# Narrowband Internet-of-Things to Enhance the Vehicular Communications Performance
## 2 Modified V2V Benchmark
Due to the property of inherent sparse for the mmWaves channel, the total number of the received links is limited to four. The V2V benchmark for N moving vehicles based on LTE structure is proposed under the use of DSRC protocol, which is licensed to work in the 5.9 GHz band. The deployment of such MIMO configuration is depicted clearly in Figure 3.  
Figure 3: The physical layer modification for the V2V communications process. Figure 2: MIMO antennas deployment in V2V-LTE infrastructure. The channel matrix is derived based on the combining matrix; \(\mathcal{H}_{\mathbb{C}}\) to form the base-band channel as:  
\[\mathcal{H}=(\mathcal{H}_{\mathbb{C}})^{H}\times\mathbb{C} \tag{2}\]  
Therefore, the received signals through these communication links are defined in the following mathematical representation as shown in (3). In this equation, one transmitting antenna and four receiving antennas are allocated. Therefore, the receiving, transmitting, and noise vectors are defined as \([y]_{1\times 4}\), \([x]_{4\times 1}\), and \([n]_{4\times 1}\), respectively. \[[y]_{1\times 4}= \begin{bmatrix}\begin{bmatrix}\left(\mathcal{H}_{\mathbb{C}} \right)^{H}\\ \left(\mathcal{H}_{\mathbb{C}}\right)^{H}\\ \left(\mathcal{H}_{\mathbb{C}}\right)^{H}\\ \left(\mathcal{H}_{\mathbb{C}}\right)^{H}\\ \left(\mathcal{H}_{\mathbb{C}}\right)^{H}\end{bmatrix}\times\mathbb{C}\times[x ]_{4\times 1}\\ +\begin{bmatrix}\left(\mathcal{H}_{\mathbb{C}}\right)^{H}\\ \left(\mathcal{H}_{\mathbb{C}}\right)^{H}\\ \left(\mathcal{H}_{\mathbb{C}}\right)^{H}\\ \left(\mathcal{H}_{\mathbb{C}}\right)^{H}\end{bmatrix}\times[n]_{4\times 1}\end{bmatrix}  \tag{3}\]  
In order to attain the orthogonality and to mitigate the channel's effect, the W-DFT is proposed. This proposition is in addition to append the channel matrix with zeros. Thus, the complexity issue is mitigated. Figure 4 depicts the wavelet proposition to enhance the QoS of the V2V systems. The results of applying the W-DFT compared to the conventional transmitted signal are depicted in Figure 5. A clear 55% modification has been attained as a modification for the proposed W-DFT. Accordingly, the noisy signals have been modified significantly based on enhancing the side-lobes above the adaptive threshold. From the attained results, the W-DFT is a promising technique that could replace the IFFT easily with guaranteed modifications not only in terms of the power management but also in the aliasing error. Therefore, it modifies the estimation methods in the multipath fading channels. Figure 4: Flowchart of the W-DFT process. Each transmitted OFDM signal value in the transmitted vector is expressed in the time-domain as:  
\[\mathbf{x}(n)=\frac{1}{\sqrt{N}}\sum_{i=0}^{N-1}d(i)e^{i\left(\frac{2\pi in}{N} \right)},\;0\leq i,n\leq(N-1) \tag{4}\]  
where it consists of \(N\) orthogonal subcarriers that are formed through an \(N\) points IFFT. The original data is represented by \(d(. )\), and the orthogonality is attained through the following exponential term \(e^{i\left(\frac{2\pi in}{N}\right)}\). In order to employ the wavelet criterion, the time-domain signal in (4) is written as [24]:  
\[f(x)=\sum_{t=-\infty}^{\infty}\left\{x_{(\varphi,t)}\phi(x-t)+\overline{x}_{( \varphi,t)}\overline{\phi}(x-t)\right\}+\sum_{m=0}^{\infty}\sum_{t=-\infty}^{ \infty}\left\{x_{(\varphi,t)}\psi\left(2^{m-1}x-t\right)+\overline{x}_{( \varphi,t)}\overline{\psi}\left(2^{m-1}x-t\right)\right\} \tag{5}\]  
In this equation, the decomposition levels are defined by \(m\), the wavelet scaling, and the wavelet functions are defined as \(\phi()(. )\), and \(\overline{\psi}\), respectively. The \(\overline{(})\) stands for complex conjugation. Figure 6 depicts the modification of the communication block diagram including the wavelet-stage modification. The communication link modification is applied to each transmitted signal in Figure 2. On the receiver side, the minimum mean square error (MMSE) equalization stage can be used after removing the guard interval.