# An Enhanced Dynamic Spectrum Allocation Algorithm Based on Cournot Game in Maritime Cognitive Radio Communication System

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## Abstract

**:**

## 1. Introduction

## 2. System Model

#### 2.1. System Components

#### 2.2. Algorithm Model

## 3. Algorithm Design

#### 3.1. Game Theory Model

#### 3.2. Establishment of Profit Function

#### 3.2.1. Revenue Function Improvement

#### 3.2.2. Price Function Improvement

#### 3.3. Nash Equilibrium Solution

#### 3.4. Algorithm

Algorithm 1: Given that there is one PU system (including one DC and some PUs) and some SUs ($S{U}_{i},$ $i=1\text{}\mathrm{to}\text{}N$) in a region grid of the MCRCS. If PUs have free spectra. For i = 1 to N, do steps (a)-(f). |

(a) $S{U}_{i}$ want to lease spectra;(b) DC obtains the detection capability of $S{U}_{i}$, which is denoted by w_{i};(c) If detection capability of $S{U}_{i}$ w_{i} = 1, then use (8) to set the lowest price for $S{U}_{i}$; Else use (8) to set the price based on the detection capability;(d) Use (6) and (8) to substitute the profit function of $S{U}_{i}$;(e) Use (9) to calculate the profit of $S{U}_{i}$;(f) Use (12) to allocate spectrum for $S{U}_{i}$. |

## 4. Simulation Results and Analysis

- (1)
- Set the maximum available spectrum bandwidth of all SUs to 15 MHz;
- (2)
- Set the revenue rate of the SU’s unit transfer rate ${\mathrm{r}}_{\mathrm{i}}=10$;
- (3)
- Set the SNR of each SUs $\gamma =10\text{}\mathrm{dB}$;
- (4)
- Set the price evaluation criteria $\alpha =2$;
- (5)
- Set the target of BER ${B}_{i}^{tar}={10}^{-4}$.

- (1)
- Compared with the traditional spectrum allocation algorithm, the EDSAA based on the Cournot model has a higher convergence speed.
- (2)
- When the detection capability and the spectrum demand factor of the SUs are the same (${w}_{1}={w}_{2}=1.0$ and ${\sigma}_{1}={\sigma}_{2}=60$), the spectrum allocated to each user is the same at each stage of the game (represented by the blue curve).
- (3)
- When the detection capabilities of SUs are equal and their spectrum demand factors are different (${w}_{1}={w}_{2}=1.0$ and ${\sigma}_{1}=60,{\sigma}_{2}=50$), in the steady state, the bandwidth allocated to each SU is different. The bandwidth of the SU with a large demand factor is wide, while the bandwidth of the SU with a small demand factor is narrow (represented by the red curve).
- (4)
- When the SUs’ spectrum demand factors are equal and their detection capabilities are different (${w}_{1}=1.0,{w}_{2}=0.6$ and ${\sigma}_{1}={\sigma}_{2}=60$), in the steady state, the bandwidth allocated to the SU is also different. The bandwidth of the SU with a strong detection capability is wider, while the bandwidth of the SU with a weak detection capability is narrower (represented by the green curve).

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**$S{U}_{1}$ and $S{U}_{2}$ price function with different detection capabilities and different evaluation criteria.

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**MDPI and ACS Style**

Zhang, J.; Yu, H.; Zhang, S. An Enhanced Dynamic Spectrum Allocation Algorithm Based on Cournot Game in Maritime Cognitive Radio Communication System. *Algorithms* **2017**, *10*, 103.
https://doi.org/10.3390/a10030103

**AMA Style**

Zhang J, Yu H, Zhang S. An Enhanced Dynamic Spectrum Allocation Algorithm Based on Cournot Game in Maritime Cognitive Radio Communication System. *Algorithms*. 2017; 10(3):103.
https://doi.org/10.3390/a10030103

**Chicago/Turabian Style**

Zhang, Jingbo, Henan Yu, and Shufang Zhang. 2017. "An Enhanced Dynamic Spectrum Allocation Algorithm Based on Cournot Game in Maritime Cognitive Radio Communication System" *Algorithms* 10, no. 3: 103.
https://doi.org/10.3390/a10030103