a Contention Window Optimization Scheme

Resource Allocation in LTE-LAA and WiFi Coexistence: a Contention Window Optimization Scheme Yuan Gao1 , Bolin Chen1 , Xiaoli Chu1 , Jie Zhang1 1

Department of Electronic and Electrical Engineering the University of Sheffield Email: ygao41@sheffield.ac.uk

Abstract—Licensed-assisted access (LAA) is a promising technology to meet the exponential increase of traffic demand by exploiting the 5GHz unlicensed spectrum. However, without proper coexistence schemes, the performance of WiFi in coexistence with LAA will be degraded significantly. Equipped with listen-beforetalk (LBT) schemes, LAA applies a channel access mechanism similar to distributed coordination function (DCF) in WiFi, which is not optimal in terms of spectrum efficiency. In this paper, we propose an optimization scheme to find the optimal combination of WiFi and LAA contention windows (CWs) that maximizes LAA throughput, while guarantees WiFi throughput above a predefined threshold. The accuracy and efficiency of the proposed scheme is evaluated by comparing with the exhaustive search: almost the same combinations of CW are achieved with much lower complexity by using the proposed scheme than the exhaustive search. Numeric results show that the proposed adaptive scheme is more effective in dense scenario, where high system (up to 40%) and LAA throughput gain (up to 100%) are achieved. The trade-off between LAA (system) throughput and WiFi throughput is also revealed. Index Terms—Licensed-Assisted Access, WiFi, contention window adaption, optimization, throughput

I. Introduction Deploying Long Term Evolution (LTE) in the 5GHz unlicensed spectrum, has been regarded as one of the most promising approaches to meet the exponential increase of traffic demand in the near future. In particular, such work is under standardization in the 3rd Generation Partnership (3GPP) Rel-13 [1], as licensed-assisted access (LAA). Despite the huge potential to meet cellular traffic surge, LTE deployment in unlicensed spectrum (LTE-U) is expected to bring challenges that remain to be solved. One of the biggest problems is the fair coexistence between LTE-U and incumbent systems in 5GHz, WiFi. WiFi performance will be severely affected by LTE without properly designed coexistence mechanisms. This is due to the fact that both technologies of WiFi and LTE use different channel access mechanisms: contention-based WiFi is more vulnerable to coexistence interference than scheduling-based LTE [2], [3]. Several coexistence mechanisms have been proposed in the literature, such as uplink power control [4], LTE blank

subframe allocation [5], a simple listen-before talk (LBT) scheme in [6], the carrier sense adaptive transmission (CSAT) proposed by LTE-U forum [7], and 3 LBT schemes (Category (Cat)2, 3, 4) are proposed by European Telecommunications Standards Institute (ETSI) [8]. All these mechanisms share two common factors. Firstly, modifications are made on LTE to avoiding interfering co-channel WiFi transmission, i.e. listen-before-talk (LBT). Secondly, LTE needs to contend unlicensed spectrum with WiFi and other LTE-U nodes. Licensed-assisted access (LAA), which is a key feature in the 3GPP Rel-13, is expected to be the most promising global solution for extending LTE in unlicensed spectrum [9]. The Cat 3 and Cat 4 LAA [8] apply channel access/contention scheme, which is similar to the distributed coordination furcation (DCF) used in WiFi. DCF has been proven to be an inefficient mechanism in terms of spectrum utilization. Various improvements of DCF have been proposed through the optimization of contention window (CW) by changing the initial CW size of DCF [10], [11]. The coexistence between Cat 3 (Cat 4) LAA and WiFi faces unfairness in terms of resource utilization [12]. Such unfairness has been mitigated by changing the signal/energy threshold applied by LAA-LBT nodes [13], and by adaptively changing the CW size of LAA-LBT schemes [14]–[16]. However, all the above works make changes only to LAA-LBT while keeping WiFi unchanged. Moreover, in [14], performance evaluation was based only on numeric results. In [15], [16], optimization problems were formulated as several integer linear programming (ILP) problems with different objectives (e.g. minimal collision probability, minimal required unlicensed spectrum), which are NP-hard. In this paper, we analyse an WiFi and LAA coexisting scenario, in which we aim to find the optimal combination of LAA and WiFi CWs to maximize LAA throughput while guarantee WiFi throughput above a certain threshold. The major contributions are summarized as follows. • Considering a WiFi and LAA coexisting scenario, we analyze WiFi and LAA throughput with respect to the combination of WiFi an LAA CWs. We derive the

explicit expressions for the relationships between WiFi (LAA) throughput and WiFi & LAA initial CW sizes, which have not been achieved by any existing works. • Based on the derived relationships, we propose an optimization scheme to find the optimal combination of WiFi and LAA CW initial sizes to maximize LAA throughput and guarantee WiFi throughput above a predefined threshold. The proposed scheme has a much lower complexity (P-hard) than solving ILP. • The accuracy and efficiency of our proposed optimization scheme are verified by comparing it with exhaustive search. The proposed scheme offers a significant LAA (system) throughput gain up to 100% (40%) over the coexisting WiFi and LAA with fixed initial CW sizes. Especially, the effectiveness of the proposed scheme in dense scenario is also revealed. The remaining of this paper is organized as follows. Section III introduces Markov models [12], and presents the problem formulation. Theoretical analysis and mathematical derivation are presented in Section III along with the proposed optimization scheme. Numerical results and performance comparisons are provided in Section IV. We conclude this paper in Section V. II. System Model and Problem Formulation

where, RL and RW are the transmission rate of LAA and WiFi, respectively. H is the size of a packet head, ACK is the size of an ACK frame. DIFS is the DCF inter-frame space defined in 802.11. T c is the average time duration for a collision and is given by: Tc =

W LW L W PcL T cL + PW c T c + Pc max(T c , T c )

Collision arises due to more than one simultaneously transmissions in a time slot. There are three types of collisions: collision between WiFi transmissions (with probability PW c ), collision between LAA transmissions (with probability PcL ), and collision between WiFi and LAA transmissions (with probability PcLW ). The average time consumed by the first and second type of collision are T cL and T cW : ⎧ H+E(p) ACK ⎪ ⎪ ⎨T cL = RL + δ + DIFS + RL + DIFS + δ ⎪ ⎪ ⎩T W = H+E(p) + δ + DIFS + ACK + DIFS + δ c RW RW

⎧ E(p)PLs,i ⎪ ⎪ L ⎪ ⎪ ⎨S i = PI δ+T s +T c ⎪ ⎪ E(p)PW ⎪ s, j ⎪ ⎩S Wj = P δ+T +T I

s

(1)

c

where: and PW s, j are the successful transmission probability of ith LAA and jth WiFi, respectively. PI is the probability that channel being idle, and δ is the slot time (9μs) of 802.11. T s is the expected time consumed by a successful transmission (either LAA or WiFi): PLs,i

Ts =

PLs T sL

+

W PW s Ts

(2)

Where PLs and PW s are the successful transmission probability of any LAA eNB and WiFi AP. T sL and T sW are the average time consumed by a successful transmission of LAA and WiFi, respectively. ⎧ H+E(p) ACK ⎪ ⎪ ⎨T sL = RL + δ + RL + DIFS + δ ⎪ ⎪ ⎩T W = H+E(p) + δ + ACK + DIFS + δ s RW RW

(3)

(5)

B. Problem Formulation We consider a scenario where n WiFi APs and m LAA eNBs coexisting and contending for the same unlicensed spectrum. In this scenario, we formulate our optimization problem as maximizing LAA throughput while guaranteeing WiFi performance above a predefined throughputˇcž m

A. System Model To analyse the throughput of n WiFi and m LAA in a coexistence scenario, we apply the system framework presented in (12) in [12]. Assume the average packet size for WiFi and LAA are the same, and donate as E(p), we have the ith LAA and jth WiFi throuhputs:

(4)

Max

S iL

(6)

i=1

s.t. : S Wj ≥ T hreshold, ∀CW L , CW W ∈ [CWMin , CWMax ], j ∈ [1, n] (7)

and (2) - (5). In a WiFi-LAA coexistence scenario, n WiFi APs and m LAA eNBs compete for the same medium resource. We donate the transmission probability of a WiFi AP and an LAA eNB are p and p, respectively. we applied the same expression in terms of transmission successful probability and collision probability in [12]. ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩

PI = nj=1 (1 − pj ) m i=1 (1 − pi ) m W n P s, j = p j k j (1 − pk ) i=1 (1 − pi ) n W PW s = j=1 P s, j PLs,i = nk=1 (1 − pk )pi m ki (1 − pi ) L PLs = m P s,i i=1 m PW = (1 − p i ) − P I − PW c s i=1 PcL = nj=1 (1 − pi ) − PI − PLs L W L PcLW = 1 − PI − PW s − P s − Pc − Pc

(8)

The transmission probabilities of LAA and WiFi is p and p take the following expressions for simplicity [10] [17]: ⎧ 2 ⎪ ⎪ ⎪ ⎨ pi = 1+CW iL (9) ⎪ 2 ⎪ ⎪ ⎩ pj = 1+CW W j

These expressions will be used in the derivation in Section III. III. LAA Throughput Optimization In this section, we propose an optimization algorithm based on mathematical derivation to solve the optimization problem 6 formulated in the previous section. A. Analysis of Throughput in Coexistence Scenario

2

We assume that all WiFi APs share the same wireless conditions and so do all the LAA eNBs, which is widely accepted [10], [11]. For simplicity, we assume that the transmission rate of WiFi and LAA to be the same, i.e. RW = RL . Thus we have: ⎧ ⎪ ⎪ ⎨T s = T sW = T sL ⎪ ⎪ ⎩T c = T cW = T cL

(10)

The expressions of LAA and WiFi throughput are simplified as follows: ⎧ E(p)PLs ⎪ ⎪ ⎪ ⎨S L = PI δ+(PLs +PWs )T s +(PcL +PWc +PcLW )T c ⎪ ⎪ E(p)PW s ⎪ ⎩S W = P δ+(PL +PW )T +(PL +PW +PLW )T I

s

s

s

c

c

c

(11)

c

In a WiFi-LAA coexistence scenario, n WiFi APs and m LAA eNBs compete for the same medium resource. According to the relations between transmission probability and CW in (9), to find the optimal contention windows of LAA and WiFi is equivalent to finding the optimal transmission probabilities of LAA and WiFi. Taking the first derivative of the LAA throughput against p and p , we have: ∂S L = (1 − mp)x + (1 − p )n−1 (1 − p)m ∗ ∂p [np (1 − x) − (1 − p )(x − x)]

(12)

∂S L = (1 − p )n−1 (1 − p)m (1 − x) − x ∂p

(13)

where according to (3) and (5), x = Tδs (→ 0) and x = TT cs (> 1). Then we take the first derivative of the WiFi throughput against p and p : ∂S W = (1 − np )x + (1 − p )n (1 − p)m−1 ∗ ∂p [mp(1 − x) − (1 − p)(x − x)]

(14)

∂S W = (1 − p )n (1 − p)m−1 (1 − x) − x ∂p

(15)

Let us first consider (13) and (15), as x > 1, we have: ⎧ ∂S L ⎪ ⎪ ⎨ ∂p < 0 ⎪ ∂S ⎪ W ⎩ ∂p < 0

WiFi throughput is monotonically decreasing with the transmission probability of LAA. To find the maximum LAA throughput against LAA transmission probability, we let (12) be 0. For simplicity, we assume(1 − p)m ≈ 1 − mp in (12), and because x CW 2L . In the interval [CW 2L , CW 1L ], LAA throughput is increasing against the contention window; in the interval [CW 1L , ∞], LAA throughput decreases with the CW. Thus for the interval [CW Min , CW 1LAA ], LAA throughput is increasing; for the searching interval [CW 1L , CW Max ], LAA throughput is decreasing. Thus, for a proper chosen CW range, LAA throughput decreases with LAA CW size, e.g. CW interval [8, 64] for 4 LAA eNBs. Solving (14), we obtain the similar insights for the change of WiFi throughput with WiFi CW. ⎧ ⎪ ⎪ ⎨ p1 = ⎪ ⎪ ⎩ p = 2

1 n−1 x xn−n+x

(19)

Thus, for proper choosing of contention window range, LAA throughput is monotone decreasing against the contention window of LAA, and WiFi throughput is monotone decreasing against the contention window of WiFi. B. Optimization Algorithm We split the optimization problem into two parts: 1) to find the solution space S that satisfies the WiFi throughput threshold condition (Algorithm 1); 2) to find the combination of LAA and WiFi CWs from the solution space generated in part 1) that maximizes the LAA throughput. To be noted that, operation TH in Algorithm 1) is given in (1) to calculate the WiFi and LAA throughputs at given LAA and WiFi CWs. The output of Algorithm 1 is S, an nx4 matrix. The first column of S contains the CW of WiFi, and the second column contains the corresponding LAA CWs that achieve the minimum WiFi throughput above its threshold. The corresponding WiFi throughput and LAA throughput are given in the third and forth columns, respectively. It is quite simple to find maximum LAA throughput in the matrix S by using ranking function in Matlab.

The complexity of the optimization algorithm is measured by the number of iterations to generate matrix S. Each iteration corresponds to the whole while loop (line 9-18) in Algorithm 1, in which we try to find the CW combination that ensures WiFi throughput just above a predefined throughput threshold. The accuracy of Algorithm 1 is evaluated by a comparison with exhaustive search, which is described in the next subsection. C. Exhaustive Search Exhaustive search is also applied in this paper to evaluate the accuracy and efficiency of proposed optimization algorithm. Exhaustive search follows the same two-step procedure in the proposed optimization scheme, i.e. 1) to generate a solution space that meets WiFi minimal throughput criterion; 2) to find the maximum LAA throughput along with its corresponding CW combination. For simplicity, exhaustive search has certain searching direction in terms of choosing CW combination, i.e. searching begins with the minimal WiFi and LAA CW sizes. In each iteration, WiFi throughput at the current CW combination is calculated and compared with the predefined WiFi throughput threshold. If WiFi throughput is smaller than the threshold, then LAA CW size increases by 1, and the iteration is performed again, until WiFi throughput is just above the threshold. CW combination and corresponding throughput are then saved in the first row of a matrix S. WiFi CW then increases by 1 up to the maximal WiFi CW, and the above

Table I WiFi System and LAA System Parameters Packet Size MAC header PHY header ACK WiFi & LAA Bit Rate CW min CW max Slot Time SIFS DIFS

12800 bits 272 bits 128 bits 112 bits + PHY header 50 Mbit/s 8 64 9 μs 16 μs 34 μs

calculation and comparison is performed again. In the matrix S, optimal CW combination and corresponding throughput are obtained easily. IV. Numerical Results and Analysis A. Comparisons With Exhaustive Search In this section, the optimization algorithm is compared with the exhaustive search. We assume the throughput threshold for each WiFi AP is 1, 2, or 4 Mbps, we consider n WiFi APs and m LAA coexisting together to compete for unlicensed spectrum resource (n, m ⊆ [2, 3, 4]). Other parameters used in the evaluations are listed in Table I, which is adopted in IEEE 802.11 ac standard [18]. As shown in Fig. 1,2,3, apart from a few scenarios (4 WiFi APs & 4 LAA eNBs, and 4 WiFi APs & 3 LAA eNBs in Fig. 1), optimization algorithm provides exactly the same results as the exhaustive search does. 70

60

50

CW Size

Algorithm 1 Finding Solution Space 1: for CW WiFi ← CW Min : 1 : CW Max do 2: Initialize CW Min , CW Max 3: CWUL pper ← CW Max 4: CWLower ← CW Min L 5: (S 1W , S 1L ) ← TH(CWW , CWUL pper ) 6: (S 2W , S 2L ) ← TH(CWW , CWLower ) L 7: loop: 8: if S 1W > 0 then 9: while CW UL pper − CW Lower > 1 do L 10: if S 2W > 0 then 11: CWUL pper ← 1/2(CWUL pper +CWLower ) L U pper W L 12: (S 2 , S 2 ) ← TH(CWW , CWL ) 13: end if 14: if S 2W < 0 then U pper 15: CWLower ← 1/2(CWL +CWLower ) L L W L 16: (S 2 , S 2 ) ← TH(CWW , CWLower ) L 17: end if 18: end while 19: CW0 ← CW Max 20: Save CWW , corresponding CW0 , SW 2 , 21: and S2L in S 22: end if 23: end for

WiFi CW Size Achieved by Exhaustive Search LAA CW Size Achieved by Exhaustive Search WiFi CW Size Achieved by Proposed Algorithm LAA CW Size Achieved by Proposed Algorithm

40

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0 4,4

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4,2

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3,2

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Number of WiFi APs and LAA eNBs

Figure 1. Optimal Combination of WiFi & LAA CWs Achieved by Exhaustive Search and Proposed Algorithm Under 1 Mbps/AP Throughput Threshold

In scenarios with the same number of WiFi APs and LAA eNBs, a higher WiFi throughput threshold leads to larger LAA CW size. This is in accordance with Theorem. 1, which means we have to sacrifice LAA throughput for WiFi throughput protection. In a scenario with a constant number of WiFi APs and the same WiFi throughput threshold, by decreasing the number

70

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3000 WiFi CW Size Achieved by Exhaustive Search LAA CW Size Achieved by Exhaustive Search WiFi CW Size Achieved by Proposed Algorithm LAA CW Size Achieved by Proposed Algorithm

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Number of Iterations

CW Size

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Exhaustive Searching Applied in Scenario Where WiFi throughput threshld is 1 Mbps Optimization Algorithm Applied in Scenario Where WiFi throughput threshld is 1 Mbps Exhaustive Searching Applied in Scenario Where WiFi throughput threshld is 2 Mbps Optimization Algorithm Applied in Scenario Where WiFi throughput threshld is 2 Mbps Exhaustive Searching Applied in Scenario Where WiFi throughput threshld is 4 Mbps Optimization Algorithm Applied in Scenario Where WiFi throughput threshld is 4 Mbps

2000

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500



0 4,4

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Figure 4. Comparison Between Optimization Algorithm and Exhaustive Search in terms of Complexity 70

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WiFi CW Size Achieved by Exhaustive Search LAA CW Size Achieved by Exhaustive Search WiFi CW Size Achieved by Proposed Algorithm LAA CW Size Achieved by Proposed Algorithm

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throughput shows the most significant increase by applying fixed initial CW sizes, while optimization scheme applied to achieve WiFi throughput above 4 Mps/AP provides the least throughput gain. In dense scenario (where 4 WiFi APs and 4 LAA eNBs coexist), optimization scheme achieves much higher spectral efficiency gain (up to 40%), than applying default CW sizes. While in a less dense scenario with 2 WiFi APs and 2 LAA eNBs, the throughput gain achieved by optimization scheme drops to 2%-7%. This shows that the proposed optimization scheme is more effective in dense scenario than in sparse scenario in terms of throughput increase. Under various WiFi


32 31

B. Throughput Gain By Using Proposed Scheme Fig. 5 shows the total throughput achieved with optimization scheme under various WiFi throughput thresholds, and fixed CW sizes. In general, total throughput increases by decreasing the number of WiFi APs and (or) LAA eNBs. Total

30

Toral Throughput (Mbps)

of LAA eNBs, smaller LAA CW size can guarantee WiFi throughput above threshold. Besides, optimal LAA throughput is higher in scenarios with less LAA eNBs. The complexity of optimization algorithm and exhaustive search are compared in Fig. 1. The number of iterations used in optimization algorithm is much less (approximately 90% to 95%) than those used by exhaustive search to achieve the same results. Interaction is equivalent to the complexity of the algorithm: the complexity of exhaustive search algorithm is O(D2 ), while the complexity of proposed search algorithm is O(Dlog2 (D)) (D is the difference between the minimal CW and maximum CW).

29 28 27 26 25 24

Total Throughput at Default CW Sizes Total Throughput Achieved in Scenario Where WiFi throughput threshld is 1 Mbps Total Throughput Achieved in Scenario Where WiFi throughput threshld is 2 Mbps Total Throughput Achieved in Scenario Where WiFi throughput threshld is 4 Mbps

23 22 4,4

4,3

3,4

4,2

3,3

2,4

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2,2


Figure 5. Total Throughput Achieved in Different Scenarios With Optimization Scheme or at Fixed CW sizes

throughput thresholds, the LAA throughput achieved with optimization scheme and fixed CW sizes are shown in Fig. 6. In general, by using fixed initial CWs at WiFi APs and LAA eNBs, LAA throughput achieved is the lowest. The

highest LAA throughput gain (60%-100%) are achieved by the proposed optimization scheme under a low WiFi throughput threshold, i.e. 1 or 2 Mbps/AP. Less LAA throughout gain, 10%-30%, are achieved under higher WiFi throughput threshold (4 Mbps/AP). This is due to the fact that the total achievable throughput is limited, if more resource is allocated to WiFi (higher WiFi throughput threshold), lower throughput can be achieved by LAA. 30

LAA Throughput (Mbps)

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LAA Throughput at Fixed Initial CW Sizes LAA Throughput Achieved in Scenario Where WiFi throughput threshld is 1 Mbps LAA Throughput Achieved in Scenario Where WiFi throughput threshld is 2 Mbps LAA Throughput Achieved in Scenario Where WiFi throughput threshld is 4 Mbps

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Figure 6. LAA Throughput Achieved in Different Scenarios With Optimization Scheme or at Fixed CW sizes

V. Conclusion In this paper, we analysed LAA and WiFi throughput in coexistence scenarios competing for the same unlicensed spectrum. By mathematical derivation, we established the relations between WiFi, LAA throughput and CW combination. Then we developed an optimization algorithm to find the CW combination that achieves maximum LAA throughput, and guarantees WiFi throughput above predefined threshold. The accuracy of the proposed optimization algorithm is validated by comparisons between exhaustive search. The proposed algorithm can achieve good fairness and spectral efficiency with much lower complexity than the exhaustive search algorithm. The proposed optimization scheme is also shown to be more effective in dense scenario, in which both higher LAA throughput and total throughput gains are achieved. The trade-off between WiFi and LAA throughput are revealed due to the fact that the total achievable system throughput are limited. Acknowledgment This paper acknowledges the support of the MOST of China for the "Small Cell and Heterogeneous Network Planning and Deployment" project under grant No. 2015DFE12820, and H2020 DECADE project. References [1] B. Chen, J. Chen, Y. Gao, and J. Zhang, “Coexistence of LTE-LAA and Wi-Fi on 5 GHz with Corresponding Deployment Scenarios: A Survey,” IEEE Communications Surveys & Tutorials, 2016.

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