# On Channel Estimation in LTE-Based Downlink Narrowband Internet of Things Systems
## 1 Introduction
in [30] and for the LTE downlink system in [31], by [PERSON] et al. It has been proven that SVD is one of the most efficient methods for reducing complexity of any complex matrix-based algorithm compared to other methods. However, a complete and efficient channel estimation scheme for the downlink NB-IoT systems is still absent in the current literature. In this work, a reduced complexity LMMSE channel estimation technique based on the SVD method along with a new interpolation method that can be practically applied to the LTE-based NB-IoT downlink system is proposed. This is an extension of our previous work published in [32]. We have further improved its performance and complexity with the application of a new interpolation method and investigated the operation of the proposed channel estimation method under different communication channel models (TU 1 Hz and EPA 1 Hz). To the best of the author's knowledge, it is for the first time that the LMMSE technique with complexity reduction has been studied, specifically to downlink NB-IoT systems. The key contributions of this work are summarized below:  
* We discuss the overview of NB-IoT technology briefly by considering its deployment, signals and physical channels, the structure of the downlink frame, and resource allocation according to 3 GPP release 13. In addition to this, we derive the downlink NB-IoT received signal model from the transmitted signal keeping relation with channel impairments. Narrowband reference signal (NRS) generation procedure for channel estimation and its mapping to the frequency-time grid is also represented. * We propose a computationally simple LMMSE channel estimation method named overlap banded SVD LMMSE for the downlink NB-IoT systems. LMMSE is the optimal channel estimator. We reduce the complexity of the LMMSE estimator by the application of SVD, banded SVD, followed by the overlap band technique while keeping the performance close to the LMMSE. Computer simulation and complexity analysis prove that the proposed overlap banded SVD LMMSE channel estimation technique makes a good balance between performance and complexity, which is important to be a better candidate for low complexity, and low power NB-IoT systems. * Lastly, we propose a new interpolation method by the application of polyphase decomposition of the finite impulse response (FIR) filter of the linear time dimensional interpolation method, which is well-known as a conventional interpolation approach [20; 21; 22; 23; 24; 25; 28] to boost the performance of the channel estimation and complexity of FIR filter design. In this case, the large FIR filter length is decreased to several small sections to increase the efficiency of the interpolator filter, and hence the inner complexity of the interpolator is reduced once more. Link level simulations with the state of art methods prove that the proposed overlap banded SVD channel estimation scheme with the proposed polyphase decomposed FIR filter interpolation method outperforms the LS, banded SVD LMMSE, and the overlap banded SVD LMMSE channel estimation method with the conventional (linear time dimensional) interpolation scheme in every aspect. The rest of the part of this paper is arranged as follows: In Section 2, we present a brief overview of NB-IoT downlink technology. We represent the NRS generation and mapping, along with NB-IoT downlink signal model in Section 3. Theoretical analysis of the proposed channel estimation and the proposed interpolation scheme is presented in Sections 4 and 5. In Section 6, computational complexity is demonstrated. Finally, we provide the performance analysis and conclusion in Sections 7 and 8, respectively.