20 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, …wireless.ece.arizona.edu/sites/default/files/2017_jsacHirz.pdf · 22 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL

20 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 35, NO. 1, JANUARY 2017

Full-Duplex-Based Rate/Mode AdaptationStrategies for Wi-Fi/LTE-U Coexistence:

A POMDP ApproachMohammed Hirzallah, Student Member, IEEE, Wessam Afifi, Student Member, IEEE,

and Marwan Krunz, Fellow, IEEE

Abstract— The rapid increase in wireless demand promptedthe FCC to open up parts of the 5-GHz band for unlicensedaccess. This caught the interest of 4G/LTE providers, who wish toextend their LTE-A services to the unlicensed spectrum (LTE-U).In LTE-U, small-cell base stations aggregate unlicensed andlicensed bands to increase the throughput. Wi-Fi/LTE-Ucoexistence is a challenging issue due to the different accessmechanisms of these two systems, which may cause high collisionrates and delays. By leveraging self-interference-suppressiontechniques, we propose joint mode/rate adaptation strategiesfor Wi-Fi/LTE-U coexistence. Specifically, a full-duplex enabledWi-Fi station can transmit and receive data simultaneouslyto increase the throughput, or transmit and sense (TS mode)simultaneously to monitor the LTE-U activity. We model theLTE-U interference as a hidden Markov process, and solve theproblem of jointly adapting Wi-Fi rates/modes using a frameworkof partially observable Markov decision process. A detectionapproach based on the sliding window correlator is analyzedfor the TS mode, which can differentiate between Wi-Fi andLTE-U signals. Our results indicate that our scheme provides1.5x (1.9x) average throughput gain for Wi-Fi system in the low(high) signal-to-interference-and-noise regime relative to a half-duplex-based scheme.

Index Terms— Wi-Fi/LTE-U coexistence, full-duplex,simultaneous transmission-sensing, HMM, POMDP, rateadaptation.

I. INTRODUCTION

THE significant increase in the wireless demand promptedthe FCC to open up parts of the 5 GHz Unlicensed

National Information Infrastructure (U-NII) band for unli-censed access. This motivated wireless operators to extendtheir LTE-A services to the unlicensed spectrum (LTE-U).LTE-U exploits carrier aggregation to combine licensed andunlicensed spectrum, targeting higher downlink (DL) through-put for user equipments (UEs). Coexistence between heteroge-neous systems such as LTE and Wi-Fi in the unlicensed bandis particularly challenging due to the difference in their accessmechanisms. In particular, Wi-Fi systems are contention based,

Manuscript received May 7, 2016; revised August 13, 2016; acceptedNovember 6, 2016. Date of publication November 23, 2016; date of cur-rent version January 12, 2017. This work was supported by the NationalScience Foundation under Grant IIP-1535573, Grant IIP-1265960, andGrant CNS-1563655.

The authors are with the Department of Electrical and Computer Engi-neering, The University of Arizona, Tucson, AZ 85721 USA (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSAC.2016.2632598

Fig. 1. Collision between LTE-U and Wi-Fi TXOP (‘F1’: Frame transmittedfrom AP).

whereas LTE/LTE-U systems are schedule based. Such het-erogeneity makes coordination and interference managementquite challenging, leading to higher collision rates, latency,and unfairness.

In an effort to reduce the impact of LTE-U onWi-Fi, two approaches have been proposed: Carrier-sensingadaptive transmission (CSAT) [2] and licensed assistedaccess (LAA) [1]. LAA, which was recently standardized in3GPP Rel-13, targeted countries that mandate using listen-before-talk (LBT) in the 5 GHz band (e.g., Europe andJapan). A base station senses the spectrum and transmits if themeasured signal is below −72 dBm. LAA transmissions maycollide with Wi-Fi transmissions below this threshold. CSAT,which is advocated by the LTE-U Forum [2], relies on channelselection and time-based duty cycle (see Figure 1). The homeeNodeB (HeNB) measures the traffic density of neighboringWi-Fi stations (STAs) during the OFF period of the LTE-Usystem and adapts its duty cycle accordingly. In the ON period,HeNB transmits DL frames without performing LBT. On theother hand, Wi-Fi STAs can access the spectrum using theenhanced distributed channel access (EDCA) scheme, whichis an extension of the distributed coordination function (DCF).The successful STA can reserve the channel for a durationcalled a transmit opportunity (TXOP), which may last for3.008 ms. During a TXOP, a Wi-Fi access point (AP) or STAtransmits several frames. After each frame, the AP/STA couldwait for an ACK from its peer [3].

Deploying LTE-U small cells in unlicensed bands maylead to severe service degradation for Wi-Fi STAs. As shownin Figure 1, the AP detects a transmission failure (e.g.,frame ‘F2’) via an ACK timeout. However, the AP cannot tellthe reason for this transmission failure (e.g., channel fadingand Wi-Fi/LTE-U interference). The AP may retransmit thecorrupted frame several times. Once the retransmission limitis exceeded, the AP could either double its contention windowsize and back off again, or it could switch to a new channel.

0733-8716 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

HIRZALLAH et al.: FULL-DUPLEX-BASED RATE/MODE ADAPTATION STRATEGIES FOR Wi-Fi/LTE-U COEXISTENCE 21

Both cases lead to performance degradation in terms of longdelays, reduced throughput, and power wastage.

In this paper, we consider Wi-Fi devices with self-interference suppression (SIS) capabilities, which enable themto perform simultaneous transmission and sensing (TS). Thisso-called full-duplex (FD) sensing provides Wi-Fi STAswith real-time channel monitoring and interference detection.Increasing the spectrum awareness at the AP helps it optimizeits actions to maintain connectivity with the STAs. SIS tech-niques can also be used to enable simultaneous transmissionand reception (TR) so as to increase the link throughput.

Wi-Fi standards (e.g., IEEE 802.11n/ac) define multiplemodulation and coding schemes (MCSs), which can be usedby the AP to adapt to channel dynamics, interference, andcontention. We leverage this degree of freedom to jointly opti-mize the MCS and transmission “mode” at the AP, taking intoaccount the AP’s belief about LTE-U interference. Specifically,in addition to adapting its coding/modulation scheme, the APcan also select to operate in a TR or TS mode, or performchannel switching (CS).

FD sensing was previously explored for opportunistic spec-trum access (OSA) systems, based on energy detection [4]and waveform-based detection [5]. Energy detection cannotdifferentiate between different types of signals (e.g., LTE-Uvs. Wi-Fi). In contrast, waveform-based sensing uses trainingsequences, located in frame header to correlate. We harnessthe unique features of LTE-U and Wi-Fi signals (e.g., OFDMsymbol duration and length of the cyclic prefix) to distinguishbetween the two. Chen et al. [6], Chaudhari et al. [7], andAxell and Larsson [8] exploited the cyclic prefix (CP) inOFDM symbols for signal detection, but only for HD systems(i.e. sensing only). Reference [6] suggested a two-sliding-window approach, in which the received samples are correlatedto detect the presence of OFDM symbols. We propose an FDsensing approach for coexisting Wi-Fi/LTE-U systems basedon the two-sliding-window correlator scheme.

Several approaches for rate control have been proposedin the literature based on SNR measurements and MAC-layer statistics (see [9] and references therein). Generally,these approaches have slow response. Another approach isbased on partially observable Markov decision processes(POMDP) [10]–[12], where the transmitter builds beliefs(probabilities) about the unknown channel conditions anduses them for selecting new rates. These works modeled theproblem considering HD radios. In our scheme, we extendthe POMDP framework and consider FD-enabled radios. Wejointly control the FD mode and rate in response to LTE-U traffic dynamic. Interference generated by the LTE-U basestation and received by Wi-Fi devices can be modeled as ahidden Markov model (HMM) process, and the joint rate/modeadaptation becomes a problem of HMM control, which canbe solved within the framework of POMDPs [13]. Afifi andKrunz [5] studied the problem of adapting the FD operationmodes but with fixed MCSs, considering an OSA setting.

Previous work on LTE-U/Wi-Fi coexistence addresseddifferent issues, ranging from evaluating the performance ofcoexisting systems through simulation/experimentation [14],to analyzing it using stochastic geometry [15]. The problem

Fig. 2. System model of LTE-U/Wi-Fi coexistence (dashed lines representinterference from HeNB to Wi-Fi AP and STA).

of channel selection for LTE-U cell has been analyzed in [16]usig a Q-learning approach. Zhang et al. [17] presented analmost blank sub-frame scheme for enabling LTE in theunlicensed band. The proportional fair allocation for LTE andWi-Fi has been derived in [18]. Achieving fair coexistencebetween LTE-U/LAA and Wi-Fi requires a comprehensivesolution that integrates the optimal assignment for the clearchannel assessment (CCA) thresholds, optimal channel accessmechanisms, and efficient interference mitigation schemes.In this work, we focus on studying the interference mitigationaspect.

Our contributions are as follows. First, we propose anFD-enabled detection scheme for the TS mode based onthe sliding window correlator (Section III). We derive theprobabilities of detection and false-alarm under imperfectSIS, while taking into account inter-symbol interference (ISI).Second, we propose a modified TXOP scheme for Wi-Fi STAswith SIS capabilities (Section IV). In this scheme, Wi-Fi STAsexploit their SIS capabilities to either operate in the TS, TR,or CS modes. Third, we present a Markov model that incopo-rates the LTE-U ON/OFF activity (Section IV-A). Finally, wepresent a POMDP framework for determining the optimal Wi-Fi transmission strategy (FD mode and transmission rate) thatmaximizes the Wi-Fi link utility (Section V). We formulate theutility for different operation modes, rewarding the link for asuccessful transmission and penalizing it when outage occurs.In a preliminary version of this paper [19], we only discussedthe sliding-window correlator detection scheme. Due to spacelimit, proofs of various results are omitted, but can be foundin an online technical report [20].

II. SYSTEM MODEL

We consider an LTE-U small cell that coexists with aWi-Fi network in the unlicensed band (see Figure 2). TheLTE-U small cell consists of an HeNB that communicateswith a number of UEs over an aggregation of licensed andunlicensed channels. Without loss of generality, we focus onthe LTE-U DL. The Wi-Fi system consists of one FD-enabledAP that communicates with a number of FD-enabled STAs.A Wi-Fi network implements an exclusive channel occupancypolicy among its STAs. Specifically, a channel is allocated toonly a single Wi-Fi. Contention is resolved using CSMA/CA,where neighboring STAs defer from accessing the channel bysetting their network allocation vector (NAV) after decodingthe duration field in the MAC header.

In LTE-U, the HeNB must search for a free channel to use.If no idle channel is found, HeNB shares the spectrum withthe Wi-Fi system according to an adaptive duty cycle. During


the OFF period, the HeNB measures the traffic intensityof neighboring Wi-Fi STAs (e.g., by recording the MACaddresses of overheard transmissions) and adapts its duty cycleaccordingly.

Let l(n), sa(n), st (n), and w(n), respectively, denote theLTE-U, Wi-Fi AP, Wi-Fi STA, and noise signals at sam-pling time n. We assume these signals follow a symmetric-circular-complex Gaussian distribution: l ∼ N c(0, σ 2

l ), sa ∼N c(0, σ 2

s ), st ∼ N c(0, σ 2s ), and w ∼ N c(0, σ 2

w). Thereceived signals in the TR mode at the FD-enabled Wi-Fi APis written as:

ra(n) =(

hla(n) ⊗ l(n))

+(

hsa(n) ⊗ st (n))

+(χahaa ⊗ sa(n)

)+ w(n) (1)

where ⊗ is the convolution operation, hla is the channelgain between the HeNB and the Wi-Fi AP, hsa is thechannel gain between Wi-Fi STA and AP, haa is the gainof the self-interference channel of the AP (the attenuationbetween its transmit and receive chains), and χa is theSIS factor of the AP (perfect SIS occurs when χa = 0).LTE-U interfering signal traverses multiple paths and suffersISI before reaching the AP. We introduce the following threemetrics: ISI to noise ratio (ISNR), residual self-interference tonoise ratio (STNR), and the interference-to-noise ratio (INR).The ISNR = β2|hla |2σ 2

l/σ 2

w quantifies the ISI relative to the

noise floor, where σ 2l

is the power of the previously receivedLTE-U symbol (no ISI occurs when β = 0). The STNR =χ2

a |haa|2σ 2s /σ 2

w quantifies the AP residual self interferencepower relative to the noise floor. We focus on the LTE-Usignal detection problem at the AP. The INR = σ 2

l |hla |2/σ 2w

indicates LTE-U signal level with respect to the AP noisefloor. The signal-to-noise ratio (SNR ) is SNR = |hsa|2σ 2

s /σ 2w.

The signal-to-interference-and-noise (SINR ) ratio for the APis written as (a similar quantity can be defined for the STA):

SINR = |hsa|2σ 2s

|hla |2σ 2l +χ2

a |haa|2σ 2s +σ 2

w

= SNR

INR + STNR +1(2)

III. CYCLIC-PREFIX-BASED DETECTION

Differentiating between different types of interference helpsthe AP tune its mode/rate based on the detected interferencetype and maximize its utility. LTE-U and Wi-Fi signals areOFDM based, with every OFDM symbol consisting of asequence of data symbols and a CP that is appended to the startof the data symbol (see Figure 3). This CP is a replication ofsome data symbols. It is added for several purposes, includingtime guarding and facilitating synchronization and decodingat OFDM receivers. CP is most likely to be contaminatedby ISI.

Consider an LTE-U OFDM symbol that consists of N datasamples and L CP samples. At the Wi-Fi receiver, the receivedanalog signal is passed through the analog-to-digital converter(ADC) to obtain discrete samples. We buffer these samplesand assign them to two windows, W1 and W2, where thetiming difference between these windows equals (N−L)δn ; δn

being the duration of a sample. The two windows are sweptover all received samples (see Figure 3), where samples in

Fig. 3. Sliding-window-based OFDM signal detector.

Fig. 4. Mτ (n) vs. n/(N + L).

these windows are correlated and compared against a certaindetection threshold. We propose the following correlationtiming metric:

Mτ (n) = |A(n)|2(max (E1(n), E2(n)))2 (3)

where A(n) is the correlation between corresponding samplesin the two windows, and E1(n) and E2(n) are the energies ofthe samples in the two windows, respectively:

A(n) = ∑L−1k=0 ra(n − k)r∗

a (n − k − N)

E1(n) = ∑L−1k=0 ra(n − k − N)r∗

a (n − k − N),

E2(n) = ∑L−1k=0 ra(n − k)r∗

a (n − k) (4)

where ∗ is complex conjugate. We refer to the time instantat which the samples in the two windows correspond tothe CP and its original duplicated part as the optimal time.The optimal time indicates the presence of an LTE-U signal,where the correlation value exceeds a certain threshold. Forother time instances (called regular times), the correlationvalue will be small. In the absence of an LTE-U signal,the correlation value will also be small. The index τ in Mτ

indicates the alignment of the sliding windows with respect toOFDM symbol’s starting point (i.e, CP). τ takes integervalues in the period (−(N + L)/2, (N + L)/2], with τ = 0corresponding to the optimal time and τ > L correspondingto regular times. Figure 4 shows Mτ (n) as a function of theOFDM symbol index when four symbols are detected. Thisfigure is generated with INR = 25 dB, L = 500, N = 6400,and ISNR = 6 dB.

We define the hypothesis testing as follows:

ra(n)

=

⎧⎪⎨⎪⎩

χasa(n) + w(n), under H0, HeNB is OFF

l(n)+χasa(n)+w(n), under H0, n is a regular time

l(n)+χasa(n)+w(n), under H1, n is the optimal time

(5)

where the first two lines in (5) represent the nullhypotheses H0, and the third line represents the alternatehypothesis H1. Define the general detection rule as follows:

δ(ra(n)) ={

1 if Mτ (n) ≥ λth

0 if Mτ (n) < λth(6)


Fig. 5. FD modes: TR and TS modes (‘S’: Sense, ‘Fa’: AP frame, ‘Fs’: STAframe, and ‘H’: Header).

where λth is the detection threshold (determined next).We derive the statistics of Mτ (n) at the optimal time, regulartimes, and in the absence of LTE-U signals in our technicalreport [20].

Proposition 1: At the optimal time, the distribution ofMτ can be approximated by a normal distribution of meanμMτ=0 = μ2

Q and variance σ2Mτ=0

=4μ2Qσ 2

Q , where μQ and σ 2Q

are defined [20].Proposition 2: At any regular time, the distribution Mτ>L

can be approximated by a gamma distribution �( k2 , 2a1),

where k/2 = 1 is the shape parameter and 2a1 =2L

(L+0.7978√

L)2 is the scale parameter.Proposition 3: In the absence of an LTE-U signal, the

distribution of Mτ (denoted as M0) can be also approximatedby gamma distribution �( k

2 , 2a1).Note that Mτ (n) has the same distribution at regular times

and in the absence of an LTE-U signal. The probability ofdetection at a threshold λth is:

Pd(λth) = Pr [{Mτ=0 ≥ λth |H1}] = Q(λth − μMτ=0

σMτ=0

)(7)

where Q (·) is the complementary cumulative function of thestandard normal distribution. The false-alarm probability isgiven by:

PF (λth) = Pr [{M0 > λth}|H0] = 1 − Fγ,1,2a1(λth) (8)

where Fγ,1,2a1(λth) is the CDF of a gamma distribution withshape parameter one and scale parameter 2a1. The proofs forthe above results can be found in [20].

A. Neyman-Person (NP) Detection

We propose an NP detection rule based on the previouslyderived statistics. Note that false-alarms occur when there isno LTE-U signal and also at regular times. Let the maximumacceptable false-alarm probability be α. The NP detectionthreshold λth in (6) is:

λth = λN P = F−1γ,1,2a1

(1 − α). (9)

The NP detector does not require any prior knowledge ofthe signal nor noise statistics; it only requires knowing theCP length. Note also that the sensing outcomes are indepen-dent of what technology LTE uses in the unlicensed band(i.e., CSAT or LAA). The two-sliding-window correlator hasa low computational complexity and small memory overhead.This sensing scheme opens the way for adapting Wi-Fi CCAthresholds in response to CSAT/LAA activities, where moresensitive energy detection thresholds can be assigned. Due tospace limit we leave this issue to future investigations.

Fig. 6. Example of a modified TXOP operation mode (‘S’: Sense, ‘Fa1’,‘Fa2’, ‘Fa3’, ‘Fa4’: Frames sent by AP, and ‘Fs1’, ‘Fs2’: Frames sent bySTA).

IV. MODIFIED WI-FI TXOP

We now propose a modified TXOP scheme for FD-enabledWi-Fi systems. We divide the TXOP into Np time slots ofequal duration, during which AP and STA can exchange ULand DL frames. We consider two FD modes: The simultaneousTransmit-Receive (TR ) mode and the simultaneous Transmit-Sense (TS ) mode, as shown in Figure 5. Wi-Fi AP switchesbetween these modes to mitigate the interference caused byLTE-U transmission. We assume that the AP is the session“master”. It instructs the STA about the recommended mode ofoperation (e.g., TR or TS ) and the associated MCS indices thatthe STA has to use by embedding this information in the DLframe’s optional header field (e.g., field ‘H’ in Figure 6). Thisinformation requires a few bits, and hence represents smalloverhead. When LTE-U interference is relatively high theWi-Fi AP has an option of quitting the TXOP period earlyand switching to a new channel. We use CS to refer to thischannel-switching mode. AP also has the option of backing offuntil LTE-U completes transmission and the channel becomesidle again.

In the TR mode, the transmitted DL and UL framescan have different MCS indices (e.g., kD and kU , respec-tively). The Wi-Fi STA first reads the ‘H’ field in theDL frame and extracts the mode/MCS indices. Next, STAinitiates a simultaneous UL transmission with MCS index kU .After transmitting DL and UL frames, the AP and STAhave to exchange ACK frames in both directions, indicatingsuccessful reception. In the TS mode, the AP sends a DLframe with an MCS index kD, and simultaneously senses forany LTE-U signal using the detection scheme introduced inSection III. At the end of each time slot, AP updates its beliefabout LTE-U HeNB interference, and selects a new FD modewith suitable MCS indices for the next time slot (as discussedin Section V).

An example of the proposed TXOP scheme is shown inFigure 6, where the AP sends five DL frames (e.g., Np = 5),each of duration �. In this example, the AP starts in theTR mode with MCS indices kD = kU , whose modulationis 64QAM. AP sends in the DL direction frame ‘Fa1’. STAreads the header field and starts transmitting the ‘Fs1’ frame inthe UL direction using 64QAM modulation. HeNB ON cyclestarts just after the start of ‘Fa1’ and ‘Fs1’ transmission, whichcauses collision. Both AP and STA are not able to decode


their received frames, and hence no ACKs are transmitted. Inthis case, the AP updates its belief about HeNB interferenceand selects a new action (as explained in Section V). Forinstance, the next optimal action might be retransmitting the‘Fa1’ frame in the TS mode with QPSK modulation. If STAis able to decode this frame, it will send back an ACK. Uponreceiving an ACK for ‘Fa1’ and sensing an HeNB signal, theAP updates its belief about HeNB interference and may decideto send the next frame ‘Fa2’ in a TS mode with a raisedmodulation of 16QAM. The process continues as shown inFigure 6. In order for the AP to select the optimal action,which maximizes the link utility in the TXOP period, it shouldbe able to quantify the amount of LTE interference that the APand STA receive. This interference is affected by the channelgains between AP/STA and HeNB. We model LTE activityand its interference using a FSMC model.

A. Finite-State Markov Channel (FSMC) ModelWe assume that hla and hls are block Rayleigh fad-

ing channels with Doppler frequency fd , so these channelsmaintain a fixed level of fading over a time slot (e.g., �).Conventional FSMC models are based on paritioning theSINR variations into a set of nonoverlapping regions, in whichthe SINR remains in one region for a certain period oftime. SINR changes only from one region to adjacent ones.We divide hla and hls channel gains into M states, where states(i), i = 1, · · · , M , s(i) ∈ S, represents the i -th SINR region(i.e., s(i) = {ζ : gi ≤ ζ <gi+1}), where gi and gi+1 are region’sboundaries. We assign these boundary thresholds according tothe supported MCS indices, as explained in Subsection IV-B.For a Rayleigh fading channel with average SINR ζ , thesteady-state probabilities of these M states can be computed

as εi = Pr (ζ ∈ s(i)) = ∫ gi+1gi

1ζ

exp− z

ζ dz [21].Let pi, j be the transition probability between the i th and

j th states, i, j ∈ {1, 2, . . . , M}. The pi, j can be expressedas a function of the level crossing rate (LCR), steady stateprobabilities, and average fade duration. LCR indicates the rateat which the signal crosses the threshold gi . It can be writtenas Lgi =

√2πgi

ζfd exp{− gi

ζ}. By averaging Lgi by the time

the channel remains in state s(i) (i.e., average fade durationεi/�), we can approximate pi,i+1 and pi,i−1 as follows:

pi,i+1 ≈ Lgi+1�/εi , for i = 1, · · · , M − 1

pi,i−1 ≈ Lgi �/εi , for i = 2, · · · , M

pi,i = 1 − pi,i+1 − pi,i−1, for i = 2, · · · , M − 1 (10)

while p1,1 = 1 − p1,2 and pM,M = 1 − pM,M−1.This FSMC model does not account for LTE dynamics

(i.e., it assumes that HeNB is always ON). In CSAT/LAA,1

HeNB alternates between ON and OFF states. Let XON andXOFF be the distribution for these periods, with means xON

and xOFF . Wi-Fi AP could estimate these distributions andtheir means through measurements and parametric estimation.We first define a simple Markov chain with two states, thenwe explain how to use it for modulating the previous FSMC.

1LAA can be modeled as an ON/OFF process, because of the “discontinuoustransmission” functionality imposed by regulation.

Let t0 be the time instant the HeNB has been sensed switchingOFF. Let t1 be the time instant when AP starts the TXOP. Let� be the index of time slots in TXOP, where � = {1, · · · , Np}.Let u11,� denotes the probability that the HeNB remains OFFfor a period of � seconds starting at time t1 + (� − 1)�.Let u12,� be the probability that HeNB switches from OFFto ON during the �th time slot. The transition probabilities,u11,�, u12,� can be written as follows:

u11,� = 1 − FXOFF (t1 − to + ��)

1 − FXOFF (t1 − to + (� − 1)�), u12,� = 1 − u11,�

where FXOFF (·) is the CDF of XOFF . The steady stateprobabilities of this OFF state can be evaluated as εOFF =xOFF /(xON + xOFF ) [22]. We scale the transition probabilitiesin (10), and define new FSMC transition probabilities. Let pi, j

denotes the probability of transition from state s(i) to state s( j ),then the transition probabilities for the new FSMC are:

pi, j = u11,� pi, j , ∀ pi, j �= 0,∀i ≤ M − 2

pi, j = u12,�/(M − i − 1), ∀ j > i + 1, ∀i ≤ M − 2

pi, j = pi j , i > M − 2

pi, j = 0, otherwise (11)

As we will explain in Section V, Wi-Fi AP takes decisionsbased on its belief about hla and hls channel gains. Weextend the FSMC model to account jointly for these channels.We introduce a two-dimensional Markov chain based on thetransition probabilities defined in (11). Let pim, j n denotesthe transition probabilities for which channels hla and hls

switch from states i to j and from states m to n, respectively.The state transitions for channel hla and hls are independent.Accordingly, pim, j n can be stated as follows:

pim, j n = pi, j pm,n, ∀i, j, m, n = 1, · · · , M. (12)

B. SINR Threshold SelectionIEEE 802.11 standards assign various MCSs with convo-

lutional coding and low-density parity-check (LDPC) codes.Let K denotes the set of supported MCSs, where K ={k : 0, · · · , |K | − 1}. IEEE 802.11ac standards specify therelative constellation error2 (RCE) values for every MCSindex. The RCE is a measure of how far constellation pointsare from their true locations, and it is defined as a root-mean-square (RMS) of the normalized difference between the powerof the true and deviated constellation points. Constellationpoints deviate their true locations due to many reasons, includ-ing hardware impairments (e.g., noise and frequency offsets),interference, and channel impairments such as fading. RCEand SINR are related according to RCE rms ≈ √

1/SINR [23].We assign the SINR thresholds for the M = |K | +1 states according to the supported MCSs. Let INR th ,k

denotes the maximum LTE-U interference to noise ratio whereWi-Fi transmission with MCS index k still supported, thenINR th,k = SNR (RCE k,rms )

2−STNR −1, where RCE k,rms isthe RCE rms that supports the kth MCS. The fading boundariesin the FSMC model are assigned as g j+1 = INR th ,k=M− j−1,

2RCE is known also as error vector magnitude (EVM).


while the lower and upper thresholds are g1 = 0 and gM+1 =∞, respectively. Let θ

(i)k be the outage function indicator for

the kth MCS index when the channel gain is in the i th state,then

θ(i)k =

{1, for INR (i) > INR th ,k, ∀k ∈ K0, otherwise.

(13)

where INR (i) denotes the actual INR of LTE-U signal (i.e.,INR (i)∈[gi , gi+1)). θ

(i)k = 1 indicates that the Wi-Fi transmis-

sion is unsuccessful.

V. DECISION THEORETIC FRAMEWORK FOR

TRANSMISSION MODE/RATE CONTROL

Wi-Fi AP mitigates the interference caused by LTE-Utransmissions by jointly adapting FD modes and transmissionrates during the TXOP period. This requires knowledge abouthla , hls , has , and hsa channel gains. The channel gains of has

and hsa can be implicitly and explicitly estimated. However,the AP cannot estimate the hla and hls channel gains, becauseWi-Fi and LTE-U uses different techologies. Wi-Fi AP canstill obtain partial knowledge about these channel gains bymonitoring the performance of Wi-Fi UL and DL links overtime. For example, AP can indirectly deduce interferencelevels through monitoring ACKs and decoding received framesduring TXOP. Therefore, AP has to jointly control rates/modesin response to LTE-U hidden processes using this partialknowledge. This motivates the need for a HMM controlscheme which can be formulated through a POMDP frame-work [13]. POMDP assigns a belief (probability) for eachunknown parameter, and updates this belief sequentially overtime based on the resultant outcomes. POMDP maximizesthe Wi-Fi utility through mapping its belief about the LTE-U interference to a set of actions, consisting of recommendedjoint rate/mode configurations. This mapping function is alsoknown as the policy of POMDP.

For simplicity, we assume that channels between Wi-FiAP and STA (i.e., has and hsa) are static, and focus onformulating the POMDP problem for the channels betweenLTE-U HeNB and Wi-Fi nodes (i.e., hla and hls ). First, weintroduce the main components needed for formulating thePOMDP problem. Then, we introduce the reward functionsand explain the policy evaluation.

a) Time Horizon: POMDP will take place over a finitehorizon equals to the duration of one TXOP period (i.e.,Tp second), where a total of Np = Tp/� frames have tobe exchanged each of � duration. In other word, therewill be Np time slots during each TXOP transmission.We denote each time slot as � ∈ {1, · · · , Np}.

b) State Space: The state space represents the status ofhla and hls channel gains. We model the state spaceaccording to the FSMC model that is presented inSubsection IV-A. We introduce a two dimensional finitestate space S : S × S, where each state corresponds tohla and hls channel gains. The number of states per eachchannel is M =|K |+ 1. We denote the (h(i)

la , h(m)ls ) state

as s(i,m) ∈ S.

c) Action Space:At the start of each time slot, Wi-Fi APhas to take two decisions simultaneously; the FD mode(e.g., TR , TS, or CS ) and the applicable transmissionrates (i.e., the MCS indices kU and kD for the UL andDL transmissions, respectively). The channel switchingCS mode is only selected when the transmission with thelowest MCS index is believed to be unsuccessful; giventhat AP has enough knowledge about suitable channelsfor switching to. AP can also replace the CS actionby a ‘backoff’ action, where it backs off until LTE-Ugets OFF and channel becomes idle again. The actionspace is written as A = {TR (kD, kU ), TS (kD), CS },and it has |K |2 +|K |+1 possible actions. We denotethe action that the AP takes at the start of timeslot � as a�.

d) Observation Space:Wi-Fi AP takes an action a� ∈ Aat the start of time slot � and waits for an observationat the end. This observation depends on the actionthat the AP takes and the true state of interference.The AP takes a TR action and receives four pos-sible observations: Decode or Undecode {D, U} forthe UL frame and ACK or NACK {A, N} for theDL frame (NACK indicates ACK timeout). At theend of a TS action, Wi-Fi AP receives four pos-sible outcomes: ACK or NACK for the DL frameand busy B or idle I for sensing LTE-U signal. Theobservation space is written as O = {{oTR }, {oTS }},where oTR ∈ {(D, A), (D, N), (U, A), (U, N)}, and oTS ∈{(I, A), (I, N), (B, A), (B, N)}. Let o� denotes the obser-vation vector that AP receives at the end of time slot �.Let q(i,m)

a�,o�denotes the probability of receiving an obser-

vation vector o� when the AP takes an action a�, whilethe channel states are s(i,m):

q(i,m)TR (kD ,kU ),oTR

=

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

(1 − θ(i)kU

) (1 − θ(m)kD

), for oTR = (D, A)

(1 − θ(i)kU

) θ(m)kD

, for oTR = (D, N)

θ(i)kU

(1 − θ(m)kD

), for oTR = (U, A)

θ(i)kU

θ(m)kD

, for oTR = (U, N)

q(i,m)TS (kD),oTS

=

⎧⎪⎪⎪⎨⎪⎪⎪⎩

(1 − PF )(1 − θ(m)kD

), for oTS = (I, A)

(1 − PF )θ(m)kD

, for oTS = (I, N)

P(i)d (1 − θ

(m)kD

), for oTS = (B, A)

P(i)d θ

(m)kD

, for oTS = (B, N)

q(i,m)CS ,o = 1/|O|, where θ

(i)kU

and θ(m)kD

are the outage

indicator functions defined in (13), while P(i)d and PF

are the detection and false-alarm probabilities defined in(7) and (8), respectively.

e) Belief Updates: Wi-Fi AP maintains a belief about theactual status of hla and hls channel gains. Let π� ∈ Bbe the AP’s belief vector about the M2 states at thestart of the time slot �, where B denotes the beliefspace. The AP takes an action a� ∈ A, monitors anobservation o� ∈O, and updates its belief vector for thenext coming time slot � + 1 according to the following


Bayes rule

π( j,n)�+1 =

q( j,n)a�,o�

∑Mi=1

∑Mm=1 pim, j nπ

(i,m)�∑M

j ′=1∑M

n′=1 q( j ′,n′)a�,o�

(∑Mi=1

∑Mm=1 pim, j ′n′π(i,m)

�

) (14)

where π( j,n)�+1 is an element in π�+1. The belief vector

will be helpful for derving the POMDP policy, becauseis has been proved to be a sufficient statistic [24].

A. Utility FormulationLet the DL and UL frames consist of ddl and dul data

symbols, where each frame lasts for a time period of� seconds. The UL and DL frame rates, namely, RkD

DL andRkU

U L , respectively, are written as:

RkDDL = ddlbkD ckD /�, RkU

U L = dulbkU ckU /� (15)

where bkD , ckD , bkU , and ckU are the modulation order andcoding rate for the DL and UL frames, respectively. LetPa and Ps denotes the power consumed in the AP andSTA frame transmissions, respectively. We define the utilityfunction Wa�,o� for the action and observation obtained at thetime slot � as:

WTR (kD ,kU ),o� =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

RkUU L + RkD

DL − ηPa − ηPs , o� = (D, A)

RkUU L − ηPa − ηPs , o� = (D, N)

RkDDL − ηPa − ηPs , o� = (U, A)

−η(Pa + Ps ), o� = (U, N)

WTS (kD),o� =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

RkDDL − ηPa , o� = (I, A)

−ηPa , o� = (I, N)

RkDDL + �kD − ηPa , o� = (B, A)

�kD − ηPa , o� = (B, N)

WCS ,o� = η(Pa + Ps ) (16)

where η is a scaling coefficient used to match power and rateterms and �kD is the awareness reward constant, which is usedto reward the AP for detecting the LTE-U signal when it is ON.We reward the AP for taking the TS action only when LTE-Uis ON. �kD and η are left as implementation parameters.

B. POMDP Problem SolutionThe AP updates its belief vector as in (14), and takes

an action based on a pre-defined policy. This policy is afunction μ that maps the belief vector π� to an action a� ∈ A(i.e., μ : π� �→ a�). The optimal policy μ∗ is the one thatmaximizes the expected reward over the TXOP period. Attime slot �, the AP incurs an immediate reward (a.k.a. myopicreward) for each action a� it takes. This action also has anexpected long term reward on future (e.g., slots � + 1 to Np )(a.k.a. reward-to-go). AP’s expected reward is the sum of thesetwo rewards, and it is formulated using the value functionVa�(π�). The optimal policy μ∗ is a sequence of actionsthat maximizes this value function over the TXOP period.The expected immediate reward for an action a� taken at thestart of time slot � is defined as:

Da�(π�) =∑o�∈O

M∑i=1

M∑m=1

π(i,m)� q(i,m)

a�,o�Wa�,o� . (17)

We plot the immediate reward as a function of LTE-U inter-ference in Subsection VI-B.2. The long term reward for anaction a� taken at time slot � is defined as:

La�(π�) = κ∑o�∈O

{ (max

a′�+1∈A

Va′�+1

(π�+1))�a�,o�,π�

}(18)

where �a�,o�,π� is the denominator in (14) and κ is a discountfactor that prioritizes the long term reward, κ ∈ [0, 1]. Noticethat the max

a′�+1∈A

Va′�+1

(π�+1) term is the optimal value function

at time slot � + 1. Consequently, the value function of takingaction a� at time slot � can be formulated by combining theimmediate reward (17) and the long term reward (18):

Va�(π�) = Da� (π�) + κ La�(π�). (19)

The optimal policy at time slot � can be derived as:

μ∗(π�) = arg maxa�∈A

Va�(π�). (20)

The value function in (19) has been proved to be a piecewiselinear and convex [24]. The domain in (20) is the beliefspace B, which is a continuous space. Obtaining the optimalsolution for POMDP is computationally feasible for smallnumber of system states (e.g., up to 10 states). The numberof states in our system is much larger, and accordinglysub-optimal or approximate solutions are preferable. Lots ofalgorithms have been proposed in literature for approximatingthe solution for POMDPs with large number of state [25], [26].We have solved the above problem using SARSOP, a point-based approximate POMDP solver [27]. SARSOP reduces thecomplexity of (19) by sampling a subset of the belief spaceR ⊂ B, and solving the problem in (20) successively. SAR-SOP updates R based on a simple online learning technique.

VI. PERFORMANCE EVALUATION

A. Sliding Window Correlator

We consider an FD enabled Wi-Fi STA with noisefloor σ 2

w = −90 dBm, and transmitted power σ 2s =

20 dBm. We set σ 2l

= σ 2w and vary σ 2

l , β, and χa .We analyze how different SIS capabilities, and ISI contamina-tion in the CP affect detector’s performance for various setupsusing numerical and simulation results. We set L = 500 andN = 6400 taking into account the sampling frequency used intypical Wi-Fi receivers fs ≥ 20 MHz and the time length of anLTE-U OFDM symbol (e.g., 72μsec). Unless otherwise stated,all simulation results were generated with 3000 realizations.

In Figures 7 and 8, we set the false alarm probability to0.01 and compute the NP detection threshold as in (9). Next,we evaluate the mis-detection probability through simulationand numerical computations as derived in (7). The detectionscheme attains the 10−3 mis-detection probability at even lowLTE-U signal level such as INR = −5 dB (see the ‘No ISI’plots in Figure 7). Detector performance degrades as more ISIand residual self interference are generated.

We analyze the receiver operating characteristic (ROC)performance of the developed detector for several INR and SISconditions (see Figures 9 and 10). The false-alarm probabilityincreases as INR decreases below a certain limit (see the ‘INR= −1 dB’ plot in Figure 9). Similar result also holds for self


Fig. 7. Mis-detection probability vs. INR for various ISI levels (PF = 0.01,no RSI).

Fig. 8. Mis-detection probability vs. INR for various RSI (PF = 0.01,ISNR = 2 dB).

Fig. 9. ROC curves for various INR levels (ISNR = 2 dB, STNR = 5 dB).

Fig. 10. ROC curves for various RSI levels (ISNR = 2 dB, INR = 2 dB).

interference; the false alarm probability increases as STNRincreases beyond a certain limit (see the ‘STNR = 10 dB’plot in Figure 10.

B. Joint Rate and Mode Adaptation Scheme1) Simulation Setup and Methodology: We start with a

simple topology consisting of a Wi-Fi pair (e.g., AP andSTA) that coexists with one LTE-U small cell. The twosystems share a channel of 20 MHz in an indoor environment.We have set channel parameters according to the tech-nical reports [1], [2]. We assume that both Wi-Fi andLTE-U have saturated traffic. AP has contended success-fully for a channel access, and occupies the spectrum

Fig. 11. TS mode reward vs. INR at the DL (SNR= 25 dB,STNR = 5 dB).

Fig. 12. TR mode reward vs. INR at the DL (UL INR= 2 dB, kD = kU ).

for a duration equals to the TXOP maximum period(i.e., 3 msec). We simulate various SINR scenarios by varyingthe location of the Wi-Fi STA and evaluating the achievedthroughput for each scenario. We set the SINR at AP and STAreceiver to be equal. Initially, we set LTE-U ON and OFFperiods to be exponentially distributed with equal means of10 msec, and then we relax these values. We consider the fol-lowing MCS indices K = {0, · · · , 7} with the correspondingmodulation orders bk ∈ {1, 1, 2, 2, 4, 4, 6, 6} and coding ratesck ∈ {1/2, 3/4, 1/2, 3/4, 1/2, 3/4, 2/2, 3/4}. We compare theperformance of our proposed joint rate/mode (JRM) adaptationscheme against the following adaptation schemes. (i ) Optimal(OPT) adaptation scheme: Wi-Fi AP has full knowledge aboutactual interference and SINR values at the AP and STAreceivers. OPT scheme has an oracle knowledge and attainsthe capacity of the FD channel. (i i ) Single MCS stepping(SMS) adaptation scheme: Wi-Fi AP steps up and down theused MCS index depending on the success and failure ofthe previous frame transmition, respectively. SMS schemeemulates other rate adaptation schemes proposed in literature,including adaptive rate fallback (ARF), but is has a fasterresponse [9]. In the third scheme, we consider a TR modewith a fixed MCS-k (TFM-k).

2) Immediate Reward Plots: The performance of theTS expected immediate reward function Da�=TS (kD) definedin (17) is shown in Figure 11 for various MCS indices. Theseplots represent the upper bound of the expected immediatereward. Lower MCS indices become more desirable as INRincreases in the DL. We also plot the immediate expectedreward function defined in (17) for TR mode Da�=TR (kD ,kU )

versus the LTE-U interference received by the STA for variousMCS indices, as shown in Figure 12. We see that by increasingthe INR received by the DL link the recommended MCS indexreduces as desired.


Fig. 13. Wi-Fi average throughput vs. SINR at AP.

Fig. 14. Wi-Fi average throughput vs. SINR at AP for various adaptationschemes.

Fig. 15. Wi-Fi average throughput vs. LTE-U OFF period mean (exponen-tially distributed).

3) Wi-Fi Performance: We study the performance of theproposed JRM scheme in comparison with TFM-k scheme(see Figure 13). JRM scheme scales with the changesin SINR. The overall average performance for the proposedscheme outperforms the fixed MCS assignment. This showsthe significance of adapting the rate for mitigating LTE-Uinterference.

Classical WLAN rate adaptation schemes, namely, Onoe,ARF/AARF, and SampleRate have relatively slow response;they adapt MCS indices every tens, hundreds, or thousands ofmsec [9]. Our scheme adapts the rate on a shorter time scale.The SMS scheme mimics these classical schemes and has afaster response. We compare the performance for our schemeagainst the SMS scheme in Figure 14. JRM scheme outper-forms the SMS because it adapts for interference while takinginto account LTE-U behavior, while SMS adapts the rate inan ad hoc fashion. We investigate the performance of JRMscheme when compared with OPT scheme(see ‘OPT-FD’ and‘OPT-HD’ plots). ‘OPT-FD’ and ‘OPT-HD’ plots represent theupper bounds that the AP can achieve for the FD and HDcases, respectively. JRM provides 1.5x to 1.9x throughput gainrelative to the OPT-HD.

4) Impact of LTE-U Behavior: Our scheme is a wareof LTE-U behavior, which is enabled with the help of thetwo-sliding-windows sensing scheme. We investigate the

Fig. 16. LTE-U throughput vs. the number of Wi-Fi nodes.

impact of LTE-U parameters on Wi-Fi performance. We fix themean for the ON period to 10 msec, and let the OFF periodbe exponentially distributed. We plot the Wi-Fi AP averagethroughput versus the mean of the OFF period (see Figure15). The increase in the mean of the OFF period enhances theperformance of Wi-Fi. JRM approaches the OPT scheme asthe mean of the OFF period exceeds that of the ON period.More results are also available in our technical report [20].

5) LTE-U Performance: In our scheme, Wi-Fi AP doesnot back off in response to collisions caused by LTE-U.Instead, Wi-Fi AP mitigates collisions by jointly adaptingrate and mode. We seek to analyze how this behavior mightimpact LTE-U performance. Let’s consider a simple CSATduty cycle adaptation scheme for which the HeNB adapts theduty cycle according to the number of Wi-Fi nodes n (e.g.,dc = 1/(n + 1)).

We set LTE-U ON and OFF periods to be 20 msec and gen-erate uniformly random Wi-Fi transmission attempts duringLTE-U OFF period, where each Wi-Fi transmission lasts for 3msec. Figure 16 shows that Wi-Fi collisions causes relativelyminimal degradation to LTE-U performance.

VII. CONCLUSIONS

Wi-Fi/LTE-U coexistence faces many challenges due to thedissimilarities between LTE-U and Wi-Fi access mechanisms.In this work, we addressed two problems: The detectionof LTE-U signal and the adaptation of Wi-Fi modes/ratesassuming an FD framework. We have introduced an FD-based sliding-window correlator that detects LTE-U signals,and analyzed the detector performance under imperfect self-interference suppression. We have introduced a POMDP-basedscheme for jointly adapting Wi-Fi FD modes and transmissionrate (i.e., MCS indices) based on the Wi-Fi belief about LTE-Uinterference. Our results indicate that joint rate and modeadaptation provides on average around 1.5x at low SINRand 1.9x at high SINR throughput gain over the optimalHD theoretical throughput. Future work includes consideringthe coexistence between several LTE small cells and Wi-Finetworks.

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Mohammed Hirzallah (S’15) received the B.Sc.degree in electrical engineering from the Univer-sity of Jordan, Amman, Jordan, in 2011, and theM.Sc. degree in electrical and computer engineeringfrom The University of Arizona, Tucson, AZ, USA,in 2015, where he is currently pursuing the Ph.D.degree. His research interests include the designand analysis of wireless protocols and systems.He investigates the problem of coexistence betweenheterogeneous wireless networks.

Wessam Afifi (S’11) is currently pursuing thePh.D. degree with the Department of Electrical andComputer Engineering, The University of Arizona.In 2015, he was a Wireless Systems Intern withNokia Technologies, San Francisco, CA, USA. Heis currently a Graduate Research Associate with TheUniversity of Arizona. His research interests lie inthe areas of wireless communications and network-ing, with emphasis on resource allocations, adaptiveprotocols, dynamic spectrum access systems, Wi-Fi/LTE-U coexistence, and full-duplex communica-

tions. He is a co-inventor of seven U.S. patent applications and has authoredseveral peer-reviewed conference papers and journal articles. He has made afew contributions to the IEEE Standards. He won the first prize in the graduatedivision of the physical sciences, mathematics, computer engineering, andcomputer science category for the Student Showcase in 2014. In 2015, hewon the GPSC Research and Project Grant. He won two Best Poster Awardsat the BWAC I/UCRCs in 2013 and 2016. He served as a TPC member anda reviewer for many conferences and journals.

Marwan Krunz (S’93–M’95–SM’04–F’10)received the Ph.D. degree in electrical engineeringfrom Michigan State University in 1995. Hejoined The University of Arizona in 1997, aftera brief post-doctoral stint with the Universityof Maryland. He held various visiting researchpositions at University Technology Sydney,INRIA-Sophia Antipolis, HP Labs, Universityof Paris VI, University of Paris V, University ofJordan, and US West Advanced Technologies. Heserved as the UA Site Director for Connection

One, an NSF IUCRC that focuses on wireless communication circuitsand systems. He is currently the Kenneth VonBehren Endowed Professorwith the Department of ECE, The University of Arizona. He also holds ajoint appointment as a Professor of Computer Science. He co-directs theBroadband Wireless Access and Applications Center, a multi-universityindustry-focused NSF center that includes over 16 industry affiliates. In2010, he was a Visiting Chair of Excellence with the University of Carlos IIIde Madrid. His research interests lie in the areas of wireless communicationsand networking, with emphasis on resource management, adaptive protocols,and security issues. He has authored over 245 journal articles and peer-reviewed conference papers, and is a co-inventor of several U.S. patents.He was an Arizona Engineering Faculty Fellow from 2011 to 2014, andan IEEE Communications Society Distinguished Lecturer from 2013 and2014. He was a recipient of the 2012 IEEE TCCC Outstanding ServiceAward. He received the NSF CAREER Award in 1998. He served on theeditorial boards of the IEEE/ACM TRANSACTIONS ON NETWORKING,the IEEE TRANSACTIONS ON MOBILE COMPUTING (TMC), the IEEETRANSACTIONS ON NETWORK AND SERVICE MANAGEMENT, ComputerCommunications Journal, and the IEEE Communications InteractiveMagazine. He currently serves on the editorial board for the IEEETRANSACTIONS ON COGNITIVE COMMUNICATIONS AND NETWORKS. Hewas the General Vice Chair of the WiOpt 2016 and a General Co-Chairof WiSec’12. He was the TPC chair of the WCNC 2016 (NetworkingTrack), the INFOCOM’04, the SECON’05, the WoWMoM’06, and the HotInterconnects 9. In 2017, he will be the next EiC of TMC. He has served onthe steering advisory committees of numerous conferences and on the panelsof several funding agencies. He was a keynote speaker, an invited panelist,and a tutorial presenter at numerous international conferences.

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