## 2 Methods
### Monte Carlo Estimation Model  
The analysis of the total dose can be summarized in the following steps:  
1. derive a closed-form expression for the total psaSAR\({}_{10g}\) with respect to the study input variables;
2. describe the study input variables by means of probability distributions and constants;
3. combine the different probability distributions by means of the Monte Carlo simulation technique;
4. provide results by means of statistical summaries. The total dose in this study is defined as:  
\[\text{SAR}_{10g_{\text{total}}}=\text{SAR}_{10g_{\text{mobile}}}+\text{SAR}_ {10g_{\text{basetation}}}+\text{SAR}_{10g_{\text{bytander}}} \tag{1}\]where \(\text{SAR}_{10g_{\text{mobile}}}\) is the 10 g SAR in the body of the user caused by exposure to the uplink signal of his/her own mobile device, \(\text{SAR}_{10g_{\text{base station}}}\) is the 10 g SAR caused by exposure to the base station downlink signal, and \(\text{SAR}_{10g_{\text{systander}}}\) is the exposure caused by the mobile uplink signal of the mobile devices of bystanders. We assume that the exposure from bystander mobile devices and base stations is homogenous over the entire body when averaged over the 6-min intervals. The contribution of the user's own mobile phone is determined by:  
\[\text{SAR}_{10g_{\text{mobile}}}=\text{psaSAR}_{10g_{\text{mobile}}}\cdot \Delta\cdot DC_{\text{own}} \tag{2}\]  
where \(\text{psaSAR}_{10g_{\text{mobile}}}\) is the maximum SAR of the mobile phone measured at maximum output power, its relative transmit power \(\left(\Delta=\frac{P_{\text{bs}}}{P_{\text{bsmax}}}\right)\), and the duty cycle of the user's own data transmission usage (\(DC_{\text{own}}\)). We determine \(\Delta\) based on the reference signal received power (\(RSRP\)) and path loss (\(PL\)) in the network and use a factor of \(N\) (0...100%) to model enhanced indoor coverage in the network:  
\[\Delta=(1-N)\cdot\frac{PL_{\text{loc}}(RSRP_{\text{loc}})}{PL_{\text{max}}}+N \cdot\frac{PL_{\text{indoor}}(RSRP_{\text{indoor}})}{PL_{\text{max}}}|\Delta \in[0.0001;1] \tag{3}\]  
\(\Delta\) is limited to 0 to \(-40\) dB (1/10,000) based on mobile station dynamic range measurements in 4G networks [8]. Similarly, we calculate the SAR from the uplink of any bystander mobile phone:  
\[\text{SAR}_{\text{bystander}} = \Delta\cdot DC_{\text{bystander}}\cdot 0.2W\cdot\frac{1}{UL_{ \text{rf}}}\cdot\frac{1}{4\pi r^{2}}\cdot CF \tag{4}\]  
which is based on the assumption that the bystander is transmitting with the same power control level \(\Delta\) as the subject's own mobile phone, but with a distinctly different bystander duty cycle \(DC_{\text{bystander}}\). The maximum output power of the bystander's mobile phone is assumed to be 0.2 W [8], with an estimated uplink radiation factor \(UL_{\text{rf}}\) (loss) of 6 dB or a factor of 4 based on various studies in this area [19; 20; 21]. Based on the assumption that the propagation is isotropic (\(\frac{1}{4\pi r^{2}}\)), we assume that there is a bystander at the distance \(r\), where \(r\) is dependent on the population density at a geographical location under investigation. The coupling factor (\(CF\)) translates the incident power density from the bystander into the induced quantity SAR. Based on [22], an average coupling factor of 0.054 \(\frac{W}{\text{kg}}/\frac{W}{\text{m}^{2}}\) is applied to convert the incident power density to SAR. Similarly, the SAR from the base station can be calculated on the basis of the incident power density (\(S\)) and a coupling factor (\(CF\)):  
\[SAR_{10g_{\text{basestation}}} = S\cdot CF \tag{5}\] \[S = \frac{((1-N)\cdot RSRP_{\text{loc}}+N\cdot RSRP_{\text{indoor}}) \cdot 12\cdot M_{RB}\cdot\frac{1}{\Delta_{\text{eff_{\text{ACSG}}}}}\cdot \Delta_{data_{\text{ACSG}}}\cdot UL_{\text{rf}}}{A_{e}}\] (6) \[A_{\text{e}} = \frac{\lambda^{2}}{4\pi}\cdot G=\frac{0.15^{2}\text{m}^{2}}{4\pi} \cdot 1.64=0.0029\,\text{m}^{2} \tag{7}\]  
The scaling factor \(N\) is again used to include indoor coverage systems in the network topology differentially.