Modeling of Synchronization and Energy ...

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The Journal of Engineering

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. 1 Content may change prior to final publication in an issue of the journal. To cite the paper please use the doi provided on the Digital Library page.

Modeling of Synchronization and Energy Performance of FBE and LBE based Standalone LTE-U Networks Jiamin Li1,2 , Hangguan Shan1,2 , Aiping Huang1,2 , Jiantao Yuan1,2 , Lin X. Cai3 1 College 2 Zhejiang

of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China

Provincial Key Laboratory of Information Processing and Communication Networks, Hangzhou, China

3 Department

of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, USA

Abstract Without the aid of licensed channel, deploying Long Term Evolution (LTE) networks over unlicensed spectrum (named standalone LTE-U networks) faces the difficulty of establishing and maintaining synchronization between user equipments and base stations. In this work, considering the two modes of Listen-Before-Talk based channel access scheme, Frame Based Equipment (FBE) and Load Base Equipment (LBE), we propose analytical frameworks to study the successful probability of synchronization and the energy consumption of synchronization in a standalone LTE-U network. Specifically, for the LBE mode, we also propose a Lattice-Poisson algorithm-based approach to derive the distribution of the channel non-occupancy period of a standalone LTE-U network. Furthermore, we explore the impact of diverse protocol parameters of both FBE and LBE modes on the two studied performance metrics. Simulation results demonstrate the accuracy of the analysis, and shed some light on the selection of FBE and LBE for standalone LTE-U networks, in terms of synchronization, energy consumption, and throughput of standalone LTE-U and Wi-Fi networks.

Index Terms Standalone LTE-U network, FBE, LBE, synchronization, energy consumption, throughput fairness, Lattice-Poisson algorithm

I. I NTRODUCTION The licensed frequency spectrum scarcity becomes a serious issue with the increase of cellular network traffic. One solution is to deploy the Long Term Evolution (LTE) network over unlicensed frequency band, i.e., LTE in Unlicensed Band (LTE-U) IET Review Copy Only


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[1]. Different from the other modes of LTE-U such as Licensed-Assisted Access (LAA), the data transmission and the signalling exchange of standalone LTE-U networks are both carried out in unlicensed band. Besides, standalone LTE-U networks have to compete for radio resource with other networks operating in unlicensed band such as Wireless Fidelity (Wi-Fi), thus facing more technical challenges. One of the critical challenges is that the synchronization between User Equipments (UEs) and Base Stations (BSs) is difficult to establish and maintain due to the random interruption from other networks operating on the same channel. Therefore, the synchronization performance of standalone LTE-U networks is dependent on the adopted channel access scheme. Study on the synchronization performance of standalone LTE-U networks with different channel access schemes has great significance to protocol design, energy saving, and the harmonious coexistence with other networks such as Wi-Fi, which is the motivation of this paper. For the channel access technology, Listen-Before-Talk (LBT) is recognized as one of the best practices for networks operating on unlicensed spectrum including both LTE-U and Wi-Fi networks, and had been widely used in their protocol design (e.g., [2], [3]). The work of [4] proposed two basic modes of LBT, i.e., Frame-Based-Equipment (FBE) in which BSs access channel periodically, and Load-Based-Equipment (LBE) in which BSs access channel on demand. The impact of LBT parameters on the coexistence performance of Wi-Fi and cellular networks was analysed in [5]. In [6] and [7], the throughput performance of Wi-Fi and LTE-U in FBE mode was studied. In [8], the authors discussed the robustness of LBE in dealing with inter-network LAA interference. The fairness between the LTE-U with LBT and the coexisting Wi-Fi was discussed in [9] and [10]. It is noteworthy that all aforementioned works ( [5]–[10]) studied LBE and/or FEB ignoring the synchronization issue, as they mainly focus on the LAA scenario. On the contrary, for the standalone scenario, throughput fairness between standalone LTE-U and Wi-Fi networks should be studied given certain synchronization performance guarantee for the standalone LTE-U UEs. However, to the best of our knowledge, there is still no research worked in the literature on the synchronization performance for standalone LTE-U networks. In this work, we develop analytical frameworks to study the successful probability of synchronization and the energy consumption of synchronization in standalone LTE-U networks. Whereby, we explore the impact of diverse protocol parameters of channel access schemes and Wi-Fi parameters such as the sensing cycle in FBE mode, the backoff window size in LBE mode, and the traffic load in a coexisting Wi-Fi network on the two aforesaid performance metrics. We further conduct extensive simulations to validate the analysis, and to study the trade-off between the two performance metrics and throughput of coexisting networks. The simulation results are presented to analyse the advantages and disadvantages of both FBE and LBE from the perspective of not only the throughput fairness but also the synchronization performance and the related energy consumption. The main contributions of this paper are three-fold.

IET Review Copy Only

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. 3 Content may change prior to final publication in an issue of the journal. To cite the paper please use the doi provided on the Digital Library page. •

First, for the LBE mode, using Lattice-Poisson algorithm we derive the distribution of the channel non-occupancy period of a standalone LTE-U network. The result bases the analysis for standalone LTE-U networks in LBE mode.

•

Second, analytical frameworks are proposed to obtain the successful probabilities and the energy consumption of synchronization of FBE and LBE based standalone LTE-U networks, respectively. Simulation results demonstrate the accuracy of the analysis.

•

Third, the throughput of the standalone LTE-U network and that of the coexisting Wi-Fi network is compared by simulation given certain synchronization performance requirement. Whereby, we provide useful insights into choosing FBE or LBE from more aspects as compared with existing research.

The rest of the paper is organized as follows. Section II describes the system model and introduces different channel access schemes in a standalone LTE-U network. Sections III and IV present the analytical models to study the synchronization performance of a standalone LTE-U network in FBE mode and LBE mode, respectively. The numerical and simulation results are presented in Section IV, followed by the conclusions in Section V.

II. S YSTEM MODEL We consider a standalone LTE-U network coexisting with a Wi-Fi network consisting of Nw nodes and assume that BS in standalone LTE-U network and Wi-Fi nodes have saturated traffic. For the Wi-Fi network, Wi-Fi nodes access channel using Distributed Coordination Function (DCF) and binary exponential backoff mechanism [11]. For the standalone LTE-U network, we consider both FBE and LBE based channel access schemes to study the impact of different channel access schemes on the synchronization performance.

A. Channel Access Scheme of the standalone LTE-U Network in FBE Mode The basic principle of FBE is that the standalone LTE-U BS senses channel periodically as shown in Fig. 1. At every sensing opportunity, the BS senses the channel for a time period of duration Tcca . If the channel is sensed idle, the BS accesses channel immediately for a duration of Te called transmission period. Otherwise, the BS waits for the next sensing opportunity after the sensing cycle of duration Tsense 1 . If the sensing cycle is not larger than the transmission period, there are k0 = ⌊Te /Tsense ⌋ sensing opportunities in the transmission period (see Fig. 1 (a)). Otherwise, there is no sensing opportunity in the transmission period, i.e., k0 = 0 (see Fig. 1 (b)). Besides, to achieve better fairness performance, in FBE mode the standalone LTE-U network can reserve a time period for Wi-Fi of duration Tr called reservation period, satisfying Tr = (k1 + 1)Tsense − Tcca , 1 In

this work, we set the sensing cycle Tsense to be an integer in milliseconds, so to keep compatible with the duration of LTE’s subframe.


(1)


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where k1 (∈ N) is the number of sensing opportunities in the reservation period. The interval between the adjacent channel access of the standalone LTE-U BS in FBE mode is denoted as T F , including the transmission period, the reservation period, and the interval from the end of the reservation period to the sensing attempt in which the BS finds channel idle (see Fig. 1). So, T F = Te + Tr + H, where the superscript F stands for FBE and H = (k2 − 1)Tsense + Tcca is the time duration of k2 sensing attempts that the BS needs before accessing channel successfully. The average value of interval T F is given by E[T F ] = Te + Tr +

∞ ∑

Psuc (1 − Psuc )k2 −1 · [(k2 − 1)Tsense + Tcca ],

(2)

k2 =1

where k2 is geometrically distributed, so the standalone LTE-U BS accesses channel at the k2 th sensing opportunity with probability Psuc (1 − Psuc )k2 −1 . Here, Psuc is the probability that the channel sensed by the standalone LTE-U BS is idle at each sensing opportunity and is given by [7]

Psuc =

 Ti Qi i −1  Pi Qi 0 (Tdifs +i0 Ti −Tcca + 1−Q )   i  , i0 ≥ 1 Tavg  T P  (T −T + i i )   difs cca 1−Qi , Tavg

Tavg = Tdifs +

(3)

i0 = 0,

( ) ∑Nw ( ) Ts T i Pi Qc Pi Qs Pi + Tc Pc + + u=1 Ps + , 1 − Qi 1 − Qi Nw 1 − Qi

(4)

where Pi (Qi ), Pc (Qc ), and Ps (Qs ) denote the probabilities that current channel state is idle, occupied with collided transmissions, and occupied with successful transmissions given busy (idle) state for the previous channel state, respectively. Tdifs and Ti are the durations of Distributed Inter-frame Spacing (DIFS) and a time slot in Wi-Fi networks, respectively. Ts


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Channel access scheme of the standalone LTE-U network in LBE mode.

(Tc ) is the channel occupancy duration due to a successful (collided) Wi-Fi transmission. For analysis simplicity, we assume that Ts (Tc ) is an integer in microseconds. In (3), i0 = max(⌈(Tcca − Tdifs )/Ti ⌉, 0) denotes the minimum number of successive idle slots needed for the standalone LTE-U BS to determine an idle channel.

B. Channel Access Scheme of the standalone LTE-U Network in LBE Mode As illustrated in Fig. 2, in LBE mode the standalone LTE-U BS accesses channel adopting a backoff mechanism with a fixed backoff window size. Before the standalone LTE-U BS sends packets, the BS chooses a backoff counter U randomly from [0, D − 1] to implement backoff process, where D is the maximum backoff window size. In the backoff process, if the channel is sensed idle of duration Tslot , the backoff counter reduces by 1. Otherwise, the standalone LTE-U BS freezes its backoff counter. When the backofff counter reduces to 0, the standalone LTE-U BS accesses channel for the duration of a transmission period (i.e., Te ). The channel non-occupancy period J of the standalone LTE-U network satisfies     0, if U = 0 J=   ∑ ∑  U · Tslot + U Ψu = U (Tslot + Ψu ), otherwise. u=1 u=1

(5)

If the randomly chosen backoff counter U is not 0, the duration of total backoff slots equals U · Tslot > 0. Let Ψu be the frozen duration for the interruption of Wi-Fi’s channel occupancy when the backoff counter reduces from u to u − 1. We assume that the same slot can only be interrupted once as the probability that the same slot is interrupted more than once is negligible. Therefore, given an i.i.d. Ψu , and for any u ∈ [1, U ], U ∈ [1, D − 1],

∑U u=1

Ψu in (5) is the total frozen duration interrupted

by Wi-Fi when the backoff counter reduces from U to 0. During the backoff period of the standalone LTE-U BS, if all Wi-Fi nodes do not send packets, then Ψu = 0 with probability (1 − τw )Nw , where τw is the probability of a Wi-Fi node sending packets at any slot. The derivation of τw is given in Appendix. If one of the Wi-Fi nodes sends packets, then Ψu equals the channel occupancy duration of a successful Wi-Fi transmission, i.e., Ψu = Ts , with probability Nw τw (1 − τw )Nw −1 . Similarly, if there are more than one Wi-Fi node sending packets, then Ψu equals the channel occupancy duration of a collided Wi-Fi



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transmission, i.e., Ψu = Tc , with probability      0      Ψu = Ts         Tc

1 − (1 − τw )Nw − Nw τw (1 − τw )Nw −1 . So, Ψu can be summarized as w.p.

(1 − τw )Nw

w.p.

Nw τw (1 − τw )Nw −1

(6)

w.p. 1 − (1 − τw )Nw − Nw τw (1 − τw )Nw −1 ,

where w.p. represents “with probability”. In LBE mode, the interval between the adjacent channel access of the standalone LTE-U BS (denoted as T L ) includes the transmission period and the channel non-occupancy period (see Fig. 2), i.e., T L = Te + J, where the superscript L stands for LBE. The average value of interval T L is given by E[T L ] = Te + E[J]. According to (5), it can be seen that J is an integer in microseconds. Therefore, E[J] =

(7) ∑∞ j=0

jg(j) can be figured out based

on the probability mass function g(j) of J. The probability mass function g(j) is to be derived in Section IV-A, based on which we will further study the synchronization and energy consumption performance of the standalone LTE-U network in LBE mode.

C. Synchronization and Energy Consumption To compare the synchronization performance of FBE and LBE modes, we study the successful probability of initial synchronization and that of maintaining synchronization in the next two sections, respectively. Further, we also investigate the related energy consumption of initial and maintaining synchronization. In both FBE and LBE modes, we consider that the BS will send a synchronizing signal immediately after accessing channel and it does not resend the synchronizing signal in the transmission and reservation periods. To focus on the analysis of the synchronization performance within a certain time, we assume that the transmission of the synchronizing signal is error-free. For any new (or handover) user, we consider that to finish initial synchronization it needs to detect the synchronizing signal successfully in a preset time duration T1 . In both FBE and LBE modes, users needs to continuously sense the channel for synchronizing signal detection, which consumes energy in initial synchronization process. After initial synchronization, the user needs to keep synchronized with the BS (i.e., maintaining synchronization) thus to detect the synchronizing signal once successfully in every T2 milliseconds. In contrast to the energy consumption of initial synchronization, for the energy consumption of maintaining synchronization, FBE is promising to save more energy as compared with LBE since the way of periodic detection of the synchronizing signal. The detailed analysis of the successful probability of synchronization and the related energy consumption in FBE and LBE modes is given in the next two sections.


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III. S YNCHRONIZATION PERFORMANCE AND ENERGY CONSUMPTION IN FBE MODE In this section, we study the synchronization performance and the related energy consumption in FBE mode. The analysis for LBE mode is presented in Section IV.

A. Initial Synchronization We first study the successful probability of initial synchronization and the related energy consumption in this subsection. As mentioned in Section II-C, a user should detect the synchronizing signal within a preset time duration T1 , and the number of sensing opportunities in T1 is g1 = ⌊T1 /Tsense ⌋. As shown in Fig. 1, users may arrive at anytime in the duration of T F and we assume that they arrive according to a Poisson distribution with a fixed rate. The successful probability of initial synchronization in FBE mode can be expressed as PIF =

∑ h≤T1 −Te −Tr

=

∑

P (H = h) +

∑

h>T1 −Te −Tr

T1 P (H = h) h + Te + Tr

k2 >g1 −k0 −k1

k2 ≤g1 −k0 −k1

=

∑

∑

P (H = (k2 − 1)Tsense + Tcca ) + Psuc (1 − Psuc )k2 −1 +

∑ k2 >g1 −k0 −k1

k2 ≤g1 −k0 −k1

(8a)

g1 P (H = (k2 − 1)Tsense + Tcca ) k0 + k1 + k2

g1 Psuc (1 − Psuc )k2 −1 . k0 + k1 + k2

(8b)

(8c)

In (8a) the successful probability of initial synchronization equals 1 when h ≤ T1 − Te − Tr (i.e., T F ≤ T1 ), because all users can finish initial synchronization in the duration T1 when T F ≤ T1 . Otherwise, it equals T1 /(h + Te + Tr ), since only when the waiting time for a user (from user’s arrival to the instant of detecting the synchronizing signal) less than T1 , can the user have opportunities to establish synchronization with the BS. For (8b) and (8c), we substitute H = (k2 − 1)Tsense + Tcca and apply the probability mass function of k2 according geometric distribution, respectively. In FBE mode, provided that the initial synchronization is successful, the average energy consumption of initial synchronization is EIF = E[T |Y F = s] · Qact , where Y F = s means that the initial synchronization in FBE mode is successful, Qact is the power consumption for detecting the synchronizing signal, and E[T |Y F = s] is the average time for a user spending in initial synchronization and is given by E[T |Y F = s] =

∑

E[T |H = h, Y F = s]P (H = h|Y F = s)

(9a)

h

=

∑ h≤T1 −Te −Tr

=

∑ k2 ≤g1 −k0 −k1

+

∑ k2 >g1 −k0 −k1

h + Te + Tr P (H = h|Y F = s) + 2

∑ h>T1 −Te −Tr

T1 P (H = h|Y F = s) 2

(9b)

(k2 − 1)Tsense + Tcca + Te + Tr P (H = (k2 − 1)Tsense + Tcca |Y F = s) 2 T1 P (H = (k2 − 1)Tsense + Tcca |Y F = s). 2


(9c)


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In (9b), for h ≤ T1 − Te − Tr , E[T |H = h, Y F = s] = (h + Te + Tr )/2, because that a user can arrive at any time in the duration T F , so the distribution of its waiting time follows a uniform distribution over the interval [0, h + Te + Tr ]. Similarly, E[T |H = h, Y F = s] = T1 /2 when h > T1 − Te − Tr . For P (H = (k2 − 1)Tsense + Tcca |Y F = s) in (9c), we have P (H = (k2 − 1)Tsense + Tcca |Y F = s)

= =

P (Y F = s|H = (k2 − 1)Tsense + Tcca )P (H = (k2 − 1)Tsense + Tcca ) P (Y F = s) P (Y F = s|H = (k2 − 1)Tsense + Tcca )Psuc (1 − Psuc )k2 −1 , (10) PIF

where P (Y = s|H = (k2 − 1)Tsense + Tcca ) equals 1 if k2 ≤ g1 − k0 − k1 , otherwise it equals g1 /(k0 + k1 + k2 ).

B. Maintaining Synchronization In this subsection, we analyse the successful probability of maintaining synchronization and the related energy consumption. The number of sensing opportunities during the period of T2 is g2 = ⌊T2 /Tsense ⌋, of which the first k0 +k1 sensing opportunities are in the transmission period and reservation period (see Fig. 1). The successful probability of maintaining synchronization in FBE mode is g2 −(k0 +k1 ) F PM =

∑

Psuc (1 − Psuc )k2 −1 ,

(11)

k2 =1

where the upper limit of the summation is g2 − (k0 + k1 ), because the BS does not send the synchronizing signal in the transmission and reservation periods. Therefore, the user cannot detect the synchronizing signal in the first k0 + k1 sensing opportunities. The average energy consumption of maintaining synchronization is g2 −(k0 +k1 ) F = EM

∑

Psuc (1 − Psuc )k2 −1 Ek′ 2 ,

(12)

k2 =1

where Ek′ 2 = k2 · [Tact · Qact + (Tsense − Tact ) · Qidle ] is the energy consumption of maintaining synchronization when the user detects the synchronizing signal successfully at the (k0 + k1 + k2 )th sensing opportunity, with Qidle and Tact being the power consumption of the user in idle state and the duration of detecting the synchronizing signal each time, respectively.

IV. S YNCHRONIZATION PERFORMANCE AND ENERGY CONSUMPTION IN LBE MODE In this section, we study the synchronization performance and the related energy consumption in LBE mode. To this end, we first study the distribution of the channel non-occupancy period J.


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A. Probability Mass Function g(j) The probability mass function of a random variable taking values in the non-negative integers can be derived from its probability generating function [12]. In the following, we first analyse the probability generating function of J, based on which we then calculate its probability mass function. b b Let J(z) denote the probability generating function of J. Based on (5), with some manipulation J(z) can be calculated as b =U b (Td c J(z) slot (z)Ψu (z)),

(13)

b (z), Td c where U slot (z), and Ψu (z) represent the probability generating functions of U , Tslot , and Ψu , respectively. As long as we notice that U takes for discrete uniform distribution, Tslot is a constant, and Ψu has three values (Ts , Tc , and 0) as shown b (z), Td c in (6), U slot (z), and Ψu (z) can be found out respectively as follows [12] D b (z) = 1 − z , U D(1 − z)

(14)

Tslot Td , slot (z) = z

(15)

cu (z) = [Nw τw (1 − τw )(Nw −1) ]z Ts + [1 − (1 − τw )Nw − Nw τw (1 − τw )Nw −1 ]z Tc + (1 − τw )Nw . Ψ

(16)

To find g(j), we use a numerical approach Lattice-Poisson algorithm developed in [13], [14]. The inversion formula used in the algorithm is lj−1 ∑ 1 b −iπx/(jl) )eiπx/l , J(re g(j) ≈ 2jlrj

(17)

x=−lj

for real r and integer l. The results we present in Section V are calculated using l = 1 and r = 10−4/j , which results in an error less than 10−8 in the numerical inversion process.

B. Initial Synchronization As shown in Fig. 2, a user may arrive at any time in the period of T L . Similar to Section III-A, the user should finish the initial synchronization in the duration of T1 . Therefore, the successful probability of initial synchronization in LBE mode can be given by PIL =

∑ j≤T1 −Te

g(j) +

∑ j>T1 −Te

T1 g(j). j + Te

(18)

Notice that the successful probability of initial synchronization in (18) equals 1 if J ≤ T1 − Te (i.e., T L ≤ T1 ), and it equals T1 /(j + Te ) if J > T1 − Te .



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In LBE mode, provided that the initial synchronization is successful, the average energy consumption of initial synchronization is EIL = E[T |Y L = s] · Qact , where Y L = s means that the initial synchronization in LBE mode is successful, and E[T |Y L = s] is the average time for a user expanded in initial synchronization and can be given by E[T |Y L = s]

=

∑ j

=

E[T |J = j, Y L = s]P (J = j|Y L = s)

∑

j≤T1 −Te

=

∑

j≤T1 −Te

j + Te P (J = j|Y L = s) + 2 j + Te g(j) + 2 PIL

∑ j>T1 −Te

∑ j>T1 −Te

T1 P (J = j|Y L = s) 2

T12 g(j) , 2(j + Te ) PIL

(19)

where in the second equation, E[T |J = j, Y L = s] equals (j + Te )/2 if j ≤ T1 − Te and T1 /2 otherwise, because of the uniform distribution of users’ waiting time. In the third equation, P (J = j|Y L = s) can be written as P (J = j|Y L = s) =

P (Y L = s|J = j)P (J = j) P (Y L = s|J = j)g(j) = , L P (Y = s) PIL

(20)

where P (Y L = s|J = j) equals 1 if j ≤ T1 − Te and it equals T1 /(j + Te ) otherwise.

C. Maintaining Synchronization According to Fig. 2, to keep synchronized with the BS in the duration of T2 , the channel non-occupancy period should not exceed T2 − Te . Thus, the successful probability and the average energy consumption of maintaining synchronization in LBE mode can be expressed, respectively, as ∑

L PM =

g(j),

(21)

j≤T2 −Te L = EM

T∑ 2 −Te

g(j) · (j · Qact ).

(22)

j=0

V. V ERIFICATION AND DISCUSSION We validate the proposed theoretical models of the standalone LTE-U synchronization and the related energy consumption in this section. Furthermore, we study the effects of different protocol parameters on synchronization performance and related energy consumption in FBE and LBE modes, respectively. In addition, under the condition of required synchronization performance, we study the throughput of standalone LTE-U and Wi-Fi networks thus to understand the tradeoff between throughput and fairness performance of the two networks.

A. Settings We simulate a scenario where a standalone LTE-U network coexists with multiple Wi-Fi nodes in a 20MHz channel. The main parameters of standalone LTE-U and Wi-Fi networks are listed in Table I. The parameters of Wi-Fi follows the IEEE IET Review Copy Only

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. 11 Content may change prior to final publication in an issue of the journal. To cite the paper please use the doi provided on the Digital Library page. TABLE I PARAMETERS

802.11ac Parameters [11]

Values

Standalone LTE-U Parameters [15]

Values

Bit rate of data rdata

100Mbps

Duration of transmission period Te

10ms

Bit rate of control signal rctrl

1Mbps

Duration of the BS sensing Tcca

18µs

Bits of PHY header lphys

128bits

Duration of sensing cycle in FBE Tsense 1,5,10ms

Bits of MAC header lmac

272bits

Backoff window size in LBE D

64,256,512

Bits of ACK packet lack

240bits

Duration of a backoff slot in LBE Tslot

9µs

Duration of SIFS tsifs (DIFS tdifs ) 16µs (34µs) Duration of UE detecting period Tact

71.4µs

Packet length lpay

12000bits

Power consumption for detection Qact

0.2W

Duration of a backoff slot Ti

9µs

Power consumption for idle state Qidle

0.001W

802.11ac standard [11]. The minimum contention window W , the maximum backoff stage m, and the maximum retransmission limit R are set as 32, 5, and 7, respectively. The channel occupancy time of a successful Wi-Fi transmission is Ts = lphys /rctrl + (lpay +lmac )/rdata +tdifs +tsifs +tack , where tack = (lphys +lack )/rctrl . The channel occupancy of a collided Wi-Fi transmission is given by Tc = lphys /rctrl + (lpay + lmac )/rdata + tdifs . Here, lphys , lpay , lmac , and lack are the number of bits of physical layer header, data packet, MAC layer header, and Acknowledgment (ACK), respectively. tdifs , tsifs , and tack are the durations of DIFS, Short Inter-Frame Space (SIFS), and ACK, respectively. rctrl and rdata are the bit rate of control signals and data signals, respectively.

B. Numerical and Simulation Results The successful probabilities of initial and maintaining synchronization in FBE and LBE modes are studied in Fig. 3, where the tuples in Figs. 3(a) and 3(b) (Figs. 3(c) and 3(d)) represent ⟨Nw , Tsense , k1 ⟩ (⟨Nw , D⟩). It can be seen that the numerical results well match the simulation results. Fig. 3(a) (Fig. 3(b)) shows that the successful probability of initial (maintaining) synchronization in FBE mode increases as the time reserved for Wi-Fi (i.e., k1 ) or the sensing cycle (Tsense ) or the Wi-Fi traffic load (in Nw ) decreases. Similarly, Fig. 3(c) (Fig. 3(d))) shows that the successful probability of initial (maintaining) synchronization in LBE mode increases as the backoff window size (D) or the Wi-Fi traffic load (in Nw ) decreases. When the aforesaid protocol parameters of channel access schemes or the Wi-Fi traffic load decreases, the opportunities for the standalone LTE-U BS accessing channel increase and thus the successful probability of synchronization increases. It is noteworthy that the probability of maintaining synchronization is 0 when T2 ≤ 10ms in both Fig. 3(b) and Fig. 3(d), since in the considered model users cannot detect the synchronizing signal twice in one transmission period (10ms). In Fig. 3(b), the probability of maintaining synchronization is 0 when k1 = 20 and T2 ≤ 210ms. This is due to that users cannot detect the synchronizing IET Review Copy Only


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1

1

0.9

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Probability of maintaining synchronization

Probability of initial synchronization


0.8 0.7 0.6

Sim. Sim.

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(c) Initial synchronization performance in LBE mode Fig. 3.

900

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(a) Initial synchronization performance in FBE mode

0.5

Num. Num. Num.

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(d) Maintaining synchronization performance in LBE mode

The successful probability of synchronization under different parameters.

signal in both the transmission period (10ms) and reservation period (200ms for k1 = 20 and Tsense = 10ms). Comparing Fig. 3(a) with Fig. 3(b) or Fig. 3(c) with Fig. 3(d), we can observe that, given fixed protocol parameters and an identical value of T1 and T2 , the successful probability of initial synchronization is higher than that of maintaining synchronization. This is because that, in the FBE (LBE) mode, to maintain synchronization a user needs to wait for the BS for the whole time duration of T F (or T L ) to access channel again, but it may wait for a time duration less than T F (or T L ) in initial synchronization. Moreover, it can be found by comparing Fig. 3(b) with Fig. 3(d) that, under the condition of T2 = 100ms and Nw = 10 the successful probability of maintaining synchronization in FBE mode is less than 90%, while it can be more than 90% in LBE mode with D = 64, 256, 512. It means that if the required successful probability of maintaining synchronization is 90%, T2 in FBE mode needs to be set much larger than that in LBE mode. The reason is that as compared with the periodical detection of the standalone LTE-U BS in FBE mode, in LBE mode the BS detects channel continuously, thus there are more opportunities


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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. 13 Content may change prior to final publication in an issue of the journal. To cite the paper please use the doi provided on the Digital Library page. 14

25

12 Energy consumption (mW)

Energy Consumpition (mW)

20 Sim. Sim. Sim. Sim. Num. Num. Num. Num.

FBE, Tsense=5ms 15

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LBE, D=512 Sim. Sim. Sim. Num. Num. Num.

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LBE, D=512

LBE, D=64

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(b) Maintaining synchronization

(a) Initial synchronization Fig. 4.

5

The average energy consumption of synchronization in FBE mode and LBE mode when T1 = T2 = 500ms.

to access channel and in turn maintaining synchronization can be achieved in an easier way. In both FBE and LBE modes, the average energy consumption of initial (maintaining) synchronization is plotted in Fig. 4 at T1 = T2 = 500ms. It is shown that the average energy consumption increases with the number of Wi-Fi nodes in both modes. This is because that as the number of Wi-Fi nodes increases, the interval between the adjacent access becomes larger, thus the total time for a user to detect the synchronizing signal increases. Fig. 4(a) indicates that, in FBE mode the energy consumption of initial synchronization with a large sensing cycle (e.g., Tsense = 5ms) is much higher than that in LBE mode, because in FBE mode the time for a user to detect the synchronizing signal with a large sensing cycle is much longer than that in LBE mode. However, it is also observed from Fig. 4(b) that in FBE mode the energy consumption of maintaining synchronization is much lower than that in LBE mode, as the user detects the synchronizing signal continuously in LBE mode but the user detects the synchronizing signal every Tsense in FBE mode. In the following, we further explore the throughput performance of standalone LTE-U and Wi-Fi networks when the successful probability of synchronization meet a preset requirement. In Fig. 5, we simulate the throughput of standalone LTE-U and Wi-Fi networks when the probability of maintaining synchronization achieves for 90% under T2 = 200ms. As shown in Fig. 3, in FBE mode only when Tsense = 1ms can satisfy the requirement, while LBE mode can meet the requirement with D = 64, 256, 512. It can be seen in Fig. 5 that, with the aforesaid protocol parameters, no matter in FBE mode or LBE mode the throughput of the LTE-U network decreases with the number of Wi-Fi nodes, since the channel occupancy ratio of the standalone LTE-U network decreases. For the tested settings of LBE mode, not only the throughput of the standalone LTE-U network but also the total throughput of both networks increase as the backoff window size D reduces. This is because that given the number of Wi-Fi nodes, the standalone LTE-U network’s backoff process is shorter with a smaller D, thus the channel occupancy ratio of the standalone LTE-U network increases. However, with backoff window size D decreases, the throughput of the standalone LTE-U



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Standalone LTE−U LBE, Standalone LTE−U LBE, Standalone LTE−U LBE, Standalone LTE−U FBE,

1

D=64 D=256 D=512 Tsense=1ms

WLAN WLAN WLAN WLAN WLAN WLAN WLAN WLAN

Throughput

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Fig. 5. The throughput of standalone LTE-U and Wi-Fi networks when the probability of maintaining synchronization achieves for 90% under T2 = 200ms.

network increases at the expanse of Wi-Fi throughput (i.e., at a cost of less fairness). To provide a harmonious coexistence between standalone LTE-U and Wi-Fi networks, one can take a large D such as 512. For instance, when Nw = 10 and D = 512, the throughput of Wi-Fi accounts for 43.17% of the total throughput, which is 35.86% and 16.03% higher than that with D = 64 and D = 256, respectively. On the other hand, for LBE mode with D = 512, although the successful probability of synchronization still can meet the requirement, not only the total throughput of both networks but also the throughput of the standalone LTE-U network can be less than those in FBE mode. Furthermore, under the same synchronization performance requirement, it is possible that FBE can provide better throughput fairness for both networks. For example, for Nw = 10, the throughput of Wi-Fi coexisting with a FBE-based standalone LTE-U network increases 14.75% as compared with coexisting with a standalone LTE-U network in LBE mode and with D = 512.

VI. C ONCLUSION In this paper, we have proposed analytical frameworks to analyze the synchronization performance in a FBE or LBE based standalone LTE-U network. Specifically, we have derived the successful probability and the average energy consumption of initial and maintaining synchronization, and analyzed the throughput of standalone LTE-U and Wi-Fi networks. Several insights are found from the theoretical analysis and simulation results. As compared with FBE, in LBE mode the user can meet the synchronization requirements in a shorter time duration, and the energy consumption of initial synchronization is lower with a small backoff window size. However, a small backoff window size leads to serious inter-system unfairness. In FBE mode, the energy consumption of maintaining synchronization is lower than that in LBE mode. Further, FBE can offer higher throughput for the standalone LTE-U network and better inter-system fairness as compared with LBE mode under a large backoff window


Page 15 of 16



size. From our analysis, the synchronization performance can be improved by suitably adjusting the standalone LTE-U network’s channel access parameters, which provides reference to practical application.

A PPENDIX When sending packets, Wi-Fi nodes might not only conflict with each other but also conflict with the standalone LTE-U network’s BS coexisting in the same unlicensed band. Denote the probability of a Wi-Fi node sending a packet at any time slot as τw , and the collision probability as pw . Denote the probability of the standalone LTE-U BS accessing channel as τL , and the collision probability as pL . Without considering transmission error and assuming both Wi-Fi nodes and the standalone LTE-U network have saturated traffic, we have pw = 1 − (1 − τw )Nw −1 (1 − τL ),

(23)

pL = 1 − (1 − τw )Nw .

(24)

According to [12], it can be obtained that τw−1

=

R (1 − pw )W (1 − (λpw )m ) λm W (pm 1 w − pw ) + − , R R 2(1 − pw )(1 − λpw ) 2(1 − pw ) 2

(25)

where R is the retry limit of Wi-Fi nodes, W is the minimum contention window size, and λ ≥ 1 is the backoff multiplier. Given the backoff window size D, the probability of the standalone LTE-U network BS accessing channel in LBE mode can be expressed as [16] τL =

2 . D+1

(26)

Based on (23) - (26), τw , τL , pw and pL can be obtained by numerical approach.

R EFERENCES

[1] R. Zhang, M. Wang, L. X. Cai, Z. Zheng, X. Shen, and L.-L. Xie.:‘LTE unlicensed: The future of spectrum aggregation for cellular networks’, IEEE Wireless Commun., Jun. 2015, 22, (3), pp. 150-159, doi:10.1109/MWC.2015.7143339 [2] R. Ratasuk, M. A. Uusitalo, N. Mangalvedhe, A. Sorri, S. Iraji, C. Wijting, and A. Ghosh.:‘License-exempt LTE deployment in heterogeneous network’. Proc. ISWCS, Paris, FR, Aug. 2012, pp. 246-250 [3] A. Al-Dulaimi, S. Al-Rubaye, Q. Ni, and E. Sousa.:‘5G communications race: Pursuit of more capacity triggers LTE in unlicensed band’, IEEE Veh. Technol. Mag., Mar. 2015, 10, (1), pp. 43-51, doi:10.1109/MVT.2014.2380631



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[4] ‘Broadband radio access networks (BRAN); 5 GHz high performance RLAN; harmonized EN covering the essential requirements of article 3.2 of the R&TTE directive’, Eur. Telecommun. Standards Inst., Sophia Antipolis, France, Tech. Rep. EN 301 893 v1.7.1, Jun. 2012 [5] Y. Song, K. W. Sung, and Y. Han.:‘Coexistence of Wi-Fi and cellular with listen-before-talk in unlicensed spectrum’, IEEE Commun. Lett., Jan. 2016, 20, (1), pp. 161-164, doi:10.1109/LCOMM.2015.2504509 [6] R. Zhang, M. Wang, and L. X. Cai.:‘Modeling and analysis of MAC protocol for LTE-U co-existing with Wi-Fi’. Proc. GLOBECOM, SanDiego, CA, Dec.2015 [7] F. Liu, E. Bala, E. Erkip, M. C. Beluri, and R. Yang.:‘Small cell traffic balancing over licensed and unlicensed bands’, IEEE Trans. Vehicular Tech., Det. 2015, 64, (12), pp. 5850-5865, doi:10.1109/TVT.20142387798 [8] Ericsson.:‘Discussion on LBT protocols’, 3GPP, Tech. Rep. R1-151996, Apr. 2015 [9] A. Kanyeshuli.:‘LTE-in unlicensed band: Medium access and performance evaluation’. Master thesis, University of Agder, 2015 [10] H. He, H. Shan, A. Huang, L. X. Cai, and T. Q. S. Quek.:‘Proportional fairness-based resource allocation for LTE-U coexisting with Wi-Fi’, IEEE Access, to be published, doi:10.1109/ACCESS.2016.2604822 [11] E. H. Ong, J. Kneckt, O. Alanen, Z. Chang, T. Huovinen, and T. Nihtila.:‘IEEE 802.11ac: Enhancements for very high throughput WLANs’. Proc. PIMRC, Toronto, Canada, Sep. 2011, pp. 849-853 [12] T. Sakurai and H. L. Vu.:‘MAC access delay of IEEE 802.11 DCF’, IEEE Trans.Wireless Commun., May 2007, 6, (5), pp. 1702-1710, doi:10.1109/TWC.2007.360372 [13] T. Sakurai and H. L. Vu.:‘Accurate delay distribution for IEEE 802.11 DCF’, IEEE Commun. Lett., Apr. 2006, 10, (4), pp. 317-319, doi:10.1109/LCOMM.2006.1613759 [14] J. Abate, G. L. Choudhury, and W. Whitt.:‘An introduction to numerical transform inversion and its application to probability models’, Computational Probability, pp. 257-323. Norwell, MA: Kluwer, 2000 [15] T. Tirronen, A. Larmo, and J. Sachs.:‘Reducing energy consumption of LTE devices for machine-to-machine communication’. Proc. GC Wkshps, California, USA, Dec. 2012, pp. 1650-1656 [16] T. S. Ho and K. C. Chen.:‘Performance evaluation and enhancement of the CSMA/CA MAC protocol for 802.11 wireless LANs’. Proc. PIMRC, Taipei, Taiwan, Oct. 1996, pp. 392-396


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