# Multi-Technology Multi-Operator Site Sharing: Compliance Distance Analysis for EMF Exposure
## 3 Compliance Distance Calculations  
In [22], the International Electrotechnical Commission (IEC) specified in their standard IEC62232 that the most accurate compliance boundary is obtained as an iso-surface shape that can be enclosed in volumes with simpler shapes to define more conservative boundaries, such as a box shape, which is suitable for the sector coverage antenna, with horizontal, side, and vertical directions. In this work, the box-shaped compliance boundary was used to take into account the horizontal and vertical beamwidths and the gains of the antennae. Following some related works [23; 24; 25; 26; 27], we used the compliance distance (R\({}_{\rm CD}\)) to refer to the distance from the antenna at which TER = 1, which means that the accumulated exposure reaches the maximum limit. The TER was calculated on the basis of the power density \(S_{\rm inc}\); therefore, Equation (2) was modified to Equation (3), as shown below [6]. \[TER=\sum_{\rm f>30~{}MHz}^{\rm 300~{}GHz}\left(\frac{S_{\rm inc,f}}{S_{\rm inc,RL,f }}\right) \tag{2}\]  
At distance R (m) from the antennae, the \(S_{\rm inc}\) is the power density, which can be expressed as:  
\[S_{\rm inc,f}=\frac{\left(P_{\rm T}\cdot G_{A}\right)_{\rm f}}{4.\pi.R^{2}} \tag{3}\]  
Equation (3) can be substituted in the nominator of Equation (2), so the TER would be:  
\[TER=\sum_{\rm f>30~{}MHz}^{\rm 300~{}GHz}\left(\frac{\left(P_{\rm T}\cdot G_{A} \right)_{\rm f}}{4.\pi.R^{2}.S_{\rm inc,RL,f}}\right) \tag{4}\]  
At compliance distance R\({}_{\rm CD}\), the TER = 1, then:  
\[R_{\rm CD}=\left(\frac{1}{4\pi}\sum_{\rm f>30~{}MHz}^{\rm 300~{}GHz}\frac{P_{ \rm T,f}\cdot G_{A,f}}{S_{\rm inc,RL,f}}\right)^{1/2} \tag{5}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Exposure Limit** & **Freq. Range** & **E-Field (V/m)** & **H-Field (A/m)** & **PD (W/m\({}^{2}\))** \\ \hline \multirow{4}{*}{**ICNIRIP-OW**} & 0.1–30 MHz & 660/\(f_{M}\)\({}^{0.7}\) & 4.9/\(f_{M}\) & _NA_ \\  & 300–400 MHz & 61 & _0.16_ & _10_ \\  & 400–200 MHz & 3\(f_{M}\)\({}^{0.5}\) & 0.008\(f_{M}\)\({}^{0.5}\) & _f\({}_{M}\)_/40 \\  & 2–300 GHz & N\(A\) & N\(A\) & _50_ \\ \hline \multirow{4}{*}{**ICNIRIP-GP**} & 0.1–30 MHz & 300/\(f_{M}\)\({}^{0.7}\) & 2.2/\(f_{M}\) & _NA_ \\  & 300–400 MHz & 27.7 & _0.073_ & 2 \\  & 400–200 MHz & 1.375\(f_{M}\)\({}^{0.5}\) & 0.0037\(f_{M}\)\({}^{0.5}\) & _f\({}_{M}\)_/200 \\  & 2–300 GHz & N\(A\) & N\(A\) & _10_ \\ \hline \multirow{4}{*}{**FCC-OW**} & 0.3–0.3 MHz & _614.0_ & _1.630_ & _100.0_ \\  & 3.0–30 MHz & _1842f_ & _4.89f_ & _900/\(f^{2}\)_ \\  & 30–300 MHz & _61.40_ & _0.163_ & _1.00_ \\  & 0.3–1.5 GHz & - & - & _f300_ \\  & 1.5–100 GHz & - & - & _5.00_ \\ \hline \multirow{4}{*}{**FCC-GP**} & 0.3–1.34 MHz & _614.0_ & _1.630_ & _100_ \\  & 1.34–30 MHz & _824f_ & _2.19f_ & _180/\(f^{2}\)_ \\ \cline{1-1}  & 30–300 MHz & 27.50 & _0.0730_ & _0.20_ \\ \cline{1-1}  & 0.3–1.5 GHz & - & - & _f1500_ \\ \cline{1-1}  & 1.5–100 GHz & - & - & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The ICNIRP and FCC maximum limits for frequencies 0.1 MHz to 300 GHz. With the introduction of 5G NR, which uses a high grade of massive Multi-Input Multi-Output (mMIMO), some recent studies have investigated EMF exposure by considering more factors [28; 29; 30; 31; 32], such as the actual radiated power, system utilization load, and spatial/time duty cycle [32; 33]. Furthermore, according to IEC 62232 [22], EMF assessments for human exposure can be performed on the basis of actual situations. In [34; 35], the authors investigated the time-averaged instantaneous radiation and the theoretical maximum exposure from 5G NR base stations, and their results stated that the actual maximum exposure was very low compared with the theoretical maximum exposure for NR mMIMO. In this study, we used the power rating factor as a reduction in the total transmitted power to compute the compliance distance. Thus, Equation (5) becomes Equation (6):  
\[R_{CD}=\left( \begin{array}{cc}\frac{1}{4\pi}&\sum_{f>30}^{300\,GHz}\frac{ \rho_{rf}.P_{Tf}.G_{Af}}{S_{inc,RL,f}}\end{array}