# Narrowband Internet-of-Things to Enhance the Vehicular Communications Performance
## 3 Simulation Results Performance  
In this section, a detailed environment has been simulated to cover the proposed system's performance. The NB-IoT simulated model is covered based on the work of [7], where the channel model is used as a Typical Urban. Moreover, the architecture of VANET communications is described in [14]. Accordingly, an extensive MATLAB simulation has been performed in order to validate the proposed work. It has been checked based on the latency, and interference elimination criteria. Therefore, the simulation parameters are limited to:  
* MIMO system with one transmitting and four receiving antennas using the weighted averaging method;
* The receiver equalizer is limited to the MMSE at a Doppler shift of 300 Hz;
* OFDM signal with 600 points and a 0.25 guard interval;
* A 15 kHz as orthogonal carrier's spacing frequency;
* Six taps ITU-R channel with a delay spread of 2.51 \(\upmu\)s;
* 2/3 convolutional encoder;
* Modulation techniques including 64 QAM and 16-APSK;
* The channel bandwidth of 200 kHz based on the NB-IoT scenario;  
Figure 7: The comparison results based on CCDF curves. The vehicle's speed range of 20 km/h-to-70 km/h;  
Transmission range of 15 m.  
The following Tables 1-3 summarize the system performance of five randomly chosen signals based on the three decomposition performance factors, namely CMSE, CMCorr, and CSOAD. It is clearly shown that the harmonic wavelet is faster than the Daubechies. From all these results the harmonics wavelet reaches the same CMSE value at a faster decomposition level; it achieves the same value with a percentage of 33.1% faster than the previously published work in [25]. Table 2 depicts the reconstruction performance based on the Correlation matrix criterion. Here, the reconstruction speed is still faster than the conventional work, however, it is somehow slower than the achieved results of using the CMSE evaluation criterion. Table 3 depicts the results of the proposed work based on the Sum of the Absolute Difference criterion. Again, the harmonics are still faster than the Daubechies. However, it is the fastest among the three performance criteria. It reaches up to 62.5% reconstruction enhancement based on the speed point of view. Accordingly, and as a drawn result, the harmonics wavelet gives better reconstruction performance compared to the use of Daubechies wavelets in [25]. In order to check the proposed work performance from the MSE and the signal-to-noise ratio, Figure 8 depicts the results of two MIMO deployment scenarios; \(1\times 1\), and \(1\times 4\) with a self-interference cancellation proposition as depicted in Figure 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Signals Number**} & \multirow{2}{*}{
\begin{tabular}{c} **Mean-Squared** \\ **Error (CMSE)** \\ \end{tabular} } & \multicolumn{2}{c}{**Daubechies**} & \multicolumn{1}{c}{**Harmonics**} \\ \cline{3-5}  & & **The** & **The** & **The** \\  & & **Decomposition** & **Function Type** & **Decomposition** \\  & & **Level** & & **Level** \\ \hline
10 & 0.082 & 6 & db13 & 3 \\
15 & 0.072 & 4 & db10 & 2 \\
35 & 0.091 & 8 & db14 & 4 \\
40 & 0.13 & 8 & db16 & 5 \\
150 & 0.082 & 7 & db27 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: CMSE evaluation criterion performance comparison. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Signals Number**} & \multirow{2}{*}{
\begin{tabular}{c} **Correlation** \\ **Matrix (CMCorr)** \\ \end{tabular} } & \multicolumn{2}{c}{**Daubechies**} & \multicolumn{1}{c}{**Harmonics**} \\ \cline{3-5}  & & **The** & **The** & **The** \\
14 & 0.588 & 7 & db14 & 5 \\
30 & 0.733 & 8 & db27 & 5 \\
65 & 0.91 & 6 & db17 & 3 \\
95 & 0.881 & 5 & db31 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: CMCorr evaluation criterion performance comparison.