# Non-Cooperative Spectrum Access Strategy Based on Impatient Behavior of Secondary Users in Cognitive Radio Networks

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## Abstract

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## 1. Introduction

## 2. System Model and Problem Statement

_{p}(x), f

_{p}(x), F

_{s}(x), f

_{s}(x) denote the cumulative distribution function (CDF) of ${X}_{p}$, the probability density function (PDF) of ${X}_{p}$, the CDF of ${X}_{s}$ and the PDF of ${X}_{s}$, respectively.

_{s}, then the effective arrival rate to access the channel is λ

_{s}q. In addition, due to the limitation of the delay requirement, an SU will choose to give up the transmission and leave the system, if its required waiting time exceeds the tolerable waiting time $\tau $ before it gets the right to use the channel. We assume that the tolerable waiting time $\tau $ follows exponential distribution with mean 1/r. The M/G/1 + M queueing theory with impatient customers can be used to model and analyze the system. Moreover, we assume that SUs will not leave the system until finishing the whole transmission once they start transmitting.

_{n}and stayers arrive at b

_{n}, n = 1, 2, …, we denote the actual transmission time of SU by G

_{s}, and let Gs(x) be the corresponding distribution function. According to the level crossing methods, for any fixed level x > 0, the system point downcrossing and upcrossing rates of level x are equal in the steady state. Therefore, we can get:

_{0}represents the stationary probability of the channel being idle and P

_{0}can be expressed as follows:

_{sw}(y) to complete the second iteration as:

_{p}is given by:

_{sw}(x) in (7). We can prove the convergence of ${\varphi}_{n}^{\ast}(s)$. The proof is given in the Appendix.

_{0}can be obtained according to (5) and (16):

## 3. Spectrum Access Strategies of SUs

_{S}(q) denote the average net benefit of SUs which choose to access the channel with the probability q. Considering that each SU can receive a reward of R due to transmission completion, from (1) U

_{S}(q) can be written as:

#### 3.1. Individual Equilibrium Strategy

_{e}denote the individual equilibrium access strategy and no SU can improve its own benefit by unilaterally changing the strategy under the Nash equilibrium state. For a new arrival SU, if U

_{S}(0) ≤ 0, then even if there is no other SU to share the spectrum, the tagged SU has to suffer a non-positive benefit by joining. It implies none of the SUs will choose to access the channel no matter what channel state (even if the channel is idle). In order to avoid trivialities, we assume U

_{S}(0) > 0. If there exists a unique access probability ${q}_{e}$ ($0<{q}_{e}<1$) satisfying U

_{S}(q

_{e}) = 0, then the strategy of SUs joining with probability q

_{e}is the unique Nash equilibrium mixed strategy. In the case U

_{S}(1) > 1, even if all SUs choose to access the channel, they can still enjoy a non-negative benefit, so the strategy of joining with probability ${q}_{e}=1$ is the unique equilibrium strategy.

_{e}if q

_{e}satisfies the following conditions:

#### 3.2. Socially Optimal Strategy

_{o}). Therefore, the aim of socially optimal strategy is to find a joining probability ${q}_{o}$ to maximize the net benefit S

_{o},which is given by:

#### 3.3. Spectrum Pricing

## 4. Numerical Results

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix

## References

- Wang, J.; Gao, Y.; Yin, X.; Li, F.; Kim, H.J. An enhanced PEGASIS algorithm with mobile sink support for wireless sensor networks. Wirel. Commun. Mob. Comput.
**2018**, 2018, 9472075. [Google Scholar] [CrossRef] - Lin, Y.; Zhu, X.L.; Zheng, Z.G.; Dou, Z.; Zhou, R.L. The individual identification method of wireless device based on dimensionality reduction and machine learning. J. Supercomput.
**2019**, 75, 3010–3027. [Google Scholar] [CrossRef] - Kumar, D.P.; Amgoth, T.; Annavarapu, C.S.R. Machine learning algorithms for wireless sensor networks: A survey. Inform. Fusion
**2019**, 49, 1–25. [Google Scholar] [CrossRef] - Wang, J.; Gao, Y.; Liu, W.; Wu, W.B.; Lim, S. An asynchronous clustering and mobile data gathering schema based on timer mechanism in wireless sensor networks. Comput. Mater. Contin.
**2019**, 58, 711–725. [Google Scholar] [CrossRef] - Wang, J.; Gu, X.J.; Liu, W.; Sangaiah, A.K.; Kim, H.J. An empower hamilton loop based data collection algorithm with mobile agent for WSNs. Hum-Cent. Comput. Inf. Sci.
**2019**, 9, 18. [Google Scholar] [CrossRef] - Park, J.H.; Lee, W.C.; Choi, J.P.; Choi, J.W.; Um, S.B. Applying case-based reasoning to tactical cognitive sensor networks for dynamic frequency allocation. Sensors
**2018**, 18, 4294. [Google Scholar] [CrossRef] [PubMed] - Wang, J.; Gao, Y.; Liu, W.; Sangaiah, A.K.; Kim, H.J. An intelligent data gathering schema with data fusion supported for mobile sink in WSNs. Int. J. Distrib. Sens. Netw.
**2019**, 15. [Google Scholar] [CrossRef] - Dou, Z.; Si, G.Z.; Lin, Y.; Wang, M.Y. An adaptive resource allocation model with anti-jamming in IoT network. IEEE Access
**2019**, 7, 93250–93258. [Google Scholar] [CrossRef] - Zhang, Z.Y.; Guo, X.H.; Lin, Y. Trust management method of D2D communication based on RF fingerprint identification. IEEE Access
**2018**, 6, 66082–66087. [Google Scholar] [CrossRef] - Nguyen, T.; Pan, J.; Dao, T. An Improved Flower Pollination Algorithm for Optimizing Layouts of Nodes in Wireless Sensor Network. IEEE Access
**2019**, 7, 75985–75998. [Google Scholar] [CrossRef] - Yin, Y.; Xu, Y.; Xu, W.; Min, G.; Pei, Y. Collaborative Service Selection via Ensemble Learning in Mixed Mobile Network Environments. Entropy
**2017**, 19, 358. [Google Scholar] [CrossRef] - He, S.; Xie, K.; Xie, K.; Xu, C.; Jin, W. Interference-aware Multi-source Transmission in Multi-radio and Multi-channel Wireless Network. IEEE Syst. J.
**2019**, 13, 2507–2518. [Google Scholar] [CrossRef] - He, S.; Xie, K.; Chen, W.; Zhang, D.; Wen, J. Energy-aware Routing for SWIPT in Multi-hop Energy-constrained Wireless Network. IEEE Access
**2018**, 6, 17996–18008. [Google Scholar] [CrossRef] - Wang, D.; Song, B.; Chen, D.; Du, X.J. Intelligent cognitive radio in 5G: AI-based hierarchical cognitive cellular networks. IEEE Wirel. Commun.
**2019**, 26, 54–61. [Google Scholar] [CrossRef] - Kotobi, K.; Mainwaring, P.B.; Tucker, C.S.; Bilen, S.G. Data-throughput enhancement using data mining-informed cognitive radio. Electronics
**2015**, 4, 221–238. [Google Scholar] [CrossRef] - Haykin, S. Cognitive radio: Brain-empowered wireless communications. IEEE J. Sel. Areas Commun.
**2005**, 23, 201–220. [Google Scholar] [CrossRef] - Tang, B.; Tu, Y.; Zhang, Z.Y.; Lin, Y. Digital signal modulation classification with data augmentation using generative adversarial nets in cognitive radio networks. IEEE Access
**2018**, 6, 15713–15722. [Google Scholar] [CrossRef] - Tu, Y.; Lin, Y.; Wang, J.; Kim, J.U. Semi-supervised learning with generative adversarial networks on digital signal modulation classification. CMC-Comput. Mater. Contin.
**2018**, 55, 243–254. [Google Scholar] - Zhang, J.; Jin, X.; Sun, J.; Wang, J.; Sangaiah, A. Spatial and semantic convolutional features for robust visual object tracking. Multimed. Tools Appl.
**2018**, in press. [Google Scholar] [CrossRef] - Zhang, J.; Lu, C.; Li, X.; Kim, H.; Wang, J. A full convolutional network based on DenseNet for remote sensing scene classification. Math. Biosci. Eng.
**2019**, 16, 3345–3367. [Google Scholar] [CrossRef] - Zhang, J.; Lu, C.; Wang, J.; Wang, L.; Yue, X. Concrete cracks detection based on FCN with dilated convolution. Appl. Sci.
**2019**, 9, 2686. [Google Scholar] [CrossRef] - Zhang, J.; Jin, X.; Sun, J.; Wang, J.; Li, K. Dual model learning combined with multiple feature selection for accurate visual tracking. IEEE Access
**2019**, 7, 43956–43969. [Google Scholar] [CrossRef] - Yin, Y.; Chen, L.; Xu, Y.; Wan, J.; Mai, Z. QoS prediction for service recommendation with deep feature learning in edge computing environment. Mob. Netw. Appl.
**2019**. [Google Scholar] [CrossRef] - Lin, Y.; Wang, C.; Wang, J.X.; Dou, Z. A novel dynamic spectrum access framework based on reinforcement learning for cognitive radio sensor networks. Sensors
**2016**, 16, 1675. [Google Scholar] [CrossRef] [PubMed] - Zakariya, A.Y.; Rabia, S.I. Analysis of an interruption-based priority for multi-class secondary users in cognitive radio networks. In Proceedings of the 2016 IEEE International Conference on Communications (ICC), Kuala Lumpur, Malaysia, 22–27 May 2016. [Google Scholar]
- Joo, C.; Shroff, N.B. A novel coupled queueing model to control traffic via QoS-aware collision pricing in cognitive radio networks. In Proceedings of the IEEE INFOCOM 2017—IEEE Conference on Computer Communications, Atlanta, GA, USA, 1–4 May 2017. [Google Scholar]
- Wang, Y.C.; Tang, X.; Wang, T. A unified QoS and security provisioning framework for wiretap cognitive radio networks: A statistical queueing analysis approach. IEEE Trans. Wirel. Commun.
**2019**, 18, 1548–1565. [Google Scholar] [CrossRef] - Wang, S.; Maharaj, B.T.; Alfa, A.S. Queueing analysis of performance measures under a new configurable channel allocation in cognitive radio. IEEE Trans. Veh. Technol.
**2018**, 67, 9571–9582. [Google Scholar] [CrossRef] - Kosta, A.; Pappas, N.; Ephremides, A.; Angelakis, V. Age of information and throughput in a shared access network with heterogeneous traffic. In Proceedings of the 2018 IEEE Global Communications Conference (GLOBECOM), Abu Dhabi, United Arab Emirates, 9–13 December 2018. [Google Scholar]
- Wang, L.C.; Wang, C.W.; Adachi, F. Load-balancing spectrum decision for cognitive radio networks. IEEE J. Sel. Areas Commun.
**2011**, 29, 757–769. [Google Scholar] [CrossRef] - Jagannathan, K.; Menache, I.; Modiano, E.; Zussman, G. Non-cooperative spectrum access - the dedicated vs. free spectrum choice. IEEE J. Sel. Areas Commun.
**2012**, 30, 2251–2261. [Google Scholar] [CrossRef] - Zhu, S.; Wang, J.T.; Li, W.W. Optimal service rate in cognitive radio networks with different queue length information. IEEE Access
**2018**, 6, 51577–51586. [Google Scholar] [CrossRef] - Wang, J.; Huang, A.P.; Wang, W. Admission control in cognitive radio networks with finite queue and user impatience. IEEE Wirel. Commun. Lett.
**2013**, 2, 175–178. [Google Scholar] [CrossRef] - Jin, S.F.; Ge, S.Y.; Yue, W.Y. Performance evaluation for an opportunistic spectrum access mechanism with impatience behavior and imperfect sensing results. In Proceedings of the 2015 Seventh International Conference on U-Biquitous and Future Networks, Sapporo, Japan, 7–10 July 2015. [Google Scholar]
- Li, H.S.; Han, Z. Socially optimal queuing control in cognitive radio networks subject to service interruptions: To queue or not to queue? IEEE Trans. Wirel. Commun.
**2011**, 10, 1656–1666. [Google Scholar] - Do, C.T.; Tran, N.H.; Nguyen, M.V.; Hong, C.S.; Lee, S. Social optimization strategy in unobserved queueing systems in cognitive radio networks. IEEE Commun. Lett.
**2012**, 16, 1944–1947. [Google Scholar] [CrossRef] - Smith, P.J.; Senanayake, R.; Dmochowski, P.A.; Evans, J.S. Distributed spectrum sensing for cognitive radio networks based on the sphericity test. IEEE Trans. Commun.
**2019**, 67, 1831–1844. [Google Scholar] [CrossRef] - Lu, Y.; Duel-Hallen, A. A sensing contribution-based two-layer game for channel selection and spectrum access in cognitive radio Ad-hoc networks. IEEE Trans. Wirel. Commun.
**2018**, 17, 3631–3640. [Google Scholar] [CrossRef] - Zhang, Y.; Wang, J.T.; Li, W.W. Optimal pricing strategies in cognitive radio networks with heterogeneous secondary users and retrials. IEEE Access
**2019**, 7, 3631–3640. [Google Scholar] [CrossRef] - Stanford, R.E. Reneging phenomena in Single channel queues. Math. Oper. Res.
**1979**, 4, 162–178. [Google Scholar] [CrossRef]

**Figure 1.**Sample path of the virtual wait of secondary users (SUs) considering the impatient behavior.

**Figure 2.**The impact of spectrum access fee m on the social benefit S and the SU equilibrium access probability q

_{e}.

**Figure 3.**The impact of r on the social benefit S under different spectrum pricing mechanisms in Exp model.

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**MDPI and ACS Style**

Zeng, Z.; Liu, M.; Wang, J.; Lan, D.
Non-Cooperative Spectrum Access Strategy Based on Impatient Behavior of Secondary Users in Cognitive Radio Networks. *Electronics* **2019**, *8*, 995.
https://doi.org/10.3390/electronics8090995

**AMA Style**

Zeng Z, Liu M, Wang J, Lan D.
Non-Cooperative Spectrum Access Strategy Based on Impatient Behavior of Secondary Users in Cognitive Radio Networks. *Electronics*. 2019; 8(9):995.
https://doi.org/10.3390/electronics8090995

**Chicago/Turabian Style**

Zeng, Zhen, Meng Liu, Jin Wang, and Dongping Lan.
2019. "Non-Cooperative Spectrum Access Strategy Based on Impatient Behavior of Secondary Users in Cognitive Radio Networks" *Electronics* 8, no. 9: 995.
https://doi.org/10.3390/electronics8090995