According to [17] , the Wi-Fi Direct protocol is based on the standard WLAN infrastructure mode. This network known as a P2P Group is a topology consisting of a mandatory P2P Group Owner (GO) and zero or more P2P Clients. A P2P Group is functionally equivalent to a Basic Service Set (BSS) in legacy Wi-Fi network and the GO takes over all the functions of a real Access Point. In this architecture, a P2P device, if implemented with multiple MAC functionality, can also support simultaneous operation by connecting to a P2P Group and to a conventional Wi-Fi Access Point . Figure 1 illustrates the Wi-Fi Direct architecture .

Several features have been implemented in Wi-Fi Direct technology such as: Device Discovery, Service Discovery, Group Formation, Power Saving Schemes and Security [3] [15] - [18] .

The P2P Device Discovery procedure enables two devices to find each other in their wireless range and establish a connection. It is based on the standard discovery method used in traditional Wi-Fi, involving the scanning and finding phases denoted in the IEEE 802.11-2012 standard [19] . During the scanning phase, a P2P device performs traditional Wi-Fi scan (passive scan) through all supported channels in order to collect information on existing P2P groups and Wi-Fi networks. In the finding phase, the P2P Device alternates between two states (Search and Listen) in order to come to a common channel for the communication.

Service Discovery is an optional procedure in Wi-Fi Direct. The procedure starts after the Device Discovery and prior to the Group Formation procedure. By using Generic Advertisement Service (GAS) protocol [20] . It allows a P2P Device to limit the search to specific P2P devices or types and to connect to the latter only if they offer the intended service [15] .

After successfully completing the Device Discovery procedure, which is mandatory, and the optional Service Discovery procedure, P2P Devices can establish the P2P Group. During the Group Formation, the device that will act as GO is determined. Three types of P2P Group Formation schemes are possible in Wi-Fi Direct: Standard Group Formation, Autonomous Group Formation and Persistent Group Formation.

In Wi-Fi Direct, the P2P GO, which acts as a Soft-AP, must be a battery powered device and have limited lifetime. Hence, Wi-Fi Direct introduces two novel schemes for power saving in the P2P Devices. These schemes are: Opportunistic Power Save (OppPS) and Notice of Absence (NoA) .

Wi-Fi Direct requires all P2P Devices to implement Wi-Fi Protected Setup (WPS) [21] in order to secure the connection establishment process and communication in the P2P Group. In WPS scheme, the P2P GO implements the internal Registrar whereas the P2P Client implements Enrollee. The internal Registrar generates and issues the network credentials to Enrollee. The Enrollee (P2P Client) reconnects to the internal Registrar (P2P GO) using the new credentials.

Several studies have been carried out on Group Formation and GO selection, which is a critical aspect directly affecting the performance of Wi-Fi Direct networks, including latency, power consumption, quality of service, throughput and so on.

Authors in [22] proposed multi-hop communication in Wi-Fi Direct using P2P Concurrent Device and Ad-hoc On Demand Distance Vector (AODV) reactive routing protocol [23] . Routing is established during Device Discovery phase to allow multi-hop communication.

In [24] , authors proposed EMC (Efficient Multi group formation and Communication) protocol for Wi-Fi Direct. In EMC scheme, the P2P GO is elected based on remaining battery status of the device.

In [5] , authors proposed a dynamic election of P2P GO in Wi-Fi Direct. The elected leaders can be replaced dynamically based on clustering strategy such as battery status, speed of the user and direction of motion etc. The authors also presented a template for writing clustering algorithms for efficient Group Formation.

Authors in [18] proposed a combined metric approach to select the P2P GO based on several parameters. The parameters are normalized and weighted to compute Intent Values of each device. An election algorithm is then used to select the P2P GO. The same idea is explored in [7] , but the authors go further by proposing a framework for multi-hop ad hoc networking using Wi-Fi Direct in Android smart devices. The framework includes a connection establishment protocol and a group management protocol.

The work carried out in [16] proposes a modified group formation scheme among multiple devices. The proposed scheme formulates the GO selection problem as an optimization problem which is solved using integer programming (IP). The GOs are selected based on link capacities with the objective to maximize the overall network throughput.

In [25] , authors proposed an alteration to the standard Group Formation. In their proposed scheme, during GO Negotiation, each device sends an flag bit set to 1, to indicate its willingness to serve as the so called Emergency Group Owner (EGO). The EGO is present in the group after the GO is selected. The EGO takes over the group and assumes GO role if the GO leaves voluntarily or involuntarily.

In [26] the authors propose the GO selection method by maximizing bit rate. However, the performance of the proposed system is severely acted when GO selection is required for Internet connectivity via a Wi-Fi access point or a cellular base station (BS). Wi-Fi access point or a cellular base station (BS). One of the reasons for the poor performance of this method is that the quality of the link between the GO and the AP/BS imposes a bottleneck on the average network throughput. Furthermore, the work is limited to the formation of a single group, and the proposed scheme cannot be used to create several P2P groups to connect users with high population density [16] .

Another method is proposed by . This method is particularly useful during the device discovery phase. WD2 applies a parameter to control the number of messages sent. Before sending the probe packets, each device generates copies which are sent consecutively. Assuming there are N devices that can discover each other, receiving multiple packets enables the devices to discover each other . Despite its advantages, WD2 introduces an additional overhead due to the increased number of messages exchanged to accurately measure RSSI and calculate the intent value.

None of the works presented above explores the possibility of using techniques based on Artificial Intelligence (AI), in particular Artificial Neural Networks (ANN), to elect the GO.

Data quality is essential for effective training of Artificial Neural Network models. Machine Learning techniques are designed to identify and exploit hidden patterns in data for predicting the outcome of future events for classification and regression problems [28] . Data collection is an important step since Machine Learning require representative data, possibly without bias, to build an effective Machine Learning model for our problem. In this section we describe the key steps in data preparation, which include data collection, pre-processing and division into training and test sets.

1) Data collection: The data used to train our models come from simulations, real measurements in ad hoc network environments and synthetic data obtained from various repositories [29] - [32] . Features collected from our dataset include:

(a) ID: This feature simply refers to the device ID.

(b) Received Signal Strength Indicator (RSSI), which measures the quality of the signal received by a device. The data rate of the wireless link is badly affected by low RSSI. If the P2P group is used for content distribution for example, the strong connection between the group members and the GO is more crucial. The RSSI of GO to group members have significant impact on the P2P group performance.

(c) Battery level, indicating the amount of energy remaining in the device. P2P devices, including the GO, are battery powered devices. If the battery life is not considered in electing a GO, there is a probability that a P2P device having low value of remaining battery is elected as GO. The GO being the most active device in the P2P group would exhaust soon and the P2P group will be broken.

(d) Processing capability (CPU clock and memory), which reflects the device’s computing and storage capacity. The device which becomes GO shall be equipped with enough processing power and large memory to better serve the connected clients. The processing power and memory requirements for GO might become more significant when the P2P group consists of a large number of nodes and the group is intended for multimedia application.

(e) Number of neighbors: Number of devices in direct range. A node with more neighbors can ensure better connectivity within the network. Because the P2P group is intended to connect large number of devices, then it is important to elect as GO the P2P device which has more devices in its range to connect as clients. There should also be a limit on maximum number of nodes in a P2P Group. In our case, this is the maximum number of devices that can be connected simultaneously (the amount of device it can support without compromising network quality).

(f) Device mobility: Indicates the speed of movement of each device. In realistic mobile ad-hoc environments, each mobile host is free to change its mobility parameters randomly at any time . Less mobile devices are preferred to become GO to minimize frequent topology changes and to make the group more stable. There are several models of mobility, such as Gauss-Markov Mobility (GMM), Random Waypoint (RWP), Random Walk (RW), Random Direction (RD), and Recurrent Self-Similar Gauss-Markov (RSSGM) . In our case, the data presented for this feature were obtained using the RSSGM model, which shows the greatest accuracy compared to other models [31] .

These data, obtained from 356 pieces of equipment are then aggregated to form a dataset representative of the different network conditions that the models will have to manage.

2) Data preprocessing: Pre-processing is an important step to ensure that the data are in an optimal format for training ANN models. The following steps are applied:

(a) Data cleaning: Missing or abnormal data (such as outliers) are processed. Missing values can be imputed using the mean or median of the other values in the same column. In our dataset, we do not have any missing data or outliers.

(b) Normalization: Features such as RSSI, battery level and CPU clock can have very different scales. To ensure that each feature contributes equally to model training, data are normalized to a standard range (usually between 0 and 1). Here we have used the Min-Max Scaler method [34] . The formula to scale a feature is given by Equation 1, where $x$, $x_{\min }$ and $x_{\max }$ are respectively the value to scale, the minimum value and the maximum value of the dataset.

$x_{\text{scaled}}=\frac{x-x_{\min }}{x_{\max }-x_{\min }}$ (1)

(c) Categorizing feature values: In order to determine the suitability of a device and to understand the values of these features, we have graded these values according to different mentions. This procedure is described in Table 1 and Table 2 , which present the categorization the RSSI, Battery and CPU level feature values respectively. For RSSI, we use the categorization proposed in [26] .

As one of our models is a binary classification model then for the Intent Value column we will categorize the values into two classes 0 and 1 according to Table 3 .

This distribution is justified by the fact that in the classic GO selection, the role is assigned to the device that has emitted the highest value of intent. We have therefore considered values between 0 and 7 to be low and those between 8 and 15 to be high. And 8 is the midpoint of the range [0, 15]. In the Wi-Fi Direct protocol, two Intent values are compared at the time of negotiation, whereas our predictive models only know the local characteristics (RSSI, battery level, memory, etc.) of a device and try either to predict whether this node has a good chance of becoming a GO, or to predict what its Intent Value might be. Consequently, as our models have no knowledge of the other nodes at the time of prediction, we simply teach it to classify nodes as GO or noGO according to their Intent Value level in absolute value. This is where the empirical threshold of 8 comes into play. This threshold is not a protocol truth, but a practical approach that we have used to formulate the problem in binary classification, which makes it possible to identify nodes with a high propensity to become GOs where several nodes will be compared. This balanced cut-off also makes it possible to create a symmetrical binary classification, leading to a more balanced model.

3) Data Processing Division: To properly evaluate model performance, we have used the standard Machine Learning distribution. The dataset is divided into three distinct sets:

This division allows us to ensure that the models generalize well beyond the data on which they have been trained.

Our classification ( Figure 3 ) and regression ( Figure 4 ) models are structured in the form of a multi-layer neural network (Multi-Layer Perceptron, MLP). MLP is composed of multiple layers, including an input layer, hidden layers, and an output layer, where each layer contains a set of perception elements known as neurons. The neurons of the input layer of our model is composed of the device features mentioned in section 2, except for the ID.

Both networks include two hidden layers (each with eight neurons) using the Rectified Linear Unit (ReLU) as activation function (Equation 3). The ReLU function is chosen for its acceleration of learning and mitigation of the problem of the gradient disappearing. In fact, the simplicity of the ReLU reduces the time required to perform calculations during forward and reverse propagation in the network, which speeds up the learning process. ReLU tends to activate only some of the neurons at a time, making the network lighter and less costly in terms of computation . In addition, unlike other functions, the ReLU allows a freer flow of the gradient, avoiding problems where the gradients become too small for effective updating during training . Our models have 2 hidden layers, each consisting of 8 neurons. The choice of these quantities was guided by the tests carried out during the training. In ANN, the number of hidden layers and the number of neurons generally depend on the number of input features and the size of the dataset [11] . In our case, we have observed that increasing these values tends to overfitting.

The output layers of both models are formed by a single neuron. For the classification model, since we are doing a binary classification a Sigmoid activation function (Equation 4) is used for the output, producing a probability indicating whether a device is suitable for election as a GO or not. Beside the classification model, the regression model calculates the Intent Value of each node. Precise calculation of this value enables more nuanced and dynamic decision-making, by adjusting the probability of a device being chosen as a GO according to changing network conditions. So the output layer of our regression model is activated with Linear activation (Equation 5), to produce a continuous value representing the Intent Value, ranging from 0 to 15 according to the Wi-Fi direct technology specification.

If we note $Y^{\left(n\right)}=\langle y_1^{\left(n\right)},y_2^{\left(n\right)},\cdots ,y_m^{\left(n\right)}\rangle$ the set of neurons in the $n^{th}$ layer, the functioning of the neurons in the model is broken down into two phases:

$X_i^{\left(j+1\right)}=\underset{k=1}{\overset{m}{{\displaystyle \sum }}}{w}_{ik}^{\left(j\right)}{y}_k^{\left(j\right)}+b^{\left(j+1\right)}$ (2)

$Z_i^{\left(j\right)}=\max \left(0,X_i^{\left(j\right)}\right)=\{\begin{array}{l}{X}_i^{\left(j\right)},\text{if}{X}_i^{\left(j\right)}>0\hfill \\ 0,\text{otherwise}\hfill \end{array}$ (3)

The output values of the two models are obtained at the output layer level by Equation 4 for the classification model and Equation 5 for the regression model.

$Y=\frac{1}{1+{\text{e}}^{-Z_i^{\left(j\right)}}}$ (4)

$Y=\{\begin{array}{ll}0,\hfill & \text{if}{Z}_i^{\left(j\right)}\le 0\hfill \\ Z_i^{\left(j\right)},\hfill & \text{if}{Z}_i^{\left(j\right)}\in \left]0,15\right[\hfill \\ 15,\hfill & \text{if}{Z}_i^{\left(j\right)}\ge 15\hfill \end{array}$ (5)

The hardware and software conditions in the experimental environment of this article are shown in Table 4 .

In order to evaluate the GO selection and Intent Value prediction performance of our models, several evaluation indicators are selected, depending on the type of model.

For the classification model, these indicators are:

$\text{Accuracy}=\frac{{\displaystyle {\sum }_{i=1}^N{T}_{C_i}}}{\text{Total Predictions}}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+\text{FN}}$ (6)

The precision of the model can be formally defined as the frequency of correct predictions for actual positive instances as in Equation 7:

$\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP}}$ (7)

The accuracy curve shows the evolution of the model’s accuracy during training, for both the training set and the validation set. It shows whether the model continues to improve its predictions.

$\text{TPR}\left(\text{Recall}\right)=\frac{\text{TP}}{\text{TP}+\text{FN}}$ (8)

$\text{F-measure}=2\times \frac{\text{Precision}\times \text{TPR}}{\text{Precision}+\text{TPR}}$ (9)

The regression model designed to calculate the Intent Value is evaluated using specific metrics that measure the accuracy of the predictions of continuous values. Noting that $n$ is the number of samples, $y$ is the observed Intent Value, $\hat{y}$ is the predicted Intent Value and $\bar{y}$ is the mean, these parameters are:

$\text{MedAE}\left(y,\hat{y}\right)=\text{med}\left(\left|y_i-{\hat{y}}_i\right|\right)$ (10)

where med is the median function calculated on absolute errors $\left|y_i-{\hat{y}}_i\right|$.

$\text{MAE}\left(y,\hat{y}\right)=\frac{1}{n}\underset{i=0}{\overset{n-1}{{\displaystyle \sum }}}\left|y_i-{\hat{y}}_i\right|$ (11)

$\text{MSE}\left(y,\hat{y}\right)=\frac{1}{n}\underset{i=0}{\overset{n-1}{{\displaystyle \sum }}}{\left(y_i-{\hat{y}}_i\right)}^2$ (12)

$R^2\left(y,\hat{y}\right)=1-\frac{{{\displaystyle \sum }}_{i=0}^{n-1}{\left(y_i-{\hat{y}}_i\right)}^2}{{{\displaystyle \sum }}_{i=0}^{n-1}{\left(y_i-\bar{y}\right)}^2}$ (13)

After training our models by applying a weighting to the other features to generate the “Intent Value” column in our dataset, we were able to adjust the target to better reflect the underlying relationships between inputs and outputs (Equation 1). This strategy created consistency between the inputs and the target variable, which improved model performance. This weighting process strengthens the links between relevant features and the target, which is often essential in ANN based approaches.

The performance curves obtained from the classification model are shown below:

A summary of the performance of our classification model is presented in Table 6 .

The classification model used to elect the Group Owner (GO) in a Wi-Fi Direct network showed solid performance with an overall accuracy of 88%, an AUC of 1.00, and a minimum loss of 0.33. The use of class weighting better managed the potential imbalance between GO and noGO classes, improving the model’s ability to correctly identify nodes that could be GO. This ensures a more accurate selection of the GO, resulting in smaller architecture and very good performance.

The performance of our regression model was obtained by calculating the metrics presented in section 4 (Equations 10, 11, 12, and 13), that measure the accuracy of continuous value predictions. These performances are summarised as follows:

In order to visualize the intent values prediction results, we have represented the 10 first instances in Table 7 .

With an MSE of 0.74, a MAE of 0.61 and an R² of 0.94, our regression model with the weighted dataset demonstrated solid performance, indicating that it explained 94% of the variance in the data. The error and loss curves show fast learning and efficient generalisation, without overlearning. The majority of the predictions match the actual values, although differences are apparent for the extreme values of Intent-Value (14-15). Overall, the model is accurate and stable. Table 8 summarises the performance of the Regression model.