A 3D Non-stationary MmWave Channel Model for Vacuum Tube Ultra-High-Speed Train Channels
Yingjie Xu, Kai Yu, Li Li, Xianfu Lei, Li Hao, Cheng-Xiang Wang
aa r X i v : . [ ee ss . SP ] F e b A 3D Non-stationary MmWave Channel Model forVacuum Tube Ultra-High-Speed Train Channels
Yingjie Xu , Kai Yu , Li Li , Xianfu Lei , Li Hao , Cheng-Xiang Wang National Mobile Communications Research Laboratory, School of Information of Science and Engineering,Southeast University, Nanjing 210096, China. Purple Mountain Laboratories, Nanjing 211111, China. China Railway Eryuan Engineering Group Co. Ltd, Chengdu, Sichuan 610031, China. School of Information Science and Technology, Southwest Jiao Tong University, Chengdu 610031, China. * Corresponding Author: Cheng-Xiang WangEmail: [email protected], [email protected], { ll5e08, xflei, lhao } @home.swjtu.edu.cn, [email protected] Abstract —As a potential development direction of futuretransportation, the vacuum tube ultra-high-speed train (UHST)wireless communication systems have newly different channelcharacteristics from existing high-speed train (HST) scenarios.In this paper, a three-dimensional non-stationary millimeter wave(mmWave) geometry-based stochastic model (GBSM) is proposedto investigate the channel characteristics of UHST channels invacuum tube scenarios, taking into account the waveguide effectand the impact of tube wall roughness on channel. Then, basedon the proposed model, some important time-variant channelstatistical properties are studied and compared with those inexisting HST and tunnel channels. The results obtained showthat the multipath effect in vacuum tube scenarios will bemore obvious than tunnel scenarios but less than existing HSTscenarios, which will provide some insights for future researchon vacuum tube UHST wireless communications.
Index Terms —vacuum tube UHST channels, mmWave, GBSM,waveguide effect, non-stationarity
I. I
NTRODUCTION
With the social development and population growth, trans-portation is developing rapidly. In the future, vacuum tubetransportation systems can overcome the limitations of currentwheel-rail transportation environment such as air resistanceand train wheel-rail resistance on the speed of trains, andthe train speed can reach thousands of kilometers per hour[1], becoming an important development direction of HSTtransportation systems. For vacuum tube UHST train-to-ground wireless communication systems, the applications ofthe fifth generation (5G) wireless communication networks,which only support up to 500 km/h mobility [2], are notenough. Accordingly, this will promote research on ultra highmobility in the sixth generation (6G) wireless communicationnetworks [3].There are many channel models which can well reflectthe wireless channel propagation characteristics in existingHST and tunnel scenarios [4]–[7]. In [8] a deterministicchannel model for HST scenarios was proposed, and chan-nel small-scale fading characteristics were investigated. AmmWave massive MIMO GBSM for HST communication systems was shown in [9], where the author studied HSTchannel statistical properties. The channel statistical propertiesin tunnel scenarios were investigated in [10] by proposinga three-dimensional (3D) non-stationary GBSM. However,these models cannot be directly used for vacuum tube UHSTchannels. The vacuum and narrow space environment havenewly different effects on its wireless channel, and the ultrahigh speed will bring larger Doppler frequency and more fasthandovers [11]. In [12], a propagation graph channel modelfor vacuum tube UHST scenarios was proposed, and severalchannel properties were analyzed, such as multipath, K factor,and channel capacity. However, it focused on channels withoutconsidering mmWave technologies that can provide high datarate transmissions to communication systems. The general 3Dnon-stationary 5G wireless channel model in [13] can reflectchannel characteristics of most scenarios. However, due tothe assumption of random cluster distribution and missingconsideration of the waveguide effect in channels, it cannotbe directly applied to the vacuum tube UHST channel.To the best of author’s knowledge, non-stationary mmWavevacuum tube UHST channel models are still missing in the lit-erature. To fill the research gaps, a 3D non-stationary mmWaveGBSM for vacuum tube UHST scenarios is proposed in thispaper. In the model, it is assumed that the scattering clustersare distributed on the inner wall of the tube, and then thevacuum tube UHST channel properties are studied.The remainder of this paper is organized as follows. A 3Dnon-stationary mmWave GBSM is proposed in Section II andchannel statistical properties are derived in Section III. SectionIV illustrates simulation results and discussions about UHSTchannels. Finally, conclusions are shown in Section V.II. A 3D N ON -S TATIONARY MM W AVE
MIMO GBSM
FOR V ACUUM T UBE
UHST S
CENARIOS
A. Description of Vacuum Tube UHST Communication Net-work Architecture
The communication network architecture for vacuum tubeUHST scenarios is shown in Fig. 1. In communication sys- ontrol StationDistributed Antenna SystemAccess PointMRS
Fig. 1. A UHST network architecture for vacuum tube scenarios. tems, it is considered to adopt technologies, such as distributedantenna system (DAS), radio over fiber (RoF), and mobilerelay station (MRS) [10]. The access points (APs) are usedand fixed on the top of the metal tube inner wall to form theDAS. They are connected by the RoF, and finally connectedto the control station (CS) at the station. A small MRS isinstalled on surface of the train to reduce high penetration lossof the signal entering train compartment. By distributing theDAS and the MRS in communication systems, the propagationspace between base stations and the train is divided intomultiple parts. This paper will aim to investigate the channelbetween AP and MRS.
B. The mmWave MIMO GBSM for Vacuum Tube UHST Sce-narios
Let us consider a MIMO system with Q and P antennaelements at the receiver (Rx) and transmitter (Tx) side andlet A Tp ( t ) and A Rq ( t ) denote 3D position vectors of the p thtransmit antenna and the q th receive antenna. Based on the5G general channel model [13], a 3D non-stationray GBSMis proposed, where the channel propagation environment ischaracterized as a 3D cylindrical model with radius R . TheCartesian coordinate system is used to describe the locationof the Tx and the Rx. It is assumed that the Rx (MRS) ontrain moves towards the Tx (AP), as shown in Fig. 2.
1) Channel Impulse Response:
The complete channel ma-trix is given by H = [ P L · SH · BL · OL ] · H s , where P L represents the path loss, SH represents the shadowing, BL represents the blockage loss, and OL represents the oxygenand molecular absorption loss. Widely used path loss modeland shadowing model are shown in [14]. The blockage loss iscaused by train and obstacles in vacuum tube UHST scenariosand its model is taken from [15] here. The oxygen andmolecular absorption loss model for mmWave can be found in[16]. Note that the parameter values in above models shouldbe measured additionally and will be different from thosemeasured in the standard atmosphere because of the vacuumenvironment in UHST channels.The small-scale fading can be denoted as a complex matrix H s = [ h pq ( t, τ )] P × Q , where h pq ( t, τ ) is the channel impulseresponse (CIR) between A Tp ( t ) and A Rq ( t ) that consists ofline-of-sight (LoS) component and non-line-of-sight (NLoS)components. The NLoS components include single-bounced(SB) and multi-bounced (MB) components. The propagationenvironment between Tx and Rx is abstracted by effectiveclusters that characterize the first and last bounce of the (cid:127) ! (cid:127) ! " $% (t) &’ (t) * ’ + , S ingle-Bounced Components Virtual link
Multi-Bounced Components (cid:127) (cid:129)(cid:141),(cid:143) (cid:144) (t)(cid:127) (cid:129)(cid:141), ! (cid:144) (t) (cid:127) (cid:129)(cid:141), ! " (t) (cid:129)(cid:141),(cid:143), ! " (t)$ (cid:129)(cid:141),(cid:143), ! " (t) (cid:129)(cid:141),(cid:143) " (t) $ (cid:129)(cid:141),(cid:143) " (t) $ (cid:129)(cid:141),(cid:143) (cid:144) (t) (cid:129)(cid:141),(cid:143), ! (cid:144) (t) (cid:129)(cid:141),(cid:143)(cid:144) (t) $ (cid:129)(cid:141),(cid:143), ! (cid:144) (t) Fig. 2. A 3D non-stationary mmWave MIMO GBSM for vacuum tube UHSTscenarios. channel. Assuming there are a total of N ( t ) effective clusterson tube wall at time t in channel, and L n is the time-variant number of rays within Cluster n . Note that each ray ineach cluster should have its own power and delay to supporthigher spectral resolution in models, which is the differencebetween mmWave channels and conventional channels. TheCIR h pq ( t, τ ) can be expressed as [13] h pq ( t, τ ) = h LoSpq ( t ) · δ ( τ − τ LoS ( t )) | {z } LoS + N X n =1 L n X l n =1 h NLoSpq,n,l n ( t ) · δ ( τ − τ n ( t ) − τ l n ( t )) | {z } NLoS . (1)In (1), τ LoS ( t ) is the delay of LoS component, τ n ( t ) is thedelay of Cluster n and the delay τ l n ( t ) of the l n th rays within Cluster n is taken into account to support mmWave scenarios.Moreover, to model high mobility and non-stationarity ofUHST channels, all parameters in the model are time-variant.Suppose the train speed vector at the Rx is v R , and initialdistance vector between the Rx and Tx is D . The key channelparameters are defined in Table I.For the LoS component, the complex channel h LoSpq ( t ) canbe written as h LoSpq ( t ) = s K pq ( t ) K pq ( t ) + 1 e − j πDLoSpqλ e j πf LoSpq ( t ) · t (2)where f LoSpq ( t ) can be calculated as f LoSpq ( t ) = 1 λ (cid:10) D LoSpq ( t ) , v R (cid:11)(cid:13)(cid:13) D LoSpq ( t ) (cid:13)(cid:13) . (3)The delay τ LoS ( t ) can be expressed as τ LoS ( t ) = (cid:13)(cid:13) D LoSpq ( t ) (cid:13)(cid:13) c (4)where k·k calculates the Frobenius norm and D NLoSpq,n,l n ( t ) canbe calculated as D LoSpq ( t ) = A Rq ( t ) − A Tp ( t ) . (5) ABLE ID
EFINITION OF K EY P ARAMETERS . Parameters Definition D LoSpq ( t )
3D distance vector between A Tp ( t ) and A Rq ( t ) of the LoS component D NLoSpq ( t )
3D distance vector between A Tp ( t ) and A Rq ( t ) of the NLoS components D Rqp,n ( t ) , D Tqp,n ( t )
3D distance vectors between
Cluster n and the Rx (Tx) array center D Rpq,n,l n ( t ) , D Tpq,n,l n ( t )
3D distance vectors between the l n th rays within Cluster n and the Rx (Tx) array center D initial distance vector between Tx and Rx α Rpq,n ( t ) , β Rpq,n ( t ) azimuth and elevation angles between Cluster n and the Rx array center α Tpq,n ( t ) , β Tpq,n ( t ) azimuth and elevation angles between Cluster n and the Tx array center α Rpq,n,l n ( t ) , β Rpq,n,l n ( t ) azimuth and elevation angles between the l n th rays within Cluster n and the Rx array center α Tpq,n,l n ( t ) , β Tpq,n,l n ( t ) azimuth and elevation angles between the l n th rays within Cluster n and the Tx array center A Rq ( t ) , A Tp ( t )
3D position vectors of the q th antenna at Rx and the p th antenna at Tx v R
3D velocity vector of receive array K pq ( t ) Rician factor f LoSpq ( t ) , f NLoSpq,n,l n ( t ) Doppler frequency between A Tp ( t ) and A Rq ( t ) of the LoS (NLoS) component N ( t ) the total number of effective clusters at time tP n,l n ( t ) the normalized power of l n th rays within Cluster n λ the wavelength of the signal For NLoS components, the complex channel h NLoSpq,n,l n ( t ) canbe written as h NLoSpq,n,l n ( t ) = s P n,l n ( t ) K pq ( t ) + 1 e j ( ϕ n,ln − πDNLoSpq,n,ln ( t ) λ ) × e j πf NLoSpq,n,ln ( t ) · t (6)where ϕ n,l n is initial phase, D NLoSpq,n,l n ( t ) and f NLoSpq,n,l n ( t ) canbe calculated as D NLoSpq,n,l n ( t ) = (cid:13)(cid:13) D Tpq,n,l n ( t ) (cid:13)(cid:13) + (cid:13)(cid:13) D Rpq,n,l n ( t ) (cid:13)(cid:13) + e τ n ( t ) · c (7) f NLoSpq,n,l n ( t ) = 1 λ D D Rpq,n,l n ( t ) , v R E(cid:13)(cid:13)(cid:13) D Rpq,n,l n ( t ) (cid:13)(cid:13)(cid:13) (8)where e τ n ( t ) · c represents the virtual link distance and e τ n ( t ) is avirtual delay. The distance vectors D Rpq,n,l n ( t ) and D Tpq,n,l n ( t ) are determined by the AoAs and AoDs of l n th rays, as shownin (9) and (10). D Rpq,n,l n ( t ) = R q − cos β Rpq,n,l n ( t )cos α Rpq,n,l n ( t ) cos β Rpq,n,l n ( t ) cos α Rpq,n,l n ( t )cos β Rpq,n,l n ( t ) sin α Rpq,n,l n ( t )sin α Rpq,n,l n ( t ) T + D − A Rq ( t ) (9) D Tpq,n,l n ( t ) = R q − cos β Tpq,n,l n ( t )cos α Tpq,n,l n ( t ) cos β Tpq,n,l n ( t ) cos α Tpq,n,l n ( t )cos β Tpq,n,l n ( t ) sin α Tpq,n,l n ( t )sin α Tpq,n,l n ( t ) T − A Tq ( t ) . (10)Similarly, the distance vectors D Rpq,n ( t ) and D Tpq,n ( t ) of Cluster n can be calculated by replacing α Rpq,n,l n ( t ) , β Rpq,n,l n ( t ) in (9) with α Rpq,n ( t ) , β Rpq,n ( t ) and replacing α Tpq,n,l n ( t ) , β Tpq,n,l n ( t ) in (10) with α Tpq,n ( t ) , β Tpq,n ( t ) .
2) Cluster Evolution in Time Domains for UHST channel:
The cluster evolution in time domains for UHST channelis achieved by updating cluster information and geometriccharacteristics of channels. Here we use the birth and deathprocess [9] to describe the time evolution of clusters, givenappropriate cluster survival and recombination rates.For survived clusters, firstly, which clusters are survivedshould be determined. Let P T (∆ t ) denote the survival prob-ability of a cluster after ∆ t and its calculation are given in[13]. Then, the position vector of receiving antenna is updatedas A Rq ( t + ∆ t ) = A Rq ( t ) + v R ∆ t. (11)Similarly, the distance vectors in (5), (9) ∼ (12) need to beupdated accordingly. Next, the delay of Cluster n is updatedas τ n ( t + ∆ t )= (cid:13)(cid:13)(cid:13) D Rpq,n,l n ( t + ∆ t ) (cid:13)(cid:13)(cid:13) + (cid:13)(cid:13)(cid:13) D Tpq,n,l n ( t + ∆ t ) (cid:13)(cid:13)(cid:13) c + e τ m ( t + ∆ t ) (12)where the virtual delay e τ m ( t +∆ t ) at time t +∆ t is calculatedas e τ n ( t + ∆ t ) = e − ∆ tς e τ n ( t ) + (1 − e − ∆ tς ) X . The random vari-able X and e τ n have the same distribution but are independentof each other and ς is a scenario-dependent parameter [13].Finally, the mean power of l n th rays within Cluster n need tobe updated as [10] e P n,l n ( t + ∆ t ) = e P n,l n ( t ) 3 τ n ( t ) − τ n ( t + ∆ t ) + τ l n τ n ( t ) + τ l n . (13)It should be noted that the updated power in (13) should benormalized before being substituted into (6).For new cluster generations, the number of new clustersgenerated at a stationary interval should be determined at first.In the fully enclosed tube, the channel keyhole effect [17]related to waveguide will cause the multipath componentsin signal to change with distance. As the distance betweenhe Rx and Tx increases, the multipath components willexperience more similar channel fadings. Moreover, it hasbeen confirmed that the scattering surface roughness σ h willaffect the scattering and reflection loss of the signal, and thusthe number of multipaths reaching the Rx. By consideringabove phenomenons in vacuum tube channel, it is assumedthat the number of new clusters generated at time t follows aPoisson distribution, and its mean value is E [ N new ( t )] = λ G λ R (1 − P T ( t ))(1 − (cid:13)(cid:13) D LoS ( t ) (cid:13)(cid:13) D ) ρ s ρ s (14)where ρ s is the scattering coefficient when the roughness σ h = 0 . The scattering coefficient ρ s is calculated as [18] ρ s = e ( − πσh cos( β ) λ ) ) (15)where ¯ β is the mean elevation angle of the incident ray.After the number of new cluster determined, key parametersfor new cluster need to be given. Here, the calculation ofthe ray power P n,l n is referenced in [18]. The number ofrays in cluster follows the Poisson distribution and the angleparameters follow the Von Mises distribution [10]. The virtualdelay τ n follows the exponential distribution [19].III. S TATISTICAL P ROPERTIES
In this section, several typical statistical properties of themmWave channel model for vacuum tube UHST scenarioswill be derived.
A. The Time-Variant Transfer Function
The time-variant transfer function H pq ( t, f ) is the Fouriertransform of the CIR h pq ( t, τ ) relative to τ , which can beexpressed as H pq ( t, f ) = ∞ Z −∞ h pq ( t, τ ) e − j πτf dτ = h LoSpq ( t ) e − j πτ LoS ( t ) f + N X n =1 L n X l n =1 h NLoSpq,l n ( t ) e − j π ( τ n ( t )+ τ ln ( t )) f . (16) B. Space-Time-Frequency Correlation Function
In order to investigate the correlation of UHST channels,the space-time-frequency correlation function (STFCF) is cal-culated as R pq,p ′ q ′ ( δ p , δ q , ∆ f, ∆ t ; t, f )= E [ H pq ( t, f ) H ∗ p ′ q ′ ( t + ∆ t, f + ∆ f )] (17)where δ p = (cid:13)(cid:13) A Tp − A Tp ′ (cid:13)(cid:13) , δ q = (cid:13)(cid:13) A Rq − A Rq ′ (cid:13)(cid:13) . Due to theLoS component is determined based on Tx and Rx’s relativeposition while NLoS components are determined based onparameters which are randomly generated, for simplicity, itis assumed here that the LoS and NLoS components areuncorrelated [13]. Then (17) can be written as R pq,p ′ q ′ ( δ p , δ q , ∆ f, ∆ t ; t, f )= R LoS pq,p ′ q ′ ( δ p , δ q , ∆ f, ∆ t ; t, f ) + R NLoS pq,p ′ q ′ ( δ p , δ q , ∆ f, ∆ t ; t, f ) . (18) The correlation function of the LoS component is expressedas follows [10]: R LoSpq,p ′ q ′ ( δ p , δ q , ∆ f, ∆ t ; t, f )= KK + 1 H LoSpq ( t, f ) · H LoS ∗ p ′ q ′ ( t + ∆ t, f + ∆ f ) . (19)For NLoS components, the correlation function is expressedas R NLoSpq,p ′ q ′ ( δ p , δ q , ∆ f, ∆ t ; t, f )= 1 K + 1 N X n =1 L n X l n =1 H NLoSpq ( t, f ) · H NLoS ∗ p ′ q ′ ( t + ∆ t, f + ∆ f ) . (20)In STFCF, let ∆ f = 0 , q = q ′ , p = p ′ , the function willbe reduced to the time-variant ACF. Let ∆ t = 0 , ∆ f = 0 , q = q ′ (or p = p ′ ), the function will be reduced to the time-variant cross-correlation function (CCF) of the Rx (or Tx).Let ∆ t = 0 , q = q ′ , p = p ′ , the function will be reduced tothe time-variant frequency correlation function (FCF). C. Stationary Interval
The stationary interval is the minimum time interval duringwhich the channel response remains constant. It can be usedto determine the channel estimation frequency in ultra-high-speed mobile scenes [10]. It is defined as the maximum lengthof time that the ACF of the power delay profile (PDP) exceedsa certain threshold ς , namely, I = inf { ∆ t | R Λ ( t, ∆ t ) ≤ ς } (21)where inf {·} is the infimum of a function, R Λ ( t, ∆ t ) is thethe ACF of the PDP and its calculation is given in [13]. Thethreshold ς can be adjusted according to certain scenario andset to 80 % here.IV. R ESULTS AND D ISCUSSIONS
In this section, channel properties of the proposed channelmodel are simulated and analyzed. According to the size ofexisting vacuum tube train design of Hyperloop One [20], thecross section radius of vacuum tube is set R = 2 m here. Thematerial of tube wall is low carbon steel [20] which can beapproximated as a smooth surface, therefore the roughness isset σ h = 0 here. In metal tube, the position coordinates of theTx is set as ( x T , y T , z T ) = (0 , , while the initial positioncoordinates of the Rx is set as ( x R , y R , z R ) = ( D , , ,where D is the initial distance. At the Rx and Tx, a × MIMO linear antenna array communication systems are takeninto consideration and antenna spacing are set as ∆ x T =∆ x R = λ [10]. Also, other parameters like carrier frequency f c = 58 GHz and the train speed v R = 1080 km/h. Inthe calculation of P T (∆ t ) , the generation and recombinationrate are set as r b = 80 / m , r d = 4 / m , respectively. Theremaining parameters are randomly generated with referenceto the 5G general channel model [13], and the equal areamethod (EAM) [10] is used to obtain discrete AoA and AoDangle characteristics in channel model. ig. 3. Spatial CCFs comparison of simulation model and simulation resultsat different time instants ( R = 2 m, σ h = 0 , r b = 80 / m , r d = 4 / m , D = 600 m, v R = 1080 km/h, f c = 58 GHz, k = k = 6 ). A. The Time-Variant Spatial CCF
The spatial CCFs comparison of the simulation model andsimulation results at different time instants are shown in Fig. 3.Since the parameters are time-variant, such as azimuth AoAand elevation AoA, the spatial cross-correlation characteristicsare different at different time instants, and also, the simulationmodel and simulation results curve fit well.
B. The Time-Variant ACF
The ACFs comparison of simulation model and simulationresults at different time instants are illustrated in Fig. 4. Thecurve fit of the simulation model and the simulation resultis very good. The comparisons of ACFs of the simulationmodel for different v R at t = 0 s are shown in Fig. 5. As trainspeed increases, the ACF downward trend accelerates, and theattenuation is more rapid. In the future UHST scenarios, trainscan reach thousands of kilometers per hour, which means thesmaller coherence time will be considered in UHST channels. C. Comparison with Existing HST and Tunnel Channels
In tunnel scenarios, the material of tunnel wall is generallyreinforced concrete. Here, the roughness is set σ h = 0 . [21] to simulate tunnel environment. The HST channel modelin [9] is used to modeling existing HST channel here. Somechannel characteristics compared in above scenarios are shownas follows.The number of clusters changed with distance in threechannels are illustrated in Fig. 6. Due to extremely smallspace environment of the vacuum tube and tunnel, the num-ber of clusters in their channels is much less than that inHST channels, and the same phenomenon in tunnel wirelesscommunication can be found in [12]. Moreover, comparedwith nearly smooth surface of vacuum tube, the signal willexperience greater loss after passing through the roughertunnel wall, which will reduce the effective propagation path Fig. 4. ACFs comparison of simulation model and simulation results atdifferent time instants ( R = 2 m, σ h = 0 , r b = 80 / m , r d = 4 / m , D = 600 m, v R = 1080 km/h, f c = 58 GHz, k = k = 6 ).Fig. 5. Comparisons of ACFs of the simulation model for different v R at t = 0 s ( R = 2 m, σ h = 0 , r b = 80 / m , r d = 4 / m , D = 600 m, f c = 58 GHz, k = k = 6 ). to the Rx [11]. Fig. 7 compares the stationary intervals ofvacuum tube UHST scenarios with existing HST scenarios.In existing HST scenarios, at a train speed of 360 km/h in 58GHz, the stationary interval is about 0.35 ms, while it shouldbe consider smaller in UHST channel, which is about 0.05ms. V. C ONCLUSIONS
In this paper, a 3D non-stationary mmWave channel modelfor vacuum tube UHST communication systems has beenproposed and its channel statistical properties have beenstudied, including time-variant ACF and spatial CCF. Theresults show that the non-stationarity of UHST channels. Thesimulation results match the simulation model well. Moreover,by comparing channel properties of vacuum tube UHSTscenarios with existing tunnel and HST scenarios, it is found ig. 6. Comparisons of the number of clusters in different scenarios ( D =1000 m, v R = 1080 km/h, f c = 58 GHz, k = k = 6 ).Fig. 7. Comparisons of empirical CCDFs of stationary intervals in differentscenarios ( D = 600 m, f c = 58 GHz, k = k = 6 ). that there are more multipaths in vacuum tube UHST channelthan tunnel channels but less than HST channels. For futurework, more statistical properties of UHST channel need to beinvestigated and the available measured date also need to beconsidered to modify the model once there are some channelmeasurements on vacuum tube UHST scenarios.A CKNOWLEDGMENTThis work was supported by the National Key R&D Program of Chinaunder Grant 2018YFB1801101, the China Railway Eryuan Engineering GroupCo. Ltd Project under Grant KYY2019110(19-21), the National NaturalScience Foundation of China (NSFC) under Grant 61960206006, the FrontiersScience Center for Mobile Information Communication and Security, the HighLevel Innovation and Entrepreneurial Research Team Program in Jiangsu, theHigh Level Innovation and Entrepreneurial Talent Introduction Program inJiangsu, the Research Fund of National Mobile Communications ResearchLaboratory, Southeast University, under Grant 2020B01, the FundamentalResearch Funds for the Central Universities under Grant 2242020R30001,the EU H2020 RISE TESTBED2 project under Grant 872172, and the OpenResearch Fund of National Mobile Communications Research Laboratory,Southeast University under Grant 2021D05. R EFERENCES[1] M. Jin and L. Huang, “Development status and trend of ultra high-speedvacuum pipeline transportation technology,”
Science and TechnologyChina , vol. 5, no. 11, pp. 1-3, Mar. 2017.[2] X.-H. You, C.-X. Wang, J. Huang, et al., “Towards 6G wireless com-munication networks: vision, enabling technologies, and new paradigmshifts,”
Sci. China Inf. Sci. , vol. 41, no. 1, Jan. 2021.[3] C.-X. Wang, J. Huang, H. Wang, X. Gao, X.-H. You, and Y. Hao, “6Gwireless channel measurements and models: Trends and challenges,”
IEEE Veh. Technol. Mag. , vol. 15, no. 4, pp. 22-32, Dec. 2020.[4] C.-X. Wang, J. Bian, J. Sun, W. Zhang, and M. Zhang, “A survey of5G channel measurements and models,”
IEEE Commun. Surveys Tuts. ,vol. 20, no. 4, pp. 3142–3168, 4th Quart., 2018.[5] Y. Liu, C.-X. Wang, and J. Huang, “Recent developments and futurechallenges in channel measurements and models for 5G and beyondhigh-speed train communication systems,”
IEEE Commun. Mag. , vol.57, no. 9, pp. 50-56, Sept. 2019.[6] Y. Liu, A. Ghazal, C.-X. Wang, X. Ge, Y. Yang, and Y. Zhang, “Channelmeasurements and models for high-speed train wireless communicationsystems in tunnel scenarios: a survey,”
Sci. China Inf. Sci. , vol. 60, no.8, pp. 1-17, Oct. 2017.[7] C.-X. Wang, A. Ghazal, B. Ai, Y. Liu, and P. Fan, “Channel mea-surements and models for high-speed train communication systems: Asurvey,”
IEEE Commun. Surveys Tuts. , vol. 18, no. 2, pp. 974–987,Apr.-Jun. 2016.[8] K. Guan, B. Ai, B. Peng, D. He, G. Li, J. Yang, Z. Zhong, and T.K¨urner, “Towards realistic high-speed train channels at 5G millimeter-wave band—part II: Case study for paradigm implementation,”
IEEETrans. Veh. Technol. , vol. 67, no. 10, pp. 9129-9144, Oct. 2018.[9] Y. Liu, C.-X. Wang, J. Huang, J. Sun, and W. Zhang, “Novel 3-Dnonstationary mmwave massive mimo channel models for 5G high-speed train wireless communications,”
IEEE Trans. Veh. Technol. , vol.68, no. 3, pp. 2077–2086, Mar. 2019.[10] Y. Liu, C.-X. Wang, C. F. Lopez, G. Goussetis, Y. Yang, and G.K. Karagiannidis, “3D non-stationary wideband tunnel channel modelsfor 5G high-speed train wireless communications,”
IEEE Trans. Intell.Transp. Syst. , vol. 21, no. 1, pp. 259–272, Jan. 2020.[11] C. Qiu, L. Liu, Y. Liu, Z. Li, J. Zhang, and T. Zhou, “Key technologies ofbroadband wireless communication for vacuum tube high-speed flyingtrain,” in
Proc. IEEE VTC , Kuala Lumpur, Malaysia, Apr. 2019, pp.1–5.[12] B. Han, J. Zhang, L. Liu, and C. Tao, “Position-based wireless channelcharacterization for the high-speed vactrains in vacuum tube scenariosusing propagation graph modeling theory,”
Radio Science , vol. 55, no.4, pp. 1-12, Apr. 2020.[13] S. Wu, C.-X. Wang, e. M. Aggoune, M. M. Alwakeel, and X. You, “Ageneral 3-D non-stationary 5G wireless channel model,”
IEEE Trans.Commun. , vol. 66, no. 7, pp. 3065–3078, Jul. 2018.[14] Aalto University et al., “5G channel model for bands up to 100 GHz,”v2.0, Mar. 2014.[15] V. Nurmela et al., METIS, ICT-317669/D1.4, “METIS Channel Mod-els,” Jul. 2015.[16] ITU-R, “Preliminary draft new report ITU-R M. [IMT-2020.EVAL],”Niagara Falls, Canada, R15-WP5D-170613-TD-0332, Jun. 2017.[17] L. Liu, C. Qiu, Z. Li, B. Han, Y. Liu, and T. Zhou, “Thoughts onkey technologies of broadband wireless communication for high-speedvacuum pipeline flying train,”
J. The China Railway Soc. , vol. 41, no.1, pp. 65–73, Jan. 2019.[18] P. Ky¨osti et al. (Sep. 2007).
WINNER II Chan-nel Models, Ver-sion 1.1.
Sci. China Inf. Sci. , vol. 60, no. 8, pp. 1-13,Aug. 2017.[20] Z. Feng, X. Fang, H. Li, A. Cheng, and Y. Pan, “Technological devel-opment of high speed maglev system based on low vacuum pipeline,”
Engineering Science , vol. 20, no. 6, pp. 105–111, June 2019.[21] H. Wei, G. Zheng, and M. Jia, “The measurements and simulations ofmillimeter wave propagation at 38 GHz in circular subway tunnels,” in