# An Improved Orthogonal Matching Pursuit Algorithm for CS-Based Channel Estimation
## 2 Materials and Methods
### Improvement of the OMP Algorithm
#### 2.2.2 Improvement of the OMP Algorithm
The simulation results show that, compared with the conventional MMSE estimation method, CS-based methods significantly save on the reference signal overhead and improve channel estimation performance. Therefore, they improve the effectiveness and reliability of the communication system at the same time. Also, compared with the conventional OMP and SOMP algorithms, the improved algorithms use longer observation vectors to calculate the path gain after obtaining the accurate path delay, which lowers the CRLB, and they are able to further enhance the performance of the MSE and BER in channel estimation, so they further improve the reliability of the communication system effectively. The limitation of the proposed scheme is that it assumes the known channel sparsity, which is unavailable in most fast-varying systems. In practice, a rough estimate of the sparsity can be obtained based on the LS criterion. In addition, the improved algorithms increase the complexity of the reconstruction algorithm, and the computation time increases exponentially with the increase in sparsity, but the additional computations are acceptable for the estimation of wireless channels with significant sparsity. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Channel Estimation Method**} & \multirow{2}{*}{**MMSE**} & \multirow{2}{*}{**OMP/P-OMP**} & \multicolumn{2}{c}{**SOMP/P-SOMP**} \\  & & & & _(J = 16)_ \\ \hline \multirow{2}{*}{Data block length (\(N\))} & 256 & \multirow{2}{*}{256} & \multirow{2}{*}{256} \\ \cline{1-1} \



The improved scheme is not applicable to OFDM systems employing frequency domain pilots, but it can be applied to TDS-OFDM systems and is applicable to the improvement of other matching pursuit algorithms. As summarized, the proposed scheme is of great significance for the reliable transmission of wireless communication systems based on a transmission block structure employing time domain pilots. Conceptualization, L.S. and W.X. ; methodology, L.S. and W.X. ; software, L.S. and X.Y. ; validation, L.S., X.Y. and H.Y. ; formal analysis, L.S. and H.Y. ; investigation, L.S. and W.X. ; resources, W.X. ; data curation, L.S. ; writing--original draft preparation, L.S. ; writing--review and editing, L.S. ; supervision, W.X. All authors have read and agreed to the published version of the manuscript. This work is supported by the Fundamental Research Funds for the Central Universities. Not applicable. Data Availability Statement: Data are contained within the article. The research presented in this paper is supported by the Communication University of China: Beijing, China. The authors declare no conflict of interest. ## References

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