## 5 Estimation of a Realistic Value of the Field Level from the MPE Value  
As highlighted in the introduction, the value obtained by the MPE techniques is an unrealistic upper limit, since it assumes that all the resources of the communication system are assigned to a single user for a period of time of 6 or 30 min according to the international guidelines [38]. The MPE value is then scaled according to the national regulations by an appropriate correction factor that takes into account the stochastic nature of the communication process in cellular systems in order to obtain a realistic value. This requires a complex statistical analysis that takes into account the period of time during which the user has access to the communication channel and the radiation characteristics of the traffic beams. An interesting analysis is reported in [39; 40; 41; 42]. Following the general simplicity of the approach of this work, we use the formula reported in [43], which provides a simple estimate of the average value of the reduction factor (in power) called \(F_{ant}\) in the paper:  
\[F_{ant}\simeq\frac{4\pi}{\Omega}\frac{1}{D} \tag{13}\]  
where \(\Omega\) is the solid angle of the domain served by the antenna and \(D\) is the directivity of the beam in the direction of the measurement point. Below, we will suppose that the directivity is almost equal to the gain \(G\) of the antenna. This value can be obtained by the plot of the envelope of beams and the knowledge of the maximum gain of the antenna. Figure 6: Estimated \(E_{5G}^{max}\) (V/m) using different methods. SSB/SS-RSRP: EMP from SSB RE power without \(F_{beam}\) correction; Beam Env: maximum SSB RE power corrected by \(F_{beam}^{0.95}\) obtained from envelope radiation patterns; \(F_{beam}\): maximum SSB RE power corrected with measured \(F_{beam}\)[24]; FR: value estimated from the RE’ power measurement in the whole frame [26]; CSI-RS: values obtained from CSI-RS REs power [26]; ZS: value obtained with Zero Span measurement [26]; PDSCH CD: value obtained from PDSCH RE power measured in the Code Domain [26]; CSI-RSRP: value obtained from CSI-RSRP [26]. The two green lines show the limits range in which the maximum field value belongs with a 95% probability estimated using Channel Power measurement on full-loaded frames [24]. The value given by Equation (13) is basically a mean value, while the current regulation requires the correction term to be at 95% probability [20]. However, in [43], it is shown that in the case of a large number of users, Equation (13) gives only a slight underestimation of the value at the 95% probability. In order to take into account this underestimation, we introduce a correction parameter denoted as \(F_{corr}\). Accordingly, a conservative value of the level in the measurement point in realistic conditions \(E_{5G}^{0.95}\) is obtained by the \(E_{5G}^{\max\ 0.95}\) and the Gain of the AAS value is  
\[E_{5G}^{0.95}=E_{5G}^{\max\ 0.95}\sqrt{F_{corr}}\sqrt{\frac{4\pi}{\Omega}\frac{1} {D_{eq}}} \tag{14}\]  
A comparison with the accurate estimate of the beam-sweep effect using the statistical approach, as obtained in Ref. [41], shows that \(s_{ant}=1.5\) is sufficient to obtain a conservative value of the reduction factor with 0.95 probability [43]. It is understood that if a more accurate estimation of \(F_{corr}\) is required, it is possible to consider the specific propagation scenario in the numerical simulation, as shown in [43]. Considering a coverage range of \(120^{\circ}\times 30^{\circ}\) and the Gain of the antenna, we have  
\[E_{5G}^{0.95}=2.6\times 0.50=1.3\,\mathrm{V/m} \tag{15}\]  
For comparison, a (largely) conservative value of the statistical factor is proposed in the technical report IEC62669 [44]. This value provides an estimation of the reduction factor versus the percentage of utilization of the resources of the communication system. In particular, the worst condition is obtained in the case of a large number of users (i.e., almost full use of the resources of the communication system).