July  2017, 13(3): 1255-1271. doi: 10.3934/jimo.2016071

Equilibrium analysis of an opportunistic spectrum access mechanism with imperfect sensing results

1. 

School of Information Science and Engineering, Key Laboratory for Computer Virtual Technology, and System Integration of Hebei Province, Yanshan University, Qinhuangdao 066004, China

2. 

Department of Intelligence and Informatics, Konan University, Kobe 658-8501, Japan

3. 

School of Information Science and Engineering, Key Laboratory for Computer Virtual Technology, and System Integration of Hebei Province, Yanshan University, Qinhuangdao 066004, China

The reviewing process of the paper was handled by Yutaka Takahashi as Guest Editor.

Received  October 2015 Published  October 2016

In order to reduce the average delay of secondary user (SU) packets and adapt to various levels of tolerance for transmission interruption, we propose a novel opportunistic channel access mechanism with admission threshold and probabilistic feedback in cognitive radio networks (CRNs). Considering the preemptive priority of primary user (PU) packets, as well as the sensing errors of missed detection and false alarm caused by SUs, we establish a type of priority queueing model in which two classes of customers may interfere with each other. Based on this queueing model, we evaluate numerically the proposed mechanism and then present the system performance optimization. By employing a matrix-geometric solution, we derive the expressions for some important performance measures. Then, by building a reward function, we investigate the strategies for both the Nash equilibrium and the social optimization. Finally, we provide a pricing policy for SU packets to coordinate these two strategies. With numerical experiments, we verify the effectiveness of the proposed opportunistic channel access mechanism and the rationality of the proposed pricing policy.

Citation: Shunfu Jin, Wuyi Yue, Shiying Ge. Equilibrium analysis of an opportunistic spectrum access mechanism with imperfect sensing results. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1255-1271. doi: 10.3934/jimo.2016071
References:
[1]

O. AltradS. MuhaidatA. Al-DweikA. Shami and P. Yoo, Opportunistic spectrum access in cognitive radio networks under imperfect spectrum sensing, IEEE Transactions on Vehicular Technology, 63 (2014), 920-925. doi: 10.1109/TVT.2013.2281334. Google Scholar

[2]

S. AtapattuC. Tellambura and H. Jiang, Energy detection based cooperative spectrum sensing in cognitive radio networks, IEEE Transactions on Wireless Communications, 10 (2011), 1232-1241. doi: 10.1109/TWC.2011.012411.100611. Google Scholar

[3]

A. BhowmickM. DasJ. BiswasS. Roy and S. Kundu, Throughput optimization with cooperative spectrum sensing in cognitive radio network, Proceeding of the 4th IEEE International Advance Computing Conference, (2014), 329-332. doi: 10.1109/IAdCC.2014.6779343. Google Scholar

[4]

G. Bochechka and V. Tikhvinskiy, Spectrum occupation and perspectives millimeter band utilization for 5G networks, Proceeding of ITU Kaleidoscope Academic Conference: Living in a Converged World-Impossible without Standards?, (2014), 69-72. doi: 10.1109/Kaleidoscope.2014.6858482. Google Scholar

[5]

S. GeS. Jin and W. Yue, Throughput analysis for the opportunistic channel access mechanism in CRNs with imperfect sensing results, Proceeding of Queueing Theory and Network Applications, 383 (2015), 55-62. doi: 10.1007/978-3-319-22267-7_5. Google Scholar

[6]

G. GhoshS. Chatterjee and P. Das, Cognitive radio and dynamic spectrum access-A study, International Journal of Next-Generation Networks, 6 (2014), 43-60. doi: 10.5121/ijngn.2014.6104. Google Scholar

[7]

A. GorcinK. QaraqeH. Celebi and H. Arslan, An adaptive threshold method for spectrum sensing in multi-channel cognitive radio networks, Proceeding of the 17th International Conference on Telecommunications, (2010), 425-429. doi: 10.1109/ICTEL.2010.5478783. Google Scholar

[8]

R. Hassin and M. Haviv, To Queue or Not To Queue: Equilibrium Behavior in Queueing Systems, Springer, Boston, 2003. doi: 10.1007/978-1-4615-0359-0. Google Scholar

[9]

H. HuH. ZhangY. Xu and N. Li, Minimum transmission delay via spectrum sensing in cognitive radio networks, Proceeding of IEEE Wireless Communications and Networking Conference, (2013), 4101-4106. Google Scholar

[10]

H. HuH. Zhang and H. Yu, Efficient spectrum sensing with minimum transmission delay in cognitive radio networks, Mobile Networks and Applications, 19 (2014), 487-501. doi: 10.1007/s11036-014-0528-5. Google Scholar

[11]

M. KahvandM. Soleimani and M. Dabiranzohouri, Channel selection in cognitive radio networks: A new dynamic approach, Proceeding of the 11th IEEE Malaysia International Conference on Communications, (2013), 407-411. Google Scholar

[12]

J. Kim and G. Hwang, Cross-layer modeling and optimization of multi-channel cognitive radio networks under imperfect channel sensing, Journal of Industrial & Management Optimization, 11 (2015), 763-777. doi: 10.3934/jimo.2015.11.807. Google Scholar

[13]

K. KimK. Kwak and B. Choi, Performance analysis of opportunistic spectrum access protocol for multi-channel cognitive radio networks, Journal of Communications and Networks, 15 (2013), 77-86. doi: 10.1109/JCN.2013.000013. Google Scholar

[14]

H. Li and Z. Han, Socially optimal queuing control in cognitive radio networks subject to service interruptions: To queue or not to queue?, IEEE Transactions on Wireless Communications, 10 (2011), 1656-1666. Google Scholar

[15]

Y. LiangK. ChenG. Li and P. Mahonen, Cognitive radio networking and communications: An overview, IEEE Transactions on Vehicular Technology, 60 (2011), 3386-3407. doi: 10.1109/TVT.2011.2158673. Google Scholar

[16]

Y. LiangY. ZengE. Peh and A. Hoang, Sensing-throughput tradeoff for cognitive radio networks, IEEE Transactions on Wireless Communications, 7 (2008), 1326-1337. doi: 10.1109/ICC.2007.882. Google Scholar

[17]

M. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, Courier Dover Publications, Baltimore, 1981. Google Scholar

[18]

S. TanJ. Zeidler and B. Rao, Opportunistic spectrum access for cognitive radio networks with multiple secondary users, IEEE Transactions on Wireless Communications, 12 (2013), 6214-6227. Google Scholar

[19]

N. TranC. DoS. Moon and C. Hong, Pricing mechanisms and equilibrium behaviors of noncooperative users in cognitive radio networks, Proceeding of IEEE Global Communications Conference, (2013), 913-918. doi: 10.1109/GLOCOM.2013.6831190. Google Scholar

[20]

Y. WangJ. LiL. HuangY. JingA. Georgakopoulos and P. Demestichas, 5G mobile: Spectrum broadening to higher-frequency bands to support high data rates, IEEE Vehicular Technology Society, 9 (2014), 39-46. doi: 10.1109/MVT.2014.2333694. Google Scholar

[21]

B. Wang and K. Liu, Advances in cognitive radio networks: A survey, IEEE Journal of Selected Topics in Signal Processing, 5 (2011), 5-23. Google Scholar

show all references

References:
[1]

O. AltradS. MuhaidatA. Al-DweikA. Shami and P. Yoo, Opportunistic spectrum access in cognitive radio networks under imperfect spectrum sensing, IEEE Transactions on Vehicular Technology, 63 (2014), 920-925. doi: 10.1109/TVT.2013.2281334. Google Scholar

[2]

S. AtapattuC. Tellambura and H. Jiang, Energy detection based cooperative spectrum sensing in cognitive radio networks, IEEE Transactions on Wireless Communications, 10 (2011), 1232-1241. doi: 10.1109/TWC.2011.012411.100611. Google Scholar

[3]

A. BhowmickM. DasJ. BiswasS. Roy and S. Kundu, Throughput optimization with cooperative spectrum sensing in cognitive radio network, Proceeding of the 4th IEEE International Advance Computing Conference, (2014), 329-332. doi: 10.1109/IAdCC.2014.6779343. Google Scholar

[4]

G. Bochechka and V. Tikhvinskiy, Spectrum occupation and perspectives millimeter band utilization for 5G networks, Proceeding of ITU Kaleidoscope Academic Conference: Living in a Converged World-Impossible without Standards?, (2014), 69-72. doi: 10.1109/Kaleidoscope.2014.6858482. Google Scholar

[5]

S. GeS. Jin and W. Yue, Throughput analysis for the opportunistic channel access mechanism in CRNs with imperfect sensing results, Proceeding of Queueing Theory and Network Applications, 383 (2015), 55-62. doi: 10.1007/978-3-319-22267-7_5. Google Scholar

[6]

G. GhoshS. Chatterjee and P. Das, Cognitive radio and dynamic spectrum access-A study, International Journal of Next-Generation Networks, 6 (2014), 43-60. doi: 10.5121/ijngn.2014.6104. Google Scholar

[7]

A. GorcinK. QaraqeH. Celebi and H. Arslan, An adaptive threshold method for spectrum sensing in multi-channel cognitive radio networks, Proceeding of the 17th International Conference on Telecommunications, (2010), 425-429. doi: 10.1109/ICTEL.2010.5478783. Google Scholar

[8]

R. Hassin and M. Haviv, To Queue or Not To Queue: Equilibrium Behavior in Queueing Systems, Springer, Boston, 2003. doi: 10.1007/978-1-4615-0359-0. Google Scholar

[9]

H. HuH. ZhangY. Xu and N. Li, Minimum transmission delay via spectrum sensing in cognitive radio networks, Proceeding of IEEE Wireless Communications and Networking Conference, (2013), 4101-4106. Google Scholar

[10]

H. HuH. Zhang and H. Yu, Efficient spectrum sensing with minimum transmission delay in cognitive radio networks, Mobile Networks and Applications, 19 (2014), 487-501. doi: 10.1007/s11036-014-0528-5. Google Scholar

[11]

M. KahvandM. Soleimani and M. Dabiranzohouri, Channel selection in cognitive radio networks: A new dynamic approach, Proceeding of the 11th IEEE Malaysia International Conference on Communications, (2013), 407-411. Google Scholar

[12]

J. Kim and G. Hwang, Cross-layer modeling and optimization of multi-channel cognitive radio networks under imperfect channel sensing, Journal of Industrial & Management Optimization, 11 (2015), 763-777. doi: 10.3934/jimo.2015.11.807. Google Scholar

[13]

K. KimK. Kwak and B. Choi, Performance analysis of opportunistic spectrum access protocol for multi-channel cognitive radio networks, Journal of Communications and Networks, 15 (2013), 77-86. doi: 10.1109/JCN.2013.000013. Google Scholar

[14]

H. Li and Z. Han, Socially optimal queuing control in cognitive radio networks subject to service interruptions: To queue or not to queue?, IEEE Transactions on Wireless Communications, 10 (2011), 1656-1666. Google Scholar

[15]

Y. LiangK. ChenG. Li and P. Mahonen, Cognitive radio networking and communications: An overview, IEEE Transactions on Vehicular Technology, 60 (2011), 3386-3407. doi: 10.1109/TVT.2011.2158673. Google Scholar

[16]

Y. LiangY. ZengE. Peh and A. Hoang, Sensing-throughput tradeoff for cognitive radio networks, IEEE Transactions on Wireless Communications, 7 (2008), 1326-1337. doi: 10.1109/ICC.2007.882. Google Scholar

[17]

M. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, Courier Dover Publications, Baltimore, 1981. Google Scholar

[18]

S. TanJ. Zeidler and B. Rao, Opportunistic spectrum access for cognitive radio networks with multiple secondary users, IEEE Transactions on Wireless Communications, 12 (2013), 6214-6227. Google Scholar

[19]

N. TranC. DoS. Moon and C. Hong, Pricing mechanisms and equilibrium behaviors of noncooperative users in cognitive radio networks, Proceeding of IEEE Global Communications Conference, (2013), 913-918. doi: 10.1109/GLOCOM.2013.6831190. Google Scholar

[20]

Y. WangJ. LiL. HuangY. JingA. Georgakopoulos and P. Demestichas, 5G mobile: Spectrum broadening to higher-frequency bands to support high data rates, IEEE Vehicular Technology Society, 9 (2014), 39-46. doi: 10.1109/MVT.2014.2333694. Google Scholar

[21]

B. Wang and K. Liu, Advances in cognitive radio networks: A survey, IEEE Journal of Selected Topics in Signal Processing, 5 (2011), 5-23. Google Scholar

Figure 1.  Transmission process of a PU packet
Figure 2.  Transmission process of an SU packet
Figure 3.  Throughput $\phi$ of SU packets
Figure 4.  Block rate $\beta$ of SU packets
Figure 5.  Average delay $W(\lambda_{su})$ of SU packets
Figure 6.  Change trend for the net benefit of an SU packet
Figure 7.  Change trend for the social welfare
Table 1.  Parameter settings in numerical experiments
ParametersValues
slot1 ms
transmission rate in physical layer11 Mbps
arrival rate of SU packets0.3
mean size of an SU packet1760 Byte
arrival rate of PU packets0.05
mean size of a PU packet2010 Byte
feedback probability0.0-1.0
energy threshold1.0-7.0
simulation scale3 million slots
sensing time0.1 ms
sensing frequency10 times/ms
ParametersValues
slot1 ms
transmission rate in physical layer11 Mbps
arrival rate of SU packets0.3
mean size of an SU packet1760 Byte
arrival rate of PU packets0.05
mean size of a PU packet2010 Byte
feedback probability0.0-1.0
energy threshold1.0-7.0
simulation scale3 million slots
sensing time0.1 ms
sensing frequency10 times/ms
Table 2.  Numerical results for the admission price $F$
Admission threshold $H$Admission probability $r$Feedback probability $q$Admission price $F$
40.40.41.0873
30.40.41.0687
20.40.41.0272
20.40.01.0341
20.40.71.0163
20.80.71.0640
20.10.70.9938
Admission threshold $H$Admission probability $r$Feedback probability $q$Admission price $F$
40.40.41.0873
30.40.41.0687
20.40.41.0272
20.40.01.0341
20.40.71.0163
20.80.71.0640
20.10.70.9938
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