1 Joint Communication and Computation Design in Transmissive RMS Transceiver Enabled Multi-Tier

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Joint Communication and Computation Design in

Transmissive RMS Transceiver Enabled Multi-Tier

Computing Networks

Zhendong Li, Wen Chen, Senior Member, IEEE, Ziwei Liu, Hongying Tang, and Jianmin Lu, Member, IEEE

Abstract—In this paper, a novel transmissive reconﬁgurable

meta-surface (RMS) transceiver enabled multi-tier computing

network architecture is proposed for improving computing ca-

pability, decreasing computing delay and reducing base station

(BS) deployment cost, in which transmissive RMS equipped with

a feed antenna can be regarded as a new type of multi-antenna

system. We formulate a total energy consumption minimization

problem by a joint optimization of subcarrier allocation, task

input bits, time slot allocation, transmit power allocation and

RMS transmissive coefﬁcient while taking into account the

constraints of communication resources and computing resources.

This formulated problem is a non-convex optimization problem

due to the high coupling of optimization variables, which is

NP-hard to obtain its optimal solution. To address the above

challenging problems, block coordinate descent (BCD) technique

is employed to decouple the optimization variables to solve the

problem. Speciﬁcally, the joint optimization problem of subcar-

rier allocation, task input bits, time slot allocation, transmit

power allocation and RMS transmissive coefﬁcient is divided

into three subproblems to solve by applying BCD. Then, the

decoupled three subproblems are optimized alternately by using

successive convex approximation (SCA) and difference-convex

(DC) programming until the convergence is achieved. Numerical

results verify that our proposed algorithm is superior in reducing

total energy consumption compared to other benchmarks.

Index Terms—reconﬁgurable meta-surface (RMS) transceiver,

multi-tier computing network, block coordinate descent (BCD)

technique, successive convex approximation (SCA), difference-

convex (DC) programming.

I. INTRODUCTION

THE continuous evolution of wireless communications has

spawned many emerging applications and services, e.g.,

telemedicine, industrial Internet and smart Internet-of-Things

(IoT) [1], [2]. In these computing and communication-oriented

application scenarios, a large number of devices and sensors

need to carry out continuous communication and computing,

which greatly increases the requirements for devices and sen-

sors. Currently, such computing and communication networks

This work is supported by National key project 2020YFB1807700 and

2018YFB1801102, by Shanghai Kewei 20JC1416502 and 22JC1404000,

Pudong PKX2021-D02 and NSFC 62071296.

Z. Li, W. Chen, and Z. Liu are with the Department of Electronic

Engineering, Shanghai Jiao Tong University, Shanghai 200240, China (e-mail:

lizhendong@sjtu.edu.cn; wenchen@sjtu.edu.cn; ziweiliu@sjtu.edu.cn).

H. Tang is with the Science and Technology on Microsystem Lab-

oratory, Shanghai Institute of Microsystem and Information Technol-

ogy, Chinese Academy of Sciences, Shanghai 200050, China (e-mail:

tanghy@mail.sim.ac.cn).

J. Lu is with the Wireless Technology Laboratory, Huawei Technologies,

Shanghai 201206, China (e-mail: lujianmin@huawei.com).

(Corresponding author: Wen Chen.)

face two main challenges. First, due to the small size of

these devices and sensors, the communication, storage and

computing capabilities are usually limited, so they cannot

support computing-intensive tasks well, which will result in

large computing delays and affect users’ quality-of-service

(QoS) [3]. Therefore, the key issues that the next generation

communication network needs to solve are considering how

to reduce the computing delay and improve the computing ca-

pability of the network. In addition, since the next-generation

communication network may use higher frequency bands, the

propagation loss will become larger, so its coverage will be

reduced. In order to achieve the same coverage as existing

communication networks, the number of base stations (BSs)

deployed needs to be increased. Moreover, in order to improve

the QoS of users, the BS of the next-generation communication

network will adopt more antennas, which will increase the

required radio frequency (RF) chains, thereby increasing the

cost of a single BS. Therefore, how to reduce the deployment

cost of the BS is another key challenge that needs to be solved

urgently in the next-generation communication network.

A. Related Works

1) MEC systems: To address the ﬁrst challenge, powerful

computing nodes (CNs) or mobile edge computing (MEC)

servers can be deployed at the network edge (i.e. usually

co-located with an access point (AP) or BS), which is the

recently proposed MEC technology [4]–[8]. This technology

mainly provides cloud-like computing by deploying MEC

servers distributedly in the network, and is widely regarded

as an effective means to liberate mobile devices from heavy

computing tasks. In the MEC system, devices and sensors

with limited computing capability can ofﬂoad computation-

intensive and latency-sensitive tasks to nearby BSs and APs

equipped with MEC servers for remote execution, which

can greatly reduce computing latency [9]. It is worth noting

that the prerequisite for achieving such a goal is that the

computing tasks of the devices and sensors can be successfully

ofﬂoaded. However, since some devices and sensors may

be located at the cell edge, their ofﬂoading rate is limited,

which makes the computing delay at CN or MEC longer

than local computing. As a result, these devices and sensors

often have to rely on their own resources for computing,

which often cannot well support applications for computation-

intensive and latency-sensitive tasks. Therefore, it is imperative

to improve the ofﬂoading capability from the communication

arXiv:2210.15399v1 [eess.SP] 27 Oct 2022

perspective, thereby improving the performance of computing

and communication networks.

2) Design of MEC systems: In recent years, the design of

MEC communication systems has been widely discussed in

academia [10]–[16]. Note that in the MEC system, ofﬂoading

strategies play a crucial role. At present, MEC ofﬂoading

strategies are mainly divided into binary ofﬂoading strategies

and partial ofﬂoading strategies [17]. The binary ofﬂoading

strategy mainly decides whether computing tasks are executed

locally on devices and sensors or ofﬂoaded to CNs or MEC

servers for remote execution. The typical tasks used for

this ofﬂoading strategy are usually simple and indivisible.

The partial ofﬂoading strategy usually needs to divide the

computing task into several sub-tasks, and these sub-tasks can

be executed locally through devices and sensors and ofﬂoaded

to the CNs or MEC servers for parallel execution. Such parallel

computing can greatly improve the computing capability and

reduce the computing delay of the MEC system. The typical

tasks used for this ofﬂoading strategy are usually multiple ﬁne-

grained processes. In addition, since the rate of ofﬂoading

will also affect the performance of the MEC system, based

on the above two ofﬂoading strategies, many research works

have studied the joint communication and computing resource

allocation in different scenarios to improve the performance

of the MEC system.

In previous work, the research on MEC systems can be di-

vided into single-user MEC systems [10]–[13] and multi-user

MEC systems [4], [14]–[16]. In single-user MEC communi-

cation systems, Zhang et al. provided a theoretical framework

for energy-optimal MEC under stochastic wireless channels

by optimizing the execution of mobile applications in mobile

devices (i.e., mobile execution) or ofﬂoading to the cloud (i.e.,

cloud execution) to save energy for mobile devices [10]. You

et al. proposed an energy-efﬁcient computing framework that

includes a set of policies to control CPU cycles for local

computing modes, energy transfer, and ofﬂoad time division

for other ofﬂoading modes [12]. As for the multi-user MEC

system, Ren et al. studied the delay minimization problem

in the multi-user time division multiple access system with

joint communication and computing resource allocation [14].

Dai et al. proposed a novel two-layer computation ofﬂoading

framework in heterogeneous networks. Then, in a multi-

task MEC system, the joint computation ofﬂoading and user

association problem is formulated to minimize the overall

energy consumption [15]. In addition to the research on the

basic MEC system, some emerging communication systems

assisted by the MEC are also investigated. Bai et al. studied

the application of MEC in unmanned aerial vehicle (UAV)

communication networks, and designed an energy-efﬁcient

physical layer security optimization algorithm [11]. Liu et al.

studied the application of MEC in the Internet-of-Vehicles,

and introduced a vehicle fog edge computing paradigm. It

is then formulated as a multi-stage Stackelberg game to be

solved. However, for multi-user MEC systems, the distribution

locations of devices and sensors are usually random and

different. Devices and sensors located at the cell edge have

a large path loss to the APs or BSs, which will consume more

communication resources for ofﬂoading, resulting in uneven

resource allocation and user fairness issues.

3) RMS communication systems: Moreover, faced with the

challenge of high cost of BS deployment in next-generation

communication networks, reconﬁgurable meta-surface (RMS)

may be a potential solution. RMS has recently been proposed

as an emerging technology combining metamaterials and

communications, which can be used to reduce network costs,

improve network coverage, spectrum- and energy- efﬁciency

[18]–[22]. RMS consists of numerous low-cost passive units,

and the amplitude and phase shift of the incident signal can

be changed by artiﬁcially adjusting these units. It is worth

noting that since RMS is a passive device, it only adjusts

the amplitude and phase of the incident signal, so it will not

introduce additional noise, which makes it well applied to a

collaborative communication network [19]. In addition, com-

pared with the existing multi-antenna technologies equipped

with a large number of RF chains, the hardware cost and power

consumption required by passive RMS are much lower, which

also greatly stimulates research on RMS-based multi-antenna

communication systems. Overall, these advantages mentioned

above have greatly promoted the application of RMS in next-

generation communication networks [23], [24].

4) Design of RMS enabled communication systems: Based

on the above advantages, RMS has attracted extensive atten-

tion in academia and industry. Nowadays, RMS is mainly

used to assist and enable traditional communication networks,

where by combining active-passive beamforming design, the

performance of the network can be improved with reﬂective or

transmissive RMS [25]–[33]. First, some works on reﬂective

RMS-assisted communication networks has been carried out.

Ur Rehman et al. addressed the joint active and passive

beamforming optimization problem under ideal and practical

IRS phase shifts for an IRS-assisted multi-user downlink

MIMO system, where the spectrum efﬁciency is maximized by

minimizing the sum mean squared error (MSE) of the user’s

received symbols [25]. Zen et al. considered an IRS-assisted

uplink non-orthogonal multiple access (NOMA) system in

which a semi-deﬁnite relaxation technique is employed to

maximize the sum rate of users [28]. Furthermore, the research

on transmissive RMS-assisted communication networks is also

in progress. Zhang et al. proposed an intelligent omni-surface

(IOS) assisted downlink communication system, where the

IOS is able to forward the received signal to the user in a

reﬂection or transmission manner, thereby enhancing the wire-

less coverage [30]. Niu et al. investigated a MIMO network

assisted by reﬂection-transmission reconﬁgurable intelligent

surface (RIS), where the weighted sum rate is maximized

based on an energy splitting (ES) scheme [33]. Furthermore, in

addition to assisting and enabling traditional communication

networks, the RMS can also act as transceivers in communica-

tion networks. Since the reconﬁgurability of the RMS helps it

to expand the number of passive units without increasing the

number of expensive and bulky active antennas, the reﬂective

RMS equipped with an active feed antenna can be used as a

new type of transmitter [34]. Since the feed blockage of the

transmissive RMS transceiver is less than that of the reﬂective

RMS transceiver, the aperture efﬁciency can be designed to

be higher, and the operating bandwidth can be designed to

be more stable, so it is more efﬁcient [35], [36]. At present,

some work on the uplink and downlink transmissive RMS

transceiver design has been carried out [36], [37], but it is still

in its infancy. Meanwhile, the application of the transmissive

RMS transceiver in various communication scenarios also has

potential.

B. Motivation and Contributions

Based on the above backgrounds and challenges, in order to

improve the computing capability, reduce the computing delay,

and reduce the BS deployment cost of the communication

and computing network, we propose a transmissive RMS

transceiver enabled multi-tier computing networks, where the

decoding-and-forward (DF) relay is equipped with a CN,

and transmissive RMS transceiver is equipped with an MEC

server. In general, the computing capability of the DF relay

should be comparable to or greater than that of the device

to make computational cooperation feasible. To the best of

our knowledge, the current research on communication and

computing networks with transmissive RMS transceivers is

still in its infancy, and the demand for improving network com-

puting capability, reducing computing delay, and reducing BS

deployment cost has greatly promoted this work. In this paper,

we minimize total energy consumption by jointly optimizing

the subcarrier allocation, task input bits, time slot allocation,

transmit power allocation, and RMS transmissive coefﬁcient.

It is challenging to address this non-convex optimization

problem due to the high coupling of optimization variables.

Hence, we need to design an effective optimization algorithm

for solving it. In summary, the main contributions of this paper

can be summarized as follows:

•We propose a novel transmissive RMS transceiver en-

abled multi-tier computing framework, where the devices

and sensors can ofﬂoad tasks to DF relay and RMS

multi-antenna system for calculations, thereby improving

computing capability and reducing computing latency

of the networks. Meanwhile, we formulate the energy

consumption minimization problem for joint optimization

of the subcarrier allocation, task input bits, time slot allo-

cation, transmit power allocation, and RMS transmissive

coefﬁcient. Since the objective function and the partial

constraints are non-convex due to the high coupling of

the optimization variables, the problem is a non-convex

optimization problem and is challenging to solve directly.

•To address the formulated energy consumption minimiza-

tion problem, we ﬁrst divide the non-convex optimization

problem into three sub-problems based on the block

coordinate descent (BCD) algorithm. Speciﬁcally, in the

ﬁrst sub-problem, given the time allocation, task input

bits, and RMS transmissive coefﬁcient, we solve the

joint optimization problem for the subcarrier allocation

and user transmit power allocation. In the second sub-

problem, we deal with the joint optimization problem

for the time allocation and task input bits by apply-

ing successive convex approximation (SCA) when the

subcarrier allocation, user transmit power allocation and

RMS transmissive coefﬁcient are ﬁxed. For the third

sub-problem, the RMS transmissive coefﬁcient can be

obtained by using difference-convex (DC) programming

and SCA when other optimization variables are given.

Finally, the three sub-problems are optimized alternately

until convergence is achieved.

•Through the numerical simulation, we verify the effec-

tiveness of the proposed joint optimization algorithm for

the subcarrier allocation, task input bits, time slot allo-

cation, transmit power allocation and RMS transmissive

coefﬁcient compared with the benchmark algorithms, i.e.,

it can decrease the total energy consumption. In addition,

the proposed multi-layer ofﬂoad-computation scheme is

superior to other ofﬂoad schemes, and the introduction of

transmissive RMS transceivers can greatly reduce the cost

of overall network deployment, which has great potential

in next-generation communications.

The rest of this paper is organized as follows. Section

II elaborates the system model and optimization problem

formulation for the transmissive RMS transceiver enabled

multi-tier computing networks. Section III presents the pro-

posed optimization algorithm for the formulated optimization

problem. In Section IV, numerical results demonstrate that

our algorithm has good convergence and effectiveness. Finally,

conclusions are given in Section V.

Notations: Scalars are denoted by lower-case letters, while

vectors and matrices are represented by bold lower-case letters

and bold upper-case letters, respectively. |x|denotes the abso-

lute value of a complex-valued scalar x. For a square matrix X,

tr(X),rank(X),XH,Xm,n and kXkdenote its trace, rank,

conjugate transpose, m, n-th entry and matrix norm, respec-

tively, while X0represents that Xis a positive semideﬁnite

matrix. Similarly, for a general matrix A,rank(A),AH,

Am,n and kAkalso denote its rank, conjugate transpose, m, n-

th entry and matrix norm, respectively. In addition, CM×N

denotes the space of M×Ncomplex matrices. INdenotes

an dentity matrix of size N×N.jdenotes the imaginary unit,

i.e., j2=−1.E{·} represents the expectation of random

variables. Finally, the distribution of a circularly symmetric

complex Gaussian (CSCG) random vector with mean µand

covariance matrix Cis denoted by CN (µ, C), and ∼stands

for ‘distributed as’.

II. SYSTEM MODEL AND PROBLEM FORMULATION

In this section, we mainly describe the system model and

problem formulation.

A. Network Model

As shown in the Fig. 1, we consider a multi-tier MEC

network model based on a relay-transmissive RMS multi-

antenna system, which includes Ksingle-antenna task nodes

(TN), a single-antenna DF relay and Mtransmissive elements

RMS multi-antenna system. In this paper, we consider the

orthogonal frequency division multiple access (OFDMA) sys-

tem, where the channel of bandwidth Bis divided into N

subcarriers, each with a bandwidth of W=B/N. Inter-

subcarrier interference is negligible, and the cyclic preﬁx is

large enough to overcome inter-symbol interference. Note that

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1JointCommunicationandComputationDesigninTransmissiveRMSTransceiverEnabledMulti-TierComputingNetworksZhendongLi,WenChen,SeniorMember,IEEE,ZiweiLiu,HongyingTang,andJianminLu,Member,IEEEAbstractInthispaper,anoveltransmissiverecongurablemeta-surface(RMS)transceiverenabledmulti-tiercomputingnetworkarc...

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