# Artificial Intelligence-Based Discontinuous Reception for Energy Saving in 5G Networks
## 2 Related Work
### Recurrent Neural Network for Predicting Sequential Data  
Recurrent Neural Network (RNN) is a part of AI that is widely used for predictions over sequential data [26]. Long short-term memory (LSTM) network is one of the popular kinds of RNN that performs well while predicting the long-term dependent time sequences [15]. LSTM is different from other kinds of RNN due to its gated structure and internal cell state in every single unit, as shown in Figure 4. LSTM neural network utilizes various previous inputs to decide the values of internal gates (forget gate, input gate, input modulation gate, output modulation gate), which contributes to cell state. Cell state helps the LSTM to remember or forget the impact of past inputs while deciding the prediction results. This is the main reason LSTM has better performance for predicting the long-term dependent sequences [14; 15]. Table 1 shows the notations used in our work.  
LSTM unit includes forget gate \(F_{T}\) that can be mathematically shown by Equation (1). The output of forget gate varies from 0 to 1, due to sigmoid \(Sig=\frac{1}{1+e^{-T}}\) function. The letters \(w_{x}\) and \(w_{h}\) in the Equation (1) represent the weights associated with the current input \(x_{T}\) and previous output \(h_{T-1}\), respectively. The term \(b_{F}\) is the bias for the forget gate. Similarly, the input gate (\(I_{T}\)) and input modulation gate (\(G_{T}\)) can be calculated by Equations (2) and (3), respectively. The hyperbolic tangent function in input and output modulation gates can be mathematically written as \(\tanh(T)=2 Sig(2T)-1\) and ranges from \(-1\) to \(+1\). Moreover, \(b_{I}\) and \(b_{C}\) are biases for input gate and cell state, respectively.  
\[F_{T}=Sig(w_{x}x_{T}+w_{h}h_{T-1}+b_{F}) \tag{1}\]  
\[I_{T}=Sig(w_{x}x_{T}+w_{h}h_{T-1}+b_{I}) \tag{2}\]  
\[G_{T}=\tanh{(w_{x}x_{T}+w_{h}h_{T-1}+b_{C})} \tag{3}\]  
Figure 3: Directional communication with multiple beams in 5G network.  
Cell state \(C_{T}\) and the output layer \(O_{T}\) can be calculated by Equations (4) and (5), respectively. The final prediction results can be observed by output modulation gate (\(h_{T}\)) using Equation (6).  
\[C_{T}=F_{T}\otimes C_{T-1}+I_{T}\otimes G_{T} \tag{4}\]  
\[O_{T}=Sig(w_{x}x_{T}+w_{h}h_{T-1}+b_{O}) \tag{5}\]  
\[h_{T}=O_{T}\otimes\tanh(C_{T}) \tag{6}\]  
During the training process, LSTM learns to extract the relationship between the input and desired output (upcoming value of sequence) by adjusting various weight values in Equations (1)-(3) and (5). Once the model is trained with the least error, the learned weight values can be used in Equations (1)-(6) to calculate the output values of a sequence (prediction). The error between prediction result and observed (actual) value can be computed by the root mean square error (RMSE) and is given as:  
\[\text{RMSE}=\sqrt{\frac{\sum_{T=1}^{N}(Predicted_{T}-Observed_{T})^{2}}{N}} \tag{7}\]  
where the notation \(T\) represents the number of samples and \(N\) shows the maximum number of samples.  
\begin{table}
\begin{tabular}{l l l l} \hline \hline
**Abbreviation** & **Notation** & **Abbreviation** & **Notation** \\ \hline Forget gate & \(F_{T}\) & DRX active time & \(T_{Ac}\) \\ \hline Input modulation gate & \(G_{T}\) & DRX ON time & \(T_{ON}\) \\ \hline Input gate & \(I_{T}\) & DRX Inactivity timer & \(T_{IN}\) \\ \hline Output layer & \(O_{T}\) & Packet inter-arrival time & \(\lambda_{\kappa}\) \\ \hline Cell state & \(C_{T}\) & DRX Dynamic sleep time & \(T_{DY}\) \\ \hline Output modulation gate & \(h_{T}\) & Weight corresponding to each gate & \(w_{i}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of abbreviations.  
Figure 4: Gated structure of single long short-term memory (LSTM) unit.