Research ArticleAn Adaptive WLAN Interference Mitigation Scheme forZigBee Sensor Networks
Jo Woon Chong,1 Chae Ho Cho,2 Ho Young Hwang,3 and Dan Keun Sung4
1Department of Biomedical Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609, USA2Department of Biomedical Engineering, University of Connecticut, Storrs, CT 06269, USA3Department of Computer Engineering, Kwangwoon University, 20 Gwangun-ro, Nowon-gu, Seoul 139-701, Republic of Korea4Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro,Yuseong-gu, Daejeon 305-338, Republic of Korea
Correspondence should be addressed to Dan Keun Sung; [email protected]
Received 23 April 2015; Revised 19 June 2015; Accepted 27 July 2015
We propose an adaptive interference avoidance scheme that enhances the performance of ZigBee networks by adapting ZigBees’transmissions to measured wireless local area network (WLAN) interference. Our proposed algorithm is based on a stochasticanalysis of ZigBee operation that is interfered with by WLAN transmission, given ZigBee and WLAN channels are overlaid in theindustrial, scientific, andmedical (ISM) band.We assume thatWLANdevices have higher transmission power than ZigBee devices.Then, the high transmission power of WLAN devices causes the capture effect when WLAN and ZigBee transmit simultaneously.On the other hand, ZigBee performs backoff during clear channel assessment (CCA) operation if the WLAN is transmitting itsframes on the channel. We adopt a widely usedWLAN queueing/transmission model that is based on aMarkov chain concept. Wemodel a ZigBee device’s operation using the Markov chain that includes WLAN interference statistically derived from the WLANqueueing/transmission model. Our proposed algorithm is evaluated in a simulated ZigBee network in the presence of varyingWLAN interference. Numerical results show that our WLAN interference mitigation scheme finds the ZigBee control parameters,among a candidate set, which enhances ZigBee network performance compared to the conventional ZigBee operation.
1. Introduction
Wireless local area network (WLAN), Bluetooth, and ZigBeetechnologies have been adopted in various types of devicesas user demands for wireless services in local or personalareas increase. For example, WLAN access points (APs) havebeen widely deployed in indoor or outdoor environments,and tablets or laptops use WLAN technology for an internetconnection. Bluetooth technology has been used in wirelessheadsets for audio devices, hands-free sets formobile phones,and wireless keyboards and mouses for personal computers.ZigBee technology has gained attention from many com-panies since it consumes relatively less energy than otherwireless technologies and can be implemented at low cost [1].However, WLAN, Bluetooth, and ZigBee devices all operateon the 2.4GHz industrial, scientific, andmedical (ISM) band;hence if they coexist, they interfere with one another [2–6].
ZigBees are required to conform to the physical layer(PHY) and medium access control (MAC) techniques ofIEEE 802.15.4, which is standardized for low-rate wirelesspersonal area networks (WPANs). IEEE 802.15.4 definesoperations in the 2.4GHz (worldwide), 868MHz (Europe),and 915MHz (Americas and Australia) ISM bands [7–10].The maximum data rate is 250 kbps per channel and thetransmission distance is around 10–20m in indoor environ-ment. The ZigBee protocol supports both beacon-enabledand beaconless modes. In the beacon-enabled mode [11],a coordinator synchronizes nodes by sending beacons. Asuperframe is limited by two consecutive beacons and iscomposed of active and inactive periods. The active periodcan be divided into a contention access period (CAP) and acontention-free period (CFP). Slotted carrier sense multipleaccess/collision avoidance (CSMA/CA) and time divisionmultiple access (TDMA) are channel access modes in CAP
Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2015, Article ID 851289, 16 pageshttp://dx.doi.org/10.1155/2015/851289
2 International Journal of Distributed Sensor Networks
andCFP, respectively [12–16]. In the beaconlessmode, unslot-ted CSMA/CA is a channel access mode. During the inactiveperiod in a superframe, all the nodes go into sleep.
Slotted and unslotted CSMA/CA mechanisms performoperations of initialization, backoff, clear channel assessment(CCA), starting the transmission, and acknowledgement(optional) [17, 18]. Initialization is a procedure of settinga node’s local backoff exponent variable to an initial valuewhenever a frame is successfully transmitted by the node.The backoff is a procedure of keeping the node silent beforetrying to assess the channel medium. This backoff lowersa frame collision probability by randomizing its channelassessment time. After the backoff, the node performs CCA.If the channel is assessed to be busy, the node performsbackoff again after doubling backoff window size. This is toreduce a frame collision probability [19]. If the channel isassessed to be free during two CCAs, on the contrary, it startsits transmission. If the sending node requires an acknowl-edgement, the receiving node transmits an acknowledgementwhen the transmission is successful. Otherwise, the sendingnode regards it as transmission failure and retransmits itsframe.
WLAN and Bluetooth devices have higher transmissionpowers compared to ZigBee devices by a factor of approx-imately ten to thousand times [17, 20]. In particular, theoperating bandwidth of WLAN devices is wider than that ofZigBee devices; hence, if WLAN and ZigBee devices coexistand their operating bands are overlaid, the performanceof ZigBee networks can be severely degraded by WLANnetworks. On the other hand, WLAN transmission can bemerely interfered with by ZigBees’ transmissions. In thispaper, we evaluate the performance of ZigBee networksinterfered with by WLAN networks and propose an adaptiveWLAN interference mitigation scheme for ZigBee networks.Our algorithm is based on the analysis and design of ZigBee’smedium access control (MAC) operation when the ZigBeesare interfered with by WLAN transmissions. Our hetero-geneous interference analysis is based on a Markov chainconcept, adoptingWLANandZigBee operationmodels fromIEEE 802.11 and IEEE 802.15.4 specifications, respectively [20,21]. The proposed interference avoidance algorithm adaptsZigBees’ transmissions to the measured WLAN interference,in order to maximize ZigBee networks’ performance. Ourproposed unified analysis and design of ZigBee networkshave wide applicability in that they can be utilized inpredicting and enhancing the performance of random accessMAC-based networks interferedwith by other heterogeneousrandom access MAC-based networks or virtual slot-basednetworks.
The rest of this paper is organized as follows. We describerelated work in Section 2. ZigBee and WLAN protocols areexplained in Section 3. The coexisting ZigBee and WLANnetwork environment that we consider is presented. InSection 4, the ZigBee operation interfered with by WLANtransmissions is modeled based on a stochastic analysis witha Markov chain concept. Interference avoidance algorithmsfor ZigBee networks interfered with by WLAN are proposedin Section 5. Section 6 describes performance measures and
gives analytical and simulation results. Finally, Section 7concludes this paper.
2. Related Work
Themutual interference problems amongWLAN, Bluetooth,and ZigBee networks in the 2.4GHz ISM band have beeninvestigated in [22–30]. In [22, 23], the ZigBee frame errorrate (FER) was measured when ZigBee devices coexistwith WLANs and microwave ovens. Cochannel interferenceamong ZigBee, Bluetooth,WLAN, andmicrowave ovens wasevaluated in terms of frame loss of each system in [24]. TheZigBee packet error rate (PER) was evaluated through sim-ulation when WLAN transmissions interfere with ZigBees’operation [25]. The opposite interference analysis, that is,ZigBee devices’ interference on WLAN, was performed in[26, 27], which suggests that the effect of ZigBee transmis-sions on the WLAN is relatively insignificant compared tothe reverse. In physical (PHY) layer, the performance of IEEE802.15.4 ZigBee in the presence of IEEE WLAN (802.11b)and/or Bluetooth interference was analyzed in [28]. Here,they obtained the bit error rate (BER) performance undera varying signal-to-interference-plus noise ratio (SINR). In[29], the coexistence of ZigBee and WLAN in smart gridenvironments was investigated by measuring ZigBees’ PERwhen ZigBee coexists withWLAN. In these studies, the inter-ference is observed mainly in the PHY layer, and the WLANinterference to ZigBee is observed to be relatively severer thanthe reverse. This is due to the higher transmission powerof WLAN devices compared to that of ZigBee devices. Tostandardize a coexistence algorithm for Bluetooth networksinterfered with by WLAN networks, IEEE 802.15.2 work-ing group (WG) has investigated the interference betweenWLAN and Bluetooth networks [30]. However, it focused onnot ZigBee but Bluetooth.
The previous studies related to interference analysismainly dealt with the operation among homogeneous ZigBeedevices [31–33] or WLAN devices [34–38] without consid-ering the heterogeneous interaction between ZigBee andWLAN. There exist analysis studies on the ZigBees’ MACoperation interfered with byWLAN, but theWLAN interfer-ence is modeled by unrealistic the M/G/1 model [39, 40]. Wemodel a WLAN queueing/transmission model reflecting arealisticWLANMACoperation and transmission procedure,that is, CSMA/CA [34, 41].The ZigBee network performanceinterfered with by WLAN interference is modeled by aMarkov chain concept with WLAN interference parame-terized in the Markov chain model. The proposed inter-ference avoidance algorithm maximizes ZigBee networks’performance, for example, throughput, delay, and energyconsumption, by controlling ZigBees’ MAC parameters aswell as ZigBee’s frame size based on this analysis results.
The previous studies of the interference between WLANand ZigBee [2–6] suggested that the way of mitigatingthe interference between WLAN and ZigBee is for ZigBeedevices to avoid WLAN operating channels when ZigBeedevices use their channels. Here, static and dynamic channelassignment methods are considered. The static assignmentcan be ineffective when the number of WLAN APs increases
International Journal of Distributed Sensor Networks 3
or nodes are mobile [3] while the dynamic assignmentmethods can address these problems by avoiding nearbyWLAN channels [42, 43]. However, these dynamic methodsalso become inefficient when there exists little WLAN traffic[2, 44].The interference problems have also been investigatedin the aspects of wireless sensor placement or sensor networktopology [45–47]. In [45], the signal strength within anarea is measured for IEEE 802.11a/b/g/n while a method fordetermining the optimal sensor placement based on [45] wasproposed, which led to a reduction in the number of sensorsto cover the area in [46]. A proactive method mediatingthe interference of WLAN and ZigBee devices is proposedin [48], and another in [49], with the concept of fairnessadditionally considered. A coexistence algorithm enablingZigBee links to exploit WLAN white is proposed in [50]. Anerror detection and recoverymethod using partial packets areproposed to enhance link reliability in [51].
3. System Model
3.1. ZigBee and WLAN Networks. A ZigBee network canbe configured in star or peer-to-peer topology. In the startopology, one ZigBee device, which is a full-function device(FFD), becomes a personal area network coordinator (PNC).Other ZigBee devices, which can be either reduced-functiondevices (RFDs) or FFDs, communicate with each otherunder the control of PNC. ZigBees start communication afterassociating themselves with PNC.The peer-to-peer topologyis different from the star topology in the fact that devices candirectly communicatewith each otherwithout PNC’s relayingrole. A ZigBee has 16 channels in the 2.4GHz ISM band. Theoperation channels of ZigBee devices in the same network areconfigured by the same channel. For MAC protocol, ZigBeescan use either CSMA/CA (mandatory) or TDMA (optional)[17]. When ZigBee devices gain channel access, they transmitdata using a direct sequence spread spectrum (DSSS) physicallayer technique.
A WLAN network consists of basic service sets (BSSs),where WLAN devices communicate with each other underthe control of access points (AP). Both IEEE 802.11b andIEEE 802.11g PHYs have thirteen channels, respectively,each of which has 22MHz bandwidth [52, 53]. The WLANdevices within the same BSS contend for channel access totransmit their frames. IEEE 802.11 incorporates CSMA/CAand TDMA services in the MAC protocol. IEEE 802.11b andIEEE 802.11 g use DSSS and orthogonal frequency divisionmultiplexing (OFDM), respectively, in transmitting data.
Figure 1 illustrates coexisting WLAN and ZigBee net-works. For PHY layer techniques, IEEE 802.11b and IEEE802.11g for WLAN and IEEE 802.15.4 for ZigBee operatingin the 2.4GHz ISM band are considered. Hence, if theiroperating bands are overlaid, the WLAN operation bandis considered to completely or significantly overlay ZigBeeoperation band [17, 52–54]. For MAC layer techniques,mandatory slotted CSMA/CA mechanisms of WLAN andZigBee are considered. We mainly focus on the operationof MAC protocols. Figures 2 and 3 illustrate the CSMA/CAmechanisms of ZigBee and WLAN devices, respectively. Theunit slot lengths of ZigBee, IEEE 802.11b, and IEEE 802.11g are
ZigBee PNCZigBee DEVWLAN APWLAN DEV
ZigBee communication linkWLAN communication linkInterference
WLAN network
ZigBee network
Figure 1: ZigBee and WLAN networks with mutual interference.
320 𝜇s, 20𝜇s, and 9 𝜇s, respectively [17, 52, 53]. ZigBee andWLAN devices decrease their backoff counter values if theshared channel is not busy. However, ZigBee device senses itsshared channel twice only after the backoff counter expires(when the backoff counter value reaches 0) while WLANalways senses its shared channel; hence, a ZigBee does notfreeze its backoff counter during other ZigBees’ transmissionsunless its backoff counter expires while WLAN freezes itduring other WLANs’ transmissions. Also, ZigBee increasesits backoff stage and randomly selects its backoff countervalue when the channel is busy or its transmitted frame iscollided while WLAN does the same procedure only whenits transmitted frame is collided.
3.2. Coexistence of ZigBee and WLAN: Medium Access Mech-anisms. Figure 4 shows three possible cases of simultaneouschannel access from ZigBee and WLAN devices when theycoexist, as shown in Figure 1. In case 1, whenWLAN starts itstransmission earlier, it ignores ZigBee transmission andkeepsits transmission procedure. Here, the WLAN transmissionincludes both successful and collided WLAN transmissions.In case 2, on the other hand, when ZigBee starts its trans-mission earlier, it detects the WLAN transmission duringCCA periods and defers its transmissions. In case 3, whenWLAN and ZigBee start their transmissions at the sametime, the WLAN transmission interferes with the ZigBeetransmission while the ZigBee transmission does not. This isdue to the difference between transmission powers ofWLANand ZigBee. Although there exists a skew between ZigBeeandWLAN transmissions in case 3, the same analysis can begiven since one ZigBee CCA duration (128 𝜇𝑠) partially occu-pies the ZigBee unit slot (320𝜇s).We statistically parametrizeWLAN interference in Section 4 in the process of modelingthe operation of ZigBees.
4 International Journal of Distributed Sensor Networks
Frame A
Frame B
Idle slot
CCA
Backoff counter value
3 2 1 0 3 2 16 5 49 8 7 0
3 2 14 03 2 145 0
ZigBee device A
ZigBee device B
Figure 2: CSMA/CA mechanism of ZigBee devices.
Frame A
Busy
Busy
Frame B
Idle slot
Backoff counter value
WLAN device A
WLAN device B
3 2 1 0
2 1 0
9 8 7 6 5 47
3 25 4 69 8 7
Figure 3: CSMA/CA mechanism of WLAN devices.
4. ZigBee Operation Model Interfered with byWLAN Transmission
4.1. ZigBee Operation: Markov Chain. The operation of aZigBee device is basically modeled by a Markov chain modelas shown in Figure 5 [32]. A node in the Markov chainrepresents a state 𝑠
𝑖,𝑗, where 𝑖 and 𝑗 are backoff stage and
backoff counter values, respectively. A directed arrow betweentwo nodes indicates the direction of state transition, andthe number on the directed arrow indicates the transitionprobability between states [55, 56].The states can be classifiedinto backoff states or nonbackoff states depending on thevalues 𝑖 and 𝑗. The backoff state is defined as {𝑠
𝑖,𝑗| 𝑖 ∈
[0, 𝑚], 𝑗 ∈ [0, 𝐶𝑊𝑖−1]}, where𝐶𝑊
𝑖is the contention window
size at backoff stage 𝑖 and 𝑚 is the maximum backoff stagevalue. The nonbackoff states are the remaining states, whichcannot be reached by the backoff procedure but can be by theCCA procedure.
A ZigBee device initializes its operation at a randomlyselected backoff state of the first row, that is, {𝑠
𝑖,𝑗| 𝑖 = 0, 𝑗 ∈
[0, 𝐶𝑊0−1]}.The ZigBee decreases its backoff counter by one
(𝑗 → 𝑗 − 1) per each backoff unit slot 𝜎 until the counterreaches 0 (𝑗 = 0). When 𝑗 reaches 0, the ZigBee performschannel sensing, called CCA, to check channel occupancy.When the first CCAoutcome informs that the channel is busy,the ZigBee increments its backoff stage by one (𝑖 → 𝑖 + 1)and randomly selects 𝑗 from [0, 𝐶𝑊
𝑖+1− 1]. If the channel is
sensed as idle, the second CCA is performed. If the secondCCA determines the channel is busy, the Zigbee does thesame procedure as the busy case of the first CCA operation.
Otherwise, the device sends its frame to its correspondingreceiver.
The transition probabilities between states are given by
P {𝑠𝑖,𝑗
| 𝑠𝑖,𝑗+1
} = 1, 𝑖 ∈ (0,𝑚) , 𝑗 ∈ (0, 𝐶𝑊𝑖− 2) ,
P {𝑠𝑖,−1
| 𝑠𝑖,0} = 1 − 𝜌, 𝑖 ∈ (0,𝑚) ,
P {𝑠𝑖,𝑗
| 𝑠𝑖−1,0
} =𝜌
𝐶𝑊𝑖
,
𝑖 ∈ (1, 𝑚) , 𝑗 ∈ (0, 𝐶𝑊𝑖− 1) ,
P {𝑠𝑖,𝑗
| 𝑠𝑖−1,−1
} =𝜁
𝐶𝑊𝑖
,
𝑖 ∈ (1, 𝑚) , 𝑗 ∈ (0, 𝐶𝑊𝑖− 1) ,
P {𝑠0,𝑗
| 𝑠𝑖,−1
} =(1 − 𝜁)
𝐶𝑊0
,
𝑖 ∈ (1,𝑚 − 1) , 𝑗 ∈ (0, 𝐶𝑊0− 1) ,
P {𝑠0,𝑗
| 𝑠𝑚,0
} =𝜌
𝐶𝑊0
, 𝑗 ∈ (0, 𝐶𝑊0− 1) ,
P {𝑠0,𝑗
| 𝑠𝑚,−1
} =1
𝐶𝑊0
, 𝑗 ∈ (0, 𝐶𝑊0− 1) ,
(1)
where 𝜌 and 𝜁 are the 1st and 2nd CCA busy probabilities,respectively. The WLAN interference is reflected in 𝜌 and𝜁 in this Markov chain. Since the parameters except 𝜌 and
International Journal of Distributed Sensor Networks 5
n ZigBee devices
Case1
Case2
Case3
ZigBee CCAZigBee data transmission
Data
Collision Collision
(ZigBee)
Data(ZigBee)
Data(ZigBee)
Interference(WLAN)
Interference(WLAN)
Interference
Deferredtransmission
(WLAN)
(WLAN) interference
Interference(WLAN)
2 1 0 23 1 0 234 1 0−1 −1−1
1 ZigBee slot =16 WLAN slots
nwl WLAN devices
Figure 4: CCA operation of ZigBee devices interfered with by WLAN.
1, 1
0, 1
1, 21, 0 1 1 1
0, 20, 0 111
111
· · ·
· · ·
· · ·
· · · · · · · · ·· · ·
1 − 𝜁
1 − 𝜁
1 − 𝜁 1 − 𝜌
1 − 𝜌
1 − 𝜌
𝜌
𝜌
𝜌𝜁
𝜁
𝜁
0, −1
1, −1
m, −1 m, 0 m, 1 m, 2
0, W0 − 2 0, W0 − 1
1, W1 − 2 1, W1 − 1
m, Wm − 2 m, Wm − 1
Figure 5: ZigBee operation model using a Markov chain concept.
𝜁 are given system parameters [17], 𝜌 and 𝜁 need to becharacterized to complete an analysis model for the ZigBeeoperation in the presence of WLAN interference.
To obtain 𝜌 and 𝜁, we tag one ZigBee which sensesthe shared channel even when 𝑗 > 0 but with turningoff the connection between the CCA and backoff counterelements1. The tagged ZigBee operates the same in the CCAand transmission modes as other normal ZigBees. As aresult, 𝜌 and 𝜁 are equal to the first and second channelbusy probabilities of this tagged ZigBee, respectively. Figure 6shows an operation example of coexisting ZigBee andWLANdevices with a tagged ZigBee. The channel busy status isdetected by the tagged ZigBee in three types of intervals:(i) only WLAN devices transmit frames (Intervals 1 and 7),(ii) only other ZigBee devices transmit frames (Intervals 2,3, and 5), or (iii) WLAN and ZigBee devices simultaneouslytransmit frames (Interval 6). Hence, 𝜌 is written by
𝜌 = 𝜌wl + 𝜌zb − 𝜌wl+zb, (2)
where 𝜌wl, 𝜌zb, and 𝜌wl+zb denote the tagged ZigBee’s firstchannel busy probabilities caused by WLAN devices, other
ZigBee devices, and both of WLAN and ZigBee devices,respectively.
Similarly, the second CCA busy probability 𝜁 is written by
𝜁 = 𝜁wl + 𝜁zb − 𝜁wl+zb, (3)
where 𝜁wl, 𝜁zb, and 𝜁wl+zb denote the tagged ZigBee’s secondchannel busy probabilities caused by WLAN devices, otherZigBee devices, and both of WLAN and ZigBee devices,respectively.
4.2. WLAN Interference Affecting ZigBee Clear ChannelAssessment Operations: 𝜌 and 𝜁. To derive 𝜌wl, WLAN trans-missions on the shared channel need to be analyzed in theviewpoint of the tagged ZigBee. Let Ψwl, 𝜎wl, and 𝑇cca be thenumber of WLAN consecutive idle slots, oneWLAN backoffunit duration in seconds, and one ZigBee CCA duration inseconds, respectively. Specifically, Ψwl is a random variable,which can be counted in a network viewpoint, determined byWLAN transmission characteristics including transmissionprobability, success probability, collision probability, frame
6 International Journal of Distributed Sensor Networks
ZigBee
ZigBee ZigBee transmission
ZigBee
ZigBee ZigBee
ZigBeeZigBee
WLAN
WLAN
WLAN WLAN interference
Collision
Inte
rval
1
Inte
rval
2
Inte
rval
3
Inte
rval
4
Inte
rval
5
Inte
rval
6
Inte
rval
7
TVTaggedZigBee device
(i − 1)th ZigBee device
ith ZigBee device
kth WLAN device
Figure 6: ZigBee transmission cases interfered with by WLAN.
length, and backoff unit duration.Then, two possible channelbusy cases due to WLAN transmission can occur: (1) oneZigBee CCAduration is shorter thanWLAN consecutive idleduration (𝑇cca < Ψwl𝜎wl) and (2) one ZigBee CCA duration islonger thanWLANconsecutive idle duration (𝑇cca > Ψwl𝜎wl).If 𝑇cca < Ψwl𝜎wl, then 𝜌wl is equal to WLAN channel activity.On the other hand, if 𝑇cca > Ψwl𝜎wl, then 𝜌wl is equal to 1.Hence, 𝜌wl is given by
𝜌wl = P {𝑇cca < Ψwl𝜎wl}
⋅ [p𝑠wl
(𝑇𝑠wl
+ 𝑇cca) + (1 − p𝑠wl
) (𝑇𝑐wl
+ 𝑇cca)
E {Ψwl} 𝜎wl + p𝑠wl
𝑇𝑠wl
+ (1 − p𝑠wl
) 𝑇𝑐wl
]
+ P {𝑇cca ≥ Ψwl𝜎wl} ,
(4)
where WLAN channel activity expressed in the first termis a function of successful transmission probability p
𝑠wl,
successful transmission duration 𝑇𝑠wl, and collision duration
𝑇𝑐wl
as well as 𝜎wl, 𝑇cca, and E{Ψwl}. Note that E{Ψwl} isa function of WLAN transmission probability 𝜅wl and thenumber of active WLAN devices 𝑛wl as follows:
E {Ψwl} =1
1 − (1 − 𝜅wl)𝑛wl
− 1. (5)
We can also approximate P{𝑇cca < Ψwl𝜎wl} as (seeAppendix A)
P {𝑇cca < Ψwl𝜎wl} = (1 − 𝜅wl)𝑛wl ⌈𝑇cca/𝜎wl⌉
, (6)
where ⌈𝑥⌉ denotes the ceiling function of 𝑥.
Using (4)–(6), we have
𝜌wl
=(1 − 𝜅wl)
𝑛wl⌈𝑇cca/𝜎wl⌉[p𝑠wl
𝑇𝑠wl
+ (1 − p𝑠wl
) 𝑇𝑐wl
]
[1/ (1 − (1 − 𝜅wl)𝑛wl
) − 1] 𝜎wl + p𝑠wl
𝑇𝑠wl
+ (1 − p𝑠wl
) 𝑇𝑐wl
+ 1 − (1 − 𝜅wl)𝑛wl⌈𝑇cca/𝜎wl⌉
.
(7)
To derive 𝜌zb, the ZigBee transmissions in terms of thetagged ZigBee need to be investigated. We first define theCCA-start probability 𝜅 of a ZigBee in backoff states as
𝜅 =∑𝑚
𝑖=0𝜋𝑖,0
∑𝑚
𝑖=0∑𝑊𝑖−1
𝑗=0𝜋𝑖,𝑗
=2 [1 − (𝜌 + 𝜁 − 𝜌𝜁)
𝑚+1]
∑𝑚
𝑖=0(C𝑊02𝜂𝑖 + 1) (𝜌 + 𝜁 − 𝜌𝜁)
𝑖
×1
1 − (𝜌 + 𝜁 − 𝜌𝜁),
(8)
where 𝜋𝑖,𝑗
is the stationary probability of 𝑠𝑖,𝑗
and 𝜂𝑖is the
additional backoff exponent value of backoff stage 𝑖2. The
denominator is a summation over backoff states ({𝑠𝑖,𝑗
|
𝑖 ∈ [0, 𝑚], 𝑗 ∈ [0, 𝐶𝑊𝑖− 1]}) since CCA-start probability
assumes that a device is in the backoff states. 𝜂max and 𝜂minare the maximum and minimum backoff exponent values,respectively. Then, we have 𝜂
𝑖= min {𝑖, 𝜂max − 𝜂min}. Due
to 𝑛 − 1 other ZigBee transmissions, two possible channelbusy events of the tagged ZigBee can occur: successful andcollided transmissions of other ZigBees. In the successfultransmission interval, only one of other ZigBees reaches theCCA-start state with probability (𝑛 − 1)𝜅(1 − 𝜅)
𝑛−1, andWLAN devices do not interfere for two consecutive CCAs
International Journal of Distributed Sensor Networks 7
with probability (1 − 𝜌wl)(1 − 𝜁wl) and do not transmitduring total ZigBee communication time with probability(1 − 𝜅wl)
⌈𝐿 tx(𝜎/𝜎wl)⌉𝑛wl , where 𝐿 tx(𝜎/𝜎wl) denotes total Zig-Bee communication time. In the collided transmission, atleast two other ZigBee devices reach the CCA-start state
simultaneously with probability (1 − 𝜅)[1 − (1 − 𝜅)𝑛−1
−
(𝑛 − 1)𝜅(1 − 𝜅)𝑛−2
], and WLAN devices do not interfere fortwo consecutive CCAs (1 − 𝜅wl)
⌈𝐿 tx(𝜎/𝜎wl)⌉𝑛wl . Let p𝑡and p
𝑠
be transmission and successful transmission probabilities ofZigBees except the tagged ZigBee, respectively.Then, we have
where 𝐿𝑓is the ZigBee frame length, 𝛿 is the acknowledge-
ment waiting time, and 𝐿ack is the acknowledgement framelength. ⌊𝑥⌋ denotes the floor function of 𝑥.
Consider that T1,T2, . . . is a sequence of intervals of suc-
cessful transmissions of the tagged ZigBee, and W1,W2, . . .
is a sequence of channel busy duration in T1,T2, . . ., respec-
tively. T1,T2, . . . is a sequence of positive independent and
identically distributed random variables such that
0 < E {T𝑖} < ∞ (10)
and W1,W2, . . . is a sequence of random variables (rewards)
satisfying
E {W𝑖} < ∞. (11)
Let Y𝑡= ∑
K𝑡𝑖=1
𝑊𝑖where K
𝑡= sup{𝑛 : J
𝑛≤ 𝑡} and J
𝑛= ∑𝑛
𝑖=1T𝑖.
Using the elementary renewal theorem for renewal rewardprocesses, we have
lim𝑡→∞
1
𝑡E {Y𝑡} =
E {W1}
E {T1}. (12)
Using (12), 𝜌zb is given by
𝜌zb =p𝑡[p𝑠𝐿bs + (1 − p
𝑠) 𝐿bc]
p𝑡[p𝑠𝐿𝑠+ (1 − p
𝑠) 𝐿𝑐] + (1 − p
𝑡), (13)
where 𝐿𝑠and 𝐿
𝑐are successful transmission and collision
duration in ZigBee unit slots, respectively, and 𝐿bs and 𝐿bcare busy duration out of 𝐿
𝑠and 𝐿
𝑐, respectively.
𝜌wl+zb is approximated as
𝜌wl+zb ≈ 𝜌zb [
[
1 −
Uwl (1 − U⌈𝐿𝑓⌉+⌊𝛿⌋+⌈𝐿ack⌉
wl )
1 − Uwl
⋅1
⌈𝐿𝑓⌉ + ⌊𝛿⌋ + ⌈𝐿ack⌉
]
]
,
(14)
whereUwl = (1−𝜅wl)(𝜎/𝜎wl)𝑛wl is the probability that 𝑛wlWLAN
devices do not transmit data during 𝜎 (see Appendix B).Substituting (7), (13), and (18) into (2), we finally get 𝜌.
For the second CCA, two possible busy events can occur:(i) Ψwl𝜎wl > 𝜎 + 𝑇cca, that is, WLAN has longer consecutiveidle duration compared to a unit backoff slot plus one CCAduration of a ZigBee, and (ii) 𝑇cca ≤ Ψwl𝜎wl ≤ 𝜎 + 𝑇cca, thatis, WLAN consecutive idle duration is in the range from oneZigBee CCA duration to a ZigBee backoff unit slot plus oneZigBee CCA duration. Hence, we have
𝜁wl ≈ P {Ψwl𝜎wl > ⌈𝑇cca⌉ + 𝑇cca} (1
1 − 𝜌wl)
⋅⌈𝑇cca⌉
E {Ψwl} 𝜎wl + p𝑠wl
𝑇𝑠wl
+ (1 − p𝑠wl
) 𝑇𝑐wl
+
(⌈Tcca⌉+𝑇cca)/𝜎wl
∑
𝑥=𝑇cca/𝜎wl
P {Ψwl = 𝑥} (1
1 − 𝜌wl)
⋅(𝑥𝜎wl − 𝑇cca)
E {Ψwl} 𝜎wl + p𝑠wl
𝑇𝑠wl
+ (1 − p𝑠wl
) 𝑇𝑐wl
.
(15)
Using the approximations of P{Ψwl𝜎wl > ⌈𝑇cca⌉ + 𝑇cca} andP{Ψwl = 𝑥} in Appendix A, we get 𝜁wl
𝜁wl ≈ (1
1 − 𝜌wl)
(1 − 𝜅wl)𝑛wl⌈(⌈𝑇cca⌉+𝑇cca)/𝜎wl⌉
⌈𝑇cca⌉
E {Ψwl} 𝜎wl + p𝑠wl
𝑇𝑠wl
+ (1 − p𝑠wl
) 𝑇𝑐wl
+ (1
1 − 𝜌wl)
⋅
∑(⌈𝑇cca⌉+𝑇cca)/𝜎wl𝑥=𝑇cca/𝜎wl
(1 − 𝜅wl)𝑛wl(𝑥−1)
[1 − (1 − 𝜅wl)𝑛wl
] (𝑥𝜎wl − 𝑇cca)
E {Ψwl} 𝜎 + p𝑠wl
𝑇𝑠wl
+ (1 − p𝑠wl
) 𝑇𝑐wl
.
(16)
In addition,
𝜁zb = (1
1 − 𝜌zb)
⋅p𝑡[p𝑠𝐿 is + (1 − p
𝑠) 𝐿 ic]
p𝑡[p𝑠𝐿𝑠+ (1 − p
𝑠) 𝐿𝑐] + 𝜅 + (1 − 𝜅 − p
𝑡),
(17)
where 𝐿 is and 𝐿 ic denote the duration during which thesecond busy CCA events occur out of 𝐿
𝑠and 𝐿
𝑐, respectively.
The second CCA is considered to be busy during the firstslot of data or the acknowledgement transmission in thesuccessful transmission case (p
𝑠) while it is considered to be
busy, in the collision case (1 − p𝑠), during the first slot of data
transmission. Hence, 𝐿 is = 2⌈𝐿cca⌉ and 𝐿 ic = ⌈𝐿cca⌉.
8 International Journal of Distributed Sensor Networks
Again, we have
𝜁wl+zb ≈ 𝜁zb [
[
1 − p𝑠
Uwl (1 − U𝐿 iswl )
(1 − Uwl)
1
𝐿 is
− (1 − p𝑠)Uwl (1 − U
𝐿 icwl )
(1 − Uwl)
1
𝐿 ic]
]
,
(18)
where the second and third terms represent the ratios ofsimultaneous transmissions among ZigBee transmissionsmaking the second CCA busy in the successful and collidedtransmission cases, respectively (see Appendix B). Substitut-ing (16), (17), and (18) into (3), we finally get 𝜁.
5. Adaptive Interference Avoidance Algorithm
Our proposed algorithm adaptively controls ZigBee trans-missions based on the amount of WLAN interference tomaximize the performance of ZigBee network. Our proposedmethodbasically assumes thatWLANdevices highly contendfor channel access. First, a WLAN AP estimates the WLANchannel activity 𝜌wl. The WLAN channel activity 𝜌wl ismonitored by a WLAN AP. For the number of associatedWLAN nodes, a WLAN AP can keep track of it. However,some associated WLAN nodes may be inactive while theothers are active. Here, it is difficult for a WLAN AP todirectly know about the number𝑁wl of active WLAN nodes.The channel activity is reflected in∑
𝑐−1
𝑖=0𝐴[𝑚]𝑖and∑
𝑐−1
𝑖=0𝐵[𝑚]𝑖
in (21) and (22), which are used to calculate 𝑁wl in (20).WLAN AP then informs ZigBee of 𝑁wl and 𝜌wl from whichthe PNC calculates the number 𝑁
∗
zb of ZigBee devices aswell as the length 𝐿
∗
zb for each ZigBee frame. The PNCbroadcasts 𝑁
∗
zb and 𝐿∗
zb to ZigBee devices which decide ifthey send data or not considering 𝑁
∗
zb and the total numberof Zigbee devices. This situation can be feasibly given whenthere are devices having bothWLAN and ZigBee modules ina network. If a ZigBee device transmits, it sends its frame aftersegmenting the frame into the length of 𝐿∗zb. This procedurerepeats periodically.
5.1. Autoregressive-Moving-Average (ARMA) Estimation of𝑁wl. 𝑁wl is estimated using the following expression [34]:
𝑁wl =log (1 − 𝑝wl)
log (1 − 𝜅wl)+ 1, (19)
where 𝜅wl and 𝑝wl are WLAN transmission and collisionprobabilities, respectively. The estimation of 𝜅wl and 𝑝wl isderived by ARMA(𝛽,𝑐) [57]. First, 𝜅wl is estimated as follows:
𝜅wl [𝑚 + 1] = 𝛽𝜅wl [𝑚] +(1 − 𝛽)
𝑐
𝑐−1
∑
𝑖=0
𝐴 [𝑚]𝑖 , (20)
where 𝑐 and 𝛽 are the number of measured samples andARMAmodel parameter, respectively. 𝜅wl[𝑚] is transmissionprobability in the 𝑚th beacon interval. 𝐴[𝑚]
𝑖is 1 only if AP
observes the beginning of the WLAN station’s transmission
at the 𝑖th slot of the𝑚th beacon interval. Otherwise,𝐴[𝑚]𝑖is
0.Collision probability 𝑝wl is similarly estimated as follows:
𝑝wl [𝑚 + 1] = 𝛽𝑝wl [𝑚] +(1 − 𝛽)
𝑐
𝑐−1
∑
𝑖=0
𝐵 [𝑚]𝑖 , (21)
where 𝑝wl[𝑚] is collision probability in the 𝑚th beaconinterval and 𝐵[𝑚]
𝑖is 0 when the WLAN station observes
the channel is idle or successfully transmits its frame atthe 𝑖th slot of the 𝑚th beacon interval. On the other hand,𝐵[𝑚]𝑖is 1 when the WLAN station observes the channel
is busy or transmits with collisions. We estimate 𝑝wl and𝜅wl periodically and recursively at the end of every beaconinterval. When 𝑝wl is equal to 0, 𝑁wl is estimated to be 1.
5.2. Determination of 𝑁∗zb and 𝐿∗
zb. ZigBee determines 𝑁∗
zband 𝐿
∗
zb whichmaximize ZigBee performance measures suchas throughput, energy consumption, or delay.
The normalized throughput S is defined as
S
=successfully transmitted bits in a ZigBee network
observation time (secs)
×1
𝑅,
(22)
where𝑅denotes ZigBee PHYdata rate. Regarding the averagetime of state transition as a renewal period, E{S} can beexpressed as [32]
where 𝐿𝑝is payload length in slots and 𝛾 is successful
frame transmission probability after two successful CCAs.Since ZigBees sense a shared channel for only two successfulCCAs, the frame successful transmission after CCAs is onlydependent onWLAN transmissions. Hence, considering that⌈⌈𝐿 tx⌉(𝜎/𝜎wl)⌉ is the number of WLAN slots within 𝐿 tx, 𝛾 isexpressed as
𝛾 = (1 − 𝜅wl)⌈⌈𝐿 tx⌉(𝜎/𝜎wl)⌉𝑁wl
, (24)
where 𝐿 tx and 𝜎wl are transmission length in slots andWLAN’s unit time, respectively.
The energy consumption E is defined as the amount ofenergy consumed per transmission unit slot by a ZigBee
International Journal of Distributed Sensor Networks 9
where 𝐸rx, 𝐸𝑠, and 𝐸𝑐are consumed energies for reception,
successful transmission, and collision, respectively.Access delayD is defined as elapsed interval from the time
when the frame reaches the head-of-line of a transmitter’sbuffer and the time when the frame arrives at a receiverwithout collision. By Little’s law [35], E{D} is given as
E {D} =𝑛
E {S} /𝐿𝑝⋅ 𝜎, (26)
where E{S}/𝐿𝑝
represents ZigBee frame delivery rate.Throughput, energy consumption, and delay are affectedby WLAN parameters, for example, 𝑁wl and 𝜌wl (or 𝜅wl)as shown in (23), (25), and (26). After receiving ��wl and𝜅wl from a WLAN AP, the ZigBee PNC finds 𝑁
∗
zb and 𝐿∗
zbthat maximize required performance index, for example,throughput, energy consumption, or delay, depending onservice requirements. For example, if ��wl and 𝜅wl are 3and 0.12 with a constraint that energy consumption shouldbe minimized, then the ZigBee PNC finds 𝑁
∗
zb and 𝐿∗
zbminimizing (25). And it can be a problem if the energy con-sumption in calculating the number of interference nodes,𝑁∗
zb and 𝐿∗
zb, surpasses the transmission energy saved by ourproposed algorithm. However, the relatively stable nature ofWLAN condition enables us to assume that the calculationdoes not occur too frequently. To reduce the computationalcomplexity of the algorithm, we made a matching table inadvance, which has inputs of 𝑁wl and 𝜌wl and gives outputsof 𝑁∗zb and 𝐿
∗
zb from the table.
6. Numerical Result
We configured coexisting ZigBee andWLANnetworks usingOPNET Modeler 14.5 as shown in Figure 7 and Matlab. AZigBee network interfered with by saturated and unsaturatedWLAN nodes is considered. Here, all the ZigBee devices in anetwork are considered to be affected byWLAN interference.
In our interference analysis, ZigBee devices are assumedto always have frames to transmit while IEEE 802.11b/gWLAN devices are considered to have frames that arrive attheir buffers in a Poisson manner with the intensity of 𝜆wl.Hence, when we define qwl as the probability ofWLAN trafficgeneration in each slot, qwl = Exp(−𝜆wl𝑇). This analysis canbe regarded as saturationmode analysis by increasing𝜆wl andqwl. 𝜅wl is expressed as in [41]:
𝜅wl = 𝜋𝑒wl0,0
(q2wl𝑊0wl
(1 − pwl) (1 − qwl) (1 − (1 − qwl)𝑊0wl )
−q2wl (1 − pwl)
1 − qwl) ,
(27)
where 𝜋𝑒wl0,0
is stationary probability of a device which has abackoff counter value of zero with no waiting frame. pwl isthe collision probability of a device. The expected slot timeE{T} can be derived as
𝐿𝑓𝐸tx + (⌊𝛿⌋ + Tack)𝐸rx, respectively.Our analysis framework is verified by comparing
throughput, delay, and energy consumption obtained fromour framework with those from simulation results. Eachsimulation point is obtained by averaging over fifteensimulation run results with the duration of 600 seconds.The range bars are also drawn on the plot. Figure 8 shows aZigBee network’s normalized throughput E{S} with varyingWLAN interference load 𝜆wl when 𝑛 and 𝑛wl are fixed to25 and 3. The analytical results obtained from the proposedmodel are validated and agree well with the simulationresults. When the length of a ZigBee frame 𝐿
𝑓is equal to
8 and 𝜆wl is set to 0.047, E{S} is equal to 0.09. However, ifthe ZigBee network is interfered with by the WLAN with𝜆wl = 0.116, E{S} decreases to 0.03. Fixing 𝜆wl to 0.047, E{S}increases as 𝐿
𝑓,slot gets larger because WLAN interference isnot severe. However, when 𝜆wl = 0.139, as 𝐿
𝑓increases from
8 to 12, E{S} does not significantly change since the ZigBeeframe is exposed to severe WLAN interference which causesmore collisions between ZigBee and WLAN transmissions.Here, E{S} exhibits a steeper decrease as 𝐿
𝑓gets larger.
Figures 10 and 12 show mean energy consumption E{E} andaccess delay E{D} for varying 𝜆wl. Similar to E{S}, as 𝐿
𝑓gets
larger, E{E} and E{D} abruptly get worse. Figures 9, 11, and13 show E{S}, E{E}, and E{D} of a ZigBee network when 𝑛wlincreases from 3 to 6 with the fixed total amount of WLANnetwork load, 𝜆wl. The ZigBee performance is slightlydegraded when 𝑛wl increases from 3 to 6 since more WLANdevices generate less ZigBee’s transmission opportunitiesdue to WLAN devices’ increased contention on the sharedchannel. However, this degradation is not considerablesince the total traffic load 𝜆wl is fixed and shared by WLANdevices.
For the saturated WLAN mode, the estimation of 𝑁wlis done by simply measuring 𝜅wl and 𝑝wl. Figure 7 showsa ZigBee network interfered with by WLAN interferers,where six Zigbee devices always have frames to transmit to acoordinator while WLAN transmissions are simply modeled
10 International Journal of Distributed Sensor Networks
Table 1: WLAN and ZigBee related parameter values.
Parameter Value Description𝐸rx 0.0113472mJ Energy consumption for ZigBee to receive (mJ)𝐸tx 0.0100224mJ Energy consumption for ZigBee to transmit (mJ)𝐿ack 1.1 slots Length of Ack frame in ZigBee𝐿 cca 0.4 slots One ZigBee CCA duration𝐿𝑓
4∼20 slots Length of a frame in ZigBee𝐿nack 1.1 slots Length of Nack duration in ZigBee𝐿𝑝
𝐿𝑓× 80 − 120 bits Length of payload in ZigBee (bits)
𝑇collwl 944 𝜇s Length of collided transmission in WLAN (sec)𝑇𝑝wl
364 𝜇s Length of payload in WLAN (sec)𝑇succwl 944 𝜇s Length of successful transmission in WLAN (sec)𝛿 1 slot Duration of Ack wait in ZigBee𝜎 320 𝜇s Length of one backoff unit in ZigBee (sec)𝜎wl 20 𝜇s Unit slot length of one backoff unit in WLAN (sec)
Figure 7: Our test coexisting environment.
by the M/G/1 model. Here, the PNC is considered to beequipped with WLAN AP functionality. Figures 14(a) and14(b) show E{S} of a ZigBee network, the former withoutour proposed algorithm and the latter with the algorithm.We initially set the number 𝑛wl of WLAN devices to 0.We sequentially added more WLAN interference load byincreasing 𝑛wl to 1, 2, and 3, respectively, and set 𝑛wl back to
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
Nor
mal
ized
thro
ughp
ut,S
0 0.02 0.04 0.06 0.08 0.1 0.12
nzb = 25, nwl = 3
WLAN load 𝜆wl
Lfzb = 4
Lfzb = 8Lfzb = 12
Figure 8: Throughput of a ZigBee network interfered with byWLAN devices (𝑛wl = 3).
0. Here, the proposed algorithm focuses on controlling theZigBee frame length 𝐿zb without controlling 𝑛zb, in orderto minimize the algorithm computational complexity. Thelength of ZigBee frames is initially set to 1600 bits. Theproposed algorithm shows consequently higher throughputin the overall range of 𝑛wl. For every 5 minutes, the avoidancealgorithm shows E{S} around 170,000, 0, 0, 0, and 170,000for 0–5, 5–10, 10–15, 15–20, and 20–25 minutes’ intervals,respectively, and the ZigBee operation without the avoidancealgorithm gives the same.
For the nonsaturated WLAN mode, the estimation of𝑁wl needs additional information such as a WLAN traf-fic model. However, this additional information about theWLAN traffic model is difficult to be known in advance. Asmentioned, hence, our model assumes that WLAN devices
International Journal of Distributed Sensor Networks 11
0.25
0.2
0.15
0.1
0.05
00 0.05 0.1 0.15 0.2 0.25
Nor
mal
ized
thro
ughp
ut,S
nzb = 25, nwl = 6
WLAN load 𝜆wl
Lfzb = 4
Lfzb = 8Lfzb = 12
Figure 9: Throughput of a ZigBee network interfered with byWLAN devices (𝑛wl = 6).
0 0.02 0.04 0.06 0.08 0.1 0.12
3
2.5
2
1.5
1
0.5
0
Ener
gy co
nsum
ptio
n of
a Zi
gBee
stat
ion
per s
lot, nzb = 25, nwl = 3
WLAN load, 𝜆wl
Lfzb = 4
Lfzb = 8Lfzb = 12
E(m
J/slo
t)
Figure 10: Energy consumption of a ZigBee network interferedwithby WLAN devices (𝑛wl = 3).
highly contend for channel access. The number of interferingWLAN devices is increased by one (from zero to three)every 5 minutes as in the saturated WLANmode. The lengthof WLAN frames is set to 4800 𝜇s with input load of 0.04while that of ZigBee frames is initially set to 1600 bits. Here,the proposed algorithm focuses on adapting this length ofZigBee frames 𝐿zb to measured WLAN interference with 𝑛zbmaintained. The throughput of the ZigBee network withoutinterference avoidance algorithms is around 170,000, 130,000,
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090
0.2
0.4
0.6
0.8
1
1.2
1.4nzb = 25, nwl = 6
Ener
gy co
nsum
ptio
n of
a Zi
gBee
stat
ion
per s
lot,
E(m
J/slo
t)
WLAN load, 𝜆wl
Lfzb = 4
Lfzb = 8Lfzb = 12
Figure 11: Energy consumption of a ZigBee network interfered withby WLAN devices (𝑛wl = 6).
0
5
10
15
20
25
30
35
40
0 0.02 0.04 0.06 0.08 0.1 0.12
Mea
n ac
cess
del
ay,D
(ms)
WLAN load 𝜆wl
Lfzb = 4
Lfzb = 8Lfzb = 12
nzb = 25, nwl = 3
Figure 12: Delay of a ZigBee network interfered with by WLANdevices (𝑛wl = 3).
100,000, 70,000, and 170,000 bits/sec for 0–5, 5–10, 10–15, 15–20, and 20–25 minutes’ intervals, respectively, as shown inFigure 15(a). Meanwhile, the proposed avoidance algorithmenhances the performance of the ZigBee network by showingbetter throughput 170,000, 140,000, 120,000, 105,000, and170,000 bits/sec for 0–5, 5–10, 10–15, 15–20, and 20–25 min-utes’ intervals, respectively, as shown in Figure 15(b). Thereis no error in measuring 𝑁wl during 5–10 minutes’ intervalsince 𝑁wl is equal to one. However, errors are introduced inmeasuring 𝑁wl during 10–15 and 15–20 minutes’ intervals,
12 International Journal of Distributed Sensor Networks
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.094
6
8
10
12
14
16
18
20
22
24
Mea
n ac
cess
del
ay,D
(ms)
WLAN load 𝜆wl
Lfzb = 4
Lfzb = 8Lfzb = 12
nzb = 25, nwl = 6
Figure 13: Delay of a ZigBee network interfered with by WLAN devices (𝑛wl = 6).
Time (min)0 5 10 15 20 25
Thro
ughp
ut (b
its/s
)
0
2
4
6
8
10
12
14
16
18×104
(a) Conventional algorithm
Time (min)0 5 10 15 20 25
Thro
ughp
ut (b
its/s
)
0
2
4
6
8
10
12
14
16
18×104
(b) Proposed algorithm
Figure 14: Throughput of a ZigBee network with conventional and proposed algorithms interfered with by WLAN in the saturation mode.
that is, three and four, respectively, due to frequent collisionsfrom hidden WLAN nodes. Since the optimum throughputof around 170,000, 145,000, 125,000, 105,000, and 170,000coming from the accurate estimation of𝑁wl is higher than thethroughput of our proposed algorithm, it gives better resultsif we can accurately measure 𝑁wl.
7. Conclusion
In this paper, we have proposed a unified analysis frameworkfor the ZigBee operation in a ZigBee network interfered withby heterogeneous WLAN networks. Moreover, we proposedan efficient WLAN interference avoidance algorithm for aZigBee network which controls ZigBee frame length and
devices based on the measured WLAN interference in anadaptive way. WLAN interferences are modeled based on thecurrent IEEE 802.11 to consider realistic effects of interferenceon a ZigBee network’s performance while a ZigBee networkis also modeled based on the current IEEE 802.15.4 with aMarkov chain concept. The simulation results show a closeagreement to the analytical results obtained from our frame-work. The proposed interference avoidance algorithm hasshown the improvement of ZigBee networks’ performance byadapting the ZigBee frame length to the WLAN interferencelevel. The simulation results show that the proposed andconventional algorithms give similar performance when theWLAN interferers in the saturated mode interfere withZigBee networks. However, when the number of WLAN
International Journal of Distributed Sensor Networks 13
Time (min)0 5 10 15 20 25
Thro
ughp
ut (b
its/s
)
0
×105
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
(a) Conventional algorithm
Thro
ughp
ut (b
its/s
)
0
×105
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
Time (min)0 5 10 15 20 25
(b) Proposed algorithm
Figure 15: Throughput of a ZigBee network with conventional and proposed algorithms interfered with by WLAN in the nonsaturationmode.
interferers is in the nonsaturated mode, the proposed algo-rithm gives better ZigBee performance than the conventionalalgorithm. In particular, as the number of nonsaturatedWLAN interferers with the input load of 0.04 increases, theproposed algorithm shows a small drop in performancewhilethe conventional algorithm does a large drop. This is due tothe algorithm’s operation of adapting the length of ZigBees’frames to the measured WLAN interference.
We expect that the proposed analysis framework can beutilized in predicting the performance of ZigBee networksin the presence of heterogeneous WLAN networks as wellas design of the parameter settings for efficient ZigBeecommunication. Also, our proposed unified analysis of aZigBee network can be applied in predicting and designingvarious types of coexisting heterogeneous communicationnetworks.
Appendices
A. Approximation of P{Ψwl𝜎wl ≤Tcca}, P{Ψwl𝜎wl >
⌈Tcca⌉ + Tcca}, and P{Ψwl = 𝑥}
P{Ψwl𝜎wl ≤ Tcca} can be approximated to P{Ψwl ≤
⌈Tcca/𝜎wl⌉}. P{Ψwl ≤ ⌈Tcca/𝜎wl⌉} means the number ofWLAN consecutive idle slots is equal to or smaller than thenumber of slots, that is, Tcca/𝜎wl. This can be derived by thesummation of all the probabilities, from the probability thatWLAN transmits its frame directly at the first slot to theprobability that WLAN transmits at the ⌈Tcca/𝜎wl⌉th slot asfollows:
P {Ψwl𝜎wl ≤ 𝑇cca} ≈ P{Ψwl ≤ ⌈𝑇cca𝜎wl
⌉}
= {1 − (1 − 𝜅wl)𝑛wl
}
⌈𝑇cca/𝜎wl⌉−1
∑
𝑖=0
{(1 − 𝜅wl)𝑛wl
}𝑖
= {1 − (1 − 𝜅wl)𝑛wl
}{1 − (1 − 𝜅wl)
𝑛wl}⌈𝑇cca/𝜎wl⌉
1 − (1 − 𝜅wl)𝑛wl
= 1 − (1 − 𝜅wl)𝑛wl ⌈𝑇cca/𝜎wl⌉
.
(A.1)Similarly, P{Ψwl𝜎wl > ⌈𝑇CCAwl
⌉ + 𝑇CCA} and P{Ψwl = 𝑥} canbe expressed as
P {Ψwl𝜎wl > ⌈𝑇cca⌉ + 𝑇cca}
≈ (1 − 𝜅wl)𝑛wl ⌈(⌈𝑇cca⌉+𝑇CCA)/𝜎wl⌉
,
P {Ψwl = 𝑥} ≈ {(𝜅wl)𝑛wl
}𝑥−1
{1 − (1 − 𝜅wl)𝑛wl
} .
(A.2)
B. Approximation of 𝜌wl+zb
We define Uwl as the probability that none of 𝑛wl WLANdevices interfere with ZigBee data transmissions during aZigBee unit slot, given that the previous slot was not occupiedby the transmission of WLAN devices. Uwl can be expressedas {(1 − 𝜅wl)
𝜎/𝜎wl}𝑛wl , where 𝜎/𝜎wl represents the number of
WLAN backoff unit slots in a ZigBee unit backoff slot. Whenthe length of a frame is denoted by 𝐿
𝑓𝑥= ⌈𝐿
𝑓⌉ + ⌊𝛿⌋ +
⌈𝐿ack⌉, the average fraction 𝑧 of the collided part out of 𝐿𝑓𝑥is
expressed as
z = 𝐿𝑓𝑥
− {Uwl (1 − Uwl) + 2U2
wl (1 − Uwl) + ⋅ ⋅ ⋅
+ (𝐿𝑓𝑥
− 1)U𝐿𝑓𝑥−1
wl (1 − Uwl) + 𝐿𝑓𝑥U𝐿𝑓𝑥
wl } .
(B.1)
Then z is equal to 𝐿𝑓𝑥
− X, where
X = Uwl (1 − Uwl) + 2U2
wl (1 − Uwl) + ⋅ ⋅ ⋅
+ (𝐿𝑓𝑥
− 1)U𝐿𝑓𝑥−1
wl (1 − Uwl) + 𝐿𝑓𝑥U𝐿𝑓𝑥
wl .
(B.2)
14 International Journal of Distributed Sensor Networks
Rearranging X yields (B.3):
(1 − Uwl)X = Uwl (1 − Uwl) + U2
wl (1 − Uwl) + ⋅ ⋅ ⋅
+ U𝐿𝑓𝑥−1
wl (1 − Uwl) + U𝐿𝑓𝑥
wl (1 − Uwl) .
(B.3)
Finally, X is derived as
X = Uwl + U2
wl + ⋅ ⋅ ⋅ + U𝐿𝑓𝑥−1
wl + U𝐿𝑓𝑥
wl
=
Uwl (1 − U𝐿𝑓𝑥
wl )
(1 − Uwl).
(B.4)
Since 𝜌wl+zb is defined as the collided ratio due to simultane-ous ZigBee and WLAN transmissions, 𝜌wl+zb = 𝜌𝑧/𝐿
𝑓𝑥.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
Acknowledgment
This researchwas supported in part by Basic Science ResearchProgram through theNational Research Foundation of Korea(NRF) funded by theMinistry of Science, ICT& Future Plan-ning (NRF-2012R1A1A1041835) and in part by the ResearchGrant of Kwangwoon University in 2015.
Endnotes
1. This assumption does not affect the original ZigBeenetwork operation since the tagged ZigBee in the statesof 𝑗 > 0 does not cease to decrease its backoff countereven when the channel is sensed to be busy.
2. If the Markov chain is time-homogeneous, irreducible,positive recurrent, and aperiodic, then the chain con-verges to the stationary distribution regardless of itsinitial condition [55]. The stationary distribution 𝜋
𝑖,𝑗
satisfies the equation
𝜋 = 𝜋P,
where 𝜋 = [𝜋𝑖,𝑗] and P is state transition probability
matrix.
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