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Rate-Splitting Multiple Access Aided Mobile Edge
Computing with Randomly Deployed Users
Pengxu Chen, Hongwu Liu, Yinghui Ye, Liang Yang, Kyeong Jin Kim, and Theodoros A. Tsiftsis
Abstract—In this paper, a rate-splitting multiple access
(RSMA) scheme is proposed to aid a mobile edge computing
(MEC) system where multiple randomly deployed users offload
their computation tasks to a MEC server. Considering that users
are divided into the center and edge groups, a cognitive radio
(CR)-inspired rate-splitting is designed to enable the paired users
to simultaneously offload to MEC server. Under the CR princi-
ples, the rate-splitting parameters are jointly designed to attain
the maximum achievable rate for the secondary user, meanwhile
maintaining the primary user’s offloading performance same as
in orthogonal multiple access. For the case of the paired users
with fixed locations, we derive a closed-form expression for the
successful computation probability (SCP) achieved by the RSMA-
aided MEC (RSMA-MEC) scheme and formulate a SCP maxi-
mization problem to obtain the optimal offloading parameters.
To reveal the impact of the user locations on the offloading
performance of the RSMA-MEC system, various distance-based
user pairing schemes are investigated by invoking stochastic
geometry techniques. We provide closed-form expressions for
the SCPs achieved by the user pairing schemes to characterize
the offloading performance. Pros and cons of the user locations
to maximize the SCP are highlighted. Simulation results verify
the accuracy of the analytical results and clarify the superior
offloading performance achieved by the RSMA-MEC scheme,
which attains a higher SCP than the existing schemes.
Index Terms—Rate-splitting multiple access (RSMA), cognitive
radio (CR), mobile edge computing (MEC), stochastic geometry.
I. INTRODUCTION
With the proliferation of real-time services, e.g., augmented
reality, virtual reality, intelligent robots, and autonomous driv-
ing, plenty of user equipments (UEs) are suffering from ever-
increasing computing pressures. As a promising solution for
latency-critical and computation-intensive applications, mobile
edge computing (MEC) enables UEs to offload their tasks to
edge servers for nearby processing, which boosts computing-
performance and reduces network-latency over centralized
remote cloud processing [1], [2]. By integrating computing,
storage, and networking resource at MEC servers or base-
stations (BSs), the sixth generation (6G) of wireless networks
P. Chen and H. Liu are with the School of Information Science and
Electrical Engineering, Shandong Jiaotong University, Jinan 250357, China
(e-mail: cpx17863275219@163.com, liuhongwu@sdjtu.edu.cn).
Y. Ye is with Shaanxi Key Laboratory of Information Communication
Network and Security, Xi’an University of Posts & Telecommunications,
Xi’an 710061, China (e-mail: connectyyh@126.com).
L. Yang is with College of Computer Science and Electronic Engineering,
Hunan University, Changsha 410082, China, (e-mail: liangy@hnu.edu.cn).
K. J. Kim is with Mitsubishi Electric Research Laboratories, Cambridge,
MA 02139 USA (e-mail: kkim@merl.com).
T. A. Tsiftsis is with the School of Intelligent Systems Sci-
ence and Engineering, Jinan University, Zhuhai 519070, China (e-mail:
theo tsiftsis@jnu.edu.cn).
is envisioned to provide benefits of ultra-low latency, ultra-
high bandwidth, and trusted computing for heterogeneous
applications [3].
A. Technical Literature Review
Offloading from massive UEs to MEC servers significantly
intensifies spectrum scarcity. Thus, wireless resource blocks
need to be utilized efficiently and suitable multiple access
schemes are required to attain high spectral efficiency (SE)
and guarantee quality of service (QoS) for MEC networks [4].
Towards that end, non-orthogonal multiple access (NOMA)
has been used in MEC networks to achieve enormous potential
benefits, including offloading latency minimization, energy
efficiency (EE) improvement, and computation successful rate
maximization [5]–[11]. On the other hand, applications of
cognitive radio (CR) techniques have established a significant
and ever-expanding field in wireless communications to in-
crease spectrum utilization and facilitate coexistence between
licensed and unlicensed transmissions in either the overlay or
underlay spectrum access mode. Thus, the integration of CR
techniques will be beneficial to future 6G wireless commu-
nications in developing spectrum agile multiple access and
corresponding MEC networks. To alleviate spectrum scarcity
of NOMA-aided MEC (NOMA-MEC) networks, CR tech-
niques have been widely applied in [6]–[11], where the QoS
requirements of the primary users (PUs) can be guaranteed by
intelligently controlling access parameters such as frequency
band and power level of the secondary users (SUs) [12].
However, as an essential component of NOMA receivers,
the decoding order of successive interference cancellation
(SIC) has a great impact on detection performance [13]–[15].
Taking into account channel state information (CSI) and QoS
requirements, several works on SIC processing have been
proposed to improve the system performance of NOMA-MEC
networks [10], [16]. To ensure power-level diversity required
for successful SIC processing, user scheduling and power
control strategies are needed in uplink NOMA networks [17].
As a multiple access strategy for future wireless com-
munications, rate-splitting multiple access (RSMA) was in-
vestigated for non-orthogonal transmission, interference man-
agement, and rate maximization [18]–[20]. Due to the high
SE/EE, reliability, and robustness for downlink and uplink
multiuser transmissions, RSMA has been regarded as a
promising enabling technology for the 6G wireless networks
[21]–[25]. In downlink RSMA, inter-user interference can
be partially decoded and partially treated as noise, which
not only balances the decoding performance and complexity,
2
but also provides flexibility to bridge NOMA and space
division multiple access (SDMA) [26]–[29] (see also [30]
and references therein). In [31], a more general downlink
rate-splitting framework was proposed for the multiple-input
multiple-output (MIMO) system with imperfect CSI at the
transmitter by exploiting the channel second-order statistics.
Compared to NOMA and SDMA, splitting messages according
to a priority strategy is beneficial to control power-domain
interference effectively and achieve a higher SE for downlink
transmission [26], [28], [32]. In [33], intelligent reflecting
surfaces (IRSs) were applied to aid the downlink RSMA
system, which achieved an enhanced outage performance
compared to IRS-aided downlink NOMA system. The RSMA-
assisted downlink transmission framework for cell-free mas-
sive machine-type communications was proposed in [34]. In
contrast to downlink RSMA, the split signal streams from
all users are fully decoded at the BS receiver using SIC in
uplink RSMA [20], [35]–[38]. Compared to uplink NOMA
with SIC processing, the benefit of applying uplink RSMA
is to achieve the full capacity region of multiple access
channels (MACs) [35]. However, the applications of RSMA
for uplink MACs are still in their infancy. Since the split signal
streams of all uplink users significantly increase the detection
complexity at the receiver, the optimal performance of uplink
RSMA strongly depends on the rate-splitting parameters and
the SIC decoding order at the receiver [20]. In [38], a rate-
splitting scheme was proposed to reduce user scheduling
complexity for an uplink NOMA system, in which the split
signal streams can be successively decoded even with the
same received power-level. In [39], two rate-splitting schemes
were proposed for an uplink NOMA system to improve user
fairness and outage performance. Considering the partial rate
constraints among users, the sum-rate was maximized by
applying uplink RSMA [20]. With the aid of minimum mean
square error (MMSE)-based SIC, uplink RSMA was used to
guarantee max-min user fairness in a single-input multiple-
output (SIMO) NOMA system [37]. For physical layer net-
work slicing, uplink RSMA was used to realize ultra-reliable
and low-latency (URLLC) and enhanced mobile broadband
communications (eMMB) [40]. In the aerial networks, up-
link RSMA was applied for enhancing the communication
reliability, reducing interference, and improving the weighted
sum-rate performance, respectively [19], [41], [42]. Moreover,
combining beamforming with uplink RSMA, the benefit of
RSMA was exploited for satellite communications [43], [44].
For uplink user cooperation, cooperative RSMA was proposed
in [45]. In [46], outage performance was analyzed for a
two-user uplink RSMA system considering all possible SIC
decoding order. Also, uplink rate-splitting was applied for
device-to-device cooperation in fog radio access networks
[47].
B. Motivations and Contributions
Although NOMA-MEC has enabled multiple UEs to offload
their tasks simultaneously to a BS, the adopted NOMA with
SIC cannot achieve the full capacity region of uplink MACs,
which constrains the system performance of NOMA-MEC
networks. On the other hand, to achieve full capacity region of
uplink MACs, exhaustive search was required to determine the
optimal SIC decoding order and transmit power allocation in
uplink RSMA [20], [37], which prohibits using uplink RSMA
from latency-critical MEC applications. To apply RSMA for
uplink MACs, the effective interference management and the
low-complexity SIC processing are imminent. In [48], a CR-
inspired rate-splitting scheme was proposed to maximize the
achievable rate of a SU, meanwhile maintaining the PU’s
outage performance same as in orthogonal multiple access
(OMA).
Motivated by the capacity region achieved by uplink RSMA
and CR-inspired rate-splitting, which avoids exhaustive search
to determine the optimal rate-splitting parameters, we propose
a RSMA-aided MEC (RSMA-MEC) scheme to increase the
successful computation probability (SCP) and reduce offload-
ing latency in a MEC system, which consists of a single
MEC server and multiple randomly deployed users. Since the
user locations significantly impact their channel conditions,
a reasonable and practical location modeling is essential to
evaluate the system performance. Therefore, we assume that
the locations of randomly deployed users follow a homoge-
neous Poisson Point Process (HPPP) [49]. Considering that
user locations and associated inter-user interference affect
transmission reliability, we divide users into a center group
and an edge group to form a two-user CR-inspired RSMA
and apply it to assist MEC 1. Specifically, from the center
group or the edge group, a user is selected as the PU. Then,
a user from the other group is selected as the SU. To reveal
the impact of user locations on the system performance of the
RSMA-MEC system, we consider various distance-based user
pairing schemes. When the PU and SU are randomly selected
from the center and edge groups (or from the edge and center
groups), respectively, the user pairing scheme is named by
RCRE (or RERC). To ensure that the PU can tolerate a relative
high interference-temperature, the nearest user in the center
group or the edge group is preferred to be selected as the PU.
Accordingly, when the nearest user in the center group (or the
edge group) is selected as the PU, the user pairing schemes
that choose the nearest and farthest users in the other group
as the SU are named by NCNE and NCFE (or NENC and
NEFC), respectively.
The main contributions of this paper are summarized as
follows:
•An RSMA-MEC scheme is proposed to assist randomly
deployed users to offload their tasks to the MEC server.
In the proposed RSMA-MEC scheme, the paired two
users are treated as the PU and SU, respectively, and
the CR-inspired rate-splitting is conducted at the SU,
which allows the PU and SU to simultaneously offload
to the MEC server and avoids the deterioration of the
1Although uplink RSMA can accommodate more than two users for
simultaneous transmissions, multiple users in each user-pair results in an
increased SIC processing complexity and the prolonged decoding delay,
which is not preferable for the considered delay-critical MEC system. To
accommodate more than two users in each user-pair, advanced SIC techniques
with low complexity and ultra-low decoding delay are required in the future
works.
3
PU’s offloading. Towards that end, the optimal power
allocation factor, rate-splitting factor, and SIC decoding
order are jointly designed under the CR principles, which
maximizes the achievable rate for the SU.
•In the case of the fixed user locations, we derive a
closed-form expression for the SCP achieved by the
RSMA-MEC scheme for the MEC system. Subject to the
constraints of latency budget and computation capability,
a SCP maximization problem is formulated. Then, we
obtain the closed-form expression for the optimal offload-
ing time and task-offloading factor, which can achieve the
allowed maximum SCP for the MEC system. In addition,
the obtained optimal offloading parameters can be used
to reduce the offloading latency for the MEC system.
•The analytical expressions for the SCPs of various user
pairing schemes are derived. With the obtained optimal
offloading parameters, simulation results are presented
to verify the derived analytical expressions and reveal
the impact of user pairing on the SCP for the RSMA-
MEC system. Particularly, the NCNE and NENC are
the best schemes to achieve the maximum SCP when
the PU is selected from the center and edge groups,
respectively, while RCRE and RERC are the most light-
weight schemes when the PU is selected from the center
and edge groups, respectively. Compared to the existing
NOMA-MEC scheme, the superior SCP performance of
the proposed RSMA-MEC scheme is verified by simula-
tion results.
The remainder of this paper is organized as follows: Section
II presents the RSMA-MEC system model. In Section III,
the CR-inspired rate-splitting scheme is presented. In Section
IV, the SCP achieved by the RSMA-MEC scheme is derived
and the optimal offloading parameters are obtained by solving
the formulated SCP maximization problem. In Section V,
various distance-based user pairing schemes are studied. In
Section VI, simulation results are presented to corroborate the
superior performance of the proposed RSMA-MEC scheme,
and Section VII summarizes this work.
II. SY ST EM MO DE L
The considered RSMA-MEC system consists of a MEC
server and multiple randomly deployed users who want to
offload their computation tasks to the MEC server. We assume
that each user is equipped with a single antenna to offload data
to the MEC sever, which is integrated at a BS equipped with
a single receive-antenna. The coverage area of the BS, also
the coverage of the MEC server, is represented by a disk with
radius RE, as depicted in Fig. 1. The MEC server is located
in the center of the disk and serves the randomly deployed
users within the coverage area. Moreover, the coverage area
of the MEC server is divided into two regions distinguished
by a radius RC. Accordingly, the users located in the disk
with radius RCform the center group and the users located in
the remaining region within the coverage area form the edge
group. We assume that the locations of the users in the center
group (the edge group) follow a HPPP with a density µΦC
(µΦE), [50], [51].
h
a
h
b
R
C
R
E
Ua and Ub offload the partial
tasks to the MEC server a nd then
compute the remaining tasks.
MEC server
t
1
ė
0
Parameters
determination
t
4
ė
0
Results
downloading
t
2
Task offloading by Ua and
Ub
t
3
Task computing at
Ua, Ub, and the MEC
server
center user
edge user
T
U
b
U
a
澳
Fig. 1. The RSMA-MEC System Model.
To assist task offloading from multiple users to the MEC
server, multiple user-pairs can be formed with each pair
consisting of one user selected from the center group and
another one selected from the edge group 2. In this paper,
we consider the distance-based user pairing, i.e., two users
are paired by using their distances to the MEC server, which
can be obtained from CSI statistics. Through allocating the
orthogonal time/frequency resource blocks to different user-
pairs and applying the two-user uplink RSMA within each
pair, which prevents excessive inter-user interference in each
pair, simultaneous offloading from multiple users to the MEC
server can be realized. Without loss of generality, we first
consider RSMA-MEC offloading within one user-pair, in
which the paired users are denoted by Uaand Ub, respectively.
Moreover, we assume that each user is equipped with a single-
core CPU or a less powerful multi-core CPU and works in
either the transmission mode or the computation mode [5].
For the user Uk(k∈ {a, b}), its computation tasks contain
the data of Mkbits, which are bit-wise independent and can
be arbitrarily segmented into sub-tasks. Constrained by the
limited computing capability, each user may not be able to
compute all the tasks by itself within the latency budget T,
which is assumed to be less than the coherence time of channel
fading. Therefore, the paired users perform uplink RSMA to
offload a portion of their tasks of ηkMkbits to the MEC server
and then compute the remaining tasks of (1 −ηk)Mkbits by
themselves, where ηk(0 ≤ηk≤1) is the task offloading
factor of Uk.
In the considered RSMA-MEC system, an entire computa-
tion period consists of four time phases as depicted in Fig.
1. In the first time phase of the computation period, t1, the
2When multiple systems are considered for uplink RSMA, a new cooper-
ating or co-existing system model is required to realize simultaneous uplink
transmissions and interference management. For this new system model, we
need to conduct extensive investigations for developing a new CR-inspired
uplink RSMA and extending our employed HPPP model by incorporating
interference management.
4
offloading and rate-splitting parameters are determined for the
paired users. After that, Uaand Uboffload their tasks to the
MEC server using uplink RSMA in the second time phase t2.
In the third time phase t3, the successfully offloaded tasks are
computed at the MEC server, meanwhile Uaand Ubcompute
their remaining tasks locally. In this paper, we assume that
the MEC server begins its computation immediately after the
completion of the offloading, i.e., there is no queue delay
at the MEC server. In the last time phase t4, the computed
results of the offloaded tasks are fed back to Uaand Ub,
respectively. As it will be shown in the next subsection, since
the optimal rate-splitting parameters are determined using
the simple closed-form expressions, the consumed time t1
for the rate-splitting parameter determination can be ignored.
Considering that the data size of the download results is small
enough [52], t4can be neglected compared to t2and t3
[5], [53]–[55]. Thus, the considered offloading-computation
scenario mainly consists of the task offloading phase t2, in
which Uaand Uboffload partial tasks to the MEC server,
and the task execution phase t3, in which Ua,Ub, and MEC
server compute their respective tasks simultaneously. Given
the offloading-computation latency budget T, which is less
than the channel coherence interval, the computation period
satisfies t2+t3≤T.
A. Task Offloading Phase
In this subsection, the operations of Ua,Ub, and the MEC
server in the task offloading phase are presented.
The channel fading from Ukto the MEC server is denoted
by √ℓkhk, where hkdenotes the small-scale fading coefficient,
which is modeled as independent and identically distributed
(i.i.d.) circular symmetric complex Gaussian (CSCG) random
variables with zero mean and unit variance. ℓkis the distance-
related path-loss component determined by ℓk≜(1 + dv
k)−1
with dkdenoting the distance from Ukto the MEC server and
vdenoting the path-loss exponent. In this study, the bounded
path loss model is considered to ensure that the path loss is
always greater than one for any distance, i.e., 1 + dv
k>1.
Moreover, we assume that the users are fixed or have low
mobility. Then, quasi-static fading is adopted in the system
model, which indicates that the channel fading coefficient
hkkeeps constant within the entire computation period and
can change from one computation period to another one. In
addition, we assume perfect CSI to evaluate the theoretical
system performance achieved by the RSMA-MEC scheme
[11], [14], [39].
In the two-user uplink RSMA, Ubsplits its message signal
˜xbinto two sub-messages ˜xb,1and ˜xb,2. Without loss of gen-
erality, we assume that the message signals, {˜xb,˜xb,1,˜xb,2},
are independently encoded using independent Gaussian codes
to generate the transmit signals, {xb, xb,1, xb,2}, respectively.
For Ua, the transmit signal is denoted by xa. We assume all
the transmit signals have the unit power in expectation. For
each transmission block, the received signal at the MEC server
can be expressed as:
yMEC =pPaℓahaxa+pαPbℓbhbxb,1
+p(1 −α)Pbℓbhbxb,2+w, (1)
where Pkis the transmit power of Uk,wis the complex
additive white Gaussian noise at the MEC server with zero
mean and variance σ2, and αis the power allocation factor
satisfying 0≤α≤1.
To attain the allowed maximum achievable rate for Ua,
SIC with the decoding order xb,1→xa→xb,2is utilized
at the MEC server. To reveal the theoretical performance of
the proposed RSMA-MEC scheme, we assume perfect SIC in
this study as those in [11], [14]. In general, all possible SIC
decoding orders at the MEC server can be classed into three
types as follows: xb,1→xb,2→xa,xa→xb,1→xb,2, and
xb,1→xa→xb,2. By using the logarithmic product law, it
can be shown that the achievable rates of Uaand Ubobtained
by applying xb,1→xb,2→xa(xa→xb,1→xb,2) equal to
those of applying xb→xa(xa→xb). In such a case, the SIC
processing in the considered RSMA-MEC system is equivalent
to that of a two-user uplink NOMA system. Consequently, the
decoding order xb,1→xa→xb,2is adopted in this paper to
generate robustness with respect to different CSI conditions,
as it will be shown in Section III.
Let ρa≜Paℓa
σ2and ρb≜Pbℓb
σ2denote the equivalent transmit
signal-to-noise ratios (SNRs) of Uaand Ub, respectively, the
received signal-to-interference-plus-noise-ratios (SINRs) and
SNR for decoding xb,1,xa, and xb,2are given by
γb,1=αρb|hb|2
ρa|ha|2+ (1 −α)ρb|hb|2+ 1,(2)
γa=ρa|ha|2
(1 −α)ρb|hb|2+ 1,(3)
and
γb,2= (1 −α)ρb|hb|2,(4)
respectively. Then, the task bits that can be offloaded via the
transmissions of xaand xb(or xb,1and xb,2) are given by
¯
Ra=t2BRaand ¯
Rb=¯
Rb,1+¯
Rb,2=t2B(Rb,1+Rb,2),(5)
where Ra= log2(1 + γa),Rb,1= log2(1 + γb,1), and
Rb,2= log2(1 + γb,2)denote the achievable rates for Uaand
Ubto transmit xa,xb,1, and xb,2, respectively, and Bis the
bandwidth of the frequency band allocated to Uaand Ub.
Corresponding to the transmissions of xa,xb,1, and xb,2,
the target offloading tasks are defined as ˆ
Ra≜ηaMa,ˆ
Rb,1≜
βηbMb, and ˆ
Rb,2≜(1 −β)ηbMb, respectively, where βis the
rate-splitting factor satisfying 0≤β≤1. If xa,xb,1, and xb,2
are decoded successfully, the total number of task bits to be
computed at the MEC server can be expressed as:
MMEC =ˆ
Ra+ˆ
Rb,1+ˆ
Rb,2=ηaMa+ηbMb.(6)
B. Task Execution Phase
We consider a hybrid offloading scenario that includes
partial offloading (0< ηk<1), fully local computation
(ηk= 0) and complete offloading (ηk= 1) [50]. In the task
execution phase, Uaand Ubcompute the task bits (1−ηa)Ma
and (1 −ηb)Mb, respectively, meanwhile the MEC server
computes the task bits MMEC .
5
The computation capabilities of each user and the MEC
server are denoted by fuser and fMEC , respectively, which
represent the corresponding CPU frequencies, respectively.
Denoting the number of the CPU cycles required for com-
puting one task bit by CCPU , if MkCCPU
fuser ≤T, a user can
compute all of its tasks locally. Otherwise, the time required
for carrying out the local computation can be written as:
tUk
3=(1 −ηk)MkCCPU
fuser
,(7)
To indicate the computation capability difference between the
MEC server and users, we assume fMEC =Nfuser with N >
1. Then, the execution time for the offloaded tasks MMEC can
be written as:
tMEC
3=MMEC CCPU
fMEC
=MMEC CCPU
Nfuser
.(8)
Considering the computation capability difference between the
MEC server and users, the time duration of the task execution
phase can be expressed as:
t3= max ntUk
3, tMEC
3o
= max (1 −ηk)MkCCPU
fuser
,MMEC CCPU
Nfuser .(9)
III. CR-INSPIRED RATE-SPLITTING
In the considered RSMA-MEC system, Uaand Ubshare
the same time/frequency resource block on the premise that
they do not introduce intolerable interference to each other.
Inspired by the CR principles [48], we treat Uaand Ubas
the PU and SU, respectively, and design a CR-inspired rate-
splitting to realize the two-user uplink RSMA. In the operation
of the CR-inspired rate-splitting, the offloading from the SU
to the MEC server is allowed only when the PU’s offloading
performance can be guaranteed to be the same as in OMA. In
other words, the delay-limited task offloading of the PU cannot
deteriorate compared to the scenario in which the PU occupies
the time/frequency resource block alone. In this section, we
elaborate the design principle, operations, and optimal rate-
splitting parameters of the CR-inspired rate-splitting.
The CR-inspired rate-splitting aims to attain the allowed
maximum achievable rate for the SU, meanwhile maintaining
the PU’s SCP the same as in OMA. To prevent error propa-
gation in SIC with the decoding order xb,1→xa→xb,2, the
successful detections of xb,1and xaare required. Further, the
signal xacan be detected successfully only when the following
constraints are satisfied, i.e.,
¯
Rb,1≥ˆ
Rb,1and ¯
Ra≥ˆ
Ra.(10)
When ¯
Rb,1≥ˆ
Rb,1, to ensure that the PU’s offloading does
not deteriorate during SIC with the decoding order xa→xb,2,
an interference threshold τis determined as [48]:
τ= max 0,ρa|ha|2
εa−1,(11)
where εa≜2
ηaMa
t2B−1. This interference threshold can be
computed at the MEC server and broadcasted to the SU prior
to offloading. Recalling the expressions for γaand ¯
Rain
Section II, if (1 −α)ρb|hb|2≤τ, we have the following
relationships:
Pr ¯
Ra≥ˆ
Ra= Pr t2Blog21 + ρa|ha|2
(1−α)ρb|hb|2+1 ≥ˆ
Ra
≥Pr t2Blog21 + ρa|ha|2
τ+1 ≥ˆ
Ra
(a)
=Pr t2Blog21 + ρa|ha|2≥ˆ
Ra,(12)
where the equality in step (a) holds due to the fact
Pr ρa|ha|2
τ+1 ≥εa= Pr ρa|ha|2≥εaconsidering that the
interference threshold is designed to tolerate any interfer-
ence whose power is less than or equal to τ[14], [16]. In
other words, if the received power of the interference signal
p(1 −α)Pbℓbhbxb,2satisfies (1 −α)ρb|hb|2≤τunder the
condition of Pr ¯
Rb,1≥ˆ
Rb,1= 1, the PU can offload
its tasks of ηaMabits successfully to the MEC server with
the same probability as that the PU occupies the allocated
time/frequency resource block alone. Thus, by assuming that
Pr ¯
Rb,1≥ˆ
Rb,1= 1 is guaranteed during the offloading, as it
will be explained later in this section, the successful detection
of xacan be guaranteed if τ > 0and (1 −α)ρb|hb|2≤τ.
The procedure of the CR-inspired rate-splitting can be
summarized as follows. First, the PU feeds back its CSI and
Pato the MEC server after estimating the CSI. Second, the
MEC server calculates τaccording to (11) and broadcasts it
to the SU in t1. Last, the SU compares τto its CSI and
determines the optimal rate-splitting parameters. With respect
to all possible CSI realizations, the operation of the CR-
inspired rate-splitting and associated optimal α∗and β∗are
jointly designed as follows:
Case I: 0< ρb|hb|2≤τ. In this case, the maximum
interference power-level caused by the SU’s offloading is not
greater than the interference threshold τ. Thus, the SU can
allocate all of Pbto transmit its signal. To maximize the
offloaded task-bits ¯
Rb=t2B(Rb,1+Rb,2)for the SU, all
of Pbshould be allocated to transmit xb,2, which is decoded
at the last stage of SIC without suffering from interference,
such that ¯
Rb=t2BRb,2is maximized. Consequently, there is
no power allocated to transmit xb,1.
As a result, the CR-inspired rate-splitting sets xb,2=xbin
Case I and the optimal rate-splitting parameters are given by
α∗= 0 and β∗= 0.(13)
Since rate-splitting is not performed at the SU in Case I, the
SIC decoding order xb,1→xa→xb,2degrades to xa→xb.
Then, the maximum task-bits that can be offloaded to the MEC
server by Uaand Ubin Case I can be expressed as
¯
R(I)
a=t2Blog21 + ρa|ha|2
ρb|hb|2+ 1,(14)
and
¯
R(I)
b=t2Blog21 + ρb|hb|2,(15)
respectively.
Case II: 0< τ < ρb|hb|2. In this case, the interference
resulted by the transmission of xb,2will surpass τif all Pb
6
is allocated to its transmission. Therefore, the transmit power
for the transmission of xb,2should satisfy (1−α)ρb|hb|2≤τ.
To maximize the offloaded task-bits ¯
Rb=t2B(Rb,1+Rb,2),
Rb,2= log2(1 + γb,2)should be maximized firstly subject to
the constraint Rb,2≤log2(1 + τ). Obviously, the maximum
Rb,2= log2(1 + τ)is achieved by setting γb,2=τ. Then, the
optimal power allocation factor in this case can be computed
as:
α∗= 1 −τ
ρb|hb|2.(16)
Substituting the above α∗into (2), the maximum offloaded
task-bits corresponding to the transmission of xb,1is given
by ¯
Rb,1=t2Blog21 + ρb|hb|2−τ
ρb|hb|2+τ+1 . Then, the maximum
task-bits that can be offloaded by Uaand Ubin this case can
be expressed as
¯
R(II)
a=t2Blog21 + ρa|ha|2
τ+ 1 ,(17)
and
¯
R(II)
b=t2Blog21+ ρb|hb|2−τ
ρa|ha|2+τ+ 1+t2Blog2(1+τ),
(18)
respectively.
Since the received SINR/SNR γa(α∗)and γb,2(α∗)provide
the necessary conditions for the successful detection of xaand
xb,2in SIC processing xb,1→xa→xb,2, only the failure
detection of xb,1can result in error propagation in SIC. To
avoid error propagation in SIC resulted by the failure detection
of xb,1,¯
R(II)
b,1≥ˆ
Rb,1needs to be satisfied to ensure the suc-
cessful detection of xb,1or equivalently ¯
R(II)
b≥ˆ
Rb=ηbMb.
Otherwise, both the PU and SU encounter outage. In the
CR-inspired rate-splitting, we set the target offloading task
ˆ
Rb,2=t2Blog2(1 + τ)for the transmission of xb,2. Recalling
ˆ
Rb,2= (1 −β)ηbMb, the optimal rate-splitting factor in Case
II is obtained by solving t2Blog2(1 + τ) = (1 −β)ηbMb,
which is given by
β∗= 1 −t2Blog2(1 + τ)
ηbMb
.(19)
As a result, only when Pr( ¯
Rb,1≥ˆ
Rb,1) = 1, i.e., ¯
Rb,1≥
ˆ
Rb,1(β∗)always holds true, the SU is allowed to offload its
tasks using rate-splitting; Otherwise, the SU keeps silence in
Case II. Even if the SU does not offload in Case II, the PU
can offload the task bits ¯
R(II)
a=t2Blog2(1 + ρa|ha|2).
Case III: τ= 0. In this case, the PU cannot successfully
offload its task of ηaMabits to the MEC server due to a weak
channel gain. We assume that the PU does not aware its weak
channel gain and still transmits to offload. Then, the SU will
allocate all Pbto transmit xb,1=xbwith the aim of avoiding
error propagation resulted by the failure detection of xa. Thus,
the optimal rate-splitting parameters are given by
α∗= 1 and β∗= 1,(20)
respectively, and the SIC decoding order xb,1→xa→xb,2
degrades to xb→xa. In Case III, the maximum task-bits that
can be offloaded by Uaand Ubare given by
¯
R(III)
a=t2Blog2(1 + ρa|ha|2)(21)
and
¯
R(III)
b=t2Blog21 + ρb|hb|2
ρa|ha|2+ 1,(22)
respectively.
Remark 1: In Cases I and III, the PU and SU perform the
offloading in the same way as that in the two-user NOMA-
MEC system. Therefore, the PU and SU will achieve the same
offloading performance as those in the two-user NOMA-MEC
system when Cases I and III occur. In Case II, the SU adjusts
its rate-splitting parameters flexibly to maximize the offloaded
task-bits, whereas the PU can successfully offload the task-
bits ηaMato the MEC server within the latency budget T,
just as it operates in OMA with delay-limited transmissions.
In Cases I and III, the optimal rate-splitting parameters are
binary. In Case II, the closed-form expressions for the optimal
rate-splitting parameters are presented in (16) and (19), which
can be easily computed at the SU. Therefore, the time phase
t1spent to find the optimal rate-splitting parameters is much
smaller than t2and t3, which justifies ignoring the time phase
t1in the considered RSMA-MEC system.
IV. SC P AN ALYS IS A ND MAXIMIZATION WITH FIXE D PU
AN D SU
In this section, a closed-form expression is derived for the
SCP achieved by the RSMA-MEC scheme considering that
the PU and SU have the fixed locations. Then, the optimal
offloading parameters are determined by solving the SCP
maximization problem.
A. SCP Analysis
For the considered RSMA-MEC system, when MkCCPU
fuser >
T,k∈ {a, b}, the SCP is defined as the probability of the event
that all the offloaded tasks are successfully computed at the
MEC server and all the remaining tasks are successfully and
locally computed at the paired users within the latency budget
T. When max tUa
3, tUb
3, tMEC
3> t3, the SCP is obviously
zero. Under the condition of max tUa
3, tUb
3, tMEC
3≤t3, the
SCP can be expressed as:
Ps=P(I)
s+P(II)
s+P(III)
s,(23)
where
P(I)
s= Pr n0< ρb|hb|2≤τ, ¯
R(I)
a≥ηaMa,¯
R(I)
b≥ηbMbo,
(24)
P(II)
s= Pr n0< τ < ρb|hb|2,¯
R(II)
a≥ηaMa,¯
R(II)
b≥ηbMbo,
(25)
and
P(III)
s= Pr nτ=0,¯
R(III)
a≥ηaMa,¯
R(III)
b≥ηbMbo,(26)
represent the SCP achieved by the RSMA-MEC scheme in
Cases I, II, and III, respectively. In other words, if the fixed PU
and SU offload tasks to the MEC server, both of their offloaded
task bits should be successfully decoded at the MEC server
7
during t2, meanwhile, the MEC server executes all the received
task bits and the PU and SU execute their own remaining task
bits successfully during t3.
Theorem 1: When the PU and SU have the fixed locations,
the SCP achieved by the RSMA-MEC scheme is given by
Ps=
ρae−εb
ρb−εa(1+εb)
ρa
ρa−ρb−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
,
if max tUa
3, tUb
3, tMEC
3≤t3,
0,otherwise,
(27)
where εb≜2
ηbMb
t2B−1.
Proof: See Appendix A.
Remark 2: For the RSMA-MEC system containing the fixed
PU and SU, Theorem 1 provides a closed-form expression for
the SCP, which involves only the CSI statistics and offloading
parameters, so that the SCP can be easily computed. In
addition, the results in Theorem 1 offer a possibility to obtain
the optimal offloading parameters that achieve the allowed
maximum SCP without involving instantaneous CSI.
Remark 3: When MkCCPU
fuser ≤T, both Uaand Ubcan
successfully compute their own tasks locally within the latency
budget, so that we have Ps= 1. In such a case, the optimal
offloading parameters can determined by η∗
a=η∗
b= 0,t∗
2= 0
and t∗
3=MkCCPU
fuser . As a result, rate-splitting is not conducted
when MkCCPU
fuser ≤T.
B. SCP Maximization
In the considered RSMA-MEC system, offloading from the
paired users occurs when MkCCPU
fuser > T . Accordingly, the SCP
maximization problem can be formulated as:
P0: max
t2,t3,ηa,ηbPs
C1:MkCCPU
fuser
> T, k ∈ {a, b},
C2:t2>0, t3>0, t2+t3≤T, (28)
C3: 0 < ηa<1,0< ηb<1.
Since the objective function Psin non-convex, the SCP
maximization problem is a non-convex problem, which cannot
be solved using the existing standard algorithms. However,
with the aid of the expression in (27), we have the following
proposition.
Proposition 1: When the PU and SU have the fixed loca-
tions, the maximum SCP can be achieved when t2+t3=T
and tUa
3=tUb
3=tMEC
3=t3are satisfied.
Proof: Using the monotonicity of Pswith respect to t2,
ηa, and ηb, the results in Proposition 1 can be proved by
contradiction.
Remark 4: The results in Proposition 1 indicate that the
maximum SCP can be achieved only if all the computation
capabilities of the MEC server, Ua, and Ubare fully exploited
during the task execution phase t3. Consequently, the MEC
server, Ua, and Ubcompute the task-bits as much as possible,
which results in the shortest duration for t3and also ensures
that the maximum SCP can be achieved.
Based on the results in Proposition 1, we can obtain the
optimal offloading parameters that maximize the SCP as in
the following corollary.
Corollary 1: When the PU and SU have the fixed locations,
the optimal offloading parameters that maximize the SCP are
given by
η∗
a=(N+ 1)Ma−Mb
(N+ 2)Ma
,(29)
η∗
b=(N+ 1)Mb−Ma
(N+ 2)Mb
,(30)
t∗
2=T−(Ma+Mb)CCPU
(N+ 2)fuser
,(31)
t∗
3=(Ma+Mb)CCPU
(N+ 2)fuser
.(32)
Proof: Substituting the condition tUa
3=tUb
3=tMEC
3=t3,
which guarantees that the maximum SCP is achievable, into
(7) and (8), we obtain the expressions (29) and (30). Then, t∗
3
is obtained by using (29) and (30), so does t∗
2.
Remark 5: The results in Corollary 1 provide several
insights on the optimal offloading and SCP maximization as
explained in the following. First, the offloading parameters
depend on the computation capabilities of the nodes, task-
bits, and latency budget, being irrespective of the paired user
locations. Thus, the results in Corollary 1 are immediately
applicable to the RSMA-MEC system containing the randomly
deployed users no matter where are the locations. Second, the
expressions of (29) and (30) indicate that more task bits should
be offloaded if the MEC server has a stronger computation
capability and vice versa. With the obtained t∗
2and t∗
3in (31)
and (32), not only the maximum SCP can be achieved, but
also paving a way to reduce the latency budget. For example,
by fixing the offloading time t2with the given Maand Mb,
the task computing time t3decreases with the increasing of
either fuser or N. Further, the constraints 0< η∗
a<1and
0< η∗
b<1indicate that 1
N<Ma
Mb< N + 1, which
requires a comparable tasks for the paired users. Considering
t2>0, the allowed maximum task bits to be computed by
the RSMA-MEC scheme satisfies Ma+Mb<(N+2)fuserT
CCPU
.
As N→ ∞,η∗
aand η∗
bapproach one, which means that
complete offloading is preferable if the MEC server has an
extremely strong computation power. In practice, since Nis
a finite number, partial offloading is conducted.
Remark 6: As Pa
σ2→ ∞ and Pb
σ2→ ∞, asymptotic
expressions for P(I)
sand P(II)
sin the high SNR region can
be derived as
P(I)
s=1
1 + εa1+dv
a
1+dv
b
and P(II)
s=εa
εa+1+dv
b
1+dv
a
,(33)
respectively, which results in P(I)
s+P(II)
s= 1 in the high SNR
region. In addition, we have P(III)
s= 0 for Case III. Thus, the
8
SCP approaches one as Pa
σ2→ ∞ and Pb
σ2→ ∞. As a result,
the optimal offloading parameters can be summarized as:
(η∗
a, η∗
b, t∗
2, t∗
3)=
0,0,0,MkCCPU
fuser ,MkCCPU
fuser ≤T,
shown in Corollary 1,MkCCPU
fuser
>T.
(34)
Substituting (34) into (27), the achieved maximum SCP can
be written as
P∗
s=ρae−ε∗
b
ρb−ε∗
a(1+ε∗
b)
ρa
ρa−ρb−ρbe−ε∗
a
ρa−ε∗
b(1+ε∗
a)
ρb
ρa−ρb
,(35)
where ε∗
k≜
2
η∗
kMk
t∗
2B−1,MkCCPU
fuser
> T,
0,otherwies.
V. DISTANCE-BA SE D USE R PAIRING
As indicated by the SCP expression in (27), the locations of
the paired users have a great impact on the SCP. In this section,
we investigate the distance-based user pairing for the RSMA-
MEC system where multiple users are randomly deployed.
According to the operation of the CR-inspired rate-splitting in
Case II, we know that with a higher interference threshold τ
allowed by the PU, a higher achievable rate can be attained
by the SU. Since a higher interference threshold is related
to a shorter distance from a near user to the MEC server,
the nearest user to the MEC server in the center group or
edge group is preferred to be selected as the PU. Once the
nearest user in the center group is selected as the PU, we
consider two user pairing schemes, namely, the NCNE and
NCFE schemes, in which the nearest user and the farthest
user in the edge group are respectively selected as the SU.
Similarly, if the nearest user in the edge group is selected
as the PU, we consider the NENC and NEFC schemes, in
which the nearest user and farthest user in the center group are
respectively selected as the SU. For the purpose of comparison,
we also consider the RCRE (RERC) scheme, in which the PU
and SU are randomly selected from the center and edge groups
(the edge and center groups), respectively. Once the PU and
SU are selected, the CR-inspired rate-splitting is conducted by
the paired users to aid their offloading.
Let Ξ∈ {RCRE,RERC,NCNE,NCFE,NENC,NEFC}
denote the user pairing scheme, the probability density func-
tions (PDFs) of the distance from the selected PU and SU to
the MEC are denoted by fΞ
PU (x)and fΞ
SU (y), respectively. With
the derived optimal rate-splitting parameters and the optimal
offloading parameters, the SCP achieved by the user pairing
scheme Ξcan be expressed as:
PΞ
s=ZZ Ps|x,y fΞ
PU (x)fΞ
SU (y)dxdy. (36)
Since PΞ
s= 0 if max tUa
3, tUb
3, tMEC
3> t3, we only consider
PΞ
sfor max tUa
3, tUb
3, tMEC
3≤t3in this section.
A. RCRE Scheme
In this subsection, we investigate the impact of the RCRE
scheme on the SCP for the considered RSMA-MEC system.
In the RCRE scheme, the PU and SU are randomly selected
from the center and edge groups, respectively. Since the paired
users are randomly selected, the RCRE scheme provides each
user a fair opportunity to offload the task-bits to the MEC
server.
Since the locations of users follow the HPPP, fRCRE
PU (x)
and fRCRE
SU (y)can be respectively expressed as:
fRCRE
PU (x) = (2x
R2
C
,0≤x≤RC,
0,otherwise; (37a)
fRCRE
SU (y) = (2y
R2
E−R2
C
, RC≤y≤RE,
0,otherwise.(37b)
By substituting (37a) and (37b) into (36), the SCP achieved
by the RCRE scheme can be derived as
PRCRE
s=ZRE
RCZRC
0
ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
xdx
×4
R2
C(R2
E−R2
C)ydy, (38)
where ρa=Pa
(1+xv)σ2and ρb=Pb
(1+yv)σ2.
It is difficult to derive an exact closed-form expression
for the SCP PRCRE
s. Alternatively, we use the Chebyshev-
Gaussian quadrature to obtain an approximation for PRCRE
s
as follows:
PRCRE
s≈
N1
X
i=1
2ωip1−ϕ2
isi
RC(R2
E−R2
C)
×ZRE
RC
ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
ydy
≈
N1
X
i=1
ωip1−ϕ2
isi
RC(RE+RC)
N2
X
j=1
ϖjq1−φ2
jzj
×ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
,(39)
where N1and N2are the parameters that determine the
trade-off between complexity and accuracy for the Chebyshev-
Gaussian quadrature-based approximation, ωi=π
N1,ϕi=
cos 2i−1
2N1π,si=RC
2(ϕi+ 1),ϖj=π
N2,φj= cos 2j−1
2N2π,
zj=RE−RC
2φj+RE+RC
2,ρa=Pa
(1+siv)σ2, and ρb=
Pb
(1+zjv)σ2.
B. NCFE Scheme
Selecting a near user as the PU not only provides a high
interference threshold for the SU’s rate-splitting, but also
enables the PU itself to offload more task-bits to the MEC
server. In this subsection, we derive the expression for the
SCP achieved by the NCFE scheme, in which the PU is the
9
nearest user in the center group, while the SU is the farthest
user in the edge group.
With respect to the homogeneous PPPs, we first derive
the cumulative distribution functions (CDFs) for the distances
of the PU and SU selected by the NCFE scheme, then we
derive the corresponding PDFs. The distances from the nusers
in the center group to the MEC server can be written as
{x1, x2,·· · , xn}. For the distance of the selected PU, who
is the nearest user in the center group subject to 0< x ≤RC,
the CDF can be expressed as
FNCFE
PU (x) = P(x≤xi)
P(|C| ≥ 1) =1−P(x>xi)
1−P(|C|= 0)
=1−e−πµΦCx2
1−e−πµΦCR2
C
,(40)
where i∈ {1,2, ..., n}and |C|represents the number of users
in the center group. Otherwise, FNCFE
PU (x) = 0.
Similarly, the distances from the musers in the edge group
to the MEC server are expressed as {y1, y2, ..., ym}. In the
NCFE scheme, the farthest user in the edge group is selected
as the SU, whose distance satisfies RC≤y≤REand the
corresponding CDF is given by
FNCFE
SU (y) = P(yj≤y)
P(|E| ≥ 1) =1−P(yj>y)
1−P(|E|= 0)
=e−πµΦE(R2
E−y2)
1−e−πµΦE(R2
E−R2
C),(41)
where j∈ {1,2, ..., m}and |E|represents the number of users
in the edge group. Otherwise, FNCFE
SU (y)=0. Then, we can
derive the PDFs by taking derivatives of the CDFs and we get
the following expressions:
fNCFE
PU (x) =
2πµΦCxe−πµΦCx2
1−e−πµΦCR2
C,0≤x≤RC,
0,otherwise;
(42a)
fNCFE
SU (y) =
2πµΦEye−πµΦE(R2
E−y2)
1−e−πµΦE(R2
E−R2
C), RC≤y≤RE,
0,otherwise.
(42b)
By substituting (42) into (36), the SCP achieved by the
NCFE scheme can be evaluated as:
PNCFE
s=λ
ZRE
RCZRC
0
ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
×4e−πµΦCx2xdx ×e−πµΦE(R2
E−y2)ydy, (43)
where ρaand ρbare the same as those for the expression (38)
and λ=π2µΦCµΦE
1−e−πµΦCR2
C1−e−πµΦE(R2
E−R2
C).
By using Chebyshev-Gaussian quadrature, we obtain the
approximation for the SCP as follows:
PNCFE
s≈RC(RE−RC)λ
×
N1
X
i=1
ωi
q1−ϕ2
isi
N2
X
j=1
ϖjq1−φ2
jzje−πµΦE(R2
E−zj2)
×ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
e−πµΦCsi2
.
(44)
C. NCNE Scheme
In the NCNE scheme, the nearest users in the center and
edge groups are respectively selected as the PU and SU,
respectively. For the selected PU, the PDF of its distance is
the same as that in (42a). For the SU, its distance satisfies
RC≤y≤REand the corresponding CDF is given by
FNCNE
SU (y) = P(y≤yj)
P(|E| ≥ 1) =1−P(y > yj)
1−P(|E|= 0)
=1−e−πµΦE(y2−R2
C)
1−e−πµΦE(R2
E−R2
C).(45)
By taking the derivative of (45), the corresponding PDF can
be evaluated as:
fNCNE
SU (y) =
2πµΦEye−π µΦE(y2−R2
C)
1−e−πµΦE(R2
E−R2
C), RC≤y≤RE,
0,otherwise.
(46)
By submitting (42a) and (46) into (36), the SCP of NCNE
scheme can be derived as
PNCNE
s=λ
ZRE
RCZRC
0
ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
×4e−πµΦCx2xdx ×e−πµΦE(y2−R2
C)ydy. (47)
Then, applying the Chebyshev-Gaussian quadrature, the SCP
achieved by the NCNE scheme is approximated as:
PNCNE
s≈RC(RE−RC)λ
×
N1
X
i=1
ωi
q1−ϕ2
isi
N2
X
j=1
ϖjq1−φ2
jzje−πµΦE(zj2−R2
C)
×ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
e−πµΦCsi2
.
(48)
D. PU from Edge Group
For the CR-inspired rate-splitting, the PU can be selected
from the edge group. To attain a relative high interference
threshold, we also consider to select the nearest user in the
edge group to the MEC server as the PU. Then, the nearest and
farthest users in the center group are respectively selected as
the SU, which are denoted by the NENC and NEFC schemes,
respectively. For the purpose of comparison, we also consider
the RERC scheme, in which the PU and SU are randomly
selected from the edge and center groups, respectively.
By applying the similar procedures as those in the previous
subsections, closed-form expressions for the approximated
10
1 2 3 4 5 6 7 8 9 10 11
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RSMA, Ana
RSMA, Sim
NOMA
Complete offloading with RSMA, Ana
Complete offloading with RSMA, Sim
Complete offloading with NOMA
Full local computation
Fig. 2. Psversus task data size (Pa=Pb= 10 dBm).
SCPs achieved by the RERC, NENC, and NEFC schemes can
be obtained as follows:
PRERC
s≈
N1
X
i=1
2ωip1−ϕ2
isi
RC(R2
E−R2
C)
×ZRE
RC
ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
ydy
≈
N1
X
i=1
ωip1−ϕ2
isi
RC(RE+RC)
N2
X
j=1
ϖjq1−φ2
jzj
×ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
,
(49)
PNENC
s≈λRC(RE−RC)
×
N1
X
i=1
ωi
q1−ϕ2
isi
N2
X
j=1
ϖjq1−φ2
jzje−πµΦE(R2
E−zj2)
×ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
e−πµΦCsi2,
(50)
and
PNEFC
s≈λRC(RE−RC)
×
N1
X
i=1
ωi
q1−ϕ2
isi
N2
X
j=1
ϖjq1−φ2
jzje−πµΦE(zj2−R2
C)
×ρae−εb
ρb−εa(1+εb)
ρa−ρbe−εa
ρa−εb(1+εa)
ρb
ρa−ρb
×e−πµΦC(R2
C−si2),(51)
where ρa=Pa
(1+zjv)σ2and ρb=Pb
(1+siv)σ2.
Remark 7: Since the optimal rate-splitting parameters de-
signed in Section III do not rely on a specific user pairing
scheme, they can be applied straightforwardly in all the consid-
ered user pairing schemes to maximize the SCPs. In addition,
0 5 10 15 20 25 30 35
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RSMA, Ana
RSMA, Sim
NOMA
Complete offloading with RSMA
Complete offloading with NOMA
(a) Psversus transmit power
0 5 10 15 20 25 30 35
0
1
2
3
4
5
6
7
RSMA
NOMA
Complete offloading with RSMA
Complete offloading with NOMA
(b) Average throughput versus transmit power
Fig. 3. SCP and average throughput versus transmit power with various PU’s
locations (Pa=Pb).
the optimal offloading parameters provided in Corollary 1 are
independent of the user locations. Thus, for all the considered
user pairing schemes, these optimal offloading parameters can
also be applied straightforwardly to maximize the SCPs.
VI. SIMULATION RESU LTS
In this section, the simulation results are presented to
characterize the system performance achieved by the RSMA-
MEC scheme and to verify the accuracy of the derived
analytical expressions. Unless otherwise stated, the following
system parameters are used in the simulation: B= 1 MHz,
CCPU = 1000 cycles/bit, N= 5,T= 10 ms, υ= 4,
fuser = 0.5GHz, and σ2= 10−9W. For the purpose
of comparison, the offloading performance achieved by the
NOMA-MEC scheme [50] is also provided. In the following
figures, “Ana” and “Sim” represent the results obtained via the
analytical expressions and simulations, respectively.
A. SCP performance with the fixed PU and SU
In this subsection, the impacts of various system parameters
on the SCP are investigated for the case in which the paired
users (PU and SU) have the fixed locations.
In Fig. 2, we compare the SCP achieved by the RSMA-
MEC scheme with that of the NOMA-MEC scheme [50] for
11
0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RSMA
RSMA, PU and SU
exchange locations
Fig. 4. Psversus transmit power with various task lengths (Pa=Pb).
different task data size settings. Specifically, we set da= 5 m
and Ma= 20 kbits, Mbvaries from 1 kbits to 11 kbits in the
simulation. As revealed by the curves in Fig. 2, the analytical
results match the simulation results well, which verifies the
accuracy of the analytical results in Theorem 1. It can also be
observed that the SCP achieved by the RSMA-MEC scheme
decreases with the increasing of Mbdue to the decreasing of
offloading time t2. However, the SCP achieved by the RSMA-
MEC scheme is still higher than that of the NOMA-MEC
scheme for various task data size and db. For the complete
offloading, the SCP performance obtained by the RSMA-MEC
scheme is also better than that obtained by the NOMA-MEC
scheme. This is because the RSMA-MEC scheme can take full
advantage of the PU’s τto obtain a higher achievable rate for
the SU. For the considered task data size of the PU in Fig. 2,
the SCP of the fully local computation scheme is always zero
as shown in this figure.
In Fig. 3, we plot the SCP and average throughput against
the transmit power considering different locations of PU. We
set db= 30 m, Ma= 18 kbits, and Mb= 11 kbits in
the simulation. Specifically, the average throughput of Uk
is calculated by Ck=ˆ
RkPs. The curves in Fig. 3(a) also
verify the accuracy of the derived theoretical expression for
the SCP. As shown in this subplot, for each location of PU,
the SCP of the proposed RSMA-MEC scheme increases with
the increasing of the transmit power. This is because a higher
transmit power leads to a higher ρa(ρb), resulting in a larger
Ps, as expected in (35). It can also be seen from Fig. 3(a) that
the shorter da, the greater the SCP is, because that a shorter
dacan bring a larger ρa. For the considered task data size,
the complete offloading scheme always achieves Ps= 0. In
Fig. 3(b), we evaluate the average throughput achieved by Ub,
i.e., Cb, to verify the superior performance of the proposed
RSMA-MEC scheme. With the increasing of the transmit
power, the curves of Cbfirst increase monotonically. After the
transmit power surpasses a large value, the values of Cbalmost
converge to ˆ
Rb, which benefits from the large SCP achieved
by the RSMA-MEC scheme. Moreover, the curves in Fig. 3
clarify that the proposed RSMA-MEC scheme outperforms the
NOMA-MEC scheme in terms of Psand Cbin the middle and
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0.9
0.92
0.94
0.96
0.98
1
5
6
7
8
9
10
Latency (ms)
(a) N=5
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
0.9
0.92
0.94
0.96
0.98
1
7
8
9
10
Latency (ms)
(b) N=10
Fig. 5. The way to reduce latency.
high transmit power regions, which verifies that the proposed
RSMA-MEC scheme can exploit the transmit power more
efficiently than the NOMA-MEC scheme.
Fig. 4 demonstrates the SCP against the transmit power for
various combinations of the task data size. In the simulation,
we set da= 6 m and db= 30 m and consider the opposite
scenario with da= 30 m and db= 6 m. As indicated by
the curves in Fig. 4, for each combination of the task data
size, the SCP achieved by the RSMA-MEC scheme increases
with the increasing of the transmit power. Besides, a smaller
task data size can achieve a larger Psdue to the fact that a
larger t2is resulted by a smaller Maor Mbaccording to (31),
while Psincreases monotonically with the increasing of t2.
For the scenario where the far user is a PU, the SCP decreases.
This is because a larger distance of PU achieves a smaller
τaccording to (11), which results the frequent occasions of
Case I. Accordingly, the achievable rate of the SU decreases,
which results in a decreased Ps. Futher, we can see that the
SCPs achieved by in two contrary scenarios are the same when
Ma=Mb, as expected in (35).
The curves in Fig. 5 indicate the way to reduce latency.
In this figure, the system parameters are set as da= 5 m,
db= 25 m, Ma= 12 kbits, Mb= 10 kbits, and Pa=
Pb. Accordingly, the offloading time t2= 10 −(Ma+Mb)C
(N+2)fuser is
12
0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RSMA
NOMA
RSMA with fixed =0.75
RSMA with fixed =0.85
RSMA with fixed =0.95
Complete offloading, RSMA
Complete offloading, NOMA
Full local computation
Fig. 6. Impact of offloading factor on Ps(Pa=Pb).
6 8 10 12 14 16 18
10-3
10-2
10-1
100
RSMA
NOMA
Fig. 7. (1 − Ps)versus latency budget.
fixed, i.e., t2= 10 −(10×103+8×103)×103
(N+2)5×108where N∈ {5,10},
while t3is computed by (32). Thus, the way to reduce T=
t2+t3is to reduce t3. As shown by the curves in Fig. 5(a),
where the left vertical axis represents Psand the right vertical
axis represents the latency T. As fuser increases, the latency
Tdecreases due to the decreasing of t3, whereas Pskeeps
constant due to that t2,η∗
a, and η∗
bremain constant. It can be
seen in Fig. 5(b) that the increasing of Pscomes at the cost
of a higher latency due to a greater offloading factor and a
longer offloading time resulted by an increased N.
Fig. 6 shows the SCP versus the transmit power (Pa=Pb)
under various offloading factors. Specifically, we set da= 10
m, db= 25 m, and Ma=Mb= 10 kbits. In the simulation,
the optimal offloading factors are given by (35). For the
fixed offloading factors, we set ηa=ηb=η= 0.75,
ηa=ηb=η= 0.85, and ηa=ηb=η= 0.95, respectively.
For the considered offloading schemes, the proposed RSMA-
MEC scheme obtains the best SCP performance, which verifies
the results in Corollary 1. Compared to the NOMA-MEC
scheme, a higher SCP is observed to be achieved by the
RSMA-MEC scheme.
To clearly see how the SCP varies as the latency budget in-
creases, we employ the failed computation probability (1−Ps)
to highlight the simulation results in Fig. 7, in which we set
1.5 2 2.5 3 3.5 4 4.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 8. Psversus distance ratio db
da(da= 15 m).
da= 6 m, db= 30 m, and Ma=Mb= 10 kbits. From
the curves of Fig. 7, we can see that the failed computation
probability decreases with the growth of the latency budget
T. The reason for this phenomenon is that when Tincreases,
the paired users can spend more time to offload according
to Corollary 1, thereby increasing the SCP, as discussed in
Remark 5. For any given T, the failed computation proba-
bility becomes lower as transmit power increases, which is
consistent with the previous simulation results.
In Fig. 8, we plot the SCP versus various distance ratio,
db
da, under different transmit powers. The task length and the
distance the PU to the MEC server are set as Ma= 13
kbits, Mb= 10 kbits and da= 15 m in this simulation. As
revealed by the curves in this figure, the SCP of the proposed
RSMA-MEC scheme decreases steadily with the increasing of
db, whereas the NOMA-MEC scheme first increases its SCP
and then decreases it. This is because a larger dbleads to
a smaller ρb, which results in a reduced SCP. The reason for
the phenomenon that Psof our proposed RSMA-MEC scheme
is higher than that of the NOMA-MEC scheme is explained
as follows. When Case I occurs, the SCP performance of
our proposed RSMA-MEC scheme keeps the same as that
of the NOMA-MEC scheme. For the occurrences of Case
II, the RSMA-MEC scheme ensures the offloading of PU
while maximizing the achievable rate of SU, which is the
superiority of the proposed RSMA-MEC scheme over the
NOMA-MEC scheme. In summary, for the considered db,
the SCP performance of the proposed RSMA-MEC scheme is
always better than that achieved by the NOMA-MEC scheme.
B. SCP Performance Achieved by User Pairing Schemes
In this subsection, we investigate the impact of the user
pairing schemes on the SCP performance in the MEC system
containing randomly deployed users. Unless otherwise stated,
we set µΦC=µΦE= 0.005,RE= 40 m, Ma= 15 kbits,
and Mb= 10 kbits in the simulation. In particular, we set
RC=q1
2REsuch that the number of the active users in the
center group is the same as that in the edge group on average.
To reveal the impact of the Gaussian Chebyshev parameters
on the accuracy of the approximated SCP, we plot the accuracy
13
5 10 15 20 25 30 35 40 45
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
NCNE
NCFE
RCRE
NENC
NEFC
RERC
Fig. 9. The accuracy of the Chebyshev-Gaussian quadrature-based approxi-
mation versus N1(N2=N1,Pa=Pb= 15 dBm).
of the approximated SCPs (39), (44), (48), (49), (50), and (51)
in terms of N1, as shown in Fig. 9. Specifically, the accuracy
of the approximated SCP for the user pairing scheme Ξis
calculated by AΞ= 1 −|(PΞ
s,Ana−P Ξ
s,Sim)|
PΞ
s,Sim
, where PΞ
s,Ana and
PΞ
s,Sim are the approximated SCP value and simulated SCP
value of the user pairing scheme Ξ, respectively. It can be
seen from Fig. 9, the accuracy of these approximated results
increases with the increasing of N1and approaches the perfect
accuracy (AΞ= 1) when N1=N2≥25.
In Fig. 10, we plot Psagainst the transmit power (Pa=
Pb) for all the considered user pairing schemes. As can be
seen from this figure, the approximated expressions obtained
by Chebyshev-Gaussian quadrature, i.e., (39), (44), (48), (49),
(50), and (51), exactly match with the simulation results. Also,
the Gaussian Chebyshev parameters are set as N1=N2=
25 and the corresponding approximation accuracy has already
been verified by Fig. 9. We can see that the SCP increases with
the increasing of the transmit power for all the considered user
pairing schemes. Besides, one can also see from Fig. 10 that
the NCNE scheme achieves the highest SCP among all the
user pairing schemes. In addition, the NCFE scheme achieves a
higher SCP than the NEFC scheme. For the NCNE and NENC
schemes containing the small path loss, the PU selected from
the center group yields a higher SCP than the PU selected
from the edge group. For the random user pairing schemes,
the PU selected from the center group also achieves a higher
SCP than the PU selected from the edge group. For the NEFC
scheme, the distance between the PU and the SU is shorter
than those of the other user pairing schemes, which results in
the lowest SCP in the low transmit power region. However,
the SCP achieved by the NEFC scheme is still higher than that
of the RERC scheme in the middle and high transmit power
regions. In summary, the user pairing schemes that select PU
from the center group can attain the SCP performance gain
over those select the PU from the edge group.
To compare the SCP performance of the RSMA-MEC
scheme with that of the NOMA-MEC scheme for different
user pairing schemes, we plot the SCP versus transmit power
in Fig. 11 and Fig. 12.
0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
NCNE, Ana
NENC, Ana
RCRE, Ana
RERC, Ana
NCFE, Ana
NEFC, Ana
Markers: simulation results
Fig. 10. Psachieved by RSMA-MEC with various user pairing schemes.
0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RSMA with RCRE, Ana
RSMA with RCRE, Sim
RSMA with NCFE, Ana
RSMA with NCFE, Sim
RSMA with NCNE, Ana
RSMA with NCNE, Sim
NOMA with RCRE
NOMA with NCFE
NOMA with NCNE
Fig. 11. Pscomparison between RSMA-MEC and NOMA-MEC with various
user pairing schemes (PU is a center group user).
In Fig. 11, the user pairing schemes performed by the
RSMA-MEC scheme are compared with the NOMA-MEC
scheme when the PU is selected from the center group. As
shown by the curves in Fig. 11, the theoretical results match
the simulation results well. It can be seen from the Fig. 11, the
RSMA-MEC scheme outperforms the NOMA-MEC scheme
when different user pairings are realized. For the RSMA-MEC
scheme, both the NCNE and NCFE user pairings achieve a
higher SCP than the RCRE user paring. Further, the NCFE
user pairing outperforms the RCRE user pairing for any given
transmit power. For the NOMA-MEC scheme, the NCNE user
pairing achieves a better SCP performance than the RCRE and
NCFE user pairings in the low and middle transmit power
regions, whereas the NCFE user pairing achieves the highest
SCP compared with the RCRE and NCNE user pairings in the
high transmit power region.
In Fig. 12, we consider the scenario where the PU is selected
from the edge group. Similar to the results in Fig. 11, the
RSMA-MEC scheme achieves a higher SCP than the NOMA-
MEC scheme when different user pairings are realized.For
the RSMA-MEC scheme, the NENC yields the best SCP
performance compared to the RERC and NEFC. Furthermore,
the RERC user pairing outperforms the NEFC user pairing
in the low transmit power region. However, the NEFC user
14
0 5 10 15 20 25 30
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RSMA with RERC
RSMA with NEFC
RSMA with NENC
NOMA with RERC
NOMA with NEFC
NOMA with NENC
Fig. 12. Pscomparison between RSMA-MEC and NOMA-MEC with various
user pairing schemes (PU is an edge group user)
pairing achieves a higher SCP than the RERC user pairing
in the middle and high transmit power regions. In summary,
whether the PU is selected from the center group or the edge
group, the RSMA-MEC scheme always achieves a higher SCP
than the NOMA-MEC scheme for the considered user pairing
schemes.
In Fig. 13, we plot the SCP versus RE
RCfor the user pairing
schemes considering that the PU is selected from the center
group. In the first subplot, REis fixed as 50 m and the radius
of the center group RCcan vary. It can be seen from the curves
of the first subplot, RCcan affect the SCP achieved by the
NCNE and RCRE schemes, whereas the impact of RCon the
SCP is negligible for the NCFE scheme. As RCdecreases, the
NCNE scheme has more choices to select a SU with a shorter
db, whereas the RCRE scheme has more choices to select a
PU with a smaller path loss to improve the SCP. In the second
subplot, RCis fixed as 16 m and the disk’s radius REcan vary.
We can observe that the SCP achieved by the RCRE and NCFE
schemes decreases considerably with the increasing of RE
RC,
whereas the NCNE scheme always achieves the SCP closing to
1. There are several reasons for this phenomenon. Considering
that the range of the edge group increases with the increasing
of RE, the NCFE scheme may choose the SUs with a larger
db, so does the RCRE scheme, which results in a severe path
loss. Considering that the NCNE scheme selects the nearest
users in the center and edge groups, respectively, the change
of REdoes not affect the SCP performance. In a nutshell, no
matter what ranges the center and edge groups are, the RSMA-
MEC scheme with different user pairings always surpasses the
NOMA-MEC with the corresponding user pairings when the
PU is selected from the center group.
The curves in Fig. 14 reveal that the RSMA-MEC scheme
achieves a higher SCP than the NOMA-MEC scheme when
the PU is selected from the edge group. From the first subplot
of Fig. 14, we can see that the decreasing of RCenhances the
SCP performance for the RERC, NEFC, and NENC schemes.
It can be seen from the second subplot of Fig. 14, the SCP
achieved by the RERC scheme decreases considerably with
the increasing of RE
RC, whereas the NENC and NEFC schemes
always achieve a higher SCP performance. Further, the NENC
2345
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2345
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RSMA with RCRE
RSMA with NCFE
RSMA with NCNE
NOMA with RCRE
NOMA with NCFE
NOMA with NCNE
Fig. 13. Psversus RE
RC(PU is a center group user, Pa=Pb= 13 dBm).
2345
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2345
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
RSMA with RERC
RSMA with NEFC
RSMA with NENC
NOMA with RERC
NOMA with NEFC
NOMA with NENC
Fig. 14. Psversus RE
RC(PU is an edge group user, Pa=Pb= 13 dBm).
outperforms the NEFC for the considered RC. The results in
Figs. 13 and 14 can be summarized as follows. First, the SCP
performance achieved by the RCRE and RERC schemes is
sensitive to RCand RE. Second, RCseverely affects the SCPs
achieved by the NCNE, NENC, and NEFC schemes. Last, RE
can significantly affect the SCP achieved by the NCFE scheme.
VII. CONCLUSIONS
In this paper, we have proposed an RSMA-MEC scheme
to enhance the offloading performance for a MEC system
consisting of a single MEC server and multiple randomly
deployed users. To enable simultaneous offloading from the
paired users to the MEC server, a CR-inspired rate-splitting
has been designed with the aim of maximizing the SU’s
achievable rate, meanwhile maintaining the PU’s offloading
performance same as in OMA. For the case of the fixed
user locations, we have derived the closed-form expression for
the SCP achieved by the RSMA-MEC scheme. The optimal
offloading parameters have been obtained by solving the
SCP maximization problem. Taking into account the user
locations, various user pairing schemes have been applied to
realize the uplink RSMA-aided offloading. We have derived
closed-form expressions for the SCPs achieved by the user
15
pairing schemes by invoking stochastic geometry techniques,
which characterizes the offloading performance of the RSMA-
MEC system. Simulation results have verified the superior
offloading performance achieved by the RSMA-MEC scheme
and revealed pros and cons of the user locations on maximizing
the SCP. Compared to the existing NOMA-MEC scheme,
simulations results have verified that the RSMA-MEC scheme
achieves a better SCP performance.
APPENDIX A: A P ROO F OF TH EO RE M 1
To derive closed-form expression for the SCP, we evaluate
P(I)
s,P(II)
s, and P(III)
s, respectively.
Corresponding to Case I, P(I)
scan be expressed as:
P(I)
s= Pr |ha|2>εa(1 + ρb|hb|2)
ρa
,|hb|2>εb
ρb.(52)
Considering that |hi|2(i=a, b) follows exponential distribu-
tion, P(I)
scan be evaluated as:
P(I)
s=Z∞
εb
ρbZ∞
εa(1+ρby)
ρa
e−xe−ydxdy =ρae−εb
ρb−εa(1+εb)
ρa
ρbεa+ρa
,(53)
where εb≜2
ηbMb
t2B−1.
Corresponding to Case II, P(II)
scan be evaluated as:
P(II)
s= Pr |ha|2>εa
ρa
,|hb|2>ρa|ha|2ε−1
a−1
ρb
,
|hb|2≥εa+εb+εaεb−ρa|ha|2
ρb
= Pr |ha|2>εa(1 + εb)
ρa
,|hb|2>ρa|ha|2ε−1
a−1
ρb
+ Pr εa
ρa
<|ha|2<εa(1 + εb)
ρa
,
|hb|2>εa+εb+εaεb−ρa|ha|2
ρb
=Z∞
εa(1+εb)
ρaZ∞
ρaε−1
ay−1
ρb
e−xe−ydxdy
+Z
εa(1+εb)
ρa
εa
ρaZ∞
εa+εb+εaεb−ρay
ρb
e−xe−ydxdy
=
ρb e−εb
ρb−εa(1+εb)
ρa−e−εa
ρa−εb(1+εa)
ρb!
ρa−ρb
+ρbεae−εb
ρb−εa(1+εb)
ρa
ρbεa+ρa
.(54)
Considering that τ= 0 in Case III, we have Pr R(III)
a≥
ηaMa= 0, which results in P(III)
s= 0. Then, it is readily
arrived at (27) by combining the derived P(I)
s,P(II)
s, and
P(III)
s.
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