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1
Grant-Free NOMA through Optimal Partitioning
and Cluster Assignment in STAR-RIS Networks
Mohd Hamza Naim Shaikh, Member, IEEE, Abdulkadir Celik, Senior Member, IEEE,
Ahmed M. Eltawil, Senior Member, IEEE, and Galymzhan Nauryzbayev, Senior Member, IEEE
Abstract—The integration of reconfigurable intelligent sur-
faces (RISs) and grant-free non-orthogonal multiple access (GF-
NOMA) has emerged as a promising solution for enhancing
spectral efficiency and massive connectivity in future wireless
networks. This paper proposes a GF-NOMA communication
network enabled by simultaneously transmitting and reflecting
RISs (STAR-RIS). In the proposed GF-NOMA, all user equip-
ments (UEs) have instantaneous access to resource blocks (RBs)
without the need for grant acquisition and power control as
in the traditional grant-based NOMA schemes. Specifically, we
have considered two regimes of interest: 1) the max-min fair
(MMF) regime and 2) the max-sum throughput (MST) regime.
To achieve the required power disparity, a two-level power control
mechanism is proposed; initially, the UEs are clustered according
to their channel gains. Additionally, we introduce a multi-level
GF-NOMA (MGF-NOMA) scheme that adjusts the transmit
power levels for each UE in the cluster. The second level of power
disparity is achieved through the assignment of STAR-RISs to the
clusters and optimal partitioning of STAR-RIS to support each
of the cluster members. Furthermore, we have also derived the
closed-form equations for the optimal partitioning of STAR-RIS
within the clusters for both regimes of interest. Simulation results
demonstrate that the proposed STAR-RIS-aided MGF-NOMA
yields a gain of 60% and 20% in the MST regime with active and
passive RIS realization, respectively. Furthermore, the active and
passive RIS-based MGF-NOMA achieve nearly the equivalent
fairness that can be obtained through optimal power control
in the MMF regime. The finding emphasizes the potential of
integrating STAR-RIS with GF-NOMA as a robust and promising
solution for future wireless communication systems.
Index Terms—Reconfigurable Intelligent Surface (RIS), Si-
multaneously transmitting and reflecting RIS (STAR-RIS), non-
orthogonal multiple access (NOMA), Grant-free NOMA, max-
min optimization, max-sum rate, fairness, spectral efficiency.
I. INTRODUCTION
Over the last few years, the demand for increased mobile
transmission capacity has grown tremendously. Approximately
70% of the world’s population will be mobile-connected by
2023, and the total number of mobile users will rise from
5.1 billion in 2018 to 5.7 billion in 2023, as reported by
This research was partially funded by the Science Committee of the Min-
istry of Science and Higher Education of the Republic of Kazakhstan (Grant
No. AP19677079) and Nazarbayev University under Collaborative Research
Program Grant no. 11022021CRP1513 (PI: Galymzhan Nauryzbayev).
Mohd Hamza Naim Shaikh and Galymzhan Nauryzbayev are with the
School of Engineering and Digital Sciences, Nazarbayev University, Astana,
Kazakhstan (email: {hamza.shaikh, galymzhan.nauryzbayev}@nu.edu.kz).
Abdulkadir Celik and Ahmed M. Eltawil are with the Computer, Elec-
trical, and Mathematical Sciences & Engineering Division, King Abdullah
University of Science and Technology, Thuwal, Saudi Arabia (email: {ab-
dulkadir.celik, ahmed.eltawil}@kaust.edu.sa).
A conference version of this work was presented at IEEE GLOBE-
COM’2023 [1].
the Cisco Mobility Report [2]. The total number of mobile
devices is expected to expand by over 48 percent, to around
13 billion, in the same time frame. The massive growth in
the number of mobile-connected devices and the introduction
of services that require high data rates, such as HD video
streaming via mobile networks, are the primary drivers of the
persistently rising demand for capacity. As a result, the migra-
tion to novel emerging approaches, such as the reconfigurable
intelligent surface (RIS), is a critical solution for emerging
wireless communications standards. As of late, RISs have
been recognized as a revolutionary technology envisioned for
next-generation wireless networks and are expected to enhance
spectral efficiency (SE) while minimizing power consumption
and hardware costs. Due to their low cost and low energy
usage, RISs are anticipated to play a crucial role in the beyond
5G wireless networks [3].
A. Background and Related Work
1) Reconfigurable Intelligent Surface: RISs consist of an
array of a large number of low-cost passive elements that can
be dynamically adjusted to alter their phases to have various
impacts on impinging electromagnetic (EM) signals such as
reflection, absorption, polarization, etc. [4]. By intelligently
controlling the behavior of the EM waves, RISs can help
enhance the signal quality, coverage, and energy efficiency
of wireless networks while simultaneously mitigating interfer-
ence and latency [5], especially in environments with intricate
propagation characteristics or scarce resources. RIS’s low-cost
hardware and energy usage enable affordable, reconfigurable,
and software-controlled wireless communication for a green
future [6]. Moreover, the modest hardware footprint of RIS
makes it easy to install on exterior urban structures like
buildings, factory ceilings, roofs, and so on. As a result, RIS
may seamlessly integrate into the wireless communication
environment without changing its architecture or operating
requirements. Also, RIS may be densely deployed in wireless
networks at a low cost while maintaining good flexibility
and interoperability [7], [8]. The performance of RIS-aided
systems has been extensively explored, and analytical perfor-
mance reviews can be found in [9]–[13].
2) Simultaneously Transmitting and Reflecting RISs: Previ-
ous research predominantly focused on RISs that could reflect
signals in their front half-space, limiting their service to one
side of the RIS [14], [15]. To overcome this constraint, the
concept of simultaneously transmitting and reflecting RISs
(STAR-RISs), also known as STAR intelligent omni-surfaces
2
(STAR-IOSs), was introduced. STAR-RISs possess the unique
capability of serving users on both sides by simultaneously
transmitting and reflecting signals. With the ability to indepen-
dently control reflecting and refracting beamforming, STAR-
RISs/STAR-IOSs provide a complete 360-degree smart radio
environment [16]. Several comprehensive frameworks have
been proposed to analyze STAR-RISs/IOSs, encompassing
their implementation, hardware models, and channel mod-
els [17]–[19]. Furthermore, the transmission and reflection
coefficients of each STAR element can also be adjusted
independently, which increases the flexibility and adaptability
of STAR-RIS in wireless communication. This advancement
has generated increased research interest in deploying STAR-
RISs in wireless networks, as they offer advantages such as
expanding network coverage [20], reducing power consump-
tion [21], and enhancing system throughput [22].
3) Active STAR-RISs: However, STAR-RISs and conven-
tional RISs still suffer from the "double-fading" effect, where
the large-scale fading of the base station (BS)-STAR-RIS link
and the STAR-RIS to user link are multiplied. For instance,
in a STAR-RIS-aided virtual line-of-sight (LoS) transmission,
the received power decreases as (d1d2)−2, where d1and d2
represent the path lengths of the two cascaded links. Conse-
quently, it poses a challenge for passive STAR-RISs to achieve
significant capacity gains due to the multiplicative fading
effect. Overcoming this challenge necessitates a large number
of passive elements for practical performance improvement,
and the substantial surface area of STAR-RISs introduces
deployment and maintenance challenges. To address this issue,
active RISs were introduced, incorporating amplifiers into
the reflecting elements. Active RISs actively reflect signals
with amplification, effectively countering the "multiplicative
fading" effect, albeit at the cost of increased power consump-
tion. Active RISs have demonstrated the potential to enhance
wireless systems, as evidenced by previous research [23]–[25].
4) Non-orthogonal Multiple Access: In addition, Cisco also
reported that machine-type communication (MTC) devices are
the fastest-growing mobile device category, followed by smart-
phones [2]. The massive MTC (mMTC) traffic generated by
these technologies is both intermittent and short-lived, necessi-
tating tolerance against delay and time-frequency synchroniza-
tion requirements. Thus, alongside RIS, non-orthogonal multi-
ple access (NOMA) has demonstrated its potential as a viable
solution to enable enhanced massive connectivity by multi-
plexing multiple user equipments (UEs) on the same network
resources [26]. NOMA has also been explored in conjunction
with emerging technologies, including index modulation [27],
cognitive radios [28], and unmanned aerial vehicles (UAV)-
assisted wireless communication networks [29]. In particular,
the power-domain NOMA (PD-NOMA), a widely recognized
variant of NOMA, increases SE by multiplexing UEs with
distinct channel gains and varying transmit powers. Because
of this power disparity, the receivers are able to successfully
implement the decoding process through successive interfer-
ence cancellation (SIC) [30].
5) RIS-aided NOMA: The findings reveal that the amalga-
mation of RIS and NOMA facilitates high data rate transmis-
sion and elevates overall system performance [31]. Moreover,
the integration of RIS and NOMA culminates in more efficient
utilization of spectral resources, enabling the fulfillment of
diverse quality-of-service (QoS) requirements [32]. The au-
thors have studied the performance of a RIS-aided NOMA
communication system for an ideal hardware scenario in [33]
and [34] and compared it with its OMA counterpart. On the
other hand, in [35], the authors have investigated the impact
of non-ideal hardware in a RIS-aided NOMA communication
system. Furthermore, the authors in [36] have shown that
STAR-RIS outperforms traditional RIS in NOMA systems
in terms of ergodic rates. Nevertheless, as the UE density
escalates, PD-NOMA grapples with power control complexity,
resource allocation overhead, and challenges in obtaining pre-
cise channel state information (CSI) [37]. In order to alleviate
the complexity and overhead arising from the power control
mechanism of PD-NOMA, recent research has advocated the
use of grant-free NOMA (GF-NOMA) schemes [38].
6) Grant-free NOMA: In GF-NOMA, multiple users share
the same time-frequency resources without any prior schedul-
ing, making it more suitable for low-latency communication
scenarios. Moreover, as the need for grant acquisition by UEs
is eliminated, signaling overhead and computational complex-
ity are also reduced. Thus, PD-GF-NOMA schemes allow UE
to access assigned resource blocks (RBs) without needing a
grant, according to [39]. However, the key to GF-NOMA’s
efficacy is ensuring adequate reception power disparity among
UEs. To address this challenge, RISs have garnered significant
attention due to their capacity to generate the required received
power disparity at the receiver in PD-NOMA [33]. Indeed,
the GF-NOMA scheme can be implemented through virtual
RIS partitioning, wherein each RIS portion adjusts its phase
configuration to improve the channel gain of individual UEs to
bolster channel gain disparity for the maximum NOMA gain.
Specifically, the authors in [40] provided a lower complexity-
based sub-optimal solution by applying a consecutive search
algorithm. Likewise, in [41], the authors proposed a novel
3D assignment algorithm to jointly allocate RIS and UEs
into clusters and assign RIS to a particular UE within the
cluster. Furthermore, they also proposed a low-complexity
implementation of the proposed 3D approach in the form of
a 2D assignment algorithm.
B. Main Contributions
Motivated by the above, in this paper, we propose a novel
STAR-RIS-aided GF-NOMA communication system. The ma-
jor contributions of this work can be summarized as
•We propose a user clustering, RIS assignment, and par-
titioning scheme where the users are clustered based on
the required power disparity. Subsequently, RISs are allo-
cated to the clusters along with the requisite partitioning
mechanism, wherein all UEs within a specific NOMA
cluster have instantaneous access to RBs and transmit at
the same power level. The required power disparity is
achieved by allocating the RIS portions to UEs in such
a manner that they achieve the desired reception power
disparity.
•Furthermore, we also proposed a multi-level GF-NOMA
(MGF-NOMA) scheme that utilizes the received signal
3
strength (RSS) to group UEs into a particular group.
These clusters are then assigned uniform power levels
that are communicated through broadcast signals. MGF-
NOMA dynamically adjusts the UE grouping and power
levels based on the availability of RBs and the number
of UEs awaiting access. In addition to exploiting the
channel gain differences, MGF-NOMA further enhances
the power reception through the manipulation of the
power levels of the group of UEs.
•The joint UE clustering and STAR-RIS assignment and
partitioning for the max-min (MM) rate or max-sum (MS)
rate represents a computationally challenging problem
classified as non-deterministic polynomial-time (NP)-
hard. We present sub-optimal solution methodologies for
both regimes of interest, i.e., MM and MS rates. In the
former, we utilize a linear bottleneck assignment (LBA)
for UE clustering and RIS assignment, along with our
proposed optimal RIS partitioning. For the latter sce-
nario, we utilize a linear sum assignment (LSA) for UE
clustering and RIS assignment, along with our proposed
optimal RIS partitioning. Furthermore, the proposed solu-
tion methodologies are intended to work with both active
and passive RIS architectures. Specifically, the active RIS
(aRIS) configuration involves a fully connected design
wherein each element maintains a connection with a
dedicated power amplifier.
•The simulation results demonstrate that a significant per-
formance improvement can be achieved by the proposed
STAR-RIS-aided GF-NOMA schemes. Specifically, com-
pared to existing grant-based approaches, the single-
level GF (SGF)-NOMA and MGF-NOMA show gains
of 14% and 20% in terms of the MS rates, respectively.
Furthermore, when utilizing aRIS, these gains increase
to 53% and 60%, respectively. Similarly, in the case
of the MM rate, the proposed STAR-RIS-aided MGF-
NOMA achieves nearly fully fair network performance,
comparable to optimal PD-NOMA (OPD-NOMA). These
results highlight the potential of RIS as a powerful
solution for implementing GF-NOMA-based networks in
future wireless systems.
C. Paper Organization and Notations
The paper is organized as follows: Section II provides a
comprehensive overview of the system model, specifically fo-
cusing on the network and channel models for the STAR-RIS-
aided GF-NOMA scenario. Section III delves into the problem
formulation and presents the proposed solution methodology.
Section IV introduces the proposed approach to power allo-
cation. Additionally, it also provides the derivation for the
optimal partitioning of RIS. Section V presents the numerical
results obtained through the simulations. Finally, Section VI
concludes the paper by summarizing the key findings and
highlighting their significance.
The main notations utilized in this paper are as follows:
boldface lower case represents vectors (e.g., x), whereas upper
case represents matrices (e.g., X). The i-th element of a
vector or set is represented by xior X{i}, respectively.
TABLE I: LIS T OF NOTATI ON S
NOTATIO N DESCRIPTION
RcCell radius
Rin Inner radius for STAR-RIS deployment
Rout Outer radius for STAR-RIS deployment
RSet of |R| =RRBs, indexed by 1≤r≤R
BBandwidth per RB
USet of |U| =UUEs, indexed by 1≤u≤U
MSet of |M| =MSTAR-RISs, indexed by 1≤
m≤M
NmNo. of elements in RISm
RBrr-th RB
RISmm-th STAR-RIS
CNo. of clusters
KMax. cluster size, ⌈U/C⌉
χ(u)
rBinary UE clustering indicator, 1if UEu∈ Cr,
otherwise 0.
XBinary UE clustering matrix with entries χ(u)
r
Cr
Cluster set of UEs utilizing RBr, where Cr≤K,
Cr={UEu|χ(u)
r= 1,∀u∈ U,Pu∈U χ(u)
r≤K}
δ(m)
r
Binary RIS allocation indicator, 1 if RISmis assigned to Cr
and partitioned between UEu∈ Cr, 0 otherwise
∆Binary RIS assignment matrix with entries
δ(m)
r,∆∈ {0,1}
ρRIS allocation vector with entries in [0, 1]
ρ(m)
r,i RIS allocation factor of UEi∈ Crfor RISm
ϱ(m)No. of partitions in RISm
g(m)
uUEu−RISmchannel
˜g(m)RISm−BS channel
huUEu−BS channel
Φ(m)
r,i Response matrix of RISmconfigured to support
Cr
G(m,n)
r,i Gain of n-th element of RISm
Gmax Maximum gain of the active elements
y(m)
rReceived signal at BS over RBraided by RISm
nRIS element index
xuTransmitted symbol of UEu
ξrAdditive white Gaussian noise (AWGN) at BS
∼ CN 0, σ 2
ξr
e
CrSorted Cras per RSS
yrReceived signal at BS over RBr
waNoise vector for RISmwhose elements ∼ CN 0, σ 2
RIS
Rth QoS requirement of UEs
AuAdmission awaiting UEs set, where
max(|Au|) = U−K
TrTemporary cluster, where max(|Tr|) = K
Similarly, the entry on the i-th row and j-th column of the
matrix Xis denoted by X[i, j]. Likewise, random variables
are italicized to distinguish them from constant variables and
are not represented in boldface (e.g., A, B). Moreover, upper
indices and powers are distinguished through small brackets
e.g., x(2), x2. A complex Gaussian distribution with mean
µand variance σ2is denoted by the notation CN(µ, σ2);
4
Fig. 1: Illustration of the proposed STAR-RIS network, highlighting the UE deployment and transmit/reflection region of RISmassigned to Cr.
Γ(·)denotes the Gamma function. The STAR-RIS, RB/clusters
and UEs are indexed using the subscripts m,r, and u,
respectively. Furthermore, the sets and their cardinality are
denoted with calligraphic and regular upper-case letters (e.g.,
|A| =A). Additionally, Table I provides a summary of the
major notations used throughout the paper.
II. SY ST EM MO DE L
In this section, we delve into the system model, structured
over four subsections: Section II-A details the network ar-
chitecture, covering UE distribution along with STAR-RIS
deployment and partitioning, which is followed by an outline
of STAR-RIS’s operational modes and their functional dynam-
ics in Section II-B. Section II-C elaborates on the principles
underlying the communication channels in the proposed net-
work model. Finally, Section II-D develops the received signal
models and formulates corresponding signal-to-interference-
plus-noise ratio (SINR) expressions.
A. Network Model
We consider an uplink NOMA network where a single BS
simultaneously serves a set of UUEs that are clustered into
Cclusters, with each cluster being assigned a specific RB,
as illustrated in Fig. 1. The set of UEs, clusters, and RBs
are denoted by U,C, and R, respectively. As directed by BS
through control signaling, UEutransmit at a predetermined
power level, P(u)
t. The UEs are assumed to be uniformly1
distributed within a circular cell area with a radius of Rc.
1While we have assumed a uniform user distribution in our work, kindly
note that the proposed optimization framework still holds for other user
distribution models. Furthermore, the key conclusions and insights drawn from
our findings will remain intact regardless of the specific user distribution
model employed, demonstrating the robustness and applicability of our
approach.
In order to demonstrate the suitability of the proposed GF-
NOMA techniques for massive connectivity, we consider a
dense network scenario where the number of UEs greatly
exceeds the number of available RBs, i.e., U≫R. Therefore,
to effectively utilize the limited RB resources, the UEs are
grouped into clusters. Consequently, the number of clusters C
is equal to the number of RBs R, and the terms RB and cluster
are used interchangeably throughout this paper. Although the
number of RBs in the network is fixed, and, in turn, the
number of clusters is also fixed, the number of UEs and
cluster sizes can alter dynamically based on the spatiotemporal
characteristics of network traffic. Consequently, the maximum
cluster size is dependent on the UEs’ density and can be
defined as K=U
C. Thereby, the cluster set utilizing RBr
can be defined as Cr={UEu|χ(u)
r= 1,∀u∈ U}, where
Cr=Pu∈U χ(u)
r=Cr≤K. Here, χ(u)
rrepresents the binary
UE clustering indicator, with χ(u)
r= 1 indicating that UEu
belongs to the r-th cluster, and χ(u)
r= 0 otherwise.
To further enhance the network performance and facilitate
the implementation of GF-NOMA, MSTAR-RISs are uni-
formly deployed in a ring with inner and outer radii of Rin
and Rout, respectively. Here, Rin ensures that RISs are placed
in the far-field of BS as shown in Fig. 1. Moreover, STAR-
RISs ensure that the signals from the UEs at both sides of RISs
are served efficiently either through reflection or transmission.
Each of these STAR-RISs is assumed to be equipped with
Nelements, and the set of STAR-RISs is denoted by M.
Likewise, each of STAR-RISs can be exploited by one or more
members of a cluster through virtual partitioning of STAR-
RIS; however, STAR-RIS cannot be assigned to more than
5
Fig. 2: Illustration of virtual STAR-RIS partitioning and STAR-RIS opera-
tional modes for Cr.
one cluster2. Accordingly, the m-th STAR-RIS is denoted by
RISm. The binary assignment matrix representing the STAR-
RIS is symbolized as ∆and comprises elements δ(m)
r, where
δ(m)
rassumes a value of 1 if RISmis assigned to Crcluster
and its response is optimized to cater the UEs within Cr.
Conversely, δ(m)
r= 0.
B. Operational Modes of STAR-RIS
The literature highlights that STAR-RIS offers three oper-
ating protocols: energy splitting (ES), mode switching (MS),
and time switching (TS) [16], [21].
1) Energy Splitting: In the ES protocol, all elements of the
STAR-RIS operate concurrently in both transmission (T) and
reflection (R) modes, with the total radiation energy divided
based on an energy splitting ratio of ζ(n)
T:ζ(n)
R. Consequently,
the T&R-coefficient matrices for STAR-RIS are represented
as ΦES
T= diag ζ(1)
Tejφ(1)
T, ζ(2)
Tejφ(2)
T,·· · , ζ (N)
Tejφ(N)
Tand
ΦES
R= diag ζ(1)
Rejφ(1)
R, ζ(2)
Rejφ(2)
R,·· · , ζ (N)
Rejφ(N)
R, where
ζ(n)
T, ζ(n)
R∈[0,1] and ζ(n)
T2+ζ(n)
R2= 1.
However, the ES protocol faces limitations due to the
following reasons:
•Optimizing both T&R coefficients of each element neces-
sitates a relatively high overhead for exchanging config-
uration information between the BS and the STAR-RIS
[21].
•The physics-based model indicates that achieving inde-
pendent configuration of T&R coefficients is nontrivial.
For practical passive-lossless STAR-RIS elements, the
amplitudes and phases of the reflected and transmitted
fields are constrained by boundary conditions and the law
2In scenarios where the number of STAR-RISs is fewer than the number of
clusters, each STAR-RIS can be divided into two or more sub-RISs and the
proposed scheme can then be incorporated with these sub-RISs. Thus, with
a minor adaptation, the proposed scheme of RIS assignment and element
allocation can still be worked.
of energy conservation, leading to correlations between
T&R coefficients [42].
2) Mode Switching: The MS protocol allows each element
to operate in either T-mode or R-mode, enabling independent
phase shift control. Consequently, the elements are divided into
two groups: NTelements operate in T-mode, and NRelements
operate in R-mode, where NT+NR=N. It can be observed
that MS protocol is a special case of ES protocol where
the T&R coefficients are limited to binary options. Though
MS protocol might not achieve the same full-dimension T&R
beamforming gain as ES, the simplicity of the MS protocol,
with its "on-off" operating method and independence of T-
mode and R-mode elements, makes it an appealing option in
real-world applications, especially when compared to the more
complex ES protocol.
3) Time Switching: Conversely, the TS protocol utilizes the
time domain by assigning all elements to either T-mode or R-
mode in separate, orthogonal time slots, setting it apart from
the ES and MS protocols. This time-based strategy simplifies
the design by separating the T&R coefficient controls. How-
ever, the requirement for periodic element switching in the
TS protocol necessitates precise time synchronization, which
adds to the complexity of hardware implementation. In the
context of STAR-RIS, where users can be present on both
sides of the system, the use of NOMA is limited to scenarios
where users are situated on a single side of the STAR-RIS. In
contrast, OMA suits the TS protocol, allowing service to users
on both sides in distinct time slots. As a result, the TS protocol
is inherently incompatible with NOMA, given its reliance on
orthogonal time slots for operation.
In this study, the MS mode of operation is adopted for
STAR-RIS, enabling the elements to switch between T-mode
and R-mode depending on the physical position of UE. Thus,
Φ= diag (ζ)is the response matrix of STAR-RIS, where
ζn=|ζn|exp (jφn), n ∈[1, N], with |ζn|and φnbeing
the amplification factor and the imparted phase shift at the
n-th element of STAR-RIS. For the lossless passive RIS
(pRIS), Gn=|ζn|2= 1,∀nmay be assumed without
loss of generalization, implying that the pRIS cannot impart
any power gain to the impinging signal other than a simple
reflection with modified phase. In contrast, for aRIS, |Gn|>
1,∀n, implying that, in addition to changing the phase of the
reflected signal, aRIS imparts a proportional power increase.
The actual gain realized practically by the elements of STAR-
RIS is constrained by the physical implementation of aRIS.
Mathematically, it can be expressed as 1<|Gn| ≤ Gmax ,∀n,
where Gmax represents the maximum gain achievable by the
active components.
To support multiple users within a cluster, we consider
a virtual STAR-RIS partitioning approach that assigns each
cluster member with a partition and determines its size and
operational mode depending on STAR-RIS and UE location.
Assuming that RISmis assigned to support Cr, the number
of elements allocated for UEi∈ Cris denoted by N(m)
r,i =
lρ(m)
r,i Nm, where ρ(m)
r,i ∈[0,1] are the RIS allocation factors
such that Pi∈Crρ(m)
r,i δ(m)
r≤1and Pi∈CrN(m)
r,i δ(m)
r≤N
ensure that the total number of elements allocated to the cluster
6
member does not exceed the physically available total number
of elements at that STAR-RIS. Fig. 2 depicts virtual STAR-
RIS partitioning of Cr={UEi,UEj}such that UEilocated
in the T-region and UEjin the R-region. In this case, an
optimal STAR-RIS assignment and partitioning approach is
necessary to determine the best STAR-RIS and optimal size
of its partition based on the STAR-RIS location, UEs’ channel
conditions, and QoS demand, which is the main focus of this
work.
C. Channel Model
The channels between the UEs, RISs, and BS are presumed
to be quasi-static and flat-fading with the assumption of
perfectly known CSI. All the small-scale fading coefficients
for the channel between UEs, RISs, and BS can be charac-
terized through the Nakagami-mfading model, respectively.
Furthermore, the number of partitions in RISmis denoted
as ϱ(m)≜P∀r∈R P∀m∈M P∀u∈U δ(m)
rχ(u)
r=Cr. The
phase shift matrix corresponding to the portion of RISm
configured for the i-th UE in cluster Cr, RIS(m)
r,i , is denoted
as Φ(m)
r,i . Accordingly, the complete phase shift configuration
matrix for RISmaligned to the UEs in Cris denoted as
Φ(m)
r=fmΦ(m)
r,1,...,Φ(m)
r,ϱm, where fm(·)is a mapping
function that selects the elements of RISmto ϱmpartitions.
Moreover, the channel from UEi∈ Crto RISmis repre-
sented by g(m)
r,i =hg(m,1)
r,i ,...,g(m,ϱm)
r,i i, consisting of the
channels from UEi∈ Crto all ϱmpartitions of RISm. The
elements of g(m,j)
r,i =g(m,1)
r,i ,...g(m,N (m)
r,i )
r,i follow Nakagami-
mfading, ∀(m, r, i, j)and the corresponding large-scale path
loss is denoted by β(m)
i. Similarly, the channel between
RISmand BS is denoted as ˜g(m)
r=h˜g(m,1)
r,...,˜g(m,ϱm)
ri,
comprising channels from all the ϱmpartitions of RISmto
BS. The elements of ˜g(m,j)
r= ˜g(m,1)
r. . . ˜g(m,N(m)
r,i )
rfollow
the Nakagami-mfading, ∀(m, r, i, j)and the corresponding
large-scale path loss is denoted by ˜
β(m). Finally, hidenotes
the small-scale fading coefficient that follows Nakagami-m
fading, and βiis the large-scale path loss, respectively, for the
direct link between UEi∈ Crand the BS.
D. Received Signal Model & SNR Formulation
As illustrated in Fig. 2, for a reference user UEi∈ Cr
assisted by RISm(i.e., δ(m)
r= 1), the signal received at BS
on RBrcan be written as
y(m)
r(∆) =y(m)
r,i (∆) + X
j∈Cr
i=j
y(m)
r,j (∆)
+q˜
β(m)˜g(m,i)
rΦ(m)
r,i w(m)
a,i
| {z }
Active Noise
+ξr
|{z}
AWGN
,(1)
where the first term is the received signal from UEi∈ Cr,
the second term is the received signal from UEj∈ Cr, j =i,
the third term is the active noise, which can be expressed as
w(m)
a,i and its element w(m)
a,i ∼ CN 0, σ2
RISbeing the AWGN
term at the active elements of the STAR-RISs. Furthermore,
xi∈ CN(0,1) is the transmitted symbol of UEi∈ Crand
Φ(m)
r,i represents the response matrix of the subpart of Rm
that is configured to support UEiof Cr, respectively. Lastly,
ξris the AWGN at the BS with wr∈ CN(0, σ2
ξr).
The first term of (1) can be expressed as follows
y(m)
r,i (∆) =
pβihi
| {z }
Direct Link
+q˜
β(m)β(m)
i˜g(m,i)
rΦ(m)
r,i g(m,i)
r,i
| {z }
Via RIS(m)
r,i aligned for UEi∈ Cr
+
X
∀m′∈M
m′=mX
∀r′∈R
r′=r
δm′
r′q˜
β(m′)β(m′)
i˜g(m′,i)
rΦm′
r′,ig(m′,i)
r,i
| {z }
Via RIS(m′)
r′aligned for Cr′
qP(i)
txi,
(2)
which can also be used for the second term by replacing j
with i.
It has the following components:
•Signal received from the direct link, √βihi
•Signal received from the STAR-RIS allocated to the
cluster, q˜
β(m)β(m)
i˜g(m,i)
rΦ(m)
r,i g(m,i)
r,i
•Signal received from other STAR-RISs in the network,
P∀m′∈M
m′=mP∀r′∈R
r′=r
δm′
r′q˜
β(m′)β(m′)
i˜g(m′,i)
rΦm′
r′,ig(m′,i)
r,i
Now, in (2), the received signal power from all other RISs
i.e.,RIS(m′)
r′and from the non-aligned portion of allocated
RIS can be neglected3compared to the received signal power
from the aligned portion of RISmi.e.,RIS(m)
r,i . Therefore,
for simplicity, we can express the received signal at BS on
RBrin (1) by considering only the signal reflected from the
relevant aligned portions of RISm,i.e.,RIS(m)
r,i , as follows
y(m)
r(∆) = X
∀i∈Crpβihi+q˜
β(m)β(m)
i˜g(m,i)
rΦ(m)
r,i g(m,i)
r,i
×qP(i)
txi+q˜
β(m)˜g(m,i)
rΦ(m,i)
rw(m)
a,i +ξr.(3)
Considering the number of elements of RIS(m)
r,i , denoted as
N(m)
r,i , and aligning the phases for the necessary number of
elements corresponding to each cluster member, the phases
for STAR-RIS elements associated with the portion of the i-th
UE, denoted as Φ(m)
r,i , can be configured as φ(m,n)
r,i = arg[hi]−
arg[˜g(m,n)
r] + arg[g(m,n)
r,i ]for all n[43]. After configuring
the required phase shifts, the received signal y(m)
r(∆)can be
detailed as follows
y(m)
r(∆) = X
∀i∈Cr
pβi|hi|+q˜
β(m)β(m)
i
N(m)
r,i
X
n=1 qG(m,n)
r,i
טg(m,n)
rg(m,n)
r,i iqP(i)
txi+ϑi+ξr,(4)
3This assumption has been numerically evaluated in the results section,
please refer to Section VI-C.
7
where ϑi=q˜
β(m)PN(m)
r,i
n=1 √G(n)˜g(m,n)
rw(n)
adenotes for
the active noise.
At the BS, the received signal, y(m)
r(∆), is decoded using
the SIC scheme. This iterative scheme decodes the signal from
the UE with the highest received power first, treating the
signals from other UEs as interference. The decoded signal
is then subtracted from the combined received signal, and
the process is repeated iteratively for the remaining UEs in
the ordered cluster set ˜
Cr. Thus, SINR for the i-th UE in
the ordered cluster set ˜
Crcan be mathematically expressed as
follows:
Υ(m)
r,i (∆) =
P(i)
thZ(d)
i+Z(c)
ii2
P(i)
tPCr
j=i+1 hZ(d)
j+Z(c)
ji2+σ2
ϑi+σ2
ξr
,(5)
where Z(d)
i=√βi|hi|and Z(c)
i=
q˜
β(m)β(m)
iPN(m)
r,i
n=1 qG(m,n)
r,i ˜g(m,n)
rg(m,n)
r,i are terms
related to direct and cascaded links for UEi∈ Cr, respectively;
and σ2
ϑi=GN ˜
β(m)Γ( ˜m+1/2)
Γ( ˜m)σ2
RIS.
Since the above SINR expression is not tractable, we make
an approximation for analytical purposes by utilizing the
expected values of Z(d)
iand Z(c)
i, the effective SINR can be
given as
Υ(m)
r,i (∆,ρ) =
P(i)
tEhZ(d)
ii2+P(i)
tEhZ(c)
ii2
P(i)
tPCr
j=i+1 EhZ(d)
ji2+ E hZ(c)
ji2+σ2
ϑi+σ2
ξr
.
(6)
The expectations can be evaluated as EhZ(d)
ii2=βiand
EhZ(c)
ii2=˜
β(m)β(m)
iEhG(m)
r,i i2, respectively. Fur-
thermore, G(m)
r,i =PN(m)
r,i
n=1 qG(m,n)
r,i ˜g(m,n)
rg(m,n)
r,i which
can further be simplified as
EhG(m)
r,i i2= E
N(m)
r,i
X
n=1 qG(m,n)
r,i ˜g(m,n)
rg(m,n)
r,i
2
=ρ(m)
r,i 2G(m)
r,i N21
˜mgmgi
Γ( ˜mg+ 1/2)2
Γ( ˜mg)2
Γ(mgi+ 1/2)2
Γ(mgi)2
=ρ(m)
r,i 2c G(m)
r,i N2,(7)
where c=1
˜mgmgi
Γ( ˜mg+1/2)2
Γ( ˜mg)2
Γ(mgi+1/2)2
Γ(mgi)2with ˜mg,mgi
being the shape factor for the ˜g(m)
rand g(m)
r,i links, respectively.
By substituting these values in (6), we can have
Υ(m)
r,i (∆,ρ) =
¯γi+ρ(m)
r,i 2c G(m)
r,i N2ˆγi
PCr
j=i+1 ¯γj+ρ(m)
r,j 2c G(m)
r,j N2ˆγj+ Ξi+ 1
,(8)
where ¯γi=βiP(i)
t/σ2
w,ˆγi=˜
β(m)β(m)
iP(i)
t/σ2
wand Ξi=
σ2
ϑi/σ2
ξr. Accordingly, the rate for UEican be given as
R(m)
r,i (∆,ρ) = Blog21+Υ(m)
r,i (∆,ρ).(9)
Remark 1: The received signal model, SINR, and rate
formulated for aRIS in (4), (8) and (9) can be reduced to
that of passive RISs (pRISs) by setting ϑi= 0 and Ξi= 0.
Remark 2: The accuracy of this approximation can be ver-
ified through numerical simulation plots, which are presented
in Section VI.
III. PROB LE M FORMULATION AND SOLUTION
METHODOLOGY
In this section, we first present joint UE clustering, STAR-
RIS partitioning, and STAR-RIS assignment formulations for
two different regimes of interest: the Max-Min Fair (MMF)
regime and the Max-Sum Throughput (MST) regime in the
considered distributed STAR-RIS-aided GF-NOMA network,
which is followed by an outline of the proposed solution
methodology.
A. Problem Definition
The MMF regime aims at the joint optimization of UE clus-
tering, STAR-RIS assignment, and partitioning to maximize
the minimum UE throughput of the entire network, which can
be formulated as follows
Pf
o: max
X,∆,ρmin
∀(r,u,m)nlog21+Υ(m)
r,u (∆,ρ)o
s.t.
C1
1:X
r∈R
χ(u)
r= 1,∀u∈ U,
C2
1:X
∀u∈U
χ(u)
r≤U
R,∀r∈ R,
C3
1:X
∀u∈U X
∀m∈M
χ(u)
rδ(m)
r≤1,∀r∈ R,
C4
1:X
∀r∈R X
∀m∈M
δ(m)
r≤M,
C5
1:χ(u)
r∈ {0,1}, δ(m)
r∈ {0,1},
0≤ρ(m)
r,u ≤1,∀(r, u, m),
(10)
where Υ(m)
r,u (∆,ρ)denotes the SINR of UEu∈ Crwith
X∈ {0,1}U×Ris the binary UE clustering matrix with entries
χ(u)
r. In Pf
o,C1
1assures that each UE is admitted to a cluster;
C2
1restricts the size of clusters to a maximum of ⌈U/R⌉;
C3
1enforces the condition that each cluster is supported by, at
most, a single STAR-RIS; C4
1limits the total number of STAR-
RIS assignments by the total number of available STAR-RISs;
and C5
1outlines the specific domain and boundaries governing
the optimization variables.
Likewise, the MST regime aims at the joint optimization
of UE clustering, STAR-RIS assignment, and partitioning to
8
.
.
.
.
.
.
.
.
.
.
.
.
(a) Algorithm 1 - Iterative UE Clustering
.
.
.
.
.
.
.
.
.
.
.
.
(b) Algorithm 2 - RIS assignment and partitioning.
Fig. 3: Illustration of the proposed solution methodology.
maximize the total throughput of the entire network, which
can be formulated as follows
Pt
o: max
X,∆,ρX
∀r∈R X
∀u∈U
log2n1 + χ(u)
rΥ(u)
r(∆,ρ)o
s.t. C1
1,C2
1,C3
1,C4
1,C5
1,
C1
2:Υ(u)
r≥2Rth/B −1,∀u∈ Cr,∀r∈ R,
(11)
which takes all constraints of Pf
o, in addition to the QoS
constraints in C1
2that satisfies all UEs with a predetermined
QoS demand, i.e., Rth [bps].
Both Pf
oand Pt
ofall within the realm of non-convex mixed-
integer non-linear programming (MINLP) problems due to the
combinatorial nature of problem and non-convexity of the
sub-problems for a given combination of integer variables.
Therefore, finding an optimal solution for these problems is
computationally prohibitive in real life, even for a moderate
size of the network, necessitating efficient yet fast solution
methodologies, which are outlined next.
B. Solution Methodology
As illustrated in Fig. 3, Pf
oand Pt
ocan be decomposed into
following two sub-problems:
SP1As depicted in Fig. 3a, we propose an iterative UE
clustering approach that admits UEs from non-clustered
set of UEs based on underlying operational regime of
interest. Each iteration starts with the cost matrix calcu-
lation between the RBs or clusters and the set of UEs
currently in queue for admission, denoted as Ak, based
on direct links between UEs and BSs. Subsequently, the
cost matrix Qkis utilized to admit UEs to the cluster
through solving either the LBA or the LSA algorithms for
MMF and MST regimes, respectively. At each iteration,
the cost matrix element q(u)
rrepresents the MM/MS rate
of cluster rif u-th UE of Akis admitted to Cr. Upon the
completion of the admission decisions, the UE clustering
algorithm generates and provides the resulting cluster sets
denoted as Cr,∀r. The detailed procedure is outlined in
Algorithm 1.
SP2For cluster sets Crprovided by Algorithm 1, SP2first
obtains cost matrix ˜
Q, whose elements ˜q(m)
r⋆
ρ(m)
rrep-
resents the MM/MS rate of cluster rif RISmis assigned
to Cr. To this aim, we utilize optimal RIS partitions ⋆
ρ(m)
r,
which are derived in closed-form.Subsequently, the cost
matrix is utilized to assign the RISs to the clusters using
the LBA and LSA algorithms for achieving the MMF
and MST objectives, respectively. Upon finalizing the
allocation, the RIS partitioning and assignment algorithm
provides the RIS allocation matrix along with the optimal
partition parameter. A detailed step-by-step procedure for
the RIS assignment is presented in Algorithm 2.
IV. TRANSMIT POW ER ALLOCATI ON A ND OPTIMAL RIS
PARTITIONING
In UL-NOMA schemes, the BS uses SIC to decode mes-
sages transmitted by UEs in descending order of signal re-
ception power. Notably, the optimal grant-based UL-NOMA
scheme ensures that the UE with the highest channel gain has
the highest transmit power, enabling the other cluster members
to cause interference and improve their SINRs. This strategy,
nevertheless, is unfair in terms of energy expenditure and
would result in shortening the lifetime of the network, which
is crucial for low-power mMTC. As a remedy, this section
proposes two simple transmit scheme at the UE side while
fine-tuning reception power at BS through the optimization of
RIS partitions.
A. MGF-NOMA and SGF-NOMA
In MGF-NOMA, the BS standardizes the transmission
power for UE across several distinct levels, which is achieved
by classifying each group of UEs to transmit at a specific
power level based on their respective RSS. The process of
determining these power levels follows several steps.
9
Initially, the UEs are ordered according to their RSSs and
then divided into K=⌈U/R⌉distinct groups. The group
containing RUEs with k-th highest RSS is denoted by Uk
such that Uk=R,k∈1,2, ..., K −1, and UK=U
mod R. The power control range of UEs is defined as Pmax =
10 log10(P(u)
max ) + 30 and Pmin = 10 log10(P(u)
min ) + 30 in the
dBm scale, where P(u)
max and P(u)
min correspond to the maximum
and minimum UE transmit powers, respectively. The precise
power levels for each group are determined by averaging
the optimal power levels, which are obtained through grant-
based NOMA schemes. On the other hand, the SGF-NOMA
considers a single transmit power level for all UEs. These
power levels are calculated prior to the transmission period
and can be directly broadcasted to UEs over control channels.
B. Optimal STAR-RIS Partitioning under MMF Regime
The MMF regime aims to provide a uniform QoS perfor-
mance across the network by maximizing the rate of worst
performing UE. In the rest of this subsection, we will omit the
cluster and RIS indices for the sake of a clear presentation and
focus on generic cluster consisting of KUEs. Accordingly,
the RIS partitioning problem under the MMF regime can be
formulated as
P1: max
0⪯ρ⪯1min
i{log2(1 + Υi(ρ))}
C1
3: s.t.
K
X
i=1
ρi≤1,
(12)
where 0and 1are the vectors of zeros and ones of the same
size of ρ. The constraint C1
3ensures that the total number of
allocated elements does not exceed the available total number
of elements. As per the standard definition of MMF, the system
performance can be improved by allocating more elements
to the worst-performing UE to boost its SINR towards the
maximum achievable limit. In this manner, the unique and
optimal MMF rate can be achieved by all UEs within the
cluster. Consequently, we can reformulate problem (12) in its
equivalent form as follows
P2: max
0⪯ρ⪯1,ΛΛ
C1
4: s.t. Υi(ρ)≥Λ,∀i,
C2
4:
K
X
i=1
ρi≤1,
(13)
where C1
4ensures that all UEs reach the SINR no less than
Λ, which is introduced as an auxiliary variable. The following
lemma presents a closed-form solution for P2.
Lemma 1: For a UE cluster of size K, the optimal parti-
tioning factors enabling the MMF rate are given as
⋆
ρi=v
u
u
u
t
(⋆
Λ + γei)(Ξi+ 1) QK
j=i+1 ⋆
Λ + γej + 1−¯γi
c GiN2ˆγi
,
(14)
where
⋆
Λis the optimal MMF rate in P2,
γei ="¯γi
PK
j=i+1 ¯γj+ (ρ∗
j)2c GjN2ˆγj+ Ξi+ 1 −⋆
Λ#+
,
and [x]+= max{x, 0}. The optimal solution given in (14) can
be calculated recursively in the reverse chronological order for
all uand is subject to the constraints of PK
i=1
⋆
ρi= 1, and
¯γi+ (ρ∗
i)2c GiN2ˆγi
PK
j=i+1 ¯γj+ (ρ∗
j)2c GjN2ˆγj+ Ξi+ 1 =⋆
Λ + γei,(15)
which implies that all UEs achieve minimum SINR of
⋆
Λ.
Proof 1: The proof is provided in Appendix A. ■
C. Optimal STAR-RIS Partitioning under MST Regime
In the maximum throughput regime, the goal is to maximize
the sum rate of all the UEs within the cluster under the given
rate constraint. In a similar manner to the earlier scenario
of MMF rate, the problem of optimal RIS partitioning to
maximize the sum rate of the users within the cluster can
be formulated as
P3: max
ρ
K
X
i=1 {log2(1 + Υi(ρ))}
C1
5: s.t. log2(1 + Υi(ρ)) ≥Rth/B,
C2
5:0≤ρi≤1,
C3
5:
K
X
i=1
ρi≤1,
(16)
where Rth is the common QoS constraint for all UEs. Like-
wise, the constraints C2
5and C3
5in P3ensures that the total
number of allocated elements does not exceed the available
total number of elements.
In order to solve P3, we reformulate the original problem
by expanding the summation and utilizing the properties
of logarithmic functions to get a more simple and elegant
equivalent form as below
P4: max
ρ
K
X
i=1
ρ2
ic GiN2ˆγi
C1
6: s.t. Υi(ρ)≥γth,
C2
6:0≤ρi≤1,
C3
6:
K
X
i=1
ρk≤1,
(17)
where γth = 2Rth/B −1is the equivalent SNR threshold to
ensure the QoS requirements for all the users.
Lemma 2: For a UE cluster of size K, the optimal RIS
partitioning that provide the maximized sum rate are given as
⋆
ρi=
s(γth+γi)(Ξi+1) QK
j=i+1(γth +γj+1)−¯γi
c GiN2ˆγi+
, i = 1,
1−PK
i=2
⋆
ρi, i = 1,
(18)
where, in a reverse chronological order, γi=
¯γi
PK
j=i+1¯γj+( ⋆
ρj)2c GjN2ˆγj+Ξi+1 −γth +
can be evaluated
10
recursively. The optimal solution satisfies the constraints of
PK
i=1
⋆
ρi= 1, and
¯γi+ ( ⋆
ρi)2c GiN2ˆγi
PU
j=i+1 ¯γj+ ( ⋆
ρj)2c GjN2ˆγj+ Ξi+ 1
=γth +γi.(19)
Proof 2: The proof is provided in Appendix B. ■
V. UE CLUSTERING AND RIS ASS IG NM EN T
In this section, we present the iterative UE clustering and
RIS assignment schemes for both MMF and MST regimes.
The solution methodology, as illustrated in Fig. 3 also, is
provided in the form of pseudo code as Algorithm 1 and
Algorithm 2. These algorithms are initially presented for the
MGF-NOMA framework, but they can be easily adapted to the
SGF-NOMA regime by considering a single identical power
level for all UEs. In the subsequent sections, we offer a
more detailed explanation of Algorithm 1 and Algorithm 2
in Sections V-A and V-B, respectively.
A. UE Clustering
After acquiring CSI from all UEs in Line 2, the BS
proceeds to determine the following parameters in Lines 3
and 4: the number of UEs, the maximum allowable cluster
size, and the number of clusters. In Line 5, the UEs are
sorted in descending order based on their RSS, facilitating
the iterative UE admission process. This sorted UE index set,
denoted as ˜
U, plays a crucial role in Line 6, where it is
employed to partition the set of UEs into Ksubsets labeled as
Uk=˜
U {(k−1)R+ 1 : kR}, with k∈[1, K]. Transitioning
to Line 7, the clusters are initialized. Here, Cris initialized
using the r-th element extracted from the first partition, ∀r.
The iterative process for UE admission unfolds between
Line 9 and Line 19, encompassing the subsequent stages: Line
10 updates the cluster by admitting the UEs that are awaiting to
be admitted. Then, in Line 11, the COST MATRIX procedure is
called to compute the cost matrix Qkfor the k-th round of UE
admission, details of which will be discussed in the subsequent
paragraph. Subsequently, Line 13 and Line 15 utilize the
LBA and LSA procedures to identify fresh admissions that
maximize the minimum user rate and the sum rate of all
clusters, respectively. These assignment procedures ensure that
either all clusters admit UE if R≤Ak, or if R > Ak,
UEs are assigned to appropriate clusters. Upon concluding the
iterative UE admission process, Line 20 updates the power
levels for the clusters. Finally, in Line 21, random access
response (RAR) messages are sent to the UEs that indicate
the allocated RBs and their corresponding power levels.
The cost matrix Qk∈RR×Akis calculated using nested for
loops between Line 25 and 36. Within each iteration of the
inner loop (indexed by u), Line 26 creates a temporary cluster
Trby admitting the u-th member of set Akinto Cr. Line
28 determines the power levels according to the previously
discussed MGF-NOMA (or SGF-NOMA) scheme. Line 31
and 33 compute the values of Qk[r, u]based on the objective
function of interest by evaluating the minimum and sum rates
of the temporary cluster Tr, respectively. Finally, the computed
Algorithm 1 : Iterative UE Clustering
1:Input: R,U,η
2: gm/h←Acquire CSI from SRS sent by UEk,∀u∈ U
3: C←R// Determine number of clusters
4: K←U
R// Determine maximum cluster size
5: ˜
U ← SORT DESC END (Rss,∀u)// UE ordering based on RSS of SRS signals
6: Uk=˜
U {(k−1)R+ 1 : kR}, k ∈[1, K ]// Form UE groups for
MGF-NOMA
7: Cr← U1{r}, r ∈[1,...,R]// Initialize clusters
8: χu
r←1, u ∈ Cr// Initialize UE clustering matrix
9: for k=1:K−1do // Iterative UE admission starts
10: Ak← Uk+1 // Form set of admission awaiting UEs
11: Qk←COST MATRIX UE (Cr,Ak)// Create cost matrix for user
clustering
12: if η= 0 then
13: Yk←LBA(Qk)// MM rate assignment
14: else if η= 1 then
15: Yk←LSA(Qk)// MS rate assignment
16: end if
17: Cr← CrSAk{u}, yu
r= 1,∀(r, u)// Update clusters
18: χu
r←1, u ∈ Cr// Update UE clustering matrix
19: end for
20: l← L(Cr+ 1),∀r
21: UEi←(r, lr[i])), UEi∈ Cr,∀i, ∀r// Send RARs out
22: return X
23: procedure COST MATRIX UE(Cr,Ak)
24: Qk←0R×A// Initialize Qto matrix of zeros
25: for r=1:Rdo
26: for u=1:Akdo
27: Tr← CrSAk{u}// Temp. admit u-th UE of Akto Cr
28: l← L(k+ 1) // transmit power level
29: γj
r←Obtain SINR of UEj,∀j∈ Tr
30: if η= 0 then
31: qu
r←min
j∈Tr
log2(1 + Υj
r)
32: else if η= 1 then
33: qu
r←Pj∈Trlog2(1 + Υj
r)
34: end if
35: end for
36: end for
37: return Qk
38: end procedure
39: procedure LBA(Qk)
40: ⋆
Y←max
Ymin
∀r,∀u{qu
ryu
r}
41: s.t. Pr∈R yu
r= 1,∀u∈ U
42: Pu∈U yu
r= 1,∀r∈ R
43: return ⋆
Y
44: end procedure
45: procedure LSA(Q)
46: ⋆
Y←max
YPr∈R Pu∈U qu
ryu
r
47: s.t. Pr∈R yu
r= 1,∀u∈ U
48: Pu∈U yu
r= 1,∀r∈ R
49: return ⋆
Y
50: end procedure
cost matrix Qkis returned to facilitate the subsequent UE
assignment procedure.
B. RIS Assignment
Following the completion of UE admission and cluster
formation, the next step is to assign RISs to the formed clusters
and support the UEs within the cluster through optimal RIS
partitions. In Algorithm 2, Line 2 invokes the cost matrix func-
tion for RIS assignment. The cost matrix ˜
Q ∈ RR×Bis formed
through two nested for loops, as explained in the procedure
between lines 10-22. Lines 12 and 13 contain two loops that
allocate a RISmfrom the set of RISs, M, to the cluster Cr.
The RIS is optimally partitioned and configured to achieve
the desired objectives of the MMF rate and the MST rate in
Lines 15 and 18, respectively. Following the rate calculations
11
Algorithm 2 : RIS Assignment and Partitioning
1:Input: R,U,M,X,η
2: ˜
Q←COST MATRIX STAR-RIS(Cr,M)// CM for STAR-RIS assignment
3: if η=0 then
4: Ym←LBA( ˜
Q)// MM rate assignment
5: else if η= 1 then
6: Ym←LSA ( ˜
Q)// MS rate assignment
7: end if
8: δm
r←1iff ym
r= 1,∀m//Update RIS assignment matrix
9: return ∆
10: procedure COST MATR IX RI S(Cr,M)
11: ˜
Q←0R×M// Initialize Qto matrix of zeros
12: for r=1:Rdo
13: for m=1:Mdo
14: if η= 0 then
15: ⋆
ρ←Obtain from Lemma 1 // Calculate ⋆
ρas per Lemma 1
16: qm
r←min
k∈Crnlog21 + Υk⋆
ρo // Evaluate minimum
rate with ⋆
ρ
17: else if η= 1 then
18: ⋆
ρ←Obtain from Lemma 2 // Calculate ⋆
ρas per Lemma 2
19: qm
r←Pk∈Crnlog21 + Υk⋆
ρo // Evaluate sum rate
with ⋆
ρ
20: end if
21: end for
22: end for
23: return ˜
Q
24: end procedure
in Lines 16 and 19, the LBA/LSA technique is used again in
Lines 4 and 6 to determine the RIS assignment. For example,
if the LSA returns y2
4= 1 ∈Ymfor user clustering, this
indicates that RIS4is allocated to C2. Subsequently, in Line
8, the elements of the RIS assignment matrix δr
mare updated,
and finally, the final assignment matrix ∆is returned in Line
19.
The overall time complexity of the suggested methodol-
ogy for the MMF/MST rate objective is dominated by the
complexity of the CO ST MATR IX and L BA/LSA proce-
dures. The cost matrix calculation complexity for UE clus-
tering and RIS assignment is given by OPK−1
k=1 RAk
and O(RM), respectively. Considering the well-known cubic
complexity of LBA/LSA solutions, the overall complexity
can be obtained as OPK−1
k=1 RAk+ (max(R, Ak))3and
ORM + (max(R, M ))3, which constitutes the entire com-
plexity of Algorithm 1 and Algorithm 2 together [38], [41].
VI. NUMERICAL RE SU LTS
In this section, we present numerical results to assess the
effectiveness of the proposed STAR-RIS-aided GF-NOMA
communication scheme. For the purpose of simulating and
evaluating network performance, we employ Monte Carlo
(MC) simulations. Each MC simulation result is an average
of over 1000 randomly generated network topologies. In these
simulations, we utilize the 3GPP Urban Micro (UMi) model
at a carrier frequency of 3 GHz to compute all large-scale
path loss values, which aligns with prior work [44], [45].
Additionally, we assume a Nakagami-mshape parameter of
˜mg=mgi= 5 for the cascaded STAR-RIS link and mu= 1
for the direct UE-to-BS links, with a spread parameter of unity
for all the links. Unless stated otherwise, we use the default
system parameters as listed in Table II.
TABLE II: SIMULATION PAR AM ET ER S
PARAMETER VALUE PAR AM ETE R VALUE
U100 N1024
R20 Rth 0.125 Mbps
M20 fc3GHz
C20 Pt23 dBm
Pmin −40 dBm Pmax 23 dBm
B250 KHz σ2, σ2
ris −120 dBm
Rc250 mPact
max 23 dBm
Rin 20 mPtot 1W
Rout 50 mGmax 20 dB
TABLE III: Power level lookup table (in dBm)
Cluster Size 2 3 4 5 6
UE123 23 23 23 23
UE223 23 23 23 23
UE3- 10.65 14.70 16.95 18.68
UE4- - 5.12 9.61 12.53
UE5- - - 1.54 6.19
UE6- - - - 1.05
A. Benchmark Scheme - OPD-NOMA
As a benchmark, we have selected the uplink OPD-NOMA
scheme. In OPD-NOMA, the BS assigns optimal power levels
to each user based on their CSI. To evaluate the performance
of OPD-NOMA, we follow the clustering approach described
in Algorithm 1, but instead of assigning identical transmit
power to all users within a cluster, we determine the optimal
power level for each individual user. This process is repeated
for all clusters in the network. We analyze the optimal power
allocation for the UEs in the uplink OPD-NOMA using the
geometric programming solver of the CVX disciplined convex
optimization toolbox [46]. This optimization considers both
MMF and MST rate schemes, allowing us to achieve an
optimal power allocation that maximizes the fairness and
overall network sum rate. In addition, it also provides the total
average power transmitted by the UEs in the MMF and MST
rate schemes. This allows for a fair comparison of the system
performances, as we can compare the performance at similar
power consumption of the UEs under different schemes.
B. MGF-NOMA
By combining transmit power levels across different cluster
sizes as L=SK
k=1 L(k), the BS can create a lookup table
known to all UEs in advance. Table III presents a power level
lookup table based on the maximum (lmax = 23 dBm) and
minimum (lmin =−40 dBm) UE output power specifications,
considering K≤6. Utilizing the information provided in
Table III, the power level vector for each cluster, denoted as
lr,∀r,∀l, can be determined. For example, in Fig. 1, the
highlighted cluster is assigned to RBr, and the corresponding
power level vector is lr= [23 23]. Consequently, the
members of this cluster can transmit at these designated power
levels.
12
100 200 300 400 500 600 700 800 900 1000
No. of elements at STAR-RIS (N)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Rate (Mbps)
MSR - approx
MSR - exact
MMR - approx
MMR - exact
Fig. 4: MS and MM rates for different N, here U= 4 and M= 3.
C. Comparison between Exact and Approximate Model
Figure 4 illustrates the rate results obtained from comparing
the exact received signal model and the rate formulated by the
approximation, as represented by (2) and (9), respectively. The
results indicate that the approximate MS rate (MSR) serves
as a lower bound for the exact MSR, while the approximate
MM rate (MMR) closely aligns with the exact MMR. This
demonstrates the accuracy and precision of the approximate
model used for analytical formulation in Section II. Notably,
the analytical results closely match the outcomes of the exact
simulation, allowing us to rely on the approximate analytical
results for further discussions and analysis. Furthermore, as
evident from the above result, it can also be inferred that
the impact of the second and third reflections will be more
minimal, given that the first reflection from the non-aligned
portions of the allocated RIS and the first reflection from
the other RISs in the network are having very little impact.
Thus, the assumption of only considering the received signal
power from the aligned portion of RISs and neglecting other
higher-order random reflections is highly valid, as numerically
demonstrated in the above result.
D. Comparison between NOMA and OMA
Figure 5 displays the rates for both NOMA and OMA.
In this scenario, the STAR-RIS operates in the TS mode,
dynamically switching between reflection and transmission
based on the UE’s relative position with respect to the STAR-
RIS. It is evident that the rate increases linearly with the num-
ber of STAR-RIS elements. Furthermore, NOMA consistently
outperforms OMA in terms of rate across different numbers
of STAR-RIS elements. This highlights the advantages of
employing NOMA in RIS-aided wireless systems, even when
considering different power levels.
E. MMF & MST Rate
Fig. 6a depicts the MMF and MST rates with respect to
the transmit power of the UEs for RIS-aided SGF-NOMA.
100 200 300 400 500 600 700 800 900 1000
No. of elements at STAR-RIS (N)
1
1.5
2
2.5
3
3.5
4
4.5
Rate (Mbps)
MSR - NOMA
MSR - OMA
Pt = 23 dBm
Pt = 0 dBm
Fig. 5: NOMA and OMA rates for different N, here U= 4.
The MST and MMF rates for the OPD-NOMA without RIS
are also presented as a baseline to assess the benefits of
using a grant-free scheme without power control instead of a
grant- and power-control-based scheme. Furthermore, the sum
rate and minimum rate of MGF-NOMA with RIS are plotted
to evaluate the benefits of employing RIS in MGF-NOMA
implementation. The result shows that a significant gain can
be achieved from RIS-aided GF-NOMA over OPD-NOMA
for both MST and MMF schemes. The only exception is the
MMF rate for the passive RIS-based SGF-NOMA, which is
lower than the OPD-NOMA.
For instance, the MST rate for the OPD-NOMA is 81.25
Mbps, while the corresponding MST rate with the passive RIS-
based SGF- and MGF-NOMA are 92.55 and 97.26 Mbps at
Pt= 20 dBm, which is the average transmit power of UEs in
OPD-NOMA and MGF-NOMA. Likewise, the corresponding
rate for aRIS-based SGF-NOMA and MGF-NOMA is 125.5
Mbps and 130.3 Mbps, respectively. The MMF scheme in
OPD-NOMA achieves a rate of 0.52 Mbps. However, with the
proposed passive RIS-aided SGF-NOMA and MGF-NOMA
schemes, the corresponding rates are 0.49 and 0.67 Mbps,
respectively, at an average transmit power of UEs set to
Pt= 18 dBm, which is the average transmit power of UEs in
OPD-NOMA. On the other hand, with the aRIS-aided SGF-
NOMA and MGF-NOMA schemes, the MMF rates of 0.94
and 1.07 Mbps can be achieved, showcasing a significant
performance improvement compared to OPD-NOMA.
Similarly, the MST and MMF rates are shown in Fig. 6b for
varying the number of elements at the RIS. It can be observed
that the MST rate and MMF rate increase with N, as evident
in Fig. 6b. Furthermore, it can be observed that even at lower
N, the MST rate in the proposed RIS-based scheme is greater
than that of OPD-NOMA, implying that a RIS with even a
smaller number of elements is sufficient to have a similar
performance to that of OPD-NOMA. The sum rate can be
further enhanced when the number of elements increases in the
proposed MST rate scheme. Furthermore, it also suggests that
13
-10 -5 0 5 10 15 20 23
Transmit Power (dBm)
20
40
60
80
100
120
140
MST Rate (Mbps)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
MMF Rate (Mbps)
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
(a)
100 200 300 400 500 600 700 800 900 1000
No. of elements at STAR-RIS (N)
70
80
90
100
110
120
130
140
MST Rate (Mbps)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
MMF Rate (Mbps)
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
(b)
Fig. 6: MST and MMF rates for the proposed RIS-aided GF-NOMA and OPD-NOMA with respect to: a) transmit power, and b) number of RIS element at
U= 100.
40 50 60 70 80 90 100 110 120
No. of UEs (U)
70
80
90
100
110
120
130
140
MST Rate (Mbps)
0
0.5
1
1.5
2
2.5
3
MMF Rate (Mbps)
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
Fig. 7: MST and MMF rates for the proposed RIS-aided GF-NOMA and
OPD-NOMA with respect to the number of UEs.
we can achieve similar performance through MGF NOMA,
which is more energy efficient than SGF-NOMA. Likewise, it
can also be observed that even with lower values of N, aRIS
and pRIS-aided GF-NOMA achieve significantly higher and
nearly the same MMF rate, respectively, when compared to
the benchmark OPD-NOMA.
Fig. 7 shows the MST and MMF rates with respect to the
number of UEs in the network. The results reveal that the
proposed MST rate scheme achieves a higher sum rate with
an increasing number of UEs, indicating improved spectrum
utilization within specific RBs. For instance, at U= 80, the
suggested aRIS and pRIS-aided GF-NOMA with the MST
scheme outperform the OPD-NOMA without RIS by up to 55
and 20%, respectively. The MMF scheme, on the other hand,
exhibits decreasing rates as the number of UEs increases. Ad-
ditionally, the performance of OPD-NOMA also deteriorates
with an increasing number of UEs in the cluster. Moreover, the
MST rate performance of aRIS-aided MGF-NOMA and pRIS-
aided SGF-NOMA is found to be comparable, emphasizing
the effective elimination of the need for power control at
the UEs through optimal utilization of RIS resources. In
contrast, the MMF rate shows superior performance in RIS-
aided MGF-NOMA compared to SGF-NOMA, owing to the
effective interference mitigation capabilities of MGF-NOMA
compared to SGF-NOMA, which lacks interference reduction
mechanisms.
Furthermore, a time-based scheduling approach can be
utilized when users cannot be grouped into clusters due to
an excessively large user base or higher QoS requirements.
In this scenario, the BS will schedule the users and allocate
service in designated time slots. The proposed methodology
in this work is designed to operate within these allocated time
slots, with the surplus of users being managed through an
effective scheduling system. To summarize, the upper limit of
users that can be simultaneously supported in the same RB is
variable and contingent on several factors, such as the state
of the channel, the efficiency of SIC, and the specific QoS
demands. When this threshold is exceeded, implementing a
scheduling strategy becomes vital to sustain network efficiency
and to guarantee equitable service distribution among all users.
F. Fairness
Fig. 8 depicts the fairness in rate for both MST and MMF
regimes as the number of UEs/elements increases. It can also
be observed that for the RIS-aided MGF/SGF-NOMA, the
MMF regime gives better fairness as compared to the MST
regime, which further improves as the number of elements
14
40 50 60 70 80 90 100 110 120
No. of UEs (U)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Jains Fairness Index (MST Regime)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Jains Fairness Index (MMF Regime)
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
(a)
100 200 300 400 500 600 700 800 900 1000
No. of elements at STAR-RIS (N)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Jains Fairness Index (MST Regime)
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Jains Fairness Index (MMF Regime)
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
aRIS - mNOMA
aRIS - sNOMA
pRIS - mNOMA
pRIS - sNOMA
OPD - NOMA
(b)
Fig. 8: Jain’s fairness index for the proposed RIS-aided GF-NOMA and OPD-NOMA with respect to: a) number of UEs, and b) number of RIS elements.
increases, as shown in Fig. 8b. The Jain’s fairness index,
which measures the fairness of rates among the UEs, has been
computed as
F=PU
i=1 Ri2
UPU
i=1 R2
i
.(20)
The result shows that, in the MMF regime, OPD-NOMA
gives maximum fairness, which is obvious since there is an
inherent power control mechanism. The result shows that
the proposed aRIS-aided MGF-NOMA’s MMF rate scheme
closely approximates the maximum achievable fairness ob-
served in OPD-NOMA. Additionally, the results highlight
that MGF-NOMA exhibits higher fairness compared to SGF-
NOMA. This can be attributed to the fact that in the SGF-
NOMA scheme, we only have control over the allocation
of RIS elements, whereas, in the MGF-NOMA scheme, we
have a power control mechanism along with the RIS element
allocation, which enhances the overall fairness of the network.
Thus, there is a trade-off with respect to rate and fairness;
while the proposed MST scheme enhances the rates, the
fairness is reduced. Hence, as evident from the above results,
the employment of RIS can also enhance the fairness of the
GF-NOMA schemes along with the increase in the SE.The
above results highlight the trade-off between rate and fairness
in the proposed GF-NOMA scheme. While in the MST regime,
RIS enhances the UE rates, it also leads to a reduction in
fairness. On the other hand, in the MMF regime, RIS not only
improves the minimum UE rate but also enhances fairness
among the UEs, as evidenced by the aforementioned results.
This suggests that the integration of RIS into GF-NOMA can
offer benefits in terms of both rate and fairness.
VII. CONCLUSION
In this paper, we suggest a UE clustering, RIS assignment,
and partitioning scheme that can be combined with the GF-
NOMA scheme. Specifically, we proposed a STAR-RIS-aided
GF-NOMA where, to achieve the required power disparity, we
proposed a two-level power control mechanism. Initially, the
UEs with diverse channel gains are grouped to form a cluster
with different power levels; later on, the RISs are assigned
to these clusters with optimal allocation of elements for each
cluster member. We specifically considered two regimes of in-
terest: the former improved fairness, while the latter improved
the network sum rate considerably. For both regimes, we pro-
vide the closed-form expressions for the STAR-RIS element
allocation. According to the simulation findings, the proposed
scheme outperforms the benchmark scheme. We specifically
compared the results of aRIS/pRIS-aided GF-NOMA to the
benchmark OPD-NOMA. The numerical findings show that
the proposed schemes outperform the benchmark schemes.
Specifically, the MST regime provides the maximum network
sum rate, while the MMF regime provides better fairness
among the UEs within the network. With regard to future
work, the employment of power control at the aRIS, as
opposed to element allocation, can be considered.
APPENDIX
A. Proof of Lemma 1
To maximize the minimum user rate within the NOMA
cluster, the optimal element allocation is obtained when all
cluster members attain the same SINR while exploiting all the
available elements. That is, we should obtain Υi(ρ) = ⋆
Λ,∀i,
and PK
i=1
⋆
ρi= 1 at the optimal point. For a given auxiliary
variable ¯
Λ, we iteratively solve system of equations consisting
of Υi(ρ) = ¯
Λ,∀i, until PK
i=1
⋆
ρi= 1 is satisfied, which
provides
⋆
Λand ⋆
ρi,∀i.
B. Proof of Lemma 2
To maximize the sum throughput of the NOMA cluster
within the constraints of the minimum rate requirement of
15
each user, the optimal allocation scheme is to assign elements
to all UEs except for UE with the highest channel gain.
Thus, the data rates of all those UEs are just equal to their
minimum required data rate. Lastly, the remaining elements
can be allocated to the UE with the highest channel gain.
Intuitively, it can also be understood from the fact that the
user with the maximum channel gain contributes the most
to the sum throughput of a NOMA cluster; thus, it should
be allocated the maximum number of elements. Thus, from
(18), ⋆
ρican be evaluated. Likewise, the subsequent ⋆
ρican
be evaluated iteratively by substituting the previous ⋆
ρiin the
reverse chronological order. Lastly, for UE with the highest
channel gain, all the remaining elements are allocated.
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Mohd Hamza Naim Shaikh (Member, IEEE) re-
ceived the B.Tech. and M.Tech. degrees from Ali-
garh Muslim University, Aligarh, India, and the
Ph.D. degree from IIIT Delhi, Delhi, India. He is
a postdoctoral research fellow with the Department
of Electrical and Computer Engineering, School of
Engineering and Digital Sciences at Nazarbayev
University, Astana, Kazakhstan. His research inter-
ests include next-generation communication tech-
nologies, such as FD radios, massive MIMO, RIS,
and NOMA.
Abdulkadir Celik (Senior Member, IEEE) (Senior
Member, IEEE) received the first M.S. degree in
electrical engineering in 2013, the second M.S. de-
gree in computer engineering in 2015, and the Ph.D.
degree in co-majors of electrical engineering and
computer engineering from Iowa State University,
Ames, IA, USA, in 2016. He was a Postdoctoral
Fellow with the King Abdullah University of Sci-
ence and Technology, Thuwal, KSA, from 2016
to 2020, where he is currently a Senior Research
Scientist with the Communications and Computing
Systems Laboratory. Dr. Celik is the recipient of IEEE Communications
Society’s 2023 Outstanding Young Researcher Award for Europe, Middle
East, and Africa (EMEA) region. He currently serves as an editor for
IEEE Communications Letters, IEEE Wireless Communication Letters, and
Frontiers in Communications and Networks. His research interests are in the
broad areas of next-generation wireless communication systems and networks.
reflecting surface aided multiuser system,” IEEE Wireless Commun.
Lett., vol. 9, no. 6, pp. 834–838, 2020.
[46] M. Grant and S. Boyd, “CVX: Matlab software for disciplined
convex programming, version 2.1,” Mar. 2014. [Online]. Available:
http://cvxr.com/cvx
Ahmed Eltawil (Senior Member, IEEE) received
the M.Sc. and B.Sc. degrees (Honors) from Cairo
University, Giza, Egypt, in 1999 and 1997, respec-
tively, and the Ph.D. degree from the University of
California at Los Angeles, Los Angeles, CA, USA,
in 2003. He has been a Professor of electrical engi-
neering and computer science with the University
of California at Irvine (UCI), Irvine, CA, USA,
since 2005. He is currently a Professor of electrical
and computer engineering with the King Abdullah
University of Science and Technology (KAUST),
Thuwal, Saudi Arabia, where he joined the Division of Computer, Electrical
and Mathematical Sciences and Engineering (CEMSE) in 2019. At KAUST,
he is the Founder and the Director of the Communication and Computing
Systems Laboratory (CCSL). His research is in the area of efficient archi-
tectures for computing and communications systems in general and wireless
systems in particular, spanning the application domains of body area networks,
low-power mobile systems, machine learning platforms, sensor networks,
and critical infrastructure networks. Dr. Eltawil is a Senior Member of the
National Academy of Inventors, USA. He received several awards, including
the NSF CAREER Award supporting his research in low-power computing
and communication systems. He is a Distinguished Lecturer at the IEEE.
He was selected as the “Innovator of the Year” for 2021 by the Henry
Samueli School of Engineering at the University of California at Irvine. For
his contributions to societal benefit through wireless innovations, he received
two certificates of recognition from the United States Congress. He has been
on the technical program committees and steering committees for numerous
workshops, symposia, and conferences in the areas of low-power computing
and wireless communication system design.
Galymzhan Nauryzbayev (Senior Member, IEEE)
received the B.Sc. and M.Sc. degrees (Hons.) in Ra-
dio Engineering, Electronics, and Telecommunica-
tions from the Almaty University of Power Engineer-
ing and Telecommunication, Almaty, Kazakhstan, in
2009 and 2011, respectively, and the Ph.D. degree
in Wireless Communications from The University
of Manchester, U.K., in 2016. From 2016 to 2018,
he held several academic and research positions
with Nazarbayev University, Kazakhstan, L. N. Gu-
milyov Eurasian National University, Kazakhstan,
and Hamad Bin Khalifa University, Qatar. In 2019, he joined Nazarbayev
University as an Assistant Professor. His research interests include wire-
less communication systems, focusing on reconfigurable intelligent surface-
enabled communications, multiuser MIMO systems, cognitive radio, signal
processing, energy harvesting, visible light communications, NOMA, and
interference mitigation. He served as a technical program committee member
for numerous IEEE flagship conferences. He is a Vice-Chair of the National
Research Council of the Republic of Kazakhstan.
