Outage Analysis of Train-to-Train CommunicationModel over Nakagami-mm Channel in High-Speed Railway

is paper analyzes the end-to-end outage performance of high-speed-railway train-to-train communication model in highspeed railway over independent identical and nonidentical Nakagami-m channels. e train-to-train communication is intertrain communication without an aid of infrastructure (for base station). Source train uses trains on other rail tracks as relays to transmit signals to destination train on the same track. e mechanism of such communication among trains can be divided into three cases based on occurrence of possible-occurrence relay trains. �e �rst present a new closed form for the sum of squared independent Nakagami-m variates and then derive an expression for the outage probability of the identical and non-identical Nakagami-m channels in three cases. In particular, the problem is improved by the proposed formulation that statistic for sum of squared Nakagami-m variates with identical m tends to be in�nite. Numerical analysis indicates that the derived analytic results are reasonable and the outage performance is better over Nakagami-m channel in high-speed railway scenarios.


Introduction
Railway has played a signi�cant role in helping transport passengers and goods.Accidents in railway always result in loss of lives and property.Safety issues have drawn increasing research attention due to the personal and property security.
A part of railway accidents is brought by malfunction of control center system.e train-to-train communication will serve as an assisting role which coordinates operations among trains based on multihop, when control center system is broken.It aims at detecting a potential collision and then broadcasting prewarning messages concerning this emergency to other trains on the same and neighboring tracks.
e multihop train-to-train communication model in physical layer lies in the thoughts that the source train uses the trains operating on other tracks as relays to transmit signals to destination train on the same track.Such mechanism can be divided into three cases based on occurrence of other relay trains.ese relay trains occur following the Poisson Process [1], and therefore the arrival procedure follows the distribution of negative exponent.e proposed train-totrain communication model, introducing OFDM and MIMO technique, realizes the intertrain adhoc communication based on the Poisson Process in high-speed railway scenarios.
Since 2006, train-to-train communication has been researched by several organizations, such as the German Aerospace Center (DLR).Reference [2] discusses the RCAS approach consisting only of mobile adhoc components without the necessity of extensions of the railway infrastructure, while [3] describes an overview of the state of the art in collision avoidance related with transportation systems for maritime transportation, aircra, and road transportation, and the RCAS is introduced.Reference [4] proposes a channel model for direct train-to-train communication appropriate for the 400 MHz band, and [5] presents an infrastructure-less cross-layer train-to-train communication system exploiting all characteristics of a pervasive computing system, like direct communication in mobile adhoc networks.Reference [6] designs an infrastructure-less adhoc inter-vehicle communication system that ful�lls these International Journal of Antennas and Propagation requirements with respect to the boundary conditions in the railway environment.Reference [7] presents analysis and results of a comprehensive measurement campaign investigating the propagation channel in case of direct communication between railway vehicles.
Despite that the fact the RCAS designed by the DLR has progressed tremendously in physical layer, it only work well for the train operation velocity lower than 200 Km/h, which is not able to function in the high-speed railway.Generally speaking, the velocity of high-speed railway train is up to 360 Km/h.In this case, safety distance among trains is 10 Km [8].e proposed train-to-train communication model in physical layer has been evaluated by BER previously.In this paper, we continue to analyze the proposed multihop trainto-train communication model using outage probability.We �rst present a new closed-form for the sum of squared independent Nakagami- variates with identical  [9], the proposed formulation improves the problem that statistic for sum of squared Nakagami- variables with identical  is in�nite.en we derive an expression for the outage probability of the identical  (   or   ) and nonidentical Nakagami- channels [10] in three cases.Such outage analysis is �rst applied to the multihop train-to-train communication model.e previous research indicates that the BER of train-to-train communication model reaches 10 −6 when receiving SNR is 10 dB, which meets the requirements of the International Union of Railway (UIC).erefore the threshold should be set to 10 dB.If the receiving signal SNR is below that value, the signal quality at receiver cannot realize normal communication among trains and the trainto-train communication is regarded as outage.e maximum distance of train-to-train communication is set to 6 Km and it is probable that  value of Nakagami- channel in two receiving path at receiver is different, for example, one path is    and the other path is   .is paper considers the Nakagami- channel not only with identical  but also with nonidentical  in receiver's receiving path.e rest of this paper is organized as follows.Section 2 gives a description of the proposed train-to-train communication model based on multihop.Section 3 derives expressions for the outage probability of three conditions.Section 4 shows the outage probability simulation results of this model.In Section 5, this paper is concluded.

Proposed Train-to-Train Communication Model
In this section, three cases of train-to-train communication model are presented in Figures Step 2. For  = , the PDF of   can be efficiently expressed as Step 3.According to the same procedure as Steps 1 and 3, the sum of  Nakagami- RVs can be expressed as  e outage event happens when the Y falls below given threshold Y 0 under Nakagami- channel and its probability is de�ned as where  is average receiving signal-to-noise ratio.
Next the outage probabilities of train-to-train communication model under three cases are analyzed. 1 and  2 are sum of 4 squared Nakagami- variables at receiver.e outage probability  outI of case I is expressed as 0 is the threshold SNR.Inserting (13) or (15) into (17), the  outI under Nakagami- channel with identical  and nonidentical  can be written as follows.

Numerical Analysis
In this section, we show numerical results of the analytical outage probability of train-to-train communication model in three cases.We plot the performance curves in terms of average signal-to-noise ratio (SNR) and also show computer simulation results for veri�cation.According to the previous research, when the receiving SNR is 10 dB, the Bit Error rate (BER) is 10 −6 which satis�es the communication requirements of high-speed railway set by UIC.erefore, outage performances at SNR = 10 dB are crucial to the research of train-to-train communication model.If the wireless communication link in railway is disrupted, the railway safety is threatened severely.Figures 7, 9, and 11 show the numerical and simulation results of outage probability of train-to-train communication model versus SNR in case I, case II, and case III when    or   .For    in Nakagami- channel, the channel approximates Rayleigh channel, while for    the channel is Rice channel [14].Because the condition of propagation channel is increasingly becoming better with the increment of parameter , the outage performances of Rayleigh channel are not superior to those of Rice channel.As SNR is 10 dB, in Rayleigh channel, the outage probabilities of case I, case II,  and case III are, 0.02, 0, and 0, respectively, while those of case I, case II, and case III are all 0 in Rice channel.AS for case I in Rayleigh channel, the outage probability is 0.02, which is bad for wireless communication.But the  parameter in highspeed railway is usually bigger than    in fact [14].Figures 8,10,and 12 show the numerical and simulation results of outage probability of train-to-train communication model versus SNR in case I, case II, and case III when    and   .e outage probability is 7 * 10 −4 , 0, and 0 for three cases at SNR = 10 dB.Low outage probability contributes to the normal receipt of transmit signal and is rewarding to detection and decision of signal.

Conclusion
is paper analyzes the end-to-end outage performance of high-speed-railway train-to-train communication model over independent identical and nonidentical Nakagami- channels.e mechanism of such communication among trains can be divided into three cases based on occurrence of possible-occurrence relay trains.Numerical and simulation analysis shows that the outage probability of train-to-train communication model in three cases is approximately 0 over Nakagami- (  ) channel in high-speed railway, which ensures the normal receipt of transmit signal.

F 1 :F 2 :F 3 :
Train-to-train communication model of case I. Train-to-train communication model of case II.Communication model of case III.

3. 1 .F 4 :F 5 :F 6 :
Case I.In Figure 4,  1 and  2 are SNR of receiving signal at R1 and D, respectively.Since each node applies 2 * 2 MIMO, Communication model of case I. Communication model of case II.Communication model of case III.

2 F 7 :
Outage probability of train-to-train communication in case I when    or   .

2 F 8 :
Outage probability of train-to-train communication in case I when   .

2 F 9 :
Outage probability of train-to-train communication in case II when    or   .

3 F 10 :
Outage probability of train-to-train communication in case II when   .

1 F 11 :
Outage probability of train-to-train communication in case III when    or   .

2 F 12 :
Outage probability of train-to-train communication in case III when    and   .

)
Corollary 2 (PDF of the sum of Squared Nakagami- RVs with identical ).e CDF of   is given by [11]eorem 3 (PDF of the Sum of Squared Nakgami- RVs with nonidentical ).Let {  ,  = ,  ,  be a set of RVs following the PDF presented in(2), with       ⋯     .ePDF of the sum is given by[11] () .
(19)3.2.Case II.In Figure 5,  1 are SNR of receiving signal at R1,  2 ,  3 are SNR of receiving signal at R2, and  4 ,  5 are receiving signal SNR at D.e In Figure6,   are SNR of receiving signal at R1,  2 ,  3 are SNR of receiving signal at R2,  4 ,  5 are receiving signal SNR at R3, and  6 ,  7 and  8 are receiving signal SNR at D.