# 3D Poisson-Based Neighborhood Capacity Analysis for Millimeter Wave Communications

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Scenario

## 3. Analysis

## 4. Results and Discussion

#### 4.1. Model Validation

#### 4.2. Impact of Cell Radius

#### 4.3. Impact of Maximum Product Gain

#### 4.4. Impact of Beam Alignment Error

#### 4.5. Impact of Modulation

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Conflicts of Interest

## Abbreviations

BS | base station |

CCDF | complementary cumulative distribution function |

CDF | cumulative distribution function |

LoS | line of sight |

mmWave | millimeter wave |

ME | Mobile Equipment |

NLoS | Non line of sight |

OUT | OUTage |

probability density function | |

PMF | probability mass function |

PPP | Poisson point process |

RV | random variable |

SNR | signal to noise ratio |

w.p. | with probability |

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**Figure 1.**Theoretical and simulated Shannon capacity under perfect beam alignment for $\rho =100$ m and $G=10$ dB as a function of the SNR: (

**a**) 28 GHz channel, (

**b**) 73 GHz channel (t: theory, s: Monte Carlo simulation).

**Figure 2.**Maximum link capacity under perfect beam alignment for $G=10$ dB and different cell radii as a function of the neighbor order: (

**a**) 28 GHz channel, (

**b**) 73 GHz channel.

**Figure 3.**Maximum link capacity under perfect beam alignment for $\rho =100$ m and different maximum product gains ${G}^{2}$ as a function of the neighbor order: (

**a**) 28 GHz channel, (

**b**) 73 GHz channel.

**Figure 4.**Theoretical Shannon capacity obtained in the presence of beam alignment error for $\rho =100$ m, $G=10$ dB, and $g=0$ dB as a function of the SNR: (

**a**) 28 GHz channel, (

**b**) 73 GHz channel.

**Figure 5.**Theoretical capacity obtained using the QPSK modulation in the absence of beam alignment error for $\rho =100$ m and $G=10$ dB as a function of the SNR: (

**a**) 28 GHz channel, (

**b**) 73 GHz channel.

**Table 1.**Adopted parameters [2].

${a}_{\mathrm{out}}$ | 33.3 mm^{−1} | ${\alpha}_{1}$ | 61.4 dB (28 GHz) | ${\beta}_{2}$ | 2.92 (28 GHz) |

${b}_{\mathrm{out}}$ | 5.2 | 69.8 dB (73 GHz) | 2.69 (73 GHz) | ||

${a}_{\mathrm{los}}$ | 14.9 mm^{−1} | ${\alpha}_{2}$ | 72.0 (28 GHz) | ${\sigma}_{1}$ | 5.8 dB (28 GHz) |

${P}_{\mathrm{S}}$ | 0.1 W | 82.7 (73 GHz) | 5.8 dB (73 GHz) | ||

W | 1 GHz | ${\beta}_{1}$ | 2 (28 GHz) | ${\sigma}_{2}$ | 8.7 dB (28 GHz) |

$\mathcal{F}$ | 10 dB | 2 (73 GHz) | 7.7 dB (73 GHz) |

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## Share and Cite

**MDPI and ACS Style**

Comisso, M.; Buttazzoni, G.; Pastore, S.; Vatta, F.; Babich, F.
3D Poisson-Based Neighborhood Capacity Analysis for Millimeter Wave Communications. *Sensors* **2022**, *22*, 2098.
https://doi.org/10.3390/s22062098

**AMA Style**

Comisso M, Buttazzoni G, Pastore S, Vatta F, Babich F.
3D Poisson-Based Neighborhood Capacity Analysis for Millimeter Wave Communications. *Sensors*. 2022; 22(6):2098.
https://doi.org/10.3390/s22062098

**Chicago/Turabian Style**

Comisso, Massimiliano, Giulia Buttazzoni, Stefano Pastore, Francesca Vatta, and Fulvio Babich.
2022. "3D Poisson-Based Neighborhood Capacity Analysis for Millimeter Wave Communications" *Sensors* 22, no. 6: 2098.
https://doi.org/10.3390/s22062098