1 Energy Efﬁcient Train-Ground mmWave Mobile Relay System for High Speed Railways

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Energy Efﬁcient Train-Ground mmWave Mobile

Relay System for High Speed Railways

Lei Wang, Bo Ai, Fellow, IEEE, Yong Niu, Member, IEEE, Zhangdui Zhong, Fellow, IEEE,

Shiwen Mao, Fellow, IEEE, Ning Wang, Member, IEEE, and Zhu Han, Fellow, IEEE

Abstract—The rapid development of high-speed railways

(HSRs) puts forward high requirements on the corresponding

communication system. Millimeter wave (mmWave) can be a

promising solution due to its wide bandwidth, narrow beams, and

rich spectrum resources. However, with the large number of an-

tenna elements employed, energy-efﬁcient solutions at mmWave

frequencies are in great demand. Based on a mmWave HSR

communication system with multiple mobile relays (MRs) on top

of the train, a dynamic power-control scheme for train-ground

communications is proposed. The scheme follows the regular

movement characteristics of high-speed trains and considers

three phases of train movement: the train enters the cell, all

MRs are covered in the cell, and the train leaves the cell. The

transmit power is further reﬁned according to the number of

MRs in the cell and the distance between the train and the

remote radio head. By minimizing energy consumption under

ever, permission to use this material for any other purposes must be obtained

from the IEEE by sending a request to pubs-permissions@ieee.org. This study

was supported by the National Key Research and Development Program under

Grant 2021YFB2900301; in part by National Key R&D Program of China

(2020YFB1806903); in part by the National Natural Science Foundation of

China Grants 61801016, 61725101, 61961130391, and U1834210; in part

by the State Key Laboratory of Rail Trafﬁc Control and Safety (Contract

No. RCS2021ZT009), Beijing Jiaotong Universityand supported by the open

research fund of National Mobile Communications Research Laboratory,

Southeast University (No. 2021D09); in part by the Fundamental Research

Funds for the Central Universities, China, under grant number 2022JBQY004

and 2022JBXT001; and supported by Frontiers Science Center for Smart

High-speed Railway System; in part by the Fundamental Research Funds

for the Central Universities 2020JBM089; in part by the Project of China

Shenhua under Grant (GJNY-20-01-1). S. Mao’s work is supported in part by

the NSF Grant ECCS-1923717. Z. Han’s work is partially supported by NSF

CNS-2107216 and CNS-2128368. (Corresponding authors: B. Ai, Y. Niu.)

L. Wang is with the State Key Laboratory of Rail Trafﬁc Control and

Safety, Beijing Jiaotong University, Beijing 100044, China, and also with

Beijing Engineering Research Center of High-speed Railway Broadband

Mobile Communications, Beijing Jiaotong University, Beijing 100044, China

(email: lleiwang@bjtu.edu.cn).

B. Ai is with the State Key Laboratory of Rail Trafﬁc Control and Safety,

Beijing Jiaotong University, Beijing 100044, China, and also with Peng Cheng

Laboratory and Henan Joint International Research Laboratory of Intelligent

Networking and Data Analysis, Zhengzhou University, Zhengzhou 450001,

China (email: boai@bjtu.edu.cn).

Y. Niu is with the State Key Laboratory of Rail Trafﬁc Control and Safety,

Beijing Jiaotong University, Beijing 100044, China, and also with the National

Mobile Communications Research Laboratory, Southeast University, Nanjing

211189, China (email: niuy11@163.com).

Z. Zhong is with the State Key Laboratory of Rail Trafﬁc Control

and Safety, Beijing Jiaotong University, Beijing 100044, China (e-mail:

zhdzhong@bjtu.edu.cn).

S. Mao is with the Department of Electrical and Computer Engineering,

Auburn University, Auburn, AL 36949-5201 USA (email: smao@ieee.org).

N. Wang is with the School of Information Engineering, Zhengzhou

University, Zhengzhou, China, 450001 (email: ienwang@zzu.edu.cn).

Z. Han is with the Department of Electrical and Computer Engineering

at the University of Houston, Houston, TX 77004 USA, and also with the

Department of Computer Science and Engineering, Kyung Hee University,

Seoul, South Korea, 446-701 (email: zhan2@uh.edu).

the constraints of the transmitted data and transmit power

budget, the transmit power is allocated to multiple MRs through

the multiplier punitive function-based algorithm. Comprehensive

simulation results, where the velocity estimation error is taken

into account, are provided to demonstrate the effectiveness of the

proposed scheme over several baseline schemes.

Index Terms—Energy efﬁciency, high-speed railway (HSR),

millimeter wave (mmWave), mobile relay (MR).

I. INTRODUCTION

HIGH-SPEED railways (HSRs) are in high development

due to its high mobility, great comfort, and high reliabil-

ity. Compared to traditional means of transportation, HSR is

changing how people travel and brings huge economic beneﬁts

while being convenient [1]. The HSR network is rapidly

expanding and will promote the development of various tech-

nologies, especially in the ﬁeld of HSR communications [2].

To be in line with future smart rail, HSR communication

systems are expected to provide both train control services

and mobile multimedia services for train passengers. With the

help of smart technologies, we will not only see faster high-

speed trains, but also high-speed data services for passengers,

fully automated train operation and real-time monitoring in

smart railway systems. Nevertheless, it is challenging to enable

these high data rate required applications using current railway

communication systems. The data rate of the most widely used

global system for mobile communications for railways is at

kb/s-level, and that of the long term evolution for railways is

at Mb/s-level, which is still insufﬁcient for many smart railway

wireless communication services [3]. As a result, millimeter

wave (mmWave) communication systems attract signiﬁcant

interest.

MmWave can support multi-gigabit wireless data transmis-

sion, thus becoming a strong candidate for HSR communi-

cation systems to fulﬁll the increasing capacity requirements

[4]. However, it also brings about many new challenges. A

major drawback is that mmWave communications suffer from

blockage and increased path loss compared to communications

in lower frequency bands [5]. The propagation conditions

at mmWave are more severer since mmWave signals cannot

penetrate most solid materials [6]. The solution to this problem

is directional beamforming technique based on large-scale an-

tenna arrays [7]. Beamforming allows signals to be transmitted

in a speciﬁc direction through the transmitter (TX) and receiver

(RX) antennas, by which a highly directional transmission link

is established.

arXiv:2210.09873v1 [cs.IT] 18 Oct 2022

Traditionally, base stations (BSs) have been the major power

consumers in wireless communication networks, even in the

absence of data transmission. This problem is even more

severe in the mmWave band. Due to the high bandwidth,

high volume of trafﬁc and high transmit power, the energy

consumption of a single mmWave BS is signiﬁcantly higher

than that of an existing single sub-6 GHz BS. Moreover,

mmWave small BSs are usually deployed with high-power

macro BSs in heterogeneous networks (HetNets) to increase

system capacity. This means that massive trafﬁc growth comes

at the cost of huge energy consumption and a much larger

carbon footprint. However, it is not desirable to increase

system capacity through higher energy levels [8]. Although

mmWave technology can greatly improve the performance

of HSR communication networks, these high data rate links

also lead to increased device power consumption and a

corresponding growth in system energy consumption. It is

critical to overcome the energy consumption challenges of

HSR mmWave communication networks due to the rising

transmission rate demands.

Energy efﬁciency is a key performance metric for the

ﬁfth and future sixth generation communication systems, and

has attracted extensive attention from both academia and

industry [9]. The design of future wireless communication

networks should take energy efﬁciency into account and meet

more stringent energy efﬁciency requirements. HSR is widely

recognized as a green transportation that requires an organic

combination of energy efﬁciency and functional design [3]. It

is of great practical importance to study the energy efﬁciency

problem of train-ground mmWave communications for HSRs.

A. Related Work

A signiﬁcant amount of work is focused on the resource

allocation to improve the energy efﬁciency of wireless com-

munication systems [10]–[17]. With the goal of maximiz-

ing the energy efﬁciency of orthogonal frequency division

multiple access HetNets employing wireless backhaul, Ref.

[10] designs power and bandwidth allocation schemes by

decoupling the joint optimization problem into two convex

optimization problems. Zhang et al. in [11] consider a HetNet

derive a closed-form expression for the power saving gain.

Trafﬁc ofﬂoading schemes for a single SBS and multiple

SBS scenarios are developed to minimize on-grid energy

consumption under the quality of service (QoS) constraint. A

multi-objective optimization problem subject to channel, time

slot, transmission power and QoS constraints is formulated

in [12] to exploit the trade-off between energy efﬁciency and

spectral efﬁciency in device-to-device (D2D) communications

supporting energy harvesting. Energy and task allocation in

wireless-powered mobile edge computing networks are also

solved by convex optimization techniques in [13]. In particular,

the authors consider randomly arriving tasks and situations

where future channel state information is unknown. A game

theory-based approach is proposed for sub-channel and power

allocation in ultra dense networks where long term evolution

(LTE) and Wireless Fidelity (WiFi) coexist [14]. Ref. [15]

studies the energy scheduling problem of D2D communication

with energy harvesting capability, especially considering the

energy consumption of the device to process data. In recent

years, deep reinforcement learning approaches have also been

used to solve energy efﬁciency maximization problems [16],

[17].

The energy consumption of mmWave communication sys-

tems is of particular concern due to the high frequency

bands and the large number of antenna elements. Several

optimization schemes have been proposed to achieve energy

efﬁcient mmWave communications [18]–[21]. For mmWave

cell-free systems, Ref. [18] selects several main paths in the

angle domain and performs information feedback and trans-

mission power allocation on these paths. Ref. [19] proposes

to utilize the energy recovered from radio frequency signals

and coordinate data transmission through multiple BSs to

improve the energy efﬁciency of ultra-dense HetNets with

mmWave massive multiple-input multiple-output (MIMO).

In [20], the authors focus on the design of analog beamformers

in mmWave multi-input single-output systems and propose a

low-complexity solution under power constraints. Digital and

hybrid mmWave beams are also designed in [21] through a

hybrid mapping algorithm to maintain the dynamic balance

between the energy efﬁciency and beam ripples.

Recently, mmWave HSR communications have been exten-

sively studied [22]–[26]. The throughput performance of the

HSR communication system with a two-hop architecture has

been shown to outperform the performance of direct commu-

nication between BSs and passengers, and deploying multiple

independent mobile relays (MRs) is superior to deploying a

single MR [22]. In this two-hop network, the type of MR

can be either amplify-and-forward or decode-and-forward, and

there is a trade-off between the performance and cost of the

MR. 5G New Radio (NR) is believed to further enhance

the performance of HSR communication systems. Ref. [23]

describes the performance requirements for deploying 5G NR

systems in HSR scenarios and provides the physical layer

design and initial access mechanism to support high-speed

mobile scenarios. Conventional beam alignment methods may

introduce large angular offsets in HSR systems, the authors

in [24] propose a fast initial access scheme by taking advan-

tage of learning results from historical beam training process.

Moreover, a network structure which utilizes low frequency

bands to improve the performance of mmWave frequencies

is applied to guarantee the robustness of the entire network.

Xu et al. in [25] consider a practical signal propagation

environment, and propose a channel tracking scheme based

on angle information, while a hybrid beamforming scheme

is also designed to reduce overhead. A channel model for

mmWave HSR systems is developed in [26], which is a three-

dimensional model that captures channel non-stationarity in

time, space and frequency.

Notably, most of these prior works do not consider the

energy efﬁciency optimization for HSR communications. Al-

though there have been some studies on energy efﬁciency

related problems, there are not many discussions on energy-

efﬁcient problem in the unique and challenging HSR scenario.

Due to the fast moving speed of high-speed trains, HSR

communications suffer from severe Doppler shift and pene-

tration loss, and these problems are more severe at mmWave

frequencies. In addition, frequent handovers are performed in

HSR systems, which is launched by a large number of user

equipment almost simultaneously and has to be completed in

a short period of time [27]. To address these issues, the third

Generation Partnership Project (3GPP) has adopted a two-hop

architecture in HSR, where data from passengers to BSs is

forwarded by roof MRs [22]. High-speed trains provide a lot

of space for large-scale antennas, and hence roof-top MR can

also provide high-speed data transmission services for HSR

passengers with the help of high frequency bands such as

mmWave [28]. Moreover, multiple MRs are expected to further

enhance system throughput. However, different from single

MR, multi-MRs consumes more energy. Providing maximum

transmit power to each MR results in the system operating

at a much lower efﬁciency than its optimal capability, and

the power consumed by the system is not fully utilized and

is greatly wasted. Therefore, how to achieve dynamic power

allocation among multiple MRs to save the energy of HSR

communication systems while meeting the data transmission

requirements is a key issue.

B. Contributions and Organization

In this paper, we consider the train-ground mmWave com-

munication for HSRs, where an mmWave remote radio head

(RRH) can serve multiple MRs installed on the train simulta-

neously [29]. Directional beamforming is employed at the TX

and RX, to compensate for the path loss at higher frequencies.

Then an energy efﬁciency optimization problem is formulated

and a power allocation scheme based on the multiplier punitive

function algorithm is developed. The scheme considers three

phases of train movement: (i) the train enters the cell, (ii) all

the MRs are covered in the cell, and (iii) the train leaves the

cell. The transmit power of the second phase is dynamically

adjusted according to the distance between the train and the

RRH, and the transmit power of the other two phases is

allocated according to the number of MRs in the cell. Main

contributions are as follows.

•This paper investigates the energy efﬁciency problem of

mmWave multi-MR HSR systems, where more than one

MR is mounted on the roof of the train. A dynamic power

allocation scheme is designed to support a number of

RRH-MR links simultaneously. In particular, the process

of the train entering or leaving the cell is divided into

several stages depending on the number of MRs in

the cell, and when all MRs are in the cell, the power

is allocated sequentially in several consecutive location

bins.

•An optimization problem is formulated to achieve high

energy efﬁciency of train-ground communications. The

optimization problem imposes a strict constraint on the

transmit power of the system, that is, the sum of the

transmit powers of multiple MRs is less than the transmit

power budget. In addition, energy consumption is mini-

mized under the constraint that the total transmitted data

is greater than the threshold.

BBU Pool

RRH

MBS

Fig. 1. A control/user-plane splitting network for HSR communications.

•The formulated optimization problem is a multivariate

non-convex non-linear problem, which is difﬁcult to

obtain the optimal power allocation results. A multiplier

punitive function-based algorithm is proposed to real-

ize power allocation of different MRs during the train

movement. Simulations verify that the optimized power

allocation scheme can improve energy efﬁciency of the

system. Moreover, the impact of errors in estimating train

speed is also analyzed.

The remainder of this paper is organized as follows. Sec-

tion II describes the system model and formulates the en-

ergy efﬁciency maximization problem into a non-convex non-

linear minimization problem. Section III proposes a multiplier

punitive function-based algorithm to solve the optimization

problem. Section IV presents performance evaluation and

explores the effect of speed error. Finally, Section V concludes

this paper.

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. System Model

To meet the high-speed transmission demands of HSR

passengers, a control/user-plane splitting network architecture

is adopted in this paper [3], as shown in Fig. 1. Control

signaling is carried on the control-plane, and data information

from passengers is ofﬂoaded to the track-side mmWave RRH.

The network is also a HetNet deployment, with the mmWave

RRH deployed within the coverage of macro cell for high

data rate transmission, and MBS operating in lower frequency

bands for coverage and reliability. Due to the high cost, it

is impractical to deploy continuous mmWave RRHs. This

separation of user plane and control plane allows ﬂexible

deployment of mmWave RRHs to improve transmission rates

in small areas while maintaining coverage performance.

To provide reliable connectivity for passengers, multiple

MRs are deployed on top of the train, forming a two-hop ar-

chitecture. MRs are mainly used for receiving and forwarding

data, and all communications between RRHs and passengers

are completed through MRs, thus avoiding severe train body

penetration loss. Compared to a single MR, multiple MRs take

advantage of space diversity gain to further improve system

throughput. In the ﬁrst hop, MRs establish connections with

the RRH through radio access links, which can be both at

frequency bands below 6 GHz and mmWave frequencies. In

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1EnergyEfcientTrain-GroundmmWaveMobileRelaySystemforHighSpeedRailwaysLeiWang,BoAi,Fellow,IEEE,YongNiu,Member,IEEE,ZhangduiZhong,Fellow,IEEE,ShiwenMao,Fellow,IEEE,NingWang,Member,IEEE,andZhuHan,Fellow,IEEEAbstractTherapiddevelopmentofhigh-speedrailways(HSRs)putsforwardhighrequirementsonthecorrespon...

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