## 2 Methods
### Monte Carlo Estimation Model
#### Model Input  
Key to our statistical model are the categorized \(RSRP\) and \(PL\) measurements in a Swiss mobile LTE network. Figure 1 shows the cumulative distribution functions (CDF) of the measured \(RSRP\) and \(PL\) data for different geographical locations used in this study. In the Monte Carlo model, we randomly draw \(RSRP\) and \(PL\) pairs to simulate the mobile phones' received power, which is related to the incident power density, and the mobile phones' output power and available data rate, which are inversely related to the path loss. As there is still very little traffic in real 5G networks, we used the LTE data and the processes described above to extrapolate to the foreseeable behavior in 5G networks. Specifically, we scaled the LTE data by the improved spectral efficiency and data bandwidth (more than tenfold) in the hypothetical 5G networks. Based on [22], an average coupling factor of 0.054 \(\frac{\text{W}}{\text{kg}}/\frac{\text{W}}{\text{m}^{2}}\) is applied to convert the incident power density from base station and bystanders to SAR. To determine psaSAR\({}_{\text{10}g_{\text{mobile}}}\), we analyzed the full psaSAR test reports [26] of the latest models from Apple, Samsung, and Huawei with more than 2000 SAR measurements in total covering the frequency range from 700 MHz-2.6 GHz. We found that the average psaSAR values from the phones of these vendors are 0.16, 0.3, and 0.52 W/kg, respectively, with standard deviations of \(<\)3 dB. Because of the small spread, a psaSAR\({}_{\text{10}g_{\text{mobile}}}\) value of 0.33 W/kg was selected, and the statistical distribution of the mobile phone psaSAR is not included in the Monte Carlo analysis. As there are no data in the literature covering the analysis of uplink usage statistics in modern 4G mobile networks, we generated hypothetical usage patterns. We generated uplink data traffic,as summarized in Table 1. The traffic is quantized in atomic units that are transmitted at the maximum possible data rate at once, e.g., uploading a video and streaming units that require a certain data rate for a specific duration (e.g., a video call). We randomly distributed the required atomic and streaming data units for each user type over a 14 h time frame from 8 am to 10 pm, with a resolution of 1 s, referred to as \(DR_{\text{required}}(t\), user), being the required data rate in each second. As the data rate may be limited due to the signal quality, we then filtered the peak data rate of \(DR_{\text{required}}(t\), user) for the following path loss and data rate pairs: \(\geq\)130, 10 Mbps; \(<\)130, 15 Mbps; \(<\)120, 20 Mbps; \(<\)110, 30 Mbps; \(<\)100, 45 Mbps; \(<\)90, 60 Mbps; \(<\)80, 90 Mbps; \(<\)70, 120 Mbps; and \(<\)60, 180 Mbps. These data rates were chosen based on an uplink to downlink ratio of 1/10, a minimum downlink data rate requirement of 100 Mbps at the cell edge, and a maximum downlink data rate of approximately 2 Gbps. In the case that the available data rate (depending on the \(PL\)) is insufficient at any instant of time, the transmission duration is prolonged at the maximum rate until all data is transmitted. In the simulations, it is assumed that all cell types can reach their full theoretical capacity in the future, even though this may not be the case for all types to date. Figure 1: Cumulative distribution functions of the categorized path loss (**top**) and reference signal received power (**bottom**) measurements in a Swiss LTE network. The resulting filtered data rate time course is referred to as \(DR_{\text{required}_{\text{limited}}}(t\), user, \(PL)\).