## 4 Fairness-Aware Machine Learning Based Power and RB Allocation with Multiple Relays
### Relays Deployment and Users Association
Given the resource blocks allocation set \(\mathcal{D}_{k}\quad\forall k\in\mathcal{K}\), the power allocation problem has been solved using two-layer feedforward neural network. The hidden layer neurons use sigmoid function as activation function and output neurons implement linear function as shown in Figure 7:7 We use Bayesian Regularization method to train the neural network. This method typically requires more training time but gives good results for difficult and noisy dataset. The Bayesian Regularization method uses Levenberg-Marquardt optimization to update the weight and bias values. It minimizes a combination of squared errors and weights, and then determines the correct combination for better generalization. In this method, the training does not stops after six consecutive validation (improve) fails and by default max_fail = inf. The training continues until an optimal combination of errors and weights is reached. More detail on the use of Bayesian regularization, along with Levenberg-Marquardt training, can be found in [29]. We use MATLAB 2019a App, Neural Net Fitting (nftool) which is a two-layer (one for hidden layer activation functions and other for output layer activation functions) feedforward network. The mean-squared-error graph for the training and testing is shown in Figure 7:8 It shows that the MSE reaches to 0.087358 in 498 epochs. Our input/output samples to training network were channel gain/allocated power. Since, the total transmit power is a sum of linear functions of the channel gain, therefore, the neural network is got trained in a single epoch. An epoch is a full pass through the entire dataset and the calculation of new weights and biases. Figure 18 shows that the gradient coefficient reaches to 0.00076591 in 499 epochs. The lower value of gradient ensures the training and testing of the network. Other parameters such as Mu, Num Parameters, and Sum Squared Param are the stop criteria defined in Bayesian regularization backpropagation function 'trainbr' [30]. Error histogram in Figure 19 visualizes the errors between target values and the predicted values after training a feedforward neural network. In this figure we can see that the data fitting errors are minimum and they are distributed within a closed range around zero. Around 88.1% errors fall between \(-0.3\) and \(0.33\). Figure 7:9 Receiver Operating Characteristic (ROC curve). \[K = \text{Total number of clusters being formed}.\]0 Neural network architecture for power allocation, \(K=10\). \[K = \text{Total number of clusters being formed}.\]1 The mean-squared-error for the training and testing of the power allocation module. \[K = \text{Total number of clusters being formed}.\]2 The neural network training states. ### Performance Evaluation with Machine Learning Techniques

First, we apply the neural network for the RB and power allocation modules with a single relay. For the SAMM scheme in Figure 20 shows 30.25% increase in the EE. This is because of the limitations of the BOPA method which sometimes returns no result, whereas, the neural network is trained on diverse dataset and always gives the output result. We also compare our proposed schemes with LERPA of [11]. LERPA uses max-min criteria for RB allocation and fractional programming based transmission power control. In case of LTE network with multiple relays as shown in Figure 7 or Figure 9, the users associated with relay \(q\) experience interference due to the neighboring relays \(q_{neigh}\). This interference decreases the users' throughput as shown in \[K = \text{Total number of clusters being formed}.\]3 However, the EE maximization based NN power allocation continues to dominate in the multiple relay scenario. Since the transmission is orthogonal between BS and RNs, only the relay's associated users are affected by the other relays transmissions. The equal power MT throughput does not affect because almost all the users are associated with BS.