## 2 3 GPP Reference Model of Antenna Patterns  
The assessment of adjacent-beam interference levels in 5G wireless systems is based on the antenna pattern model, which is recommended by the 3 GPP. This model describes the transmission properties of an antenna array in the form of an ordered set of radiating elements that form \(N_{H}\) rows and \(N_{V}\) columns. In this case, the analytical form of the array power radiation pattern in spherical coordinates \(\mathbf{\Omega}=(\theta,\phi)\) is as follows [30]:  
\[g_{0}(\theta,\phi)=A(\theta,\phi)+10\log\left(\frac{1}{K}\!\!\sum_{k=1}^{K}\! \left|\sum_{m=1}^{N_{H}}\sum_{n=1}^{N_{V}}w_{k,n,m}\cdot v_{n,m}(\theta,\phi) \right|^{2}\right), \tag{1}\]  
where \(A(\theta,\phi)\) is the power radiation pattern of the antenna array element, \(K\) is the number of array beams, \(v_{n,m}(\theta,\phi)\) are the array of factors related to the position of the radiating elements, and \(w_{k,n,m}\) are weighting factors of the individual array coefficients, which depend on the orientation of the antenna array. The radiation pattern of each element of the antenna array is described by the relationship [30]  
\[A(\theta,\phi)=G_{\text{max}}-\text{min}(-(A_{H}(\phi)+A_{V}(\theta)),G_{0}), \tag{2}\]  
where \(G_{0}=30\) dB, \(G_{\text{max}}=7.5\) dBi represents the gain of the radiating element and is a constant value, \(A_{H}(\phi)\) and \(A_{V}(\theta)\) are the patterns of the radiating element in the azimuth and elevation planes, respectively, and \(G_{0}\) represents the ratio of maximum directivity of the antenna to directivity in a specified rearward direction. Whereas the characteristics \(A_{H}(\phi)\) and \(A_{V}(\theta)\) are defined in logarithmic measure as follows [30]:  
\[A_{H}(\phi)=-\text{min}\left(12\bigg{(}\frac{\phi}{\phi_{3 dB}}\bigg{)}^{2},G_{ 0}\right),\ A_{V}(\theta)=-\text{min}\left(12\bigg{(}\frac{\theta-\Theta_{0}} {\theta_{3 dB}}\bigg{)}^{2},G_{0}\right), \tag{3}\]  
where \(\phi_{3\text{dB}}\) and \(\theta_{3\text{dB}}\) represent the angular spread of the pattern at the level of \(-3\) dB in the azimuth and elevation planes, respectively, i.e., \(A_{H}(\phi_{3\text{dB}}/2)=-3\) dB and \(A_{V}((\theta_{3\text{dB}}/2)+\Theta_{0})=-3\) dB, where \(\Theta_{0}=90^{\circ}\). In the presented analysis, the values of \(\phi_{3\text{dB}}=80^{\circ}\) and \(\theta_{3\text{dB}}=65^{\circ}\) are adopted based on the recommendation in [30]. The antenna array coefficients \(v_{n,m}(\theta,\phi)\) are determined based on the following formula [30]  
\[v_{n,m}(\theta,\phi)=\exp\bigg{(}2\pi j\bigg{(}(n-1)\frac{d_{V}}{\lambda}\cos \theta+(m-1)\frac{d_{H}}{\lambda}\sin\theta\sin\phi\bigg{)}\bigg{)} \tag{4}\]  
and the weighting factors \(w_{k,n,m}\) are determined by the expression [30]  
\[w_{k,n,m}=\frac{1}{\sqrt{N_{H}N_{V}}}\exp\bigg{(}2\pi j\bigg{(}(n-1)\frac{d_{V }}{\lambda}\cos\theta_{k}+(m-1)\frac{d_{H}}{\lambda}\sin\theta_{k}\sin\phi_{k }\bigg{)}\bigg{)}, \tag{5}\]  
where \(\lambda\) is the length of the emitted wave, \(d_{V}\) and \(d_{H}\) are the distances between the radiating elements of the antenna array in the elevation and azimuth directions, respectively, \(\theta_{k}\) and \(\phi_{k}\) represent the deflection angles of individual antenna beams relative to the perpendicular direction to the antenna surface in the elevation and azimuth planes, respectively. In our analysis, we used a vertical patch as an antenna array of \(12\times 8\) elements for which the vertical and horizontal spacings are \(d_{V}/\lambda=0.7\) and \(d_{H}/\lambda=0.5\), respectively. For these parameters, the main lobe HPBWs of the antenna beam are \(12.6^{\circ}\) and \(6^{\circ}\) for the azimuth and elevation planes, respectively. Figure 1 depicts the 3D reference pattern model [23]. Unfortunately, the radiation pattern of the antenna array, which is generated based on Equation (1), changes along with the change in direction of the main lobe.