# Performance Evaluation of GFDM Channel Estimation Using DFT for Tactile Internet Application
## 3 Experimental Results  
Two experimental schemes are defined. The first scheme is to observe the effect of pilot subcarrier spacing under multipath channels using exponential power delay profile. The second scheme is to analyze the influence of NYUSIM model using a power delay profile, as shown in Figure 4. The GFDM properties are adjusted to fulfill the tactile internet system requirements. Table 3 indicates the parameters for those two schemes. The Monte-Carlo method is applied for evaluating SER. First, we discuss the first scheme simulation. Figure 5 shows the MSE and SER performance of the first scheme. For the MSE performance, it can be seen that when pilot subcarrier spacing increase, the error occurs due to unclear pilot observations. The interference, as well as noise, can be overcome by increasing the number of pilot symbol in order to acquire better observation. This means that the smaller value of \(\Delta k\) leads to better estimation for both LS and DFT-based estimation methods. Therefore, the error floor grows vertically with the increase of \(\Delta k\). The effective rate for \(\Delta k=3\) and 6 is reduced by \(\eta=86\%\) and 93%, respectively. In addition, DFT-based channel estimation shows better performance than LS channel estimation. By removing the sample outside the maximum channel impulse response, this will reject interference and noise. The gap occurred between DFT-based estimation and LS estimation at MSE \(10^{-2}\) is 10 dB for \(\Delta k=3\) and 6 dB for \(\Delta k=6\). Figure 4: Power delay profile generated from NYUSIM simulator: (**a**) Umi scenario; (**b**) Uma scenario; (**c**) Rma scenario. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**First Scheme**} & \multicolumn{3}{c}{**Second Scheme**} \\ \hline Parameter & Value & Parameter & Value \\ Modulation Order (\(\mu\)) & 2 (QPSK) & Modulation Order (\(\mu\)) & 2 (QPSK) \\ Number of subsymbol (M) & 5 & Number of subsymbol (M) & 5 \\ Number of subcarrier (\(K\)) & 128 & Number of subcarrier (\(K\)) & 128 \\ Cyclic prefix length (\(Ncp\)) & 1/8 & Cyclic prefix length (\(Ncp\)) & 1/8 \\ Pilot subcarrier spacing (\(\Delta k\)) & 3 and 6 & Pilot subcarrier spacing (\(\Delta k\)) & 3 \\ Pulse shaping filter & Raised Cosine (RC) & Pulse shaping filter & Raised Cosine (RC) \\ Roll-off factor (\(\alpha\)) & 0.1 & Roll-off factor (\(\alpha\)) & 0.1 \\ GFDM Demodulator & Zero Forcing & GFDM Demodulator & Zero Forcing \\ Channel taps & 4 & Channel taps & 23, 39, 2 \\ Power delay profile & Exponential & Power delay profile & Umi, Uma, Rma \\ Pilot symbol & Complex & Pilot symbol & Complex \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental setup parameters. For the SER performance, DFT-based estimation also shows better performance than LS estimation. GFDM perfect compensation is obtained when the CIR is known completely at the receiver. Therefore, when performing equalization in the frequency domain, the channel frequency response can be found by transforming the known CIR. In other words, the channel estimation does not require pilot symbols. The degradation of DFT-based and LS channel estimation methods from GFDM perfect compensation strongly depends on the number of pilot symbols and the type of receiver. Since the same receiver is employed to these two estimation channel methods, this factor is not considered. Hence, the only factor is the number of pilot symbols. Increasing the number of pilot symbols in the subcarrier and time slot will increase SER performance to the perfect CSI condition. However, the effective data rate \(\eta\) will reduce accordingly. More observation are acquired at the receiver leads to good MSE reduction and this also leads to better SER performance. The improvement of DFT-based estimation is 1 dB over LS estimation at SER \(10^{-2}\) for \(\Delta k\) = 3 and 2 dB enhancement for \(\Delta k\) = 6.