Statistics of Capacity Analysis in High Speed Railway Communication Systems

Transcription

1 Tamkang Journal of Science and Engineering, Vol. 14, No. 3, pp (211) 29 Statistics of Capacity Analysis in High Speed Railway Communication Systems Qiu-Yan Liu*, Miao Wang and Zhang-Dui Zhong State Key Laboratory of Rail Control and Safety, Beijing Jiao Tong University, Beijing 144, China Abstract In this paper, statistics of capacity including level crossing rate (LCR), average fade duration (AFD) and outage probability (OP) with time varying Doppler Effect are analyzed in high speed railway communication systems. The scenario is assumed that there exists a Ricean faded line-of sight (LOS) channel according to the high reliability requirements in real environments. First, a simple but versatile mathematic model is proposed for time varying Doppler shift calculation in both straight and curved tracks. Then, closed-form expressions of capacity statistics, such as LCR, AFD and OP, are c th derived. Simulation results show that LCR is in proportion to maximum frequency shift and 2 2. The range of capacity threshold from 5 bits/s/hz to 7 bit/s/hz is of great importance. System can provide reliable communication more than 9% successfully with AFD lower than 1-3 s when capacity threshold is 5 bit/s/hz. Most systems can provide great performance below 5 bit/s/hz. However, system performance is degraded to 9% outage when capacity threshold is higher than 5 bit/s/hz, and few systems are able to guarantee capacity higher than 7 bit/s/hz successfully. Key Words: High Speed Railway, Doppler Shift, Outage Capacity, Level Crossings, Rice Fading Channels 1. Introduction High speed railway is a promising direction which arises more interest in wireless communication system in high speed environment. So far, several tests of high speed railway up to 4 km/h have been taken all over the world [1,2]. The classical system design and performance analysis usually focus on mobile system in the urban or quasi-urban without consideration of speed [35]. Unlike traditional environments, Doppler Effect becomes another pivotal factor degrading system performance, which increases randomness of received signal. Some researchers did notable work on Doppler Effect evaluation or Doppler spectrum in the statistical view of signal level [68]. Wireless channels are modeled by a time-varying *Corresponding author @bjtu.edu.cn process due to transmission impairments such as the multipath propagation and the Doppler spread. Both the received signal envelope and the capacity of the channels are random. Statistical characterization of the received signal envelope in terms of level crossing rate (LCR), how often the signal crosses a certain threshold, and average fade duration (AFD), how long the signal stays below a given threshold, in fading and shadowing mobile radio environments, is useful in the design of a mobile radio communication system and the analysis of its performance [914]. For instance, LCR and AFD provide information about the statistics of burst error [12], which facilitates the design and selection of error correction technique [13,14]. The remainder of this paper is organized as follows. Section 2 describes time varying Doppler shift model of wireless communication system is presented for lineof-sight (LOS) component for high speed railway. The

2 21 Qiu-Yan Liu et al. closed-form expressions of LCR, AFD and OP of capacity are derived in section 3. Section 4 shows some simulation results and discussions for special cases. Finally, extensive understandings and conclusions are drawn in section System Model Unlike public wireless communication system, wireless communication system for railway is dedicated to transmitting control and dispatching information. Base stations (BSs) are therefore located along the railway to guarantee high reliability. Compared to the attenuation caused by distance and fading, the effect of altitude variation on received signal is of no account. In a very simple way, the two-dimension diagram of wireless communication system for railway is depicted in Figure 1. Cellsite planning is mainly determined by large scale fading rather than fast fading [15]. Hence the coordinate sequence of all BSs is set as a discrete sequence {(p 1,q 1 ), (p 2,q 2 ),, (p i,q i ),, (p m,q m )} in advance. In fact, the track of the train is not always straight because of some obstacles in the way, like hills, rivers or woods. The location of the mobile station (MS) depends on the track of the train, which is represented as a continuous time function (x(t), y(t)). Assuming hand-off protocol based on distance adopted, the i th BS is on service if (1) (2) To analyze the Doppler effect, in Figure 2, a(t) and b(t) are defined as horizontal acceleration and vertical acceleration, respectively, which are related with geography and intervals between adjacent railway stations. From the physical point of view, the instantaneous velocity mapped to x, y axis and the direction angle are given by (3) (4) (5) Accordingly, the coordinate of MS is also expressed as a function of acceleration. (6) (7) Then, the angle between the incoming wave and the velocity is In mathematic view, discrete sequence is a special kind of multi-partition function. Then, the continuous time function of the service BS (p(t),q(t)) is Figure 1. Diagram of wireless communication system for railway. Figure 2. Diagram of Doppler Effect.

3 Statistics of Capacity Analysis in High Speed Railway Communication Systems 211 (8) We can write the Doppler Shift of the direct LOS component f s as and maximum Doppler Spread f max as 3. Second Order Statistics of Capacity (9) (1) For the received signal envelope in the fading models, expressions for the LCR and AFD have been derived for Ricean channels [16]. (11) (12) (13) where ( 2f s ) 2, 2 /, = arcsin( ), ( max ) 2 f 1 2 {arcsin 1 sin[ 2 arcsin( )] 2, f max 1, Q(,) is Marcum function; is the envelop of the direct LOS component, is standard variation of none-line-of-sight (NLOS) component, < f min < f max is the minimum cut-off frequency caused by obstacles, < = f min /f max <1. Lemma 1: If G[f (t)] is a monotonic increasing function of f (t). The conclusion can be reached that level crossing rate (LCR), average fading duration (AFD) as well as fade duration distribution of G[f (t)] and f (t) are identical, on condition that is chosen as the margin for G[f (t)] and for f (t) ( = G()). The above is under the assumption that the second order statistics of both G[f (t)] and f (t) exist. The proof of the lemma is given in [17]. In a wireless system, instantaneous capacity can be expressed using Shannon s universal equation as (14) where h(t) 2 is the instantaneous channel power gain, is the average transmit signal-to-noise ratio (SNR), h(t) 2 corresponds to the instantaneous received SNR. Considering the dynamical behavior of C(t) and resorting to the concept of capacity outage with respect to a given threshold c th, we may define fade durations as the durations during which the process C(t) remains below c th. Clearly, the length of these time durations varies randomly in a manner depending on the behavior of the channel fading h(t). The present work is concerned with the study of the frequency of the capacity going below c th (LCR), the average length if these random time durations (AFD) and the PDFs of the durations. The PDF of the fade durations will be denoted by P C (c th ). From (14), it can be concluded that C(t) is a monotonic increasing function of h(t). LCR, AFD, P C (c th )of the capacity process can be deduced from the results for h(t) by simply changing the threshold to the corresponding one. From (14), for C(t)=c th, the following expression can be obtained (15) After substituting (15) in (11), (12) and (13), the quantities N C (c th ), T C (c th ), P C (c th ) can be expressed as (16) (17) (18)

4 212 Qiu-Yan Liu et al. Here, N c (c th )isinproportiontof max in that only is related with f max. 4. Cases Study Sine function seems to have wonderful agreements with the fact that the train undergoes all inevitable states static, accelerating, maximum speed, decelerating, and stop. Here, we define (19) (2) From the physical point of view, A and a depends on geography. In the plain area, the train s track is straight with smaller A and a, on the contrary, A and a are larger in hilly area. Similarly, B and b are related with velocity and the interval between two adjacent stations. B and b are usually larger for express trains than conventional trains. In fact, the sign of A decides the direction that the train will turn to and positive means left, negative means right. B is always positive because the train never goes back. Now, we have to find typical values of parameters. The stations are the locations where the velocity of the train is zero. Assuming all the intervals between two adjacent stations are the same that the distance from the first station to the second station is given by with zero velocity (21) (22) (23) (24) (25) Here, d is the interval between two adjacent stations which is rational to be designed as about o(1) km [18]. The typical value of a is related with curvature R of the train track and velocity v whose typical value are about 5 m and 25~36 km/h in high speed railway environments [19,2]. Hence, we have (26) (27) The maximum velocity is achieved when cos a t = cos b t = -1. Assuming the maximum velocity of the train is about 1 m/s, we have (28) Substituting equation (24), (25), (26) and (28) into (21), we have (29) Then, the typical value of A and B are 1-2 and 1-2, respectively. In addition, typical values of important parameters are listed in Table 1. Figure 3 illustrates LCR of capacity with frequency band at 9 MHz, 1.8 GHz and 5.6 GHz. It is obvious that LCR is about in proportion to maximum frequency shift which is consistent with equation (16). Hence, with other parameters fixed, capacity of high frequency system fluctuates more frequently that introduces more outages and degrades system performance significantly. Considering typical range of capacity threshold, LCR keeps very small when the train is beside another BS with wonderful communication conditions. However, system performance becomes worse when the train is in the middle of two BSs with maximum velocity. LCR of capacity with different capacity thresholds are given in Figure 4. The worst cases happen when the train arrives at the middle of two adjacent BSs. First, it is identical with equation (16) that LCR is of direct proportion to c th 2 2. Second, LCR in the worst condition is about 3, 6 and 11 with capacity threshold c th 2 bit/s/hz, 4 bit/s/hz, and 6 bit/s/hz. We can evaluate the loose up bounds of

5 Statistics of Capacity Analysis in High Speed Railway Communication Systems 213 Table 1. Typical values of other important parameters Parameters Typical value Simulation value Parameters Typical value Simulation value A o (1-2 ).1 B o (1-2 ).5 a o (1-3 ) 2*1-3 cos b o (1-3 ) 1-3 f 9M, 1.8G, 2G 9M a ~1 = o (1-1 ).5 P o (1W) 1W 1 1 c th o (1 bit/s/hz) 2 bit/s/hz o (1 db) 19 db Figure 3. Level crossing rates with different frequency. AFD are 16.7 ms, 8.3 ms, 4.5 ms. Compared with frame duration ms of GSM system, it is simply verified that system performance is degraded significantly for 9 MHz GSM system with flat channel assumption when data rates is higher than 6 bit/s/hz with other parameters fixed. Figure 5 shows the average LCR versus capacity threshold at different working frequency. As shown in iconograph, system can provide reliable communication more than 9% successfully with AFD lower than 1-3 s when capacity threshold is 5 bit/s/hz. However, system performance is degraded to 9% outage when capacity threshold is higher than 5 bit/s/hz. Figure 6 presents the variation of average LCR as capacity threshold increasing with different frequency. In these cases, there exists a maximum LCR when capacity threshold is about 7 bit/s/hz. Most systems can provide great performance below 7 bit/s/hz while few systems are able to guarantee capacity higher than 7 bit/s/hz successfully. 5. Conclusions and Future Work Statistics of capacity including level crossing rate Figure 4. Level crossing rates with different capacity thresholds. (LCR), average fade duration (AFD) and outage probability (OP) with time varying Doppler Effect have been analyzed in high speed railway communication systems. Both straight and curved tracks have been considered in the versatile time varying Doppler shift model. Simulation results show that LCR is in proportion to maximum c th frequency shift and 2 2 which is consistent with the closed-form expression derives before. The range of capacity threshold from 5 bits/s/hz to 7 bit/s/hz is of great importance. System can provide reliable communication more than 9% successfully with AFD lower than 1-3 s when capacity threshold is 5 bit/s/hz. Most systems can provide great performance below 5 bit/s/hz. However, system performance is degraded to 9% outage when capacity threshold is higher than 5 bit/s/hz, and few systems are able to guarantee capacity higher than 7 bit/s/hz successfully. Furthermore, although sine function is appropriate to describe horizontal acceleration function, it is not always very proper to denote vertical acceleration function. In the future, some efforts have to be paid to

6 214 Qiu-Yan Liu et al. Figure 5. AFD and outage probability versus capacity threshold. Figure 6. Average LCR and outage probability versus capacity threshold. find a more graceful function which can figure out the fact more accurately and generally. Acknowledgements The authors would like to thank to the anonymous reviewers for their suggestions. And this work is supported by the joint state key program of the NSFC of China and the national railway ministry of China (Grant No. 6831), program for Changjiang scholars and innovative research team in University (Grant No. IRT 949) and the programs of state key laboratory of traffic control and safety (RCS28ZZ6 and RCS28ZZ 7). References [1] Hannah, F., China Inaugurates 2 mph Fastest Rail Service in World in Time for Olympics, London: The Times Retrieved (28). [2] Christopher, P. H. and Christopher, P., From Bullet to Symbol of Modern Japan, London Routledge (26). [3] Jeff, K., Eli, O. and Dinesh, R., Wireless Network Design Optimization Models and Solution Procedures, New York: Springer (21). [4] Hamdi, K. A. and Pap, L., A Unified Framework for Interference Analysis of Noncoherent MFSK Wireless Communications, IEEE Trans. Commun., Vol. 58, pp (21). [5] Suraweera, H. A., Garg, H. K. and Nallanathan, A., Performance Analysis of Two Hop Amplify-and-Forward Systems with Interference at the Relay, IEEE Commun. Lett., Vol. 14, pp (21). [6] Sadia, M. and Huseyin, A., Evaluation of Frequency Offset and Doppler Effect in Terrestrial RF and in Underwater Acoustic OFDM Systems, IEEE Military Communications Conference, San Diego, CA, USA (28). [7] Mottier, D. and Castelain, D., A Doppler Estimation for UMTS-FDD Based on Channel Power Statistics, IEEE 5 th Vehicular Technology Conference 1999-fall, Vol. 5, pp (1999). [8] Benedetto, J. J., Donatelli, J., Konstantinidis, I. and Shaw, C., Zero Autocorrelation Waveforms: A Doppler Statistic and Multifunction Problems, IEEE International Conference on Acoustics, Speech and Signal Processing, Vol. 5, pp (26). [9] Stüber, G. L., Principles of Mobile Communication, New York: Kluwer Academin Publishers (22). [1] Marvin, K. S. and Mobamed-Slim, A., Digital Communicaiton over Fading Channels, 2 nd edtion. John Wiley & Sons (25). [11] Matthias, P., Mobile Fading Channels, John Wiley & Sons (22). [12] Muhammad, F. H. and Peter, J. S., Level Crossing Rates of Interference in Cognitive Radio Networks, IEEE Trans Wireless Commun., Vol. 9, pp (29).

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