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312 B.-H. LUU, S.-C. LAM, N.-H. NGUYEN, ET AL., PERFORMANCE OF THE USER IN THE TDD NOMA CELLULAR . . .
Performance of the User in the TDD NOMA Cellular
Networks Enabling FFR
Bach-Hung LUU 1, Sinh-Cong LAM 1, Nam-Hoang NGUYEN 1, Trong-Minh HOANG 2
1Faculty of Electronics and Telecommunications, VNU-University of Engineering and Technology, Hanoi, Vietnam
2Telecommunication Faculty No1, Posts and Telecommunications Institute of Technology, Hanoi, Vietnam
congls@vnu.edu.vn
Submitted February 3, 2024 / Accepted April 9, 2024 / Online first April 30, 2024
Abstract. Improving the user performance and spectrum
efficiency are urgent problems for 5G and beyond 5G (B5G)
cellular networks to support high Quality of Services such as
enhanced mobile broadband, ultra-reliable, and low latency
communications. Together with Fractional Frequency Reuse
(FFR), Time Division Duplex (TDD) and Non-Orthogonal
Multi-Access (NOMA) are promising the potential solutions
for these problems. While the related researches focus on
the single or combination two of three techniques, this paper
proposes a system that combination of all three techniques to
improve the data rate on the uplink sub-band. Specifically,
each couple of Cell-Center User (CCU) and Cell-Edge User
(CEU) in a given cell, that is defined by the FFR technique, is
allowed to transmit on the same sub-band by the meaning of
power-domain NOMA technique. In addition, the TDD tech-
nique allow the sharing sub-band between the user and Base
Station (BS). The analytical results in Nakagami-𝑚fading
and regular path loss model shows that achievable total data
rate on the shared sub-band in the proposed system model
is 18.2% and 125% higher than that in the regular one with
TDD and NOMA, respectively. The data rate improvement of
the proposed system model proves the feasibility of co-exits
of these techniques in the B5G systems.
Keywords
Fractional frequency reuse, time division technique,
non-orthogonal multiplexing access, Poisson point
process
1. Introduction
The high Quality of Service requirements of the users
in the recent years have been promoting the development
and implementation of the cellular systems such as B5G. In
these systems, the radio spectrum is utilized and exploited
at a very high efficiency by the advanced techniques to pro-
vide a large bandwidth and then a high performance to the
users [1]. FFR, which was first introduced for the 4G sys-
tem and recommended in 3GPP documents, is considered
the core technique of the B5G system [1], [2]. In this tech-
nique, the BS follows the pre-defined criteria, such as instan-
taneous received, long-term signal powers and distance from
the served users, to classify before serving them on the spe-
cific sub-band with appropriate power levels. Through the
deployment of FFR technique, the network performance and
frequency spectrum can be significantly improved. In addi-
tion, TDD and NOMA are emerging as the most potential
techniques in the B5G systems [1].
In the previous cellular systems such as 3G and 4G,
the uplink and downlink are separated in frequency domain
by the meaning of Frequency Division Duplex (FDD) tech-
nique. However, due to the asynchronous of uplink and
downlink throughput, some of uplink sub-bands are unoccu-
pied while bandwidth shortage can occur in the downlink.
Therefore, the TDD technique was introduced to share band-
width between uplink and downlink [3] so that the spectrum
efficiency is improved. The feasibility of the TDD tech-
nique on the modern cellular networks has been studied in
the literature. In [4], the coverage probability in both up-
link and downlink were evaluated in the two-tier system with
dynamic and static TDD. The simulation results show that
there should be a trade-off between the uplink and down-
link performance.The downlink achievable rate of the user
in the free-cell system with Multiple-Input-Multiple-Output
(MIMO) and TDD technique was studied in [5]. In addi-
tion, by proposing a cluster-based radio frame coordination
using codebooks, the authors in [6] proved that the uplink
performance can be significantly improved while the uplink
throughput maintains at a high value. Recently, the combina-
tion of TDD with other emerging techniques such as MIMO
with and without cooperative communication was studied to
enhance the performance of AI-empowered networks [7], [8].
Besides, the NOMA technique was initially developed
for 5G networks to allow a BS to simultaneously serve sev-
eral users on a given sub-band to improve the overall net-
work performance where the users are distinguished by the
serving power [9]. The authors in [10] compared the user
outage probability in the downlink coordinated multi-point
DOI: 10.13164/re.2024.0312
RADIOENGINEERING, VOL. 33, NO. 2, JUNE 2024 313
system with and without NOMA. The paper’s results illus-
trated that there exists a set of network parameters so that the
NOMA system achieves a similar outage probability as the
system without NOMA. The performance of NOMA tech-
nique was studied in the system with energy harvesting [11].
Furthermore, the combination of TDD and NOMA was stud-
ied [7, 12, 13]. In [13], the feasibility of TDD - NOMA
combination was examined in the system with simultaneous
wireless information and power transfer. In addition, the
combination of these techniques was also studied in cog-
nitive radio networks [12]. Moreover, the authors in [14]
proved that deep reinforcement learning is possible to use
to improve the performance of TDD - NOMA system with
reconfigurable intelligent surface assistance.
Although the discussed works provided a significant in-
sight about the feasibility NOMA technique in the modern
cellular system, he selection of user pair has not been clearly
presented. Reference [15] defined the couple of users based
on the distance from these users to the serving BSs. Par-
ticularly, each user group consists of one near and far users.
However, this is not optimal selection since the near users
may have better channel qualities than the far ones. Although
the channel quality was used in [16] to form the couple of
NOMA user, the slow-fading and inter-cell interference were
not discussed. In addition, the search on co-exist of TDD
and FFR techniques in a cellular system has not been well-
investigated. The authosr in [17] discussed the combination
of TDD and FFR in the hexagonal cellular network with and
without device-to-device links. The study of different FFR
schemes in the TDD cellular network with power control was
studied in [18]. Although these two works derived the ba-
sic knowledge about the operation of cellular networks with
both TDD and FFR techniques, the NOMA technique was
not presented in these works.
Hence, this paper aims to study the combination of TDD
and NOMA techniques in the uplink FFR cellular system.
Conventionally, the sub-bands in the regular FFR technique
are divided into several orthogonal groups with different op-
erational powers and assigned these sub-band groups to BSs
so that the difference between the operational power of a given
sub-band in two adjacent BSs is secure. Since this sub-band
allocation policy may result in signaling overload between
BSs, the modified FFR scheme in this paper allows sharing
the same frequency reuse pattern between all BSs. In addi-
tion, we form the active users in every cell into CCU - CEU
pairs which are distinguished by the uplink SIR. Instead of
assuming that the CCU - CEU pairs are served on different
sub-bands, the power-domain NOMA technique in this paper
allows that this pair of users are served on the same sub-
bands but with different serving powers. The Nakagami-𝑚
distribution is used to model the fast fading channel due to
its general properties. Furthermore, the paper utilizes the
stochastic geometry network layout, where the distribution
follows the spatial Poisson point process [19], to model the
distribution of BSs in the service area. Utilization of PPP
model is being widely used to replace the hexagonal cellular
network layout since it is close to the practical network de-
ployment [20], [21]. The analytical results from the derived
mathematical expressions illustrate that the proposed system
can significantly improve the total data rate on the shared
sub-band.
The remaining parts of the paper are organized as fol-
lows: Section 2 discusses about the PPP network model
that simultaneously TDD, modified FFR and NOMA tech-
niques. In addition, the resource allocation schemes and
wireless transmission conditions are also presented. Section
3 derives the performance metrics in terms of uplink user
coverage probability and data rate. The analytical and sim-
ulation results are presented and compared to other related
systems in Sec. 4. Finally, the conclusion is drawn in Sec. 5.
2. System Model
In this paper, we study a cellular FFR system that uti-
lizes both TDD and NOMA techniques where the BSs and
users are randomly distributed in the service area accord-
ing to the Spatial Poisson Point Process (PPP) as shown in
Fig. 1. Particularly, the number of BSs is a Poisson random
variable while their positions follows the spatial PPP. Thus,
𝜆(BS/km2) called the density of BSs.
The number of active users is large enough so that each
BS has at least two users to compose of CCU - CEU pair. Par-
ticularly, the user with the lower SIR is defined as CEU and
vice versa. In this paper, we assume that the SIR threshold for
the definition of CCU and CEU is upon the BS policy. By the
meaning of NOMA technique, each pair of CCU and CEU
transmit on the same uplink sub-band. Due to the thinning
properties of the PPP, CCUs and CEUs are also follows the
PPP with the same density of 𝜆u. In comparison to downlink,
the users in uplink tend to transmit a lower volume of data.
Thus, there are some unoccupied uplink sub-bands which
may be utilized for downlink transmission due to the benefit
of TDD technique. Of course, in a given BS, a sub-band only
can be used as either downlink sub-band or uplink sub-band.
Let 𝜆bis the density of BSs that utilizes the uplink sub-band
to perform data exchange. Then, 𝜆b+𝜆u=𝜆.
Figure 1 illustrates an example of an PPP uplink multi-
cell proposed network model where the user is at the origin of
2-D coordinate system and within the service area of BS 13.
Adjacent BS 2 and BS 14 are used as two different interfer-
ence sources. Particularly, the BS 2 uses the power-domain
NOMA technique to assign the uplink operational band of
the typical user for the uplink of CCU and CEU. Thus, the
couple of CCU and CEU create interference to the uplink
of the typical user which are presented by the dashed red
arrows. Since a given sub-band is used in downlink or up-
link, the BS 2 does not use the sub-band of CCU and CEU
in downlink transmission. Thus, the BS 2 does not create
interference to typical user. Meanwhile BS 14 use the uplink
operation band of the typical user for downlink transmission.
Hence, it directly produces interference to the typical user.
314 B.-H. LUU, S.-C. LAM, N.-H. NGUYEN, ET AL., PERFORMANCE OF THE USER IN THE TDD NOMA CELLULAR . . .
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Desired signal
Interfering signal
BS
User
CEU
CCU
typical
user
BS
BS
Fig. 1. System layout.
SB 1
Uplink
CCU
Uplink
CEU
Uplink
CEU
Uplink
CCU
Uplink
CEU
Uplink
CCU
SB 2 SB 4
Downlink
Uplink
CCU
Uplink
CCU
Downlink
Uplink
CCU
SB 3
Fig. 2. Uplink and downlink sub-band allocation.
Figure 2 illustrates an example of resource allocation
scheme for 4 uplink sub-bands in the proposed system. By
the meaning of FFR technique, the uplink signal quality of
the users are used to determine CCUs and CEUs. While the
traditional FFR technique requires different sub-bands for
CCU and CEU, the power-domain NOMA technique is ap-
plied to allow the sharing of sub-bands between these users.
Particularly, this technique allocates a lower power level for
the CCU and a higher one for CEU, which also satisfy the
recommendation of FFR technique. In some case, only sev-
eral allocated uplink sub-bands are used by users for data
transmission such as sub-bands SB 1, SB 2, and SB 4. The
rest of the uplink sub-bands may be free and wasted. Thanks
to the TDD technique, the proposed system can use SB 4 for
downlink transmission as illustrated in Fig. 2.
2.1 FFR Technique
With the help of FFR technique, the BSs can simultane-
ously utilize all sub-bands which are usually partitioned into
CC and CE sub-bands with the operational power of 𝑃cand
𝑃e, (𝑃e> 𝑃c), respectively. Conventionally, the user is de-
fined as the CCU and served by power 𝑃cif its downlink SIR
on the control channel, 𝑆 𝐼 𝑅, is greater than the classification
threshold 𝑇, i.e. 𝑆 𝐼 𝑅 > 𝑇 where
𝑆𝐼 𝑅 =𝑃𝑔 𝐿(𝑟)
Í𝑢∈𝜃𝑃𝑔𝑢𝐿(𝑟𝑢).(1)
In (1), 𝑔and 𝐿(𝑟)are the power channel gain and path
loss between the user and its serving BS at a distance of 𝑟;
Í𝑢∈𝜃𝑃𝑔𝑢𝐿(𝑟𝑢)is the total interference from the adjacent
BSs in set 𝜃. According to 3GPP document [22], the trans-
mission power of users and BSs in the indoor environment
are greater than 20 dBm while the Gaussian noise power is
about –103 dBm/Hz. When 20 MHz bandwidth is utilized,
the transmission power in each Hz is about –53 dBm/Hz
which is extremely greater than the Gaussian noise power.
Thus, the impact of Gaussian noise power on the network
performance can be omitted. Hence, the Gaussian noise is
ignored in the coverage probability and data rate analysis
in this paper. In contrast, the CEU should have 𝑆 𝐼 𝑅 < 𝑇 .
Thus, the CCU and CEU classification probability are de-
fined as the conditional probability Pe(𝑇)=P(𝑆𝐼 𝑅 < 𝑇 )
and Pc(𝑇)=1− Pc. Consequently, the transmission power
of the typical user in the FFR system is
(𝑃cif 𝑆𝐼 𝑅 > 𝑇,
𝑃eif 𝑆𝐼 𝑅 < 𝑇. (2)
The corresponding desired signal power is
(𝑃c𝑔c𝐿(𝑟)if 𝑆𝐼 𝑅 > 𝑇,
𝑃e𝑔e𝐿(𝑟)if 𝑆𝐼 𝑅 < 𝑇 (3)
where (𝑔e, 𝑔c)and 𝐿(𝑟)are the power channel gains and path
loss between the user and its serving BS at distance 𝑟.
2.2 NOMA Technique
While FFR refers to sub-band sharing between BSs, the
power-domain NOMA technique allows more than one users
use the same sub-band to perform wireless communication
with their serving BSs. Conventionally, there is a primary
user which can transmit a high transmission power, while
others are secondary users and only deploy lower powers. In
this paper, we form a CCU and CEU into a pair where the
CEU acts as the primary user and CCU is considered the
secondary user. Let 𝜃cand 𝜃eas the set of CCUs and CEUs.
Thus, 𝜃cand 𝜃ehave the same density of 𝜆ubut each user in
𝜃cis independent to others in 𝜃e.
Due to the deployment of FFR and NOMA techniques,
the typical user is affected by interference from couples of
CCU and CEU at the adjacent cell. Thus, the interfering at
the serving BS of the typical user from adjacent cell 𝑘is
𝐼𝑘=𝑃c𝑔𝐿(𝑑c, 𝑘 ) + 𝑃e𝑔e, 𝑘 𝐿(𝑑e,𝑘 )(4)
where 𝑑c,𝑘 and 𝑑e, 𝑘 are the distance from the CCU and CEU
at adjacent cell 𝑘to the serving BS of the typical user, 𝑔c, 𝑘
and 𝑔e,𝑘 are the corresponding channel power gains.
Since the set of the adjacent cells of the typical user is
𝜃, the total uplink interference of the typical user is
𝐼u=𝐼uc +𝐼ue (5)
RADIOENGINEERING, VOL. 33, NO. 2, JUNE 2024 315
where 𝐼uc =Í𝑘∈𝜃c𝑃c𝑔c,𝑘 𝐿(𝑑c, 𝑘 )and 𝐼ue =
Í𝑘∈𝜃e𝑃e𝑔e,𝑘 𝐿(𝑑e, 𝑘 )are the interference from CCUs and
CEUs, respectively.
2.3 TDD Technique
To avoid the waste of unused uplink sub-band, the TDD
technique is proposed to used in the system model to allow
the BS use some uplink sub-bands as the downlink resource.
In this paper, the uplink sub-band is used as a downlink sub-
band if and only if it is not used by any user. Let 𝑝as the
uplink/downlink sharing coefficient to indicate the probabil-
ity that a uplink sub-band is used by the BS; 𝑝=0if the non
of uplink sub-bands are shared to BSs; 𝑝=1if all uplink
sub-bands are able to occupied by BSs. Thus, the density of
BSs that transmit on the same uplink sub-band is 𝜆b=𝑝𝜆.
In other words, besides the interfering users at adjacent cells,
the BS of the typical user is affected by interference from
adjacent BSs with a density of 𝑝𝜆. The total interference is
𝐼b=
𝑢∈𝜃b
𝑃b𝑔𝑢𝑟−𝛼
𝑢.(6)
With assumption that the number of users is large enough so
that all uplink sub-bands are utilized, 𝜆u+𝜆b=𝜆. Then,
𝜆u=(1−𝑝)𝜆. Consequently, the total interference at the
serving BS of the typical user is
𝐼=𝐼b+𝐼uc +𝐼ue.(7)
Combining with the definition of the desired signal in (3),
the uplink SIR of the typical user is
𝑆𝐼 𝑅 =(𝑆 𝐼 𝑅c=𝑃c𝑔c𝐿(𝑟)
𝐼if 𝑆𝐼 𝑅 > 𝑇,
𝑆𝐼 𝑅 e=𝑃e𝑔e𝐿(𝑟)
𝐼if 𝑆𝐼 𝑅 < 𝑇. (8)
3. Small-Scale and Large-Scale
Fadings
Large-scale fading: In wireless communication, the
signal travels over distances usually suffers the path loss due
to various conditions such as refraction, reflection, free-space
loss and so on. In this paper, the regular path loss model,
where the path loss over a distance of 𝑟is 𝐿(𝑟)=𝑟−𝛼, is used
to compute the power loss of the signal as it travels from the
source to the destination.
Small-scale fading: Since Nakagami-𝑚random vari-
able is able to model the generalized wireless channel, it
is adopted in this paper to represent the small-scale fading.
Thus, the channel power gain follows normalized gamma
random variable with PDF
𝑓G(𝑥)=𝑚𝑚𝑥𝑚−1
Γ(𝑚)e−𝑚𝑥 , 𝐹G(𝑥)=𝛾(𝑚, 𝑚𝑥)
Γ(𝑚)(9)
0123456
g
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Gg(g)
m=0.5
Upper Bound
Lower Bound
Exact form
0123456
g
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Gg(g)
m=2
Lower Bound
Upper Bound
Exact form
Fig. 3. Upper and lower bound of 𝐹G(𝑔).
where 𝑚is the shape of Nakagami random variable; 𝛾(𝑥)
and Γ(𝑥)are the incomplete and complete gamma functions.
Utilizing the results in [23], the lower bound and upper bound
of 𝐹G(𝑥)is given by
𝑚(1−e−𝑎𝑥 )𝑚≤𝐹G(𝑥) ≤ 𝑚1−e−𝑏 𝑥 𝑚
(10)
where 𝑎=1and 𝑏= Γ(𝑚+1)−1/𝑚if 𝑚 < 1; and
𝑎= Γ(𝑚+1)−1/𝑚and 𝑏=1if 𝑚 > 1.
From Fig. 3, it can conclude that 𝐹G(𝑔) ≈ 1−e−𝜁 𝑥 𝑚
where 𝜁= Γ(𝑚+1)−1/𝑚. Utilizing Newton’s generalized
binomial theorem, 𝐹Gr (𝑔)is expanded as follows:
𝐹G(𝑔)=
𝑀
𝑘=0
𝜌(𝑚, 𝑘 )e−𝑘𝜁 𝑥 (11)
where 𝜌(𝑚, 𝑘 )=Î𝑘
ℎ=1
𝑚−ℎ+1
ℎ;𝑀is an integer number, and
the accuracy of expansion increases with 𝑀. In this paper,
for sufficient accuracy, 𝑀=𝑚if 𝑚is an integer number,
𝑀=[𝑚] + 10 if 𝑚is a non-integer number.
4. Performance Evaluation
4.1 Laplace Transform of Intercell Interference
Theorem 4.1 The closed-form expression of Laplace trans-
form of the uplink Interference at the serving BS of the typ-
ical user from the CCUs at adjacent cells in the system that
utilizes both FFR and NOMA techniques is given by
Luc (𝑠)=exp −2𝜋𝜆u𝐶𝑃
2
𝛼
c𝑠
𝑚2
𝛼,(12)
where 𝐶=Í𝑁
𝑛=1𝐶𝑛
𝑚
(− 1)𝑛+1
2−𝑛𝑎 +1
2+Í𝑁
𝑛=0𝐶𝑛
𝑚
(− 1)𝑛+1
2+𝛼(𝑚+𝑛).
316 B.-H. LUU, S.-C. LAM, N.-H. NGUYEN, ET AL., PERFORMANCE OF THE USER IN THE TDD NOMA CELLULAR . . .
Proof 4.2 The Laplace transform is defined as Luc =
E[exp (−𝑠𝐼uc )]. Substituting the interference’s definition
in (5), the Laplace transform is expanded by
Luc (𝑠)=E"Ö
𝑘∈𝜃c
exp −𝑠𝑃c𝑔c, 𝑘 𝐿(𝑑c,𝑘 )#.(13)
Since 𝑔c,𝑘 and 𝑔e, 𝑘 are a random gamma variable with
Laplace transform 𝐸[−𝑠𝑔]=(1+𝑠/𝑚)−𝑚,
Luc (𝑠)=E"Ö
𝑘∈𝜃c1+𝑠𝑃c
𝑚𝐿(𝑑c,𝑘 )−𝑚#.(14)
Employing the properties of probability generating function
with reminding that 0< 𝑑c, 𝑘 <∞[19],
Luc (𝑠)=exp −2𝜋𝜆u∫∞
01−1+𝑠𝑃c
𝑚𝑡 𝛼−𝑚𝑡d𝑡.(15)
To compute the integrals in the above equation, we utilize the
the binomial expansion formulas of 1
(1+𝑥)𝑚which states that
1
(1+𝑥)𝑚=(Í𝑁
𝑛=0𝐶𝑛
𝑚(−1)𝑛𝑥𝑛if 𝑥 < 1,
Í𝑁
𝑛=0𝐶𝑛
𝑚(−1)𝑛𝑥−𝑚−𝑛if 𝑥 > 1(16)
where 𝐶𝑛
𝑚=𝑛+𝑚−1
𝑚−1;𝑁is an integer number; 𝑁is large
enough so that the converse of the expansion is obtained.
Since 𝑠𝑃c
𝑚𝑡−𝛼<1=> 𝑡 > 𝑠 𝑃c
𝑚1/𝛼
, to evaluate the integral
𝐼(𝑃c)of (15), we separate it into two parts as follows
𝐼c(𝑃c)=∫∞
(𝑠𝑃c/𝑚)1/𝛼1−1+𝑠𝑃c
𝑚𝑡 𝛼−𝑚𝑡d𝑡
+∫(𝑠𝑃c/𝑚)1/𝛼
01−1+𝑠𝑃c
𝑚𝑡 𝛼−𝑚𝑡d𝑡. (17)
The first integral in (17) is computed as follows
𝐼1c (𝑃c)=∫∞
𝑠𝑃c
𝑚1/𝛼 1−
𝑁
𝑛=0
𝐶𝑛
𝑚(−1)𝑛𝑠𝑃c
𝑚𝑡 𝛼𝑛!𝑡d𝑡
=
𝑁
𝑛=1
𝐶𝑛
𝑚(−1)𝑛+1𝑠𝑃c
𝑚𝑛∫∞
𝑠𝑃c
𝑚1/𝛼𝑡1−𝑛𝛼 𝑡d𝑡. (18)
Similarity, the second integral in (17) is computed as
𝐼2c (𝑃c)=∫𝑠𝑃c
𝑚1/𝛼
0 1−
𝑁
𝑛=0
𝐶𝑛
𝑚(−1)𝑛𝑠𝑃c
𝑚𝑡 𝛼−𝑚−𝑛!𝑡d𝑡.
The integral can be separated into two following parts
𝐼2c (𝑃c)=∫𝑠𝑃c
𝑚1/𝛼
0
𝑡d𝑡
+
𝑁
𝑛=0
𝐶𝑛
𝑚(−1)𝑛+1𝑠𝑃c
𝑚−𝑚−𝑛∫𝑠𝑃c
𝑚1/𝛼
0
𝑡1+𝛼(𝑚+𝑛)d𝑡.
The integrals of 𝐼1c (𝑃c)and 𝐼2c (𝑃c)can directly compute.
Hence, 𝐼(𝑃c)=𝐼1c (𝑃c) + 𝐼2c (𝑃c)and equals to
𝐼(𝑃c)=𝑠𝑃c
𝑚2
𝛼 Í𝑁
𝑛=1𝐶𝑛
𝑚
(− 1)𝑛+1
2−𝑛𝑎 +1
2
+Í𝑁
𝑛=0𝐶𝑛
𝑚
(− 1)𝑛+1
2+𝛼(𝑚+𝑛)!.
Consequently, the Laplace transform is obtained as in (12).
The theorem is proved.
Theorem 4.3 The closed-form expression of Laplace trans-
form of the uplink Interference at the serving BS of the typical
user from the CEUs at the adjacent cells in the system that
utilizes both FFR and NOMA techniques is given by
Lue (𝑠)=exp −2𝜋𝜆u𝐶𝑃
2
𝛼
e𝑠
𝑚2
𝛼.(19)
Proof 4.4 The only difference between the interference from
CCUs and CEUs is the transmission power of the interfering
source. Particularly, the transmission power of CCUs is 𝑃c
while that of CEU is 𝑃e. Thus, the Laplace transform of the
interference from CEUs can be obtained from Theorem 4.1
by changing the transmission power from 𝑃cto 𝑃e.
Theorem 4.5 The expression of Laplace transform of the
uplink Interference at the serving BS of the typical user from
the BSs in the system that utilizes both FFR and NOMA
techniques is given by
Lb(𝑠)=exp −2𝜋𝜆u∫∞
𝑟1−1+𝑠𝑃b
𝑚𝑡 𝛼−𝑚𝑡d𝑡.(20)
Proof 4.6 Compared to the interfering CCUs, the set of in-
terfering BSs has the following differences. (1) The power
of each interfering BS is 𝑃b; (2) The density of interfering
BSs is 𝜆(3) The interfering BSs should be farther than the
serving BS of the typical user, i.e. 𝑟u> 𝑟. By following the
approach in Theorem 4.1, the Laplace transform is obtained.
Theorem 4.7 The Laplace transform of the total interference
on a given frequency band is
L(𝑠)=Luc (𝑠)Lue (𝑠)Lb(𝑠).(21)
Proof 4.8 From (7), the total interference is the sum of 𝐼ue ,
𝐼uc, and 𝐼b. Thus, the Laplace transform of the total interfer-
ence is the product of the corresponding Laplace transform
of the interference.
RADIOENGINEERING, VOL. 33, NO. 2, JUNE 2024 317
4.2 Coverage Probability
In the cellular system, the coverage probability is used
to evaluate the ability to meet signal strength requirements
of the typical user. Mathematically, the coverage probability
of the typical user with uplink SIR of 𝑆 𝐼 𝑅zdefined as:
Pz=P𝑆𝐼 𝑅z>ˆ
𝑇.(22)
Thus, the typical user can be either CCU with a probability
of P(𝑆𝐼 𝑅 > 𝑇 )and CEU with a probability of P(𝑆𝐼 𝑅 < 𝑇 ).
Thus, the coverage probability is formulated as:
P=ERP𝑆𝐼 𝑅 c>ˆ
𝑇|𝑆𝐼 𝑅 > 𝑇+P𝑆 𝐼 𝑅e>ˆ
𝑇|𝑆𝐼 𝑅 < 𝑇.
Theorem 4.9 The coverage probability of the CCU in the
proposed system is obtained by
Pc(ˆ
𝑇)=
EÍ𝑀
𝑘=1(−1)𝑘+1𝜌(𝑚, 𝑘)Lb(𝑘𝑠c)Luc(𝑘 𝑠c)Lue (𝑘𝑠c)
Í𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)L (ℎ𝑠b)
EÍ𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)L (ℎ𝑠b)
where 𝑠c=𝜁ˆ
𝑇𝑟 𝛼
𝑃c;𝑠e=𝜁ˆ
𝑇𝑟 𝛼
𝑃eand 𝑠b=𝜁ˆ
𝑇𝑟 𝛼
𝑃b.
Proof 4.10 Utilizing the definition of SIR in (8), then
Pc(ˆ
𝑇)=P𝑃c𝑔c𝐿(𝑟)
𝐼b+𝐼ue +𝐼uc
>ˆ
𝑇
𝑃𝑔𝐿(𝑟)
𝐼> 𝑇
=
Ph𝑔c>ˆ
𝑇𝐼b+𝐼ue+𝐼uc
𝑃c𝐿(𝑟), 𝑔 > 𝑇 𝐼
𝑃𝐿 (𝑟)i
Ph𝑔 > 𝑇 𝐼
𝑃𝐿 (𝑟)i.(23)
From the approximation form of 𝐹G(𝑔)in (11), the coverage
probability is approximated by
Pc(ˆ
𝑇)=
EÍ𝑀
𝑘=1(−1)𝑘+1𝜌(𝑚, 𝑘)exp−ˆ
𝑇 𝑘𝜁 𝑟 𝛼
𝑃c(𝐼b+𝐼ue+𝐼uc )
Í𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)hexp −𝑇ℎ𝜁 𝑟 𝛼
𝑃c𝐼i
EhÍ𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)hexp −𝑇𝑘 𝜁 𝑟 𝛼
𝑃c𝐼ii .
Utilizing the results of Theorems 4.1, 4.3, 4.5, we obtain
P(𝑟)=
EÍ𝑀
𝑘=1(−1)𝑘+1𝜌(𝑚, 𝑘)Lb(𝑘𝑠c)Luc(𝑘 𝑠c)Lue (𝑘𝑠c)
Í𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)L (ℎ𝑠b)
EÍ𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)L (ℎ𝑠b)
where L(𝑠c)is the Laplace transform of intercell interference
on the control channel. Reminding that all users transmit on
the control channel at a power of 𝑃c, and the density of inter-
fering users on this channel is 𝜆,L( 𝑠c)can be obtained from
Theorem 4.1 as follows:
L(𝑠)=exp −2𝜋𝜆𝐶 𝑃
2
𝛼
c𝑠
𝑚2
𝛼.(24)
The theorem is proved.
Theorem 4.11 The coverage probability of the CEU user in
the proposed system is given by
Pe(ˆ
𝑇)=EÍ𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)L (𝑠e)
1−EÍ𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)L (𝑠c)
−
EÍ𝑀
𝑘=1(−1)𝑘+1𝜌(𝑚, 𝑘)Lb(𝑘𝑠e)Luc(𝑘 𝑠e)Lue (𝑘𝑠e)
Í𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)L (ℎ𝑠b)
1−EÍ𝑀
ℎ=1(−1)ℎ+1𝜌(𝑚, ℎ)L (ℎ𝑠b).
Proof 4.12 Utilizing the definition of SIR in (8),
Pe(ˆ
𝑇)=P𝑃e𝑔e𝐿(𝑟)
𝐼b+𝐼ue +𝐼uc
>ˆ
𝑇
𝑃𝑔𝐿(𝑟)
𝐼< 𝑇
=
Ph𝑔e> 𝑇 𝐼b+𝐼ue+𝐼uc
𝑃e𝐿(𝑟), 𝑔 < 𝑇 𝐼
𝑃𝐿 (𝑟)i
Ph𝑔 > 𝑇 𝐼
𝑃𝐿 (𝑟)i
=
Ph𝑔e> 𝑇 𝐼b+𝐼ue+𝐼uc
𝑃e𝐿(𝑟)i
1−Ph𝑔 > 𝑇 𝐼
𝑃𝐿 (𝑟)i−
Ph𝑔e> 𝑇 𝐼b+𝐼ue+𝐼uc
𝑃e𝐿(𝑟), 𝑔 > 𝑇 𝐼
𝑃𝐿 (𝑟)i
1−Ph𝑔 > 𝑇 𝐼
𝑃𝐿 (𝑟)i.
Utilizing the similar approach in Theorem 4.9, the CEU cov-
erage probability is obtained as (25).
4.3 Capacity
This section derives the Shanon capacity of the typical
user in the proposed system with TDD and NOMA deploy-
ment and the regular TDD one. Theoretically, the capacity of
the typical user in the cellular network with received signal
quality, 𝑆𝐼 𝑅z, is allocated an unit bandwidth is defined as
𝐶=Elog2(1+𝑆𝐼 𝑅 z).(25)
As discussed in the literature, the typical user capacity can
be computed by the coverage probability results as follows:
𝐶=∫∞
0
Plog2(1+𝑆𝐼 𝑅 z)> 𝑡d𝑡
=∫∞
0
P𝑆𝐼 𝑅 z>e𝑡−1d𝑡. (26)
By following the definition of user coverage probability
in (22), the typical user capacity is re-written as follows
𝐶=∫∞
0
Pze𝑡−1d𝑡. (27)
In the regular TDD system without NOMA deployment
where the users and BSs share the same bandwidth, there
are one user and one BS that utilize the same frequency band
in each cell. Specifically, the user and BS shares the uplink
318 B.-H. LUU, S.-C. LAM, N.-H. NGUYEN, ET AL., PERFORMANCE OF THE USER IN THE TDD NOMA CELLULAR . . .
sub-band with a probability of 𝑝. Thus, the total interference
of the shared sub-band in (7) degrades into:
(𝐼bc =𝐼b+𝐼uc if CCU and BS share sub-band,
𝐼be =𝐼b+𝐼ue if CEU and BS share sub-band.(28)
Thus, the total capacity on the sub-band of interest is:
•If the CCU and BS share the same sub-band
Cc=log2(1+𝑆𝐼 𝑅uc)+𝑝log2(1+𝑆 𝐼 𝑅bc )(29)
where 𝑆𝐼 𝑅 uc and 𝑆𝐼 𝑅bc are obtained from (8) by sub-
stituting 𝐼with 𝐼bc.
•If the CEU and BS share the same sub-band
Ce=log2(1+𝑆𝐼 𝑅ue)+𝑝log2(1+𝑆 𝐼 𝑅be )(30)
where 𝑆𝐼 𝑅 ue and 𝑆𝐼 𝑅be are obtained from (8) by sub-
stituting 𝐼with 𝐼be.
In the proposed FFR system with TDD and NOMA combi-
nation where each sub-band is shared by the CCU, CEU and
BS. Thus, the total capacity on the given sub-band is:
𝐶=log2(1+𝑆𝐼 𝑅 c)+log2(1+𝑆𝐼 𝑅e)+log2(1+𝑆 𝐼 𝑅b)
where 𝑆𝐼 𝑅 cand 𝑆𝐼 𝑅eare defined in (8); 𝑆 𝐼 𝑅bcan be obtained
from (8) by replacing 𝑃cor 𝑃ewith 𝑃b.
5. Simulation and Discussion
In this section, we analyze the coverage probability of
the CCU and CEU user with different values of network
parameters such as density of BSs, SIR threshold. In addi-
tion, the ratio of sharing between the users and BSs is also
analyzed.
5.1 Analytical Validation
To validate the analytical results, Monte Carlo simula-
tion technique is utilized in this section. The main procedure
of the simulation is described as following steps:
1. Set initial values: 𝜆,𝑝; simulation number 𝑁s;𝑁c=0;
𝑁e=0.
2. Generate the number of BSs 𝑛b.
3. Generate distance from the typical to all BSs.
4. Generate channel power gains from the typical user to
all BSs.
5. Compute SIR on the control channel as in (1) and com-
pare it to the classification threshold 𝑇to determine
CCU and CEU.
6. With 𝑝, the interfering BSs, CCUs, CEUs of the typical
user are 𝑝 𝑛b,(1−𝑝)𝑛band (1−𝑝)𝑛b, respectively.
7. Generate the distance and channel power gains from the
typical user to CCUs, CEUs. Noted that the distance to
the BSs are generated in Step 2.
8. Compute the 𝑆 𝐼 𝑅cand 𝑆 𝐼 𝑅eof CCU and CEU as
in (8) and compare with the coverage threshold ˆ
𝑇. If
𝑆𝐼 𝑅 c>ˆ
𝑇,𝑁c=𝑁c+1. If 𝑆 𝐼 𝑅e>ˆ
𝑇,𝑁e=𝑁e+1.
9. Repeat Steps 2–8 𝑁stimes. Thus, the coverage proba-
bility of CCU and CEU are 𝑁c/𝑁sand 𝑁e/𝑁s.
To make the performance trend closer to the practical
network, the analytical and simulation parameters are se-
lected by following the 3GPP recommendation [22]. Specif-
ically, the selected parameters are summarized as Tab. 1.
In Fig. 4, the uplink coverage probability of the CCU,
CEU and the typical user are plotted and compared with the
Monte Carlo simulation results. As shown in this figure, all
theoretical curves visually match with the corresponding sim-
ulation ones. This indicates the accuracy of the theoretical
analysis in Sec. 4.2.
Since the coverage threshold ˆ
𝑇represents the minimum
requirement of SIR power level for the BS to detect the trans-
mitted signal from users. Thus, as shown in Fig. 4, the
user coverage probability rapidly reduces with ˆ
𝑇(dB). Spe-
cially, when ˆ
𝑇increases from –15 dB to –10 dB, the coverage
probability of the typical user declines by around 47% from
0.6 to 0.32. Furthermore, if the typical user can detect the
very weak signals which correspond to the very low cov-
erage threshold 𝑇, the CCU and CEU coverage probability
can reach to the maximum value of 1. In contrast, when the
typical user requires very strong signals to perform further
processing, its coverage probability can reduce to around 0
or can be called out-of-coverage area.
Parameters Values
Density of BSs 𝜆=1000 BS/km2
Path loss coefficient 𝛼=3
CCU transmission power 𝑃c=10 dBm
CEU transmission power 𝑃e=25 dBm
BS transmission power 𝑃b=40 dBm
Nakagami shape 𝑚=2
sub-band sharing probability 𝑝=0.4
Tab. 1. Simulation parameters.
-25 -20 -15 -10 -5 0 5 10
Coverage Threshold
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Coverage Probability
CCU-Theory
CEU-Theory
TypicalUE-Theory
CCU-Simulation
CEU-Simulation
TypicalUE-Simulation
Fig. 4. Theoretical analysis vs simulation.
RADIOENGINEERING, VOL. 33, NO. 2, JUNE 2024 319
In the proposed system model, the CCU and CEU have
the same statistical properties but the CEU is served by the
higher transmission power than the CCU. However, the CCU
has a significantly better channel condition than CEU. Thus,
the CCU still achieves a higher coverage probability than the
CEU as seen in Fig. 4. In addition, the coverage probability
of the typical user is the average of CCU and CEU coverage
probabilities. Thus, the curve of coverage probability of the
typical user lies between that of CCU and CEU.
5.2 Effects of Transmission Power on the User
Coverage Probability
In Fig. 5, the impact of BS transmission power on the
coverage probability of the typical user is visualized with dif-
ferent values of coverage threshold ˆ
𝑇(dB). Due to the TDD
utilization, the BS has a right to utilize the uplink sub-band to
perform data transmission and becomes a interference source
of the typical user. Consequently, the coverage probability of
the typical user reduces. It is obviously that a higher trans-
mission power of BS causes a higher interference power to
the typical user and consequently a lower coverage proba-
bility. Specially, when the BS transmission power increases
from 5 dB to 10 dB, the typical user’s coverage probability
reduces by 33.3% from 0.6 to 0.4.
5.3 Effects of Sharing Ratio on the User Data
Rate
Although deployment of TDD technique results in a de-
cline in the coverage probability of the typical user, this tech-
nique can bring benefits to the downlink and overall data rate
on the shared sub-band. When the uplink/downlink sharing
coefficient 𝑝increases, the BS is able to transmit on the up-
link with a higher probability. Thus, the downlink data rate
on the shared sub-band increases with the coefficient 𝑝. As
seen from Fig. 6, when 𝑝increases by two times from 0.2 to
0.4 and BS transmission power 𝑃b=20 dBm, the data rate
increases by 87.8% from 0.33 (bit/s/Hz) to 0.62 (bit/s/Hz).
It is noted that the typical user on the shared sub-band in
the proposed system with combination of TDD and NOMA
suffers interference from the couple of CCU and CEU in
every cell, as well as the adjacent BSs that transmit on this
sub-band. Meanwhile, in the system with TDD only, besides
interference from adjacent BSs as the same as in the proposed
system, the typical user on the shared sub-band is addition-
ally affected by interference from either CCU or CEU. In
other words, the typical user in the proposed system suffers
a higher interference level than another in the existing one
with TDD only. However, the difference between interfer-
ence levels is relatively small due to the smallness of user
transmission power compared to the BS transmission power.
Thus, the downlink data rate in the proposed system is very
close to the another in the TDD system as shown in Fig. 6.
In addition, when the number of BSs that utilize the
uplink sub-band increases with the uplink/downlink sharing
coefficient 𝑝. Thus, the interference on the shared sub-band
increases while the data rate reduces. As the result, the
data rate of the couple of CCU and CEU reduces. Upon
the changes of 𝑝, the total data rate on the shared sub-band
reduces or increases. Specifically,
•When 𝑝is a small number such as 𝑝 < 0.3in the case of
𝑃b=25 dBm, the BS operates on the shared sub-band
with a very low probability. Thus, the contribution of
the downlink data rate on the total data rate of the shared
sub-band is very small. Consequently, the total data rate
on the shared sub-band reflects the down trend of CCU
and CEU data rate. For example, the total data rate
reduces by approximately 12% from 1.34 (bit/s/Hz) to
1.18 (bit/s/Hz) as 𝑝increases from 0 to 0.3.
•When 𝑝is large enough, the BS uses the shared sub-
band with a higher density. Thus, the contribution of
the downlink data rate on the total data rate of the shared
sub-band is remarkable. As the result, the total data rate
on the shared sub-band follows the upward of the down-
link data rate. Particularly, when 𝑝moves from 0.4 to
0.7, the total data rate on the shared sub-band grows by
around 6.7% from 1.19 (bit/s/Hz) to 1.27 (bit/s/Hz) in
the case 𝑃b=25 dBm.
-15 -10 -5 0 5 10 15
Coverage Threshold
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Coverage Probability
P=0dB-Theory
P=0dB-Simmulation
P=5dB-Theory
P=5dB-Simmulation
P=10dB-Theory
P=10dB-Simmulation
Fig. 5. Coverage probability of typical user vs coverage
threshold.
0 0.2 0.4 0.6 0.8
uplink/downlink sharing coefficient p
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Downlink Data Rate on Shared Sub-band (bit/s/Hz)
Pb=20dBm
TDD + NOMA
TDD
0 0.2 0.4 0.6 0.8
uplink/downlink sharing coefficient p
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Downlink Data Rate on Shared Sub-band (bit/s/Hz)
Pb=25dBm
TDD + NOMA
TDD
Fig. 6. Downlink data rate on the shared sub-band.
320 B.-H. LUU, S.-C. LAM, N.-H. NGUYEN, ET AL., PERFORMANCE OF THE USER IN THE TDD NOMA CELLULAR . . .
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
uplink/downlink sharing coefficient p
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Total data rate on shared sub-band (bit/s/Hz)
Pb = 20 dBm TDD system
Pb = 20 dBm NOMA System
Pb = 20 dBm Proposed System
Pb = 25 dBm TDD system
Pb = 25 dBm Proposed System
Fig. 7. Data rate on shared sub-band vs sharing coefficient 𝑝.
It is also seen from Fig. 7 that the data rate on the shared
sub-band in the proposed system is significantly higher than
that in the TDD one. Specifically, when the sharing coeffi-
cient 𝑝=0.2and 𝑃b=20 dBm which means that the BS is
allowed to use 20% of the total uplink sub-bands, the pro-
posed system can provide a data rate of 1.3 (bit/s/Hz) which
is 18.2% than that in the TDD system.
In all systems, the users have a higher priority to use
the uplink sub-bands and the sharing of uplink sub-band with
BSs only takes places if there are some free sub-bands and the
TDD technique is enabled. Therefore, the uplink/downlink
sharing coefficient in Fig. 7 also indicates the uplink sub-
band utilization of the users. For example, 𝑝=0.3means
that 70% of uplink sub-bands are utilized by the users, and
the rest of sub-band which accounts of 30% can be used by
BSs if the TDD technique is enabled. In the system with
NOMA technique only, the BSs are unable to the uplink sub-
bands through they are free. Thus, the average total data
rate on shared sub-band in the NOMA system reduces as 𝑝
increases. Meanwhile, the proposed system with NOMA and
TDD technique, all occupied uplink sub-bands are allocated
to the BSs to avoid the waste of sub-band and improve the
total data rate on the shared sub-band. Particularly, Figure 7
illustrates that the total data rate on the shared sub-band is at
around 1.34 (bit/s/Hz) which is about 125% higher than that
in the NOMA system.
6. Conclusion
In this paper, the FFR cellular system that combines
TDD and NOMA technique is introduced where each BS
selects a couple of CCU and CEU to share the same sub-
band. Due to the policy of the FFR and power-domain
NOMA techniques, the CCU utilizes a lower power than
the CEU to communicate with the serving BS. In addition,
the BS is allowed to utilize the uplink sub-band with a pre-
defined probability by the TDD technique. To examine the
performance of the typical user in the proposed system, the
coverage probability is derived in the wireless condition of
Nakagami-𝑚as the fast fading and regular path loss as the
slow fading. Through the analytical result, it is stated that
the utilization of NOMA technique in uplink TDD system
has a very slightly impact on the downlink performance. In
addition, the combination of TDD and NOMA techniques in
the proposed FFR system can provide a higher total data rate
on the shared sub-band of 18.2% and 125% in comparison
to the system with TDD and NOMA, respectively. However,
there should be more works on the feasibility of TDD, FFR
and NOMA techniques. Particularly, the SIR in complicated
transmission conditions such as in the indoor area varies by
time slot. Thus, the utilization of SIR to classify the CCU
and CEU can take place during a very short time and result
in a high computing load. In addition, sub-band sharing be-
tween users and BSs in the proposed system requires a large
amount of signalings which can cause the signaling overload
at the BSs.
Acknowledgments
This work has been supported by VNU University of
Engineering and Technology under project number CN23.16.
References
[1] AGIWAL, M., ROY, A., SAXENA, N. Next generation 5G
wireless networks: A comprehensive survey. IEEE Communica-
tions Surveys & Tutorials, 2016, vol. 18, no. 3, p. 1617–1655.
DOI: 10.1109/COMST.2016.2532458
[2] SONG, M., SHAN, H., YANG, H. H., et al. Joint optimization of frac-
tional frequency reuse and cell clustering for dynamic TDD small cell
networks. IEEE Transactions on Wireless Communications, 2022,
vol. 21, no. 1, p. 398–412. DOI: 10.1109/TWC.2021.3096383
[3] KIM, H., KIM, J., HONG, D. Dynamic TDD systems for 5G and
beyond: A survey of cross-link interference mitigation. IEEE Com-
munications Surveys & Tutorials, 2020, vol. 22, no. 4, p. 2315–2348.
DOI: 10.1109/COMST.2020.3008765
[4] XIE, Z., WU, X., CHEN, X., et al. Coverage analysis of dynamic TDD
in two-tier heterogeneous ultra dense networks. In IEEE 92nd Vehic-
ular Technology Conference (VTC2020-Fall). Victoria (BC, Canada),
2020, p. 1–5. DOI: 10.1109/VTC2020-Fall49728.2020.9348431
[5] PAPAZAFEIROPOULOS, A., KOURTESSIS, P., RENZO, M. D.,
et al. Performance analysis of cell-free massive MIMO sys-
tems: A stochastic geometry approach. IEEE Transactions on
Vehicular Technology, 2020, vol. 69, no. 4, p. 3523–3537.
DOI: 10.1109/TVT.2020.2970018
[6] WANG, Y.-C., CHOU, C.-W.Efficient coordination of radio frames to
mitigate cross-link interference in 5G D-TDD systems. Computer Net-
works, 2023, vol. 232, p. 1–13. DOI: 10.1016/j.comnet.2023.109840
[7] ZHAO, F., CHEN, W., LIU, Z., et al. Deep reinforcement learn-
ing based intelligent reflecting surface optimization for TDD multi-
user MIMO systems. IEEE Wireless Communications Letters, 2023,
vol. 12, no. 11, p. 1951–1955. DOI: 10.1109/LWC.2023.3301496
RADIOENGINEERING, VOL. 33, NO. 2, JUNE 2024 321
[8] GE, L. J., NIU, S. X., SHI, C. P., et al. Cascaded deep neu-
ral network based adaptive precoding for distributed massive
mimo systems. Radioengineering, 2024, vol. 33, no. 1, p. 34–44.
DOI: 10.13164/re.2024.0034
[9] MAKKI, B., CHITTI, K., BEHRAVAN, A., et al. A survey of
NOMA: current status and open research challenges. IEEE Open
Journal of the Communications Society, 2020, vol. 1, p. 179–189.
DOI: 10.1109/OJCOMS.2020.2969899
[10] SUN, Y., DING, Z., DAI, X., et al. Stochastic geometry based mod-
eling and analysis on network NOMA in downlink CoMP systems.
IEEE Transactions on Vehicular Technology, 2023, vol. 73, no. 1,
p. 1–7. DOI: 10.1109/TVT.2023.3301627
[11] TITEL, F., BELATTAR, M. Optimization of NOMA downlink
network parameters under harvesting energy strategy using multi-
objective GWO. Radioengineering, 2023, vol. 32, no. 4, p. 492–501.
DOI: 10.13164/re.2023.0492
[12] ALKHAMEES, T. Y., MILSTEIN, L. B. Impact of sharing disrup-
tion in MC CR-NOMA. IEEE Access, 2023, vol. 11, p. 82871–82881.
DOI: 10.1109/ACCESS.2023.3300659
[13] ALAMU, O., OLWAL, T. O., DJOUANI, K. Cooperative NOMA
networks with simultaneous wireless information and power transfer:
An overview and outlook. Alexandria Engineering Journal, 2023,
vol. 71, p. 413–438. DOI: 10.1016/j.aej.2023.03.057
[14] KILINC, F., TASCI, R. A., CELIK, A., et al. RIS-assisted
grant-free NOMA: User pairing, RIS assignment, and phase
shift alignment. IEEE Transactions on Cognitive Communica-
tions and Networking, 2023, vol. 9, no. 5, p. 1257–1270.
DOI: 10.1109/TCCN.2023.3288108
[15] MANKAR, P. D., DHILLON, H. S. Downlink analysis of noma-
enabled cellular networks with 3GPP-inspired user ranking. IEEE
Transactions on Wireless Communications, 2020, vol. 19, no. 6,
p. 3796–3811. DOI: 10.1109/TWC.2020.2978481
[16] JAIN, M., SONI, S., SHARMA, N., et al. Performance analysis at
far and near user in NOMA based system in presence of SIC error.
AEU - International Journal of Electronics and Communications,
2020, vol. 114, p. 1–9. DOI: 10.1016/j.aeue.2019.152993
[17] VU, H. V., LE NGOC, T. Performance analysis of underlaid
full-duplex D2D cellular networks. IEEE Access, 2019, vol. 7,
p. 17633–176247. DOI: 10.1109/ACCESS.2019.2958300
[18] FIROUZABADI, A. D., RABIEI, A. M., VEHKAPERA, M. Frac-
tional frequency reuse in random hybrid FD/HD small cell net-
works with fractional power control. IEEE Transactions on Wire-
less Communications, 2021, vol. 20, no. 10, p. 6691–6705.
DOI: 10.1109/TWC.2021.3075987
[19] ANDREWS, J. G., BACCELLI, F., GANTI, R. K. A tractable ap-
proach to coverage and rate in cellular networks. IEEE Transac-
tions on Communications, 2011, vol. 59, no. 11, p. 3122–3134.
DOI: 10.1109/TCOMM.2011.100411.100541
[20] KAVITHA, P., SHANMUGAVEL, S. Analytical evaluation of chunk-
based tractable multi-cell OFDMA system. Radioengineering, 2018,
vol. 7, no. 1, p. 313–325. DOI: 10.13164/re.2018.0313
[21] CHOI, C.-S. Modeling and analysis of downlink communica-
tions in a heterogeneous LEO satellite network. IEEE Transac-
tions on Wireless Communications, 2024, Early Access, p. 1–15.
DOI: 10.1109/TWC.2024.3351876
[22] 3GPP E-UTRA Further Enhancements to LTE Time Division Duplex
(TDD) for Downlink-Uplink (DL-UL) Interference Management and
Traffic Adaptation. 2012, Technical report 3GPP TR 36.828 V11.0.
[23] ALZER, H. On some inequalities for the incomplete gamma func-
tion. Mathematics of Computation, 1997, vol. 66, no. 218, p.771–778.
DOI: 10.1090/S0025-5718-97-00814-4
About the Authors . . .
Bach-Hung LUU received the Bachelor of Electronic and
Communication Engineering Technology from University of
Engineering and Technology, Vietnam National University
in 2022 and continues his studies towards M.E.
Sinh-Cong LAM (corresponding author) received the Bach-
elor of Electronics and Telecommunication (Honours) and
Master of Electronic Engineering in 2010 and 2012, respec-
tively from University of Engineering and Technology, Viet-
nam National University (UET, VNUH). He obtained his
Ph.D. degree from University of Technology, Sydney, Aus-
tralia. His research interests focus on modeling, performance
analysis and optimization for 5G and B5G, stochastic geom-
etry model for wireless communications
Nam-Hoang NGUYEN received the Ph.D. degree from the
Vienna University of Technology, Austria, in 2002. He has
been working with the University of Engineering and Tech-
nology, Vietnam National University, Hanoi, since 2011,
where he was promoted to an Associate Professor in 2018.
His research interests include resource management for mo-
bile communications networks and future visible light com-
munications.
Trong-Minh HOANG earned bachelor’s degrees in Physics
Engineering (1994) and Electronic and Communications En-
gineering (1999) from Hanoi University of Science and Tech-
nology. His master’s degree (2003) and Ph.D. degree (2014)
in Electronic and Telecommunication Engineering from the
Posts and Telecommunications Institute of Technology, Viet-
nam. He studies wireless network routing, security, and
performance in edge computing, sensor networks, wireless
mobile networks, and beyond 5G technologies. Assoc. Prof
Dr. Trong-Minh Hoang is currently the head of the telecom-
munication network department and a Senior EEE member.
