# ITFDS: Channel-Aware Integrated Time and Frequency-Based Downlink LTE Scheduling in MANET
## 2 Proposed Method
### Dynamic Class-based Establishment (DCE)  
The symbols used for this proposed systems that \(T,\ T_{1},\ T_{2}\) are the matrices, \(r,\ s\) are the elements of the transmission time interval, \(\delta\) is the transmission state probability, \(k\) denotes the state, \(\gamma\) is the constant value, \(R\) denotes the resultant length, \(Q\) is the queue value, \(\text{delay}_{i}\) denotes the delay value, \(P_{c}\) denotes the parameter of channels, \(w_{k}\) is the weighted value, \(T_{w}\) denotes the transmission range for the weighted value, \(W_{i}(t)\) denotes the weighted time domain value in TTI, \(Q_{l,k}\) denotes the queue length between the user \(i\) and \(k\), \(Q_{\text{th}_{i,k}}\) denotes the threshold value of the queue size of the users \(i\), \(k\), \(T_{v}\) denotes the transmission rate for user \(v\), \(T_{\text{beginning}}\) is the transmission range in the beginning of the dynamic class-based establishment process.  
Transmission Time Interval (TTI) can be created by using the matrix \(T_{1}\) and \(T_{2}\):  
\[T=T_{1}\ \cup\ T_{2}\]  
\[T_{1}=\left(\begin{array}{cccccc}1-s&s&0&0&0&\ldots\\ r(1-s)&rs+(1-r)(1-s)&s(1-r)&0&0&\ldots\\ \end{array}\right) \tag{9}\]  
\[T_{2}=\left(\begin{array}{cccccc}0&r(1-s)&rs+(1-r)(1-s)&r(1-s)&0&\ldots\\ \ldots&\ldots&\ldots&\ldots&\ldots&\ldots\\ \end{array}\right) \tag{10}\]  
Figure 4: LTE architecture.  
The transmission condition is:  
\[\delta\,T=\delta \tag{11}\]  
where:  
\[\delta=[\delta_{0},\delta_{1},\delta_{2},\ \ldots\ldots\ldots,\ \delta_{k}\,, \ldots\ldots] \tag{12}\]  
where \(\delta_{k}\) is the transmission state probability of the state \(k\). Equation (11) can be modified as  
\[[\delta_{0},\delta_{1},\delta_{2},\ \ldots\ldots\ldots,\ \delta_{k}\,, \ldots\ldots]\ [T]=[\delta_{0},\delta_{1},\delta_{2},\ \ldots\ldots\ldots,\ \delta_{k}\,, \ldots\ldots] \tag{13}\]  
By solving Equation (12), we get:  
\[\delta_{1}=\gamma\,\delta_{0}\,\delta_{2}=\gamma^{2}\ \delta_{0},\ \ldots \ldots,\ \delta_{k}=\gamma^{k}\ \delta_{0} \tag{14}\]  
where:  
\[\gamma=\frac{r\ (1-s)}{s\ (1-r)} \tag{15}\]  
Finally:  
\[\delta_{0}+\delta_{1}+\delta_{2}+\ldots\ldots\ldots+\delta_{k}+\ldots+\delta_ {\infty}=1 \tag{16}\]  
After simplifying Equation (15), we get:  
\[\delta_{0}=1-\gamma \tag{17}\]  
\[\delta_{0}=\frac{(s-r)}{s\ (1-r)} \tag{18}\]  
The resultant length of the class in the queue is  
\[R(Q)=\sum_{k=1}^{\infty}k\delta_{k} \tag{19}\]  
The length of the queue is related to resultant length of the class. It satisfies the following condition:  
\[R(Q)\ \leq delay_{i} \tag{20}\]  
Additionally, the constraints for the optimization problem are:  
\[\left\{\begin{array}{c}R(Q)\ \leq delay_{i}\\ s_{i}\geq\ s_{i}+1\\ s_{i}\geq r_{i}\\ s_{1}+s_{2}+\ldots+s_{n}\leq\ 1\end{array}\right. \tag{21}\]  
The DCE algorithm is used to allocate the queue-based transmission from the group of non-identified TTI (Algorithm 2), the optimization is achieved using the dynamic class-based establishment algorithm that the data broadcasting has been maintained with the transmission range.  
The DCE scheduling mechanism is executed as the beginning of the scheduling event. Here by metric weights of all \(w_{k}\) on the RB \(i\ \in\ K\) are determined. Although there are different formulas to handle various flows QoS, although various flows QoS \(\delta\) is calculated only once for all the available flows at the current TTI. After that, flows are compared with each other to select the flow \(j\in K\) with the highest metric. The possible overhead, in this case, is as a result, the overhead complexity to execute DCE in a TTI.