Modeling, Simulation and Fairness Analysis of Wi-Fi and Unlicensed LTE Coexistence

1 Modeling, Simulation and F airness Analysis of W i-Fi and Unlicensed L TE Coe xistence Morteza Mehrnoush, Rohan Patidar , Sumit Ro y , and Thomas Henderson Uni versity of W ashington, Seattle, W A-98195 Email: {mortezam, rpatidar , sroy , tomhend}@uw .edu Abstract —Coexistence of small-cell L TE and Wi-Fi networks in unlicensed bands at 5 GHz is a topic of active inter est, primarily driven by industry groups affiliated with the two (cellular and Wi-Fi) segments. A notable alternative to the 3GPP Rel. 13 defined L TE-Licensed Assisted Access (L TE-LAA) mechanism for coexistence is the unlicensed L TE (L TE-U) Forum [1] that prescribed Carrier Sense Adaptive T ransmission (CSA T) whereby L TE utilizes the unlicensed band as a supplemental downlink unlicensed carr ier (to enhance downlink data rate) to normal operation using licensed spectrum. In this work, we pro vide a new analytical model for perf ormance analysis of unlicensed L TE with fixed duty cycling (L TE-DC) in coexistence with Wi-Fi. Further , the analytical results are cross-v alidated with ns-3 (www .nsnam.org) based simulation r esults using a newly developed coexistence stack. Thereafter , notions of fair coexistence ar e in vestigated that can be achieved by tuning the L TE duty cycle. The results show that as the number of Wi-Fi nodes increases, the Wi-Fi network in coexistence with L TE-DC with 0.5 duty cycling achieves a higher throughput than with an identical Wi-Fi network. Index T erms —Wi-Fi, L TE-DC, 5GHz Unlicensed, Coexistence. I . I N T RO D U C T I O N W ireless networks (e.g cellular and W i-Fi) are deployed un- der two modes of spectrum regulation: licensed (i.e. exclusi ve use) for cellular , and unlicensed spectrum (whereby sources hav e no interference protection by rule) as for Wi-Fi. This fundamental difference is reflected in the access mechanisms of the two regimes: scheduled time and/or frequency sharing by the cellular base-station, whereas Wi-Fi networks use a distributed random time-shared Distributed Coordination Function (DCF) access mechanism. The exploding growth of mobile network traf fic (fed by high-end devices running bandwidth-hungry applications) has led network operators to consider v arious ‘offload’ strategies in (typically indoor) hot- spots, whereby local traffic access is provided by broadband wireless LANs. W i-Fi has been the network of choice, b ut with the emergence and maturation of L TE-Unlicensed technology , operators now have a choice of deploying one or both. A target for such coexistence operation is the 5 GHz UNII bands where a significant swath of additional unli- censed spectrum was earmarked by the FCC in 2014 [2]. T wo different specifications for unlicensed L TE operation hav e been proposed: L TE Licensed Assisted Access (L TE- LAA) and L TE Unlicensed (L TE-U). L TE-LAA (de veloped by 3GPP) integrates a Listen-Before-T alk (LBT) mechanism [3] similar to carrier sensing multiple access collision avoidance (CSMA/CA) for W i-Fi, to enable spectrum sharing worldwide. This work was supported in part by the National Science Foundation (NSF) under A ward 1617153. L TE-U employs adaptiv e duty cycling - denoted as Carrier Sense Adaptive T ransmission (CSA T) - to adapt the ON and OFF duration for L TE channel access [4]. L TE-U is proposed for regions where LBT is not required and is promoted by the L TE-U forum [4]. As currently specified, both L TE-LAA and L TE-U utilize carrier aggregation between a licensed carrier and an (additional) unlicensed carrier for enhanced data throughput on the downlink (DL), and all uplink traffic is transmitted on the licensed carrier . Our work is distinct from standardized L TE-U in se veral important aspects - we only consider unlicensed L TE with fixed duty cycling which we denote as L TE-DC 1 . Further, we do NO T consider the impact of rate adaptation on either W i- Fi or L TE-U performance and assume saturation (full buf fer) conditions. As such, we caution against any extrapolation or other untenable application of our throughput or fairness results to actual deployment scenarios that do not conform to our assumptions. Many industry inspired explorations regarding coexistence of W i-Fi and L TE-U are based on simulations or experiments which are independently unv erifiable. There is thus a need for a transparent and comprehensi ve analysis methodology for this problem, to which we attempt to make a significant contribution. Our coexistence throughput model is backed by results from actual network simulation of the coe xistence stack simulated within ns-3 2 , and paves the way for exploring Wi-Fi and L TE-DC fairness, a critical criterion for ev aluation of any coexistence system. The specific contributions of this work include: • A new analytical model for throughput of W i-Fi in coexistence with L TE-DC for full buf fer load condition; • Simulating the coexistence scenario using the ns-3 simu- lator by developing the coexistence scenario and validat- ing the analytical model based on the simulation results; • Applying v arious structured definitions of fair sharing to this use-case and ev aluating W i-Fi access and throughput fairness for them. This paper is organized as follows. Section II presents the related works by industry and academia. Section III describes the W i-Fi and L TE-DC access mechanisms in coe xistence network. In Section IV , the analytical throughput modeling of the coexistence network is presented. Section V illustrates the ns-3 simulation and numerical results for comparison. Section 1 L TE-U implicitly assumes CSA T ; thus L TE-DC is our shorthand for L TE- U with fixed duty cycling. 2 The most popular open source network simulator for academic research, see www .nsnam.org. 2 Opera to r A Opera tor B Wi-Fi Wi-Fi (a) (b) Wi-Fi LTE-DC Fig. 1: (a) coexistence of two W i-Fi networks. (b) coexistence of a W i-Fi network with an L TE-DC network which is transmitting in DL. VI discusses the W i-Fi fairness in coexistence with the L TE- DC. Section VII illustrates the numerical results of fairness in vestigation of the coexistence system. Finally , section VIII concludes the paper . I I . R E L A T E D W O R K An early work that explored 5 GHz L TE and Wi-Fi co- existence [5] from a radio resource management perspective showed that W i-Fi can be severely impacted by L TE transmis- sions in some conditions, suggesting the need for measures of fair coexistence. Thereafter Nokia Research [6] proposed a bandwidth sharing mechanism whereby the impact on Wi- Fi network throughput can be controlled by restricting L TE activity . In situations where a large number of Wi-Fi users try to access the network, users may spend a long time in back-off (i.e. medium is idle); if L TE could exploit these silent times, ov erall bandwidth utilization efficienc y could increase without negati vely impacting W i-Fi performance. In [7], a performance ev aluation of L TE and Wi-Fi coexistence was conducted via simulation which showed that while L TE system performance is slightly affected, Wi-Fi is significantly impacted by L TE transmissions. W i-Fi channel access is most often blocked by L TE transmissions, causing the W i-Fi nodes to stay in the listen mode more than 96% of the time. In [8], Google’ s in vestigation sho ws that in many circum- stances, L TE-U coexists poorly with W i-Fi in the 5 GHz band. The underlying causes include: a) L TE-U’ s duty-cycling causes L TE transmissions to begin abruptly , often in the middle of W i-Fi transmissions, interrupting them and causing W i-Fi to ratchet down the transmission rates via rate control in response to increased error rates; and b) the lack of an ef fective coexistence mechanism in scenarios where L TE-U and Wi- Fi de vices hear each other at moderate but non-ne gligible power levels. In [9], the research noted that L TE-U and W i-Fi coexistence is a balancing act between throughput and latency . Either throughput or latency of a co-channel Wi-Fi network is negati vely affected if the L TE duty cycle period is too low or too high, respectiv ely . They also illustrate that with 50% duty cycling, the W i-Fi throughput would be affected by more than half. On the other hand, Qualcomm [10] in vestigated the coexistence of Wi-Fi with L TE-U through simulation and showed that significant thr oughput gain can be achiev ed by aggregating L TE across licensed and unlicensed spectrum; further (and importantly), this throughput improv ement does not come at the expense of degraded Wi-Fi performance and both technologies can fairly share the unlicensed spectrum. In [11] report to FCC, W i-Fi coexistence with L TE-U was measured by impact on Wi-Fi throughput, latency , and V oIP dropped calls via simulation. The study concluded that L TE- U (as prescribed) does not meet the ‘fair’ coexistence crite- rion and additional measures are necessary . In [12], Huawei discussed the fundamental differences in the physical and Medium Access Control (MAC) layer design between L TE and Wi-Fi, that may negativ ely impact the channel occupancy of co-channel Wi-Fi, especially in some high-load cases. Howe ver , L TE Pico performs much more robustly e ven with high-load interfering access point (AP) nearby . Sev eral factors contribute to this result, including link adaptation and Hybrid Automatic Repeat Request (HARQ) retransmission in L TE. In [13], the fairness of W i-Fi airtime in the coexistence of Wi-Fi/L TE-LAA LBT and W i-Fi/L TE-U with CSA T is in vestigated. The paper shows that both mechanisms can provide the same level of fairness to Wi-Fi transmissions if a suitable proportional fair rate allocation is used. Consequently , the choice between using CSA T and LBT is a decision driv en by the L TE operators. In [14], the effect of large L TE-U duty cycle on the association process of W i-Fi was explored. A National Instrument (NI) experimental set-up was used to show that a significant percentage of Wi-Fi beacons will either not be transmitted in a timely fashion or will not be receiv ed at the L TE-U BS which makes it difficult for the L TE-U BS to adapt its duty cycle in response to the Wi-Fi usage. The results in this paper illustrated that in order to maintain association fairness, the L TE-U should not transmit at the maximum duty cycles of 80% even if it deems the channel to be vacant. In summary , industry-driven research shows a) are taken negati ve consequences occur for Wi-Fi with the proposed L TE-DC coexistence mechanisms, while others b) claim that the fair coexistence is feasible with necessary tweaks or en- hancements. Transparent analytical inv estigations on this topic hav e been sparse. One notable effort is [15] where channel access probability for W i-Fi stations is computed in presence of L TE-DC. While they model the (expected) decrease in W i- Fi channel access due to L TE-DC, the additional collision probability of Wi-Fi caused by interference with the onset of an L TE-U ON period is not considered. The analytical model 3 T ABLE I: Glossary . Parameter Definition W 0 W i-Fi minimum contention window m W i-Fi maximum retransmission stage PhyH preamble with physical header MA CH MA C header A CK Acknowledgment length σ W i-Fi slot time δ propagation delay DIFS distributed interframe space SIFS short interframe space T on L TE-DC ON period T of f L TE-DC OFF period T C L TE-DC total cycle period α L TE-DC duty cycle N B W i-Fi packet data portion size T d W i-Fi data portion duration CCA Clear Channel Assessment n w Number of W i-Fi APs in coexistence r 0 MCS0 data rate r w W i-Fi data rate r l L TE-DC data rate P c,w W i-Fi Collision Probability τ w a Wi-Fi station transmission probability per slot P c,w − l Collision probability from L TE-DC to W i-Fi P c,t total collision probability n k maximum number of packets fit in one OFF period L b ( k ) lower bound of the interval for contention U b ( k ) upper bound of the interval for contention p 0 h ( k ) probability of k -th packet hitting the ON edge P 0 s ( k ) successful transmission probability of k -th packet E n av erage number of packets fit in the OFF period P trw W i-Fi transmission probability P sw W i-Fi successful transmission probability T put w W i-Fi throughput T put l L TE-DC throughput τ wo a Wi-Fi station transmission probability per slot in Wi-Fi only network P c,wo Collision probability of Wi-Fi in Wi-Fi only network T put wo W i-Fi throughput in Wi-Fi only network T sw expected duration of a successful packet T cw expected duration of a collided packet in [16] for the coexistence of Wi-Fi and L TE-DC does not provide any close form expressions (for collision probability and throughput) and their scenario does not conform to the real specification of L TE-DC [4]. W e hope that our contribution to this important problem validated by actual network simulation provides a basis for resolving some of the importance coexis- tence issues. I I I . C O E X I S T E N C E O F L T E - D C A N D W I - F I : M A C P RO TO C O L M E C H A N I S M S A brief revie w of the W i-Fi DCF and L TE-DC MA C is presented, to highlight their basic dif ferences - L TE-DC is a scheduled time division multiple access (TDMA) based while W i-Fi is random access CSMA/CA. A. W i-F i DCF The W i-Fi distributed coordination function (DCF) MA C employs CSMA/CA [17] as illustrated in Fig. 2. Each node attempting transmission must first ensure that the medium has been idle for a duration of DCF Interframe Spacing (DIFS) using the energy detection (ED) 3 and carrier sensing (CS) 4 mechanism. When either of ED or CS is true, the clear channel assessment (CCA) flag is indicated as busy . If the channel has been detected idle for DIFS duration and the station is not accessing immediately after a successful transmission, it transmits. Otherwise, if the channel is sensed busy (either immediately or during the DIFS) or the station is again seeking channel access after a successful transmission, the station persists with monitoring the channel until it is measured idle for a DIFS, then selects a random back-of f duration (in units of slot time σ = 9 µs ) and counts down. Specifically , a station selects a back-off counter uniformly at random in the range of [0 , 2 i W 0 − 1] where the v alue of i (the back-off stage) is initialized to 0 and W 0 is the minimum contention window chosen initially . Each failed transmission due to packet collision 5 results in incrementing the back-off stage by 1 (binary exponential back-off or BEB) and the node counts down from the selected back-off value. During back- off, a node decrements the counter ev ery slot duration as long as no other transmissions are detected. If during countdo wn a transmission is detected, the counting is paused; nodes continue to monitor the busy channel until it goes idle for DIFS period before the back-of f countdown is resumed. Once the counter hits zero, the node transmits a packet. Any node that did not complete its countdown to zero in the current round, carries over the back-off value and resumes countdown in the next round. Once a transmission has been completed successfully , the value of i is reset to 0. The maximum value of back-off stage i is m ; it stays in m -th stage for one more unsuccessful transmission (for a total of 2 attempts at back-off stage m ). If the final transmission is unsuccessful, the node drops the packet and resets the back-off stage to i = 0 . For any successful transmission, the intended receiver will transmit an acknowledgment frame (ACK) after a Short Interframe Spacing (SIFS) duration post reception; the ACK frame structure is sho wn in Fig. 3 which consists of preamble and MAC header . The A CK frame chooses the highest basic data rate (6 Mbps, 12 Mbps, or 24 Mbps) for transmitting the MA C header which is smaller than the data rate used for data transmission. B. LTE-DC L TE-DC uses a duty-cycling approach (i.e. alternating the ON and OFF period, where the L TE ev olved Node B (eNB) is allowed to transmit only during the ON duration) where the duty cycle (ratio of ON duration to one cycle period) is determined by perceived W i-Fi usage at the L TE-DC eNB, using carrier sensing. During the ON period, the L TE-U eNB schedules DL transmissions to UEs, unlike Wi-Fi in which transmissions are governed by the CSMA/CA process. Fig. 4 shows the L TE-DC transmission for the duty cycle of 0.5. If a single W i-Fi AP is detected, the maximum duty cycle could be 3 The ability of W i-Fi to detect any external (out-of-network) signal using an energy detector . 4 The ability of Wi-Fi to detect and decode an incoming Wi-Fi signal preamble. 5 A collision ev ent occurs if and only if two nodes select the same back-of f counter value at the end of a DIFS period (if there is no hidden terminal). 4 Packet Time slot DIFS Busy Backoff SIFS Resume Backoff ACK DIFS L-STF (2Sym) L-LTF (2Sym) L-SIG (1Sym) Preamble (5 OFDM Symbol) MAC header (30 Bytes) Frame Control Duratio n ID Address 1, 2, 3 Seq. Control Address 4 Data Frame Body FC S 4 Bytes N B Bytes DIFS Fig. 2: W i-Fi CSMA/CA contention and frame transmission. The W i-Fi frame structure with Preamble, MA C header , and data portion. 2 Bytes Frame Control Duration ID Address 1 FCS 2 Bytes 6 Bytes 4 Bytes MAC header L-STF (2Sym) L-LTF (2Sym) L-SIG (1Sym) Preamble (5 OFDM Symbol) Fig. 3: W i-Fi A CK frame structure set at 0.5. The L TE-U Forum specifications [4] provide limits on the a) actual durations of ON state (both minimum and maximum) and b) the minimum OFF duration. Specifically , the maximum ON duration is 20 ms and the minimum ON duration is 4 ms as long as there is data in L TE-DC eNB’ s buf fer . The minimum OFF duration of the eNB is 1 ms. Therefore, if no activ e Wi-Fi stations are detected, an L TE-DC eNB can start transmissions with the maximum ON period of 20 ms and OFF period of 1 ms, resulting in a maximum duty cycle of 95%. L TE-DC uses the base L TE subframe structure, i.e., the subframe length of 1 ms; each sub-frame consists of two 0 . 5 ms slots. Each subframe consists of 14 OFDM symbols as indicated in Fig. 4, of which 1 to 3 are Physical Downlink Control Channel (PDCCH) symbols and the rest are Physical Downlink Shared Channel (PDSCH) data. L TE-DC eNBs start downlink transmissions synchronized with slot boundaries, for (at least) one subframe (2 L TE slots) duration. After transmission, the intended receiv er (or receiv ers) transmits the ACK on uplink via the licensed band if the decoding is successful. In L TE, a Resource Block (RB) is the smallest unit of radio resource which can to to a UE, equal to 180 kHz bandwidth ov er a Transmission Time Interval (TTI) of one subframe (1 ms). Each RB of 180 kHz bandwidth contains 12 sub- carriers, each with 14 OFDM symbols, equaling 168 Resource Elements (REs). Depending upon the modulation and cod- ing schemes (QPSK, 16-QAM, 64-QAM), each symbol or resource element in the RB carries 2, 4 or 6 bits per symbol, respectiv ely . In the L TE system with 20 MHz bandwidth, there are 100 RBs av ailable. I V . A N A L Y T I C A L T H R O U G H P U T M O D E L I N G O F T H E C O E X I S T E N C E N E T W O R K The fundamental contribution to a new coexistence analysis (i.e. prediction of Wi-Fi throughput in the presence of L TE- DC eNB) is based on the T wo-Dimensional (2-D) Markov model. The ke y changes come via the amended W i-Fi packet collision probabilities due to the presence of L TE-DC eNB transmissions; this determines the effecti ve av ailable airtime for Wi-Fi transmission and the way throughput is calculated during L TE-DC OFF period. W e assume that both W i-Fi and L TE-DC systems transmit on a 20 MHz channel; there are n w W i-Fi nodes (AP and stations) which are transmitting both in down and uplinks with full buf fer (i.e. saturation) and one L TE-DC eNB which is transmitting only in DL to L TE stations. The 2-D Markov chain model for Wi-Fi DCF is shown in Fig. 5 for the saturated nodes. Let { s ( t ) = j, b ( t ) = k } denote the possible states in the Markov chain, where s ( t ) is the retransmission stage and b ( t ) the back-off counter v alue. In [18], when the back-off stage reaches the maximum value (i.e. m ), it stays in m fore ver . Howe ver , in Wi-Fi when the maximum value is reached, the back-off stage stays at m for one more attempt, i.e. m + 1 ; then it resets to zero in case of an unsuccessful transmission. The Markov chain and corre- sponding one step transition probabilities in [18] are modified based on Section III-A as follows. Considering the stationary distribution for the Markov model as b j,k = lim t →∞ P { s ( t ) = j, b ( t ) = k } , j ∈ (0 , m + 1) , k ∈ (0 , W i − 1) , the modified one step transition probability of the Markov chain is,          P { j, k | j, k + 1 } = 1 , k ∈ (0 , W i − 2) j ∈ (0 , m + 1) P { 0 , k | j, 0 } = 1 − P c,w W 0 , k ∈ (0 , W 0 − 1) j ∈ (0 , m + 1) P { j, k | j − 1 , 0 } = P c,w W i , k ∈ (0 , W i − 1) j ∈ (1 , m + 1) P { 0 , k | m + 1 , 0 } = P c,w W 0 , k ∈ (0 , W 0 − 1) (1) where P c,w is the collision probability of W i-Fi nodes, W 0 is the minimum contention window size in CSMA/CA, W i = 2 i W 0 is the contention window size at the retransmission stage i , and i = m is the maximum retransmission stage (i.e., i = j for j ≤ m and i = m for j > m ). 5 DIFS and backoff LTE-U ON LTE-U OFF Case 1 Case 2 Case 3 Wi-Fi Packet transmitted Wi-Fi Packet collided SIFS ACK T p 1 4 2 3 5 6 7 12 13 14 8 9 1 0 11 Data OFDM Symbols LTE Subframe Control OFDM Symbols Fig. 4: L TE-DC coexisting with W i-Fi which causes the ov erlap of Wi-Fi frame with L TE-DC ON edge T o simplify the calculation, we introduce the following vari- ables derived from (1) and using the Marko v Chain properties:    b j, 0 = P c,w b j − 1 , 0 , 0 < j ≤ m + 1 b j, 0 = P j c,w b 0 , 0 , 0 ≤ j ≤ m + 1 b 0 , 0 = P c,w b m +1 , 0 + (1 − P c,w ) P j = m +1 j =0 b j, 0 , (2) the last equation implies that, j = m +1 X j =0 b j, 0 = 1 − P m +2 c,w 1 − P c,w ! b 0 , 0 . (3) In each retransmission stage, the back-off transition proba- bility is b j,k = W i − k W i b j, 0 , 0 ≤ j ≤ m + 1 , 0 ≤ k ≤ W i − 1 . (4) W e can deriv e b 0 , 0 by the normalization condition, i.e., m +1 X j =0 W i − 1 X k =0 b j,k = 1 , b 0 , 0 = 2 W 0  (1 − (2 P c,w ) m +1 ) (1 − 2 P c,w ) + 2 m ( P m +1 c,w − P m +2 c,w ) (1 − P c,w )  + 1 − P m +2 c,w 1 − P c,w . (5) Hence, the probability that a node transmits in a time slot is calculated using (3) and (5) as, τ w = m +1 X j =0 b j, 0 = 2 W 0  (1 − (2 P c,w ) m +1 )(1 − P c,w )+2 m ( P m +1 c,w − P m +2 c,w ) (1 − 2 P c,w ) (1 − 2 P c,w )(1 − P m +2 c,w )  + 1 . (6) The collision probability of a Wi-Fi station with at least one of the other remaining ( n w − 1 Wi-Fi) stations is given by P c,w = 1 − (1 − τ w ) n w − 1 , (7) l P W  1 m,W m -1 m ,1 m ,0 1 1 1 0,W 0 -1 0,1 0,0 1 1 1 0,W 1 -1 1,1 1,0 1 1 1 m ', W ' m ' - 1 m ' , 1 m ' , 0 1 1 l P 1 0 , W ' 0 - 1 0 , 1 0 , 0 1 1 ( 1 ) l P  1 0 , W ' 1 - 1 1 , 1 1 , 0 1 1 1 ' l P W l P 1 ' l P W 1 ' l P W 1 m ' + 1 , W ' m ' - 1 m ' + 1 , 1 m ' + 1 , 0 1 1 1 m ' + e l , W ' m ' - 1 m ' + e l , 1 m ' + e l , 0 1 1  Re t r y l imit ( e l ) 1 m+ 1 ,W m -1 m+ 1,1 m+ 1,0 1 1 ' ) 1 ( 0 W P l  ' ) 1 ( 0 W P l  ' ) 1 ( 0 W P l  w c P , w c P , 1  w c P , 0 , 1 W P w c  0 , 1 W P w c  0 , 1 W P w c  Fig. 5: Markov chain model for the W i-Fi DCF with binary exponential back-off where P c,w is coupled to τ w . Modeling Collision between W i-F i & LTE-DC Inter-netw ork collisions between W i-Fi packets and L TE- DC occurs at the transition from OFF to ON period as illustrated in Case 3 of Fig. 4. The occurrence of this e vent depends on various factors: the total airtime for a Wi-Fi packet transmission equaling the sum of the W i-Fi data packet duration, SIFS duration, and A CK duration, denoted as T p = MA CH + PhyH + T d + SIFS + ACK. W e assume that any ov erlap of a W i-Fi packet airtime T p duration with the L TE-DC ON period causes the W i-Fi packet collision. For calculating the collision probability from L TE-DC to W i-Fi, we initially assume that one W i-Fi station coexisting with L TE-DC (hence no contention among the W i-Fi network), and thereafter e xtend it to multiple W i-Fi stations (to capture the W i-Fi contention). 6 1 1 z 1 2 z 1 T on T off z 2 T C 1 2 z 1 z 2 n k z nk T p n k +1 z nk +1 (a) (b) (c) Fig. 6: Illustration: Modeling collision and successful packet transmission at the end of L TE-DC OFF period. z i is the random backoff number and the backoff time is backoff number multiplied by the time slot σ z i . The probability of a collision between a W i-Fi station transmission and L TE-DC downlink is calculated as P c,w − l = n k +1 X k =1 P ( C | H = k ) p 0 ( H = k ) = n k +1 X k =1 1 k p 0 h ( k ) , (8) where n k = b T of f T p c is the maximum number of consecutive W i-Fi packets that fit within an OFF duration. H is the random variable for the overlap probability of the W i-Fi packets transmitted in OFF period with L TE-DC ON edge and C is the collision of the last transmitted packet during OFF period. Thus, P ( C | H = k ) = 1 k is the collision probability reflecting the fact that only the last transmitted packet (among k transmitted packets during the OFF period) is lost due to collision. T o compute p 0 ( H = k ) = p 0 h ( k ) , that represents the probability that the k -th packet overlaps with the L TE- DC ON edge, refer to Fig. 6 for an illustrativ e example. Suppose that T of f = 5 ms and packet airtime T p = 2 . 3 ms. In this case, the transmitting W i-Fi station either starts from [0 , W 0 − 1] contention window or [0 , 2 W 0 − 1] in case of collision with the previous L TE-DC ON edge. T o simplify matters, we assume that the first packet in an OFF period chooses the random backoff from [0 , 2 W 0 − 1] because the last packet in the previous OFF period is lost (with high probability). This assumption simplifies the deriv ation and we will show in the following sections that this approximation is valid for most cases by comparing the collision probability from this theoretical model and ns-3 simulation results. Thus, the probability that the first transmitted packet in OFF period ov erlaps the next ON edge is p 0 h (1) = P ( L b (1) < z 1 < U b (1)) , (9) where z 1 represents the random back-off v alue (in terms of number of contention time slots) that will lead to a packet transmission collision. σ is the time slot duration, L b (1) = b ( T of f − T P − DIFS ) /σ c and U b (1) = b ( T of f − DIFS ) /σ c are the upper and lower bounds of the collision interval duration. The random back-of f number of the first packet follows Uniform distribution, i.e. z 1 ∼ U [0 , 2 W 0 − 1] . Thus, the probability that the first packet overlaps with the ON edge is p 0 h (1) =        0 , for L b (1) > 2 W 0 − 1 P 2 W 0 − 1 z 1 = L b (1)  1 2 W 0  , for 0 ≤ L b (1) ≤ 2 W 0 − 1 1 , for L b (1) < 0 (10) For the second packet onward in each OFF period, the station chooses the random backoff uniformly from [0 , W 0 − 1] because there is no collision, i.e. first retransmission stage of Markov model. Assuming k − 1 packets are successfully transmitted, the probability of collision for k -th packets is calculated as: p 0 h ( k ) = min { 2 W 0 − 1 ,U b ( k ) } X z 1 =0 p ( z 1 ) × P (max { 0 , L b ( k ) − z 1 } < Z ( k ) < min { W s , U b ( k ) − z 1 }| z 1 ) , (11) where L b ( k ) = b ( T of f − k ( T P + DIFS )) /σ c and U b ( k ) = b ( T of f − ( k − 1) T P − k DIFS ) /σ c are the lower and upper bounds of interval for k > 1 , W s = ( k − 1) W 0 − 1 is the maximum sum of backof f numbers, and Z ( k ) = P k i =2 z i is the sum of the backof f values from the second to the k -th packet. Since the z i are mutually Independent and Identically Distributed (IID), the Probability Density Function (PDF) of Z ( k ) is the k − 1 -fold conv olution of uniform PDF p ( z k ) = 1 W 0 . Thus, P c,w − l which is the collision probability from L TE- DC to Wi-Fi depends on T of f and airtime of the packet, that means collision probability is a function of α = T on T C - the duty cycle of L TE-DC ON period - and T C . The collision caused by L TE-DC ( P c,w − l ) and collision from other W i-Fi stations ( P c,w ) is next combined to calculate the total probability of collision as: P c,t = 1 − (1 − P c,w )(1 − P c,w − l ) = 1 − (1 − τ w ) n w − 1 (1 − P c,w − l ) . (12) In order to compute the P c,t and τ w for more than one stations ( n w > 1 ) in the network ( τ w depends on P c,t , so it is a function of α and T C as well), we first jointly solve eq. (6) and (12), where for the coexistence of W i-Fi and L TE-U, P c,t is replaced by P c,w in eq. (6). The transmission probability of W i-Fi is the probability that at least one of the n w stations transmit a packet during a time slot: P trw = 1 − (1 − τ w ) n w . (13) The successful transmission probability of W i-Fi is the e vent that exactly one of the n w stations makes a transmission attempt given that at least one of the W i-Fi APs transmit: P sw = n w τ w (1 − τ w ) n w − 1 P trw . (14) The av erage throughput of W i-Fi in co-existence is calcu- lated as: T put w = E n T d P sw T C r w , (15) 7 where r w is the W i-Fi data rate. E n is the av erage number of successfully transmitted packets in the OFF period, and is multiplied by T d to calculate the effecti ve duration of data transmission in one cycle ( T C ). P sw in the numerator captures the ef fect of contention/collision between W i-Fi nodes and collision between W i-Fi packet and L TE-DC ON edge. The E n is calculated as: E n = k = n k X k =1 k ( P 0 s ( k ) − P 0 s ( k + 1)) , (16) where P 0 s ( k ) is the transmission probability that a sequence of k Wi-Fi packets are successfully transmitted in one cycle in coexistence with L TE-DC and ( P 0 s ( k ) − P 0 s ( k + 1)) is the probability that exactly the k -th packet is successful. Thus for a single station in the W i-Fi network, the success- ful transmission probability of the first packet is calculated as: P 0 s (1) = P (0 < z 1 < min { L b (1) , 2 W 0 − 1 } ) =      1 , for L b (1) > 2 W 0 − 1 P min { L b (1) , 2 W 0 − 1 } z 1 =0 1 2 W 0 , for 0 ≤ L b (1) ≤ 2 W 0 − 1 0 , for L b (1) < 0 (17) and the successful probability of transmission for all ( k > 1 ) subsequent packets is calculated as: P 0 s ( k ) = min { 2 W 0 − 1 ,U b ( k ) } X z 1 =0 p ( z 1 ) × P (0 < Z ( k ) < min { W s , L b ( k ) − z 1 }| z 1 ) . (18) For more than one Wi-Fi station in the network ( n w > 1 ), the P 0 s ( k ) should be re-computed; the probability that at least one node transmits - P trw - must now capture the ef fect of collision with other Wi-Fi stations and the collision with L TE- DC downlink. In this case, the random number of backof f time slots z k for k -th packet as shown in Fig. 6 follows the Geometric distribution, i.e. P ( z k = i ) = P trw (1 − P trw ) i , i = 0 , 1 , ..., ∞ . Hence, the total contention time slots in any generic OFF period Z 0 ( k ) = P k j =1 z j is the sum of k IID Geometric random variables, resulting in a negati ve Binomial distribution: P ( Z 0 ( k ) = i ) =  i + k − 1 k − 1  P k trw (1 − P trw ) i , (19) where i is the total number of contention time slots and k is the number of transmitted packets, in the OFF period. So the success probability for k packets is calculated as: P 0 s ( k ) = P ( Z 0 ( k ) ≤ L b ( k ) − k ) = L b ( k ) − k X i =0  i + k − 1 k − 1  P k trw (1 − P trw ) i . (20) The throughput of the L TE-DC considering the L TE-DC ON time, duty cycle, and proportion of data symbols in each subframe is calculated as, T put l ( α ) = 13 14 T on T C r l = 13 14 αr l , (21) T ABLE II: Wi-Fi Parameters. Parameter value PhyH 20 µs MA CH (34 bytes) /r w µs r 0 6 Mbps, 12 Mbps, 24 Mbps A CK (14 bytes) /r 0 + 20 µs δ 0.1 µs σ 9 µs DIFS 34 µs SIFS 16 µs T d N B /r w µs where 13 14 T on is the fraction of the L TE-DC TXOP in which the data is transmitted, i.e. 1 PDCCH symbol in a subframe with 14 OFDM symbols is considered, and r l is the L TE- LAA data rate. The ef fect of W i-Fi packet collision to L TE- DC is very minor as the collision from W i-Fi to L TE-DC just ov erlap with very initial part of the L TE T on duration because the TXOP of L TE is larger than W i-Fi. From the other side, L TE has a strong physical layer to compensate for any partial ov erlap/interference with it’ s subframe. So, in this calculation we assumed L TE-DC is collision free. V . N S - 3 S I M U L ATI O N A N D N U M E R I C A L R E S U LT S ns-3 is an open source network simulator supporting cred- ible simulation of protocol stacks for W i-Fi and L TE [19]. 802.11a is well supported in ns-3 and for L TE-DC we ob- tained L TE signal with desired duty cycling using wav eform generator function in ns-3. In all scenarios, both Wi-Fi and L TE-DC nodes are positioned within a small circle to ensure all nodes are exposed to each other . The full buf fer traffic in UL/DL is considered and setup the flows of the network to be UDP in order to isolate the effect of transport layer on throughput. The simulation code for an example coexistence scenario is available for downl oad using the current version ns-3.27, see [20]. W e consider two different data rates of 6 Mbps and 54 Mbps and two dif ferent T C . As already noted, constant data rates only are considered (with no rate control). The other W i-Fi network parameters are listed in T able II. In Fig. 7 one Wi-Fi node (AP transmitting in DL using the data rate of 6 Mbps), coexists with L TE-DC operating with cycle period ( T C ) of 10 ms, and duty cycle ( α ) is varied between 0.4 to 0.7. Fig. 7a illustrates the probability of collision of W i-Fi ( P c,w − l ) in coexistence with L TE-DC. The theoretical estimates closely follow the simulation results. As can be seen, the collision probability fluctuates as a function of packet size because it depends on the packet airtime and the number of packets that fit into one OFF period. This means that the proportion of the random backoff duration and the packet airtime influences how many packets are transmitted through the fixed OFF period and affects the collision ev ent of the final transmitted packet (with the ON edge). Increasing the duty cycle ( α ) also increases the collision probability because fewer packets are transmitted during the OFF period and the last transmitted packet would collide with the ON edge, so the ratio of the collided to transmitted packet will increase. In Fig. 7b, the simulated throughput performance of Wi-Fi AP in DL for duty cycles of 0.4 to 0.7 is shown to match 8 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Packet Size (Bytes) P c,w−l Sim, α =0.4, T C =10ms The, α =0.4, T C =10ms Sim, α =0.5, T C =10ms The, α =0.5, T C =10ms Sim, α =0.7, T C =10ms The, α =0.7, T C =10ms Sim, α =0.8, T C =10ms The, α =0.8, T C =10ms (a) Probability of Collision 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Packet Size (Bytes) Throughput (Mbps) Sim, α =0.4, T C =10ms The, α =0.4, T C =10ms 0.6 times Wi−Fi only Throughput Sim, α =0.5, T C =10ms The, α =0.5, T C =10ms 0.5 times Wi−Fi only Throughput Sim, α =0.7, T C =10ms The, α =0.7, T C =10ms 0.3 times Wi−Fi only Throughput Sim, α =0.8, T C =10ms The, α =0.8, T C =10ms 0.2 times Wi−Fi only Throughput (b) Throughput Fig. 7: The comparison of theoretical and ns-3 simulation results for T C = 10 ms and W i-Fi data rate of 6 Mbps. 1 W i-Fi node (the AP transmitting in DL) coexisting with L TE-DC. theoretical model results. By increasing the duty cycle, the throughput decreases because fewer packets are transmitted and also the probability of collision is higher . The throughput fluctuation as a function of the packet size is seen in Fig. 7a, reflecting the variability in the packet collision probability mentioned above. The throughput of one W i-Fi only system (with one W i-Fi AP , DL transmission) multiplied by the OFF cycle ( 1 − α ) is shown in the figure as the upper bound of the W i-Fi throughput if there is no interference from L TE-DC. Wi- Fi in coexistence with L TE-DC achiev es a lower throughput than the W i-Fi only case because of interference which leads to the collision of the last transmitted packet in OFF period. Generally , at smaller packet sizes the predicted throughput is closer to the upper bound, as more number of packets are transmitted in the OFF period, and hence the proportion of collided to transmitted packets decreases. W e note that this fluctuation in the probability of collision and throughput was observed in [16] but presented without further analysis of underlying causes. In Fig. 8, the throughput of W i-Fi AP in DL is illustrated for W i-Fi data rate of 6 Mbps, cycle period T C = 30 ms, and duty cycle range 6 0.3 to 0.6 that shows very good agreement between our model estimates and ns-3 simulation. Here, the throughput fluctuation is smaller compared with Fig. 7b because the OFF period is larger . Moreover , the throughput performance of W i-Fi in coexistence is closer to the duty cycled W i-Fi only throughput. This also implies that the throughput, in this case, is higher than the throughput in Fig. 7b. Therefore, to achieve a higher throughput at larger packet sizes, the T C should increase correspondingly . In Fig. 9, the throughput performance of W i-Fi AP in DL is illustrated where the W i-Fi data rate is 54 Mbps, cycle period T C = 10 ms, and duty cycles are 0.4 to 0.7. There is no fluctuation in the throughput performance in the plotted curv es, 6 Maximum duty cycle of 0.6 satisfies the maximum 20 ms L TE-DC ON period mandated by the standard. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Packet Size (Bytes) Throughput (Mbps) Sim, α =0.3, T C =30ms The, α =0.3, T C =30ms 0.7 times Wi−Fi only Throughput Sim, α =0.5, T C =30ms The, α =0.5, T C =30ms 0.5 times Wi−Fi only Throughput Sim, α =0.6, T C =30ms The, α =0.6, T C =30ms 0.4 times Wi−Fi only Throughput Fig. 8: The comparison of theoretical and ns-3 simulation results for T C = 30 ms and W i-Fi data rate of 6 Mbps. 1 W i-Fi node (the AP transmitting in DL) coexisting with L TE- DC. due to smaller packet airtime at the higher data rate, which leads to fewer packet collisions. In this scenario, there is a small gap between the Wi-Fi throughput in coexistence system and W i-Fi only throughput due to smaller interference from L TE-DC, i.e. a lower probability of collision. In Fig. 10, n w W i-Fi node (UL/DL transmission) coexists with L TE-DC with the W i-Fi data rate of 6 Mbps, cycle period ( T C ) of 10 ms, the packet size of 1500 bytes, and duty cycle ( α ) is changing from 0.4 to 0.7. Fig. 10a illustrates the probability of collision of W i-Fi ( P c,t ) and Fig. 10b the throughput of Wi-Fi in coexistence with L TE-DC via changing the number of stations. The theoretical results match the simulation results validating that the analytical model 9 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 5 10 15 20 25 Packet Size (Bytes) Throughput (Mbps) Sim, α =0.4, T C =10ms The, α =0.4, T C =10ms 0.6 times Wi−Fi only Throughput Sim, α =0.5, T C =10ms The, α =0.5, T C =10ms 0.5 times Wi−Fi only Throughput Sim, α =0.7, T C =10ms The, α =0.7, T C =10ms 0.3 times Wi−Fi only Throughput Fig. 9: The comparison of theoretical and ns-3 simulation results for T C = 10 ms and Wi-Fi data rate of 54 Mbps. 1 Wi-Fi node (the AP transmitting in DL) coexisting with L TE-DC. adequately captures the inter-network collision probability in coexistence. The collision probability and throughput curves for 0.4 and 0.5 duty cycles are equal because, as can be seen in Fig. 7b for one node, the collision probability and throughput for 1500 bytes are the same. This illustrates that depending on the packet airtime and L TE-DC OFF period, the same probability of collision and throughput can be achie ved in coexistence for two dif ferent duty cycles (the same trend is valid for more number of nodes). The same happens at 1100 bytes for duty cycles of 0.7 and 0.8 in Fig. 7b. In Fig. 11 the scenario is the same as Fig. 10, except the cycle period, is 30 ms, and the duty c ycle ( α ) is v aried from 0.3 - 0.6. For the duty cycle of 0.3 and 0.6, the Wi-Fi throughput is closer to the Wi-Fi only throughput because the proportion of packet airtime and OFF period is such that the number of packets that can be successfully transmitted during OFF period is larger . The scenario in Fig. 12 is the same as Fig. 11 except the cycle period is 10 ms, the data rate is 54 Mbps, and the duty cycle is varied from 0.4 - 0.7. The theoretical and simulation results are suitably matching. There is a gap between the W i-Fi throughput in coexistence and W i-Fi only throughput because of collision with the L TE-DC ON edge. The gap is almost the same for different duty cycles; this is due to the small packet airtime compared with the OFF period which leads to a small and almost equal probability of collision which leads to throughput loss of W i-Fi in coexistence system compared with W i-Fi only system (gap between the curves). Summary: • The fluctuation of throughput for 6 Mbps and T C = 10 ms scenario results from the packet airtime being com- parable with T of f ; throughput curves are smooth for the other two scenarios, i.e. 6 Mbps in 30 ms and 54 Mbps in 10 ms. Howe ver , the same behavior for higher data rate, e.g. 54 Mbps, is expected when a station is 0 5 10 15 20 25 30 35 40 45 50 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 n w P c,t Sim, α =0.4, T C =10ms The, α =0.4, T C =10ms Sim, α =0.5, T C =10ms The, α =0.5, T C =10ms Sim, α =0.7, T C =10ms The, α =0.7, T C =10ms (a) Probability of Collision 0 5 10 15 20 25 30 35 40 45 50 0.5 1 1.5 2 2.5 3 3.5 4 n w Throughput (Mbps) Sim, α =0.4, T C =10ms The, α =0.4, T C =10ms 0.6 times Wi−Fi only Throughput Sim, α =0.5, T C =10ms The, α =0.5, T C =10ms 0.5 times Wi−Fi only Throughput Sim, α =0.7, T C =10ms The, α =0.7, T C =10ms 0.3 times Wi−Fi only Throughput (b) Throughput Fig. 10: The comparison of theoretical and ns-3 simulation results for T C = 10 ms and W i-Fi data rate of 6 Mbps. n w W i-Fi node transmitting in UL/DL and coexisting with L TE- DC. allowed to transmit over TXOP period in which the TXOP is comparable with T of f in IEEE 802.11n and 802.11ac standards. The effect of TXOP and block A CK in coexistence with L TE-DC is deferred for future work. • When the T of f is much larger than the packet airtime, the W i-Fi only throughput multiplied by the duty cycle ( α ) is a good approximation of W i-Fi throughput in coexistence network as can be seen in Fig. 9 (especially at smaller packet sizes and it deviates for larger packet sizes). V I . F A I R N E S S I N C O E X I S T E N C E A pragmatic approach to ‘fair’ Wi-Fi and L TE-DC coexis- tence is to achie ve a suitably defined fairness metric by tuning the L TE-DC parameters T C and α . While the L TE-U Forum did not provide any formal definition and test scenarios of ‘fair coexistence’, there hav e been several inv estigations on 10 0 5 10 15 20 25 30 35 40 45 50 1 1.5 2 2.5 3 3.5 4 4.5 n w Throughput (Mbps) Sim, α =0.3, T C =30ms The, α =0.3, T C =30ms 0.7 times Wi−Fi only Throughput Sim, α =0.5, T C =30ms The, α =0.5, T C =30ms 0.5 times Wi−Fi only Throughput Sim, α =0.6, T C =30ms The, α =0.6, T C =30ms 0.4 times Wi−Fi only Throughput Fig. 11: The comparison of theoretical and ns-3 simulation results for T C = 30 ms and W i-Fi data rate of 6 Mbps. n w W i-Fi node transmitting in UL/DL and coexisting with L TE- DC. 0 5 10 15 20 25 30 35 40 45 50 6 8 10 12 14 16 18 20 n w Throughput (Mbps) Sim, α =0.4, T C =10ms The, α =0.4, T C =10ms 0.6 times Wi−Fi only Throughput Sim, α =0.5, T C =10ms The, α =0.5, T C =10ms 0.5 times Wi−Fi only Throughput Sim, α =0.7, T C =10ms The, α =0.7, T C =10ms 0.3 times Wi−Fi only Throughput Fig. 12: The comparison of theoretical and ns-3 simulation results for T C = 10 ms and W i-Fi data rate of 54 Mbps. n w W i-Fi node transmitting in UL/DL and coexisting with L TE- DC. this topic - notably [10] and [21] whose conclusions trend in opposite directions. In the in vestigation by CableLabs [21], they first established a baseline of ho w two W i-Fi networks share a channel; then, they replaced one of the Wi-Fi APs with an L TE-U eNB and repeated the tests, using v arious duty cycle configurations. This parallels the 3GPP definition of fairness for the L TE-LAA coe xistence with W i-Fi [22] whereby “LAA design should target fair coexistence with existing W i-Fi networks, so as to not impact W i-Fi services more than an additional Wi-Fi network on the same carrier, with respect to throughput and latency”. Hence, we use this notion of fairness for our own in vestigations below . W ith reference to the operating scenario in Fig. 1, we say that fairness is achiev ed if the appropriate metric (access or throughput) is not worse if a W i-Fi network is replaced by an L TE-DC network, i.e. the same access probability or throughput is achiev ed for scenario in Fig. 1 (a) and Fig. 1 (b). W e assume that in scenario (a), there are n w stations in each W i-Fi network, so totally N = 2 n w W i-Fi stations are contending for transmission; in scenario (b) the n w W i-Fi stations are replaced with an L TE-DC network in which the eNB is transmitting on do wnlink to the stations. A. W i-F i Access F airness Access fairness is achiev ed by tuning the α or T C such that the probability of channel access is identical in both scenarios. In W i-Fi only scenario with two networks and total N = 2 n w W i-Fi stations (twice as the number of W i-Fi stations in the coexistence scenario) - Fig. 1 (a) - the probability of channel access is τ wo = 2 W 0  (1 − (2 P c,wo ) m +1 )(1 − P c,wo )+2 m ( P m +1 c,wo − P m +2 c,wo ) (1 − 2 P c,wo ) (1 − 2 P c,wo )(1 − P m +2 c,wo )  + 1 , P c,wo = 1 − (1 − τ c,wo ) N − 1 , (22) where using (6) in which P c,wo is replaced by P c,w . In the coexistence of Wi-Fi and L TE-DC, just n w W i-Fi stations, belonging to one Wi-Fi network, contend for channel access during the L TE-DC OFF period. So, as calculated in the previous section, the probability of accessing the channel is: τ w ( α, T C ) = 2 W 0  (1 − (2 P c,t ) m +1 )(1 − P c,t )+2 m ( P c,t m +1 − P c,t m +2 ) (1 − 2 P c,t ) (1 − 2 P c,t )(1 − P c,t m +2 )  + 1 , P c,t ( α, T C ) = 1 − (1 − P c,w )(1 − P c,w − l ) , (23) where τ w is a function of α and T C . This follows from (6) with P c,w replaced by the P c,t . T o achiev e access fairness, we thus propose to min α | τ w ( α, T C ) − τ wo | , s.t. 0 < α < 1 , (24) where the T C range depend on the maximum and minimum values of ON and OFF period of L TE-DC, per the L TE-U standard. B. W i-F i Throughput F airness In coexistence, the Wi-Fi throughput (15) depends on the L TE-DC parameters α and T C , which can be tuned to achieve W i-Fi throughput. For a given T C , we optimize α to achieve throughput fairness. For the two W i-Fi networks with N = 11 2 n w contending Wi-Fi stations, the total throughput in W i-Fi only is calculated as: T put wo = P tr P s T d (1 − P tr ) σ + P tr (1 − P s ) T cw + P tr P s T sw r w , P tr = 1 − (1 − τ wo ) N , P s = N τ wo (1 − τ wo ) N − 1 P tr , T sw = MA CH + PhyH + T d + SIFS + δ + A CK + DIFS + δ T cw = T sw (25) where the τ wo and collision probability P wo is giv en by Eq (22). So, in the coexistence network n w W i-Fi stations, belonging to one W i-Fi network, contend for channel access during the L TE-DC OFF period. W e propose to tune α of L TE- DC such that the throughput fairness is achieved as follows: T put w ( α, T C ) = T put wo 2 , (26) i.e., the optimization problem to achiev e Wi-Fi throughput fairness is min α     T put w ( α, T C ) − T put wo 2     s.t. 0 < α < 1 . (27) V I I . C O E X I S T E N C E F A I R N E SS : N U M E R I C A L R E S U LT S The two different notions of fairness in coexistence of W i- Fi and L TE-DC network are in vestigated for three different scenarios: A) T C = 10 ms with r w = 6 Mbps, B) T C = 30 ms with r w = 6 Mbps, and C) T C = 10 ms with r w = 54 Mbps. The packet size is kept fixed at 1500 bytes and the L TE duty cycle parameter α is tracked as a function of the number of stations to achieve the desired fairness metric. The fairness problems in eq. (24) and (27) is numerically solved using the MA TLAB numerical solver . Since we already v alidated the analytical model, we are just using the numerical results for in vestigating the fairness. A. W i-F i Access F airness In access fairness, the L TE duty c ycle ( α ) is chosen such that the same access probability of W i-Fi in coexistence and W i-Fi only network is achieved. Fig. 13 illustrates the optimized α versus the number of W i-Fi stations, for the three different scenarios. In all of these scenarios, α could be very large and the L TE-DC gets most of the airtime. So, the av ailable airtime and correspondingly the throughput of W i-Fi is very small. This fact implies that by achieving the access fairness, the L TE-DC is very unfair to W i-Fi regarding airtime and throughput. B. W i-F i Throughput F airness Fig. 14 sho ws the optimized α for throughput fairness for same scenarios as Fig. 13. For one Wi-Fi client and downlink, scenario A requires the smallest L TE-DC duty cycle for achie ving the f airness, while for scenario B, α is the lar gest. This is because the packet airtime is comparable with the 0 5 10 15 20 25 30 35 40 45 50 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 n w α T C =10 ms, r w =6 Mbps − Scenario A T C =30 ms, r w =6 Mbps − Scenario B T C =10 ms, r w =54 Mbps − Scenario C Fig. 13: The optimized duty cycle ( α ) to achieve the access fairness vs. different number of stations - the W i-Fi packet size is 1500 bytes. 0 5 10 15 20 25 30 35 40 45 50 0.35 0.4 0.45 0.5 0.55 0.6 0.65 n w α T C =10 ms, r w =6 Mbps − Scenario A T C =30 ms, r w =6 Mbps − Scenario B T C =10 ms, r w =54 Mbps − Scenario C Fig. 14: The optimized duty cycle ( α ) to achieve the through- put fairness vs. different number of stations - the W i-Fi packet size is 1500 bytes. L TE-DC OFF duration, i.e. the OFF duration is very small in scenario A. As the number of stations increases, the duty cycle increases which implies that Wi-Fi - Wi-Fi coexistence causes more throughput drop than the L TE-DC. Hence, L TE-DC can use a larger portion of the airtime and still be fair to W i-Fi compared with another Wi-Fi. Fig. 15 sho ws the throughput of Wi-Fi when fairness is achiev ed - note that the curve with 2 n w node and r w = 6 Mbps is the throughput for scenario A and B, and the curve with 2 n w node and r w = 54 Mbps is the throughput for scenario C. Summary: • Access fairness results in a very large optimal L TE-DC duty cycle which implies a very small throughput for Wi- Fi. • In throughput fairness, as the number of W i-Fi nodes 12 0 5 10 15 20 25 30 35 40 45 50 0 2 4 6 8 10 12 14 16 n w Throughput (Mbps) Throughput Fair, half throughput of 2n w Wi−Fi only, r w =6 Mbps − Scenario A, B Throughput Fair, half throughput of 2n w Wi−Fi only, r w =54 Mbps − Scenario C Fig. 15: The Wi-Fi throughput (half throughput, i.e. T put wo 2 , which is calculated from (25)) when the throughput fairness is achieved for the W i-Fi packet size of 1500 bytes. increases, the Wi-Fi network requires smaller airtime (larger α ) to achie ve fairness. This implies that for duty cycle value α = 0 . 5 , W i-Fi could achieve a higher throughput in coexistence with L TE-DC than another similar size W i-Fi network. • The L TE-U Forum specifications [23] recommend that L TE-U share the channel with one full buf fer W i-Fi link (one Wi-Fi network) by tuning its duty cycle below 0.5. For n w = 1 , our results show that throughput fairness satisfies the L TE-U Forum condition but for n ≥ 5 , this condition is not satisfied. The abov e results are tak en together suggest that the f airness metrics considered may not be suf ficient; thus, a deeper in vestigation of this matter is necessary and is deferred to future work. V I I I . C O N C L U S I O N In this work, we first presented a new analytical model for computing the throughput performance of W i-Fi in coe xistence with L TE-DC. The analytical results suitably match the ns- 3 simulation results, validating the proposed model. Further , access and throughput f airness of W i-Fi in coexistence with the L TE-DC network are in vestigated as a function of the L TE-DC duty cycle. The results indicate that in most of the scenarios considered: by increasing the number of W i-Fi nodes, the W i-Fi network in coexistence with L TE-DC with α = 0 . 5 achiev es a higher throughput than coexisting with another similar W i-Fi network. Several directions of future work are indicated: an analytical model for L TE-U with CSA T , and a deeper inv estigation into coexistence fairness between Wi-Fi and L TE-U. AC K N OW L E D G M E N T The authors would like to thank Drs. Monisha Ghosh and V anlin Sathya (U Chicago) for helpful discussions. R E F E R E N C E S [1] L TE-U Forum, “http://www .lteuforum.org/. ” [2] FCC, “Revision of Part 15 of the Commission’ s Rules to Permit Unlicensed National Information Infrastructure (U-NII) Devices in the 5GHz Band, ” in F ederal Communications Commission , Feb 2013. 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