# Application of Radio Environment Map Reconstruction Techniques to Platoon-based Cellular V2X Communications

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## Abstract

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## 1. Introduction

- a scheme to reduce the control information exchanged for REM reconstruction in platooning based on OK is proposed. The REM reconstruction capability is evaluated via the mean square error and traded-off versus signaling overhead;
- a suitable semivariogram modeling for OK interpolation in the scenarios under consideration is proposed;
- an analysis of the optimal patterns of vehicles’ positions for reliable REM reconstruction is performed;
- expressions for the communication cost related to the REM reconstruction are derived for a centralized and a distributed architecture.

## 2. System Model

#### 2.1. Use Case and Scenario

#### 2.2. REM Reconstruction with OK

#### 2.3. Centralized vs. Distributed Architecture

#### 2.3.1. Centralized Architecture

#### 2.3.2. Distributed Architecture

## 3. Semivariogram Modeling

#### 3.1. Semivariogram Models

#### 3.2. Model Selection

## 4. Performance Evaluation

#### 4.1. Vehicle Selection

#### 4.2. REM Reconstruction Accuracy

#### 4.3. Communication Cost

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Scenarios under consideration comprising a platoon of vehicles assisted by a base station (BS). (

**a**) Asymmetric case, where the BS is aligned with the antenna of the platoon leader. (

**b**) Symmetric case, where the line connecting the BS with the platoon leader forms an angle $\varphi $ with the perpendicular line, so that the BS is aligned with the platoon middle point.

**Figure 2.**Example of the proposed reconstruction architectures in a platoon of five vehicles. (

**a**) Centralized, (

**b**) distributed. Vehicles 1, 3 and 5 access actual radio environment map (REM) values, while estimates are needed for vehicles 2 and 4.

**Figure 3.**Example of spherical, exponential and Gaussian semivariogram modeling fitting versus empirical semivariogram.

**Figure 4.**Optimal patterns of vehicles’ positions with available REM values that achieve the minimum MSE of REM reconstruction for different values of P in a platoon with $N=10$.

**Figure 5.**Path-loss and shadowing estimation results versus shadowing correlation distance in the symmetric case with $L=2$ m.

**Figure 6.**Minimum MSE of path-loss and shadowing estimation versus shadowing correlation distance in the symmetric case with $L=10$ m.

**Figure 7.**Minimum MSE of path-loss and shadowing estimation versus shadowing correlation distance in the asymmetric case with $L=2$ m.

**Figure 8.**Estimated cost versus number of vehicles for the centralized (symmetric and asymmetric) and distributed REM reconstruction schemes with $L=2$ m and $L=10$ m.

**Table 1.**Semivariogram modeling (mean square error (MSE) and Akaike information criterion (AIC)) in the symmetric case for $L=2$ and $L=10$. Minimums are highlighted in violet color.

Spherical | Exponential | Gaussian | ||||
---|---|---|---|---|---|---|

$\mathit{L}=\mathbf{2}$ | MSE | AIC | MSE | AIC | MSE | AIC |

$P=3$ | 2.59 | 5.56 | 4.15 | 6.97 | 4.09 | 6.93 |

$P=4$ | 2.43 | 4.01 | 4.22 | 6.21 | 3.93 | 5.93 |

$P=5$ | 2.08 | 1.61 | 3.64 | 4.41 | 3.31 | 3.94 |

$P=6$ | 1.47 | −2.44 | 2.94 | 1.72 | 2.59 | 0.96 |

$P=7$ | 0.90 | −8.36 | 2.23 | −2.00 | 1.95 | −2.95 |

$P=8$ | 0.54 | −15.57 | 1.76 | −6.11 | 1.43 | −7.77 |

$P=9$ | 0.31 | −24.32 | 1.46 | −10.37 | 1.14 | −12.60 |

$\mathit{L}=\mathbf{10}$ | MSE | AIC | MSE | AIC | MSE | AIC |

$P=3$ | 122.49 | 17.13 | 248.56 | 19.25 | 226.98 | 18.98 |

$P=4$ | 127.76 | 19.86 | 260.69 | 22.71 | 230.58 | 22.22 |

$P=5$ | 115.53 | 21.70 | 229.26 | 25.13 | 205.41 | 24.58 |

$P=6$ | 87.75 | 22.10 | 194.89 | 26.88 | 174.08 | 26.21 |

$P=7$ | 60.08 | 21.05 | 158.15 | 27.82 | 138.80 | 26.91 |

$P=8$ | 42.53 | 19.37 | 133.84 | 28.54 | 111.24 | 27.06 |

$P=9$ | 32.35 | 17.51 | 118.10 | 29.17 | 94.52 | 27.16 |

**Table 2.**Semivariogram modeling (MSE and AIC) in the asymmetric case for $L=2$ and $L=10$. Minimums are highlighted in violet color.

Spherical | Exponential | Gaussian | ||||
---|---|---|---|---|---|---|

$\mathit{L}=\mathbf{2}$ | MSE | AIC | MSE | AIC | MSE | AIC |

$P=3$ | 18.07 | 11.37 | 14.82 | 10.79 | 4.98 | 7.52 |

$P=4$ | 20.00 | 12.44 | 17.79 | 11.97 | 5.08 | 6.96 |

$P=5$ | 19.83 | 12.89 | 18.06 | 12.42 | 4.92 | 5.92 |

$P=6$ | 19.10 | 12.95 | 17.69 | 12.49 | 3.90 | 3.42 |

$P=7$ | 18.10 | 12.65 | 16.67 | 12.07 | 2.64 | −0.83 |

$P=8$ | 17.29 | 12.17 | 15.79 | 11.44 | 1.58 | −6.98 |

$P=9$ | 16.18 | 11.28 | 15.71 | 11.01 | 0.80 | −15.78 |

$\mathit{L}=\mathbf{10}$ | MSE | AIC | MSE | AIC | MSE | AIC |

$P=3$ | 278.89 | 19.60 | 228.51 | 19.00 | 41.83 | 13.91 |

$P=4$ | 292.43 | 23.17 | 261.93 | 22.73 | 35.65 | 14.75 |

$P=5$ | 296.11 | 26.41 | 269.92 | 25.94 | 31.15 | 15.15 |

$P=6$ | 293.34 | 29.34 | 272.68 | 28.90 | 22.70 | 13.98 |

$P=7$ | 291.02 | 32.10 | 275.34 | 31.70 | 14.57 | 11.13 |

$P=8$ | 285.06 | 34.59 | 268.62 | 34.11 | 9.38 | 7.27 |

$P=9$ | 284.00 | 37.10 | 269.47 | 36.59 | 6.37 | 2.89 |

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**MDPI and ACS Style**

Roger, S.; Botella, C.; Pérez-Solano, J.J.; Perez, J.
Application of Radio Environment Map Reconstruction Techniques to Platoon-based Cellular V2X Communications. *Sensors* **2020**, *20*, 2440.
https://doi.org/10.3390/s20092440

**AMA Style**

Roger S, Botella C, Pérez-Solano JJ, Perez J.
Application of Radio Environment Map Reconstruction Techniques to Platoon-based Cellular V2X Communications. *Sensors*. 2020; 20(9):2440.
https://doi.org/10.3390/s20092440

**Chicago/Turabian Style**

Roger, Sandra, Carmen Botella, Juan J. Pérez-Solano, and Joaquin Perez.
2020. "Application of Radio Environment Map Reconstruction Techniques to Platoon-based Cellular V2X Communications" *Sensors* 20, no. 9: 2440.
https://doi.org/10.3390/s20092440