# MIMO Channel Estimation in an SDR Platform for Evaluation of D&F Relay Nodes
## 6 Numerical Results and Performance Analysis
### Impact of Channel Estimation and Equalization on Received RG  
In this subsection, the performance of the channel estimation, interpolation, and equalization techniques studied are investigated by using the Error Vector Magnitude (EVM) metric.  
Figure 7 shows the obtained results for the Cumulative Distribution Functions (CDF) of the received RG with respect to the RMS EVM [%]. The developed SDR platform was used and the LOS scenario was considered. The black plot represents the EVM of the received signal without implementing the channel estimation and equalization techniques. It can be observed, from Figure 7, that when the developed algorithms were considered, the error decreased considerably, with an improvement between 38% and 57% for 90% of the time. Furthermore, it was found that, when the ZF equalizer was employed, the EVM was higher than when the MMSE equalizer was used. However, the traces associated with the BCI and BLI methods and the MMSE equalizer had a lower EVM than  
Figure 5: Measurement scenario with LOS between eNB and RN.  
Figure 6: Measurement scenario with NLOS between eNB and RN.  
that associated with LS-BNNI-MMSE. On the other hand, one of the boxes in Figure 7 represents the expanded version of the curves using the LS-BCI-MMSE and LS-BLI-MMSE methods, from which the improvement in the EVM of the received RG when using LS-BCI-MMSE can be appreciated.  
Four three-dimensional surfaces representing the Resource Grid of the FDD-LTE Downlink are shown in Figure 8. In Figure 8a-d, the X-, Y-, and Z-axes correspond to the OFDM Symbol Index (in the time-domain), Subcarrier Index (in the frequency-time), and power (in dB) of the RG, respectively. In each of the figures, only the 14 first OFDM symbols and 100 first subcarriers of the received RG are illustrated. On the other hand, in Figure 8a, the Resource Grid transmitted by the eNB in our SDR platform is shown, compared with the received RG at the receiver (i.e., the implemented Decode-and-Forward Relay Node). In the first instance, we compare the transmitted RG in Figure 8a with the received RG in Figure 8b. The presented result in Figure 8b is before performing the channel estimation methods and equalization techniques. It can be appreciated that the power of the received RG degraded greatly, on the order of 20 dB, with respect to the transmitted RG. Furthermore, when testing with the schemes presented in the previous section, it can be seen that the power of the received RG was on the order of the transmitted RG power, as can be seen from Figure 8c,d. Nevertheless, despite the obtained enhancement, it can be observed that the received RG after employing the LS-BCI-ZF techniques led to lost symbols, which explains the considerable differences of the EVM between the curves using ZF and MMSE equalization, as presented above. Therefore, the schemes that employed the MMSE equalizer had lower EVM and, between them, the best performance was obtained with Bi-Cubic interpolation.  
Figure 7: EVM of the Received Resource Grid in 2\(\times\)2 MIMO, 16-QAM, and LOS scenario.