# Inter-Beam Co-Channel Downlink and Uplink Interference for 5G New Radio in mm-Wave Bands +
## 3 Evaluation of Co-Channel Interference in Multi-Beam Antenna
For the selected time-cluster (ellipsoid), this coordinate is described by [29]:  
\[r_{T}=-\frac{1}{2a}b_{y}^{2}D\sin\theta_{T}\cos\phi_{T}+\frac{1}{2a}\sqrt{ \left(b_{y}^{2}D\sin\theta_{T}\cos\phi_{T}\right)^{2}+4 ab_{y}^{2}\left(a_{x} ^{2}-\frac{D^{2}}{4}\right)}, \tag{9}\]  
where \(a=\left(b_{y}\sin\theta_{T}\cos\phi_{T}\right)^{2}+a_{x}^{2}\left(\cos^{2} \theta_{T}+(\sin\theta_{T}\sin\phi_{T})^{2}\right)\). Appropriate coordinate transformation resulting from translation the system origin to the Rx allows determining AOA, \((\theta,\phi)\), for propagation paths reaching the Rx [29]:  
\[\theta=\arctan\frac{\sqrt{\left(r_{T}\sin\theta_{T}\cos\phi_{T}+D\right)^{2}+ \left(r_{T}\sin\theta_{T}\sin\phi_{T}\right)^{2}}}{r_{T}\cos\theta_{T}}, \tag{10}\]  
\[\phi=\arctan\frac{r_{T}\sin\theta_{T}\sin\phi_{T}}{r_{T}\sin\theta_{T}\cos \phi_{T}+D}. \tag{11}\]  
In addition to the AOAs of propagation paths reaching the Rx with delays, the local scattering paths are also included. In this case, the AOAs are generated using the von Mises distribution described by Equation (3). Powers \(\widetilde{p}\) of individual paths are determined based on the PDP or TDL. To generate these powers, we use exponential distributions, \(f(\widetilde{p})\), whose parameters (i.e., mean values \(p_{n}\) for \(n=1,2,\ldots,N\)) are equal to powers of the taps or local extremes occurring in the TDL or PDP, respectively:  
\[f(\widetilde{p})=\left\{ \begin{array}{ll}\frac{1}{p_{n}}\exp\Bigl{(}\frac{ \widetilde{p}}{p_{n}}\Bigr{)}&\text{for}\quad\widetilde{p}\geq 0,\\ 0&\text{for}\quad\widetilde{p}<0,\end{array} \right. \tag{12}\]  
where \(p_{n}\) is the \(n\)th local extreme of the PDP (or \(n\)th tap value of the TDL), which corresponds to the propagation paths reaching from the \(n\)th semi-ellipsoid, i.e., with the delay \(\tau_{n}\). As a simulation result, we get the set of \(\{(\theta,\phi,\widetilde{p})\}\) that enables estimating \(\widetilde{p}_{S,I}(\theta,\phi)\)[29]. Additional multiplication of each \(\widetilde{p}\) value by the appropriate value of \(\left|g(\theta,\phi)\right|^{2}\) gives us the set of \(\{(\theta,\phi,p)\}\), which is the basis for estimating \(p_{S,I}(\theta,\phi)\). A detailed description of the practical implementation of the estimation procedure is provided in [30]. As a result, we can determine \(P_{S}\) and \(P_{I}\) based on Equation (5). For the DL scenario, the SIR may be calculated based on Equation (4), because the serving and interfering beams are generated by the same gNodeB, i.e., \(D_{S}=D_{I}=D\). However, for the UL scenario, the SIR assessment requires additional consideration of attenuation resulted from a difference in the distances between the gNodeB and UE-S or UE-I. Considering this fact, we have:  
\[SIR=\frac{P_{S}}{P_{I}}\Delta PL\ \ \ \leftrightarrow\ \ SIR(\text{dB})=P_{S}(\text{dBm})-P_{I}\ \ (\text{dBm})+\Delta PL(\text{dB}) \tag{13}\]  
where:  
\[\Delta PL=\frac{PL(D_{S})}{PL(D_{I})}\ \ \leftrightarrow\ \ \Delta PL(\text{dB})=PL(D_{S})(\text{dB})-PL(D_{I})\ \ (\text{dB}) \tag{14}\]  
represents the relationship between attenuation of propagation environment for different distances, \(PL(D_{S})\) and \(PL(D_{I})\) are path losses for the wireless links between the UE-S or UE-I and gNodeB, respectively. For assessing \(\Delta PL\), we use a close-in free space reference distance path loss model presented in [37]. To take the influence of variable weather conditions into account that are related to atmospheric precipitation, the used path loss model should be corrected based on ITU-R recommendations [38; 39] or other approaches proposed in the literature, e.g., [40; 41]. Generally, the proposed methodology of the interference evaluation consists of the following stages:  
* defining the scenario parameters,
* determining the MPM parameters,
* determining the PASs for the serving and interfering links based on simulation studies,
* calculating the powers for the determined PASs,
* calculating the SIR finally.