# Radio Channel Capacity with Directivity Control of Antenna Beams in Multipath Propagation Environment

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## Abstract

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## 1. Introduction

## 2. Related Works

## 3. Capacity and Antenna Beam Parameters

## 4. Multi-Elliptical Propagation Model and Power Angular Spectrum Estimation

## 5. Antenna Orientation and Received Power for LOS/NLOS Conditions

#### 5.1. Assumptions for Simulation Studies

- carrier frequency is equal to ${f}_{c}=28\text{}\mathrm{GHz};$
- PDPs are based on tapped-delay line (TDL) models from the 3GPP TR 38.901 standard [15], i.e., the TDL-B and TDL-D for NLOS and LOS conditions, respectively; these TDLs are adopted for analyzed ${f}_{c}$ and rms delay spread, ${\sigma}_{\tau},$ for so-called the normal-delay profile and urban macro (UMa) scenario, i.e., ${\sigma}_{\tau}=266\text{}\mathrm{ns};$
- Rician factor defining the direct path component in the scenario for LOS conditions is appropriate for TDL-D [15], i.e., $\kappa =13.3\text{}\mathrm{dB};$
- intensity coefficients of the local scattering components, i.e., the 2D von Mises distribution parameters, are equal to ${\gamma}_{\theta}={\gamma}_{\phi}=60;$
- distance between the TX and RX is equal to $D=50\text{}\mathrm{m};$
- beam power patterns consider only the main lobe of the antenna systems. These patterns are modeled by a Gaussian model [43] for the appropriate beam parameters, i.e., HPBWs and gain.
- gains of the transmitting and receiving antennas are calculated based on the following formula [45,46]:$${G}_{T,R}=\frac{41253\eta}{HPB{W}_{T\theta ,R\theta}HPB{W}_{T\phi ,T\phi}},$$
- Low heights of the transmitting (7 m) and receiving (1.5 m) antennas are based on measurement scenarios [14];
- analyzed ranges of beam directions are as follows: $90\xb0\le \alpha \le 270\xb0$ and $-90\xb0\le \beta \le 90\xb0;$
- steps of changing the antenna directions in simulation studies are $\Delta \alpha =\Delta \beta =1\xb0;$
- to obtain average statistical results in the MPM, $L=10$ paths are generated at the TX for each time-cluster (semi-ellipsoid). On the other hand, $M=360$ Monte-Carlo simulations were run for each analyzed scenario; in this case, the average resolution of generating the AODs is about $0.1\xb0.$

#### 5.2. LOS Conditions

#### 5.3. NLOS Conditions

## 6. Antenna Orientation and Radio Channel Capacity

## 7. Conclusions

- a dozen or so times increase in the radio channel capacity compared to the omnidirectional antenna;
- the direction selection of the maximum received signal level increase by about 2 bit/s/Hz the channel capacity regardless of the TX–RX distance;
- the control system for selecting the reception direction of the maximum signal level increases the capacity of the link, and its efficiency increases with increasing distance.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

2D | two dimensional |

3D | three dimensional |

3GPP | 3rd Generation Partnership Project |

5G | fifth-generation |

AOA | angle of arrival |

AOD | angle of departure |

AWGN | additive white Gaussian noise |

CI | close-in free-space reference distance (path loss model) |

HPBW | half-power beamwidth |

LOS | line-of-sight |

METIS | Mobile and wireless communications Enablers for the Twenty-twenty Information Society |

MIMO | multiple-input-multiple-output |

MiWEBA | Millimetre-Wave Evolution for Back-haul and Access |

MPM | multi-elliptical propagation model |

NLOS | non-line-of-sight |

PAS | power angular spectrum |

probability density function | |

PDP | power delay profile |

PL | path loss |

PLE | path loss exponent |

RX | receiver |

SNR | signal-to-noise ratio |

TDL | tapped-delay line |

TR | technical report |

TX | transmitter |

UMa | urban macro |

## References

- Akpakwu, G.A.; Silva, B.J.; Hancke, G.P.; Abu-Mahfouz, A.M. A survey on 5G networks for the Internet of Things: Communication technologies and challenges. IEEE Access
**2018**, 6, 3619–3647. [Google Scholar] [CrossRef] - Agiwal, M.; Roy, A.; Saxena, N. Next generation 5G wireless networks: A comprehensive survey. IEEE Commun. Surv. Tutor.
**2016**, 18, 1617–1655. [Google Scholar] [CrossRef] - ITU. Recommendation ITU-R M.2083-0. IMT Vision—Framework and Overall Objectives of the Future Development of IMT for 2020 and Beyond; M Series Mobile, Radiodetermination, Amateur and Related Satellite Services; International Telecommunication Union (ITU): Geneva, Switzerland, 2015. [Google Scholar]
- Panwar, N.; Sharma, S.; Singh, A.K. A survey on 5G: The next generation of mobile communication. Phys. Commun.
**2016**, 18, 64–84. [Google Scholar] [CrossRef] [Green Version] - Busari, S.A.; Huq, K.M.S.; Mumtaz, S.; Dai, L.; Rodriguez, J. Millimeter-wave massive MIMO communication for future wireless systems: A survey. IEEE Commun. Surv. Tutor.
**2018**, 20, 836–869. [Google Scholar] [CrossRef] - Vannithamby, R.; Talwar, S. (Eds.) Towards 5G: Applications, Requirements and Candidate Technologies; Wiley: Chichester, UK, 2017; ISBN 978-1-118-97983-9. [Google Scholar]
- Marzetta, T.L.; Larsson, E.G.; Yang, H.; Ngo, H.Q. The massive MIMO propagation channel. In Fundamentals of Massive MIMO; Cambridge University Press: Cambridge, UK; New York, NY, USA, 2016; pp. 139–156. ISBN 978-1-107-17557-0. [Google Scholar]
- Muirhead, D.; Imran, M.A.; Arshad, K. A survey of the challenges, opportunities and use of multiple antennas in current and future 5G small cell base stations. IEEE Access
**2016**, 4, 2952–2964. [Google Scholar] [CrossRef] - Kutty, S.; Sen, D. Beamforming for millimeter wave communications: An inclusive survey. IEEE Commun. Surv. Tutor.
**2016**, 18, 949–973. [Google Scholar] [CrossRef] - Ziółkowski, C.; Kelner, J.M. Statistical evaluation of the azimuth and elevation angles seen at the output of the receiving antenna. IEEE Trans. Antennas Propag.
**2018**, 66, 2165–2169. [Google Scholar] [CrossRef] - Kelner, J.M.; Ziółkowski, C. Multi-Elliptical Geometry of Scatterers in Modeling Propagation Effect at Receiver. In Antennas and Wave Propagation; Pinho, P., Ed.; IntechOpen: London, UK, 2018; pp. 115–141. ISBN 978-953-51-6014-4. [Google Scholar]
- Kelner, J.M.; Ziółkowski, C. Path Loss Model Modification for Various Gains and Directions of Antennas. In Proceedings of the 2018 12th European Conference on Antennas and Propagation (EuCAP), London, UK, 9–13 April 2018. [Google Scholar]
- Kelner, J.M.; Ziółkowski, C. Evaluation of angle spread and power balance for design of radio links with directional antennas in multipath environment. Phys. Commun.
**2019**, 32, 242–251. [Google Scholar] [CrossRef] - Rappaport, T.S.; MacCartney, G.R.; Samimi, M.K.; Sun, S. Wideband millimeter-wave propagation measurements and channel models for future wireless communication system design. IEEE Trans. Commun.
**2015**, 63, 3029–3056. [Google Scholar] [CrossRef] - 3GPP 5G. Study on Channel Model for Frequencies from 0.5 to 100 GHz (3GPP TR 38.901 Version 16.0.0 Release 16); 3rd Generation Partnership Project (3GPP), Technical Specification Group Radio Access Network: Valbonne, France. 2019. Available online: https://www.academia.edu/39972623/3_rd_Generation_Partnership_Project_Technical_Specification_Group_Radio_Access_Network_Study_on_channel_model_for_frequencies_from_0_5_to_100_GHz_Release_14 (accessed on 2 December 2021).
- Shannon, C.E. A Mathematical theory of communication. Part I and II. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] [Green Version] - Shannon, C.E. A Mathematical theory of communication. Part III and IV. Bell Syst. Tech. J.
**1948**, 27, 623–656. [Google Scholar] [CrossRef] - Shin, H. Capacity and Error Exponents for Multiple-Input Multiple-Output Wireless Channels. Ph.D. Thesis, Seoul National University, Seoul, Korea, 2004. [Google Scholar]
- Kim, Y.; Kwon, S. Capacity Analysis of opportunistic scheduling in Nakagami-m fading environments. IEEE Trans. Veh. Technol.
**2015**, 64, 5379–5384. [Google Scholar] [CrossRef] - Singh, R.; Soni, S.K.; Raw, R.S.; Kumar, S. A new approximate closed-form distribution and performance analysis of a composite Weibull/log-normal fading channel. Wirel. Pers. Commun.
**2017**, 92, 883–900. [Google Scholar] [CrossRef] - Zhou, J.; Yao, Y.; Shao, G.; Kikuchi, H. Doppler shift and capacity analysis of MIMO antenna arrays in a novel 3D geometric channel model. Wirel. Pers. Commun.
**2017**, 96, 1–22. [Google Scholar] [CrossRef] - Khalid, S.; Abbas, W.B.; Kim, H.S.; Niaz, M.T. Evolutionary algorithm based capacity maximization of 5G/B5G hybrid pre-coding systems. Sensors
**2020**, 20, 5338. [Google Scholar] [CrossRef] [PubMed] - Jamshed, M.A.; Ur-Rehman, M.; Frnda, J.; Althuwayb, A.A.; Nauman, A.; Cengiz, K. Dual band and dual diversity four-element MIMO dipole for 5G handsets. Sensors
**2021**, 21, 767. [Google Scholar] [CrossRef] - Kilzi, A.; Farah, J.; Nour, C.A.; Douillard, C. Mutual successive interference cancellation strategies in NOMA for enhancing the spectral efficiency of CoMP systems. IEEE Trans. Commun.
**2020**, 68, 1213–1226. [Google Scholar] [CrossRef] - Jiang, H.; Tang, D.; Zhou, J.; Xi, X.; Feng, J.; Dang, J.; Wu, L. Approximation algorithm based channel estimation for massive MIMO antenna array systems. IEEE Access
**2019**, 7, 149364–149372. [Google Scholar] [CrossRef] - Arshad, J.; Rehman, A.; Rehman, A.U.; Ullah, R.; Hwang, S.O. Spectral efficiency augmentation in uplink massive MIMO systems by increasing transmit power and uniform linear array gain. Sensors
**2020**, 20, 4982. [Google Scholar] [CrossRef] - Ahamed, M.M.; Faruque, S. 5G network coverage planning and analysis of the deployment challenges. Sensors
**2021**, 21, 6608. [Google Scholar] [CrossRef] - Gupta, A.; Jha, R.K. A survey of 5G network: Architecture and emerging technologies. IEEE Access
**2015**, 3, 1206–1232. [Google Scholar] [CrossRef] - Adedoyin, M.A.; Falowo, O.E. Combination of ultra-dense networks and other 5G enabling technologies: A survey. IEEE Access
**2020**, 8, 22893–22932. [Google Scholar] [CrossRef] - Hemadeh, I.A.; Satyanarayana, K.; El-Hajjar, M.; Hanzo, L. Millimeter-wave communications: Physical channel models, design considerations, antenna constructions, and link-budget. IEEE Commun. Surv. Tutor.
**2018**, 20, 870–913. [Google Scholar] [CrossRef] [Green Version] - Lee, J.; Kim, M.-D.; Park, J.-J.; Chong, Y.J. Field-measurement-based received power analysis for directional beamforming millimeter-wave systems: Effects of beamwidth and beam misalignment. ETRI J.
**2018**, 40, 26–38. [Google Scholar] [CrossRef] [Green Version] - Pradhan, C.; Li, A.; Zhuo, L.; Li, Y.; Vucetic, B. Beam misalignment aware hybrid transceiver design in mmWave MIMO systems. IEEE Trans. Veh. Technol.
**2019**, 68, 10306–10310. [Google Scholar] [CrossRef] - Ahmadi Almasi, M.; Vaezi, M.; Mehrpouyan, H. Impact of beam misalignment on hybrid beamforming NOMA for mmWave communications. IEEE Trans. Commun.
**2019**, 67, 4505–4518. [Google Scholar] [CrossRef] [Green Version] - Friis, H.T. A Note on a simple transmission formula. Proc. IRE
**1946**, 34, 254–256. [Google Scholar] [CrossRef] - Actual, D.M. MiWEBA WP5: Propagation Antennas and Multi-Antenna Technique; D5.1: Channel Modeling and Characterization; Berlin, Germany, 2014; p. 96. [Google Scholar]
- Nurmela, V.; Karttunen, A.; Roivainen, A.; Raschkowski, L.; Hovinen, V.; EB, J.Y.; Omaki, N.; Kusume, K.; Hekkala, A.; Weiler, R. Deliverable D1. 4 METIS channel models. Proc. Mob. Wirel. Commun. Enablers Inf. Soc.
**2015**, 1, 223. [Google Scholar] - Parsons, J.D.; Bajwa, A.S. Wideband characterisation of fading mobile radio channels. IEE Proc. F Commun. Radar Signal Process.
**1982**, 129, 95–101. [Google Scholar] [CrossRef] - Oestges, C.; Erceg, V.; Paulraj, A.J. A physical scattering model for MIMO macrocellular broadband wireless channels. IEEE J. Sel. Areas Commun.
**2003**, 21, 721–729. [Google Scholar] [CrossRef] [Green Version] - Ziółkowski, C.; Kelner, J.M. Antenna pattern in three-dimensional modelling of the arrival angle in simulation studies of wireless channels. IET Microw. Antennas Propag.
**2017**, 11, 898–906. [Google Scholar] [CrossRef] - Ziółkowski, C.; Kelner, J.M. Estimation of the reception angle distribution based on the power delay spectrum or profile. Int. J. Antennas Propag.
**2015**, 2015, e936406. [Google Scholar] [CrossRef] [Green Version] - Kelner, J.M.; Ziółkowski, C.; Wojtuń, J.; Chandra, A.; Prokeš, A.; Mikulasek, T.; Blumenstein, J. Angular Power Distribution in 60 GHz Wireless Uplink for Vehicle-to-Infrastructure Scenarios. In Proceedings of the 2021 IEEE 32nd Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC), Helsinki, Finland, 13–16 September 2021; IEEE: Piscataway, NJ, USA, 2021; pp. 899–904. [Google Scholar]
- Prokeš, A.; Blumenstein, J.; Vychodil, J.; Mikulasek, T.; Marsalek, R.; Zöchmann, E.; Groll, H.; Mecklenbräuker, C.F.; Zemen, T.; Chandra, A.; et al. Multipath Propagation Analysis for Vehicle-to-Infrastructure Communication at 60 GHz. In Proceedings of the 2019 IEEE Vehicular Networking Conference (VNC), Los Angeles, CA, USA, 4–6 December 2019; IEEE: Piscataway, NJ, USA, 2019; pp. 1–8. [Google Scholar]
- Vaughan, R.; Bach Andersen, J. Channels, Propagation and Antennas for Mobile Communications; IET Electromagnetic Waves Series; Institution of Engineering and Technology: London, UK, 2003; ISBN 978-0-86341-254-7. [Google Scholar]
- Sulyman, A.I.; Alwarafy, A.; MacCartney, G.R.; Rappaport, T.S.; Alsanie, A. Directional radio propagation path loss models for millimeter-wave wireless networks in the 28-, 60-, and 73-GHz bands. IEEE Trans. Wirel. Commun.
**2016**, 15, 6939–6947. [Google Scholar] [CrossRef] - Balanis, C.A. Antenna Theory: Analysis and Design, 4th ed.; Wiley: Chichester, UK, 2016; ISBN 978-1-118-64206-1. [Google Scholar]
- Samimi, M.K.; Rappaport, T.S. 3-D millimeter-wave statistical channel model for 5G wireless system design. IEEE Trans. Microw. Theory Tech.
**2016**, 64, 2207–2225. [Google Scholar] [CrossRef] - Bechta, K.; Ziółkowski, C.; Kelner, J.M.; Nowosielski, L. Modeling of downlink interference in massive MIMO 5G macro-cell. Sensors
**2021**, 21, 597. [Google Scholar] [CrossRef] [PubMed] - 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. [Google Scholar] [CrossRef] [PubMed]

**Figure 2.**Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams under LOS conditions (3D graph).

**Figure 3.**Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams under LOS conditions (2D graph).

**Figure 4.**Received signal power losses due to mismatch of transmitting beam direction under LOS conditions.

**Figure 6.**Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams under NLOS conditions (3D graph).

**Figure 7.**Relative power factor K(α,β) versus α and β directions of transmitting and receiving beams under NLOS conditions (2D graph).

**Figure 10.**Capacity versus SNR for omnidirectional antenna pattern and different propagation conditions.

**Figure 14.**Channel capacity versus TX–RX distance for straight and optimal directions of antenna beams under NLOS conditions.

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**MDPI and ACS Style**

Ziółkowski, C.; Kelner, J.M.; Krygier, J.; Chandra, A.; Prokeš, A.
Radio Channel Capacity with Directivity Control of Antenna Beams in Multipath Propagation Environment. *Sensors* **2021**, *21*, 8296.
https://doi.org/10.3390/s21248296

**AMA Style**

Ziółkowski C, Kelner JM, Krygier J, Chandra A, Prokeš A.
Radio Channel Capacity with Directivity Control of Antenna Beams in Multipath Propagation Environment. *Sensors*. 2021; 21(24):8296.
https://doi.org/10.3390/s21248296

**Chicago/Turabian Style**

Ziółkowski, Cezary, Jan M. Kelner, Jarosław Krygier, Aniruddha Chandra, and Aleš Prokeš.
2021. "Radio Channel Capacity with Directivity Control of Antenna Beams in Multipath Propagation Environment" *Sensors* 21, no. 24: 8296.
https://doi.org/10.3390/s21248296