# An Improved Channel Estimation Technique for IEEE 802.11p Standard in Vehicular Communications
## 3 Overview of Current Channel Estimation Schemes
### Scenario 2: Remain the Structure of the IEEE 802.11p
#### 3.2.3 Spectral-Temporal Averaging (STA) Based Scheme  
Another excellent scheme [36] that addresses the challenges of time-varying nature of V2V channel is known as STA. The STA is actually an approach to estimate the dynamic nature of such kind of communication channels. If \(i\) is the index of OFDM data symbol, then \((i-1)\) th estimated channel response which is represented by \(H_{STA,i-1}(k)\), equalizes the received data symbol \(S_{R,i}(k)\) and given by Equation (2).  
\[\hat{S}_{T,i}(k)=\frac{S_{R,i}(k)}{H_{STA,i-1}(k)} \tag{2}\]  
Where \(H_{STA,0}(k)\) is the channel response of the \(0 th\) data symbol. It is obtained from Equation (1) by using the LTSs. A modulation scheme dependent demmapper transforms \(\hat{S}_{T,i}(k)\) to \(\hat{X}_{i}(k)\). The phase tracking pilot subcarriers at \(\hat{X}_{i}(k)\) with \(k=-21,\,-7,7,21\) are also combined with the frequency domain values in the standard. Let \(H_{i}(k)\) be the initial estimate of the channel obtained by Equation (3).  
\[H_{i}(k)=\frac{S_{R,i}(k)}{\hat{X}_{i}(k)} \tag{3}\]  
\(H_{i}(k)\) is derived from the knowledge of data symbols, however, these data symbols might be incorrectly mapped especially at the lower Signal-to-Noise Ratio (SNR) conditions. Therefore, [36] considered that averaging in both the frequency and time domains can help in improving accuracy. The averaging in the frequency domain is given by Equation (4).  
\[H_{update}(k)=\sum_{\lambda=-\beta}^{\lambda=\beta}\omega_{\lambda}H_{i}(k+\lambda) \tag{4}\]  
The expression \(2\beta+1\) represents the subcarriers that are averaged. The set of weighting coefficients \(\omega_{\lambda}\) has unit sum and is equal to \(\omega_{\lambda}=1/(2\beta+1)\). The averaging in the time domain is given by Equation (5).  
\[H_{STA,i}(k)=(1-\frac{1}{\alpha})H_{STA,i-1}(k)+\frac{1}{\alpha}H_{update}(k) \tag{5}\]  
The updating parameter \(\alpha\) is related to the Doppler spread. The values of \(\alpha\) and \(\beta\) parameters are dependent on the types of vehicular channels. Significant accuracy can be achieved by adjusting these values according to the knowledge of the vehicular channel environment. One source of such knowledge is through the Global Positioning System (GPS), as discussed in [36]. However, such a kind of information is practically quite hard to obtain. It is was investigated that fixed values of these parameters can be a good balance of algorithm simplicity and an acceptable performance degradation.  
Another channel tracking technique [16] performed the initial channel estimation through the preamble just like the midamble base estimation scheme. The next symbols are then estimated in a specific order, that includes the equalization, decision direct estimation, and smoothing process. The channel tracking algorithm in the decision directed scheme is the same as Equations (2) and (3). However, at lower values of SNR, the wrong decisions can propagate and cause an error in the channel tracking process. Therefore, a smoothing process has been proposed to mitigate the part of estimation noise. The performance improvement is depicted in the simulation results. This smoothing operation brought a huge complexity into the computation process, which is mainly caused by the multiplication of larger size matrices. This computational complexity was reduced by two algorithms, known as lossless complexity reduction and lossy complexity reduction. The lossless complexity reduction deployed the Singular Value Decomposition (SVD) to lower the burden of matrix multiplication. The lossy complexity reduction, on the other hand, ignores some subcarriers to reduce complexity with little degradation in the performance.