#
Radio Resource Dimensioning for Low Delay Access in Licensed OFDMA IoT Networks^{ †}

^{1}

^{2}

^{3}

^{4}

^{*}

^{†}

^{‡}

## Abstract

**:**

## 1. Introduction

## 2. IoT Network Model

^{2}. The active sensors nodes form then a spatial PPP ${\mathrm{\Phi}}_{a}$ with intensity

^{−1}K

^{−1}, T the absolute temperature in kelvins $T=290$ K and B the bandwidth. The power of the random exponential noise power is characterized by its Laplace transform as,

**Proposition**

**1**(Typical cell properties)

**.**

**Proof.**

## 3. Proposed Statistical Dimensioning Model

#### 3.1. Dimensioning Objectives in a Typical Cell

#### 3.2. Average Delay and Choice of the Network Threshold

#### 3.3. Expressions of ${m}_{N}$ and ${v}_{N}$

#### 3.3.1. Single-User Case

**Proposition**

**2**(Single-user case)

**.**

**Proof.**

#### 3.3.2. Multiuser Case

**Proposition**

**3**(Multiuser case)

**.**

**Proof.**

#### 3.4. Distribution of the Sensor Power Consumption

**Proposition**

**4**(Total sensor power PMF)

**.**

**Proof.**

## 4. Dimensioning Tools: Interference and Fading Characterization

#### 4.1. Single-User: Case of Single Antenna Receiver

#### 4.1.1. Interference Laplace Transform

#### 4.1.2. Average Fading Distribution

**Proposition**

**5**(SISO case)

**.**

**Proof.**

#### 4.2. Single-User Case with Multiantenna Receiver

#### 4.2.1. Antenna Selection

**Proposition**

**6**(Antenna selection)

**.**

#### 4.2.2. Maximum Ratio Combiner (MRC)

**Proposition**

**7**(MRC decoder)

**.**

**Proof.**

#### 4.3. Multiuser with Multiantenna Receiver

**Proposition**

**8**(MU case with ZF-MRC decoder)

**.**

**Proof.**

## 5. Numerical Results

^{2}transmitting on average once each half-an-hour, ${n}_{a}=48$ during 20 seconds. The active node density is then ${\lambda}_{a}=5.5$ sensors per km

^{2}. We consider a cellular network with ranges between 500 m to $1.5$ km corresponding to a collector density of ${\lambda}_{b}=0.9$ nodes per km

^{2}down to $0.1$ nodes per km

^{2}(the ranges are obtained with a confidence margin of 95%). The maximal power is limited to 14 dBm and is uniformly distributed among the allocated RRs. Table 2 gives the matching between the SINR range with the required number of RRs to achieve a target rate of ${C}_{0}=500$ bps. This data are derived from the Link Layer Simulation (LLS) provided in [26] on the Physical Uplink Shared Channel (PUSCH) of LTE-Cat M. To evaluate network performances, we consider a path-loss in an urban/suburban environment with $\alpha ={10}^{-14.1}$ and $\beta =3.5$. We consider the following antenna configurations: SISO, single SIMO with ${n}_{r}=8$, multiuser SIMO with ${n}_{r}=8$ and ${n}_{u}=2$ or ${n}_{u}=4$.

#### 5.1. Accuracy of the Theoretical Model

^{2}) and different antenna configurations as well as transmission modes. As presented in the Table 3, the comparison shows that the difference between the results obtained by our statistical tools and the simulated values is very small, which verifies the accuracy of our model and approach.

#### 5.2. Average and Total Number of RR

#### 5.3. Empirical Distribution and Actual Average Delay

#### 5.4. Tolerated Delay and Overdimensioning

#### 5.5. Individual Sensor off Probability

#### 5.6. Power Distribution

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

OFDMA | Orthogonal Frequency Division Multiple Access |

IoT | Internet of Things |

PPP | Poisson Point Process |

RR | Radio Resource |

SISO | Single Input Single Output |

SIMO | Single Input Multiple Output |

MRC | Maximum Ratio Combiner |

MU-MIMO | Multiuser Multiple Input Multiple Output |

ZF | Zero-Forcing |

LPWA | Low Power Wide Area |

LTE | Long Term Evolution |

5G | Fifth Generation |

3GPP | 3rd Generation Partnership Project |

4G | Fourth Generation |

TTI | Time Transmission Interval |

CSI | Channel State Information |

SINR | Signal to Interference plus Noise Ratio |

NPUSCH | Narrowband Physical Uplink Shared Channel |

RB | Resource Block |

RRB | Radio Resource Block |

MCS | Modulation and Coding |

PMF | Probability Mass Function |

PGFL | Probability Generating Functional |

LLS | Link Layer Simulation |

PUSCH | Physical Uplink Shared Channel |

CDF | Cumulative Distribution Function |

## Appendix A. Proof of Proposition 1

## Appendix B. Proof of Proposition 2

## Appendix C. Proof of Proposition 3

## Appendix D. Proof of Proposition 5

## Appendix E. Proof of Proposition 7

#### Appendix E.1. Laplace Transform of the Interference with MRC

#### Appendix E.2. Fading Distribution

**Lemma**

**A1.**

**Proof.**

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**Figure 3.**Illustration of the scheduling with ${n}_{u}=4$. The number of RR is adjusted with respect to the furthest node in each group, to say i, situated at distance ${r}_{i}$ corresponding to the radius of the ball containing $i{n}_{u}-1$ nodes.Distance based multiuser scheduling scheme

**Figure 5.**Mean number of required Radio Resources (RRs) in a typical cell considering ${\lambda}_{b}$ ranges from $0.3$ to $0.9$ nodes/${\mathrm{km}}^{2}$ with ${\lambda}_{a}=5.5$ nodes/${\mathrm{km}}^{2}$, ${\tau}_{max}=1$ ms.

**Figure 6.**Total number of required RRs in a typical cell versus the collector intensity ${\lambda}_{b}$ with ${\lambda}_{a}=5.5$ nodes/${\mathrm{km}}^{2}$, ${\tau}_{max}=1$ ms.

**Figure 7.**The empirical Cumulative Distribution Function (CDF) of ${N}_{t}$ total number of RRs required for the typical cell in which the maximal delay ${\tau}_{max}=1$ ms, ${\lambda}_{a}=5.5$ nodes/${\mathrm{km}}^{2}$ and ${\lambda}_{b}=0.5$ nodes/${\mathrm{km}}^{2}$.

**Figure 8.**Low access delay $\tau $ with statistical dimensioning in which the maximal delay ${\tau}_{max}=1$ ms, ${\lambda}_{a}=5.5$ nodes/${\mathrm{km}}^{2}$ and ${\lambda}_{b}=0.5$ nodes/${\mathrm{km}}^{2}$.

**Figure 9.**Comparison between theoretical and empirical ${N}_{t}$ values in which ${\lambda}_{a}=5.5$ nodes/${\mathrm{km}}^{2}$ and ${\lambda}_{b}=0.5$ nodes/${\mathrm{km}}^{2}$.

**Figure 10.**Total number of required RRs in a typical cell with respect to maximal access delay ${\tau}_{max}$ with ${\lambda}_{a}=5.5$ nodes/${\mathrm{km}}^{2}$ and ${\lambda}_{b}=0.5$ nodes/${\mathrm{km}}^{2}$.

Parameters | Value |
---|---|

Intensity of active nodes | ${\lambda}_{a}=5.5$ nodes per km^{2} |

Intensity of collectors | ${\lambda}_{b}=0.1$ to $0.9$ nodes per km^{2} |

Transmission power | ${P}_{\mathrm{RR}}=6.3$ dBm |

RR per node | 1 to 6 RRs |

Configuration | SISO, single-user $1\times 8$ SIMO, |

$1\times 8$ MU-MIMO with ${n}_{u}=2$ or 4 | |

Okumura-Hata model | $\alpha ={10}^{-14.1}$, $\beta =3.5$ |

Target data rate | ≥500 bps |

RR Per Node | SINR Range (dB) |
---|---|

1 | [–20.6; $+\infty $] |

2 | [–22.6; –20.6] |

3 | [–23.6; –22.6] |

4 | [–23.7; –23.6] |

5 | [–23.9; –23.7] |

6 | [–25.1; –23.9] |

**Table 3.**The percentage change $\Delta {m}_{N}/{m}_{N,s}$ of the theoretical values ${m}_{N}$ and the empirical values ${m}_{N,s}$.

${\mathit{\lambda}}_{\mathit{b}}$ | SISO | $1\times 8$ SIMO | $1\times 8$ SIMO | $1\times 8$ MU-MIMO | $1\times 8$ MU-MIMO |
---|---|---|---|---|---|

Selection | MRC | ${\mathit{n}}_{\mathit{u}}=2$ | ${\mathit{n}}_{\mathit{u}}=4$ | ||

0.1 | 0.0012 | 0.0120 | 0.0417 | 0.0157 | 0.0392 |

0.3 | 0.0395 | 0.0435 | 0.0239 | 0.0144 | 0.0050 |

0.5 | 0.0201 | 0.0041 | 0.0398 | 0.0208 | 0.0916 |

0.7 | 0.0006 | 0.0080 | 0.0070 | 0.0206 | 0.2001 |

0.9 | 0.0206 | 0.0593 | 0.0292 | 0.0757 | 0.2811 |

**Table 4.**Statistical individual OFF probability with regard to antenna configuration, transmission mode and collector intensity ${\lambda}_{b}$.

${\mathit{\lambda}}_{\mathit{b}}$ | SISO | $1\times 8$ SIMO | $1\times 8$ SIMO | $1\times 8$ MU-MIMO | $1\times 8$ MU-MIMO |
---|---|---|---|---|---|

Selection | MRC | ${\mathit{n}}_{\mathit{u}}=2$ | ${\mathit{n}}_{\mathit{u}}=4$ | ||

0.1 | 23.40% | 5.62% | 1.01% | 1.40% | 2.90% |

0.3 | 7.13% | 0.31% | 0.03% | 0.07% | 0.27% |

0.5 | 3.97% | 0.09% | 0.02% | 0.05% | 0.20% |

0.7 | 2.84% | 0.07% | 0.01% | 0.05% | 0.20% |

0.9 | 2.30% | 0.06% | 0.01% | 0.04% | 0.21% |

**Table 5.**The power distribution with the different transmission modes in the typical cell, ${P}_{RR}=25/6$ mW, ${\lambda}_{a}=5.5$ nodes/${\mathrm{km}}^{2}$, ${\lambda}_{b}=0.5$ nodes/${\mathrm{km}}^{2}$.

Power | SISO | $1\times 8$ SIMO | $1\times 8$ SIMO | $1\times 8$ MU-MIMO | $1\times 8$ MU-MIMO |
---|---|---|---|---|---|

(mW) | Selection | MRC | ${\mathit{n}}_{\mathit{u}}=2$ | ${\mathit{n}}_{\mathit{u}}=4$ | |

Off | 3.97% | 0.09% | 0.02% | 0.05% | 0.20% |

${P}_{\mathrm{RR}}$ | 90.76% | 99.39% | 99.92% | 99.80% | 99.17% |

$2{P}_{\mathrm{RR}}$ | 2.81% | 0.35% | 0.04% | 0.10% | 0.40% |

$3{P}_{\mathrm{RR}}$ | 1.11% | 0.09% | 0.01% | 0.03% | 0.12% |

$4{P}_{\mathrm{RR}}$ | 0.10% | 0.01% | 0.00% | 0.00% | 0.01% |

$5{P}_{\mathrm{RR}}$ | 0.20% | 0.01% | 0.00% | 0.00% | 0.02% |

$6{P}_{\mathrm{RR}}$ | 1.06% | 0.06% | 0.01% | 0.02% | 0.09% |

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**MDPI and ACS Style**

Yu, Y.; Mroueh, L.; Martins, P.; Vivier, G.; Terré, M.
Radio Resource Dimensioning for Low Delay Access in Licensed OFDMA IoT Networks. *Sensors* **2020**, *20*, 7173.
https://doi.org/10.3390/s20247173

**AMA Style**

Yu Y, Mroueh L, Martins P, Vivier G, Terré M.
Radio Resource Dimensioning for Low Delay Access in Licensed OFDMA IoT Networks. *Sensors*. 2020; 20(24):7173.
https://doi.org/10.3390/s20247173

**Chicago/Turabian Style**

Yu, Yi, Lina Mroueh, Philippe Martins, Guillaume Vivier, and Michel Terré.
2020. "Radio Resource Dimensioning for Low Delay Access in Licensed OFDMA IoT Networks" *Sensors* 20, no. 24: 7173.
https://doi.org/10.3390/s20247173