# An Improved User Association Algorithm for MAP–FAPs Heterogeneous Networks

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

## 3. Problem Formulation and Optimal Solution

#### 3.1. Single Subcarrier User Rate

#### 3.2. Approximated Problem and Problem Formulation

## 4. The Proposed Algorithm

- 1.
**Initialization**L FAPs and K users are randomly generated within the scope of MAP. Initialize ${K}_{M}={K}_{{F}_{i}}=0(i=1,\dots ,L)$, ${\mathbb{K}}_{\mathbb{M}}={\mathbb{K}}_{{\mathbb{F}}_{i}}=\varnothing (i=1,\dots ,L)$. Set that the $ith(i=1,\dots ,L)$ AP can serve a maximum of ${\lambda}_{max}^{i}$ users. To simplify, assume that each FAP has the same maximum service user number, ${\lambda}_{max}$, and to make sure that every available user will be served, MAP sets its quota ${\lambda}_{max}^{0}$ to be equal to the maximum number of UEs.- 2.
**Pre-selection****for**$k=1$ to KCalculate the $kth$ user rate ${r}_{ik}(i=0,1,\dots ,L)$ when it connects to the $ith$ AP, then the $kth$ user preselects the AP who can support the highest user rate.**end**Then ${K}_{M}$, ${K}_{{F}_{i}}(i=1,\dots ,L)$, ${\mathbb{K}}_{\mathbb{M}}$ and ${\mathbb{K}}_{{\mathbb{F}}_{i}}(i=1,\dots ,L)$ are obtained.- 3.
**Final selection****if**$i=0$${K}_{M}$=${K}_{M}$, ${\mathbb{K}}_{\mathbb{M}}$=${\mathbb{K}}_{\mathbb{M}}$**end****for**$i=1$ to LCalculate $\frac{{r}_{ik}}{{r}_{0k}}(k\in {\mathbb{K}}_{{\mathbb{F}}_{i}})$. Then sort $\frac{{r}_{ik}}{{r}_{0k}}(k\in {\mathbb{K}}_{{\mathbb{F}}_{i}})$ in an increasing manner; namely, $\frac{{r}_{i1}}{{r}_{01}}\u2a7d\frac{{r}_{i2}}{{r}_{02}}\u2a7d\cdots \u2a7d\frac{{r}_{i{K}_{{F}_{i}}}}{{r}_{0{K}_{{F}_{i}}}}$. Select the last $min({\lambda}_{max},{K}_{{F}_{i}})$ users according to the order.Accordingly, we obtain${\mathbb{K}}_{{\mathbb{F}}_{i}}=\{{K}_{{F}_{i}}-min({\lambda}_{max},{K}_{{F}_{i}})+1,\dots ,{K}_{{F}_{i}}\}$, ${\mathbb{K}}_{\mathbb{M}}={\mathbb{K}}_{\mathbb{M}}\cup \{1,\dots ,{K}_{{F}_{i}}-min({\lambda}_{max},{K}_{{F}_{i}})\}$${K}_{{F}_{i}}=min({\lambda}_{max},{K}_{{F}_{i}})$${K}_{M}={K}_{M}+{K}_{{F}_{i}}-min({\lambda}_{max},{K}_{{F}_{i}})$**end**

## 5. Simulation Results

#### 5.1. Simulation Configuration

#### 5.2. Simulation Analysis

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**Performance comparison in terms of sum-throughput with different maximum service user numbers.

**Figure 7.**Performance comparison in terms of spectrum efficiency with different maximum service user numbers.

**Figure 8.**Performance comparison in terms of sum-throughput with different maximum service user numbers.

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

MAP transmission power | 43 dBm |

FAP transmission power | 20 dBm |

Bandwidth of subcarrier | 15 KHz |

Path loss (MAP) | 15.3 + 37.6 lg(d) |

Path loss (FAP) | 38.46 + 20 lg(d) |

Shadowing | Log-normal, 8 dB standard deviation |

Noise power density | −174 dBm/Hz |

Algorithms | Sum-Throughput (${10}^{7}$ bit/s) | Improvement over MAP-Only (Percent) |
---|---|---|

The proposed algorithm | 2.5536 | 2.893 |

The best AP selection | 2.5388 | 2.297 |

FAP-first | 2.5155 | 1.358 |

MAP-only | 2.4818 | 0 |

Algorithms | Spectrum Efficiency (${10}^{3}$ bit/s/Hz) | Improvement over MAP-Only (Percent) |
---|---|---|

The proposed algorithm | 1.7024 | 2.895 |

The best AP selection | 1.6925 | 2.297 |

FAP-first | 1.6770 | 1.360 |

MAP-only | 1.6545 | 0 |

Algorithms | Fairness Index | Decrease from FAP-First (Percent) |
---|---|---|

FAP-first | 0.9886 | 0 |

The proposed algorithm | 0.9881 | 0.051 |

The best AP selection | 0.9880 | 0.061 |

MAP-only | 0.9871 | 0.152 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Ye, F.; Su, C.; Li, Y.
An Improved User Association Algorithm for MAP–FAPs Heterogeneous Networks. *Symmetry* **2016**, *8*, 151.
https://doi.org/10.3390/sym8120151

**AMA Style**

Ye F, Su C, Li Y.
An Improved User Association Algorithm for MAP–FAPs Heterogeneous Networks. *Symmetry*. 2016; 8(12):151.
https://doi.org/10.3390/sym8120151

**Chicago/Turabian Style**

Ye, Fang, Chunxia Su, and Yibing Li.
2016. "An Improved User Association Algorithm for MAP–FAPs Heterogeneous Networks" *Symmetry* 8, no. 12: 151.
https://doi.org/10.3390/sym8120151