## 4 Numerical Results and Discussions
### The Simulation Setup and Neural Network Parameter Selection  
In our simulation, the proposed approaches are implemented in Matlab R2018b on a computer with 16 GB of memory and a 3.40 GHz CPU. For the parameters in the optimization problem, we set the Gaussian antenna noise at \(\sigma_{k}^{2}=-90\) dBW, and the circuit noise at \(\delta_{k}^{2}\)= \(-60\) dBW. Assuming that the required harvested energy \(e_{k}\) and the required SINR \(\gamma_{k}\) for all receiver are equal. The energy harvesting efficiency at the receiver is assumed to be the highest one such that \(\mu_{k}=1\). A standard normal distribution is used to generate channel coefficients; for example, we use a Gaussian distribution with zero mean and unit variance. The SWIPT system operates with two transceiver pairs (\(K=2\)). To gain further insight into the impact of the deep learning-based approach, and to take real-time computational efficiency into account, we use a simple FFNN and three types of RNN: the LRN, NARX, and LSTM. We use a relatively large training data set with 10,000 samples (\(N=10,000\)), and used 1000 samples (\(M=1000\)) as a testing data set. The proposed deep learning-based approaches include an input layer, two hidden layers, and an output layer. In the neural network parameter selection process, the number of considered neurons for hidden layers is 20, 40, and 60. For the LRN and NARX, the number of delays on input is set to zero, and the number of delays in each feedback loop is set to 1 (\(T=1\)). The initial values for the required SINR and harvested energy set at 6 dB and \(-20\) dBm, respectively. The network parameter selection process can strike a good value between the MSE and the computation time. For the LSTM network, we set some options for training. In particular, the gradient threshold is 0.01, and the maximum number of epochs is 1000. To reduce the amount of padding in the mini-batches, we chose a mini-batch size of 20. Since the mini-batches are small with short sequences, training is better suited to the CPU, so we specified the environment for execution as CPU. The learning rate is set to 0.001. Figure 3 shows the network performance in term of the MSE in the testing stage. As we increase the hidden layers size from 20 neurons to 60 neurons, the complexity of the network increases, and the MSE might decrease. However, the value of MSE varies slightly. The FFNN provides a bad performance in term of MSE. This is because FFNN often encounters issues like overfitting or underfitting, which makes predictions for new data be inaccurate. Therefore, the FFNN does not fit the data efficiently. In the case of the LRN approach, the MSE tends to increase, compared to NARX and LSTM networks. This is due to the feedback loop structure in each hidden layer of the LRN network (i.e., the more hidden layers are used, the more loops exist in the network). As a result, the MSE of LRN network might increase. Since LSTM network can solve the gradient vanishing and exploding problems in traditional RNNs, the LSTM network provides the lowest MSE as shown in Figure 3.  
Figure 4 shows the computation time of both training and testing stages where 10,000 samples are used for training in the FFNN, NARX, LRN and LSTM, and 1000 samples are used for testing when the hidden layer size changes from 20 neurons to 60 neurons. In all deep learning-based approaches, the training and testing time are the lowest when 20 neurons are used in each hidden layer. In Figure 4a, the computation time of the LSTM approach increases dramatically compared to other deep learning-based approaches. This is because LSTM has more backpropagation neural network modules, and the more memory information is transmitted over time, the more the cell state increases. Figure 4a also shows that the computation time increases when the hidden layer sizes increase. In Figure 4b, the testing time in deep learning-based approaches is very small, but the computation time of the optimization-based scheme is significantly larger.