Modeling link quality for highspeed railway wireless networks based on hidden Markov chain
 Jiayang Song^{1}Email authorView ORCID ID profile,
 Huachun Zhou^{1},
 Wei Quan^{1},
 Tao Zheng^{1} and
 Ping Dong^{1}
https://doi.org/10.1186/s1363801607591
© The Author(s). 2016
Received: 31 March 2016
Accepted: 20 October 2016
Published: 15 November 2016
Abstract
In highspeed railway (HSR) wireless networks, the link quality is greatly timedependent and locationvarying. Due to the high randomness, it is challenging to predict the link quality in HSR wireless networks. In this paper, we firstly conducted a certain amount of field measurement campaigns of HSR wireless network link quality. A great number of practical datasets are collected regarding packet loss rate (PLR) and roundtrip time (RTT). Then, we analyzed its changing pattern in different time scales, and further model the link quality of HSR wireless network using hidden Markov chain. Based on this, an improved algorithm was developed to simulate the variation of HSR wireless network link quality. Simulation results prove that the proposed model is capable of accurately reproducing the behavior of HSR wireless network link quality with regard to PLR and RTT. This work will offer new inspiration to the prediction of link quality for HSR wireless networks.
Keywords
1 Introduction
Highspeed railway (HSR) has brought substantial social and economic benefits. Due to its great superiorities, HSRs are widely built and operated around the world, especially in Europe and East Asia. According to International Union of Railways (UIC), 29792 km of HSR lines had been built by April 2015. With its fast development, the era of HSR has come [1].
Wireless networks play a very important role in the operations of HSR. First, wireless communication is the basis of train operation control systems, which include European Train Control System (ETCS) and CommunicationBased Train Control (CBTC) [2]. Second, wireless networks provide great convenience to HSR passengers, such as enjoying multimedia services or online gaming. Emerging wireless technologies have been utilized in HSR. For example, the TDLTE network of China Mobile had covered 23500 km of highspeed rails by August 2015 [3].
For HSR wireless networks, it is significant to establish reliable wireless links between the trains and the ground. However, the link quality in HSR usually suffers from several sever limitations including complex terrains, Doppler shift. and timevarying channel issue, as discussed in [4, 5].
Recently, many research have been carried out on analyzing the propagation characteristics in typical HSR scenarios, including viaduct, cutting, tunnels, crossing bridges, and stations [5]. In [6–10], the path loss model that considers the height of viaduct and BS antenna were analyzed in viaduct scenario. In cutting scenario, the smallscale fading characteristics were modeled at 2.35 GHz in [11, 12] and at 930 Mhz in [13–16]. In [17], the wave propagation of railway tunnels were analyzed. In [18, 19], the influence of crossing bridges and train stations were reported on propagation loss model. As regards to the measurement frequency, most of the research mentioned above were done at 930 MHz which is the downlink frequency of GSMR in China. While there exists channel measurement of broadband communication system including WCDMA [20] and LTE [21].
Nevertheless, these research cannot characterize the link quality of wireless networks already deployed along the highspeed rails, so they have limited use in helping improve the performance of existing HSR wireless networks. Also, the study on different HSR scenarios cannot provide insight to the global behavior of wireless network link quality of a complete railway line. Hence, modeling the link quality characteristics and its long term pattern of existing HSR wireless networks becomes an issue.
By evaluating the upper layer performance of deployed wireless networks, the variation of wireless link quality along a realistic HSR line can be revealed. In this context, the upper layer is considered as Internet Protocol (IP) layer of protocol stack, whose performance are normally evaluated by parameters of packet loss rate (PLR), roundtrip time (RTT).
We reason that PLR and RTT are appropriate parameters to characterize the link quality of HSR wireless networks. First, IP layer performance is the direct reflection of the radio propagation behavior. For instance, a fading channel can result in the loss of signal power that leads to increased bit error rate, which will cause the degradation of PLR and RTT. Second, the wireless channel along the HSR lines varies rapidly, but PLR and RTT are capable of characterizing it. By designing accurate measuring program, we can record the PLR and RTT every 5 s. Besides, since most of the user data in wireless network are IP packets, modeling the IP layer performance directly contributes to the design of novel network architecture.
PLR and RTT are important metrics for wireless communications. In wireless sensor networks (WSN), researchers use PLR to investigate the characteristics of link quality [22] or characterize the information quality [23]. Also, PLR and RTT are proposed as routing metrics for wireless ad hoc networks [24] and wireless mesh networks (WMN) [25]. In the domain of vehicular communication, some research have been conducted using PLR or RTT to design new network architecture [26, 27]. Besides, PLR and RTT are considered as performance indicator for testing commercial platform [28] or evaluating novel communication mechanisms [29–31]. However, no such work was carried out on characterizing the HSR wireless networks link quality using PLR and RTT.
In this paper, we try to model the link quality for HSR wireless networks with PLR and RTT. We firstly conduct a series of field measurement campaigns for PLR and RTT along realistic highspeed rails. The investigation of measurement results reveals a cyclic phenomenon of PLR and RTT. Then we utilize a hidden Markov chain (HMC) reference model to describe the measured PLR and RTT. Based on the model, an improved link quality simulation algorithm is developed. The simulation results prove that the developed algorithm can reproduce the cyclical behavior of PLR and RTT with high accuracy.
The paper is structured as follows: the measurement campaign is detailed in section 2. The investigation of collected datasets is presented in section 3. In section 4, we introduce the HMC reference model. In section 5, an improved link quality simulation algorithm based on proposed HMC model is introduced and evaluated. Section 6 concludes the paper.
2 Measurement campaign
Our measurement campaign was conducted on Beijing–Shanghai highspeed railway in China. In the measurement, the EVDO (evolutiondata optimized) network operated by China Telecom was utilized. The downlink working frequency is 869 MHz–894 MHz, and the uplink is 824 MHz–849 MHz.
During measurement, a dedicated and automated measuring instrument called wireless link monitor (WLM) was produced to measure and store the RTT, PLR, and the corresponding position. The WLM can be considered as a portable industrial computer which has wireless modems connecting to the cellular network along the HSR line. The central processing unit (CPU) of WLM is Intel Core 2 Duo, and the RAM is 2 GB.
3 Dataset analysis
In Fig. 2, it clearly shows that the variation of PLR and RTT approximately present a cyclical phenomenon. In areas B, D, F for PLR and areas H, J, L for RTT, a large part of values of PLR and RTT are relatively low, which means that the link quality of HSR wireless networks is in good condition. In contrast, the value of PLR and RTT are rather high in areas A, C, E for PLR and areas G, I, K for RTT, which indicate that the HSR wireless network link quality is under poor condition. The period of good and poor condition appears in turn. Based on the above analysis, we can preliminarily get the first conclusion: the link quality of HSR wireless networks follows a cyclical variation that good condition and poor condition occur alternately.
According to the two conclusions mentioned above, the states of HSR wireless network link quality is controlled by another variable that cannot be observed. If this invisible variable is in good condition, among the observed states of HSR wireless link quality, 1, 2, and 3 occur more often. Otherwise, 4, 5, and 6 happen with higher probabilities. We define the observed state of HSR wireless link quality as microstate, whose state space is Q = {1, 2, 3, 4, 5, 6}. The invisible variable that controls the variation of microstate is defined as macrostate. Its state space can be described by S = {G, P}. G is the abbreviation for good macrostate, and P is for poor macrostate.
Macrostate categorization
Macrostate  PLR No.  RTT No. 

Poor  1–391  1–392 
Good  392–724  393–674 
Poor  725–1454  675–1225 
Good  1455–1762  1226–1616 
Poor  1763–2029  1617–1851 
Good  2030–2356  1852–2208 
Poor  2357–2466  2209–2317 
The frequency of transitions among different macrostates is rather low. As shown in Table 1, during the period of about 1 h, the macrostates of PLR and RTT changed only six times. For poor macrostate and good macrostate, the minimum duration are, respectively, 540 s and 900 s. Considering that the average operating speed of Beijing–Shanghai highspeed railway is 280 km/h, the shortest distance of poor macrostate and good macrostate can reach 42 km and 70 km.
4 HSR wireless network link quality modeling
The sequences of PLR and RTT values evolving with time can be interpreted by a random process. To represent it, we introduce a reference model whose random variable possesses two states: macrostate and microstate, just as PLR or RTT does. The state spaces of macro and microstate are, respectively, S and Q.
The average time interval between different microstates is much less than that of different macrostates. In other words, the macrostate varies at a much slower pace than microstate does. According to the results of measurement campaign, every 1053 s on average, the macrostate of HSR wireless network link quality would change. However, the microstate varies every 5 s, since RTT and PLR were calculated and recorded every 5 s.
 (1)
A whiteloaded dice whose weight is unevenly distributed. When it is rolled, the probability that one side faces upwards is \( {p}_W^i \) where i ∈ {1, 2, 3, 4, 5, 6}. Since the dice is loaded, we define \( {p}_W^m>{p}_W^n \) for m < n.
 (2)
A blackloaded dice. The faceup probability of one side is \( {p}_B^j \) where j ∈ {1, 2, 3, 4, 5, 6}. In contrast with the white dice, we define black dice as \( {p}_B^m<{p}_B^n \) if m < n
 (3)
A whiteloaded coin, the weight of heads and tails are different. \( {P}_W^H \) is the probability that the upper side is heads after tossing it, while \( {P}_W^T \) for tails, and \( {P}_W^H>{P}_W^T \).
 (4)
A blackloaded coin. The faceup probability of heads is \( {P}_B^H \), and tails is \( {P}_B^T \), while \( {P}_B^H>{P}_B^T \).
Six sides of the loaded dice represent the six microstates of HSR wireless network link quality. Rolling whiteloaded dice stands for the generation of microstate under good macrostate, while rolling the black dice stands for that under poor macrostate. Tossing the loaded coins regulates the variation of macrostate. The white coin represents the transition from good, while the black coin represents that from poor.
 (1)
Randomly select one dice. Roll it, then the first result is generated.
 (2)
Next, select the coin whose color is identical to the dice rolled at last step. For example, if black dice was just rolled, then the black coin will be flipped.
 (3)
If the result of coin flipping is heads, continue to roll the dice just rolled before and record the result. Otherwise, roll the other dice.
 (4)
Go to step (2), until expected number of dice rolling results are recorded.
Thus, by \( {P}_W^H>{P}_W^T \) \( {P}_B^H>{P}_B^T \), the transitions from one macrostate to another one occur less frequently than that to the same one. In the longterm perspective, the macrostate of HSR wireless network link quality may remain unchanged for a certain time.
The dicecoin experiment can generate a series of output results possessing the similar cyclical behavior as the measured PLR or RTT shows. It proves that the proposed reference model can well explain how the cyclical pattern of HSR wireless network link quality evolves.
To further study the cyclical behavior of HSR wireless network link quality, we utilize HMC to describe the introduced reference model. HMC can be considered as a mixture of two stochastic processes [32]. The output of one stochastic process is observable, while the other is not. The observable process is dependent on the unobserved one. In our case, the generation of microstate and the variation of macrostate can be described by the observable process and unobservable process, respectively.
However, adopting HMC in modeling HSR link quality requires some preconditions. Markov chain concerns with the transition from one state to another, and the transition probability should be stable. In highspeed railway scenario, the stable transition probability can be guaranteed only if the following two preconditions are satisfied: (i) the distance between two base stations is constant; (ii) the speed of the train is constant.
In our measurement campaign, these two preconditions can be fulfilled. Since the dataset used to derive A and B are collected in plain terrain without passing any train stations, the base stations along the corresponding railway line follow an even distribution. Also, the speed of the train is nearly stable during the measurement. But we should note that modeling HSR link quality with HMC is suitable for specific situations where these two preconditions are satisfied. For scenarios such as train stations where the train is speeding up (or slowing down), the proposed model cannot accurately characterize the link quality of HSR.

S is the state space of the unobserved stochastic process, whose variable is referred to as state. In this case, S equals {G, P} that is the state space of macrostate.

Q is the state space of the observable stochastic process, whose element is referred to as symbol. In this case, Q equals {1, 2, 3, 4, 5, 6} that is the state space of microstate.

A is the state transition matrix. In this case, its element is the transition probability of macrostate, which is α _{ ij } shown in Eq. 1.

B is the symbol generation matrix. In this case, its element is the generation probability of microstate, which is β _{ s }(q ) shown in Eq. 2.

Π is the initial state matrix whose element is the probability of a state with which the unobserved process begins. In our case, it is determined as [0 1], since the macrostates of PLR and RTT both begin with poor.
A of PLR and RTT are noted as A _{ PLR } and A _{ RTT } . In this case, since there are two states, A _{ PLR } or A _{ RTT } can be defined as a twobytwo matrix. The elements in A _{ PLR } and A _{ RTT } are derived based on the collected dataset shown in Table 1. Take the first element (α _{ GG }) in A _{ PLR } or A _{ RTT } as an example. α _{ GG } is the probability that the state transits from good to good. Let N1 be the number of state transitions begin with good. Let N2 be the number of state transitions begin with good and end with also good. Then α _{ GG } can be calculated as N2/N1. Note that N1 and N2 can be easily counted from the collected dataset. The rest of the elements of A _{ PLR } and A _{ RTT } are derived in the same way as α _{ GG }.
B of PLR and RTT are noted as B _{ PLR } and B _{ RTT }. Both of them are defined as twobysix matrices, since there are six symbols and two states in this case. The elements in B _{ PLR } and B _{ RTT } are also calculated according to the collected dataset. Take the first element in B _{ PLR } or B _{ RTT }, which is β _{ G }(1), for instance. β _{ G }(1) represents the probability that the symbol is observed as 1 when the state is good. Let M1 be the number of observations that the state is good. Let M2 be the number of observations that the symbol is 1 while the state is good. Thus, β _{ G }(1) is calculated M2/M1. M1 and M2 can also be counted from the measurement results. The rest of the elements of B _{ PLR } and B _{ RTT } are derived similarly.
5 Simulation evaluations
 (a)
Determine the macrostate of PLR or RTT to be generated by the algorithm at very first step. From the measurement results, we can determine that the initial state of RTT and PLR macrostates are both poor, therefore, s_{1} is P at first step.
 (b)Determine the macrostate of current step based on the macrostate of last step. The probability that the macrostate is j at current step (n), providing that it was i at last step (n1), can be shown that$$ p\left({s}_n=j\right)={\alpha}_{ij},\ i,j\in S $$(10)
Then, select an element from set S randomly according to the probabilities calculated in Eq. 10. This element is the macrostate of current step.
 (c)Determine the microstate based on the macrostate of current step. Presuming at step n the macrostate is j, thus the probability that the microstate is k at step n is$$ p\left({q}_n=k\right)={\beta}_j(k),\ k\in Q $$(11)
Then, select an element from set Q randomly according the probability calculated in Eq. 11. This element is the microstate of current step.
 (d)
Replace n with n + 1. Repeat from (b) to (d), until expected total number of steps, which is N, has been executed. N is set as 2466 for simulating PLR, and 2317 for simulating RTT.
The inefficiency of normal forward induction algorithm to accurately simulate HSR link quality stems from the effect of randomness. The accuracy of simulation results is mainly determined by whether the simulated macrostate is correct at step (b) during the forward induction algorithm. If the macrostate fits the prior measurement results, then the accuracy of generated microstates at step (c) will be greatly improved. However, the macrostate is randomly determined according to the state transition probability A. The randomness makes the macrostate transition uncontrolled.
To tackle this problem, we develop an improved link quality simulation algorithm. Several probes are introduced to guide the transition between different macrostates, which would rarely happen. For example, probe n indicates the nth simulation step. At nth simulation, the macrostate of link quality will be obliged to change, regardless of state transition probability A.
P is the probe set, whose elements are probes selected according to the measurement results. For RTT, P is {393, 675, 1226, 1617, 1852, 2209}. For PLR, P is {392, 725, 1455, 1763, 2030, 2357}.
6 Conclusions
In this paper, we firstly conduct a series of field measurement campaigns for PLR and RTT along realistic highspeed rails and gathered a dataset of more than 120000 entries. A cyclical behavior of HSR wireless network link quality is revealed after the investigation of the measurement results. Based on this, we introduce an HMC reference model for describing this cyclical behavior. Also, an improved link quality simulation algorithm is developed. Finally, the assessment of the introduced model and developed simulation algorithm is provided based on simulation experiments. Evaluation results prove that the developed algorithm can reproduce the cyclical behaviors of PLR and RTT with high accuracy. Hence, we conclude that the introduced HMC reference model is valid for HSR wireless network link quality. In the future work, we will further consider the link quality prediction for HSR networks based on our proposed model.
Declarations
Acknowledgement
This paper is supported by National Basic Research Program of China (973 program) under Grant No. 2013CB329101, National High Technology of China (863program) under Grant No. 2015AA015702, and National Natural Science Foundation of China under Grant No. 61271202.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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