October 2017, 13(4): 1883-1899. doi: 10.3934/jimo.2017023

A new analytical model for optimized cognitive radio networks based on stochastic geometry

Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea

The reviewing process of the paper was handled by Wuyi Yue and Yutaka Takahashi as Guest Editors

Received  September 2015 Revised  June 2016 Published  April 2017

In this paper, we consider an underlay type cognitive radio network with multiple secondary users who contend to access multiple heterogeneous licensed channels. With the help of stochastic geometry we develop a new analytical model to analyze a random channel access protocol where each secondary user determines whether to access a licensed channel based on a given access probability. In our analysis we introduce the so-called interference-free region to derive the coverage probability for an arbitrary secondary user. With the help of the interference-free region we approximate the interferences at an arbitrary secondary user from primary users as well as from secondary users in a simple way. Based on our analytical model we obtain the optimal access probabilities that maximize the throughput. Numerical examples are provided to validate our analysis.

Citation: Seunghee Lee, Ganguk Hwang. A new analytical model for optimized cognitive radio networks based on stochastic geometry. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1883-1899. doi: 10.3934/jimo.2017023
References:
[1]

A. Babaei and B. Jabbari, Throughput Optimization in Cognitive Random Wireless Ad hoc Networks, Global Telecommunications Conference (GLOBECOM 2010), 2010 IEEE,(2010). doi: 10.1109/GLOCOM.2010.5684066.

[2]

F. BaccelliB. Blaszczyszyn and M. Karray, Up and downlink admission/congestion control and maximal load in large homogeneous CDMA networks, MONET, 9 (2004), 605-617. doi: 10.1023/B:MONE.0000042499.64488.ba.

[3]

F. Baccelli, B. Blaszczyszyn and F. Tournois, Downlink admission/congestion control and maximal load in CDMA networks, in Proc. IEEE INFOCOM, (2003). doi: 10.1109/INFCOM.2003.1208722.

[4]

A. BussonB. JabbariA. Babaei and V. Véque, Interference and throughput in spectrum sensing cognitive radio networks using point processes, Communications and Networks, Journal of, 16 (2014), 67-80. doi: 10.1109/JCN.2014.000010.

[5]

C. C. Chan and S. V. Hanly, Calculating the outage probability in a CDMA network with spatial Poisson traffic, IEEE Trans. Veh. Technol., 50 (2001), 183-204. doi: 10.1109/25.917918.

[6]

V. Chandrasekhar and J. G. Andrews, Uplink capacity and interference avoidance for two-tier cellular networks, IEEE Trans. Wireless Commun., (2009).

[7]

O. DousseM. Franceschetti and P. Thiran, On the throughput scaling of wireless relay networks, IEEE Trans. Inform. Theory, 52 (2006), 2756-2761. doi: 10.1109/TIT.2006.874537.

[8]

Federal Communications Commission, Spectrum policy task force, Rep. ET Docket, 2 (2002).

[9]

Federal Communications Commission, Notice of proposed rule making and order, Rep. ET Docket, 2 (2003).

[10]

A. Ghasemi and E. Sousa, Interference aggregation in spectrumsensing cognitive wireless networks, IEEE J. Select. Topics Signal Processing, 2 (2008), 41-56.

[11]

A. GoldsmithS. A. JafarI. Maric and S. Srinivasa, Breaking spectrum gridlock with cognitive radios: An information theoretic perspective, Proc. IEEE, 97 (2009), 894-914. doi: 10.1109/JPROC.2009.2015717.

[12]

M. HaenggiJ. G. AndrewsF. BaccelliO. Dousse and M. Franceschetti, Stochastic Geometry and Random Graphs for the Analysis and Design of Wireless Networks, IEEE J. Select. Areas Commun., 27 (2009). doi: 10.1109/JSAC.2009.090902.

[13]

J. LeeJ. G. Andrews and D. Hong, Spectrum-sharing transmission capacity, IEEE Trans. Wireless Commun., 10 (2011), 3053-3063. doi: 10.1109/TWC.2011.070511.101941.

[14]

C. Lee and M. Haenggi, Interference and outage in poisson cognitive networks, IEEE Trans. Wireless Commun., 11 (2012), 1392-1401. doi: 10.1109/TWC.2012.021512.110131.

[15]

D. Moltchanov, Distance distributions in random networks, Ad Hoc Networks, 10 (2012), 1146-1166.

[16]

T. V. Nguyen and F. Baccelli, A probabilistic model of carrier sensing based cognitive radio, New Frontiers in Dynamic Spectrum, 2010 IEEE Symposium on, (2010), 1-12. doi: 10.1109/DYSPAN.2010.5457860.

[17]

T. V. Nguyen and F. Baccelli, A stochastic geometry model for cognitive radio networks, The Computer Journal, 55 (2012), 534-552. doi: 10.1093/comjnl/bxr049.

[18]

P. PintoA. GiorgettiM. Chiani and M. Win, A stochastic geometry approach to coexistence in heterogeneous wireless networks, IEEE J. Select. Areas Commun., 2009 (2009).

[19]

W. RenQ. Zhao and A. Swami, Power control in cognitive radio networks: How to cross a multi-lane highway, IEEE J. Select. Areas Commun., 27 (2009).

[20]

X. SongC. YinD. Liu and R. Zhang, Spatial Opportunity in Cognitive Radio Networks with Threshold-Based Opportunistic Spectrum Access, Communications (ICC), 2013 IEEE International Conference on, (2013), 2695-2700. doi: 10.1109/ICC.2013.6654944.

[21] D. StoyanW. Kendall and J. Mecke, Stochastic Geometry and Its Applications, 2 edition, John Wiley and Sons, 1996.
[22]

R. Vaze, Transmission capacity of spectrum sharing ad hoc networks with multiple antennas, IEEE Trans. Wireless Commun., 10 (2011), 2334-2340. doi: 10.1109/WIOPT.2011.5930039.

[23]

X. Yang and A. Petropulu, Co-channel interference modelling and analysis in a Poisson field of interferers in wireless communications, IEEE Trans. Signal Processing, 51 (2003), 64-76. doi: 10.1109/TSP.2002.806591.

[24]

C. YinL. Gao and S. Cui, Scaling laws for overlaid wireless networks: A cognitive radio network vs. a primary network, IEEE/ACM Transactions on, 18 (2010), 1317-1329. doi: 10.1109/GLOCOM.2008.ECP.244.

[25]

C. Yin, C. Chen, T. Liu and S. Cui, Generalized results of transmission capacities for overlaid wireless networks, in Proc. IEEE Int. Symp. Inf. Theory, Seoul, Korea, (2009), 1774-1778. doi: 10.1109/ISIT.2009.5205273.

[26]

J. Zhang and J. G. Andrews, Distributed antenna systems with randomness, IEEE Trans. Wireless Commun., 7 (2008), 3636-3646.

[27]

Q. Zhao and B. Sadler, A survey of dynamic spectrum access, IEEE Signal Process. Mag., 24 (2007), 79-89.

show all references

References:
[1]

A. Babaei and B. Jabbari, Throughput Optimization in Cognitive Random Wireless Ad hoc Networks, Global Telecommunications Conference (GLOBECOM 2010), 2010 IEEE,(2010). doi: 10.1109/GLOCOM.2010.5684066.

[2]

F. BaccelliB. Blaszczyszyn and M. Karray, Up and downlink admission/congestion control and maximal load in large homogeneous CDMA networks, MONET, 9 (2004), 605-617. doi: 10.1023/B:MONE.0000042499.64488.ba.

[3]

F. Baccelli, B. Blaszczyszyn and F. Tournois, Downlink admission/congestion control and maximal load in CDMA networks, in Proc. IEEE INFOCOM, (2003). doi: 10.1109/INFCOM.2003.1208722.

[4]

A. BussonB. JabbariA. Babaei and V. Véque, Interference and throughput in spectrum sensing cognitive radio networks using point processes, Communications and Networks, Journal of, 16 (2014), 67-80. doi: 10.1109/JCN.2014.000010.

[5]

C. C. Chan and S. V. Hanly, Calculating the outage probability in a CDMA network with spatial Poisson traffic, IEEE Trans. Veh. Technol., 50 (2001), 183-204. doi: 10.1109/25.917918.

[6]

V. Chandrasekhar and J. G. Andrews, Uplink capacity and interference avoidance for two-tier cellular networks, IEEE Trans. Wireless Commun., (2009).

[7]

O. DousseM. Franceschetti and P. Thiran, On the throughput scaling of wireless relay networks, IEEE Trans. Inform. Theory, 52 (2006), 2756-2761. doi: 10.1109/TIT.2006.874537.

[8]

Federal Communications Commission, Spectrum policy task force, Rep. ET Docket, 2 (2002).

[9]

Federal Communications Commission, Notice of proposed rule making and order, Rep. ET Docket, 2 (2003).

[10]

A. Ghasemi and E. Sousa, Interference aggregation in spectrumsensing cognitive wireless networks, IEEE J. Select. Topics Signal Processing, 2 (2008), 41-56.

[11]

A. GoldsmithS. A. JafarI. Maric and S. Srinivasa, Breaking spectrum gridlock with cognitive radios: An information theoretic perspective, Proc. IEEE, 97 (2009), 894-914. doi: 10.1109/JPROC.2009.2015717.

[12]

M. HaenggiJ. G. AndrewsF. BaccelliO. Dousse and M. Franceschetti, Stochastic Geometry and Random Graphs for the Analysis and Design of Wireless Networks, IEEE J. Select. Areas Commun., 27 (2009). doi: 10.1109/JSAC.2009.090902.

[13]

J. LeeJ. G. Andrews and D. Hong, Spectrum-sharing transmission capacity, IEEE Trans. Wireless Commun., 10 (2011), 3053-3063. doi: 10.1109/TWC.2011.070511.101941.

[14]

C. Lee and M. Haenggi, Interference and outage in poisson cognitive networks, IEEE Trans. Wireless Commun., 11 (2012), 1392-1401. doi: 10.1109/TWC.2012.021512.110131.

[15]

D. Moltchanov, Distance distributions in random networks, Ad Hoc Networks, 10 (2012), 1146-1166.

[16]

T. V. Nguyen and F. Baccelli, A probabilistic model of carrier sensing based cognitive radio, New Frontiers in Dynamic Spectrum, 2010 IEEE Symposium on, (2010), 1-12. doi: 10.1109/DYSPAN.2010.5457860.

[17]

T. V. Nguyen and F. Baccelli, A stochastic geometry model for cognitive radio networks, The Computer Journal, 55 (2012), 534-552. doi: 10.1093/comjnl/bxr049.

[18]

P. PintoA. GiorgettiM. Chiani and M. Win, A stochastic geometry approach to coexistence in heterogeneous wireless networks, IEEE J. Select. Areas Commun., 2009 (2009).

[19]

W. RenQ. Zhao and A. Swami, Power control in cognitive radio networks: How to cross a multi-lane highway, IEEE J. Select. Areas Commun., 27 (2009).

[20]

X. SongC. YinD. Liu and R. Zhang, Spatial Opportunity in Cognitive Radio Networks with Threshold-Based Opportunistic Spectrum Access, Communications (ICC), 2013 IEEE International Conference on, (2013), 2695-2700. doi: 10.1109/ICC.2013.6654944.

[21] D. StoyanW. Kendall and J. Mecke, Stochastic Geometry and Its Applications, 2 edition, John Wiley and Sons, 1996.
[22]

R. Vaze, Transmission capacity of spectrum sharing ad hoc networks with multiple antennas, IEEE Trans. Wireless Commun., 10 (2011), 2334-2340. doi: 10.1109/WIOPT.2011.5930039.

[23]

X. Yang and A. Petropulu, Co-channel interference modelling and analysis in a Poisson field of interferers in wireless communications, IEEE Trans. Signal Processing, 51 (2003), 64-76. doi: 10.1109/TSP.2002.806591.

[24]

C. YinL. Gao and S. Cui, Scaling laws for overlaid wireless networks: A cognitive radio network vs. a primary network, IEEE/ACM Transactions on, 18 (2010), 1317-1329. doi: 10.1109/GLOCOM.2008.ECP.244.

[25]

C. Yin, C. Chen, T. Liu and S. Cui, Generalized results of transmission capacities for overlaid wireless networks, in Proc. IEEE Int. Symp. Inf. Theory, Seoul, Korea, (2009), 1774-1778. doi: 10.1109/ISIT.2009.5205273.

[26]

J. Zhang and J. G. Andrews, Distributed antenna systems with randomness, IEEE Trans. Wireless Commun., 7 (2008), 3636-3646.

[27]

Q. Zhao and B. Sadler, A survey of dynamic spectrum access, IEEE Signal Process. Mag., 24 (2007), 79-89.

Figure 1.  Interference-free region
Figure 2.  The probability that the sensed channel is idle
Figure 3.  The coverage probability
Figure 4.  Throughput
Table 1.  The optimal point obtained from analysis under parameter sets (a) to (d)
Parameter set Optimal point $\mathbf{b}_A^*$
(a) $\lambda_{s}=0.001, T_1=0.0001$ (0.5722, 0.4278)
(b) $\lambda_{s}=0.001, T_1=0.001$ (0.5198, 0.4802)
(c) $\lambda_{s}=0.005, T_1=0.0001$ (0.3714, 0.4143)
(d) $\lambda_{s}=0.005, T_1=0.001$ (0.3688, 0.3925)
Parameter set Optimal point $\mathbf{b}_A^*$
(a) $\lambda_{s}=0.001, T_1=0.0001$ (0.5722, 0.4278)
(b) $\lambda_{s}=0.001, T_1=0.001$ (0.5198, 0.4802)
(c) $\lambda_{s}=0.005, T_1=0.0001$ (0.3714, 0.4143)
(d) $\lambda_{s}=0.005, T_1=0.001$ (0.3688, 0.3925)
Table 2.  throughput over $b_1$ and $b_2$($\lambda_s=0.001, T_1=0.0001$)
0.41 0.42 0.43 0.44 0.45
0.55 0.611956 0.616004 0.620971 0.626117 0.630063
0.56 0.616728 0.621303 0.626249 0.630435 -
0.57 0.621165 0.625826 0.630827 - -
0.58 0.626057 0.630756 - - -
0.59 0.630405 - - - -
0.41 0.42 0.43 0.44 0.45
0.55 0.611956 0.616004 0.620971 0.626117 0.630063
0.56 0.616728 0.621303 0.626249 0.630435 -
0.57 0.621165 0.625826 0.630827 - -
0.58 0.626057 0.630756 - - -
0.59 0.630405 - - - -
Table 3.  throughput over $b_1$ and $b_2$($\lambda_s=0.001, T_1=0.001$)
0.46 0.47 0.48 0.49 0.50
0.50 0.656962 0.661976 0.667183 0.671202 0.675827
0.51 0.662102 0.666946 0.672465 0.676458 -
0.52 0.667741 0.672843 0.677074 - -
0.53 0.672488 0.676938 - - -
0.54 0.676835 - - - -
0.46 0.47 0.48 0.49 0.50
0.50 0.656962 0.661976 0.667183 0.671202 0.675827
0.51 0.662102 0.666946 0.672465 0.676458 -
0.52 0.667741 0.672843 0.677074 - -
0.53 0.672488 0.676938 - - -
0.54 0.676835 - - - -
Table 4.  throughput over $b_1$ and $b_2$($\lambda_s=0.005, T_1=0.0001$)
0.39 0.40 0.41 0.42 0.43
0.35 0.236905 0.237417 0.238089 0.237907 0.237750
0.36 0.237910 0.237729 0.237724 0.238186 0.238567
0.37 0.237818 0.237955 0.237926 0.238400 0.238395
0.38 0.237836 0.238351 0.238569 0.238292 0.238104
0.39 0.238228 0.238257 0.238475 0.238197 0.238343
0.39 0.40 0.41 0.42 0.43
0.35 0.236905 0.237417 0.238089 0.237907 0.237750
0.36 0.237910 0.237729 0.237724 0.238186 0.238567
0.37 0.237818 0.237955 0.237926 0.238400 0.238395
0.38 0.237836 0.238351 0.238569 0.238292 0.238104
0.39 0.238228 0.238257 0.238475 0.238197 0.238343
Table 5.  throughput over $b_1$ and $b_2$($\lambda_s=0.005, T_1=0.001$)
0.37 0.38 0.39 0.40 0.41
0.35 0.243218 0.244021 0.243855 0.244004 0.243705
0.36 0.243233 0.243758 0.243913 0.243568 0.243585
0.37 0.243763 0.244133 0.243675 0.243949 0.243908
0.38 0.243935 0.243805 0.243465 0.243912 0.243500
0.39 0.243420 0.243700 0.243563 0.243473 0.243394
0.37 0.38 0.39 0.40 0.41
0.35 0.243218 0.244021 0.243855 0.244004 0.243705
0.36 0.243233 0.243758 0.243913 0.243568 0.243585
0.37 0.243763 0.244133 0.243675 0.243949 0.243908
0.38 0.243935 0.243805 0.243465 0.243912 0.243500
0.39 0.243420 0.243700 0.243563 0.243473 0.243394
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