# 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:

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##### 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
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