## 3 The Conservative Maximum Power Estimation Procedure
To overcome the above problems, in this paper, we will use a statistical approach to estimate an _upperbound_ of the boost factor from the antenna data, evaluating the CDF of \(F_{beam}(\theta,\phi)\) in an angular region around \((\theta_{0},\phi_{0})\). Accordingly, the quantity that will be used in the MPE procedure is the CDF of \(F_{beam}(\theta,\phi)\) in an angular region around the measurement point, i.e.,  
\[CDF(F_{beam})=CDF\bigg{(}\frac{T(\theta,\phi)}{B(\theta,\phi)}\bigg{)} \tag{5}\]  
wherein \(\theta_{i}\leq\theta\leq\theta_{f}\) and \(\phi_{i}\leq\phi\leq\phi_{f}\), with \(\theta_{0}\in(\theta_{i},\theta_{f})\) and \(\phi_{0}\in(\phi_{i},\phi_{f})\), are spherical coordinate systems centered in the antenna. Below, we will call \(F_{beam}^{0.95}\) the value that is exceeded with a probability less than 0.95. Furthermore, if only the two main cuts of TERP and BERP are available (as often happens), the CDF will be obtained supposing separable patterns, i.e.,  
\[T(\theta,\phi) =T(\theta)T(\phi) \tag{6}\] \[B(\theta,\phi) =B(\theta)B(\phi)\]  
wherein \(T(\theta)\) and \(B(\theta)\) are the vertical cuts of TERP and BERP, respectively (represented in linear range), and \(T(\phi)\) and \(B(\phi)\) are the horizontal cuts of TERP and BERP, respectively. BERP and TERP can be used to obtain a conservative value of the maximum field level that does not require \"on air\" measurement of \(F_{beam}\). Clearly, if the value is within the limit fixed by current regulation, it gives a simple, fast, and low-cost solution to the MPE problem. The proposed procedure requires, besides the TERP and BERP of the AAS and the angular direction \((\theta_{0},\phi_{0})\) between the AAS and the measurement point (including tilting angle of the AAS if present), some basic information on the structure of 5G signal:  
* Central frequency of the SSB;
* Bandwidth \(B\);
* Numerology \(\mu\);
* duty cycle \(F_{TDC}\). If not known a priori, these quantities can be obtained by measurements of 5G on-air signals [24]. Furthermore, the procedure requires the measurement of the power-per-resource element of the reference quantity, \(P_{RE}^{ref}\). There are many possible solutions to obtain such data. Since the method is conceived as a low-cost solution, the procedure supposes the use of a scalar spectrum analyzer in zero span according to the procedure reported in [22; 24]. The steps are as follows:  
1. Preliminary calculations of \(CDF(F_{beam}(\theta,\phi))\) in different angular ranges. * Load the TERP and BERP data provided by the vendor; transform the values from dB (as usually provided by the vendors) to linear range (see Equation (3)); if only the two principal cuts are available, apply Equation (6); at the end of this step, \(T(\theta,\phi)\) and \(B(\theta,\phi)\) are available. * Plot the \(F_{beam}(\theta,\phi)=T(\theta,\phi)/B(\theta,\phi)\) and identify a suitable number of angular ranges where the function is relatively homogeneous;
* For each angular range, evaluate the CDF of the aforementioned quantity; at the end of this step, we have the curves \(CDF(F_{beam}(\theta,\phi))\) associated with the different angular ranges. * Calculations of useful parameters
* Calculation of the number of subcarriers in the Resolution Bandwidth (RBW) of the Spectrum Analyzer: \[n_{RBW}=RBW/(15\times 2^{\mu})\] (7) where \(\mu\) is the numerology;
* Calculation of the number of subcarriers of the 5G signal: \[N_{SC}=B/(15\times 2^{\mu})\] (8) where \(B\) is the bandwidth of the 5G signal;
* Setting of the Spectrum Analyzer (SA). A description of the scalar spectrum analyzer setting for SSB power measurement is reported in [22; 24]. The following setting is suggested: span zero mode, RMS detector, Max Hold mode, and central frequency of the SA equal to the central frequency of the SS-PBCH, RBW equal to 1 MHz. * Measurement: acquisition of the SSBs power level in zero-span mode and identification of the power level \(P^{SSB}\) in dBm of the SSB with the highest power.