# Predictive Modeling of Signal Degradation in Urban VANETs Using Artificial Neural Networks
## 4 Supervised Learning for Estimating the Bit Error Rate (BER)
### Choice of Learning Function  
In this section, we explore the process of selecting an appropriate learning function for our model. It is important to note that our selection is limited to the ten algorithms available in MATLAB 2016a, as this is the version we are using. To determine the most suitable option, we employ statistical indicators such as Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Correlation Coefficient (R), and Maximum Prediction Error (MaxPE) to evaluate the effectiveness of each machine-learning function. A comprehensive assessment of these learning functions, all of which were tested using MATLAB, is provided in Table 4.  
Figure 6: Representation of an obstacle in a plan. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{N*} & \multirow{2}{*}{**Number of Iterations**} & \multirow{2}{*}{**Learning Algorithms**} & \multirow{2}{*}{**Acronym**} & \multicolumn{5}{c}{**Precision Criteria**} \\ \cline{6-9}  & & & **MEAN MSE** & **MEAN RMSE** & **MEAN MAE** & **MEAN MAE** & **MEAN R** \\ \hline
1 & 15 & Levenberg-Marquardt & LM & \(3.8\times 10^{-2}\) & \(1.9\times 10^{-1}\) & \(1.5\times 10^{-1}\) & \(7.3\times 10^{-4}\) & \(6.5\times 10^{-2}\) \\
2 & 15 & Bayesian Regularization & BR & \(8.3\times 10^{-2}\) & \(2.9\times 10^{-1}\) & \(2.5\times 10^{-1}\) & \(3.2\times 10^{-4}\) & \(1.1\times 10^{-1}\) \\
3 & 15 & BPCS Quasi-Newton & BFG & \(4.0\times 10^{-2}\) & \(2.0\times 10^{-1}\) & \(1.5\times 10^{-1}\) & \(9.6\times 10^{-4}\) & \(7.1\times 10^{-2}\) \\
4 & 15 & Resilent Backpropagation & RP & \(4.0\times 10^{-2}\) & \(2.0\times 10^{-1}\) & \(1.5\times 10^{-1}\) & \(9.6\times 10^{-4}\) & \(7.1\times 10^{-2}\) \\
5 & 15 & Scaled Conjugate Gradient & SCG & \(3.8\times 10^{-2}\) & \(1.9\times 10^{-1}\) & \(1.5\times 10^{-1}\) & \(9.6\times 10^{-4}\) & \(7.1\times 10^{-2}\) \\
6 & 15 & Conjugate Gradient with Powell/Beale Restarts & CGB & \(3.4\times 10^{-2}\) & \(1.8\times 10^{-1}\) & \(1.4\times 10^{-1}\) & \(2.7\times 10^{-4}\) & \(7.4\times 10^{-1}\) \\
7 & 15 & Fletcher-Fowell Conjugate Gradient & CGF & \(4.0\times 10^{-2}\) & \(2.0\times 10^{-1}\) & \(1.5\times 10^{-1}\) & \(3.3\times 10^{-4}\) & \(6.8\times 10^{-1}\) \\
8 & 15 & Polak-Rishree Conjugate Gradient & CGF & \(3.8\times 10^{-2}\) & \(1.9\times 10^{-1}\) & \(1.5\times 10^{-1}\) & \(2.9\times 10^{-4}\) & \(7.2\times 10^{-1}\) \\
9 & 15 & One-Step Secant & OGS & \(4.0\times 10^{-2}\) & \(1.9\times 10^{-1}\) & \(1.5\times 10^{-1}\) & \(2.9\times 10^{-4}\) & \(6.8\times 10^{-1}\) \\
10 & 15 & Variable Learning Rate Backpropagation & GDX & \(5.3\times 10^{-2}\) & \(2.2\times 10^{-1}\) & \(1.8\times 10^{-1}\) & \(9.6\times 10^{-4}\) & \(7.1\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation of learning algorithms on MATLAB using 10 hidden neurons. * The Mean Absolute Error (MAE) quantifies the average magnitude of the absolute differences between the observed and forecasted values in the dataset. It provides a measure of the residuals present in the dataset: \[\text{MAE}=\frac{1}{n}\sum_{i=1}^{n}|y_{i}-\hat{y}_{i}|\] (2)
* The Mean Squared Error (MSE) represents the mean of the squared differences between the actual and predicted values within a dataset. This metric gauges the extent of variance in the residuals: \[\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}\] (3)
* The Root Mean Squared Error (RMSE) is the square root of the Mean Squared Error, serving as a metric to gauge the standard deviation of residuals: \[\text{RMSE}=\sqrt{\text{MSE}}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{ i})^{2}}\] (4)
* The Correlation Coefficient (R) quantifies the relationship between two variables.