# On Channel Estimation in LTE-Based Downlink Narrowband Internet of Things Systems
## 2 Overview of NB-IoT Downlink Technology  
3 GPP started focusing on developing the specification of NB-IoT since the beginning of 2014. In the beginning, NB-IoT was concerned with low power and low-end devices known as cat NB-1 with the option of sending a small amount of data in parallel [33]. It can be deployed in three distinct working modes: in-band, guard-band, and stand-alone. The pictorial illustration of all the modes are shown in Figure 1. At least one or several physical resource blocks (PRBs) of 180 kHz from the LTE network is needed to deploy the in-band mode, while the entire transmission power will be distributed to the base stations (eNB) of LTE and NB-IoT systems. An unused guard-band is enough to deploy the guard-band mode, which is permitted for only 5 MHz or higher operating frequency of LTE. In-band and guard-band mode reuse the spectrum of LTE base station and other resources to work within the narrow bandwidth of only 180 kHz [34]. The coexistence of NB-IoT and LTE is justified and proven through in-depth study and simulation [35]. The stand-alone mode can be operated inside the GSM bandwidth by reframing its one or more 200 kHz carrier. As stated above, because of exploiting existing LTE and GSM networks, the deployment of NB-IoT will not cost extra deployment money and time to be in operation. As NB-IoT is designed based on the existing LTE network, its signals and channels are also inherited from LTE with the specified simplification and required modification. All the signals and channels of NB-IoT for both downlink and uplink are shown in Table 1.  
Only frequency division duplex (FDD) mode of communication is supported by NB-IoT in a half-duplexing manner. With only QPSK modulation support in the downlink transmission, NB-IoT inherits the baseband numerology of LTE downlink with certain restrictions and modifications. Orthogonal frequency division multiplexing (OFDM) is used as in LTE with 15 kHz subcarrier spacing. The NB-IoT basic time unit is defined as \(T_{s}=1/(15,000\times 2048)\) seconds. A pair of slots constitute one subframe, and ten subframes constitute one frame, where the duration of slot, subframe, and frame are \(T_{slot}=15,360\times T_{s}=0.5\) ms, \(T_{sfframe}=0.5\times 2=1\) ms, and \(T_{f}=307,200\times T_{s}=10\) ms, respectively. In a radio frame, slot number is defined by \(n_{s}\), where \(n_{s}\in\{0,\ldots,19\}\). The frequency-time grid structure of NB-IoT downlink within a frame of a subcarrier spacing of 15 kHz is demonstrated in Figure 2. Every single component of the resource grid is a unique resource element which is the basis of a resource grid. It is represented by index pair (\(k\),\(l\)) in each slot, where \(k=0\ldots N_{RB}^{DL}N_{SC}^{SR}-1\) and \(l=0\ldots N_{symb}^{DL}-1\) are representing frequency and time domain, respectively. A subframe is a basic unit to allocate narrowband physical downlink shared channel (NPDSCH). Any specific transport block size (TBS), selected from the list {1, 2, 3, 4, 5, 6, 8, 10} in 3 GPP [36] can be mapped in multiple subframes in the time domain. TBSs are represented as the function of subframe number and the level of modulation and coding scheme (MCS), as shown in Table 2. A maximum TBS size of 680 bits is defined for NB-IoT downlink. The technique of repetition of the associated control signal and user data has been taken to get wide area coverage. A total of 128 and 2048 repetitions are allowed in uplink and downlink NB-IoT transmission in order to get successful signal decoding at the receiver end in the situation where the noise is even more powerful than the signal.