# Deep Reinforcement Learning for Energy-Efficient 6G V2X Networks
## 3 System Model and Problem Formulation
### Communication Model  
Given the number of RSUs with available uplink RBs and the number of vehicles with RBs required to send data to RSUs, we need to decide whether to turn the RSU on or off and determine the optimal associations of vehicles with RSUs. Our goal aims at reducing the number of turned-on RSUs depending on the required tasks and subject to the uplink bandwidth constraints exemplified by ICI and SINR.  
SINR can be expressed as the signal power divided by the noise power plus the interference power of other signals in the network. SINR can be calculated from the transmission power of the vehicle and the interference power level of other interferer RSUs in the network. SINR values for uplink transmission can be obtained as  
\[\Gamma_{n,v}=P_{v}\ d_{n,v}^{-\alpha}\ (N_{0}+I_{\text{tot}})^{-1}, \tag{1}\]  
where \(P_{v}\) is the transmission power of the vehicle \(v\); \(d_{n,v}\) is the distance between the vehicle \(v\) and the center of the RSU \(n\); \(\alpha\) is the attenuation factor, that is, the path loss, calculated from the COST 231-Hata Model [40]; \(N_{0}\) is the power spectral density of a white noise source; and \(I_{\text{tot}}\) is the aggregated uplink ICI.  
Assuming that the network model is fully loaded with traffic, omnidirectional antennas are used, and the regular coverage pattern occurs, we could approximate the uplink ICI from the RSU \(n\) with a log-normal distribution by analytically determining the statistical parameters [41]. Therefore, the aggregated uplink ICI, \(I_{\text{tot}}\), is approximated with another log-normal distribution and calculated according to  
Figure 2: A small example of V2X network topology.  
\[I_{\text{tot}}=\sum_{i=1,i\
eq n}^{N}I_{i}, \tag{2}\]  
where \(I_{i}\) is the mean value of the uplink ICI of the interfering RSU \(i\), and for each RSU, only a single interference source is considered since only one vehicle is scheduled per RB. \(I_{i}\) is computed as (in this paper, we focus on the optimization problem rather than on the interference and SINR; for further details, we refer the reader to [41])  
\[I_{i}=\frac{1}{\pi}\int_{0}^{C}\int_{0}^{2\pi}P_{v}C^{-2}\rho^{1+\alpha}(\kappa ^{2}+\rho^{2}+2\kappa\rho\cos\theta)^{-\frac{\alpha}{2}}\ d\rho d\theta, \tag{3}\]  
where \(C\) is the coverage of the RSU in kilometers, \(\kappa\) is the distance between the vehicle and the interferer RSU in kilometers, \(\rho\) is the distance from the transmitter to the receiver in kilometers, \(\theta\) is the angle of the vehicle to the directed line connecting the target RSU to the interferer RSU, and \((\kappa^{2}+\rho^{2}+2\kappa\rho\cos\theta)^{1/2}\) denotes the Euclidean distance between the target RSU and the interferer RSU [41].  
After calculating the SINR values for each vehicle, we need to calculate the RB data rate according to the SINR value, channel quality indicator (CQI) index and efficiency from the mapping table that determines various CQI indices based on different modulation orders, SINR ranges, and efficiencies [42]. We use this mapping to obtain the number of necessary RBs. For the sake of simplicity, we consider both vehicles and RSUs forming the network working in single-input-single-output (SISO) mode [42]. The CQI index is calculated in the vehicle and reported to the RSU. We use the CQI to determine the efficiency and calculate the data rate of an RB. An RB per time slot of 0.25 milliseconds consists of 12 subcarriers of 60 kHz wide in frequency, and each subcarrier consists of 14 symbols. Accordingly, the data rate of an RB (bits/milliseconds) is calculated as  
\[dr_{RB}=12\times 14\times\text{efficiency}. \tag{4}\]  
After calculating the data rates of the RBs, we can determine the number of RBs (\(R_{n,v}\)) requested by each vehicle to execute its uplink task. \(R_{n,v}\) depends on the uplink and RB's data rates, i.e., \(U_{n,v}\) and \(dr_{RB}\). We use the following formula:  
\[R_{n,v}=\frac{U_{n,v}}{dr_{RB}}. \tag{5}\]