## 3 Materials and Methods
### System Model and Problem Formulation  
It is assumed for the proposed AV network that there are I number of AVs on the road, C number of CUE interact with the BS, \(D\) number of D2D communications, and \(V\) number of V2V communications; all these transmission links share the same transmitted AV spectrum, as indicated in Figure 1. The goal of this proposed model is to develop an adaptive model to improve the performance of autonomous vehicle communication. Therefore, as shown in Figure 2, the suggested model is able to choose the destination or relay location to communicate with using constrained optimization techniques. Based on the system requirements, the decision between direct communication and cooperative communication between AV2X will be made. Therefore, AVs will communicate directly with the destination if the system need can be satisfied within the transmission distance between AV2X. While AV will use a relay vehicle to connect with the destination if the needed system performance is impacted by the transmission distance between AV2X. Through the use of the Lagrange optimization technique and deep learning algorithm, the suggested model will be assessed in terms of energy efficiency and achievable data rate. According to the proposed model, each autonomous vehicle will choose the best autonomous vehicle to communicate with based on its environment in order to efficiently and reliably obtain specific road information, send information to other autonomous vehicles, or send information to the destination. Thus, the proposed model aims to enhance the communication of the AV network by determining the maximum required distance between the AV and everything, whether it is another AV or relay vehicle, to send the data to the destination. Figure 1: Proposed AV system model. The following equations illustrate how this results in an optimization of the overall network performance in terms of energy efficiency (\(EE\)) and the maximum feasible data rate (\(R\)):  
\[ \begin{array}{c}Max\sum\limits_{i=1}^{J}d_{RXi}\\ s.t.\ C1=:\ \{I_{2X}\leq\ I_{2 Xmax}\}\\ C2=:\ \{P_{A}\leq\ P_{Amax}\}\end{array}  \tag{1}\]  
The transmission distance between relay-vehicle and the required destination, whether it is device, vehicle or even base station, to meet the necessary system performance of the \(i\)-th path is represented by \(d_{RXi}\) in the formulation of the optimization issue. The restriction C1 states that interference (\(I_{2}\)) between autonomous vehicle and everything must be less than the maximum permitted interference (\(I_{2 Xmax}\)). \(I_{2 Xmax}\) can be obtained from  
\[I_{2 Xmax}=\sum\limits_{d=1}^{D}P_{D_{d}max}\ H_{D_{d}X}+\sum\limits_{c=1}^{C}P_ {C_{c}max}\ H_{C_{c}X}+\sum\limits_{p=1}^{V}P_{V_{p}max}\ H_{V_{p}X} \tag{2}\]  
Figure 2: Flow chart for the proposed adaptive model. where \(P_{D_{d}max},\ P_{C_{c}max}\), and \(P_{V_{c}max}\) are the maximum interfered D2D transmission power (Dtx), maximum interfered CUE transmission power, and the maximum interfered V2V transmission power, respectively, which share the same AV spectrum. Symbols \(H_{D_{d}X},H_{C_{c}X}\), and \(H_{V_{c}X}\) are the channel gain coefficient between transmission D2D device (Dtx) and the destination, transmission CUE and the destination, and transmitted V2V (Vtx) and the destination, respectively. The restriction that the AV transmission power (\(P_{A}\)) must be less than the AV transmission power maximum (\(P_{Amax}\)) is identified by C2. Rayleigh fading with additive white Gaussian noise (AWGN) and propagation path loss affect the transmission lines between AV2V and AV2X [29]. Statistics-wise, it is believed that the channel fades as various links are independent of one another. The dedicated short-range communications (DSRC) standard is also regarded as the most promising wireless protocol for usage in automobile systems [30]. Short-range wireless communication channels with one-way or two-way functionality are used in DSRC technology and are intended only for usage in automobiles.