# On Channel Estimation in LTE-Based Downlink Narrowband Internet of Things Systems
## 8 Conclusions  
In this paper, a brief overview of the NB-IoT downlink system along with NRS signal generation and mapping are presented. According to the channel impairments and multipath fading, an analytical signal model for the downlink NB-IoT systems is derived. To validate the operation of low power and low complexity NB-IoT systems, two channel models (TU 1 Hz [21; 45] and EPA 1 Hz [28]) are exploited, which are especially recognized for low power communication systems design and validation. Consequently, LMMSE is used, followed by the application of the optimal rank reduction formula (SVD) to the channel matrix to get a low-rank estimator. Then, the channel matrix is subdivided into several submatrices to reduce the complexity again. Finally, a reduced complexity LMMSE channel estimation technique is proposed by overlapping the submatrices named overlap banded SVD LMMSE for the NB-IoT downlink systems. In addition, for improving the performance and complexity of the proposed channel estimation once more, a new interpolation method is presented with the application of polyphase decomposition of the FIR filter of the traditional interpolation method. Theoretical derivation and the link level simulations proved that the MSE, BER, and the instantaneous throughput performance related to the SNR of the proposed overlap banded SVD LMMSE technique with the proposed polyphase decomposed FIR filter interpolation method are almost close to the LMMSE method, and it significantly outperforms the proposed overlap banded SVD LMMSE channel estimator with the traditional interpolation scheme and LS estimator for both TU 1 Hz and EPA 1 Hz channel scenarios. Furthermore, the complexity calculation and the memory space required confirm that the overlap banded SVD LMMSE channel estimator with the proposed interpolation scheme offers less complexity than the LMMSE approach. Hence, it possesses an expected balance between performance and complexity, which is crucial to the operation of NB-IoT systems. This attribute of the proposed channel estimation method makes it superior to other related schemes to be applied in NB-IoT systems. In conclusion, by compromising negligible performance from the optimum LMMSE channel estimator (MSE of only 1.3 dB and 1.1 dB for TU 1 Hz and EPA 1 Hz channels while BER of 0.8 dB and 0.9 dB for both channel cases, respectively), the proposed estimator, consisting of very low complexity and small memory demand seems compatible and can be successfully implemented in the low power and low complexity NB-IoT systems. For further studies in the future, the authors will conduct more link-level simulations under different AWGN channel models and will focus on equalization based on LMMSE for the NB-IoT downlink systems.  
Conceptualization, M.K.H.J.; formal analysis, M.K.H.J.; investigation, M.K.H.J.; methodology, M.K.H.J.; software, M.K.H.J.; writing--original draft, M.K.H.J.; writing--review and editing, R.S.Z.; supervision, F.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The majority of the work was conducted at MESIC (a joint lab of USTC and IMECAS), and partially carried out at the USTC Center for Micro and Nanoscale Research and Fabrication. The authors would like to thank the Information Science Laboratory Center of USTC for software and hardware services. The financial support of the Chinese Government Scholarship (CSC) is greatly appreciated. The authors declare no conflict of interest.