# MIMO Channel Estimation in an SDR Platform for Evaluation of D&F Relay Nodes
## 7 Conclusions  
In this paper, a detailed study of the wireless MIMO channel between an eNB and a RN in our developed SDR platform was performed. We focused on channel estimation through an LS estimator and the Bi-Cubic (BCI), Bi-Linear (BLI), and Bi-Nearest Neighbors (BNNI) interpolation methods. In addition, the performances of the Zero-Forcing (ZF) and Minimum Mean Square Error (MMSE) equalizers were also analyzed.  
From the results, we can conclude that the developed SDR platform is an excellent tool to analyze--at a laboratory level--the behavior of channel propagation in the \"core network\" in complex scenarios and with long distances between eNB and RNs. On the other hand, the obtained results show that, in the pilot based on channel estimation, the LS estimator with cubic interpolation obtained the best performance, considering the studied 2D interpolation methods. Furthermore, the results demonstrated that 16-QAM modulation leads to better robustness in the implemented testbed. The results also showed that employing 2 \(\times\) 2 MIMO led to a substantial benefit, in terms of the performance of the core network. This technique achieved reduction of the Bit Error Rate and increasing the throughput in the 64-QAM constellation. In addition, the EVM of the SIB1 was measured, showing a great improvement in their values when using the MIMO technique.  
**Author Contributions:** [PERSON] conceived the paper, designed the experiments, performed experiments, and analyzed the data; [PERSON] and [PERSON] contributed the laboratory equipment; [PERSON] wrote the paper; [PERSON] and [PERSON] reviewed and edited the paper. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work has been supported by the Spanish Ministry of Science, Innovation and Universities within the project TEC2017-87061-C3-1-R (CIENCIA/AEI/FEDER,UE) and by the China Science and Technology Exchange Center-MST of the People's Republic of China, within the project 23016 YFE0200200. The work of [PERSON] is supported by a Pre-doctoral Contract PRE2018-085032 from the Ministry of Science and Innovation.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Additions** & **Multiplications** & **Divisions** \\ \hline BLI & 4N\({}_{Tx}\)N\({}_{Rx}\mu\) & 2N\({}_{Tx}\)N\({}_{Rx}\mu\) & 2N\({}_{Tx}\)N\({}_{Rx}\mu\) \\ BCI & 20N\({}_{Tx}\)N\({}_{Rx}\mu\) & 74N\({}_{Tx}\)N\({}_{Rx}\mu\) & 8N\({}_{Tx}\)N\({}_{Rx}\mu\) \\ PCHIP & 2N\({}_{Tx}\)N\({}_{Rx}\mu\) & - & 2N\({}_{Tx}\)N\({}_{Rx}\mu\) \\ BNNI & 2N\({}_{Tx}\)N\({}_{Rx}\mu\) & 2N\({}_{Tx}\)N\({}_{Rx}\mu\) & - \\ \hline \hline \end{tabular}
\end{table}
Table 4: Arithmetic operations required by Interpolation Methods.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Equalizers** & **Additions** & **Multiplications** & **Divisions** \\ \hline ZF & N\({}_{Tx}\)N\({}_{Rx}\frac{7N^{3}+3N^{2}-4N}{6}\) & N\({}_{Tx}\)N\({}_{Rx}\frac{7N^{3}+9N^{2}+2N}{6}\) & - \\ MMSE & N\({}_{Tx}\)N\({}_{Rx}\frac{7N^{3}+9N^{2}-4N}{6}\) & N\({}_{Tx}\)N\({}_{Rx}\frac{7N^{3}+15N^{2}+2N}{6}\) & - \\ \hline \hline \end{tabular}
\end{table}
Table 5: Arithmetic operations required by Equalization Algorithms.