# A Reciprocal-Selection-Based ‘Win–Win’ Overlay Spectrum-Sharing Scheme for Device-to-Device-Enabled Cellular Network

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Related Work

#### 1.3. Contributions and Paper Structure

- To improve QoS of EUs, EUs ask help from D2D pairs. EUs intend to share spectrum resource with D2D pairs in exchange of D2D pairs’ relaying data for them. However, how to allocate the spectrum resource between EUs and D2D pairs in overlay mode to achieve Win–Win?
- Compared to the underlay spectrum-sharing scheme, overlay spectrum-sharing scheme does not consider interference among users but reduces spectrum efficiency. Hence, how to improve spectrum efficiency in overlay spectrum-sharing scheme?

- A RSWW-OSSS is designed for a D2D-enabled cellular network in order to provide a better connective experience for EUs with the aid of cooperative communication. More explicitly, according to the proposed RSWW-OSSS, EUs are capable of achieving an increased rate with the aid of cooperation assistance provided by the D2D devices. Furthermore, in order to perform D2D transmission, the D2D devices intend to forward data for the EUs in exchange for accessing the part of cellular spectrum resource which is not used by the EUs.
- In order to improve the spectral efficiency, DTs employ the NOMA technology to simultaneously convey EUs’ and their own data at different transmit power. SIC is invoked at both the BS and D2D receivers (DRs) for separating the EUs’ and DTs’ data. As we know, NOMA technology is not introduced in overlay D2D cooperation communications in [19,20,21].
- Aiming for maximizing the utilities of both EU and D2D device, their behaviours are modelled as a two-stage Stackelberg game [31,32,33]. More explicitly, as the leader, EUs calculate the optimal time allocation coefficient in order to maximize its transmit rate. Furthermore, DTs are modelled as the followers which determine the optimal transmit powers for the cooperative transmission and D2D communication, in order to improve the achievable rate of D2D communication and simultaneously reduce the energy consumed for forwarding EUs’ data. The backward induction [34] is invoked for analysing the game and deriving the optimal strategies of EUs and DTs.
- For the sake of achieving a stable matching between multiple EUs and multiple D2D devices, we analyse the algorithmic stability of the proposed RSWW-OSSS with the aid of matching theory [35].

## 2. System Model

#### 2.1. Construction and Assumption

#### 2.2. Communication Model

#### 2.2.1. Non-Cooperative Communication Model

#### 2.2.2. Cooperative Communication Model

**PHASE 1**: During the first time slot ${t}_{1}$, the $E{U}_{m}$ transmits data to $D{T}_{n}$ and BS. The achievable rate of the direct transmission from the $E{U}_{m}$ to the BS may be expressed as:$$\begin{array}{c}\hfill {R}_{E{U}_{m}\to BS}={\tau}_{mn}{log}_{2}\left(1+\frac{{h}_{bm}{P}_{m}}{{N}_{0}}\right)\end{array}$$Furthermore, the transmit rate ${R}_{E{U}_{m}\to D{T}_{n}}$ achieved by the transmission from the $E{U}_{m}$ to the $D{T}_{n}$ may be expressed as:$$\begin{array}{c}\hfill {R}_{E{U}_{m}\to D{T}_{n}}={\tau}_{mn}{log}_{2}\left(1+\frac{{h}_{mn}{P}_{m}}{{N}_{0}}\right)\end{array}$$**PHASE 2**: During the second time slot ${t}_{2}$, the $D{T}_{n}$ simultaneously transmits $E{U}_{m}$’s and itself data with the aid of NOMA technology. The $D{T}_{n}$ transmits its own data to $D{R}_{n}$ with the power of ${P}_{mn}^{D}$ where ${P}_{mn}^{D}={\alpha}_{mn}{P}_{n}$, while forwards the $E{U}_{m}$’s data with the power of ${P}_{mn}^{B}$ where ${P}_{mn}^{B}=\left(1-{\alpha}_{mn}\right){P}_{n}$. Moreover, ${\alpha}_{mn}$ is power allocation coefficient. Equation (5) describes the data sent by the $D{T}_{n}$ when the NOMA technology is employed.$$\begin{array}{c}\hfill y=\sqrt[2]{{P}_{mn}^{B}}{S}_{mn}^{1}+\sqrt[2]{{P}_{mn}^{D}}{S}_{mn}^{2}\end{array}$$$$\begin{array}{c}SINR=\frac{{h}_{bn}\left(1-{\alpha}_{mn}\right){P}_{n}}{a{h}_{bn}{\alpha}_{mn}{P}_{n}+{N}_{0}}\hfill \end{array}$$$$a=\left\{\begin{array}{cc}\hfill 1& {P}_{mn}^{B}>{P}_{mn}^{D}\hfill \\ \hfill 0& {P}_{mn}^{B}\le {P}_{mn}^{D}\hfill \end{array}\right.$$When the BS receives data from $D{T}_{n}$, SIC technology is exploited to separate the $E{U}_{m}$’s and $D{T}_{n}$’s data. Then, both the previous data from the $E{U}_{m}$ in phase 1 and the later data from the $D{T}_{n}$ in phase 2 are combined by the BS with the aid of Maximum Ratio Combining (MRC) [40,41]. The SINR of the merged data may be expressed as:$$\begin{array}{c}\hfill SIN{R}_{MRC}=\frac{{h}_{bn}\left(1-{\alpha}_{mn}\right){P}_{n}}{a{h}_{bn}{\alpha}_{mn}{P}_{n}+{N}_{0}}+\frac{{h}_{bn}{P}_{m}}{{N}_{0}}\end{array}$$After receiving the data from $D{T}_{n}$, $D{R}_{n}$ separates the $D{T}_{n}$’s and $E{U}_{m}$’s data with the aid of SIC technology. The SINR of the $D{T}_{n}$’s data may be expressed as:$$\begin{array}{c}SIN{R}_{D2D}=\frac{{h}_{nn}{\alpha}_{mn}{P}_{n}}{b{h}_{nn}\left(1-{\alpha}_{mn}\right){P}_{n}+{N}_{0}}\hfill \end{array}$$$$b=\left\{\begin{array}{cc}1\hfill & {P}_{mn}^{B}\le {P}_{mn}^{D}\hfill \\ 0\hfill & {P}_{mn}^{B}>{P}_{mn}^{D}\hfill \end{array}\right.$$

## 3. Joint Cooperative Spectrum-Sharing Scheme

#### 3.1. Utility of $E{U}_{m}$

#### 3.2. Utility of $D{T}_{n}$

#### 3.3. Analysis of the Proposed Two-Stage Stackelberg Game

#### 3.3.1. $D{T}_{n}$’s Strategy in Stage $II$

#### 3.3.2. $E{U}_{m}$’s Strategy in Stage I

**Proposition**

**1.**

**Definition**

**1.**

#### 3.4. Matching Game for EUs and D2D Pairs

**Definition**

**2.**

**Definition**

**3.**

## 4. Simulation Results

#### Simulation Configuration

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

## References

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**Figure 3.**Sum-rate of EUs and D2D pairs versus different numbers of D2D transmission pairs when the number of EUs is 20.

**Figure 4.**D2D pairs consumed power for relaying data versus different numbers of D2D transmission pairs when the number of EUs is 20.

**Figure 5.**Sum-rate of EUs versus different numbers of D2D transmission pairs when the number of EUs is 20.

**Figure 6.**Sum-rate of D2D pairs versus different numbers of D2D transmission pairs when the number of EUs is 20.

Notation | Physical Meaning |
---|---|

${P}_{m}$ | $E{U}_{m}$’s transmit power |

${P}_{n}$ | $D{T}_{n}$’s transmit power |

${P}_{MAX}$ | EUs’ and DTs’ maximum transmit power |

${h}_{mn}$ | channel gain between $E{U}_{m}$ and $D{T}_{n}$ |

${h}_{bm}$ | channel gain between $E{U}_{m}$ and BS |

${h}_{nn}$ | channel gain between $D{T}_{n}$ and $D{R}_{n}$ |

${h}_{bn}$ | channel gain between $D{T}_{n}$ and BS |

${N}_{0}$ | power of AWGN |

Require |
---|

Let $E{U}_{m}$ and $D{T}_{n}$ exchange their profile information. |

${\mathit{DT}}_{\mathit{n}}$’s Strategy in Stage $\mathit{I}\mathit{I}$: |

▹ Given the time allocation coefficient ${\tau}_{mn}^{\ast}$ offered by the $E{U}_{m}$ in Stage $I$. |

▹$D{T}_{n}$ calculates the optimal power allocation coefficient ${\alpha}_{mn}^{\ast}$ according Equation (18) |

${\mathit{EU}}_{\mathit{m}}$’s strategy in Stage $\mathit{I}$: |

▹ Given the optimal power allocation coefficient ${\alpha}_{mn}^{\ast}({\tau}_{mn}^{\ast})$ which is shown in Equation (18) |

▹$E{U}_{m}$ calculates the optimal power allocation coefficient ${\tau}_{mn}^{\ast}$ which is the solution of Equation (24) |

(${\mathbf{\tau}}_{\mathit{mn}}^{\mathbf{\ast}}\mathbf{,}{\mathbf{\alpha}}_{\mathit{mn}}^{\mathbf{\ast}}$) is the Nash Equilibrium of the proposed two-stage Stackelberg game. |

Initialization: |
---|

Let ${L}_{m}^{EU}$ and ${L}_{n}^{D2D}$ be the preference list of $E{U}_{m}$ and $D{T}_{n}$ respectively. |

Repeat: |

for all $\forall m\in \{1,\dots ,M\}E{U}_{m}$ do |

if $E{U}_{m}$ is not matched |

▹$E{U}_{m}$ broadcasts proposal $\varphi (m,n)$ to favourable $D{T}_{n}$ according to ${L}_{m}^{EU}$. |

Set $i=0$, ${V}_{m}=0$. |

while ${V}_{m}=0$ and $i\le n$ for $0<n\le N$ |

▹$i=i+1,n={m}_{i}$. |

if $E{U}_{m}$ in the preference list ${L}_{n}^{D2D}$ of $D{T}_{n}$ |

if $D{T}_{n}$ is not matched |

▹$D{T}_{n}$ accepts the proposal $\varphi (m,n)$, set ${V}_{m}=1$. |

if $D{T}_{n}$ is matched with $E{U}_{\widehat{m}}$ |

if ${\alpha}_{\widehat{m}n}>{\alpha}_{mn}$ |

▹$D{T}_{n}$ rejects the former $E{U}_{\widehat{m}}$ and accepts the proposal $\varphi (m,n)$ of $E{U}_{m}$, set ${V}_{m}=1$. |

else |

▹ set ${V}_{m}=0$. |

for all $\forall n\in \{1,\dots ,N\}$ $D{T}_{n}$ do |

if $D{T}_{n}$ achieves more than one proposal |

▹$D{T}_{n}$ selects the one who requires lower transmit power. |

for all $\forall m\in \{1,\dots ,M\}E{U}_{m}$ do |

if $E{U}_{m}$ is already matched with $D{T}_{\widehat{n}}$ |

if $D{T}_{\widehat{n}}$ divorces matched pair $\varphi (m,\widehat{n})$ |

▹$E{U}_{m}$ is not matched. |

Until: Each EU are either assigned to one of the D2D pairs or rejected by all of D2D pairs in ${L}_{m}^{EU}$. |

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

$Cell\phantom{\rule{4pt}{0ex}}radius$ | 500 m |

$Noise\phantom{\rule{4pt}{0ex}}power({N}_{0})$ | −114 dBm |

$D2D\phantom{\rule{4pt}{0ex}}link\phantom{\rule{4pt}{0ex}}distance$ | 50 m |

$Each\phantom{\rule{4pt}{0ex}}EU\phantom{\rule{4pt}{0ex}}Tx\phantom{\rule{4pt}{0ex}}power$ | 100 mW |

$Each\phantom{\rule{4pt}{0ex}}D2D\phantom{\rule{4pt}{0ex}}pair\phantom{\rule{4pt}{0ex}}Tx\phantom{\rule{4pt}{0ex}}power$ | 100 mW |

$Pathloss\phantom{\rule{4pt}{0ex}}constant(L)$ | ${10}^{-2}$ |

$Pathloss\phantom{\rule{4pt}{0ex}}exponent(\eta )$ | 4 |

$Rate\phantom{\rule{4pt}{0ex}}requirement\phantom{\rule{4pt}{0ex}}coefficient(\xi )$ | 2.5 |

$Number\phantom{\rule{4pt}{0ex}}of\phantom{\rule{4pt}{0ex}}EUs(M)$ | 20 |

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## Share and Cite

**MDPI and ACS Style**

Li, P.; Shu, C.; Feng, J.
A Reciprocal-Selection-Based ‘Win–Win’ Overlay Spectrum-Sharing Scheme for Device-to-Device-Enabled Cellular Network. *Algorithms* **2018**, *11*, 179.
https://doi.org/10.3390/a11110179

**AMA Style**

Li P, Shu C, Feng J.
A Reciprocal-Selection-Based ‘Win–Win’ Overlay Spectrum-Sharing Scheme for Device-to-Device-Enabled Cellular Network. *Algorithms*. 2018; 11(11):179.
https://doi.org/10.3390/a11110179

**Chicago/Turabian Style**

Li, Peng, Chenchen Shu, and Jiao Feng.
2018. "A Reciprocal-Selection-Based ‘Win–Win’ Overlay Spectrum-Sharing Scheme for Device-to-Device-Enabled Cellular Network" *Algorithms* 11, no. 11: 179.
https://doi.org/10.3390/a11110179