## 4 Simulation Results and Discussions
### Performance Comparison  
In this Subsection, we compare the results between the LS, STA, CDP, traditional ELM, C-ELM [13] techniques, and our proposal, which is based on a SS-ELM neural network. For the standard ELM, the regularization parameter and the number of hidden neurons are the same as the SS-ELM, namely \(\mathrm{C}=10\) and \(n_{h}=64\). Furthermore, in our proposal, the rest of the hyper-parameters are the following: \(\lambda=100\), \(\mu=6\), and 16. Remember that these adoptions are done in order to minimize the system performance (see Section 4.2). According to [13], we adopt 512 hidden neurons and the arcsinh mapping function for the C-ELM. For the first and second configuration, Figures 14 and 15 depict the BER as a function of \(E_{b}/N_{0}\) for the different techniques evaluated. It can be seen that ELM, C-ELM, SS-ELM, and LS methods tend to have the same BER, regardless of the scenario. On the other hand, for the first and second configurations, the STA method has the worst and best BER values, respectively. The CDP method outperforms the other techniques for high SNRs only for the first configuration. These observations mean that STA and CDP do not perform uniformly for different channel configurations; consequently, these techniques are not feasible for V2V communications. Among the rest of the evaluated techniques, our proposal shows a  
Figure 12: BER of the proposed SS-ELM scheme with \(\delta\) as parameter and the LS algorithm for system configuration 1.  
uniform and slightly better performance for the evaluated scenarios, especially for higher SNRs. For instance, given a threshold of \(BER=10^{-1}\) in the first configuration, the SS-ELM allows a \(E_{b}/N_{0}\) greater than 8 dB. Meanwhile, the \(E_{b}/N_{0}\) requirement corresponds to 9, 10, and 14 dB in the case where the LS, ELM, and C-ELM approaches are used, respectively. It is worth noting that observations for SNRs greater than 20 dB can be discarded, since these values rarely occur in real settings [28]. Furthermore, it is worth noting that the vehicular communication channel evaluated in this manuscript is extremely harsh; therefore, none of the evaluated schemes achieved the BER threshold given by the standard and equal to \(10^{-3}\)[30; 31]. The superiority reported in our proposal can be explained by the use of the ELM neural network along with the exploitation of the semi-supervised machine learning scheme. With respect to conventional neural network learning algorithms, the ELM algorithm has demonstrated a better generalization performance in the presence of linear and no-linear distortions [13]. Its generalization ability comes from the parameter neurons between adjacent layers are found by reaching both the smallest training error and the smallest norm of output weights. On the other hand, semi-supervised learning has been applied to several classification and regression tasks with excellent results, in which both the labeled and unlabeled data are used to improve accuracy over supervised approaches. It occurs especially when insufficient training information is available [20]. The reason behind this is that unlabeled data naturally provide valuable information for exploring the data structure in the input space. To conclude this explanation, it is well known that the interactions among different types of impairments (such as the harsh time-varying, frequency-selective channel considered in this manuscript) are not effectively considered and handled for non-based ML-based schemes [6]. For instance, STA and CDP techniques were not designed considering the characteristics of the vehicular channel. In regular channels, STA uses frequency dependencies to improve the performance, but in vehicular communications, the channel varies rapidly in frequency, explaining the poor results for rougher channels. Meanwhile, CDP suffers greatly from low \(E_{b}/N_{0}\) because it uses the channel estimation iteratively to equalize the channel, so, in high noise environments, this estimation is contaminated, decreasing the performance.