# User Classification in Crowdsourcing-Based Cooperative Spectrum Sensing

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## Abstract

**:**

## 1. Introduction

- Considering that there may be several types of mobile user, the paper casts user classification as a dynamic clustering problem without prior information about network parameters. The fitness function is designed for the dynamic clustering problem.
- The paper proposes a distributed algorithm for user classification to obtain bounded close-to-optimal solutions. Each mobile user, rather than the FC, carries out the process of classification independently according to all sensing reports. Then, the approximation ratio of the proposed algorithm is analyzed with a Markov chain.

## 2. The System Model

#### 2.1. Behavior of Different Users

_{0}denotes the noise power, p

_{i}denotes the signal strength of primary users received by user i, m denotes the number of samples, H

_{0}denotes that the channel is idle, and H

_{1}denotes that the channel is being used by primary users.

#### 2.2. Problem Formulation

_{1}, f

_{2}, …, f

_{M}}, where f

_{i}∈{0, 1}, 0 denotes that the user is a cluster center, and 1 denotes that the user is not a cluster center. This paper defines F as the set of all feasible f. Given a clustering configuration f, the corresponding fitness function Fit(f) is used to denote clustering effect which reflects both the homogeneity within the same cluster and the heterogeneity among different clusters. This paper aims to maximize Fit(f) by choosing a proper clustering configuration f. Fit(f) can be described as

_{f}(i) denotes the minimized interdistance-to-intradistance ratio of the ith cluster. The interdistance-to-intradistance ratio is used to measure the relationship between distance within a cluster and that among different clusters. Let e

_{j}be the mean distance from users in the jth cluster to the center of the jth cluster, e

_{i}be the mean distance from users in the ith cluster to the center of the ith cluster, and m

_{ji}is the distance between the centers of the jth and ith clusters. Then, m

_{ji}/(e

_{i}+ e

_{j}) is used to denote interdistance-to-intradistance ratio of the jth and ith clusters. The higher the interdistance-to-intradistance ratio is, the better the clustering effect. Under the clustering configuration f, the lowest interdistance-to-intradistance ratio is used to evaluate the clustering effect of configuration f. Therefore, R

_{f}(i) can be described as

## 3. A Distributed Algorithm

#### 3.1. Algorithm Description

_{f}(i) (i = 1, 2, …, N(f)) independently. Then, each mobile user generates a random number following exponential distribution, and its mean equals a positive constant C.

_{f f’}, as described in (5).

_{f f’}, or stays in the role with the probability 1 − p

_{f f’}. If the mobile user stays in its role, it regenerates a new random number following exponential distribution and counts down. If the mobile user changes its current role, a new clustering configuration f' appears. This mobile user broadcasts the new clustering configuration f' to other mobile users and generates a new random number following exponential distribution to start a new countdown process. When other users receive the new clustering configuration f', they calculate R

_{f’}(i) (i = 1, 2, …, N(f')) and continue their countdown processes. When the countdown of a mobile user expires, the transition probability is calculated based on R

_{f}(i). This implementation is named the Role-Changing (RC) algorithm.

Algorithm 1: Role-Changing algorithm for user i |

Input β |

1: Mobile user i chooses its role randomly and broadcasts its role. |

2: After user i receives other users’ roles, it obtains the current clustering configuration f. |

3: Mobile user i broadcasts its sensing reports and receives other users' reports. |

4: Then, user i calculates $\sum _{i=1}^{N(f)}{R}_{f}(i)}/N(f)$ independently. |

5: User i generates a timer following exponential distribution and begins to count down. |

6: When the timer expires, user i changes its role with p_{f f’} or stay in its role with 1 − p_{f f’}. |

7: If user i changes its role, it broadcasts the new clustering configuration f'. |

8: Other users calculate $\sum _{i=1}^{N(f\prime )}{R}_{f\prime}(i)}/N(f\prime )$ under the new clustering configuration f'. |

9: User i generates a new timer following exponential distribution and begins to count down. Then, it repeats step 6–9. |

#### 3.2. Analysis of Approximation Ratio

_{f f'}denote the probability that the system moves to state f' from state f after count-down expiration. In the RC algorithm, a mobile user changes its role following the probability p

_{f f’}in (5). Therefore, W

_{f f'}can be obtained.

_{f f’}denotes the probability that a mobile user will change its current role, while W

_{f f'}denotes the probability that the system moves to the state f' from the state f. When there are M users in the system, the probability that the user is chosen is 1/M. Therefore, the probability that the system moves to state f' from state f is p

_{f f’}/M. According to the RC algorithm, each mobile user counts down following an exponential distribution that is memoryless. As each mobile user counts down with the rate 1/C, the rate of the system count-down expiration is M/C. Then, the transition rate q

_{f f'}from state f to state f' can be obtained.

## 4. Simulations

^{M}, will increase. Therefore, the approximation gap increases as | F | increases. In addition, it is also shown that the larger β is, the smaller the approximation gap is. This means the distributed algorithm is more accurate with larger values of β.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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M | 10 | 12 | 14 | 16 | 18 | |
---|---|---|---|---|---|---|

β | ||||||

20 | 0.34 | 0.41 | 0.48 | 0.55 | 0.62 | |

30 | 0.23 | 0.27 | 0.32 | 0.36 | 0.41 |

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**MDPI and ACS Style**

Zhai, L.; Wang, H.
User Classification in Crowdsourcing-Based Cooperative Spectrum Sensing. *Symmetry* **2017**, *9*, 110.
https://doi.org/10.3390/sym9070110

**AMA Style**

Zhai L, Wang H.
User Classification in Crowdsourcing-Based Cooperative Spectrum Sensing. *Symmetry*. 2017; 9(7):110.
https://doi.org/10.3390/sym9070110

**Chicago/Turabian Style**

Zhai, Linbo, and Hua Wang.
2017. "User Classification in Crowdsourcing-Based Cooperative Spectrum Sensing" *Symmetry* 9, no. 7: 110.
https://doi.org/10.3390/sym9070110