# A Systematic Analysis of Narrowband IoT Quality of Service
## 4 Results
### PHY Measurements: Coupling Loss  
The first measurement explored the RSRP and RSSI signal level parameters. This evaluation was essential to find a suitable representation of path loss for later measurements. A wide range of signal levels was simulated by manually introducing attenuation in 5 dB steps until the signal was lost. For each attenuation level, 30 packets were sent, and the downlink RSRP and RSSI (DL-RSRP and DL-RSSI) were recorded for each packet. Figure 5(a) shows that the RSRP was proportional to the coupling loss under all conditions, including signal levels below the effective noise floor (see Section 2.4). The ability to measure signal levels below the noise floor was enabled by coherently adding signal repetitions, which increased the receiver sensitivity. This measurement confirmed the sensitivity of the SARA-N211 modem of \(-135\) dBm [23]. Figure 5(b) compares the RSRP and RSSI for different signal levels. While the RSRP was proportional to coupling loss, the RSSI converged to the 180 kHz effective noise floor \(P_{N,eff,180 kHz}=-114.4\) dBm. Since the RSSI included signal, noise, and interference power, it could not fall below the effective noise floor. As such, it was unsuitable for coupling loss evaluations. Table 3 provides additional statistical detail on the RSRP and RSSI measurements. The RSRP mean values (\(\mu_{RSRP}\)) followed the manual attenuation closely for all signal levels, with a maximum error of 3% at 50 dB attenuation. On the other hand, the RSSI mean values (\(\mu_{RSSI}\)) converged to the effective noise floor, with a minimum average value of \(-112.2\) dBm at 50 dB attenuation. As expected, the standard deviation of the 15 kHz RSRP signal level (\(\sigma_{RSRP}\)) was higher than for the RSSI (\(\sigma_{RSSI}\)), which had a larger bandwidth of 180 kHz. In the 3 GPP specification, the coupling loss was estimated using the RSRP measurement [18]:  
\[\text{\emph{Coupling Loss}}\ \text{\emph{CL}}[dB]=P_{TX,NRS}-RSRP_{filtered} \tag{20}\]  
where \(RSRP_{filtered}\) is the higher layer filtered RSRP. Figure 6: Analysis of different signal level measurements as an expression for coupling loss. (**a**) Distribution of RSRP signal levels for artificial attenuation in 5 dB steps. (**b**) Comparison between RSRP and RSSI for various levels of artificial attenuation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Attenuation [dB]** &
\begin{tabular}{c} **Number of** \\ **Measurements** \\ \end{tabular} & \(\mu_{RSRP}\) **[dBm]** & \(\sigma_{RSRP}\) **[dB]** & \(\mu_{RSSI}\) **[dBm]** & \(\sigma_{RSSI}\) **[dB]** \\ \hline
10 & 30 & \(-\)98.052 & 1.406 & \(-\)90.237 & 0.909 \\
15 & 30 & \(-\)102.325 & 0.720 & \(-\)94.827 & 0.592 \\
20 & 30 & \(-\)108.063 & 1.183 & \(-\)99.966 & 0.631 \\
25 & 30 & \(-\)113.352 & 1.163 & \(-\)104.787 & 0.680 \\
30 & 30 & \(-\)118.548 & 1.647 & \(-\)108.580 & 0.647 \\
35 & 30 & \(-\)121.862 & 1.513 & \(-\)110.743 & 0.429 \\
40 & 30 & \(-\)125.244 & 1.513 & \(-\)110.834 & 0.293 \\
45 & 30 & \(-\)129.202 & 1.009 & \(-\)111.768 & 0.613 \\
50 & 30 & \(-\)133.635 & 1.716 & \(-\)112.210 & 0.932 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean values (\(\mu_{RSRP}\), \(\mu_{RSSI}\)) and standard deviation (\(\sigma_{RSRP}\), \(\sigma_{RSSI}\)) of the RSRP and RSSI measurements. The power \(P_{TX,NRS}\) allocated to an NRS depends on the system configuration [18] and was approximated hereafter proportional to the bandwidth:  
\[P_{TX,NRS}\approx P_{TX,NRS}+10 log(1/12)=35\;\mathrm{dBm}-10.8\;\mathrm{dB}=24.2 \;\mathrm{dBm} \tag{21}\]  
The minimum observed DL-RSRP value during the measurement was \(-137.3\;\mathrm{dBm}\) at 50 dB attenuation. The maximum observed MCL could therefore be approximated:  
\[MCL_{max,observed}\approx 24.2\;\mathrm{dBm}-(-137.3\;\mathrm{dBm})=161.5\; \mathrm{dB} \tag{22}\]  
In a following evaluation related to the exception report latency, a minimum DL-RSRP level of \(-139.3\;\mathrm{dBm}\) was measured, which resulted in a \(MCL_{max,observed}\) of \(163.5\;\mathrm{dBm}\).