# A Low-Complexity Channel Estimation Based on a Least-Squares Algorithm in OFDM Systems
## 6 Conclusions  
The CFRs at the odd pilot subcarriers and even pilot subcarriers are related if the number of maximum channel delay points is smaller than or equal to half the number of pilots (including virtual pilots). According to this correlation, we propose a low-complexity LS method to estimate the CFRs at the virtual even and odd pilot subcarriers, respectively. The adverse effect of unknown CFRs at the virtual pilot subcarriers for the conventional DFT-based channel estimation can be solved to enhance the channel estimation effective  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Path No. (I)** & **Propagation Delay** & **Path Power** & **Path Power (dB)** & **PSD** \\ \hline
0 & 0.0 \(\mu\)s & 0.17 & \(-\)7.7 & [PERSON] \\ \hline
1 & 0.1 \(\mu\)s & 0.46 & \(-\)3.4 & [PERSON] \\ \hline
2 & 0.3 \(\mu\)s & 0.74 & \(-\)1.3 & [PERSON] \\ \hline
3 & 0.7 \(\mu\)s & 1 & 0 & Gauss I \\ \hline
4 & 1.6 \(\mu\)s & 0.59 & \(-\)2.3 & Gauss I \\ \hline
5 & 2.2 \(\mu\)s & 0.28 & \(-\)5.6 & Gauss II \\ \hline
6 & 3.1 \(\mu\)s & 0.18 & \(-\)7.4 & Gauss II \\ \hline
7 & 5.0 \(\mu\)s & 0.72 & \(-\)1.4 & Gauss II \\ \hline
8 & 6.0 \(\mu\)s & 0.69 & \(-\)1.6 & Gauss II \\ \hline
9 & 7.2 \(\mu\)s & 0.21 & \(-\)6.7 & Gauss II \\ \hline
10 & 8.1 \(\mu\)s & 0.1 & \(-\)9.8 & Gauss II \\ \hline
11 & 10.0 \(\mu\)s & 0.03 & \(-\)15.1 & Gauss II \\ \hline \hline \end{tabular}
\end{table}
Table 6: The bad urban time-varying channel model.  
Figure 5: Simulated diagram of SNR to error rate when the carrier frequency is 2 GHz, the sampling frequency is 10 MHz, and the speed is 20 km/h for the bad urban time-varying channel model [8,10,11].  
ness of DFT-based channel estimation. While the channel estimation effectiveness of the proposed method is very similar to those of the LS methods [10; 11], it is noteworthy that the former's computational complexity is much lower than that of the LS method [11]. The proposed method does not need to know the statistical properties of the channel or insert extra pilots, as with some estimation methods. The channel estimation efficiency of our proposed method is still similar to those of the LS methods [10; 11], even if the number of maximum channel delay points is greater than half the number of pilots. Therefore, the low-complexity method proposed in this paper is very suitable for equalizer hardware implementation.  
Our proposed method has its drawbacks. It can only be applied to the comb-type pilot arrangement and the pilot spacing is the integer power of two. The two LS methods [10; 11] are applicable in both comb-type and scattered-type pilot arrangements, and pilot spacing does not need to be the integer power of two.  
Conceptualization, Y.-A.K.; methodology, Y.-A.K. and K.-F.W.; software, Y.-A.K. and K.-F.W.; validation, Y.-A.K. and K.-F.W.; formal analysis, Y.-A.K. and K.-F.W.; investigation, Y.-A.K. and K.-F.W.; resources, Y.-A.K. and K.-F.W.; data curation, Y.-A.K. and K.-F.W.; writing--original draft preparation, Y.-A.K. and K.-F.W.; writing--review and editing, Y.-A.K.; visualization, Y.-A.K. and K.-F.W.; supervision, Y.-A.K. and K.-F.W.; project administration, Y.-A.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.