Energy-Efficient Power Control of Train-ground mmWave Communication for High Speed Trains
11 Energy-Efficient Power Control of Train-groundmmWave Communication for High Speed Trains
Lei Wang, Bo Ai,
Senior Member, IEEE , Yong Niu, Xia Chen, and Pan Hui,
Fellow, IEEE
Abstract —High speed train system has proven to be a veryflexible and attractive system that can be developed undervarious circumstances and in different contexts and cultures.As a result, high speed trains are widely deployed aroundthe world. Providing more reliable and higher data rate com-munication services for high speed trains has become one ofthe most urgent challenges. With vast amounts of spectrumavailable, the millimeter wave (mmWave) system is able toprovide transmission rates of several gigabits per second forhigh speed trains. At the same time, mmWave communicationalso suffers from high attenuation, thus higher energy efficiencyshould be considered. This paper proposes an energy efficientpower control scheme of train-ground mmWave communicationfor high speed trains. Considering a beam switching method forefficient beam alignment, we first establish position predictionmodel, the realistic direction antenna model and receive powermodel. And then we allocate the transmission power rationallythrough the power minimization algorithm while ensuring thetotal amount of transmission data. Based on this, this paper alsodevelops a hybrid optimization scheme and finds the limit oftotal energy consumption when the number of segments goes toinfinity. Through simulation with various system parameters andtaking velocity estimation error into account, we demonstrate thesuperior performance of our schemes.
I. I
NTRODUCTION
High speed railway is now a mature system of transport.And high speed train (HST) systems are considered as a greentransportation system that can provide fast and convenientservices. HSTs have been widely deployed around the worldand the network is still rapidly expanding. It is expectedthat the total length will reach up to 54,550 km by 2025[1]. Providing quality broadband services for passengers isbecoming especially important. With the increasing demandof bandwidth, the current 4G wireless technology cannot
L. Wang, B. Ai, Y. Niu, and X. Chen are with the State Key Lab-oratory of Rail Traffic Control and Safety, Beijing Jiaotong University,Beijing 100044, China (E-mails: [email protected]; [email protected];[email protected]; [email protected]).P. Hui is with the Department of Computer Science and Engineering,The Hong Kong University of Science and Technology, Hong Kong, andDepartment of Computer Science and Engineering, University of Helsinki,Finland.Copyright(c) 2015 IEEE. Personal use of this material is permitted. How-ever, permission to use this material for any other purposes must be obtainedfrom the IEEE by sending a request to [email protected] study was supported by National Key R&D Program of China underGrant 2016YFE0200900; and by the National Natural Science Foundation ofChina Grants 61725101, 61801016, and U1834210; and by the China Post-doctoral Science Foundation under Grant 2017M610040 and 2018T110041;and by the Beijing Natural Fund under Grant L172020; and by Major projectsof Beijing Municipal Science and Technology Commission under Grant No.Z181100003218010; and by project 16214817 from the Research GrantsCouncil of Hong Kong and the 5GEAR project from the Academy of Finland.(
Corresponding authors: B. Ai, Y. Niu. ) meet the needs of passengers to access the Internet usingmobile terminals in a high-speed mobile environment. Thecontradiction between the increasing demand for transmissiondata of train-ground communication and the existing low-rate communication makes it urgent to solve the problem ofwireless broadband communication for HSTs.As a technology adopted by the fifth-generation (5G)wireless communication, mmWave communication is able tosupport multi-gigabit wireless services like wireless gaming,wireless Gigabit Ethernet, real-time compressed and uncom-pressed high-definition television (HDTV) streaming media,and high-speed data transfer between devices such as cameras,tablets and personal computers [2]. Therefore, it can solve theproblem of train-to-ground wireless broadband transmissioneffectively and provide stable and reliable communicationservices for passengers, which is difficult for existing oper-ators in a high-speed mobile environment. At present, thetechnology has been applied in some HST communicationsystems worldwide and have achieved good performance, likethe Japanese Shinkansen, the TVE test line of maglev trainin Germany and the maglev train in Shanghai, China [3].Due to its wide bandwidth, narrow beam and rich spectrumresources, applying mmWave to train-ground communicationfor HSTs not only conforms to the current development trendof wireless communication networks, but also satisfies theneeds of passengers for Internet access. It has become aneffective way to improve the quality of HST services.For HST communication systems, although many new tech-nologies have been proposed, there are still many importantissues need to be investigated. Due to high carrier frequency,mmWave communications suffer from higher propagation lossthan communication systems in lower frequency bands [4]. Forinstance, the free space path loss at 60 GHz band is 28 decibels(dB) higher than that at 2.4 GHz [5]. With the maturity ofdirectional antenna technology [6], mmWave communicationhas attracts considerable attention. To combat high channelattenuation, analog beamforming techniques are exploited tosynthesize directional antennas at both the transmitter andreceiver to achieve high antenna gain [7], [8]. Consequently,the omnidirectional carrier sensing is disabled, and this is thedeafness problem [9].Energy problem is another important problem that needs tobe addressed. Over the past years, the work on 5G networkshas achieved remarkable results [10], [11]. 3GPP has recentlyratified non-standalone 5G New Radio (NR) technology toaugment further LTE [12]. In the 5G era, with a large numberof base stations (BSs) deployed, the cost-efficient, flexible,and green power control solution becomes one of the most a r X i v : . [ c s . N I] J u l urgent and critical challenges [13]. The energy efficiency oftrain-ground communication for HSTs has gradually becomea key issue in green wireless communication. First, the HSTsystem is divided into five subsystems and energy system isone of them, enhancing energy efficiency can help improve theperformance of the HST system. And high energy efficiency isone of goals of future HST developments, with higher energyefficiency, the HST system will be more sophisticated [14].Second, as a mass transport system, the HST system has manyfixed costs and huge investment required, it needs specificground infrastructure which is costly to implement and main-tain. In order to fulfil its potential in meeting future transportneeds, the rail industry will need to radically progress in termsof costs. Reduce energy consumption is beneficial to reduceoperations costs to some extent [15]. Finally, compared to theroad and air industries, the rail industry is small, improvementof energy efficiency can help the rail industry keep pace withroad and air. Up until now, rail has been considered the safestand most environmentally friendly transport mode. However,driverless electric cars will completely transform how we viewroad transport. Similar leaps forward are anticipated in the airindustry, towards the production of much quieter and morefuel efficient airplanes. The rail industry cannot sit back andsimply watch all of these breakthroughs happen. Even whererail transport is head and shoulders ahead, improvements andinnovations are of the utmost necessity [16]. Therefore, there isstrong motivation and interest to investigate an energy-efficientsolution for HST wireless communication systems.This paper considers a HST network of mmWave accesspoints similar to the architecture proposed in [17]. We focuson a mmWave system that employs directional beamforming atthe transmitter (TX) and receiver (RX), using adaptive arrays.The IEEE 802.11 ad/ay standard has adopted the way ofbeamforming to increase antenna gain [18]. A beam switchingmethod is considered which uses train position informationsimilar to [19], and the information can be obtained fromthe train control system (TCS). Modern railway systems haveTCSs, which can track the position and velocity of eachtrain. Assuming that the BSs and the transceivers on the train(mobile relay) have only one RF chain, the BS uses mmWavedirectional transmission to the mobile relay on the train, andbeamforming is accomplished via a digitally controlled phasedarray. With the estimated position information of the train, thetime to switch the beam direction can be calculated. Accordingto the result of [17], this switching can be very fast ( < • We focus on the energy efficiency power control problemof train-ground mmWave communication and formulatethe problem into a nonlinear optimization problem, theoptimization model is established based on position pre-diction model, the realistic direction antenna model andreceive power model. And the position prediction modelis established based on the beam switching scheme. • We propose an energy-efficient power control schemewhere the coverage of a base station is divided intosmall segments and the transmission power is allocatedproperly through power minimization algorithm. The totalamount of transmission data is considered in the problem.We also develop a hybrid optimization scheme that onlyallocates the transmission power of the second half ofthe considered part. Furthermore, we find the limit oftotal energy consumption when the number of segmentsapproaches infinity. • Through simulation with various system parameters andtaking velocity estimation error into account, we demon-strate that our schemes can achieve lower energy con-sumption and higher energy efficiency.The rest of this paper is organized as follows. Section IIintroduces the related work on the mmWave communicationfor HSTs. Section III presents the system model and for-mulates the energy efficiency optimization problem of train-ground mmWave communication into a nonlinear minimiza-tion problem. Section IV proposes our energy-efficient powercontrol schemes. In section V, the performance of the schemeis analyzed when the number of segments tends to infinity.Section VI gives the evaluation of our schemes in termsof energy consumption and energy efficiency with velocityestimation error and various system parameters. Section VIIconcludes this paper.II. R
ELATED W ORK
There have been some schemes proposed on the mmWavecommunication system for HSTs [20]–[23]. Va et al . [20]considered a beam switching method which uses the positioninformation of the train from TCS to determine the timeof beam switching, velocity estimation error is also takeninto account to get the optimal beamwidth. Kim et al . [21]proposed a distributed antenna system-based (DAS) mmWavecommunication system for HSTs based on the hierarchicaltwo-hop network, antenna modules are distributed by ge-ographic position and the communication interruption timeduring handover was minimized to provide more reliablelinks between TX and RX. In [22], a disaster radar detectionapproach for the safety of trains was designed. Accordingto the safety level, the area around the railway is dividedinto three parts and different detection methods are usedfor different sub-areas. [23] introduced orthogonal frequency-division multiplexing (OFDM) and single carrier (SC) schemeto support mmWave communication and made a suggestionthat train-trackside mmWave systems should deploy bothOFDM and SC, and then presented train-trackside networkarchitecture adopted MIMO technologies.
The upcoming 5G mobile communication system is ex-pected to support high mobility up to 500 km/h, whichis envisioned in particular for HSTs. MmWave spectrum isconsidered as a key enabler for offering the “best experience”to highly mobile users [24]–[28]. In order to solve the problemof applying traditional MIMO to HSR scenario, Cui et al .[24] proposed a hybrid beamforming scheme using spatialmodulation (SM) which can achieve multiple antenna gain,and the scheme has been designed both in analog domainand in digital domain. [25] considered the mobile hotspotnetwork based on a hierarchical relay network structure, thedesign of baseband modem and RF front end are givenwhich can satisfy high data transfer rates for HSTs with thevelocity up to 500km/h, and the core of system structure ismitigating severe Doppler effects by allocating downlink anduplink reference signal. [26] discussed the main challengesof 5G mmWave HST communication and proposed a viableparadigm by definiting the 5G mmWave HST scenario andselecting proper objects and materials. Through reconstructionof three models, the paradigm is verified. Talvitie et al . [27]studied HST positioning problem in a 5G NR network by usingspecific NR synchronization signals. The positioning methodutilizes measurement of time of arrival and angle of departure,and the position can be tracked by an Extended KalmanFilter. [28] overcame the challenge of sensitivity of mmWavelinks by utilizing multiple antennas diversity and higher band-width. A risk-sensitive reinforcement learning framework wasformulated where each cell optimizes its transmission whileconsidering signal fluctuations.Recently, there are also some works on mmWave beamalignment and power allocation [29]–[33]. To realize fastand accurate estimation of mmWave channel, Xiao et al .[29] proposed a multipath decomposition and recovery ap-proach by exploiting the spacial sparsity. Particularly, a code-book is designed for the approach to make it applicablefor both analog and hybrid beamforming/combining deviceswith strict constantmodulus(CM) constraint. Considering thenon-orthogonal multiple access in mmWave communications,[30] studied power and beam gain allocation problem andbeamforming problem under the CM constraint to maximizethe sum rate of a 2-user mm-wave-NOMA system. Zhou et al .[31] investigated the problem of beam misalignment at boththe base station and the users and developed a performanceanalysis framework for mmWave-NOMA networks with spa-tially random users. Liu et al . [32] formulated the discretepower control and non-unified transmission duration allocationproblem for self-backhauling mmWave cellular networks as anoptimization problem and corresponding algorithms have beendesigned to solve it. Cui et al . [33] proposed a branch andbound (BB) based power allocation algorithm and a matchtheory based algorithm to maximize the sum rate for themmWave NOMA system.To the best of our knowledge, most of these works do notfocus on the energy consumption reduction problem of train-ground mmWave communication for HSTs, and energy effi-ciency problem is not considered. In this paper, we investigatethe problem and allocate the transmission power properly toachieve good performance. III. S
YSTEM M ODEL AND P ROBLEM F ORMULATION
This section describes problem formulations and the modelsneeded for energy efficiency optimization.
A. Position Prediction Model
Fig. 1. A mmWave network for HST.Fig. 2. Bird view of the mmWave network.
Consider a network model as shown in Fig. 2, where thedistance from a BS to the rail is denoted by d and the inter-BSdistance by d l . We assume that the total number of segmentsis even and from symmetry, we only need to consider the halfof the model, i.e. , the coverage of a BS is divided into N beams ( N = 2 in Fig. 2), and the coverage of the i th beam is d i , d i can be computed from the geometry.We assume that only periodic feedback from TCS canprovide an accurate current position and a velocity estimate,the communication system uses this information to predict theposition of the train until the next update is available. Thepredicted positions are used to determine the time of beamswitching.Assume that the speed of the train is constant, notice thattrains with large mass cannot accelerate or decelerate rapidly,so this assumption is reasonable. Then the position can bemodeled as x ( t ) = v ( t − t ) + x , (1)where x is the feedback location, and t is the time of thefeedback. Without loss of generality, we set x = 0 and t =0 . B. The Realistic Direction Antenna Model
In this paper, we adopt the widely used realistic directionalantenna model, which is a main lobe of Gaussian form inlinear scale and constant level of sidelobes [34]. It is thereference antenna model with sidelobe for IEEE 802.15.3c.
And we assume that the Doppler effect of the channel hasbeen eliminated by modulation methods [35]. The gain of adirectional antenna in units of decibels ( dB ) , which is denotedby G ( θ ) , can be expressed as G ( θ ) = (cid:40) G − . · ( θθ − dB ) , ◦ ≤ θ ≤ θ ml / G sl , θ ml / ≤ θ ≤ ◦ , (2)where θ denotes an arbitrary angle within the range [0 , ◦ ] , θ − dB denotes the angle of the half-power beamwidth, and θ ml denotes the main lobe width in units of degrees. Therelationship between θ ml and θ − dB is θ ml = 2 . · θ − dB . G is the maximum antenna gain, and this can be obtained by G = 10 log (cid:18) . θ − dB / (cid:19) , (3)The sidelobe gain G sl can be expressed as G sl = − . · ln( θ − dB ) − . . (4) C. Receive Power Model
The RX power is modeled as [19] P dBmrx = P dBmtx + G tx + G rx − W + 10 n log λ πd , (5)where, P dBmrx and P dBmtx are the RX and TX powers, G rx and G tx are the RX and TX antenna gains, W is the shadowingmargin, λ is the carrier wavelength, and d is the distance fromthe BS to the mobile relay on the train. We can approximate G rx and G tx with G , and compute the d as a function oftime, then the RX power is modeled as P dBmrx ( t ) = P dBmtx + 2 G − W + 10 n log λ πd ( t ) . (6)Denoting B the system bandwidth, and NF the noise figureof the receiver chain, we model thermal noise as P dBmnoise = −
174 + 10 log B + NF . (7)The received SNR is determined by not only the receivedsignal power but also the noise power and can be expressedas [36], [37] SN R ( t ) = P rx ( t ) P noise . (8) D. Problem Formulation
As we know, the transmission power allocation is a keymechanism to energy consumption, if the transmission powercan be allocated properly, the energy consumption will bereduced greatly, therefore, the transmission power should beoptimized to achieve high energy efficiency. Here, we formu-late the transmission power optimization problem to minimizeenergy consumption.The energy efficiency optimization problem of train-groundmmWave communication can be formulated as max
EE, (9)where EE denotes the energy efficiency and can be expressedas EE = DE , (10) D denotes the total amount of transmission data and the totalenergy consumption is E .When maximizing the energy efficiency, we only need tominimize the energy consumption and ensure that the amountof data is greater than a certain value simultaneously, then theproblem of (10) can be transformed as follows: (cid:26) min Es.t. D ≥ D fixed , (11)Assume that the transmission power at each segment isa constant P i , then the total energy consumption can beexpressed as E = (cid:80) i P i t .Notice that t = d i v , the problem of (11) can be expressedas min N (cid:80) i =1 d i v P i s.t. D ≥ D fixed . (12)This is a nonlinear minimization problem where objectivefunction is a linear function about P i and both d i and v canbe seen as a constant, and the constraint indicates that P i ≥ , i ∈ [1 , N ] .To reduce the energy consumption, we should ensure thetotal amount of transmission data. Now, we analyze the systemconstraint of this optimization problem. First, according to theShannon capacity formula, the achievable data rate is deter-mined by the received SNR [38], [39], and the instantaneousrate is formulated as R ( t ) = log (1 + SN R ( t )) , (13)Based on the linear position prediction model, the systemwill switch to the i th beam at time (cid:80) i − j =1 d j /v and keepsthis beam until time (cid:80) ij =1 d j /v , then the total amount oftransmission data of the i th beam is D i = (cid:90) i (cid:80) j =1 d j /v i − (cid:80) j =1 d j /v log (1 + SN R ( t )) dt, (14)Approximate the SNR of the segment with it at the midpointof this segment, as shown in Fig. 3, then D i can be estimatedas D i ≈ log (1 + SN R midi ) · d midi v , (15)where, SN R midi is the SNR at the midpoint of the i th segmentand d midi is the distance between BS and the midpoint of eachsegment of the rail.According to (8), SN R midi = P i + 2 G − W + 10 n log λ πd midi −
174 + 10 log B + NF , (16)From the geometry, d midi = ( d l − i − (cid:88) j =1 d j − d i + d , (17) Fig. 3. Midpoint approximation of the network.
From the approximate formula, we can get that the totalamount of transmission data is D = N (cid:80) i =1 d i .For problem of (12), D = N (cid:88) i =1 D i ≈ N (cid:88) i =1 log (1 + SN R midi ) · d midi v , (18)From the geometry, the inter-BS distance d i can be calcu-lated as d i = d [tan( N + 1 − i ) θ − tan( N − i ) θ ] , i ∈ [1 , N ] , (19) θ is determined by N and can be obtained by θ = arctan (cid:18) d l d (cid:19) N . (20)Second, when transmission power is a constant, that is,transmission power of each segment is the same, we denote itas P , and then D fixed can be calculated as D fixed = (cid:90) dl v log (1 + SN R ( t )) dt, (21)where SN R ( t ) = P + 2 G − W + 10 n log λ πd ( t ) −
174 + 10 log B + NF , (22) d ( t ) = (cid:34) d + (cid:18) d l − vt (cid:19) (cid:35) . (23)From above, we formulate the energy efficiency optimiza-tion problem and analyze its constraint, in the next section, thepower minimization algorithm is proposed to solve problem(12) with low complexity.IV. P OWER C ONTROL A LGORITHM
Here, we propose a power minimization algorithm for theformulated problem which can achieve rational power alloca-tion. The main idea is using Lagrangian multiplier method andbased on the algorithm, we adjust the transmission power andget the final result. To be simplified, the power minimization problem in thispaper can be expressed as min N (cid:80) i =1 a i P i s.t. N (cid:80) i =1 log (1 + c i + gP i ) ≥ D fixed , (24)where a i = d i v , (25) g = 1 −
174 + 10 log B + NF , (26) c i = 2 G − W + 10 n log λ πd midi −
174 + 10 log B + NF . (27)To solve this problem, we use Lagrangian multiplier methodand construct a Lagrangian function as follows: L = N (cid:88) i =1 a i P i − λ (cid:34) N (cid:88) i =1 log (1 + c i + gP i ) − D fixed (cid:35) , (28)Finding partial derivative of variable P i and then we get theoptimal solution. Let ∂L∂P i = 0 and d L d λ = 0 , then P i = 2 Dfixedai · N − − c i g . (29)From (29), we can obtain all transmission power allocationclearly. V. P ERFORMANCE A NALYSIS
From the analysis above, we can see that N determines θ , and d i is related to N , besides, the value of N is larger, d midi and SN R midi are more accurate. Since the number ofsegments N has a big impact on our schemes, here we analyzethe energy consumption when N tends to infinity.To be simplified, let ϕ i ( θ ) = tan( N + 1 − i ) θ − tan( N − i ) θ, (30) Q = v · D fixed d , (31) M = 2 G − W, (32)Then the energy consumption can be calculated as E = N (cid:88) i =1 d i v P i = d v N (cid:88) i =1 ϕ i ( θ ) 2 Dfixedai · N − − c i g = d vg N (cid:88) i =1 ϕ i ( θ ) · Qϕi ( θ ) · N − d v N (cid:88) i =1 ϕ i ( θ ) (cid:18) g + M + 10 n log λ π (cid:19) + d v N (cid:88) i =1 ϕ i ( θ ) · n log ( d l − i − (cid:88) j =1 d j − d i + d . (33) The formula contains three parts and we take the limitsseparately to obtain the final result.For the first part, we can obtain that lim N →∞ N (cid:88) i =1 ϕ i ( θ ) · Qϕi ( θ ) · N = H + K (2 QK − , (34)where H = d l d = tan N θ = N (cid:88) i =1 ϕ i ( θ ) , (35) K = arctan H = N θ. (36)For the second part, we can obtain that lim N →∞ N (cid:88) i =1 ϕ i ( θ ) (cid:18) g + M + 10 n log λ π (cid:19) = H (cid:18) g + M + 10 n log λ π (cid:19) . (37)For the last part, we can obtain that lim N →∞ N (cid:88) i =1 ϕ i ( θ ) · n log ( d l − i − (cid:88) j =1 d j − d i + d = H · n log d . (38)Then we can get the result that lim N →∞ E = lim N →∞ N (cid:88) i =1 d i v P i = d v (cid:20) H (cid:18) n πd λ − M (cid:19) + Kg (cid:16) QK − (cid:17)(cid:21) . (39)From (39), we can obtain the limit value of energy con-sumption and it should be noted that with the increase of N ,the value will become smaller and tends to be fixed finally.VI. P ERFORMANCE E VALUATION
In this section, we evaluate the performance of our energyefficiency schemes under various system parameters and wealso analyze the situation which takes velocity estimation errorinto account. Specifically, we make a comparison of fourschemes to show the optimization effect.
TABLE ISIMULATION PARAMETERSParameter Symbol ValueDistance from a BS to the rail d
20 mAngle of the half-power beamwidth θ − dB ◦ Shadowing margin W
10 dBPath loss exponent n λ B NF v
300 km/hTransmisson power P
40 dBm and 50dBm
We use the network geometry as shown in Fig. 2, andthe simulation parameters are summarized in Table I. In
40 60 80 100 120 140 dl (m) E n e r g y C o n s u m p t i o n ( J ) MCTPOTPAMTPA
Fig. 4. Energy consumption comparison under different d l ( P = 40 dBm ) . this example, it is assumed that the position and velocitymeasurement is done at the edge of each BS’s coverage, thepower distribution is symmetrical. A. Comparison With Other Schemes
In order to analyze the energy consumption of the schemeand further show the optimization results, a new scheme isintroduced here, that is, combining the two power allocationmethods, and four schemes are summarized as follows:
Maintain constant transmission power (MCTP) : Main-tain constant transmission power P throughout the process. Optimization transmission power allocation (OTPA) :Allocate the transmission power rationally using power mini-mization algorithm.
Mixed transmission power allocation (MTPA) : Maintainconstant transmit power P within the range [0 , d l / , and thenuse the power minimization algorithm for power allocationwithin the range [ d l / , d l / . When N tends to infinity (OTPA( N → ∞ )) : Allocatethe transmission power rationally by power minimizationalgorithm and then find the limit when N tends to infinityby formula (39).MTPA is a hybrid optimization scheme and OTPA( N → ∞ )is the limit value of OTPA. The energy consumption of fourschemes is simulated as follows.In Fig. 4, we plot the energy consumption comparison offour schemes under different inter-BS distances d l . From theresults, we can observe that energy consumption increases withthe distance and the latter three optimization schemes haveplayed a role in reducing energy consumption especially when d l > m . The energy consumption of MCTP is higher whendistance is far and the growth rate will be larger when distanceis farther, from this, we can also discover the importance ofreducing energy consumtion. To be specific, when d l = 140 m ,OTPA saves about . energy compared with MCTP.Compare OTPA and MTPA, the optimization effect of MTPAis better and can achieve lower energy consumption, but OTPAis also a good choice to some extent. Furthermore, we can seethat the energy consumption of OTPA( N → ∞ ) is lower thanOTPA, the result is as we calculated.
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Fig. 5. Energy efficiency comparison under different d l ( P = 40 dBm ) .
40 60 80 100 120 140 dl (m) E n e r g y C o n s u m p t i o n ( J ) MCTPOTPAMTPA
Fig. 6. Energy consumption comparison under different d l ( P = 50 dBm ) . In Fig. 5, we plot the energy efficiency comparison of fourschemes under different inter-BS distances d l . Again, bothOTPA and MTPA can achieve higher energy efficiency. When d l is small, the energy efficiency of OTPA is higher and theoptimization effect is better compared with MTPA. In thissituation, OTPA can be adopted as a green scheme. And with d l increases, the optimization effect of MTPA is graduallygetting better. When d l > m , the energy efficiency offour schemes is approaching the same. Besides, the energyefficiency of OTPA( N → ∞ ) is the highest which verifies ourcalculation result.We also plot the energy consumption comparison of fourschemes when P = 50 dBm in Fig. 6. Similarly, we canobserve that all three optimization schemes reduce the energyconsumption greatly and improve the energy efficiency oftrain-ground communication. The inter-BS distance is larger,the optimization effect is better. The energy efficiency com-parison results are shown in Fig. 7.In Fig. 8 and Fig. 10, we plot the energy consumptioncomparison of four schemes under different velocity v . Fromthe results, we can observe that our schemes can still achievegood performance in different speed situations, and energyconsumption decreases with the increase of velocity. When
40 60 80 100 120 140 dl (m) E n e r g y E / c i e n c y ( b i t / J ) MCTPOTPAMTPA
Fig. 7. Energy efficiency comparison under different d l ( P = 50 dBm ) .
140 180 220 260 300 v (km/h) E n e r g y C o n s u m p t i o n ( J ) MCTPOTPAMTPA
Fig. 8. Energy consumption comparison under different v ( P = 40 dBm ) .
140 180 220 260 300 v (km/h) E n e r g y E / c i e n c y ( b i t / J ) MCTPOTPAMTPA
Fig. 9. Energy efficiency comparison under different v ( P = 40 dBm ) .
140 180 220 260 300 v (km/h) E n e r g y C o n s u m p t i o n ( J ) MCTPOTPAMTPA
Fig. 10. Energy consumption comparison under different v ( P = 50 dBm ) .
140 180 220 260 300 v (km/h) E n e r g y E / c i e n c y ( b i t / J ) MCTPOTPAMTPA
Fig. 11. Energy efficiency comparison under different v ( P = 50 dBm ) . v = 300 km/h , the value of latter three schemes are very smallcompared with MCTP, and the value gradually approacheszero because the distance is only m ( d l / in calculationwhich results in a small value. Compare Fig. 8 and Fig. 10, wecan see that when P increases, energy consumption increasesfor a certain value of v . The energy efficiency comparisonresults are shown in Fig. 9 and Fig. 11. It can be seen thatwhen P = 40 dBm , the energy efficiency of OTPA is higherthan MTPA, but the situation is reversed when P = 50 dBm .In summary, our schemes consume lower energy and canachieve higher energy efficiency under different system pa-rameters. B. Velocity Estimation Error
Since the velocity estimation error has an important impacton the performance of beam switching, we now investigate itin the same method. Here, we assume the velocity estimationerror is Gaussian, i.e. ˆ v = v + v e , where v is the true velocityand v e ∼ N (0 , σ v ) .We plot the energy consumption comparison of fourschemes under different d l when σ v = (0 . v ) and σ v =(0 . v ) in Fig. 12 and Fig. 14. We can obtain that when take
40 60 80 100 120 140 dl (m) E n e r g y C o n s u m p t i o n ( J ) MCTPOTPAMTPA
Fig. 12. Energy consumption comparison under different d l when σ v =(0 . v ) .
40 60 80 100 120 140 dl (m) E n e r g y E / c i e n c y ( b i t / J ) MCTPOTPAMTPA
Fig. 13. Energy efficiency comparison under different d l when σ v =(0 . v ) .
40 60 80 100 120 140 dl (m) E n e r g y C o n s u m p t i o n ( J ) MCTPOTPAMTPA
Fig. 14. Energy consumption comparison under different d l when σ v =(0 . v ) .
40 60 80 100 120 140 dl (m) E n e r g y E / c i e n c y ( b i t / J ) MCTPOTPAMTPA
Fig. 15. Energy efficiency comparison under different d l when σ v = (0 . v ) .
40 60 80 100 120 140 dl (m) E n e r g y C o n s u m p t i o n ( J ) MCTPOTPAMTPA
Fig. 16. Energy consumption comparison under different d l when σ v =(0 . v ) ( P = 50 dBm ) .
40 60 80 100 120 140 dl (m) E n e r g y E / c i e n c y ( b i t / J ) MCTPOTPAMTPA
Fig. 17. Energy efficiency comparison under different d l when σ v =(0 . v ) ( P = 50 dBm ) . velocity estimation error into account, our schemes can alsoachieve lower energy consumption similar to the result in Fig.4, where energy consumption increases with the increase of d l . Through comparison, we can also observe that the energyconsumption of four schemes in Fig. 14 is lower than thosein Fig. 12, it is because that the value of velocity v in Fig.14 is bigger than that in Fig. 12 as the result in Fig. 8.Besides, it should be noted that the energy consumption ofOTPA( N → ∞ ) is always lower than OTPA as we expected.We also plot the energy efficiency comparison of fourschemes under different d l in Fig. 13 and Fig. 15. As wecan see, OTPA, MTPA and OTPA( N → ∞ ) can also performwell with velocity estimation error similar to the result in Fig.5. Without loss of generality, we plot the energy consumptioncomparison and energy efficiency comparison of four schemeswhen P = 50 dbm in Fig. 16 and Fig. 17.VII. C ONCLUSION
MmWave communication has the potential to solve theproblem of train-ground communication for HSTs. Consider-ing a beam switching method based on the position informa-tion of HSTs, this paper proposes an energy efficiency powercontrol scheme where the transmission power is allocatedrationally through the power minimization algorithm. We alsodevelop a hybrid optimization scheme and the situation whichthe limit of the number of segments tends to infinity isconsidered. Extensive simulations have demonstrate that ourschemes can achieve lower energy consumption and higherenergy efficiency. In the future work, we will consider aspecific channel model and evaluate the energy efficiency ofthe scheme where the Doppler effect has been eliminated.R
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Lei Wang was born in Shanxi, China, in 1997. Shereceived the B.S. degree in mathematics and ap-plied mathematics from Beijing Jiaotong University,Beijing, China, in 2019. She is currently pursuingthe M.S. degree with the State Key Laboratory ofRail Traffic Control and Safety, Beijing JiaotongUniversity, Beijing, China. Her research interest ismillimeter-wave wireless communications. Bo Ai received the M.S. and Ph.D. degrees fromXidian University, China. He studies as a Post-Doctoral Student at Tsinghua University. He was aVisiting Professor with the Electrical EngineeringDepartment, Stanford University, in 2015. He iscurrently with Beijing Jiaotong University as a FullProfessor and a Ph.D. Candidate Advisor. He is theDeputy Director of the State Key Lab of Rail TrafficControl and Safety and the Deputy Director of theInternational Joint Research Center. He is one of themain people responsible for the Beijing Urban RailOperation Control System, International Science and Technology CooperationBase. He is also a Member, of the Innovative Engineering Based jointlygranted by the Chinese Ministry of Education and the State Administrationof Foreign Experts Affairs. He was honored with the Excellent PostdoctoralResearch Fellow by Tsinghua University in 2007.He has authored/co-authored eight books and published over 300 academicresearch papers in his research area. He holds 26 invention patents. He hasbeen the research team leader for 26 national projects. His interests includethe research and applications of channel measurement and channel modeling,dedicated mobile communications for rail traffic systems. He has been notifiedby the Council of Canadian Academies that, based on Scopus database, hehas been listed as one of the Top 1% authors in his field all over the world.He has also been feature interviewed by the IET Electronics Letters. He hasreceived some important scientific research prizes.Dr. Ai is a fellow of the Institution of Engineering and Technology. He isan Editorial Committee Member of the Wireless Personal Communicationsjournal. He has received many awards, such as the Outstanding YouthFoundation from the National Natural Science Foundation of China, the QiushiOutstanding Youth Award by the Hong Kong Qiushi Foundation, the NewCentury Talents by the Chinese Ministry of Education, the Zhan TianyouRailway Science and Technology Award by the Chinese Ministry of Railways,and the Science and Technology New Star by the Beijing Municipal Scienceand Technology Commission. He was a co-chair or a session/track chairfor many international conferences. He is an IEEE VTS Beijing ChapterVice Chair and an IEEE BTS Xi’an Chapter Chair. He is the IEEE VTSDistinguished Lecturer. He is an Editor of the IEEE TRANSACTIONSON CONSUMER ELECTRONICS. He is the Lead Guest Editor of SpecialIssues of the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY,the IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, andthe International Journal of Antennas and Propagation.
Yong Niu (M’17) received the B.E. degree inElectrical Engineering from Beijing Jiaotong Uni-versity, China, in 2011, and the Ph.D. degree inElectronic Engineering from Tsinghua University,Beijing, China, in 2016.From 2014 to 2015, he was a Visiting Scholar withthe University of Florida, Gainesville, FL, USA. Heis currently an Associate Professor with the StateKey Laboratory of Rail Traffic Control and Safety,Beijing Jiaotong University. His research interestsare in the areas of networking and communications,including millimeter wave communications, device-to-device communication,medium access control, and software-defined networks. He received the Ph.D.National Scholarship of China in 2015, the Outstanding Ph.D. Graduates andOutstanding Doctoral Thesis of Tsinghua University in 2016, the OutstandingPh.D. Graduates of Beijing in 2016, and the Outstanding Doctorate Disserta-tion Award from the Chinese Institute of Electronics in 2017. He has served asTechnical Program Committee member for IWCMC 2017, VTC2018-Spring,IWCMC 2018, INFOCOM 2018, and ICC 2018. He was the Session Chairfor IWCMC 2017. He was the recipient of the 2018 International Union ofRadio Science Young Scientist Award.
Xia Chen ([email protected]) received her B.Eng.and Ph.D. degrees from Beijing Jiaotong Universityin 1997 and 2003, respectively. She has been withBeijing Jiaotong University since 2003, where sheis currently an associate professor with the Schoolof Electronic and Information Engineering. Her re-search interests include mobile channel modeling,multicarrier transmission, and radio resource man-agement of wireless networks. She is a member ofthe Chinese Institute of Electronics.