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Inter-Beam Co-Channel Downlink and Uplink Interference for 5G New Radio in mm-Wave Bands^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Multi-Ellipsoidal Propagation Model

_{xn}, and minor semi-axes b

_{yn}, c

_{zn}describe the following relationships:

## 3. Evaluation of Co-Channel Interference in Multi-Beam Antenna

- normalized power patterns ${\left|{g}_{S}\left({\theta}_{T},{\varphi}_{T}\right)\right|}^{2}$, ${\left|{g}_{I}\left({\theta}_{T},{\varphi}_{T}\right)\right|}^{2}$, and ${\left|g\left(\theta ,\varphi \right)\right|}^{2}$, of the serving and interfering transmitting and receiving beams, respectively, where $\left({\theta}_{T},{\varphi}_{T}\right)$ 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 ${\tilde{p}}_{S,I}\left(\theta ,\varphi \right)$ 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, $\left({\theta}_{T},{\varphi}_{T}\right),$ uses the properties of the normalized power radiation patterns [36]:$$\frac{1}{4\pi}{\displaystyle \underset{\left({\theta}_{T},{\varphi}_{T}\right)}{{\displaystyle \iint}}{\left|{g}_{S,I}\left({\theta}_{T},{\varphi}_{T}\right)\right|}^{2}\mathrm{sin}{\theta}_{T}d{\theta}_{T}d{\varphi}_{T}=1.}$$

- 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.

## 4. Assumptions and Scenarios of Simulation Studies

## 5. Simulation Results

#### 5.1. DL Scenario

#### 5.2. UL Scenario

#### 5.3. Exemplary Comparison of MPM with 3GPP Approach for DL Scenario

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

3D | three-dimensional |

3GPP | 3rd Generation Partnership Project |

5G | fifth-generation |

AOA | angle of arrival |

AOD | angle of departure |

CDF | cumulative distribution function |

DL | downlink |

GBM | geometry-based model |

gNodeB | 5G base station |

ITU | International Telecommunication Union |

LOS | line-of-sight |

MIMO | multiple-input-multiple-output |

mmWave | millimeter-wave |

MPM | multi-ellipsoidal propagation model |

NLOS | non-line-of-sight |

NR | New Radio |

PAS | power angular spectrum |

PDP | power delay profile |

Rx | receiver |

SIR | signal-to-interference ratio |

TDL | tapped delay line |

Tx | transmitter |

UE | user equipment |

UE-I | interfering UE |

UE-S | serving UE |

UMa | urban macro |

UL | uplink |

## Symbols

$\left(\theta ,\varphi \right)$ | AOA of individual propagation path |

$\left({\theta}_{T},{\varphi}_{T}\right)$ | AOD of individual propagation path |

${\left|g\left(\theta ,\varphi \right)\right|}^{2}$ | normalized power pattern of receiving antenna |

${\left|{g}_{I}\left({\theta}_{T},{\varphi}_{T}\right)\right|}^{2}$ | normalized power pattern of interfering transmitting antenna |

${\left|{g}_{S}\left({\theta}_{T},{\varphi}_{T}\right)\right|}^{2}$ | normalized power pattern of serving transmitting antenna |

${\alpha}_{R}$ | direction of receiving beam |

${\alpha}_{RI}$ | direction of interfering receiving beam |

${\alpha}_{RS}$ | direction of serving receiving beam |

${\alpha}_{T}$ | direction of transmitting beam |

${\alpha}_{TI}$ | direction of interfering transmitting beam |

${\alpha}_{TS}$ | 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 |

${\gamma}_{\varphi}$ | angular dispersion of local scattering components in azimuth plane |

$\theta $ | elevation AOA of individual propagation path |

${\theta}_{T}$ | elevation AOD of individual propagation path |

${\Phi}_{0}$ | direction of receiving (gNodeB) beam in relation to direction of cell sector center in UL scenario |

${\Phi}_{I}$ | direction of interfering transmitting (gNodeB) beam in relation to direction of cell sector center in DL scenario |

${\Phi}_{S}$ | direction of serving transmitting (gNodeB)beam in relation to direction of cell sector center in DL scenario |

$\varphi $ | azimuth AOA of individual propagation path |

${\varphi}_{T}$ | azimuth AOD of individual propagation path |

${\sigma}_{SIR}$ | standard deviation of SIR for confidence interval analysis |

${\overline{\sigma}}_{LOS}^{3GPP}$ | standard deviation of SIR for 3GPP model and LOS conditions |

${\overline{\sigma}}_{NLOS}^{3GPP}$ | standard deviation of SIR for 3GPP model and NLOS conditions |

${\overline{\sigma}}_{LOS/NLOS}^{Model}$ | standard deviation of SIR for Model and LOS/NLOS conditions |

${\overline{\sigma}}_{LOS}^{MPM}$ | standard deviation of SIR for MPM and LOS conditions |

${\overline{\sigma}}_{NLOS}^{MPM}$ | standard deviation of SIR for MPM and NLOS conditions |

${\tau}_{n}$ | delay of nth time-cluster in PDP/TDL |

$a$ | auxiliary variable used to compute ${r}_{T}$ |

${a}_{xn}$ | major semi-axis of nth ellipsoid along x-axis |

${b}_{yn}$ | minor semi-axis of nth ellipsoid along y-axis |

${C}_{0}$ | normalizing constant |

$c$ | lightspeed |

${c}_{zn}$ | minor semi-axis of nth 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 |

$F\left(SIR\right)$ | CDF of SIR |

$f\left(\tilde{p}\right)$ | distribution of path power |

${f}_{0}\left(\theta ,\varphi \right)$ | 2D von Mises distribution describing local scattering components |

${f}_{I}\left({\theta}_{T},{\varphi}_{T}\right)$ | distribution of AOD for interfering link |

${f}_{S}\left({\theta}_{T},{\varphi}_{T}\right)$ | 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 |

${\mathrm{I}}_{0}(\cdot )$ | 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 |

$PL\left({D}_{I}\right)$ | path loss for wireless links between UE-I and gNodeB at distance ${D}_{I}$ |

$PL\left({D}_{S}\right)$ | path loss for wireless links between UE-S and gNodeB at distance ${D}_{S}$ |

$\tilde{p}$ | power of individual propagation path |

${p}_{n}$ | mean power of nth time-cluster in PDP/TDL (nth local extreme of PDP/TDL) |

${p}_{I}\left(\theta ,\varphi \right)$ | PAS seen at the output of receiving antenna for interfering link |

${p}_{S}\left(\theta ,\varphi \right)$ | PAS seen at the output of receiving antenna for serving link |

${\tilde{p}}_{I}\left(\theta ,\varphi \right)$ | PAS in vicinity of receiving antenna for interfering link |

${\tilde{p}}_{S}\left(\theta ,\varphi \right)$ | PAS in vicinity of receiving antenna for serving link |

${r}_{T}$ | radial coordinate in spherical system with origin in Tx |

$SIR$ | SIR |

$SI{R}_{\mathrm{avg}}$ | average SIR for confidence interval analysis |

$SI{R}_{\mathrm{avg}}\pm {\sigma}_{SIR}$ | confidence intervals of SIR |

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**Figure 2.**DL spatial scenario of simulation studies [32].

**Figure 5.**PASs of UE-S and UE-I in azimuth plane for ∆α = 30°, D

_{S}= D

_{I}= 100 m, under (

**a**) LOS (TDL-D) and (

**b**) NLOS (TDL-B) conditions.

**Figure 6.**SIR versus separation angle for DL scenario, selected D = {50, 100, 150} m, and LOS (TDL-D) conditions.

**Figure 7.**SIR versus separation angle for DL scenario, selected D = {50, 100, 150} m, and NLOS (TDL-B) conditions.

**Figure 8.**CDFs of SIR for DL scenario, selected D = {50, 100, 150} m, under (

**a**) LOS (TDL-D) and (

**b**) NLOS (TDL-B) conditions.

**Figure 9.**SIR versus distance for DL scenario, selected ∆α = {15°, 20°, 30°}, under (

**a**) LOS (TDL-D) and (

**b**) NLOS (TDL-B) conditions.

**Figure 10.**SIR versus separation angle for UL scenario, selected D

_{I}= {50, 100, 150} m, D

_{S}= 100 m, and LOS (TDL-D) conditions.

**Figure 11.**SIR versus separation angle for UL scenario, selected D

_{I}= {50, 100, 150} m, D

_{S}= 100 m, and NLOS (TDL-B) conditions.

**Figure 12.**CDFs of SIR for UL scenario, selected D

_{I}= {50, 100, 150} m, D

_{S}= 100 m, (

**a**) LOS (TDL-D) and (

**b**) NLOS (TDL-B) conditions.

**Figure 13.**SIR versus distance D

_{I}for UL scenario, selected ∆α = {15°, 20°, 30°}, D

_{S}= 100 m, under (

**a**) LOS (TDL-D) and (

**b**) NLOS (TDL-B) conditions.

**Figure 14.**SIR comparison between (

**a**) MPM and (

**b**) 3GPP model for DL scenario, D = 100 m, and LOS conditions.

**Figure 15.**SIR comparison between (

**a**) MPM and (

**b**) 3GPP model for DL scenario, D = 100 m, and NLOS conditions.

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## Share and Cite

**MDPI and ACS Style**

Bechta, K.; Kelner, J.M.; Ziółkowski, C.; Nowosielski, L.
Inter-Beam Co-Channel Downlink and Uplink Interference for 5G New Radio in mm-Wave Bands. *Sensors* **2021**, *21*, 793.
https://doi.org/10.3390/s21030793

**AMA Style**

Bechta K, Kelner JM, Ziółkowski C, Nowosielski L.
Inter-Beam Co-Channel Downlink and Uplink Interference for 5G New Radio in mm-Wave Bands. *Sensors*. 2021; 21(3):793.
https://doi.org/10.3390/s21030793

**Chicago/Turabian Style**

Bechta, Kamil, Jan M. Kelner, Cezary Ziółkowski, and Leszek Nowosielski.
2021. "Inter-Beam Co-Channel Downlink and Uplink Interference for 5G New Radio in mm-Wave Bands" *Sensors* 21, no. 3: 793.
https://doi.org/10.3390/s21030793