# 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  
The co-channel interference assessment is based on the SIR measure defined as:  
\[SIR=\frac{P_{S}}{P_{I}} \begin{pmatrix}\mathrm{W}\\ \mathrm{W}\end{pmatrix} \;\;\leftrightarrow\;\;SIR(\mathrm{dB})=P_{S}(\mathrm{dBm })-P_{I}\;\;(\mathrm{dBm}), \tag{4}\]  
where \(P_{S}\) and \(P_{I}\) are the powers of the serving and interfering signal, respectively, which occur at the output of the receiving antenna. In the multi-beam receiving antenna, the interference signal is from a wireless link whose receiving antenna beam is formed in the same frequency band as the serving beam. From the SIR definition, it follows that the main problem of assessing this measure relies on determining \(P_{S}\) and \(P_{I}\). Note that these powers can be calculated based on the appropriate PASs, \(p_{S,I}(\theta,\phi)\), which are seen at the output of the receiving antenna, namely:  
\[P_{S,I}=\iint\limits_{(\theta,\phi)}p_{S,I}(\theta,\phi)d\theta d\phi. \tag{5}\]  
However, these distributions depend on the power pattern of the serving beam [30]:  
\[p_{S,I}(\theta,f)=\widetilde{p}_{S,I}(\theta,f)|g(\theta,f)|^{2}, \tag{6}\]where \(\widetilde{p}_{S,I}(\theta,\phi)\) represent the PASs in the vicinity of the receiving antenna and \(\left|g(\theta,\phi)\right|^{2}\) is the normalized power pattern of the receiving antenna. Hence, it follows that the problem of the SIR assessment boils down to determining \(\widetilde{p}_{S,I}(\theta,\phi)\). The developed methodology uses simulation tests to determine these PASs. The input data for simulation procedures that condition the estimation of \(\widetilde{p}_{S,I}(\theta,\phi)\) is a set of the following parameters and characteristics:  
* normalized power patterns \(\left|g_{S}(\theta_{T},\phi_{T})\right|^{2}\), \(\left|g_{I}(\theta_{T},\phi_{T})\right|^{2}\), and \(\left|g(\theta,\phi)\right|^{2}\), of the serving and interfering transmitting and receiving beams, respectively, where \((\theta_{T},\phi_{T})\) denotes AOD in the elevation and azimuth planes, respectively;
* gains \(G_{S}\), \(G_{I}\), and \(G\) of the serving and interfering transmitting and receiving beams, respectively;
* the Tx-Rx distances, i.e., \(D_{S}\) and \(D_{I}\) between the serving and interfering mobile stations (user equipment, i.e., UE-S and UE-I) and gNodeB for the UL scenario, respectively, or \(D_{S}=D_{I}=D\) for the DL scenario;
* the type of propagation environment defined by the TDL or PDP and rms delay spread. * Estimation of \(\widetilde{p}_{S,I}(\theta,\phi)\) consists in the generation of a set of propagation paths departing from the transmitting antennas of the serving and interfering links and their transformation in a system composed of the semi-ellipsoid set. The generation procedure of AODs, \((\theta_{T},\phi_{T})\), uses the properties of the normalized power radiation patterns [36]: \[\frac{1}{4\pi}\iint\limits_{(\theta_{T},\phi_{T})}\left|g_{S,I}(\theta_{T}, \phi_{T})\right|^{2}\sin\theta_{T}d\phi_{T}d\phi_{T}=1.\] (7)  
The function under integral is non-negative. Therefore, the normalized power radiation patterns meet the axioms of a probability density function. Hence, we can express the distribution of AOD as [36]:  
\[f_{S,I}(\theta_{T},\phi_{T})=\frac{1}{4\pi}|g_{S,I}(\theta_{T},\phi_{T})|^{2} \sin\theta_{T}. \tag{8}\]  
The geometry structure of the MPM represents the statistical locations of the scattering elements. Thus, the intersection of the radiated path with individual semi-ellipses indicates the scattering places of this path. Knowing the AODs, \((\theta_{T},\phi_{T})\), of radiated propagation paths, we can determine for each of them the radial coordinate \(r_{T}\) in a spherical system with an origin in the Tx (UE-S or UE-I).