# A Systematic Analysis of Narrowband IoT Quality of Service
## 2 Narrowband IoT Fundamentals
### Receiver Sensitivity, ECL, MCL, and Transmission Power Control in NB-IoT  
The receiver sensitivity (\(P_{RX,min}\)) defines the minimum input power level at the receiver antenna port related to a QoS threshold. This threshold is commonly specified at a Block Error Rate (BLER) of 10% for the NPUSCH and NPDSCH NB-IoT channels [1]. The BLER depends on the MCS and the amount of symbol repetitions (\(N_{Rep}\)) applied for a given Signal-to-Noise Power Ratio (SNR). Accordingly, \(SNR_{min}\) defines the minimum power ratio needed in order to achieve this QoS target. In the first step, the thermal noise needs to be considered:  
\[P_{N}=10*log(kTB/1\text{mW}) \tag{13}\]  
where \(k\) is the Boltzmann constant, \(T\) is the temperature, and \(B\) is the bandwidth. The effective noise floor (\(P_{N,eff}\)) takes into account the Noise Figure (NF) of the receiver front-end, which adds noise to the thermal noise power (\(P_{N}\)):  
\[P_{N,eff}=P_{N}+NF \tag{14}\]  
The analysis of the measurement results requires the calculation of the effective noise floor of the RSRP, the RSSI, and the 15 kHz single-tone NPUSCH. These can be calculated at room temperature, considering the corresponding Bandwidths (B) and the assumed NFs of UE and eNodeB:  
\[P_{N,eff,NPUSCH}=P_{N,15\text{kHz}}+NF_{eNodeB}=-132.2\ \text{dBm}+5\ \text{dB}=-127.2\ \text{dBm} \tag{15}\]  
\[P_{N,eff,RSSI,DL}=P_{N,180\text{kHz}}+NF_{UE}=-121.4\ \text{dBm}+7\ \text{dB}=-114.4\ \text{dBm} \tag{16}\]  
\[P_{N,eff,RSRP,DL}=P_{N,15\text{kHz}}+NF_{UE}=-132.2\ \text{dBm}+7\ \text{dB}=-125.2\ \text{dBm} \tag{17}\]  
Using the previous definitions, the receiver sensitivity (\(P_{RX,min}\)) is defined as:  
\[P_{RX,min}=P_{N}+NF+SNR_{min}=P_{N,eff}+SNR_{min} \tag{18}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Coupling Loss [dB]** & \begin{tabular}{c} **Stand-Alone Mode** \\ **Latency [s]** \\ \end{tabular} & \
\begin{tabular}{c} **Guard-Band Mode** \\ **Latency [s]** \\ \end{tabular} &
\begin{tabular}{c} **In-Band Mode** \\ **Latency [s]** \\ \end{tabular} \\ \hline
144 & 0.3 & 0.3 & 0.3 \\
154 & 0.7 & 0.9 & 1.1 \\
164 & 5.1 & 8.0 & 8.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: NB-IoT exception report latency (adapted from [1]). In NB-IoT, the receiver sensitivity is improved by applying signal repetitions [15]. Theoretically, each doubling of the repetitions increases the sensitivity by 3 dB due to coherent addition of the symbols and incoherent addition of thermal noise. NB-IoT employs up to 128 repetitions in the uplink and 2048 repetitions in downlink direction. The large number of repetitions in downlink compensates the higher effective downlink noise floor in order to balance the link budget. However, accumulating the signal repetitions takes time and is thus a tradeoff between latency and sensitivity. The appropriate number of repetitions is adjusted dynamically by the eNodeB, which assigns an ECL to each device based on the received uplink and reported downlink signal level, where a higher ECL corresponds to more problematic radio conditions and a higher number of repetitions. The exact number of repetitions per ECL is defined by the MNO. This paper refers to the three available ECL levels as ECL0, ECL1, and ECL2. The MCL is a common metric to evaluate the coverage of a radio access technology and is calculated as the difference between the transmitted power level at the antenna connector (\(P_{TX}\)) and the receiver sensitivity. Since the downlink NRS are used for channel estimation, their constant transmit power is indicated to the UE by the eNodeB and used for all physical channels. In the uplink direction, the transmission power depends on the coverage situation. For up to two repetitions, the transmission power is a function of multiple cell parameters including coupling loss. For more than two repetitions, the cell-specific maximum transmission power on slot \(i\) (\(P_{CMAX,c(i)}\)) is used. This paper refers to the transmit power of the UE as \(P_{TX,UE}\)[18].