# Fractional Frequency Reuse Optimal SINR Threshold Selection Using NIR and ISODATA

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Cellular Network Model

#### 2.2. FFR Network Layout

#### 2.3. SINR

#### 2.4. Throughput

#### 2.5. Jain’s Index of Fairness

#### 2.6. Proportionally Fair (PF) Scheduling

#### 2.7. Native Integral Ratio (NIR) Method

#### 2.8. The Iterative Self-Organizing Data Analysis (ISODATA) Method

#### 2.9. ISODATA Algorithm

- ▪
- Select an initial threshold value, ${T}_{o}$, for instance, half of the maximum dynamic range.
- ▪
- Loop
- ▪
- Divide the histogram into two such that one segment corresponds to the foreground and the other to the background.
- ▪
- Calculate the sample mean of gray values of foreground and background pixels (${h}_{f}$ and ${h}_{m}$).
- ▪
- Determine a new threshold value, ${T}_{1}$; this is the average of these two samples’ means.
- ▪
- Re-segment the histogram again into two.

- ▪
- Check if any mean value has changed. If so, go to loop or else terminate.

## 3. Methodology

#### System Algorithm

## 4. Results

#### 4.1. UE Wideband SINR Distributions

#### 4.2. Empirical Cumulative Distributed Function (ECDF) Curves

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

AMC | Adaptive Modulation and Coding |

BS | Base Station |

ECDF | Empirical Cumulative Distribution Function |

CQI | Channel Quality Indicators |

FFR | Fractional Frequency Reuse |

FR | Full Reuse |

ISODATA | Iterative Self-Organizing Data Analysis |

LTE | Long-Term Evolution |

LTE-A | Long-Term Evolution—Advanced |

MCL | Maximum-Coupling Loss |

MIMO | Multiple Input Multiple Output |

MS | Mobile Station |

NIR | Native Integral Ratio |

OFDMA | Orthogonal Frequency Division Multiple Access |

PF | Proportionally Fair |

PMI | Precoding Matrix Indicator |

PR | Partial Re-use |

RI | Rank Indicator |

RR | Round Robin |

SINR | Signal-to-Interference-plus-Noise-Ratio |

TTI | Transmission Time Interval |

TU | Typical Urban |

UE | User Equipment |

## References

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Parameter | Value |
---|---|

UE speed | 5 Km/h |

Number of cells | 21 |

UEs per cell | 10, 20, 30, 40, 50 |

Antenna pattern | TS 36.942 |

Transmit power | 40 W |

Feedback | AMC: CQI, MIMO: RI & PMI |

Shadow fading | None |

Minimum-coupling loss | 70 dB |

Noise spectral density | −174 dBm/Hz |

Simulation length | 50 sub frames (TTIs) |

Receiver model | Zero forcing |

Inter-eNodeB distance | 500 |

Transmission bandwidth | 20 MHz (100 resource blocks) |

Antennas (NTX × NRX) | 4 × 2 |

Channel model | TU |

Pathloss model | TS 36.942—Urban area, 70 dB MCL |

Scheduling algorithm | Proportional fair |

1. INITIATE |

2. AFTER EVERY 50 TTIs DO |

3. $\mathrm{FORMULATE}\text{}\mathrm{histogram}\text{}\mathrm{of}\text{}\mathrm{SIN}\mathrm{R}\text{}\mathrm{distribution},\text{}{H}_{\gamma}$ for UEs |

4. IMPLEMENT NIR method to determine threshold, T |

5. $\mathrm{T}=\mathrm{nirthresh}\text{}({H}_{\gamma}$); #Note: T = isothresh for the case of ISODATA |

6. $\mathrm{SCALE}\text{}\mathrm{T}\text{}\mathrm{to}\text{}{\Gamma}_{th}$ |

7. ${\Gamma}_{th}={H}_{{\gamma}_{lower\text{}limit}}+\left({H}_{{\gamma}_{upper}}-{H}_{{\gamma}_{lower}}\right)\times \mathrm{T}$ |

8. FFR UE MAPPING |

9. PR_zone_UEs = 0 |

10. FR_zone_UEs = 0 |

11. $\mathrm{If}\text{}\mathrm{User}\text{}\mathrm{Equip}\text{}\mathrm{SIN}\mathrm{R}\text{}\ge $${\mathsf{\Gamma}}_{th}$ |

12. ALLOT User Equip to FR zone |

13. FR_zone_UEs++ |

14. else |

15. ALLOT User Equip to PR zone |

16. PR_zone_UEs++ |

17. end |

18. $\mathrm{COMPUTE}\text{}{\beta}_{FR}$ |

19. ${\beta}_{FR}=\mathrm{FR}\text{\_}\mathrm{zone}\text{\_}\mathrm{UEs}\text{}/\left(\mathrm{FR}\text{\_}\mathrm{zone}\text{\_}\mathrm{UEs}+\mathrm{PR}\text{\_}\mathrm{zone}\text{\_}\mathrm{UEs}\text{}\right)$ |

20. $\mathrm{SET}\text{}\mathrm{new}\text{}\mathrm{values}\text{}\mathrm{of}\text{}{\mathsf{\Gamma}}_{th}$$\text{}\mathrm{and}\text{}{\beta}_{FR}$ |

1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|

Number of UEs per cell | 10 | 20 | 30 | 40 | 50 |

Total number of UEs | 210 | 420 | 630 | 840 | 1050 |

$\mathrm{Optimal}\text{}{\Gamma}_{th}$ (dB) | 4.24 | 3.33 | 3.27 | 0.11 | 3.33 |

${\beta}_{FR}$ | 0.347 | 0.53 | 0.48 | 0.59 | 0.46 |

1 | 2 | 3 | 4 | 5 | |
---|---|---|---|---|---|

Number of UEs per cell | 10 | 20 | 30 | 40 | 50 |

Total number of UEs | 210 | 420 | 630 | 840 | 1050 |

$\mathrm{Optimal}\text{}{\Gamma}_{th}$ (dB) | 3.66 | 4.26 | 3.51 | 3.87 | 3.92 |

${\beta}_{FR}$ | 0.34 | 0.33 | 0.40 | 0.36 | 0.35 |

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**MDPI and ACS Style**

Kihato, P.; Musyoki, S.; Onim, A.
Fractional Frequency Reuse Optimal SINR Threshold Selection Using NIR and ISODATA. *Telecom* **2022**, *3*, 433-447.
https://doi.org/10.3390/telecom3030023

**AMA Style**

Kihato P, Musyoki S, Onim A.
Fractional Frequency Reuse Optimal SINR Threshold Selection Using NIR and ISODATA. *Telecom*. 2022; 3(3):433-447.
https://doi.org/10.3390/telecom3030023

**Chicago/Turabian Style**

Kihato, Peter, Stephen Musyoki, and Antony Onim.
2022. "Fractional Frequency Reuse Optimal SINR Threshold Selection Using NIR and ISODATA" *Telecom* 3, no. 3: 433-447.
https://doi.org/10.3390/telecom3030023