## 3 The Conservative Maximum Power Estimation Procedure  
Measurement of \(F_{beam}\) is not an easy task. Consequently, solutions that do not require \"on-air\" measurements to estimate \(F_{beam}\) by means of numerical simulations are of great interest. Unfortunately, information on the configuration of the field radiated by Active Antenna Systems (AASs) [34] provided by the vendors is limited. In particular, the AAS radiation characteristics are summarized by the so-called \"Envelope Radiation Pattern\" [33], defined as _a non-physical radiation pattern obtained by taking, for each direction in azimuth and elevation, the maximum of the absolute, not peak-normalized to its own peak, radiation pattern among the radiation patterns that the AAS can generate for a given operating condition (deployment/coverage scenario)_.  
Summarizing the key points reported in [33] that are useful for the problem discussed in this Section, we have the following:  
* The Broadcast Envelope Radiation Pattern (BERP) is the envelope pattern of each Broadcast Beam Configuration; since the AAS can have different broadcast configurations available for specific coverage requirements, there are as many BERP as the number of configurations implemented by the AAS. * The Traffic Envelope Radiation Pattern (TERP) is the envelope pattern of the traffic beams associated with a Broadcast Configuration; TERP could be associated with more than one Broadcast Configuration. * BERP and TERP are valid in far-field and free-space propagation conditions. * BERP and TERP can be obtained by measurement or numerical simulation. * No uncertainty information on BERP and TERP is usually available. * Information on the mechanical and (if applied) electrical tilting is not included in the data and must be obtained from the operator. Consequently, the knowledge of the antenna position of the base station and of the measurement position allows us to estimate the parameter \(F_{beam}\) from TERP and BERP in the measurement direction in free-space-like conditions, e.g., in the Line of Sight condition with unobstructed first Fresnel ellipsoid, provided that the mechanical and (if applied) electrical inclination of the antenna is known. In real applications, the field at the observation point is given by the interference of many contributions caused by reflection, refraction, and diffraction phenomena, to which the direct path is added if the propagation is in the LOS (Line of Sight) condition. Multiple reflections cause the presence of fast and slow fading and a significant decrease in the field level in NLOS (Non-Line-of-Sight) conditions compared to propagation in free space. In practice, the enormous flexibility in the choice of beams and the fact that they are provided in free-space conditions make it difficult, if not impossible, to accurately estimate \(F_{beam}\) at an observation point from the knowledge of BERP and TERP. Let  
\[T(\theta,\phi) =10^{T_{dB}(\theta,\phi)/10} \tag{2}\] \[B(\theta,\phi) =10^{B_{dB}(\theta,\phi)/10} \tag{3}\]The scale factor \(F_{beam}\) between the Traffic and Broadcast power level can be estimated as the ratio  
\[F_{beam}(\theta,\phi)=\frac{T(\theta,\phi)}{B(\theta,\phi)} \tag{4}\]  
Envelope radiation patterns can have quite fast variations, especially in the case of broadcast beams (traffic beams are narrow but numerous, so they tend to cover more uniformly the region with respect to Broadcast beams, and their envelope is smoother.). This is a critical problem since a small error in the angular direction of the gNB with respect to the measurement point \((\theta_{0},\phi_{0})\) can cause a not-negligible error in the estimation of \(F_{beam}\). Furthermore, the uncertainty about the angle of inclination of the AAS also causes uncertainty about the exact \((\theta_{0},\phi_{0})\) value.