# On Channel Estimation in LTE-Based Downlink Narrowband Internet of Things Systems
## 7 Simulation Results
### Throughput Analysis  
The instantaneous throughput of the downlink NB-IoT UE for related operating SNR is also studied in our simulation. Here, the throughput is defined as the quantity of effectively received bits in the entire transmission period. Figure 13a,b represent the throughput performance comparison of the different channel estimators used in this paper for TU 1 Hz and EPA 1 Hz channels, respectively. The maximum sustainable throughput in NB-IoT downlink is 26.5 kbps [15; 46; 47]. In Figure 13a for the TU 1 Hz channel, we can see that the traditional LMMSE estimator possesses 25 kbps throughput at 15 dB SNR, which is almost close to the target downlink throughput, but it possesses high complexity and consumes excessive power, which is not suitable for the low complexity and low power NB-IoT systems. When the SVD technique is applied, the throughput performance degrades a little (24 kbps), which is also almost closer to the target data rate. Due to the uses of the channel statistics, those are less correlated to estimate the channel in the banded SVD LMMSE, the throughput performance degrades prominently (i.e., 19 kbps). When the overlap banded technique was applied to compensate for the performance loss of the channel estimator with the traditional interpolation method, it is observed that the throughput performance becomes 22 kbps. However, the application of the proposed overlap banded SVD LMMSE channel estimation method with the proposed polyphase decomposed FIR filter interpolator scheme increases the throughput up to 24 kbps which is almost the same as the SVD LMMSE technique. At the very low SNR situation, the same signal is repeatedly transmitted for having extended coverage and hence the transmission time becomes longer. Consequently, this situation degrades the throughput performance at  
Figure 12: Bit error rate (BER) comparison of the proposed technique with the conventional and proposed interpolation methods for different subvector values: (**a**) TU 1 Hz; (**b**) EPA 1 Hz.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **TU 1 Hz Channel** & **EPA 1 Hz Channel** \\ \hline LS [30] & 3.8 & 4.1 \\ LMMSE [44] & \(-1.3\) & \(-1\) \\ SVD LMMSE & \(-0.50\) & \(-0.15\) \\ Banded SVD LMMSE & 2 & 2.4 \\ Overlap banded SVD LMMSE with & 0.7 & 1 \\ conventional interpolation (Proposed) & & \\ Overlap banded SVD LMMSE with proposed & \(-0.5\) & \(-0.1\) \\ interpolation (Proposed) & & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Received SNR (dB) at BER = \(10^{-2}\) for different channel estimators.  
the lower SNR values (e.g., at \(-10\) dB SNR) to a few kbps. Similar performance is observed for the EPA 1 Hz channel in Figure 13b with average 1 kbps throughput degradation compared to the TU 1 Hz channel. Nevertheless, Figure 13a,b make it clear that the throughput performance of the proposed overlap banded SVD LMMSE technique with the proposed polyphase decomposed interpolation method is much better than the traditional LS, SVD LMMSE with banded and overlap banded methods while using the traditional interpolation method. Figure 14a,b show the throughput performance of the proposed channel estimation technique for different values of the subvector for both TU and EPA channels, respectively. Here, we can sum up that the maximum number of subvectors will give the best throughput performance.  
Figure 14: Throughput performance of the proposed technique with conventional and proposed interpolation schemes for different subvector values: (**a**) TU 1 Hz; (**b**) EPA 1 Hz.  
Figure 13: Throughput performance comparison of the proposed method for conventional and proposed interpolation schemes with LMMSE and its different counterpart channel estimators: (**a**) TU 1 Hz; (**b**) EPA 1 Hz.