# American Institute of Mathematical Sciences

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July  2017, 13(3): 1483-1494. doi: 10.3934/jimo.2017003

## Performance analysis of binary exponential backoff MAC protocol for cognitive radio in the IEEE 802.16e/m network

 1 ROBOTIS Co., Ltd., Seoul, Korea 2 Research Institute for Information and Communication Technology, Korea University, Seoul, Korea 3 The School of Electrical Engineering, Korea University, Seoul, Korea

* Corresponding author: Bong Dae Choi

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

Received  October 2015 Published  December 2016

Fund Project: The second author is supported by the National Research Foundation of Korea grants funded by Korea government(MEST)(No.2012-008099) and the third author is supported by a Korea University Grant.

We propose a distributed MAC protocol for cognitive radio when primary network is IEEE 802.16e/m WiMAX. Our proposed MAC protocol is the Truncated Binary Exponential Backoff Algorithm where the backoff window size of algorithm is doubled at each collision, and the backoff counter is operated by frame basis in IEEE 802.16e/m and is freezed at a frame with no idle slots. We model our proposed MAC protocol as a 3-dimensional discrete-time Markov chain and obtain steady state probability of the Markov chain by using a censored Markov chain method. Based on this steady state probability, we obtain the throughput, packet loss probability and packet delay distribution of secondary users. Our numerical examples show that the initial contention window size can be determined according to the number of secondary users in order to obtain higher throughput for secondary users, and the maximum backoff window has a large impact on the secondary user's packet loss probability. Secondary users' packet delay distribution is much influenced by the initial contention window size and the number of secondary users.

Citation: 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
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##### References:
An example of frame structure of IEEE 802.16e system
Secondary users' throughput versus $N_s$ ($N_p=160$)
Secondary users' throughput versus $N_s$ ($N_p=120$)
Secondary users' packet loss probability versus $m$
Secondary users' packet loss probability versus $N_p$
Delay distribution versus $W_0$ ($N_s=30$)
Delay distribution versus $W_0$ ($N_s=60$)
Parameter values used in numerical examples
 Parameter Value $N_{slot}$ 140 $\alpha$ 0.9432 $\beta$ 0.9692 $R_t$ 1
 Parameter Value $N_{slot}$ 140 $\alpha$ 0.9432 $\beta$ 0.9692 $R_t$ 1