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Optimal contention window size for IEEE 802.15.3c mmWave WPANs

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Abstract

The millimeter-wave (mmWave) band offers the potential for multi-gigabit indoor Wireless Personal Area Networks (WPANs). However, it has problems such as short communication coverage due to high propagation losses. In order to compensate for this drawback, utilization of directional antennas at the physical layer is highly recommended. In this paper, we consider the adequate contention window (CW) size for directional carrier sense multiple access with collision avoidance (CSMA/CA). To find the optimal CW size that enhances the performance of conventional directional CSMA/CA, we propose an enhanced directional CSMA/CA algorithm. The algorithm is considered in IEEE 802.15.3c, a standard for mmWave WPANs, under saturation environments. For the algorithm, we present a Markov chain model and analyze it for the no-ACK mode. The effects of directional antennas and the features of IEEE 802.15.3c Medium Access Control (MAC) such as backoff counter freezing are considered in the model. The optimal CW sizes for the two different objective functions are derived from the numerical results. The numerical results also show that the system throughput and average transmission delay of the proposed algorithm outperform those of conventional one and the overall analysis is verified by simulation. The obtained results provide the criterion for selecting the optimal parameters and developing a MAC protocol that enhances the performance of mmWave WPANs.

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Acknowledgments

The authors would like to thank the associate editor and the anonymous reviewers for their constructive and valuable comments. This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST, MSIP) (NRF-2010-0022282, 2013R1A2A2A01067452) and the Korea University Grant.

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Authors and Affiliations

  1. Research Institute for Information and Communication Technology, Korea University, Seoul, Republic of Korea

    Meejoung Kim

  2. Electronics and Telecommunications Research Institute, Daejeon, Republic of Korea

    Wooyong Lee

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  1. Meejoung Kim
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Correspondence to Meejoung Kim.

Appendix

Appendix

1.1 Calculation of P b,bo:

When a transmitter–receiver pair tries to communicate, there are two viewpoints from which the channel is considered busy: the viewpoints of the transmitter and receiver. From the transmitter’s viewpoint, the channel is considered busy when the transmitter senses it. From the receiver’s viewpoint, the channel is considered busy because of other transmitters interfering with the receiver. In the former case, the decrement of backoff counter is suspended during a busy period, while the backoff counter is decremented in the latter case, unless the interferer to the receiver is located in SRt. A collision occurs if the transmitters in SRt or the interferers in ERr send frames simultaneously. If a DEV’s backoff counter reaches zero or it selects a zero backoff counter, it has to wait for an idle BIFS before it transmits. Therefore, there should be idle slots between two busy periods.

Let P b and τ be the probabilities that a shared channel is busy at a given observation point and a station is in the transmission state, respectively. Then τ can be decomposed according to the previous channel state, which is either idle or busy. Since there are no consecutive busy periods, a DEV transmits a frame with conditional probability p tx only if the previous channel state was idle. Therefore, p tx is given by

$$p_{\rm tx} = P\left(\hbox{a device is at}\,(i,0)\,\hbox{state}|\hbox{ previous}\,BIFS\,\hbox{is idle}\right)=\frac{\tau}{1-P_{\rm b}}.$$
(A1)

In this case we calculate P b as follows: Let E(B) and E(I) be the average number of consecutive busy and idle slots, respectively. Since there is at least one idle slot after a busy period, it follows that E(B) = 1. Let p c be the probability that a collision occurs in a time slot when TTx transmits. Since a collision occurs either because of other transmitters in SRt or because of interferers in ERr,  p c can be written as

$$p_{\rm c}=1-\left(1-p_{\rm tx}\right)^{E_{\rm con}}.$$
(A2)

Then E(I) is derived as

$$E(I)=\sum\limits_{i=0}^\infty{iP(I=i)}=\frac{1}{1 - \left(1 - p_{\rm c}\right)^{\{E\left(K_{{\rm SR}_{\rm t}}^N\right)+1\}/E\left(K_{{\rm SR}_{\rm t}}^N\right)}}.$$
(A3)

Therefore, P b is expressed as

$$P_{\rm b} = \frac{{E(B)}}{{E(I) + E(B)}} = \frac{{1 - \left(1-p_{\rm c} \right)^{\left\{E\left(K_{{\rm SR}_{\rm t} }^N\right)+1\right\}/E\left(K_{{\rm SR}_{\rm t} }^N \right)} }}{{2 - \left(1 - p_{\rm c}\right)^{\left\{E\left(K_{{\rm SR}_{\rm t} }^N \right) + 1\right\}/E(K_{{\rm SR}_{\rm t}}^N)}}}.$$
(A4)

Since P b can be alternatively rewritten as P b = τ + P b,bo(1 − τ),  P b,bo is given as P b,bo = (P b − τ)/(1 − τ). Since τ is b 0, substituting b 0 in Eqs. (15) and (A4), P b,bo can be expressed as

$$P_{\rm b,bo}=\frac{{(W_0-1)\left[1-(1-p_{\rm c})^{\left\{E\left(K_{{\rm SR}_{\rm t}}^N\right) +1\right\}/E\left(K_{{\rm SR}_{\rm t}}^N\right)}\right]-2}}{{(W_0-3)+(W_0-1)\left[1-\left(1-p_{\rm c}\right)^{\left\{E\left(K_{{\rm SR}_{\rm t}}^N\right) +1\right\}/E\left(K_{{\rm SR}_{\rm t}}^N\right)}\right]}}.$$
(A5)

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Kim, M., Lee, W. Optimal contention window size for IEEE 802.15.3c mmWave WPANs. Wireless Netw 20, 1335–1347 (2014). https://doi.org/10.1007/s11276-013-0682-x

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