# Deep Learning for Joint Adapatations of Transmission Rate and Payload Length in Vehicular Networks
## 3 Joint MCS and Payload Length Adaptation for IEEE 802.11p V2V Networks  
In this section, we present our joint adaptive modulation and coding scheme (MCS) and payload length selection (AMCPLS) for IEEE 802.11p V2V networks, where the communication channel is highly varying. Based on the channel condition, our AMCPLS approach selects both the MCS and the payload length. The aim of AMCPLS is to maximize the effective physical layer throughput and to fulfill a predefined frame error rate (FER).  
We consider that the set of all available MCSs, \(\mathbb{L}\), is given by \(\mathbb{I}=\{0,1,...,I-1\}\), where \(I=\#\mathbb{I}\) is the cardinality of \(\mathbb{I}\), which is the number of the available MCSs. The set of the allowable payload lengths, \(\mathbb{L}\), is given by \(\mathbb{L}=\{0,1,...,L_{-1}\}\), where \(L=\#\mathbb{L}\) is the number of the allowable payload lengths. Assume that the MCS \(i\in\mathbb{I}\) and the payload length \(I\in\mathbb{L}\) are utilized. The total number of information data bits in a single IEEE 802.11p frame, \(N_{DBF}\), is given by  
\[N_{DBF}=K_{D}\times N_{DBS}, \tag{4}\]  
where \(K_{D}\) is obtained from (1) and \(N_{DBS}\) is as shown in Table 1. Furthermore, the total IEEE 802.11p frame duration, \(T_{f}\), is given by  
\[T_{f}=K\times T_{OS}, \tag{5}\]  
where \(T_{OS}\) is the OFDM symbol duration which is 8 us, and \(K\) is calculated as in (2). Thus, the effective data rate, \(R_{eff}\), is given by  
\[R_{eff}=\frac{N_{DBF}}{T_{f}}=\frac{K_{D}N_{DBS}}{(K_{D}+K_{ov})T_{OS}}, \tag{6}\]  
Therefore, the effective physical layer throughput, \(\Gamma\), is given by  
\[\Gamma=R_{eff}(1-FER)=\frac{K_{D}N_{DBS}(1-FER)}{(K_{D}+K_{ov})T  
detailed in Table 1, we can conclude that the effective physical layer throughput is dependent on the utilized MCS, the utilized payload length and the FER. Moreover, the FER is affected by three main factors, namely, the MCS, the payload length, and the transmission channel condition. Therefore, the effective physical layer throughput can be controlled by the MCS, the payload length, and the channel condition. The channel condition is determined by the surrounding wireless environment. This motivates us to jointly adapt both the MCS and the payload length based on the channel condition to maximize the effective physical layer throughput under a predefined FER constraint. The proposed AMCPLS scheme can be formulated as follows  
\[\{i^{*},l^{*}\}=\underset{\{i,l\}}{\text{argmax}}\{\Gamma(\{i,l\},\mathbf{g}): FER(\{i,l\},\mathbf{g})<\epsilon\}, \tag{8}\]  
where \(\epsilon\) is the target FER, \(\mathbf{g}\) is the vector that represents the channel condition, and \(\{i^{*},l^{*}\}\) is the optimum combination of the MCS and the payload length. The channel condition vector \(\mathbf{g}\) needs to include the effects of both the channel fading and the AWGN.  
We refer to the optimum solution of the problem expressed in (8) as the ideal AMCPLS. Practically, this ideal AMCPLS can not be implemented due to the following two obstacles. The first is that it is very challenging to correctly derive the FER of a wireless communication system, since the FER is a complicated function of the channel condition, the modulation and coding scheme, and the payload length. The second obstacle is that the actual channel condition, \(\mathbf{g}\), for the next frame cannot be assumed to be perfectly known in practice, since the channel is varying over different frames. In Section 5.1, we evaluate the ideal AMCPLS using numerical enumerations, where we assume that the channel condition for the next frame can be obtained. Although this solution to the ideal AMPLS may not be practical, we treat the performance of this ideal AMCPLS as a benchmark. In next section, we resort to a deep learning approach to solve the AMCPLS scheme, which is more practical.