\)-th link, and the value is determined jointly by the RS link and the RD link quality. The \(q_{i}\) equation is calculated by the following equation. \[q_{i}=\min\Big{(}|h_{S,i}|^{2},|h_{i,D}|^{2}\Big{)} \tag{3}\]  
A competition rule for the best relay node is defined. In multi-node packet communication, the control signal \(W_{i}\) for retransmission signals is generated by the competition rule. It is assumed that during a communication period T, the nodes within the group are timed as a decreasing function starting with \(W_{i}\) as the initial value, and when the value of \(W_{i}\) is zero, the node is determined to be the best relay node. Where, \(W_{i}\) denotes the probability that a communication link will be disrupted [28]. The competition rule is defined according to the magnitude of the probability of disruption in the link where the node is located. In this case, the best relay node broadcasts a signal, and the other nodes stop participating in the competition after receiving the signal [29]. The calculation of the weight \(W_{i}\) is performed using the following equation. \[w_{i}=\frac{\lambda}{q_{i}} \tag{4}\]  
In the formula, \(\lambda\) is a constant with a value of 0.01 T, \(i\) = (1, 2, 3, \(\cdots\), n). A competition rule based on the maximum channel quality nested with the minimum link quality is determined. From the equation, the minimum link quality is a pre-work for solving the maximum channel quality [14,30]. The expression of the competition rule for the \(i\)-th node to be filtered is given below. \[R_{ii}=\max_{i}\Big{\{}\min\Big{(}|h_{S,i}|^{2},|h_{i,D}|^{2}\Big{)}\Big{\}} \tag{5}\]  
In the formula, \(R\) stands for maximum link information, \(i\) = (1, 2, 3, \(\cdots\), n). In the second phase of packet communication, the best relay node forwards the signal to the destination node. The destination node receives several relay signals at the same time. Multiple signal copies are aggregated into one signal by the maximum merge method [8]. If the merged signal can be successfully decoded by the destination node, the destination node transmits a feedback signal ACK to the relay node. The relay node signal forwarding is terminated [14]. If the merged signal cannot be successfully decoded, the destination node sends a signal NACK to the relay node, which continues to forward the signal to the destination node [30]. As the number of nodes increases, the probability of the relay-forwarded signal being successfully decoded gradually decreases, and the existing studies [14,31] have proved that the existing retransmission methods cannot meet the needs of multi-node cooperative communication. An idea based on the forwarding of signals by other nodes was designed to replace relay forwarding.