# ITFDS: Channel-Aware Integrated Time and Frequency-Based Downlink LTE Scheduling in MANET
## 2 Proposed Method
### Model Formulation  
Table 1 shows the notions and symbols used throughout the paper. A simplified model of LTE is shown in Figure 2, in which eNodeB consists of user selection and resource allocation. There are k numbers of queues consisting of q\({}_{1}\), q\({}_{2}\),...,..., q\({}_{k}\) for the scheduling process. The queue list sends information to the eNodeB network. Then, the signal sends 20 slots of data with every frame consisting of several subframes with 1 ms time-to-live time span. The signal can be sent to external devices like smartphones, mobile phones, PADs and laptops. The scheduling can be done using two methods, namely frequency-based scheduling and time-based scheduling. The frequency is received into every subframe with n numbers of subcarriers. Each carrier can receive the signal and perform the scheduling process. For real time traffic, maximum weight largest delay first (MWLDF) and exponential-proportional fair (EXP/PF) are introduced. In multi-user scheduling, distribution of resources among users is done by sharing the channel capacity among them. The channel capacity is calculated by using [PERSON]'s capacity theorem. LTE downlink transmission is based on OFDM modulation. In the frequency domain, subcarriers are spaced at 15 KHz each and with different modulation codes and rates. The modulation and coding are choosing according to the channel condition. A resource block (RB) consists of 12 subcarriers. In the time domain, a resource blocks contain one TTI which includes two time slots. Each time slot has six or seven OFDM symbols. Since \(Cy(n)_{i,k}\) is the transmission rate, \((n)_{i,k}\) is nth TTI of the metric of \(i\)th user on \(k\)th RB, we have:  
\[Cy(n)_{i,k}=log_{2}\left[1+SINR(n)_{i,k}\right] \tag{1}\] \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Meaning** \\ \hline CQI & Channel Quality Indicator \\ \hline QCI & QoS Class Identifiers \\ \hline DCE & Dynamic Class-based Establishment \\ \hline QoS & Quality of Service \\ \hline PF & Proportional Fair \\ \hline MT & Maximum Throughput \\ \hline TTI & Transmission Time Interval \\ \hline MWLDF & Maximum Weight Largest Delay First \\ \hline EXP/PF & Exponential-Proportional Fair \\ \hline Cy(\(n)_{i,k}\) & Maximum limit of the transmission rate \\ \hline \(C_{i,k}\)(t) & Current channel condition \\ \hline \(\overline{C}_{i}\) & Mean data rate for \(i\)th user \\ \hline \(R_{i,k}^{\text{PF}}(n)\) & Throughput \\ \hline HOL & Head of Line \\ \hline \(\Delta_{i,k}\) & Delay \\ \hline \(W_{i}\)\((t)\) & Weighted time domain value \\ \hline \(Q_{i,k}\) & Buffer size \\ \hline PLR & Packet Loss Rate \\ \hline UE & User Equipment \\ \hline SINR & Signal-to-Interference-Noise-Ratio \\ \hline GBR & Guaranteed Bit Rate \\ \hline non-GBR & Non-Guaranteed Bit Rate \\ \hline H2H & Heart-to-Heart devices \\ \hline M2M & Machine-to-Machine devices \\ \hline T & Queue-based transmission matrix \\ \hline k & State \\ \hline \(\xi_{k}\) & Transmission state probability of the state k. \\ \hline \(R(Q)\) & Resultant length of the class in the queue \\ \hline \(P_{c}\) & Parameter of channels \\ \hline \(T_{v}\) & Transmission rate \\ \hline \(T_{w}\) & Weight of the transmission range \\ \hline \(T_{\text{beginningning}}\) & Beginning transmission range \\ \hline \(T_{\text{current}}\) & Current transmission range \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The notions and symbols used throughout the paper where, \(Cy(n)_{i,k}\) is the maximum limit of the transmission rate. It is normally not equal to the actual \(Cy(n)_{i,k}\). In order to get maximum throughput and to allocate each RB to users with maximum channel capacity, the maximum throughput (MT) algorithm is used. The metric is expressed as:  
\[R_{i,k}^{MT}(n)=Cy(n)_{i,k} \tag{2}\]  
Here, \(R_{i,k}^{MT}(n)\) is real-data of \(k\)th user in \(i\)th time slot using the MT algorithm, Equation (2) satisfies non-real-time applications.