# Multi-Objective Resource Allocation Scheme for D2D Multicast with QoS Guarantees in Cellular Networks

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## Abstract

**:**

## 1. Introduction

## 2. System Model and Problem Formulation

#### 2.1. System Model

#### 2.2. Problem Formulation

## 3. The Proposed Resource Allocation for D2D Communication

#### 3.1. Problem Equivalence

**Proposition 1.**

**Proof.**

#### 3.2. SINR Assignment for One D2D Multicast Group

**Lemma 1.**

**Proof.**

#### 3.3. Sub-Channel Allocation for Multiple D2D Multicast Groups

#### 3.4. Overall Mechanism

Algorithm 1. Resource Allocation For D2D Multicast. |

* Initialization:The eNB collects the location information of all D2D multicast groups. The initial valid sub-channel set ${\mathcal{S}}_{m}=\varnothing ,\forall m$, the initial feasible sub-channel set ${\mathcal{F}}_{m}=\mathcal{K},\forall m$, the initial available sub-channel set $\mathcal{A}=\mathcal{K}$, and the initial binary variable ${\omega}_{m,k}=0,\forall m,k$ are set up. The multi-objective optimization value brought by any D2D multicast group reusing any sub-channel is $\mathsf{\Phi}\left({\mathsf{\gamma}}_{k,m}^{C\text{}*},{\widehat{\mathsf{\gamma}}}_{n,m,k}^{D}\right)$, which is given (31). |

* Phase 1. Sub-channel Allocation:1. If $\exists m\in \mathcal{M},{\mathcal{F}}_{m}\ne \varnothing $, find the optimal matching $\left({m}^{\ast},{k}^{\ast}\right)$ which satisfies $\left({m}^{\ast},{k}^{\ast}\right)=\mathrm{arg}{\mathrm{min}}_{\left(m,k\right):m\in \mathcal{M},k\in \mathcal{C}}\mathsf{\Phi}\left({\mathsf{\gamma}}_{k,m}^{C\text{}*},{\widehat{\mathsf{\gamma}}}_{n,m,k}^{D}\right)$; Otherwise, go to step 4. 2. If the number of sub-channels allocated to m ^{*} satisfies $\left|{\mathcal{S}}_{m*}\right|\le \frac{K}{M}-1$, set ${\omega}_{m*,k*}=1$, ${\mathcal{S}}_{m}={\mathcal{S}}_{m}\cup \left\{{k}^{*}\right\}$, ${\mathcal{F}}_{m}={\mathcal{F}}_{m}\backslash \left\{{k}^{*}\right\}$, $\mathcal{A}=\mathcal{A}\backslash \left\{{k}^{*}\right\}$. Return to step 1.3. Otherwise, ${\mathcal{F}}_{m*}={\mathcal{F}}_{m*}\backslash \left\{{k}^{*}\right\}$, return to step 1. 4. If the available sub-channel set $\mathcal{A}=\varnothing ,$ go to step 5. Otherwise, for every ${k}^{\prime}\in \mathcal{A}$, find optimal ${m}^{opt}\in \mathcal{M}$ which satisfies $\left({m}^{opt},{k}^{\prime}\right)=\mathrm{arg}{\mathrm{min}}_{\left(m,k\right):m\in \mathcal{M},{k}^{\prime}\in \mathcal{A}}\mathsf{\Phi}\left({\mathsf{\gamma}}_{{k}^{\prime},m}^{C\text{}*},{\widehat{\mathsf{\gamma}}}_{n,m,{k}^{\prime}}^{D}\right)$, then set ${\mathsf{\omega}}_{{m}^{opt},{k}^{\prime}}=1$, ${\mathcal{S}}_{{m}^{opt}}={\mathcal{S}}_{{m}^{opt}}\cup \left\{{k}^{\prime}\right\}$, $\mathcal{A}=\mathcal{A}\backslash \left\{{k}^{\prime}\right\}$. 5. The sub-channel allocation can be determined by repeating the above steps. Phase 1 continues until all available sub-channels are allocated to the D2D groups. |

* Phase 2. SINR Assignment:1. For the D2D group $m\in \mathcal{M}$, obtain all SINR ${{\mathsf{\gamma}}_{n,m,k}^{D}}^{*}$ on the sub-channels by solving the problem (16). 2. According Equations (3), (4) and (9), calculate all ${p}_{m,k}^{D}({{\mathsf{\gamma}}_{k,m}^{C\text{}}}^{*},{{\mathsf{\gamma}}_{n,m,k}^{D}}^{*})$ and ${A}_{n,m,k}$. 3. The power consumption and system capacity of D2D group m are respectively given by ${p}_{m}^{D}={\displaystyle {\sum}_{k\in {\mathcal{S}}_{m}}{p}_{m,k}^{D}({{\gamma}_{k,m}^{C\text{}}}^{*},{{\gamma}_{n,m,k}^{D}}^{*})}$, ${X}_{n,m}=\left|{\displaystyle {\cup}_{k\in {\mathcal{S}}_{m}}{A}_{n,m,k}}\right|$. Repeat the above steps until the power consumptions and system capacities of all D2D groups are calculated ultimately. |

## 4. Numerical Results

_{i}is the resource allocated to D2D groups i, and M is the number of D2D groups. In Figure 7, fairness index of two schemes decreases with the increasing number of D2D groups in the network. Nevertheless, the fairness index of the proposed scheme always has higher fairness than referenced scheme since it considers a constrained multi-objective optimization problem.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

## Appendix B

## References

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**Figure 2.**Power consumption and number of D2D links versus weighted factor: (

**a**) Impact of weighted factor on power consumption; (

**b**) Impact of weighted factor on system capacity.

**Figure 3.**Power consumption and number of D2D links versus D2D group size: (

**a**) Impact of D2D group size on power consumption; (

**b**) Impact of D2D group size on system capacity.

**Figure 4.**Power consumption and number of D2D links versus cell radius: (

**a**) Impact of cell radius on power consumption; (

**b**) Impact of cell radius on system capacity.

**Figure 5.**Power consumption and number of D2D links versus signal-to-interference- plus-noise ratio (SINR) threshold of each CU: (

**a**) Impact of SINR requirement of CUs on power consumption; (

**b**) Impact of SINR requirement of CUs on system capacity.

**Figure 6.**Power consumption and number of D2D links versus SINR threshold of each D2D link: (

**a**) Impact of SINR requirement of D2D links on power consumption; (

**b**) Impact of SINR requirement of D2D links on system capacity.

**Figure 7.**Fairness index versus number of D2D multicast groups: (

**a**) Impact of the number of D2D multicast groups on fairness index for power consumption; (

**b**) Impact of the number of D2D multicast groups on fairness index for system capacity.

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

Cellular layout | one isolated cellular cell |

Cell radius, R | 300 m~700 m |

Uplink bandwidth | 180 kHz |

Noise spectral density | −174 dBm/Hz |

Path loss for cellular links | 128.1 + 37.6log10 (d (km)) |

Path loss for D2D links | 148 + 40log10 (d (km)) |

Shadowing standard deviation | 10 dB for cellular links |

12 dB for D2D links | |

Noise spectral density | −174 dBm/Hz |

Maximum transmission power of CU | 20 dBm |

Maximum transmission power of D2D | 20 dBm |

SINR threshold of CU | 0 dB~10 dB |

SINR threshold of CU link | 10 dB~35 dB |

Number of CUs, K | 20 |

Number of D2D groups, M | 3~10 |

Number of D2D receivers in each group | 10 |

D2D group size, r | 20 m~60 m |

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**MDPI and ACS Style**

Li, F.; Zhang, Y.; Aide Al-Qaness, M.A. Multi-Objective Resource Allocation Scheme for D2D Multicast with QoS Guarantees in Cellular Networks. *Appl. Sci.* **2016**, *6*, 274.
https://doi.org/10.3390/app6100274

**AMA Style**

Li F, Zhang Y, Aide Al-Qaness MA. Multi-Objective Resource Allocation Scheme for D2D Multicast with QoS Guarantees in Cellular Networks. *Applied Sciences*. 2016; 6(10):274.
https://doi.org/10.3390/app6100274

**Chicago/Turabian Style**

Li, Fangmin, Yong Zhang, and Mohammed Abdulaziz Aide Al-Qaness. 2016. "Multi-Objective Resource Allocation Scheme for D2D Multicast with QoS Guarantees in Cellular Networks" *Applied Sciences* 6, no. 10: 274.
https://doi.org/10.3390/app6100274