# An Uplink Channel Estimator Using a Dedicated Instruction Set for 5G Small Cells
## 3 Algorithm and Implementation of Channel Estimation
### Algorithm Simulation Performance  
According to the pilot structure recommended by 3 GPP-38211 described in Section 2, this paper proposes channel estimation algorithms in Section 3. Using the multipath Extended Pedestrian A (EPA) model proposed by 3 GPP-36101 [24], the LS estimation + Wiener filter interpolation algorithm was simulated. The number of OFDM subcarriers set in the simulation in this paper is 1024 (assuming it is a user's PUSCH channel). EPA is an extended pedestrian channel proposed by 3 GPP. Under the EPA channel model, the UE moves slowly, so the Doppler spread is small. It is a simulation environment model that conforms to the small cell scenario. According to the 3 GPP protocol, the Doppler of EPA is extended to 5 Hz, and the power delay data of its seven multipaths are shown in Table 1.  
For the parameters of Equation (4), according to the EPA channel model, the maximum delay spread \(\tau_{\text{cmax}}\) of the multipath channel is set to 410 ns and its reciprocal corresponds to the coherent bandwidth, which is an important parameter to characterize the constant gain and linear phase of the multipath channel. The subcarrier spacing \(f_{sub}\) is 15 kHz; according to Figure 2, in the autocorrelation matrix, \(\Delta k=2\); in the cross-correlation matrix, \(\Delta k=1\). In order to simulate the channel environment of small cells, we set the antenna correlation to low correlation. The BER curves of time-frequency Wiener filter interpolation and time-frequency linear interpolation under different modulation modes are shown in Figure 5a. The BER curve obtained by the combination of different interpolation methods under 64 QAM is shown in Figure 5b.  
In Figure 5a,b, \"F -\" indicates the interpolation method used in the frequency domain; \"T -\" represents the interpolation method used in the time domain; \"one\" refers to linear interpolation; \"second\" refers to second-order interpolation; and \"wiener\" refers to Wiener filter interpolation. From Figure 5a, when the SNR increases gradually, the effect of Wiener filtering in the time-frequency domain is obviously better than that of linear interpolation, and the overall improvement effect is between 0 and 4 db. From Figure 5b, the use of frequency domain Wiener and time domain Wiener can each bring about a 2 db gain compared with linear interpolation. However, when the SNR is high, the BNR of second-order interpolation is worse than that of linear interpolation. This is because there is only one subcarrier between the two pilots in the frequency domain, so second-order interpolation does not have an advantage over linear interpolation; in the time domain,  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline Excess tap delay (ns) & 0 & 30 & 70 & 90 & 110 & 190 & 410 \\ Relative power (dB) & 0.0 & \(-1.0\) & \(-2.0\) & \(-3.0\) & \(-8.0\) & \(-17.2\) & \(-20.8\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Delay profiles for EPA channel models.  
Figure 5: BER curve in EPA channels. (**a**) Comparison of BER curves between Wiener filter interpolation and linear interpolation. (**b**) BER Curves of different interpolation methods under 64 QAM.  
the mobility of the EPA model is low, the channel changes slowly in the time domain and linear interpolation is more suitable than second-order interpolation.