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

Seunghee Lee; Ganguk Hwang

doi:10.3934/jimo.2017023

Article Contents

2017, Volume 13, Issue 4: 1883-1899. Doi: 10.3934/jimo.2017023

This issue Previous Article Non-convex semi-infinite min-max optimization with noncompact sets Next Article Analysis of a discrete-time queue with general service demands and phase-type service capacities

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

Seunghee Lee and
Ganguk Hwang

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

Received: September 2015

Revised: June 2016

Published: November 2017

Abstract / Introduction Full Text(HTML) Figure(4) / Table(5) Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation:

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Figure 1. Interference-free region

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Figure 2. The probability that the sensed channel is idle

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Figure 3. The coverage probability

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Figure 4. Throughput

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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)

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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	-	-	-	-

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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	-	-	-	-

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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

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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

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