# American Institute of Mathematical Sciences

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:

show all references

##### References:
Interference-free region
The probability that the sensed channel is idle
The coverage probability
Throughput
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)
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 - - - -
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 - - - -
throughput over $b_1$ and $b_2$($\lambda_s=0.005, T_1=0.0001$)
 0.39 0.4 0.41 0.42 0.43 0.35 0.236905 0.237417 0.238089 0.237907 0.23775 0.36 0.23791 0.237729 0.237724 0.238186 0.238567 0.37 0.237818 0.237955 0.237926 0.2384 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 0.4 0.41 0.42 0.43 0.35 0.236905 0.237417 0.238089 0.237907 0.23775 0.36 0.23791 0.237729 0.237724 0.238186 0.238567 0.37 0.237818 0.237955 0.237926 0.2384 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
throughput over $b_1$ and $b_2$($\lambda_s=0.005, T_1=0.001$)
 0.37 0.38 0.39 0.4 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 0.2435 0.39 0.24342 0.2437 0.243563 0.243473 0.243394
 0.37 0.38 0.39 0.4 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 0.2435 0.39 0.24342 0.2437 0.243563 0.243473 0.243394
 [1] Haruki Katayama, Hiroyuki Masuyama, Shoji Kasahara, Yutaka Takahashi. Effect of spectrum sensing overhead on performance for cognitive radio networks with channel bonding. Journal of Industrial & Management Optimization, 2014, 10 (1) : 21-40. doi: 10.3934/jimo.2014.10.21 [2] Yuan Zhao, Wuyi Yue. Performance evaluation and optimization of cognitive radio networks with adjustable access control for multiple secondary users. Journal of Industrial & Management Optimization, 2019, 15 (1) : 1-14. doi: 10.3934/jimo.2018029 [3] Shengzhu Jin, Bong Dae Choi, Doo Seop Eom. Performance analysis of binary exponential backoff MAC protocol for cognitive radio in the IEEE 802.16e/m network. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1483-1494. doi: 10.3934/jimo.2017003 [4] Yuan Zhao, Wuyi Yue. Performance analysis and optimization for cognitive radio networks with a finite primary user buffer and a probability returning scheme. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1119-1134. doi: 10.3934/jimo.2018195 [5] Hyeon Je Cho, Ganguk Hwang. Optimal design for dynamic spectrum access in cognitive radio networks under Rayleigh fading. Journal of Industrial & Management Optimization, 2012, 8 (4) : 821-840. doi: 10.3934/jimo.2012.8.821 [6] Jae Deok Kim, Ganguk Hwang. Cross-layer modeling and optimization of multi-channel cognitive radio networks under imperfect channel sensing. Journal of Industrial & Management Optimization, 2015, 11 (3) : 807-828. doi: 10.3934/jimo.2015.11.807 [7] Yuan Zhao, Wuyi Yue. Cognitive radio networks with multiple secondary users under two kinds of priority schemes: Performance comparison and optimization. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1449-1466. doi: 10.3934/jimo.2017001 [8] Shunfu Jin, Wuyi Yue, Zsolt Saffer. Analysis and optimization of a gated polling based spectrum allocation mechanism in cognitive radio networks. Journal of Industrial & Management Optimization, 2016, 12 (2) : 687-702. doi: 10.3934/jimo.2016.12.687 [9] Illés Horváth, Kristóf Attila Horváth, Péter Kovács, Miklós Telek. Mean-field analysis of a scaling MAC radio protocol. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019111 [10] Koen De Turck, Sabine Wittevrongel. Receiver buffer behavior for the selective repeat protocol over a wireless channel: An exact and large-deviations analysis. Journal of Industrial & Management Optimization, 2010, 6 (3) : 603-619. doi: 10.3934/jimo.2010.6.603 [11] Sara D. Cardell, Joan-Josep Climent. An approach to the performance of SPC product codes on the erasure channel. Advances in Mathematics of Communications, 2016, 10 (1) : 11-28. doi: 10.3934/amc.2016.10.11 [12] Anupam Gautam, Selvamuthu Dharmaraja. Selection of DRX scheme for voice traffic in LTE-A networks: Markov modeling and performance analysis. Journal of Industrial & Management Optimization, 2019, 15 (2) : 739-756. doi: 10.3934/jimo.2018068 [13] Serap Ergün, Sirma Zeynep Alparslan Gök, Tuncay Aydoǧan, Gerhard Wilhelm Weber. Performance analysis of a cooperative flow game algorithm in ad hoc networks and a comparison to Dijkstra's algorithm. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1085-1100. doi: 10.3934/jimo.2018086 [14] Tomoya Tainaka, Hiroyuki Masuyama, Shoji Kasahara, Yutaka Takahashi. A Markovian approach to per-flow throughput unfairness in IEEE 802.11 multihop wireless networks. Journal of Industrial & Management Optimization, 2009, 5 (3) : 493-510. doi: 10.3934/jimo.2009.5.493 [15] 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 [16] Jinsen Zhuang, Yan Zhou, Yonghui Xia. Synchronization analysis of drive-response multi-layer dynamical networks with additive couplings and stochastic perturbations. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020279 [17] Jianping Liu, Shunfu Jin. An imperfect sensing-based channel reservation strategy in CRNs and its performance evaluation. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1149-1169. doi: 10.3934/jimo.2018197 [18] Fumio Ishizaki. Analysis of the statistical time-access fairness index of one-bit feedback fair scheduler. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 675-689. doi: 10.3934/naco.2011.1.675 [19] Grigory Panasenko, Ruxandra Stavre. Asymptotic analysis of the Stokes flow with variable viscosity in a thin elastic channel. Networks & Heterogeneous Media, 2010, 5 (4) : 783-812. doi: 10.3934/nhm.2010.5.783 [20] Makram Hamouda, Chang-Yeol Jung, Roger Temam. Asymptotic analysis for the 3D primitive equations in a channel. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 401-422. doi: 10.3934/dcdss.2013.6.401

2018 Impact Factor: 1.025

## Tools

Article outline

Figures and Tables