Research Article Wi-Fi Coexistence with Duty Cycled LTE-U · Wi-Fi collision probability; when...

Research ArticleWi-Fi Coexistence with Duty Cycled LTE-U

Yimin Pang,1 Alireza Babaei,2 Jennifer Andreoli-Fang,3 and Belal Hamzeh3

1Department of Electrical, Computer and Energy Engineering, University of Colorado Boulder, Boulder, CO 80309, USA2Ofinno Technologies, Herndon, VA, USA3Cable Television Laboratories, Louisville, CO, USA

Correspondence should be addressed to Yimin Pang; [email protected]

Received 1 July 2016; Revised 17 September 2016; Accepted 18 October 2016; Published 15 January 2017

Academic Editor: Adlen Ksentini

Copyright © 2017 Yimin Pang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Coexistence of Wi-Fi and LTE-Unlicensed (LTE-U) technologies has drawn significant concern in industry. In this paper, weinvestigate the Wi-Fi performance in the presence of duty cycle based LTE-U transmission on the same channel. More specifically,one LTE-U cell and one Wi-Fi basic service set (BSS) coexist by allowing LTE-U devices to transmit their signals only inpredetermined duty cycles.Wi-Fi stations, on the other hand, simply contend the shared channel using the distributed coordinationfunction (DCF) protocol without cooperation with the LTE-U system or prior knowledge about the duty cycle period or dutycycle of LTE-U transmission. We define the fairness of the above scheme as the difference between Wi-Fi performance loss ratio(considering a defined reference performance) and the LTE-U duty cycle (or function of LTE-U duty cycle). Depending on theinterference to noise ratio (INR) being above or below −62 dbm, we classify the LTE-U interference as strong or weak and establishmathematical models accordingly. The average throughput and average service time of Wi-Fi are both formulated as functions ofWi-Fi and LTE-U system parameters using probability theory. Lastly, we use the Monte Carlo analysis to demonstrate the fairnessof Wi-Fi and LTE-U air time sharing.

1. Introduction

The rapidly growing demand of wireless network serviceshas led the mobile network operators (MNOs) to look intothe possibility of exploring unlicensed spectrum to offloadthe data traffic from the licensed bands. Most recently,3GPP and other industry alliances are considering extendingLTE into the unlicensed spectrum (3GPP has completedstandardization of license assisted access (LAA) in release13 (DL only) and enhanced LAA (eLAA) standardization,where UL access to unlicensed spectrum is also consideredand is currently ongoing in 3PP release 14. LAA and eLAAincorporate listen-before-talk (LBT) for their channel accessto the unlicensed spectrum. In addition, the LTE-U forum,an industry alliance formed by some vendors and mobileoperators, has released an LTE supplemental downlink (SDL)coexistence specification, where an adaptive duty cycle basedcoexistence scheme is introduced.The term “LTE-U” is usedinstead of “LAA” in the LTE-U forum specification. Sincethis paper focuses on duty cycle based LTE on unlicensed

spectrum, we use the short term LTE-U for convenience.However, the channel access approach introduced in thispaper is not completely aligned with the channel accessmethod introduced by the LTE-U forum specification due tononadaptive duty cycle), to offload part of the LTE data trafficonto the unlicensed spectrum. Compared to data offloadusing Wi-Fi, this approach has the advantage of seamlessintegration into the existing LTE evolved packet core (EPC)architecture. In a proposal outlined in [1], three LTE-Umodesare introduced as supplement downlink, TD-LTE-U carrieraggregation, and standalone, the first two of which wereproposed to 3GPP as possible candidates.

Coexistence of heterogeneous networks such as Wi-Fiand LTE-U on the same band and their uncoordinated opera-tions can potentially cause significant interference, degradingthe performance of both systems. Solutions to manage theinterference between such systems are therefore necessaryfor their successful coexistence. One straightforwardmethodis to split the common radio channel through air timesharing between the Wi-Fi and LTE-U subsystems. With

Hindawi Publishing Corporation

Wireless Communications and Mobile Computing

Volume 2017, Article ID 6486380, 10 pages

https://doi.org/10.1155/2017/6486380

2 Wireless Communications and Mobile Computing

Duty cycle period

LTE offLTE on LTE on

Duty cycle:Time

Wi-Fi access gapswhen LTE is off% of cycle LTE is active

Figure 1: Air time sharing LTE-U.

this approach, LTE-U operates over the shared channelperiodically (more specifically, the radio resources of LTE-Uthat reside in the unlicensed spectrum and are shared withWi-Fi are utilized periodically), and during each period (theso-called duty cycle period, denoted as "), only a portion(defined by the LTE-U duty cycle #) of the time is utilized forthe LTE-U transmission, as shown in Figure 1. In this scheme,Wi-Fi has no cooperation with LTE-U. Wi-Fi stations haveneither knowledge about the time length of duty cycle periodnor the duty cycle; they simply access the shared channel bystandard channel sensing and random back-offmechanisms.

In an LTE system, each user equipment (UE) commu-nicates with a base station (eNB) in a deterministic mannerthrough a centralized channel access controlmechanism.Theaccess time and OFDM subcarriers of an LTE frame arepredetermined at eNB, where the MAC scheduler considersthe radio measurement and quality of service needed foreach UE in its scheduling decisions. Given the above timesharing scheme and the LTE’s centralized access structure,computation of the LTE-U performance in terms of through-put and service time is relatively simple and straightforward.However, themedium accessmechanism used byWi-Fi, con-trolled by distributed coordination function (DCF) protocoldefined in IEEE 802.11 standard, is random and distributed.Therefore, we focus on the impact of LTE-U interference onWi-Fi performance in this paper.

1.1. Previous Works. LTE-U and Wi-Fi coexistence are arelatively new area of research. Previous works in thisarea are summarized as follows: in [2], Wi-Fi and LTE-Ucoexistence in single floor and multiple floors environmentat various densities are simulated. The results show that,without any interferencemanagement scheme, LTE-U systemperformance is slightly affected from Wi-Fi, whereas Wi-Fiis significantly impacted by the LTE-U transmissions. Thisresult is reinforced in [3] by computing the Wi-Fi successfulchannel accessing probability in the presence of LTE-Utransmission. However, in [1], LTE-U is described as a betterneighbor to Wi-Fi than Wi-Fi to itself as long as a propercoexistence mechanism (called CSAT) is applied. Authors in[4] present simulation results on spectrum efficiency com-parison between Wi-Fi and LTE-U in a sparse deploymentscenario. The paper, however, lacks sufficient details on thecoexistence features and their effectiveness. Cano and Leith[5] proposed a duty cycle mechanism for LTE-U, which, byselecting an appropriate probability to access the channeland transmission duration, ensures proportional fairnessamong LTE-U and Wi-Fi nodes. Specifications regardingduty cycled based LTE-U are released and maintained by

LTE-U forum [6], where CSAT is officially introduced as theaccess mechanism.

On the other hand, the 3GPP study item technicalreport document [7] has listed listen-before-talk (LBT) as therequired function for clear channel assessment for LTE LAA.The application of LBT may potentially enhance the coexist-ence behavior of Wi-Fi and LTE. Some analysis and perfor-mance test have been reported in [8–10].

1.2. Main Results. In this paper, we define Wi-Fi averagesaturation throughputR(",#,H) (in terms of bits/Wi-Fi slottime) and average service timeD(",#,H) (in terms ofWi-Fitime slots) to be functions of ", #, and H = {$, %, &}, wherethe set H = {$, %, &} represents &-clients Wi-Fi subsystemwith LTE-U to Wi-Fi collision probability (Wi-Fi transmis-sion failure probability due to LTE-U transmission) $ andWi-Fi data payload length % (the length of MAC data payload,in terms of bytes). Given H, the throughput fairness (cf.Definition 2) of (",#) air time sharing scheme is measured bythe difference between average Wi-Fi saturation throughputloss ratio (with respect to the corresponding non-LTE-Udutycycle scenario (∞, 0,H) performance) and LTE-U duty cycle#, that is, (R(∞, 0,H) − R(",#,H))/R(∞, 0,H) − #. Ina similar way, the average service time fairness is defined as(D(",#,H) −D(∞, 0,H))/D(∞, 0,H) − #/(1 − #). Thesetwo fairness measures indicate whether Wi-Fi will lose lessor more than # portion of its performance (in the absence ofLTE-U transmission) if # portion of the channel resource isshared with LTE-U.

Our first step is to analytically formulateR(",#,H) andD(",#,H) using a probabilistic framework. The followingtwo key techniques are employed.

1.2.1. Only One Labeled Client Station among the & Wi-Fi Stations Being Affected by LTE-U Interference. As firstintroduced by [11], Wi-Fi DCF can be formulated into aMarkov chain model, which was generalized later in [12, 13].But when LTE-U is considered, the Markov property nolonger holds, because of the fact that when LTE-U is off,the Wi-Fi transmission failure probability is only Wi-Fi toWi-Fi collision probability; when LTE-U is on, the Wi-Fitransmission failure probability depends on both Wi-Fi toWi-Fi and LTE-U to Wi-Fi collision probability. For thisissue, we make an assumption that only one client stationamong the & stations, labeled as Sta-A, is affected by theLTE-U interference. The other & − 1 stations render theWi-Fi background traffic for the labeled station. When & ischosen to be large enough, the background traffic could stillbe approximately modeled using the existing framework in[11–13]. Under this assumption, functions R(",#,H) andD(",#,H) are with respect to Sta-A.

1.2.2. Different Interference Levels Lead to Different Formu-lations. The Wi-Fi DCF employs CSMA/CA with binaryexponential back-off algorithm. Depending on the energylevel being detected, the back-off timer may or may not befrozen. In short, an LTE-U transmission with interferenceto noise ratio (INR) greater than −62 dbm or a neighborWi-Fi station transmission with INR greater than −82 dbm

Wireless Communications and Mobile Computing 3

will cause the interfered Wi-Fi station to freeze its back-offtimer.We refer toweak interference as the LTE-U interferencewith its INR being less than −62 dbm and strong interferenceas interference with INR greater than −62 dbm. The mathe-matical formulations as well as the performance results arequite different between the cases of weak and strong LTE-Uinterference.

Other assumptions are just inherited from the existingframework by [11–13] onWi-Fi DCF: (1) a transmission fromone Wi-Fi station can be heard by all the other & − 1 Wi-Fi stations, and Wi-Fi to Wi-Fi INR is always greater than−82 dbm; (2) collisions among Wi-Fi or LTE-U to Wi-Fi arethe only causes to Wi-Fi failure transmission.

Then, we analyze the performance as well as the fairnessnumerically. Both the analytical functions built for the weakand strong LTE-U interference are computationally ineffi-cient and characterizing the two performance functions inclosed form is hard. On the other hand, implementingMonteCarlo analysis based on these two functions is simple. It isalso difficult and meaningless to show the fairness over allpossible combinations of", #, andH. We focus our attentionon the cases when LTE-U toWi-Fi collision probability $ = 1,which has wide measure over real systems where LTE-U INRand Wi-Fi SNR are comparable. Other parameters are alsoselected in a reasonable range according to practical systemsetting. The results demonstrated in Section 4 support theconclusions below:

(1) Fix $ = 1: under strong interference, air time sharingscheme could approximately achieve the fairness forsome (",#); under weak interference, air time sharingscheme is generally unfair.

(2) The fairness measure degrades almost linearly whenLTE-U to Wi-Fi collision probability $ increases.

(3) The fairness measure degrades almost linearly whenWi-Fi payload length % increases.

The rest of the paper is organized as follows: Section 2presents the Wi-Fi and LTE-U coexistence model and for-mulates the problem; Section 3 characterizes the average Wi-Fi saturation throughput and average service time in thepresence of LTE-U duty cycle; the impact of duty cycled LTE-U interference to Wi-Fi is discussed in Section 4; Section 5concludes the paper.

2. System Model and Problem Formulation

In this section, we first introduce the generalized Markovchain model for Wi-Fi DCF, then we formulate the Wi-Fiand duty cycled LTE-U coexistence, and lastly we define thefairness measure.

2.1. Generalized Markov Chain Model for Wi-Fi DCF. In[11], the Wi-Fi DCF is formulated into a two-dimensionalMarkov chain; the (th floor in the Markov chain (refer toFigure 2) stands for the random back-off process before the(th transmission attempt, where 0 ≤ ( ≤ *, with contentionwindow size CW! = 2!CW0, where CW0 is the contentionwindow size of the 0th back-off. This Markov chain has

transition probability +(("+1, ,"+1 | (", ,") (with a slight abuseof notation, we temporarily use & to denote the state at &thdiscrete moment),{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{{

1 ("+1 = ("; ,"+1 = ," − 1,," = 0,1 − +!! ("+1 = 0, (" =*− 1;,"+1 ∈ {0, . . . ,CW0} , ," = 0,+!!2!!+1CW0 ("+1 = (" + 1, ("+1 =*− 1;,"+1 ∈ {0, . . . , 2!!+1CW0} , ," = 0,1 ("+1 = 0, (" =*− 1;,"+1 ∈ {0, . . . ,CW0} , ," = 0.(1)

Let 7 be the duration of the Wi-Fi system slot time asdefined in IEEE 802.11 standard. Throughout the paper, wenormalize all the time variables to 7, which means 1 s isnormalized to 1/7. During each ((, 0) state, a Wi-Fi stationsenses the channel; with probability+! it detects clear channeland transmits (or retransmits) a packet. If successful, thestation stays idle or goes back to 0th contention level for a newpacket; otherwise the failed packet will be retransmitted untilit reaches the maximum number of retry attempts*. Beforethe (th attempt, a random number is generated according tothe uniform distribution Unif(0,CW! − 1) and loaded intothe back-off timer. The timer decreases the registered valueby one per slot time, and once the back-off timer is reset, thestation senses the channel for the (th attempt.

Recall that a Wi-Fi station receiving Wi-Fi interferenceover −82 dbm will freeze its back-off timer; therefore thetransition time between two neighbor states in the Markovchain may be more than oneWi-Fi system slot time. In orderto use this Markov chain model to analyze the Wi-Fi servicetime, the Bianchi model in [11] is further generalized by[12, 13] after incorporating the following two further assump-tions:

(1) The transition time "# between any two neighborstates (we call this unit decrement time for short,normalized to system slot time) is identically andindependently distributed, and interference betweenany two Wi-Fi stations is above −82 dbm threshold.

(2) Based on assumption (1) and applying central limittheorem, the time interval from a back-off timer loadswith an initial number 8! before (th attempt to thetimer being reset is a Gaussian random variable withmean 8!9("#).

We adopt the generalized Markov model of Wi-Fi in thispaper.

Next we describe the failure probability+! in each retrans-mission trial. Let : be the probability that there is no packetready to transmit, and let ; be the probability that a Wi-Fi station transmits (or retransmits) a packet in a randomlychosen time slot given a packet just left the buffer and is readyto be transmitted.The number ; is a function of the number


1 1

1 1

11 1 1

1

1

111

0, 0 0, 1 0, 2

1, 0 1, 1 1, 2

1 − P0

1 − P1

1/W0

0,W0 − 1

0,W1 − 1

P0/W1

1 − PM−1

M − 1, 1M − 1, 0 M − 1, 2

M, 0 M, 1 M, 2

PM−2/WM−1

PM−1/WM

M − 1,WM−1 − 1

M,WM − 1

· · ·

· · ·

· · ·

· · ·

· · ·

Figure 2: Markov model for Wi-Fi DCF (refer to [11]).

of Wi-Fi stations & and +!. Without LTE-U interference, theprobability+! is simply the collision probability+$ that at leasttwo Wi-Fi stations transmit simultaneously, which is+! = +$ = 1 − [1 − (1 − :) ;]"−1 . (2)

On the other hand, we have; = &−1∑!=0 (1 − +$) + ((, 0) + (1 − +$) + (*, 0) (3)

according to the transition probability defined in (1), where+((, ,) is the stationary distribution of the Markov chain.There is no close form expression of the solution to +! and;, but given the system parameters and number of stations,they can be numerically computed. When the Wi-Fi systemis saturated, the buffer in each station is never empty; that is,: = 0 and +$ = 1 − (1 − ;)"−1.

It remains to specify the distribution of unit decrementtime "#. Let "' and "$ be the time duration, normalized tothe system slot time, of one successful and failed (collided)transmission, respectively. If CTS/RTSmechanism is used,"'and "$ can be calculated as follows:"' = RTS + CTS +HDR + % + ACK + 3 × SIFS+ DIFS,"$ = RTS + DIFS; (4)

otherwise "' = HDR + % + ACK + SIFS + DIFS,"$ = HDR + % + DIFS. (5)

In both cases, % denotes the length of the data payload of aWi-Fi frame. Let +' be the probability that one of the other

& − 1Wi-Fi station transmits successfully (note it is generallynot true that +' = 1 − +$); that is,+' = (& − 1) ; (1 − ;)"−2= (& − 1) [(1 − +$)("−2)/("−1) + +$ − 1] . (6)

The unit decrement time "# has following pmf:

+(" (B#) = {{{{{{{{{{{{{{{1 − +$ B# = 1+$ − +' B# = "$+' B# = "'0 o.w.

(7)

2.2. Formulation ofWi-Fi andDutyCycled LTE-UCoexistence.Consider an infrastructure-based Wi-Fi network coexistingwith an LTE-U network on the same unlicensed band, whereinterference is coming from LTE-U subsystem to the Wi-Fistation labeled Sta-A. Considering a duty cycle period whichextends"Wi-Fi system slots (refer to Figure 1) the eNB orUEin LTE-U subsystem transmits during the LTE-U ON stageof duration #", where # ∈ [0, 1], and keeps silence duringthe LTE-U OFF stage (as discussed in [3], even during LTE-Uquiet period, the reference signalmay have same significantinterference to Wi-Fi transmission. In this paper, we assumethe LTE-U being completely off during its OFF stage). Thevariables " and # are defined to be LTE-U duty cycle periodand duty cycle, respectively. The Wi-Fi subsystem does notcooperate with LTE-U nor has any prior knowledge aboutLTE-U interference; it simply transmits data frame based onthe DCF mechanism.

As has been introduced before, assuming only one outof the & Wi-Fi stations receives LTE-U interference is for


the purpose of maintaining the Markov properties to modelthe rest of & − 1 stations, so when & is large enough, thecollision probability+! andunit decrement time"# can still beapproximately computed using the generalizedMarkov chainmodel. The & − 1 noninterference stations actually provide astationary background Wi-Fi traffic for Sta-A.

We denote a Wi-Fi subsystem as H($, %, &), where $ ∈[0, 1] is the Wi-Fi collision probability subject to LTE-Uinterference (theWi-Fi transmission failure probability, whenaWi-Fi frame and an LTE-U frame transmits simultaneously,only applies to Sta-A), % is the data payload length in eachtransmission, and & is the number of clients in the Wi-Fisubsystem which determines the Wi-Fi to Wi-Fi collisionprobability (i.e., Wi-Fi collision probability in the absence ofLTE-U transmission). Furthermore let (",#) denote an airtime sharing scheme with duty cycle period " and LTE-Uduty cycle #.

Instead of adopting the uniformed Wi-Fi throughputas in [11], we evaluate the Wi-Fi throughput (saturationthroughput of Sta-A, the same premise keeps for futurediscussion) C(",#,H) as the number of bits can be suc-cessfully transmitted per Wi-Fi slot time. The Wi-Fi servicetime D(",#,H), or the medium access delay, is defined tobe the time interval (also normalized to system slot time)from the time instant that a packet becomes the head of thequeue and starts to contend for transmission, to the timeinstant that either the packet is acknowledged for a successfultransmission or the packet is dropped. Note both C(",#,H)and D(",#,H) are random variables according to abovedefinition. Finally, we define the average Wi-Fi throughputand average service time R(",#,H) (in terms of bits/Wi-Fi slot time) and D(",#,H) (in terms of Wi-Fi time slots),respectively, for a coexistence system with Wi-Fi subsystemH($, %, &) and air time sharing scheme (",#) as

R (",#,H) = 9 [C (",#,H)] ,D (",#,H) = 9 [D (",#,H)] . (8)

For convenience, we sometimes omit the underlyingvariables (",#,H) and just use a simple notation as letter CorR = 9[C] for short.2.3. Definition of Fairness. It is a critical task to define whatfairnessmeans in this context, since there could bemanywaysto describe the fairness in such a coexistence scenario. Onestraightforward way is to compare the Wi-Fi performancewith and without the presence of LTE-U. More specifically,we want to find answer to the question:Will the performanceloss (throughput degradation and service time increase) dueto time sharing be proportional to the duty cycle #? Also,what reference values should be used when we characterizethe performance loss?The definition below gives an intuitiveway of measuring fairness.

Definition 1. For a given H($, %, &), assume the referenceWi-Fi performance to be R(∞, 0,H) and D(∞, 0,H). Thethroughput fairness E)(",#,H) is the difference between the

average throughput loss ratio and the LTE-U duty cycle #;that is,E) (",#,H) = R (∞, 0,H) −R (",#,H)R (∞, 0,H) − # (9)

and service time fairness E*(",#,H) is the difference ofaverage service time increase ratio to #/(1 − #); that is,E* (",#,H) = D (",#,H) −D (∞, 0,H)D (∞, 0,H) − #1 − # . (10)

Depending on H and (",#), the fairness measures E)and E* can be negative, positive, or zero. If both these twoparameters (E) and E*) are zero, Wi-Fi performs at exact(1 − #) “portion” of the non-LTE duty cycle performance.We consider such a time sharing scheme to be acceptableand reasonable. From this perspective, we have the followingdefinition.

Definition 2. A Wi-Fi LTE-U coexistence system with Wi-Fi subsystem H and air time sharing scheme (",#) is fairin throughput if E) ≤ 0 and fair in service time if E* ≤ 0.If a scheme is both fair in throughput and service time, thescheme is fair.

Remark 3. Please note $ is a function of LTE-U toWi-Fi INRandWi-Fi SNR. Formulating the collision probability $ is outof the scope of this paper. It is obvious that very low INR/SNRinterference causes almost no impact to Wi-Fi system whichis trivial; that is, $ ≈ 0 and E),E* ≤ 0. This paper focuseson the situations when INR and SNR are comparable, andin most subsequent discussions we assume $ = 1, whichmeans a Wi-Fi transmission will definitely fail if an LTE-Utransmission occurs at the same time. Additionally, we willshow in Section 4 how E* and E) decay when $ increasesfrom 1 to 0 in a numerical example. Readers are reminded that$ = 1 can happen to either strong or weak interference cases.

3. Impact of Duty Cycled LTE-U Interference

During the LTE-U ON period, the (th attempt of Wi-Fitransmission fails with probability++! = 1 − (1 − +$) (1 − $) . (11)

Whether the failure probability should be chosen as +! or++! depends on whether the LTE-U is on or off; therefore theSta-A DCF could no longer be modeled by Markov chain.Instead, we characterize the Sta-A throughput and servicetime in three steps:

(1) Suppose a Wi-Fi packet leaves Sta-A buffer at time"0 = B0, where B0 ∈ {0, 1, . . . ," − 1}, and at time ",,where ", ∈ {B0, . . . ,∞}; the packet will be either sentout successfully or dropped. Conditioning on B0, wecompute the conditional distribution +(#|(0(B, | B0)of the finish time ",, the conditional mean servicetime 9[D | B0], and conditional mean throughput9[C | B0].


(2) Let "+, be a function of ", that"+, = ", mod (" − 1) (12)

and the conditional distribution of "+, can be derivedfrom +(#|(0(B, | B0) as+($# |(0 (B+, | B0) = +∞∑(#:(# mod ((−1)=.#+(#|(0 (B, | B0) . (13)

If we regard the" time slots (labeled as 0, . . . ,"−1) ina duty cycle period as " states, those " states form thestate space of a one-dimension Markov chain, withtransition probability from state B0 to state B+, of+($# |(0 (B+, | B0) (14)

because knowing the start time B0 and the distributionof "+, does not depend on previous packet trans-mission start times. The distribution +(0(B0) can becomputed as the stationary distribution over these "states.

(3) Lastly, the Sta-A mean throughput 9[C] and meanservice time 9[D] can be derived as 9[C] =∑(−1.0=0 +(0(B0)9[C | B0] and 9[D] = ∑(−1.0=0 +(0(B0)9[D |B0].

3.1. The Conditional Probability +(#|(0+(B, | B0) under WeakLTE-U Interference. When LTE-U interference is weak, Sta-A keeps transmitting in the LTE-U ON stage wheneverpossible. For some B0, consider anJ dimension vectorw(/) =(K0, . . . ,K/−1) ∈ {0, . . . ,CW0 − 1}× ⋅ ⋅ ⋅ × {0, . . . ,CW/−1 − 1},where 1 ≤ J ≤ * + 1. A vector w/ with 1 ≤ J <* + 1 fully determines a back-off pattern and also uniquelydetermines the transmission finish time B,. WhenJ =*+1,depending on the last trial being successful or not, the finishtime has two possibilities. Hence the distribution +(#|(0(B, |B0) can be derived by first getting the conditional distribution

+W(%)|(0(w(/) | B0), whereW(/) is the corresponding randomvariable to w(/).

The time of (th transmission attempt M! is also a functionof w thatM! (w(/)) = B0 + 9 ["#] ( !∑0=0K0 + ("$) 0 ≤ ( ≤ J − 1, (15)and comparing M! with the values of #",", (1 + #)", 2", . . ., itcould be figured out if the (th attempt falls within the LTE-UON period, record the result by a bool functionR (M!)= {{{0 #" ≤ M! mod " < (M! + "') mod " < "1 o.w,

(16)

and combining (11) and (16), we have+ (w(/) | B0)= (/−2∏!=0 1 − (1 − +$) (1 − $R [M! (w(/))])CW! )⋅ ((1 − +$) (1 − $R [M/−1 (w(/))])

CW/−1 ) .(17)

The end time ", is a function of random vectorW(/) and",(W(/)) is the sum of the total waiting time and the timeof each transmission of back-off pattern W(/). Let ℎ(W(/))be a function of random variable W(/) of the successfulretransmission probability of theJth retrial,ℎ (W(/)) = (1 − +$) (1 − $R (M/−1 (W(/)))) . (18)

According to the DCF, the mapping W : (W(/), B0)→ ", isW (W(/), B0)= {{{{{{{B0 + 9 ["#] M/−1 + "' 1 ≤ J <* + 1B0 + ℎ (W(&)) 9 ["#] (&∑!=0Y! +*"$ + "') + (1 − ℎ (W(&))) 9 ["#] (&∑!=0Y! + (* + 1)"$) J =* + 1.

(19)

Note in (19), to make W(W(/), B0) a map, we have to dealwith the map between (W(&+1), B0) → ", so it has uniqueimage, and we take the last retransmission duration to be itsexpectation.The finish time ", has pmf:+(#|(0 (B, | B0) = ∑

w:1(w)=.#+W|(0 (w | B0) . (20)

Knowing the distribution of ",, the conditional mean 9(D |B0) can be written as

9 [D | B0] = 9 [", − B0] . (21)


For9[C | B0], we need to find out the probability that a packettransmission started at B0 being dropped, denoted as +dr(B0),+dr (B0) = ∑

w(&+1)+W|(0 (w(&+1) | B0) [1 − ℎ (w(&+1))] (22)

and the conditional mean throughput can be written as9 [C | B0] = % (1 − +dr (B0)) 9 [ 1D | B0] . (23)

3.2. The Conditional Probability +(#|(0(B, | B0) under StrongLTE-U Interference. Under strong interference, the Wi-Fiback-off timer will be blocked when LTE-U is on. As will bedemonstrated later, it effectively helps Wi-Fi to eliminate theLTE-U interference. Not only does the LTE-U interferencecause the collision toWi-Fi, but also the unit decrement time"# atWi-Fi part will have a time variant pmf.When LTE-U ison, the Wi-Fi mean unit decrement time 9["+#] becomes #"(when #" is chosen at a reasonable value, e.g., " ≥ 100). Asa result, (15) and (19) which both reply on 9["#] no longerhold true. Computation of M!(w) and ", = W(W(/), B0) needsiterative algorithm, which is given below; this algorithm hascomplexity ](&2). Shortly speaking, the counting processkeeps checking if ", mod " < #" in every iteration; if it istrue then a constant (#" − ^ mod ") is added to the partialsum of ",.", = B0

for ( = 0 : J − 1for , = 0 : K! − 1

if (", mod " < #")", = ", + #" − ", mod "else ", = ", + 9["#]end

endM! = ",;if (( < J − 1)", = ", + "$elseif (J =* + 1)", = ", + "';elseif (J =* + 1)", = ", + (1 − ℎ(w))"$ + ℎ(w)"'end

end

4. Fairness Evaluation: Monte Carlo Analysis

It is computationally unpractical to characterize the distribu-tion of +*(⋅ | B0) as a function of +(W | B0) in closed form,since the sample space of random vectorW(&)! has cardinality

of ∏&−1!=0 CW!, which is at the scale of 1011. However, basedon the analytical discussion in the previous section, it is easyto implement a Monte Carlo analysis for both the weak andstrong interference cases. The essential idea of Monte Carloanalysis, also named as Monte Carlo simulation, is to userepeated random sampling to obtain numerical results andanalyze problems that might be deterministic in principle.The procedure in our evaluation is stepped as follows.

(1) Let the first packet be generated at time 0 (slot time),and at the same time, LTE-U starts its first duty cycle.

(2) For each packet transmission/retransmission, whichmay be affected by collision (either Wi-Fi to Wi-Fi or LTE-U to Wi-Fi, or both), multiple trans-mission trials may occur during one transmis-sion/retransmission, and we uniformly generate asample vector w = {K0, . . . ,K&−1} from its samplespace ∏&−1!=0 {0, . . . ,CW! − 1} and then a Booleanvector ! = {`0, . . . , `&−1} indicating success/failurefor each trial whose distribution depends on (1)the value of w which determines if the (th Wi-Fi transmission trial, ( ∈ {0, . . . ,* − 1}, will beoverlapping with active LTE-U transmission; (2) Wi-Fi to Wi-Fi collision probability +$; (3) LTE-U to Wi-Fi collision probability $.

(3) Based on the given w and !, we can deterministicallycompute the service time of the ath transmission andrecord it.

(4) Let the next transmission start immediately (becausewe are evaluating saturate performance), and repeatsteps (2)-(3) until we derive enough numerical resultsfor analysis.

(5) The average service time 9[D] as well as the through-put 9[C] can be approximated using recorded servicetime from each transmission.

We refer to average throughput and average service timesimply as throughput and service time.The impact of LTE-Uduty cycle is discussed in terms of the following parameters:

(i) duty cycle period ";(ii) the duty cycle #;(iii) LTE-U to Wi-Fi collision probability $;(iv) Wi-Fi payload length %.

On the other hand, the parameters below are fixed:

(i) Wi-Fi system is saturated, that is, : = 0.(ii) RTS/CTS is applied, slot time7 = 9 bs,Wi-Fi physical

layer bit rate is 1Mb/s, for the random back-off,* =6, CW0 = 16, and other parameters are with respectto IEEE 802.11n standard in the 5GHz band.

(iii) The scenario contains 17 Wi-Fi client stations,according to [12], and we know the Wi-Fi to Wi-Ficollision probability +$ = 0.3739.


0

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Weak interferenceStrong interference

200 300 400 500 600 700 800 900 1000100Duty cycle period T

# R(T

, 0.3

,{1,

1000

,17}

)#R (T, 0.3, {1, 1000, 17})

versus duty cycle period T

Wi-F

i thr

ough

put f

airne

ssWi-Fi throughput fairness

(a) Throughput fairness versus (

0

0.2

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0.6

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200 300 400 500 600 700 800 900 1000100Duty cycle period T

Wi-F

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tim

e fair

ness

# D(T

, 0.3

,{1,

1000

,17}

)

Wi-Fi service time fairness #D (T, 0.3, {1, 1000, 17})versus duty cycle period T

(b) Service time fairness versus (Figure 3: Impact of duty cycle period ".

0.05

0.1

0.15

0.2

0.25

0.3

Wi-F

i thr

ough

put f

airne

ss# R

(500

,$,{1,

1000

,17}

)

Wi-Fi throughput fairness #R (500, $, {1, 1000, 17})versus LTE-U duty cycle $


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80LTE-U duty cycle $

(a) Throughput fairness versus 2

−1

0

1

2

3

4

5

6

7

# D(5

00,$

,{1,

1000

,17}

)

#D (500, $, {1, 1000, 17})versus LTE-U duty cycle $


0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80LTE-U duty cycle $

Wi-Fi service time fairness

Wi-F

i ser

vice

tim

e fair

ness

(b) Service time fairness versus 2Figure 4: Impact of duty cycle #.

4.1.The Role of Duty Cycle Period". Fixing the duty cycle # =0.3, $ = 1, and % = 1KB, Figure 3 shows the impact of dutycycle period" on throughput and service time, for both weakand strong interference scenarios. It can be observed that" ≤600ms (note one LTE-U frame duration is 10ms) will causesignificantWi-Fi performance degradation which is unfair toWi-Fi. When " is large enough, the air time sharing tendsto cause less unfairness to Wi-Fi under strong interference,

and more numerical results show (omitted due to the pagelimit) large" causing less unfairness under weak interferenceas well.

4.2. The Role of Duty Cycle #. For " = 500ms, $ = 1, and% = 1KB, the result is demonstrated in Figure 4. Whenthe interference is strong, throughput loss ratio is almost #and is linear. However, if interference is weak but signifi-


−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.2 0.4 0.6 0.8 10LTE-U to Wi-Fi collision probability q


Wi-Fi throughput fairness #R (500, 0.3, {q , 1000, 17})W

i-Fi t

hrou

ghpu

t fair

ness

# R(5

00, 0

.3,{q,

1000

, 17}

) versus collision probability q

(a) Throughput fairness versus 30 0.2 0.4 0.6 0.8 1

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

0.3

LTE-U to Wi-Fi collision probability q


Wi-F

i ser

vice

tim

e fair

ness

#D

(500

, 0.3

,{q,

1000

, 17}

)

Wi-Fi service time fairness #D (500, 0.3, {q , 1000, 17})versus collision probability q

(b) Service time fairness versus 3Figure 5:The role of LTE-U to Wi-Fi collision probability $.

cant ($ = 1), there can be additional reduction on through-put. When # ≈ 0.4, the air time sharing causes greatestthroughput unfairness. When # ≤ 0.3, the delay seems tobe linear; however, when # → 1, the service time increasesexponentially. Recall the definition of fairness and it canbe inferred for in the given network setting, a fair air timesharing scheme should have at least # ≲ 0.3. Consideringthe throughput only, strong interference approaches thethroughput fairness over almost any # ∈ [0, 1].4.3. LTE-U to Wi-Fi Collision Probability $. Fixing the dutycycle " = 500ms and # = 0.3 and % = 1KB, Figure 5 showshow the fairness varies with $, and it degrades almost linearlywith $. Particularly, $ has less effect to fairness under stronginterference because interference over −62 dbm will freezethe Wi-Fi back-up timer and the only possible LTE-U toWi-Fi collision occurrence is when an LTE-U transmission startsafter a Wi-Fi transmission.

4.4.The Role of Wi-Fi Payload Length %. Fixing " = 500ms,$ = 1, and # = 0.3, Figure 6 illustrates the impact of datalength %, for both weak and strong interference, and fairnessdegrades almost linearly with %.4.5. Why Weak Interference Is Worse at $ = 1? In thestrong interference case, Sta-A eliminates interference byfreezing the back-off timer, and after LTE-U being off, Sta-A could be immediately released from LTE-U interference,so the total loss ratio of the performance is very close tothe duty cycle #, as can be seen in Figure 4. However, wheninterference is weak, Sta-A continues to contend the channel,and it eliminates the interference by enlarging the contentionwindow size and increasing the number of attempts duringthe LTE-UON stage. Once LTE-U switches off, Sta-A will not

start transmitting until the current back-off timer is reset, andin the worst case, the recovery time could take as long as26CW09 ["#] ≈ 10249 ["#] . (24)9["#] in the above experiments is about 2.6ms. In case " isabout 100ms, Sta-A would wait for 10 duty cycle periods longbefore sensing the channel again.This effect is demonstratedclearly in Figures 3 and 4.

From the information theory perspective, when LTE-Uinterference is strong, Wi-Fi has accurate and updated chan-nel state information (CSI) on whether LTE-U is on or off;henceWi-Fi could use this CSI to skip the interference.WhenLTE-U interference is weak, Wi-Fi has very delayed CSIsince the AP knows the interference only after detecting thefailure of a previous transmission, which causes significantperformance degradation.

5. Conclusion

In this paper, we study the performance of an infrastructure-based Wi-Fi network when its operating channel in theunlicensed spectrum is air time shared with an LTE-Unetwork. We define and characterize the Wi-Fi averageperformance and fairness in the presence of duty cycled LTE-U as functions of Wi-Fi subsystem parameters and the airtime sharing scheme being used.ThroughMonte Carlo anal-ysis, we numerically demonstrate the fairness under typicalcoexistence settings. It can be observed from the results thatWi-Fi and LTE-U coexistence using simple air time sharingare generally unfair to Wi-Fi. We conclude that some otherschemes (e.g., similar to the listen-before-talk mechanismused in 802.11 networks) need to be developed for LTE-Unetworks in order to overcome the observed unfairness.


500 1000 1500 2000 2500 3000 3500 4000 4500 50000

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Wi-Fi data payload length LWeak interferenceStrong interference

versus Wi-Fi data payload length L

# R(5

00, 0

.3, {

1, L

, 17}

)W

i-Fi t

hrou

ghpu

t fair

ness

#R (500, 0.3, {1, L, 17})Wi-Fi throughput fairness

(a) Throughput fairness versus 4500 1000 1500 2000 2500 3000 3500 4000 4500 50000

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Wi-F

i ser

vice

tim

e fair

ness

# D(5

00, 0

.3, {

1, L

, 17}

) versus Wi-Fi data payload length L

(b) Service time fairness versus 4Figure 6: Impact of Wi-Fi payload length %.

Competing Interests

The authors declare that they have no competing interests.

References

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