# Inter-Beam Co-Channel Downlink and Uplink Interference for 5G New Radio in mm-Wave Bands +
## Abbreviations
\begin{tabular}{l l} \(\alpha_{TS}\) & direction of serving transmitting beam \\ \(\Delta\alpha\) & separation angle between serving and interference beams \\ \(\Delta PL\) & path loss correction coefficient (relationship between attenuation of \\  & propagation environment for different distances) \\ \(\gamma_{\theta}\) & angular dispersion of local scattering components in elevation plane \\ \(\gamma_{\phi}\) & angular dispersion of local scattering components in azimuth plane \\ \(\theta\) & elevation AOA of individual propagation path \\ \(\theta_{T}\) & elevation AOD of individual propagation path \\  & direction of receiving (gNodeB) beam in relation to direction of cell sector \\ \(\Phi_{0}\) & center in UL scenario \\  & direction of interfering transmitting (gNodeB) beam in relation to direction of \\ \(\Phi_{I}\) & cell sector center in DL scenario \\  & direction of serving transmitting (gNodeB)beam in relation to direction of cell \\ \(\Phi_{S}\) & sector center in DL scenario \\ \(\phi\) & azimuth AOA of individual propagation path \\ \(\phi_{T}\) & azimuth AOD of individual propagation path \\ \(\sigma_{SIR}\) & standard deviation of SIR for confidence interval analysis \\ \(\sigma_{LOS}^{\text{SCPP}}\) & standard deviation of SIR for 3 GPP model and LOS conditions \\ \(\sigma_{NLOS}^{\text{SCPP}}\) & standard deviation of SIR for 3 GPP model and NLOS conditions \\ \(\sigma_{NLOS}^{\text{LOS}}\) & standard deviation of SIR for Model and LOS/NLOS conditions \\ \(\sigma_{NLOS}^{\text{MPM}}\) & standard deviation of SIR for MPM and LOS conditions \\ \(\sigma_{NLOS}^{\text{MPM}}\) & standard deviation of SIR for MPM and NLOS conditions \\ \(\tau_{n}\) & delay of \(n\)th time-cluster in PDP/TDL \\ \(a\) & auxiliary variable used to compute \(r_{T}\) \\ \(a_{xxn}\) & major semi-axis of \(n\)th ellipsoid along \(x\)-axis \\ \(b_{yn}\) & minor semi-axis of \(n\)th ellipsoid along \(y\)-axis \\ \(C_{0}\) & normalizing constant \\ \(c\) & lightspeed \\ \(c_{2m}\) & minor semi-axis of \(n\)th ellipsoid along \(z\)-axis \\ \(D\) & distance between Tx and Rx or between gNodeB (Rx) and UE (Tx) in DL \\ \(D_{I}\) & distance between UE-I (Tx) and gNodeB (Rx) in UL \\ \(D_{S}\) & distance between UE-S (Tx) and gNodeB (Rx) in UL \\ \(F(SIR)\) & CDF of SIR \\ \(f(\vec{p})\) & distribution of path power \\ \(f_{0}(\theta,\phi)\) & 2D von Mises distribution describing local scattering components \\ \(f_{1}(\theta_{T},\phi_{T})\) & distribution of AOD for interfering link \\ \(f_{S}(\theta_{T},\phi_{T})\) & distribution of AOD for serving link \\ \(G\) & gain of receiving beam \\ \(G_{I}\) & gain of interfering transmitting beam \\ \(G_{S}\) & gain of serving transmitting beam \\ \(\text{l}_{0}(\cdot)\) & zero-order modified Bessel function of imaginary argument \\ \(N\) & number of all time-clusters in analyzed PDP/TDL \\ \(n\) & number of analyzed time-cluster in PDP/TDL \\ \(P_{I}\) & power of interfering signal \\ \(P_{S}\) & power of serving signal \\ \(PL\) & path loss \\ \(PL(D_{I})\) & path loss for wireless links between UE-I and gNodeB at distance \(D_{I}\) \\ \(PL(D_{S})\) & path loss for wireless links between UE-S and gNodeB at distance \(D_{S}\) \\ \(\widetilde{p}\) & power of individual propagation path \\ \(p_{n}\) & mean power of \(n\)th time-cluster in PDP/TDL (\(n\)th local extreme of PDP/TDL) \\ \(p_{I}(\theta,\phi)\) & PAS seen at the output of receiving antenna for interfering link \\ \(p_{S}(\theta,\phi)\) & PAS seen at the output of receiving antenna for serving link \\ \(\widetilde{p}_{I}(\theta,\phi)\) & PAS in vicinity of receiving antenna for interfering link \\ \(\widetilde{p}_{S}(\theta,\phi)\) & PAS in vicinity of receiving antenna for serving link \\ \(r_{T}\) & radial coordinate in spherical system with origin in Tx \\ \(SIR\) & SIR \\ \(SIR_{\text{avg}}\) & average SIR for confidence interval analysis \\ \(SIR_{\text{avg}}\pm\sigma_{SIR}\) & confidence intervals of SIR \\ \end{tabular}