# Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

_{m}and S

_{Fj}, respectively [22,23]. Then m

_{i}refers to the ith macrocell user, and F

_{j,i}refers to the ith user of S

_{Fj}.

_{j}located at $\left({x}_{j},{y}_{j}\right)$ and with a transmitting power of ${P}_{{F}_{j}}$, namely $FB{S}_{j}$. When macro base station user ${m}_{i}$ is located at $\left(x,y\right)$, urban space transmission formula $128+37.6\times {\mathrm{log}}_{10}(dist)$ [26] is adopted, where $dist$ means the distance between the user and base station. The SINR of the user can be calculated as follows:

_{j}to the user m

_{i}respectively, which are calculated as ${P}_{m,{m}_{i}}={P}_{m}\cdot {10}^{-\frac{128+37.6\cdot {\mathrm{log}}_{10}{\left({x}^{2}+{y}^{2}\right)}^{1/2}}{10}}$ and ${P}_{{F}_{j},{m}_{i}}={P}_{{F}_{j}}\cdot {10}^{-\frac{128+37.6\cdot {\mathrm{log}}_{10}{\left({\left(x-{x}_{j}\right)}^{2}+{\left(y-{y}_{j}\right)}^{2}\right)}^{1/2}}{10}}$. ${N}_{0}$ is the noise power.

_{i,j}, they will undergo interference from macro base station and other femtocells. Each k in $\{1,2,\dots ,N\}$, a femtocell F

_{k}located at $\left({x}_{k},{y}_{k}\right)$ and with transmitting power of ${P}_{{F}_{k}}$, namely $FB{S}_{k}$. When the femtocell user F

_{i,j}is located at$\left({x}_{f},{y}_{f}\right)$, the received signal power mentioned in the Equation (2) will adopt indoor space transmission formula $127+30\times {\mathrm{log}}_{10}(dist)$ [27]. The SINR can be calculated as follows:

_{j}to user F

_{j,i}which is calculated as ${P}_{{F}_{j},{F}_{j,i}}={P}_{{F}_{j}}\cdot {10}^{-\frac{127+30\cdot {\mathrm{log}}_{10}{\left({\left({x}_{f}-{x}_{j}\right)}^{2}+{\left({y}_{f}-{y}_{j}\right)}^{2}\right)}^{1/2}}{10}}$. Similar to the calculation of ${P}_{m,{m}_{i}}$, ${P}_{m,{F}_{j,i}}$, and ${P}_{{F}_{k},{F}_{j,i}}$ are the received signal power from m and F

_{j}to user F

_{j,i}. which are calculated as ${P}_{m,{F}_{j,i}}={P}_{m}\cdot {10}^{-\frac{128+37.6\cdot {\mathrm{log}}_{10}{\left({{x}_{f}}^{2}+{{y}_{f}}^{2}\right)}^{1/2}}{10}}$ and ${P}_{{F}_{k},{F}_{j,i}}={P}_{{F}_{k}}\cdot {10}^{-\frac{128+37.6\cdot {\mathrm{log}}_{10}{\left({\left({x}_{f}-{x}_{k}\right)}^{2}+{\left({y}_{f}-{y}_{k}\right)}^{2}\right)}^{1/2}}{10}}$.

_{j,i}served by $\alpha \cdot W$ spectrum will no longer be subject to cross-layer interference. The computation formula for SINR is calculated as follows:

## 3. Stackelberg Game Model and Problem Statement

#### 3.1. Common Algorithm

#### 3.2. Utility Functions

_{j}is the bandwidth occupied by femtocell F

_{j}. After the expansion of service area, partial macro users will be served by a femtocell using $\alpha \times W$ frequency band, and its average throughput capacity of users can be defined as follows:

_{j}can be defined as follows:

#### 3.3. Optimization Problems

#### 3.4. Intelligent Method Based on Gradient Algorithm

## 4. Simulation Results and Analyze

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 3.**Nash equilibrium strategy under different adjustment factors and the proposed algorithm in the paper.

Parameters | Macrocell | Femtocell |
---|---|---|

System bandwidth $W$ | 20 MHz | 20 MHz |

User density | 100/macro | 2–15/femto |

Cell radius | 500 m | 15 m |

Max transmit power of base stations ${P}_{m}({P}_{{F}_{j}})$ | 43 dBm | 20 dBm |

Fast fading | SCME | SCME |

Noise level ${N}_{0}$ | −174 dBm/Hz | −174 dBm/Hz |

${c}_{th}$ | 10 dB | 10 dB |

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Ye, F.; Dai, J.; Li, Y.
Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet. *Symmetry* **2017**, *9*, 34.
https://doi.org/10.3390/sym9030034

**AMA Style**

Ye F, Dai J, Li Y.
Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet. *Symmetry*. 2017; 9(3):34.
https://doi.org/10.3390/sym9030034

**Chicago/Turabian Style**

Ye, Fang, Jing Dai, and Yibing Li.
2017. "Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet" *Symmetry* 9, no. 3: 34.
https://doi.org/10.3390/sym9030034