A New Adaptive Modulation and Coding Method for Communication-Based Train Control Systems using WLAN*

6th IFAC Workshop on Distributed Estimation and Control in 6th 6th IFAC IFAC Workshop Workshop on Distributed Distributed Estimation Estimation and and Control Control in in Networked Systemson 6th IFAC Workshop on Distributed Estimation and Control in Networked Systems Available online at www.sciencedirect.com Networked Systems September 8-9, 2016. Tokyo, Japan Networked Systems September 8-9, 2016. Tokyo, Japan September September 8-9, 8-9, 2016. 2016. Tokyo, Tokyo, Japan Japan

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A New Adaptive Modulation and Coding A New Adaptive Modulation and Coding A New Adaptive Modulation and Method for Communication-BasedCoding Train Method for Communication-Based ⋆Train Train Control Systems using WLAN ⋆⋆ Control Systems using WLAN Control Systems using WLAN Q. Dong ∗∗ K. Hayashi ∗∗ M. Kaneko ∗∗ ∗∗ ∗ ∗ ∗∗ Q. Q. Dong K. Hayashi M. Kaneko Q. Dong Dong ∗ K. K. Hayashi Hayashi ∗ M. M. Kaneko Kaneko ∗∗ ∗ ∗ Graduate School of Informatics, Kyoto University, ∗ Graduate of University, ∗ Graduate School School Sakyo-ku, of Informatics, Informatics, Kyoto University, Yoshida-Honmachi, Kyoto,Kyoto 606-8501, JAPAN Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501, Yoshida-Honmachi, Sakyo-ku, Kyoto, 606-8501, JAPAN (e-mail: {dong; Sakyo-ku, kazunori}@sys.i.kyoto-u.ac.jp). Yoshida-Honmachi, Kyoto, 606-8501, JAPAN JAPAN (e-mail: {dong; kazunori}@sys.i.kyoto-u.ac.jp). ∗∗ (e-mail: {dong; kazunori}@sys.i.kyoto-u.ac.jp). Information Systems Architecture Science Research Division, (e-mail: {dong; kazunori}@sys.i.kyoto-u.ac.jp). ∗∗ ∗∗ Systems Architecture Science Research Division, ∗∗ Information Information Systems Architecture Science Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Information Systems Architecture Science ResearchChiyoda-ku, Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, National Institute Institute of ofTokyo, Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Chiyoda-ku, 101-8430, JAPAN National Informatics, 2-1-2 Hitotsubashi, Tokyo, 101-8430, Tokyo, 101-8430, JAPAN (e-mail: Tokyo,[email protected]). 101-8430, JAPAN JAPAN (e-mail: [email protected]). (e-mail: [email protected]). (e-mail: [email protected]). Abstract: In this paper, we propose a new Adaptive Modulation and Coding (AMC) method Abstract: In propose aaa new Adaptive Modulation and method Abstract: In this paper, we propose new Adaptive Modulation and Coding (AMC) method for Communication-Based Train Control (CBTC) systems using Wireless Local(AMC) Area Network Abstract: In this this paper, paper, we we propose new Adaptive Modulation and Coding Coding (AMC) method for Communication-Based Train Control (CBTC) systems using Wireless Local Area Network for Communication-Based Train Control (CBTC) systems using Wireless Local Area Network (WLAN). The goal of the proposed method is to enhance the control performance by choosing for Communication-Based Train Control (CBTC) systems using Wireless Local Area Network (WLAN). The the method is the by (WLAN). The goal goal ofwhich the proposed proposed method is to to enhance enhance the control control performance by choosing choosing a transmission modeof decreases the average delay with respect performance to both Medium Access (WLAN). The goal of the proposed method is to enhance the control performance by choosing aaaControl transmission mode which decreases the average delay with respect to both Medium transmission mode which decreases the average delay with respect to both Medium Access (MAC)mode contention channelthe fading according both average Ratio transmission whichand decreases average delay to with respect to Signal-to-Noise both Medium Access Access Control (MAC) contention and fading according to average Signal-to-Noise Ratio Control (MAC) contention and channel fading according to both average Signal-to-Noise Ratio (SNR) and the number of competing vehicles. effectiveness of the proposed method is shown Control (MAC) contention and channel channel fadingThe according to both both average Signal-to-Noise Ratio (SNR) and number (SNR) and the number of competing vehicles. The effectiveness of the proposed method is shown via computer (SNR) and the thesimulations. number of of competing competing vehicles. vehicles. The The effectiveness effectiveness of of the the proposed proposed method method is is shown shown via computer simulations. via computer computer simulations. simulations. via © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: AMC, CBTC, WLAN, MAC, channel fading. Keywords: Keywords: AMC, AMC, CBTC, CBTC, WLAN, WLAN, MAC, MAC, channel channel fading. fading. Keywords: AMC, CBTC, WLAN, MAC, channel fading. 1. INTRODUCTION 1. 1. INTRODUCTION INTRODUCTION 1. INTRODUCTION With a growing number of people commuting by means With aaa growing number commuting by With growing number of of people people commuting by means means of urban rail transportations in various countries, the With growing number of people commuting by means of urban rail transportations in various countries, of urban rail rail for transportations in various various countries, the requirements operation efficiency and countries, safety in the urof urban transportations in the requirements and in requirements forareoperation operation efficiency and safety safety in ururban rail transitfor becomingefficiency more stringent than before. requirements for operation efficiency and safety in urban rail more than before. ban rail transit transit are are becoming becoming more stringent stringent than before. Communication-Based Train Control (CBTC) system is ban rail transit are becoming more stringent than before. Communication-Based Train (CBTC) is Communication-Based Train Control Control (CBTC) system is one of the promising methods for meeting those system demands. Communication-Based Train Control (CBTC) system is one of methods meeting demands. one of the the promising methods for meeting those those demands. Unlike thepromising track circuit used for in traditional train control one of the promising methods for meeting those demands. Unlike the track circuit used in traditional train control Unlike the track circuit used in traditional train control systems,the CBTC able to useinthe bidirectional Unlike track iscircuit used traditional train wireless control systems, CBTC is able to use the bidirectional wireless systems, CBTC is able to use the bidirectional wireless communication between wayside equipment and the movsystems, CBTC is able to use the bidirectional wireless communication between wayside and the movcommunication between operational wayside equipment equipment andand thetransmoving vehicle to improve flexibility communication between wayside equipment and the moving vehicle to flexibility ing vehiclecapacity to improve improve operational flexibility and and transtransportation whileoperational ensuring safety. ing vehicle to improve operational flexibility and transportation capacity while ensuring safety. portation capacity while ensuring safety. portation while ensuring safety. to the mobile However, capacity due to various factors inherent However, due to various factors inherent to However, due to various factors inherent to the the mobile environments, is a communication latency of mobile packet However, due there to various factors inherent to the mobile environments, there is a communication latency of environments, there is a communication latency of packet delivery between wayside Access Points (APs) trains, environments, there is a communication latencyand of packet packet delivery between Access Points (APs) and delivery between wayside Access Points (APs)due andtotrains, trains, which may cause wayside unnecessary train braking comdelivery between wayside Access Points (APs) and trains, which may unnecessary train due which may cause cause unnecessary train braking braking due to to comcommunication blackout. This braking will deteriorate the which may cause unnecessary train braking due to communication blackout. This deteriorate the munication blackout.including This braking braking will deteriorate the control performance the ridewill comfort and energy munication blackout. This braking will deteriorate the control performance including ride and control performance including the ride comfort comfort and energy energy cost. Thus, recent works such the as Zhu et al. (2012),Wang control performance including the ride comfort and energy cost. Thus, recent works such as Zhu et al. (2012),Wang cost. Thus, recent works such as Zhu et al. (2012),Wang et al. (2015) have proposed the Multiple-Input Multiplecost. Thus, recent works such as Zhu et al. (2012),Wang et al. have proposed the Multipleet al. (2015) (2015) have enabled proposedWireless the Multiple-Input Multiple-Input MultipleOutput (MIMO) Local Area Networks et al. (2015) have proposed the Multiple-Input MultipleOutput (MIMO) enabled Wireless Local Area Networks Output (MIMO) enabled Wireless Local Area Networks (WLANs) for CBTC systems to achieve betterNetworks control Output (MIMO) enabled Wireless Local Area (WLANs) for systems achieve better (WLANs) forbyCBTC CBTC systems towireless achieve communication better control control performance improving theto (WLANs) for CBTC systems to achieve better control performance improving the communication performance by improving the wireless wireless communication performance, by where they consider the design of adaptive performance by improving the wireless communication performance, where they consider the design of performance, where theyfor consider the designusing of adaptive adaptive modulation and coding CBTC the systems Carrier performance, where they consider design of adaptive modulation and coding systems using modulation andAccess/Collision coding for for CBTC CBTC systems (CSMA using Carrier Carrier Sense Multiple Avoidance /CA) modulation and coding for CBTC systems using Carrier Sense Multiple Access/Collision Avoidance (CSMA Sense Multiple Access/Collision Avoidance (CSMA /CA) protocol by minimizing the average delay between the Sense Multiple Access/Collision Avoidance (CSMA /CA) /CA) protocol by minimizing the average delay between the protocol by minimizing the average delay between the moving vehicle and wayside AP. Nevertheless, the impact protocol by minimizing the average delay between the moving vehicle and wayside AP. the impact moving vehicle and and wayside AP. Nevertheless, Nevertheless, the (MAC) impact of channel fading Medium Access Control moving vehicle and wayside AP. Nevertheless, the impact of channel fading and Medium Access Control (MAC) of channel fading and Medium Access Control (MAC) ⋆ This of channel fading and Medium Access Control (MAC) research was supported in part by JSPS KAKENHI Grant ⋆ ⋆ This research was supported in part byand JSPS Grant This was supported part KAKENHI Grant ⋆ Numbers 15H02252, 26820143 TheKAKENHI TelecommunicaThis research research was 15K06064, supported in in part by by JSPS JSPS KAKENHI Grant Numbers 15H02252, 15K06064, 26820143 and The TelecommunicaNumbers 15H02252, 15K06064, 26820143 and The Telecommunications Advancement Numbers 15H02252,Foundation. 15K06064, 26820143 and The Telecommunications Advancement Foundation. tions tions Advancement Advancement Foundation. Foundation.

layer contention due to multiple competing vehicles have layer contention due to competing have layer contention due to multiple competing vehicles have not considered, they would have avehicles large impact layerbeen contention due while to multiple multiple competing vehicles have not been considered, while they would have a large impact not been considered, while they would have a large impact on the communications’ delays. not been considered, while they would have a large impact on on the the communications’ communications’ delays. delays. on delays. In the thiscommunications’ paper, we propose a new design of Adaptive In this paper, we propose aaa new design of In this this paper, paper, we propose new design systems of Adaptive Adaptive Modulation and we Coding (AMC) for CBTC with In propose new design of Adaptive Modulation and Coding (AMC) for CBTC systems with Modulation and and Coding (AMC) for forthe CBTC systems with CSMA/CA protocol considering impact of fading Modulation Coding (AMC) CBTC systems with CSMA/CA protocol considering the impact of fading CSMA/CA protocol considering the impact of fading channels andprotocol MAC layer contention.the Weimpact performofthefading averCSMA/CA considering channels MAC layer contention. We averchannels and MAC layer contention. We perform the average delayand analysis the impact of thethe number channels and MACwhich layerincludes contention. We perform perform the average delay analysis which includes the impact of the number agecompeting delay analysis analysis which and includes the impact impact of the the number of terminals channel error, and derive the age delay which includes the of number of competing and error, and the of competing terminals and channel error, and derive the average delay terminals of each scheme in different situations. Then, of competing terminals and channel channel error, and derive derive the average delay of each scheme in different situations. Then, average delay of each scheme in different situations. Then, by usingdelay some of information about the number of competing average each scheme in different situations. Then, by about of by using some information about the number of competing terminals and information path loss during the number train operation, we by using using some some information about the the number of competing competing terminals and path loss during the train operation, we terminals and path transmission loss during during the the train operation, we can select and a proper mode which minimizes terminals path loss train operation, we can select a proper transmission mode which minimizes can select a proper transmission mode which minimizes this select averagea delay each control mode periodwhich to improve the can properintransmission minimizes this average delay each control to this average delay in each control period to improve the control performance. of our approachthe is this average delay in in The eacheffectiveness control period period to improve improve the control performance. The effectiveness of our approach control performance. The effectiveness of our approach is confirmed through computer simulations. control performance. The effectiveness of our approach is is confirmed confirmed through through computer computer simulations. simulations. confirmed through computer simulations. 2. CBTC SYSTEMS AND PREVIOUS WORK 2. 2. CBTC SYSTEMS AND PREVIOUS WORK 2. CBTC CBTC SYSTEMS SYSTEMS AND AND PREVIOUS PREVIOUS WORK WORK In this section, we introduce the system model considered In this section, we the model considered In section, we introduce the system model considered in paper, which is basically the same as that in Zhu In this section, we introduce introduce the system system model considered in this paper, which is basically the same as that in al. this(2012). paper, which which is is basically basically the the same same as as that that in in Zhu Zhu et in this paper, in Zhu et al. (2012). et al. (2012). et al. (2012). 2.1 CBTC Architecture 2.1 2.1 CBTC Architecture 2.1 CBTC CBTC Architecture Architecture Fig.1 shows five subsystems in CBTC systems including Fig.1 five subsystems in systems including Fig.1 shows showsTrain five Supervision subsystems (ATS), in CBTC CBTC systems Train including Automatic Automatic OpFig.1 shows five subsystems in CBTC systems including Automatic Train Supervision (ATS), Automatic Train OpAutomatic Train Supervision (ATS), Automatic Train Operation (ATO), communication, Automatic Traintrain-ground Supervision (ATS), AutomaticZone TrainConOperation (ATO), train-ground communication, Zone Coneration (ATO), train-ground communication, Zone Controller (ZC) and train-ground Automatic Train Protection (ATP). The eration (ATO), communication, Zone Controller Train Protection (ATP). troller (ZC) and Automatic Train Protection (ATP). The task ATSand is toAutomatic set the train time between two trollerof(ZC) (ZC) and Automatic Traintravel Protection (ATP). The The task of ATS is to set the train travel time between two task of of ATS ATS stations is to to set setand thegenerate train travel travel time between between two neighboring the timetable for each task is the train time two neighboring stations and generate the timetable for each neighboring stations and generate the timetable for each train. ATO stations subsystem the train produce the neighboring andongenerate the could timetable for each train. on the train. ATO subsystem on the train could produce the optimalATO trainsubsystem guidance trajectory Wangcould et al.produce (2015). The train. ATO subsystem on the the train train could produce the optimal train guidance trajectory Wang et al. (2015). The optimal train guidance trajectory Wang et al. (2015). The optimal train guidance trajectory Wang et al. (2015). The

Copyright © 2016, 2016 IFAC 139Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright 2016 IFAC 139 Copyright © 2016 IFAC 139 Peer review© of International Federation of Automatic Copyright ©under 2016 responsibility IFAC 139Control. 10.1016/j.ifacol.2016.10.386

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Backbone Network

JN = E

N ∑

(eT k Qek k=0

+

]

Ru2k )

,

(3)

˜ k is the tracking error, x ˜ k is the desired where ek = xk − x train state obtained from train guidance trajectory, Q is a diagonal semi-definite matrix and R is a positive scalar.

Heading

Station 1

[

Train 1

Train 2

Train 3

Station 2

ATO

ATP

Fig. 1. Communication-based train control system guidance trajectory is a distance versus velocity profile, which represents the optimal velocity at a specific position. Moreover, ATO can control the train velocity under this trajectory according to train travel time and other factors such as energy cost. In train-ground communication subsystem, each train needs to transmit its own location, direction, velocity and identity to the wayside AP. Then, AP transfers these information to both ZC and ATS subsystem so that ZC subsystem can send the Movement Authority (MA) which represents the allowed distance for the train to proceed. An MA of a train means the distance between the tail of this train and the obstacle in front of this train. For example, from the perspective of train 1 in Fig.1, MA is the distance between the tail of train 1 and the tail of train 2. With the constraint of MA, ATO subsystem will control the train velocity as much as possible under the guidance trajectory. The ATP subsystem is responsible for calculating the braking curve according to the updated MA, which guarantees the train safety. For the train-ground communication subsystem, WLANs have been adopted for some cases because of the commercial off-the-shelf equipments and the philosophy of open standard and interoperability Whitwam (2003). 2.2 System model The equations of motion of the train can be written as 1 uk 2 1 wk 2 T − T , 2M 2M wk uk T− T, (1) vk+1 = vk + M M where qk , vk , uk , wk and T are train position, train speed, control signal, the resistance at time k and the control period, respectively. Then, according to these equations, the train state space equation can be written as qk+1 = qk + vk T +

xk+1 = Axk + Buk + Cwk ,

(2)

where

  1 2 ( ) ( ) T 1T q   xk = k , A = , B =  2M , 1 0 1 vk T M   1 2 T  − C =  2M . 1 − T M The linear quadratic cost is taken as the control performance measure as 140

In every control period T , each train sends its own location, direction, velocity and identity to ZC via a wayside AP to calculate the MA, and the MA is sent to the following train via AP. If the communication delay of sending MA is larger than T , the MA cannot be updated under this control period and packets will be discarded. Consequently, the control signal uk is replaced by brake deceleration a (≤ 0) due to a communication interruption of T for ensuring safety. In this paper, we define such event as an outage. 2.3 Previous work In previous work Zhu et al. (2012), CSMA/CA based MIMO CBTC system has been proposed to achieve better control performance, which focuses on minimizing the average delay. Define Wi as the contention window at the i-th backoff stage. Then, Wi for the exponential backoff strategy is given by { i 2 W0 i ≤ m′ Wi = W m ′ i > m′ , where m′ represents the backoff stage of the maximum contention window. The packet delay Tmac (i) at the i-th retransmission time is shown as Tmac (0) = TDIFS + σ(W0 − 1)/2 + Tdata +TSIFS + Tack ,

Tmac (i) = Tmac (i − 1) + TDIFS + σ(Wi − 1)/2 + Tdata

+TSIFS + Tack , where i ∈ [0, m], m is the maximum retransmission time, σ is the duration of an empty slot time, TDIFS is Distributed Inter-frame Spacing (DIFS), TSIFS is Short Inter-frame Spacing (SIFS), Tdata = Fdata /R is time to transmit a data frame, Fdata is the data payload in bits, R is the data transmission rate, Tack = Fack /R is time to transmit the acknowledgement frame and Fack is the acknowledgement frame in bits. Define Dk as the average delivery delay between AP and train at time k, then Dk can be calculated by Dk = (1 − pe,k )Tmac (0) + pe,k (1 − pe,k )Tmac (1) + · · ·

m +pm−1 e,k (1 − pe,k )Tmac (m − 1) + pe,k Tmac (m), (4)

where pe,k is the Frame Error Rate (FER) at time k.

Then the optimization problem in previous work becomes min Dk . Rk ,pe,k

Note that the data transmission rate Rk is determined by the Modulation and Coding Scheme (MCS) and FER pe,k is influenced by the selection of the MCS and channel state. As a result, the MCS which minimizes the optimization problem above is chosen according to the average Signalto-Noise Ratio (SNR) in every control period.

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0,0

i,0

1

m,0

1

1

1

0,1

i,1

m,1

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1

1

1

1

1

1

141

We consider the situation where N terminals want to transmit packets. Then, the probability pt,i that the terminal i begins to transmit in a random time slot could be calculated as  2(1 − pm+1  f,i )(1 − 2pf,i )   m ≤ m′ Z 1 pt,i = (5) m+1   2(1 − pf,i )(1 − 2pf,i ) ′  m>m, Z2 where

0,W0-1

i,Wi-1

m+1 ] Z1 = (1 − pm+1 f,i )(1 − 2pf,i ) + W (1 − pf,i )[1 − (2pf,i )

m,Wm-1

′

′

′

+1 (1 − 2pf,i )(1 − pm−m ). Z2 = Z1 + W 2m pm f,i f,i

So it is possible to calculate the probability of failed transmissions due to packet collision or channel error pf,i which is given by Kang (2012) as

Fig. 2. Markov chain model for backoff stage 3. PROPOSED ADAPTIVE MODULATION AND CODING SCHEME FOR CBTC SYSTEMS In this section, we propose an AMC scheme considering the impact of both the channel fading and the contention in MAC layer under the assumption that only average SNR of each train and number of competing terminals are available. 3.1 Motivation The average delay analysis in previous work only considers the packet transmission failure caused by errors due to fading on a single channel. However, in real CBTC environments, multiple trains will share one AP, and thus the impact of the contention in MAC layer should be also considered. For instance, two successive trains in the same direction may connect to the same AP when their distance interval is small and they happen to be in the coverage area of the same AP. Besides, two trains from different travel directions may share the same AP. On the other hand, the FER determined by the average SNR is used in previous work while instantaneous SNR will fluctuate due to the channel fading, which has a large impact on average delay analysis. Note that there are two types of average delay in this paper. We define the average delay in the situation that multiple trains share one AP as the average delay with respect to MAC contention and define the average delay influenced by channel fading as the average delay with respect to channel fading. Consequently, in this paper, we propose an AMC scheme which minimizes the average delay with respect to both MAC contention and channel fading. 3.2 Delay analysis

141

(1 − pt,l ),

(6)

l=1,l̸=i

where pe,i represents the probability of failed transmission of terminal i by channel error only. When every instantaneous SNR of all competing terminals is given, 2N non-linear equations provided by equations (5), (6) can be solved numerically for pf,i and pt,i . After solving the system of equations (5), (6), we can obtain the probability Ps,i that the terminal i successfully transmits the packet as Ps,i = pt,i (1 − pe,i )

N ∏

l=1,l̸=i

(1 − pt,l ),

(7)

Finally, the throughput defined as the number of data packets in bits that have been successfully transmitted per unit time of terminal i can be obtained similarly to Kang (2012) by Ps,i Fdata . (8) Pn σ + Pc,i Tc + Ps,i Ts + Pe,i Te where Pn is the probability that there is no transmission in the considered time slot, Pc,i is the collision probability of terminal i, Pe,i is the FER of terminal i given that it transmits, Tc , Ts , Te are the average collision slot time, average successful transmission slot time and average failed transmission slot time only due to channel error, respectively, given as follows Si =

Pn =

First, we analyze the average delay with respect to MAC contention according to Daneshgaran et al. (2008), Bianchi et al. (2005) and Kang (2012). Define b(t) and s(t) as the stochastic processes representing the backoff counter and the backoff stage (0, · · · , m) at time t, respectively. Then, the model of bidimensional process {s(t), b(t)} with the discrete time markov chain Kang (2012) in Fig.2 can be used with the assumptions that the probability of failed transmission of terminal i due to packet collision or channel error pf,i is independent from the number of retransmissions and that the traffic condition is saturated.

N ∏

pf,i = 1 − (1 − pe,i )

N ∏

i=1

(1 − pt,i ),

Pc,i = 1 − Pn − pt,i Pe,i = pt,i pe,i

N ∏

N ∏

l=1,l̸=i

l=1,l̸=i

(1 − pt,l ),

(1 − pt,l ),

Tc = Tdata + Tacktimeout , Te = Tdata + Tacktimeout , Ts = Tdata + TSIFS + Tack + TDIFS .

(9)

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Define Hi as the average delay of terminal i with respect to MAC contention, and it can be calculated as in Bianchi et al. (2005) by E[N ] (10) Hi = Si /E[Fdata ] where the numerator E[N ] means the average number of competing vehicles which will successfully transmit their packet, and the denominator represents the packet delivery rate. Note that the throughput in Bianchi et al. (2005) represents the number of data packets in bits that have been successfully transmitted per unit time for all terminals. However, in this paper, the throughput calculated in (8) is only for terminal i so that E[N ] = 1. Besides, the value of payload Fdata is deterministic, i.e., E[Fdata ] = Fdata . Then, assuming Rayleigh fading channels, we first derive the probability density function (PDF) of the instantaneous received SNR with MIMO transmission. Define γ¯i as the received SNR averaged over fading of terminal i, which is thus only function of the path loss between terminal i and AP, and γi as the instantaneous received SNR influenced by the channel fading of terminal i. Since the channel states and AMC scheme of the terminal i which wants to transmit packet will impact the average delay of other terminals, and viceversa, the average delay of terminal i with respect to MAC contention will be determined by γ1 , γ2 , · · · , γN . In the Rayleigh fading channel, the instantaneous SNR γ obeys exponential distribution with mean γ¯ . So the PDF of instantaneous received SNR can be written as 1 γ p(γ|¯ γ ) = e− γ¯ . γ¯ Defining zi as the instantaneous received SNR after the ideal MIMO processing at the receiver of terminal i, it can be shown that zi follows the gamma distribution. As a result, the PDF of zi conditioned on average SNR γ¯i is given by e−zi /¯γi p(zi |¯ γi ) = ziK−1 , Γ(K)¯ γiK where K is the diversity gain.

Note that FER pe,i is only determined by zi for Space-time block coding (STBC). However, for the coding of multistreams, if one of the packets from the transmit antennas is corrupted at the receiver, all packets are lost. Therefore, the FER pe,i in such a coding scheme can be calculated by pe,i (z1,i · · · zU,i ) = 1 − (1 − pe,1,i (z1,i ))

· · · (1 − pe,U,i (zU,i )),

(11)

where zj,i , pe,j,i and U are received instantaneous SNR in receive antenna j, the FER of the receive antenna j and the number of transmit antennas of terminal i, respectively. If every instantaneous SNR of all competing terminals is given, we can obtain the throughput of each terminal given by these instantaneous SNRs under the assumption of saturated traffic condition. Let z = [z1 , · · · , zN ] be the set of the instantaneous SNRs of each terminal. Then, the throughput of terminal i given z is written as Si (z) =

Ps,i (z)Fdata , Pn (z)σ + Pc,i (z)Tc + Ps,i (z)Ts + Pe,i (z)Te 142

Table 1. Average delay comparison between simulation and numerical results N = 4 with the same average SNR 16dB MCS MCS0

Simulation results 0.0031

Numerical results 0.0032

where pe,i and pt,i are determined by zi and z, respectively. Define Li (z) as the average delay with respect to MAC contention conditioned on z and the maximum delay threshold Tmax which means that if the average delay with respect to MAC contention is larger than Tmax , then this delay equals to Tmax . This is because when we calculate the average delay with respect to both MAC contention and channel fading, this delay will diverge without setting a maximum delay threshold. Then we have   Fdata , if Fdata ≤ T max Si (z) Li (z) = Si (z) (12)  Tmax else. If the average SNRs of all terminals are given, the average delay Gi with respect to both MAC contention and channel fading for STBC can be obtained by Gi =

∫

+∞

···

0

∫

+∞

Li (z)p(z1 |¯ γ1 ) · · · p(zN |¯ γN )

0

dz1 · · · dzN .

(13)

For multiple streams coding, the delay Gi becomes Gi =

∫

+∞

···

0

∫

+∞

Li (z1,1 , · · · , zU,N )p(z1,1 |¯ γ1 ) · · ·

0

γN )dz1,1 · · · dzU,N . p(zU,N |¯

(14)

Since the exact evaluation of (13) or (14) requires prohibitive computational complexity, we utilize the average SNR of terminal i instead of the instantaneous SNR of other terminals for the evaluation of FERs of other terminals, giving Li (z) = Li (zi , γ¯i ). Then, Gi is determined only by the instantaneous SNR zi conditioned on average SNR γ¯i instead of all the instantaneous SNRs z. This can reduce not only the computational complexity, but also the overhead of the information exchange among trains. Then, marginalizing over zj , j ̸= i, the approximated average ˆ i for STBC coding can be written as delay G ˆi = G

∫

+∞ 0

Li (zi , γ¯i )p(zi |¯ γi )dzi .

(15)

˜ i with multiple streams The approximated average delay G coding is determined by the instantaneous SNR of each antenna of terminal i, which can be shown similarly as ˜i = G

∫

+∞ 0

···

∫

+∞ 0

Li (z1,i , · · · , zU,i , γ¯i )p(z1,i |¯ γi ) · · ·

γi )dz1,i · · · dzU,i . p(zU,i |¯

(16)

3.3 Proposed scheme We consider that the control performance can be enhanced through minimizing the average delay with respect to both MAC contention and channel fading. Therefore, the optimization problem considered in this paper is given by

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Table 3. Simulation parameters

Table 2. Average delay comparison between simulation and numerical results N = 4 with average SNR 12dB in observed terminals and average SNR 6, 15, 25dB in other terminals MCS MCS4

Simulation results 0.0057

MCS0 MCS1 MCS2 MCS3 MCS4 MCS5 MCS6 MCS7 MCS8 MCS9 MCS10 MCS11 MCS12 MCS13 MCS14 MCS15

10

Average Delay (s)

Definition Transmission power Noise power Antenna gain Bandwidth Service brake deceleration Carrier sense level of antenna Maximum retransmission time Path loss exponent Maximum delay threshold

Numerical results 0.0060

-1

-2

10

10

20

30

40

Ri ,pe,i

159.16m

5m

station 1 Train 2

station 2 Train 1

318.32m

Heading

50

Fig. 4. Simulation setup

for STBC coding for multiple streams.

In IEEE 802.11n protocol, since each MCS has its own data rate Ri and corresponding FER performance, we ˜ i for each MSC ˆ i and G can calculate the average delay G according to terminal’s average SNR and the number of competing terminals. Then the MCS which has the minimum average delay will be chosen. Thus, during the train-ground communication, the MCS can be adaptively changed to minimize this average delay only given this train’s SNR and the number of competing trains in each control period. For example, Fig. 3 shows the average delay with respect to both MAC contention and channel fading for different MCS for 2 transmit antennas and 2 receive antennas in IEEE 802.11n protocol when the number of competing terminals is five and Tmax =0.4s. MCS0, MCS1, MCS2, MCS3, MCS4, MCS5, MCS6 and MCS7 represent BPSK with rate 1/2, QPSK with rate 1/2, QPSK with rate 3/4, 16QAM with rate 1/2, 16QAM with rate 3/4, 64QAM with rate 2/3, 64QAM with rate 3/4 and 64QAM with rate 5/6 convolutional code in Alamouti coding, respectively. On the other hand, MCS8, MCS9, MCS10, MCS11, MCS12, MCS13, MCS14 and MCS15 represent BPSK with rate 1/2, QPSK with rate 1/2, QPSK with rate 3/4, 16QAM with rate 1/2, 16QAM with rate 3/4, 64QAM with rate 2/3, 64QAM with rate 3/4 and 64QAM with rate 5/6 convolutional code in 2 streams coding. It is clearly shown that the average delay minimization highly depends on the appropriate MCS selection. Table. 1 and Table. 2 show that the average delays calculated by (15) in the same and different average SNR are almost the same as the simulation results when N = 4 and each terminal has always a packet available for transmission, which confirms the accuracy of the proposed method. 143

10-1

Outage probability

˜i,  min G

Train 4

5m

159.16m

Fig. 3. Average delay with respect to both MAC contention and channel fading when N = 5 and Tmax =0.4s

Ri ,pe,i

station 2 Train 3

SNR(dB)

 ˆi,  min G

Value 31mW -100dbm 10dBi 20MHz 1.2m/s2 -98dBm 6 3 0.4s

Heading station 1

10-3 0

143

Conventional scheme

10-2

Previous work Proposed method

10-3

0

0.1

0.2

0.3

0.4

Control period(s)

Fig. 5. Outage Probability 4. NUMERICAL RESULTS 4.1 Simulation setup In actual rail signal system, several APs are used to keep the communication unblocked. In this paper, we will neglect the influence of handover between two successive APs and focus on the delay caused by channel error and collision. The path loss model Paul (2011) is used, which is given by Pr [dBm] = Pt [dBm] + Zt + Y [dB] − 10αlog10 d + Zr ,

(17)

where Zt is the transmit antenna gain, Zr is the receive antenna gain, α is the path loss exponent, Pr is the received signal power, Pt is the transmit signal power and Y is a constant that depends on the transmission frequency. Fig.4 shows the simulation setup, where 4 trains running between stations 1 and 2 share a channel with one AP, which may be the worst situation of MAC contention in CBTC systems. The simulation parameters are shown in Table. 3, based on the parameters used in CBTC systems and IEEE 802.11n protocol as in Lin (2006). The distance

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Q. Dong et al. / IFAC-PapersOnLine 49-22 (2016) 139–144

Table 4. AMC threshold comparison for proposed and conventional schemes MCS MCS1 MCS2 MCS3 MCS4 MCS11 MCS5 MCS6 MCS7 MCS12 MCS13 MCS14 MCS15

Conv. 9dB 11.3dB 14.9dB 17.4dB 21.7dB 22.2dB 23.3dB non 24.2dB 28.9dB 30dB 31.1dB

Prev. 6.9dB 10.7dB 15.4dB 17.6dB non 23.5dB 25.3dB non 26.4dB 32.2dB 33.9dB 35.3dB

Prop. N =1 13.5dB 17.4dB 21.2dB 24.3dB non 29.5dB 31.6dB 33.2dB 41.4dB 44.9dB 47.2dB 49.1dB

Prop. N =2 12.9dB 16.8dB 20.6dB 23.6dB non 28.8dB 30.9dB 32.5dB 39.9dB 43.5dB 45.7dB 47.6dB

between two stations is set to 318.32m. The maximum delay threshold Tmax is set to 0.4s and the maximum retransmission time m equals 6. In this simulation, we consider the situation where there are always 4 trains sharing one AP during train 2’s operation and take the perspective from train 2 to focus on the delay of MA for train 2. Train 1 and train 2 start from station 1 successively with a uniformly distributed random time interval which is larger than 8s and less than train travel time. The time interval between train 3 and train 4 is also a random variable similarly to that of train 1 and train 2. The locations of the other 3 trains are distributed randomly over the rail line. Note that if one of the other trains arrives at destination, then another train will start at the starting station to make sure that there are 4 trains between station 1 and station 2. For the train-ground communication part, we also assume that the average SNR and the instantaneous SNR due to Rayleigh fading channel are unchanged during the control period.

4.2 Simulation results Fig.5 shows the outage probability at train 2 for the proposed method, the conventional adaptive modulation which uses the average packet error rate of 10% as the threshold to change to higher transmission mode, and the method in previous work Zhu et al. (2012). The SNR thresholds for switching MCSs in these methods are illustrated in Table. 4. Since the probability of packet collision increases along with the number of competing terminals, a higher rate AMC scheme will be chosen to reduce the average delay. When the number of competing terminals is small, the average delay with respect to both MAC contention and channel fading is largely influenced by the channel state and the lower rate AMC scheme which has the lower FER will be selected to decrease this average delay. As a result, AMC threshold in the proposed method decreases along with the number of competing terminals. The proposed method has much higher thresholds than other schemes because it takes into account the impact of Rayleigh fading over all the involved channels. From Fig.5, we can see that the proposed approach achieves the lowest outage probability. This is because only the proposed method considers the global impact of Rayleigh fading channels, packet collisions, channel busy times and control period. The two reference methods have similar results due to similar AMC thresholds. 144

Prop. N =3 12.4dB 16.4dB 20.2dB 23.1dB non 28.4dB 30.5dB 32.1dB 39dB 42.6dB 44.8dB 46.6dB

Prop. N =4 12.1dB 16.1dB 19.9dB 22.8dB non 28.1dB 30.2dB 31.8dB 38.3dB 41.9dB 44.1dB 46dB

Prop. N =5 11.9dB 15.8dB 19.7dB 22.6dB non 27.8dB 29.9dB 31.5dB 37.8dB 41.4dB 43.6dB 45.5dB

5. CONCLUSION The wireless communication quality between train and wayside AP largely influences the train control performance including the passenger riding comfort and energy cost. In this paper, we propose a new AMC method for the train-ground communication in CBTC systems to reduce the occurrence of outage through lowering the average delay with respect to MAC layer contention and channel fading. The results show that the proposed method achieves better outage probability performance than previous works and conventional method. In the future work, we will consider a direct method to minimize the outage probability instead of the average delay. REFERENCES F. Daneshgaran, M. Laddomada, F. Mesiti, M. Mondin and M. Zanolo. Saturation throughput analysis of IEEE 802.11 in the presence of non ideal transmission channel and capture effects. IEEE Trans.Commun., volume 56, pages 1178–1188, 2008 L. Zhu, F. R. Yu, B. Ning and T. Tang. Cross-layer handoff design in MIMO-enabled WLANs for communicationbased train control (CBTC) systems. IEEE J.Sel.Areas Commun., volume 30, pages 719–728, 2012. H. Wang, F. R. Yu, L. Zhu, T. Tang and B. Ning. A Cognitive Control Approach to Communication-Based Train Control Systems. Trans.Intell.Transp.Syst., volume 16, pages 1679–1689, 2015 G. Bianchi and I. Tinnirello. Remarks on IEEE 802.11 DCF performance analysis. IEEE Commun.Lett., volume 9, pages 765–767, 2005 K. Kang. Performance Anomaly of the IEEE 802.11 DCF in Different Frame Error Rate Conditions. J Inf Process.Syst., volume 8, pages 739–748, 2012 F. Whitwam, Integration of wireless network technology with signaling in the rail transit industry. Alcatel Telecommunications Review, volume 1,pages 43–48, 2003 G. Bianchi. Performance analysis of the IEEE 802.11 distributed coordination function. IEEE J.Sel.Areas Commun., volume 18, pages 535–547, 2000 U. Paul, R. Crepaldi, J. Lee, S.-J. Lee and R. Etkin. Characterizing WiFi link performance in open outdoor networks Proc. SECON, pages 251–259, 2011 Y. Lin and V. W. S. Wong. Frame aggregation and optimal frame size adaptation for IEEE 802.11n WLANs IEEE GLOBECOM., pages 1–6, San Francisco, CA, USA, 2006