# Preamble-Based Adaptive Channel Estimation for IEEE 802.11p +
## 4 Adaptive Channel Estimation Scheme Based on Preamble  
As mentioned above, the number of pilots defined in the IEEE 802.11p is not sufficient to track the channel variations for high-speed vehicle environments. For this reason, various channel estimation techniques have been proposed, but satisfactory performance cannot be obtained over the entire range of SNR levels. Figure 3 shows the BER performance of each channel estimation scheme obtained by using the IEEE 802.11p link level simulator and by adopting V2I channel model in urban canyon scenario mentioned in Section 2.2. In Figure 3, STA, MMSE and TRFI have different SNR region with excellent performance; thus, if a technique that exhibits excellent performance in the corresponding SNR region can be appropriately used, this leads to a performance improvement. In addition, STA and MMSE or STA and TRFI create an intersection, which means that two techniques can be used appropriately based on the intersection. Therefore, in this paper, we propose an adaptive channel estimation technique to obtain outstanding performance regardless of the level of SNR in a signal region. The proposed scheme uses one of two channel estimation techniques that exhibit excellent performance at either high- or low-SNRs.  
The adaptive channel estimation scheme chooses the channel estimation technique using a preamble. The preamble is a known bit sequence to both transmitter and receiver in order to estimate channel state information (CSI), and the LS technique is widely used in this preamble-based channel estimation due to its simplicity. LS channel estimate can be obtained as follows:  
\[H_{LS}(k)=\frac{Y(k)}{X(k)}=H_{p}(k)+\frac{Z(k)}{X(k)}, \tag{14}\]  
where \(H_{p}(k)\) is the perfect CSI and \(Z(k)\) is an additive white gaussian noise (AWGN) with zero mean and variance \(\sigma_{z}^{2}\), i.e., \(\mathcal{N}(0,\sigma_{z}^{2})\). Because \(H_{LS}(k)\) is still influenced by noise component, \(H_{i}(k)\) can be obtained by using a candidate channel estimation technique to reduce the noise effect.  
To compare the performance of candidate channel estimation schemes, modified MSE is defined as  
\[\tilde{\xi}_{i}=\frac{1}{N}\sum_{k=-26}^{26}\left|H_{LS}(k)-H_{i}(k)\right|^{2 }. \tag{15}\]Under the assumption that \(H_{i}(k)\approx H_{p}(k)\), modified MSE is approximated as follows:  
\[\tilde{\delta}_{i}\approx\frac{1}{N}\sum_{k=-26}^{26}\left|H_{LS}(k)-H_{p}(k) \right|^{2}. \tag{16}\]  
The MSE between the LS channel estimate and the perfect CSI is an inversely proportional average SNR [40]  
\[\begin{split}\delta_{LS}&=\frac{1}{N}\sum_{k=-26}^{ 26}\left(H_{LS}(k)-H_{p}(k)\right)^{H}\left(H_{LS}(k)-H_{p}(k)\right)\\ &=\frac{1}{N}\sum_{k=-26}^{26}\left(\frac{Y(k)}{X(k)}-H_{p}(k) \right)^{H}\left(\frac{Y(k)}{X(k)}-H_{p}(k)\right)\\ &=\frac{1}{N}\sum_{k=-26}^{26}\left(\frac{Z(k)}{X(k)}\right)^{H} \left(\frac{Z(k)}{X(k)}\right)\\ &=\frac{1}{N}\sum_{k=-26}^{26}\frac{Z^{H}(k)Z(k)}{X^{H}(k)X(k)} \\ &=\frac{\sigma_{z}^{2}}{\sigma_{z}^{2}}\\ &=\frac{1}{\overline{\gamma}},\end{split} \tag{17}\]  
where \(\overline{\gamma}\) is average SNR. Therefore, the better channel estimation technique between the candidate schemes is closer to the perfect CSI, and the modified MSE \(\tilde{\delta}_{i}\) approaches \(1/\overline{\gamma}\). Finally, adaptation algorithm, \(\zeta_{i}\) is:  
\[\zeta_{i}=\left|\frac{1}{\overline{\gamma}}-\tilde{\delta}_{i}\right|. \tag{18}\]  
Figure 3: BER performance of QPSK 1/2 in V2I Urban Canyon.  
The proposed scheme compares the resulting value obtained by performing the adaptation algorithm on the candidate schemes, and then selects a channel estimation scheme with the smallest resulting value.  
Figure 4 represents the flowchart of the proposed scheme. As shown in Figure 4, the proposed technique consists of the following five steps. (For ease of technical explanation, specific cases, i.e., switching between the STA and MMSE schemes or between the STA and TRFI schemes, are explained by example.)