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2020-05-18
Performance Analysis of Fractional Frequency Reuse
Schemes in Downlink Multi-Relay Multi-Cell OFDMA
and NOMA Cellular Networks
Saleh, Ali Meilad Mohamed
Saleh, A. M. M. (2020). Performance Analysis of Fractional Frequency Reuse Schemes in Downlink
Multi-Relay Multi-Cell OFDMA and NOMA Cellular Networks (Unpublished doctoral thesis).
University of Calgary, Calgary, AB.
http://hdl.handle.net/1880/112103
doctoral thesis
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UNIVERSITY OF CALGARY
Performance Analysis of Fractional Frequency Reuse Schemes in Downlink Multi-Relay
Multi-Cell OFDMA and NOMA Cellular Networks
by
Ali Meilad Mohamed Saleh
A THESIS
SUBMITTED TO THE FACULTY OF GRADUATE STUDIES
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
GRADUATE PROGRAM IN ELECTRICAL AND COMPUTER ENGINEERING
CALGARY, ALBERTA
MAY, 2020
© Ali Meilad Mohamed Saleh 2020
Abstract
With the aim of increasing the demands of high data rates, improving spectral efficiency
(SE), meeting quality of service (QoS) requirements, and increasing the energy efficiency
(EE), frequency reuse schemes are the most promising approaches for achieving these targets
and reducing the effects of interference in current and next-generation multi-cell cellular
networks. Fractional frequency reuse (FFR) schemes are among the most of the frequency
reuse schemes used to mitigate inter-cell interference (ICI), especially for outer zone users.
Relaying with FFR schemes is considered an effective strategy for enhancing capacity and
increasing cell coverage in a cooperative relaying cellular networks. This thesis develops
an analytical frequency reuse patterns that minimize the effect of ICI for FFR schemes
in cooperative and non-cooperative downlink orthogonal frequency division multiple access
(OFDMA) cellular networks.
In fifth generation (5G) and beyond wireless communication systems, non-orthogonal
multiple access (NOMA) compares favourably to orthogonal multiple access (OMA) sys-
tems due to high SE, massive connectivity, and improved user fairness. In addition, NOMA
utilizes power domain user multiplexing by using signal superposition at the transmitter
and successive interference cancellation (SIC) at the receiver. This thesis develops Power
allocation (PA) and user pairing (UP) algorithms to maximize the sum-rate of paired users
for FFR schemes in downlink NOMA-based cooperative and non-cooperative relaying while
accounting for the effect of ICI and imperfect SIC on the system performance. This the-
sis develops a novel SIC error factor formula for imperfect SIC scenarios that is used for
evaluating the overall system performance.
Finally, an analytical expression for the instantaneous signal-to-interference noise ratio
(SINR) is developed for inner and outer zone paired users while taking into account ICI and
imperfect SIC conditions in a cooperative relaying system. This expression is used to evaluate
ii
the achievable sum-rates and outage probability (OP) for both zone users in a cooperative
relaying NOMA-based FFR scheme and is compared to a non-cooperative system.
The research in this thesis offers the potential for enhancing system performance while
reducing the impact of ICI. The numerical results validate the efficacy of the proposed
schemes in enhancing the performance compared to their counterparts.
iii
Acknowledgments
I would like to thank my supervisor Prof. Abu Sesay for his endless guidance, fruitful discus-
sions and non-fading encouragement. Working under his supervision helped me developing
my research ability and improving my communication skills.
I would like to thank Prof. Geoffrey Messier and Prof. John Nielsen, who have served
in the supervisory committee; Prof. Rohana Ambagaspitya, who has been the internal
examiner in the thesis examination committee; Prof. Xiaodai Dong, who has been the
external examiner in the thesis examination committee.
I would like to thank my past and present lab mates - Dr. Ammar Almasry, Dr. Ngon
Le, Dr. Yasser Hashem, Mostafa Raeisi and my friends for their companionship, tremendous
help and continuous encouragement.
Finally, I would like to thank my family, my mother, my father, my brothers, my sister
and my lovely wife and daughters, who have witnessed the ups and downs of my research
and helped me go through difficulties. I would have not been able to make it this far without
my family kindness, patience and endless support.
iv
Table of Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Symbols, Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . x1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Problem Statement and Thesis Objectives . . . . . . . . . . . . . . . . . . . 31.2 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1 overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Notations and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 Propagation Models for Wireless Communication Systems . . . . . . . . . . 10
2.3.1 Small-Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Large-Scale Fading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 OFDMA-Based Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . 112.5 NOMA-Based Cellular Networks . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.1 Power Allocation in NOMA . . . . . . . . . . . . . . . . . . . . . . . 142.5.2 User Pairing in NOMA . . . . . . . . . . . . . . . . . . . . . . . . . . 152.5.3 Successive Interference Cancellation Technology in NOMA . . . . . . 15
2.6 Cooperative Relaying-Based Cellular Networks . . . . . . . . . . . . . . . . . 162.6.1 Classification of Relays . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.7 Inter-Cell Interference Mitigation Approaches in OFDMA-Besed Cellular Net-works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.7.1 ICIC using Frequency Reuse Schemes in Cellular Networks . . . . . . 20
3 Performance Analysis of Fractional Frequency Reuse Schemes in Multi-RelayMulti-Cell OFDMA Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.4 The Difference Set Definition and the Proposed Scheme . . . . . . . . . . . . 293.5 Performance Analysis of FRF = (1,7/3) and FRF=(1,7/4) Schemes . . . . . 303.6 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 Sum Rate Maximization for FFR Schemes with Inter-Cell Interference in
Downlink Multi-Cell NOMA-Based Networks . . . . . . . . . . . . . . . . . . 454.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.3 System and Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.4 Spectral Efficiency and Outage Probability for an FFR Scheme in NOMA . . 52
4.4.1 Spectral Efficiency and Outage Probability for Inner Zone Users . . . 52
v
4.4.2 Spectral Efficiency and Outage Probability for Outer Zone Users . . . 534.5 Proposed Power Allocation Algorithm with SIC Constraint to Maximize Achiev-
able Sum-Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.5.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.6 Achievable Sum-Rate with Proposed SIC Error Factor at the Closer UserReceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.7 Generalization of Proposed User Paring Algorithm to Maximize AchievableSum-Rate in FFR Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.8 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675 Sum Rate Maximization for FFR Schemes with Inter-Cell Interference in
Downlink Multi-Relay Multi-Cell NOMA-Based Networks . . . . . . . . . . . 695.1 Chapter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.4 Instantaneous SINR at Inner Zone Users in the First Time Slot . . . . . . . 745.5 Instantaneous SINR at Outer Zone Users in the First Time Slot . . . . . . . 765.6 Instantaneous SINR at Outer Zone Users in the Second Time Slot . . . . . . 775.7 Achievable Rate for the Inner Zone Group . . . . . . . . . . . . . . . . . . . 78
5.7.1 Problem Formulation for Inner Zone Group . . . . . . . . . . . . . . 805.8 Achievable Rate for the Outer Zone Group . . . . . . . . . . . . . . . . . . . 81
5.8.1 Problem Formulation for Outer Zone Group . . . . . . . . . . . . . . 835.9 Outage Probability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.9.1 Outage Probability for Inner Zone User mi . . . . . . . . . . . . . . . 855.9.2 Outage Probability for Inner Zone User ni . . . . . . . . . . . . . . . 885.9.3 Outage Probability for Outer Zone User mo . . . . . . . . . . . . . . 895.9.4 Outage Probability for Outer Zone User no . . . . . . . . . . . . . . . 92
5.10 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1016 Summary, Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . 1036.1 Thesis Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 1036.2 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 106A How to Generate the Proposed Frequency Patterns . . . . . . . . . . . . . . 107B SIC Error Factor (Fc) Formula . . . . . . . . . . . . . . . . . . . . . . . . . 110Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
vi
List of Tables
3.1 Chapter 3 simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1 Chapter 4 simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . 61
5.1 Chapter 5 simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . 96
vii
List of Figures and Illustrations
2.1 Layout of inner and outer zones. . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Layout of OFDM transmitter-receiver. . . . . . . . . . . . . . . . . . . . . . 122.3 The sub-carriers allocation in NOMA and OMA. . . . . . . . . . . . . . . . . 132.4 Layout of type I and type II. . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.5 Layout of frequency reuse factor of 1 (FRF=1). . . . . . . . . . . . . . . . . 202.6 Layout of frequency reuse factor of 3 (FRF=3). . . . . . . . . . . . . . . . . 212.7 A hybrid frequency reuse FRF=(1,3) scheme for multi-cell OFDMA systems. 232.8 Partial frequency reuse scheme for multi-cell OFDMA systems. . . . . . . . . 24
3.1 Transmission link with relays in each 3-sectored cell. . . . . . . . . . . . . . . 273.2 Transmission link with relays in each 4-sectored cell. . . . . . . . . . . . . . . 283.3 The layout of 36-cell structure for the FRF =(1,7/3) proposed scheme. . . . 283.4 The layout of 36-cell structure for the FRF =(1,7/4) proposed scheme. . . . 293.5 Proposed two-tiers structure for FRF=(1,7/3) scheme with one common sub-
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.6 Proposed two-tiers structure for FRF=(1,7/4) scheme with one common sub-
channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.7 SINR for the main cluster with two tiers for the proposed scheme FRF=(1,7/3)
and other schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.8 Comparison of the received SINR of the proposed schemes FRF=(1,7/4),
FRF=(1,7/3) and other schemes. . . . . . . . . . . . . . . . . . . . . . . . . 393.9 CDF of the received SINR for the main cluster with two tiers of the proposed
schemes and other schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.10 Outage probability of the received SINR for the proposed FRF=(1,7/3) scheme
and other schemes versus the threshold Γth (dB). . . . . . . . . . . . . . . . 413.11 Outage probability of the received SINR for both proposed schemes and other
schemes versus the threshold Γth (dB). . . . . . . . . . . . . . . . . . . . . . 413.12 Average SE with relays for the main cluster with two tiers of the proposed
schemes and other schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.13 Average EE with relays for the main cluster with two tiers of the proposed
schemes and other schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 Network structure for the FRF=(1,3) FFR scheme in OFDMA system. . . . 494.2 Two users downlink NOMA with the SIC model for inner zone users. . . . . 504.3 Two users downlink NOMA with the SIC model for outer zone users. . . . . 504.4 BPSK Constellation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.5 ASR for an FFR scheme in NOMA of perfect and imperfect SIC with 70 users. 624.6 ASR for an FFR scheme in NOMA of imperfect SIC (practical SIC) with 70
users. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.7 ASR for an FFR scheme in NOMA with and without SIC constraint for the
proposed UP scheme, other pairing schemes, and OMA system. . . . . . . . 64
viii
4.8 ASR for an FFR scheme in NOMA of imperfect SIC with SNR=100 dB ofthe proposed UP scheme, other pairing schemes, and OMA system. . . . . . 65
4.9 CDF of the SINR for inner and outer zone users when the number of users=24 in imperfect SIC case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.10 Outage probability of the SINR versus the threshold Γth (dB) for inner andouter zone users when the number of users =24 in imperfect SIC case. . . . . 67
5.1 Network structure for the FRF=(1,3) FFR scheme in OFDMA system . . . . 735.2 Cooperative NOMA relaying with a direct link in two time slots . . . . . . . 745.3 ASR for an FFR scheme in cooperative relaying NOMA-based of perfect and
imperfect SIC with 70 users. . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.4 ASR for an FFR scheme in cooperative relaying NOMA-based of imperfect
SIC (practical SIC) with 70 users. . . . . . . . . . . . . . . . . . . . . . . . . 985.5 Comparison of ASRs between cooperative and non-cooperative relaying of
proposed UP for an FFR scheme NOMA-based of perfect and imperfect SICwith 70 users. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.6 ASR for an FFR scheme in cooperative relaying NOMA-based of imperfectSIC with SNR=100 dB of the proposed UP scheme, other pairing schemes. . 100
5.7 ASR for an FFR scheme in cooperative and non-cooperative relaying NOMA-based of imperfect SIC with SNR=100 dB of the proposed UP scheme, otherpairing schemes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
B.1 BPSK constellation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
ix
List of Symbols, Abbreviations
Abbreviation Definition
3GPP Third generation partnership project
4G Fourth generation
5G Fifth generation
A/D Analogue-to-digital
AF Amplify-and-forward
ASR Achievable sum-rate
AWGN Additive white gaussian noise
BER Bit error rate
BPSK Binary phase-shift keying
BSs Base stations
CASFR Cluster-aware soft frequency reuse
CCDF Complementary cumulative distribution function
CDF Cumulative distribution function
CD-NOMA Code domain-NOMA
CF Compress-and-forwarding
CP Cyclic Prefix
CSI Channel state information
D/A Digital-to-analogue
DF Decode-and-forward
DPA Dynamic power allocation
EE Energy efficiency
FD Full-duplex
FFR Fractional frequency reuse
x
FFR-FI Fractional frequency reuse with full isolation
FPA Fixed power allocation
FR Frequency reuse
FRF Frequency reuse factor
FRSs Fixed relay stations
FSPA Full search power allocation
FTPA Fractional transmit power allocation
GEE Global energy efficiency
GSM Global system for mobile communication
HD Half-duplex
ICI Inter-cell interference
ICIC Inter-cell interference coordination
IFFT Inverse fast fourier transform
ISI Inter-symbol interference
LOS Line-of-sight
LTE-A Long term evolution-advanced
MIMO Multi-input multi-output
MRC Maximum ratio combining
MRSs Mobile relay stations
MS Mobile station
NLOS Non-line of sight
NOMA Non-orthogonal multiple access
OFDM Orthogonal frequency division multiplexing
OFDMA Orthogonal frequency division multiple access
OMA Orthogonal multiple access
OP Outage probability
xi
PA Power allocation
PD-NOMA Power domain-NOMA
PFR Partial frequency reuse
P/S Parallel-to-serial
QoS Quality of sevice
RSs Relay stations
RUP Reuse partitioning
RV Random variable
SC Superposition coding
SE Spectral efficiency
SIC Successive interference cancellation
SINR Signal to interference and noise ratio
SNR Signal to noise ratio
S/P Serial-to-parallel
s.t. Subject to
TS1 First-time slot
TS2 Second-time slot
TSs Time slots
UE User equipment
UP User pairing
WiMAX Worldwide interoperability for microwave access
WLANs wireless local area networks
Symbol Definition
AL Low channel gains group
AH High channel gains group
xii
bm,n Binary variable represents the relationship between m and n users
CN(·, ·) Complex normal distribution
C Achievable rate (b/s/Hz)
Disub Set of the indices of the sub-channels for the ith cell
Fc SIC error factor
G [·] Meijer’s G-function
γ SNR
Γ SINR
Γth SINR’s threshold
ηEE Achievable EE
β Amplifier gain
λth Minimum threshold to guarantee the SIC will decode correctly
δ Dirac delta function
E[·] Expectation operator
∆f Subcarrier spacing
fc Carrier frequency
g User grouping
hb Height of BS’s antenna
hm Height of MS’s antenna
I Number of interfering cells
Iinn Number of interfering cells for the inner zone case
Iout Number of interfering cells for the outer zone case
(m,n) Paired users
K Total number of subcarriers
M Total number of users
N Number of cells in each cluster
xiii
No White noise power density
L Multipath index
ρ Path loss exponent
S Number of sectors in each cell
P Transmit power
U Number of pairs
Pe Probability of error
PT Total power consumption
Pc Circuit power consumption
Pamp Amplifier power consumption
PB0 Transmit power of the BS
PR0 Transmit power of the RS
PL Path-loss
Q(·) Q-function
ζB0 Drain efficiency of the amplifier at BS
ζR0 Drain efficiency of the amplifier at RS
Pout Outage probability
y Received signal
R Relay station
dradius Cell radius
s Transmit symbol
v Time delay
w AWGN
σ noise variance
Z Number of common sub-channels between adjacent cells
xiv
Chapter 1
Introduction
In recent years, growing demands for reliable high data rate services, reductions in the carbon
footprint, and increasing energy prices have become essential design metrics in wireless com-
munication systems. Therefore, the concepts of spectral efficiency (SE) and energy efficiency
(EE) have attracted increasing attention as keys to achieving these goals in next-generation
wireless networks.
To provide a ubiquitous high data rate, wireless access will consume significantly more
energy for both operators and users equipment. From the operators’ perspective, to achieve
a high data rate and wireless coverage extension, higher transmission power is required, and
many base stations (BSs) have to be installed. From the users’ perspective, EE wireless
communication is also imperative. Therefore, wireless access increases the demand for the
limited power budget of mobile devices, which leads to a decrease in the battery life of mobile
terminals [1, 2, 3]. Many joint academic and industrial research efforts have been dedicated
to developing novel energy-saving techniques [4]. Among these efforts are the development of
low power circuit design, high-efficiency power amplifiers, energy-efficient network resource
management, cell splitting, multi-input multi-output (MIMO) and orthogonal frequency
division multiple access (OFDMA) techniques, and the third generation partnership project’s
(3GPP) long term evolution-advanced (LTE-A), which may rely on relaying (cooperative
communication) between the central BS and the user equipment (UE) as a benefit of reduced
transmission distances.
Another essential metric of wireless networks is SE. SE is defined as the ratio of the
achieved throughput to the bandwidth (bps/Hz). SE has been widely studied from the per-
spective of spectrum allocation in recent decades. SE and EE are considered key performance
1
indicators for wireless networks. For instance, the target downlink SE of 3GPP increases to
5 bps/Hz from 0.05 bps/Hz in the global system for mobile communication (GSM) [2].
The OFDMA technique is a promising approach that achieves high spectral efficiency in
cellular systems such as LTE-A, worldwide interoperability for microwave access (WiMAX)
(IEEE 802.16), and wireless local area networks (WLANs) downlink systems. This is due to
the multiple access achieved by assigning different sets of orthogonal subcarriers to different
users [5, 6]. Therefore, in OFDMA systems, there is no intra-cell interference due to the
orthogonality between allocated subcarriers.
Cooperative relaying communication is another technique used to reduce different types
of channel degradation, such as fast fading and path-loss. In cooperative relaying communi-
cations, relay stations (RSs) are placed at cell-edges to increase cell coverage and capacity
by re-transmitting the received signals from BSs to the mobile stations (MSs). By using this
configuration, it is possible to reduce the impact of path-loss due to the resulting shorter
transmission range and spatial diversity [6].
To meet the demand for high data rates in current and next-generation cellular networks,
frequency reuse (FR) techniques are required. Although full frequency reuse in each cell
in an OFDMA cellular network is able to maximize SE, it could lead to a high outage
probability, especially for outer zone users due to high inter-cell interference (ICI) from
adjacent cells [7, 8]. Therefore, inter-cell interference coordination (ICIC) is one of the many
approaches proposed to reduce the effect of interference and improve the performance of
the system. Conventional frequency reuse, fractional frequency reuse, soft frequency reuse,
adaptive frequency reuse, and full frequency reuse are examples of schemes used to minimize
ICI and improve the overall system performance, especially for outer zone users.
To achieve greater improvements in the SE and system capacity, non-orthogonal multiple
access (NOMA) has been proposed in the fifth generation (5G) and beyond systems. NOMA
uses superposition coding (SC) at the transmitter side to facilitate multiplexing for multiple
2
users in the power domain with the same time/frequency resource (i.e., the system capacity
is increased). On the other hand, NOMA uses successive interference cancellation (SIC) at
the receiver side to detect the multiplexed users’ signals. Therefore, the difference between
the portions of the transmit power of the paired users has to be relatively large to cancel the
inter-user interference successfully. Otherwise, the residual interference will be considered.
1.1 Problem Statement and Thesis Objectives
The goal of this thesis is to investigate the impact of ICI on fractional frequency reuse (FFR)
schemes in multi-relay multi-cell cooperative OFDMA and NOMA cellular networks. The
thesis focuses on minimizing ICI to improve the system performance in terms of SE, EE,
cumulative distribution function (CDF) of the signal-to-interference plus noise ratio (SINR)
of the received signal, and outage probability (OP), especially for outer zone users. The
system performance will be analyzed with a new formula to generate the frequency reuse
patterns for an frequency reuse factor (FRF) FRF=(1,7/3) scheme using a (7,3,1) difference
set and an FRF=(1,7/4) scheme using a (7,4,2) difference set in downlink cooperative and
non-cooperative relaying OFDMA cellular systems. Moreover, maximizing the sum-rate
of the paired users subject to optimal power allocation (PA) and user pairing (UP) for
FFR schemes in downlink cooperative and non-cooperative relaying NOMA-based cellular
networks have not been proposed before while taking into account the effect of ICI on the
system performance.
The FFR schemes are efficient interference mitigation techniques in multi-relay multi-cell
OFDMA cellular networks, especially for outer zone users [5, 9]. Splitting cell, sectoring,
and frequency reusing techniques are used to increase the capacity since they increase the
number of times that sub-channels are reused in each sector. These techniques are also
used to enhance the SE of the outer zone users with the expense of reduce the bandwidth
utilization.
3
Increasing the number of sectors would increase the number of relays in FFR schemes,
which would improve the SE and capacity of the outer zone area. Furthermore, the RSs
reduce the power consumption by reducing the transmission distance from the serving BS and
MS, which costs less than adding more BSs. Because of the benefits of RSs usage mentioned
above, this thesis proposes to utilize these RSs to improve the system performance for outer
zone users while taking ICI into account.
ICI will be considered in the system performance analysis for FFR schemes in OFDMA
and NOMA because it limits the performance of the overall SE of the network, especially
for outer zone users. In the 5G and beyond, NOMA is considered one of the promising
multiple access techniques due to its essential features. For example, improvements in SE, low
latency (i.e., no waiting time since the BS can serve multiple users simultaneously), massive
connectivity (i.e., multiple users are multiplexed in the power domain on one subcarrier),
and user fairness (i.e., less PA to strong user and vice-versa).
The performance of NOMA is usually evaluated with two main metrics: PA and UP
schemes, which effect in a balance between the system performance and the resource al-
location fairness [10, 11]. PA is implemented by allocating different power levels (power
proportional coefficients) for the transmit signal to multiplexed users at the transmitter
side, which relies on the channel condition between the serving BS and the user. Various PA
schemes have been proposed in the literature, such as fixed power allocation (FPA), frac-
tional transmit power allocation (FTPA), and full search power allocation (FSPA) schemes
[12, 13]. UP is implemented by selecting the users to pair either according to their distinctive
channel gains (near-far scheme) or a randomly pairing scheme. Therefore, UP is important
for interference coordination [14, 15]. Thus, the sum-rate maximization with these parame-
ters needs to be thoroughly investigated with the presence of ICI.
4
1.2 Thesis Contributions
The contributions of this thesis are ninefold.
1. The development of frequency reuse patterns to minimize the effect of ICI on the system
performance for FRF=(1,7/3) and FRF=(1,7/4) FFR schemes with three and four sectors,
respectively, in a cooperative and non-cooperative relaying downlink OFDMA multi-relay
multi-cell cellular system. The proposed algorithm can be applied in each cell within the
main cluster (seven cells) with 18 surrounding cells (two tiers). The system performance
with four sectors outperforms that with three sectors, especially for outer zone users, as
the number of relays is increased.
2. The derivation of an analytical expression for the SE of the inner and outer zone users
for FFR schemes in a downlink NOMA-based multi-cell network taking into account the
effect of ICI and imperfect SIC case.
3. The maximization of the achievable sum-rate (ASR) of each group (two paired users) for
FFR schemes in NOMA subject to power allocation, efficient SIC, and minimum quality
of service (QoS) requirements.
4. The derivation of an analytical expression for the upper and lower bounds of the PA
coefficients to maximize ASR in a downlink NOMA-based multi-cell network while taking
into account the impact of ICI and perfect SIC condition.
5. The development of UP algorithm with keeping the difference between the indices of
channel gains of paired users always constant and an imperfect SIC scenario to maximize
ASR with optimal PA coefficients for FFR schemes in a downlink NOMA-based networks.
6. The derivation of an analytical expression for the SIC error factor at the closer user
receiver in the imperfect SIC case. This expression is used for evaluating the overall
sum-rate performance for the FFR scheme in multi-cell NOMA-based networks.
7. The derivation of an analytical expression for the instantaneous SINR for inner and outer
zone users in the first and second time slots for FFR schemes in a downlink NOMA-based
5
multi-relay multi-cell network while taking into account the effect of ICI and an imperfect
SIC case. This expression is used for evaluating the achievable rate for the inner and outer
zone groups.
8. The maximization of the ASR of each group for FFR schemes in a cooperative relaying
NOMA-based subject to power allocation, efficient SIC, and QoS requirements. This
framework compares with a non-cooperative relaying scheme.
9. The derivation of an analytical expression for the OP for the inner and outer zone groups
when all channel paths are subjected to Nakagami-m fading and path-loss fading.
1.3 Thesis Outline
The remainder of this thesis consists of four chapters, which are outlined as follows. Chapter
2 reviews the important notations and definitions related to this thesis. In addition, it pro-
vides a brief summary of the propagation models for wireless communication systems. This
chapter focuses on the review of the structure and concept of the OFDMA, FFR schemes and
cooperative relaying protocols. Also, this chapter reviews the NOMA concept, power alloca-
tion at the transmitter, SIC technique at the receiver, and user pairing schemes in NOMA.
Furthermore, this chapter discusses the various ICI coordination techniques proposed in the
literature.
In Chapter 3, the proposed frequency reuse patterns using the concept of difference set
to reduce the ICI from adjacent cells are described in detail. The performance analysis of
the proposed schemes impacted by ICI is analyized and compared to other schemes with and
without relays.
In Chapter 4, the achievable sum-rate is optimized in NOMA under power allocation,
efficient SIC, and minimum QoS requirement constraints for FFR schemes in perfect and
imperfect SIC conditions. In addition, the proposed user pairing algorithm to maximize the
achievable sum-rate is presented. A new formula is derived for calculating the SIC error
6
factor Fc at a near user receiver in the imperfect SIC case. Finally, the performance of
the proposed user pairing scheme with optimal power allocation coefficients is analyzed and
compared with random user pairing, near-far user pairing, and orthogonal multiple access
(OMA) systems.
In Chapter 5, the achievable sum rate is optimized in cooperative relaying NOMA under
power allocation, efficient SIC, and minimum QoS requirement constraints for FFR schemes
in perfect and imperfect SIC conditions. An expression for the outage probability for the
inner and outer zone groups is derived under Nakagami-m fading and path-loss fading con-
ditions. Finally, the thesis is concluded in Chapter 6.
7
Chapter 2
Background
2.1 overview
In this chapter, important concepts related to the work presented in this thesis are re-
viewed. Important notations and definitions are provided, and a brief description of the
propagation models for wireless communication systems are presented. The concept of the
OFDMA system in cellular networks is presented, and the different aspects of NOMA in
5G cellular networks with an emphasis on related works are highlighted. Also, cooperative
relay-based cellular networks are reviewed. Finally, an overview of ICI mitigation approaches
in OFDMA-based cellular networks is provided.
2.2 Notations and Definitions
Cluster : is a group of cells among which the available frequency band is divided and shared.
This group of cells is repeated over and over throughout the coverage region.
Frequency Reuse (FR): is a process of reusing the same set of frequencies in cells
within a cellular system. These cells are separated by a sufficiently large distance (d) in
order to achieve the minimum possible interference between adjacent cells and to improve
capacity and spectral efficiency. The following formula d = dradius√
3N is used to calculate
the reuse distance d for hexagonal cell structures, where dradius is the cell radius and N is
the number of cells per cluster [16, 17, 18].
Frequency Reuse Factor (FRF): is the number of cells that cannot use the same
frequencies in a valid cluster. The most commonly used FRFs are: FRF= 1, 3, 4, 7, 9 and
12 (or FRF= 1, 1/3, 1/4, 1/7, 1/9 and 1/12) [18].
8
Inter-Cell Interference (ICI): is interference generated from neighbouring cells that
reuse the same frequency as the reference cell [19]. This interference in cellular systems is
the most significant limiting factor that causes system performance degradation.
Omnidirectional antenna : it radiates or receives electromagnetic waves equally well
in all directions.
Directional antenna : it radiates or receives in a particular direction, depending on
the direction of its radiation pattern.
Sectoring : is one of the most widely used techniques to reduce ICI and increase capacity
in a cellular system. Sectoring is accomplished by replacing a single omnidirectional antenna
at the BS with several directional antennas.
Spectral Efficiency (SE): is the number of bits per second (information rate b/s) that
can be transmitted over a given bandwidth (Hertz), and is expressed in b/s/Hz [20].
Energy Efficiency (EE): is the ratio between the achieved system throughput and the
total power consumption, measured in (b/s/W) or (b/J).
Difference Set (N,S,Z): corresponds to the number of cells in one cluster (N), the
number of sectors in each cell (S), and the number of common sub-channels between adjacent
cells (Z) [21].
Relay Station (RS): is a node that helps with the transmission of data between the
source and destination. It can be either a network element or user equipment that is more
intelligent than a conventional repeater and can decode, store and forward the received signal
to the destination.
To increase the system capacity in cellular systems, the reuse partitioning (RUP) [22]
technique is used. In RUP, each cell in the system is divided into two or more zones, as
illustrated in the example in Figure 2.1. In Figure 2.1, the region around the BS is called
the inner zone while the region further away from the BS is called the outer zone. Each zone
corresponds to a different FRF (i.e., in order to achieve a high spectrum efficiency, the FRF
9
should be reduced as much as possible). The transmission power level in the inner zone is
lower than that for the outer zone, which in turn reduces any interference generated by the
adjacent cells [23, 24].
BS
Inner zone
Outer zone
Figure 2.1: Layout of inner and outer zones.
2.3 Propagation Models for Wireless Communication Systems
Any wireless path (radio channel) between a transmitter and a receiver can be classified
into two classes. The first class is line-of-sight (LOS) or direct-path, where the transmitted
signal from the source is received at the destination without any obstacles between them.
The second class is non-line of sight (NLOS), where the signal is obstructed by physical
objects such as buildings, mountains, or trees [19, 25]. Therefore, the characteristic of
the electromagnetic wave propagation is varied based on the coverage area. Furthermore,
the strength of the received signal is affected by the distance between the transmitter and
receiver. Also, channel fading may be classified into small-scale fading and large-scale fading.
2.3.1 Small-Scale Fading
Small-scale fading describes the rapid fluctuations of the received signal over a short period
of time or over distances of the order of the carrier wavelength (small distance). This
kind of fading is caused by reflections off the ground and surrounding objects that generate
10
multiple copies of the transmit signal. These multiple copies arrive at the receiver at a
slightly different time, amplitude, and phase (multi-path fading) and can be constructive
or destructive. There are several different statistical distribution models commonly used to
describe the characteristics of multi-path fading, such as the Rayleigh, Ricean and Nakagami-
m fading distributions [18, 26].
2.3.2 Large-Scale Fading
Large-scale fading describes the fluctuations of the signal over a long period of time or over
distances of the order of the cell sizes (large distance). Large-scale fading is classified into
path-loss and shadowing. Path-loss is defined as the ratio between the transmitted and
received signal power. Path-loss is a function of the antennas’ heights, carrier frequency, and
propagation distance. The parameter related to the propagation environment that affects
path-loss is the path-loss exponent. The path-loss exponent describes the rate at which the
path-loss increases with distance. Shadowing is caused by diffraction and reflection of the
transmit signal by surrounding objects [18, 26].
2.4 OFDMA-Based Cellular Networks
OFDMA is a multiple access version of orthogonal frequency division multiplexing (OFDM).
In OFDM, the available bandwidth is divided into a number of parallel orthogonal narrow
sub-bands. The advantage of orthogonality is that it greatly simplifies the design of both
transmitter and receiver and significantly reduces intra-cell interference [5, 27].
These sub-carriers can be adaptively assigned to different users that experience high
signal-to-noise ratio (SNR). The advantages of this assignment are that multi-user diversity
can be achieved (i.e., system capacity is increased) and there is a reduction in power con-
sumption in different channel conditions. For example, if the channel quality is good, each
channel is allocated to the corresponding user in a given time-slot. On the other hand, if
11
the channel quality is bad (due to deep fading and narrowband interference), it is possible
to make this user wait for another time slot [20]. This mapping is the function of the BS
in a downlink scenario to inform users about the quality of the channel to get the correct
sub-carriers. The basic blocks of an OFDM transceiver system are shown in Figure 2.2 [28].
XModulator
M-PSK/M-QAMS/P
P/S
IFFT D/A
X Demodulator
M-PSK/M-QAMP/S
S/P
FFT A/D
Additive noise
Fading channel(h)
Add cyclic prefix
Remove
Cyclic prefix
Figure 2.2: Layout of OFDM transmitter-receiver.
The serial-to-parallel (S/P) block converts the incoming high-rate serial data stream into
low-rate parallel data. The inverse fast fourier transform (IFFT) block converts the data
stream into a time-domain stream. Cyclic prefix (CP) is added to the signal at the beginning
of each OFDM symbol. The CP is usually implemented by periodically appending a copy of
the last part of the OFDM symbol to the front of the transmitted OFDM symbol. The CP
acts as a buffer or guard time to eliminate inter-symbol interference (ISI) between adjacent
symbols [20]. After the CP insertion, the signal is converted to analogue form, which is more
suitable for transmission over a fading channel. An inverse process occurs at the receiver,
12
with parallel-to-serial (P/S) conversion and removal of CP.
2.5 NOMA-Based Cellular Networks
In the 5G and beyond, NOMA is one of the essential access techniques. The special features
of NOMA-based techniques include a high spectral efficiency (30% for downlink and 20%
for uplink more than in OFDMA [29]) and massive connectivity because each sub-carrier is
utilized by multiple users. In contrast, each sub-carrier in OMA is utilized by only one user,
as illustrated in Figure 2.3. The third feature of NOMA is improved user fairness resulting
from the allocation of low transmit power to nearby users (high channel gains) and high
transmit power to users that are farther away (low channel gains). In contrast, in OMA, all
users are allocated equal transmit powers.
Finally, NOMA has low latency compared to OMA. In OMA, users with bad channel
conditions are given low priority, and have to wait until users with good channel conditions
are processed [30, 31, 32, 33, 34].
NOMA
P (w)
f (Hz)
P (w)
f (Hz)
OMA
P (w)
f (Hz)
OMA
P (w)
f (Hz)
OMA
Sub-carrier Sub-carrier
NOMA
P (w)
f (Hz)
P (w)
f (Hz)
OMA
Sub-carrier Sub-carrier
Figure 2.3: The sub-carriers allocation in NOMA and OMA.
In NOMA, multiple users are multiplexing at the transmitter side in the power domain
using linear SC. At the receiver side, the users are separated by SIC. Therefore, the degree
of complexity of the receiver is based on the number of users in each group. Existing NOMA
techniques can generally be divided into two categories: power-domain NOMA (PD-NOMA)
13
and code-domain NOMA (CD-NOMA) [34].
Power-domain NOMA (PD-NOMA) is based on the principle of SC at the transmitter,
where the BS allocates different transmit power levels to multiple users depending on their
channel conditions and SIC at the receiver. Nearby users that have a good channel are
allocated less power than users located farther away with a bad channel. By using this
criterion, the balance between the achievable throughput and user fairness can be achieved
[35].
Code-domain NOMA (CD-NOMA) depends on the codebook structure, interleaving pat-
tern, spreading sequence, delay pattern, or scrambling pattern. Therefore, in CD-NOMA,
different operations are needed to allocate non-orthogonal resources to multiple users, such
as linear spreading, multidimensional modulation, interleaving, and scrambling [27, 36]. This
thesis focuses on the power-domain NOMA only.
2.5.1 Power Allocation in NOMA
Since the achievable throughput of a particular user is a function of its transmit power,
the achievable throughput of other users is also affected by that particular power allocation
(power-domain user multiplexing) [37]. Furthermore, through the larger power difference
allocated to the inner and outer zone users, the successful decoding of both zones’ users can
be achieved, which results in relatively low-complexity receivers.
Different power allocation schemes have been proposed in the literature; for example,
full search power allocation (FSPA), fractional transmit power allocation (FTPA), and fixed
power allocation (FPA) [12, 13]. Simulation results show that FSPA outperforms the other
schemes but with high computational complexity. The FPA scheme has lower complexity
but poor performance. The FTPA has a performance between the other two but needs to
predefine a specific parameter to obtain an improvement in system performance. In this
thesis, upper and lower bounds of power allocation coefficients are derived to maximize the
sum-rate for FFR schemes in a downlink NOMA-based networks.
14
2.5.2 User Pairing in NOMA
It is essential to pair the users at the transmitter to fully utilize the available bandwidth and
enhance user fairness; however, inter-user interference in each pair is expected, which will
degrade the system performance. To overcome this issue, SIC is performed at the receiver
of a strong user (nearby user) in each pair.
User pairing algorithms proposed in the literature [38] include (1) random user pairing,
and (2) non-random user pairing. Random user pairing pairs two or more users randomly
regardless of the users’ channel gain conditions. Although this algorithm has lower com-
plexity, the achievable throughput is not maximized due to ignoring the effect of channel
gains. Non-random user pairing, on the other hand, considers the users’ channel conditions
and pairs the user with the highest channel gain with the user with the lowest channel gain
[14, 15, 39]. The shortcoming of this user pairing scheme is that after pairing all the far-
thest users with the closest users, users who are close to each other end up being paired.
In this case, the inter-user interference will be high, especially in an imperfect SIC scenario,
resulting in degradation of the system performance. Therefore, user pairing is important in
managing interference between user pairs.
In this thesis, the proposed user pairing algorithm keeps the difference between the indices
of channel gains of paired users always constant. The advantages of the proposed user pairing
are that it guarantees every user in the system is selected to pair with another user in at
least one subcarrier (more user fairness is achieved), and it will work efficiently in perfect
and imperfect SIC scenarios and even with a large number of users.
2.5.3 Successive Interference Cancellation Technology in NOMA
The principle of NOMA is multiplexing the paired users in the power domain at the trans-
mitter side and using SIC at the receiver side for demultiplexing [40]. NOMA with SIC is a
promising multiple access technique for achieving better performance compared to orthogo-
15
nal multiple access, especially for outer zone users [41].
In downlink NOMA, after sorting the channel gains in decreasing order, the SIC process
is performed at the nearest user’s receiver [42]. Thus, in the case of perfect SIC, the near
user decodes the far user’s signal first and then removes the interference from the far user
by subtracting its signal from the received signal then decoding its own signal. The far
user decodes its own signal successfully by considering the interference from the near user as
noise. However, in the imperfect SIC case, there will be residual interference, which should
be considered in evaluating the system performance.
In this thesis, perfect and imperfect SIC cases are considered. In the imperfect SIC case,
the SIC error factor formula is derived at the receiver of the near user for FFR schemes in
downlink NOMA-based networks.
2.6 Cooperative Relaying-Based Cellular Networks
Cooperative communication is one of the most promising techniques for enhancing wireless
communication between BSs and MSs. Adding RSs in a cellular system can bring many ben-
efits [5, 6, 43]. First, the RSs replace a long-range high-power transmission from the BSs to
users with two or more short-range (hops), low-power relay transmissions. Second, it reduces
the impact of path loss since path loss is inversely proportional to the distance between BS
and MS. Third, it potentially generates less interference due to the low transmission power.
Finally, it extends cell coverage and provides a high throughput, especially for outer zone
users since their data can be relayed via multi-hop transmission.
In relay-assisted downlink, the BS communicates with the MS in two-time slots. In the
first-time slot, the BS broadcasts the signal to the relay and MS at the same time. In
the second-time slot, the RS amplifies the received signal and retransmits it to the MS.
Cooperative relaying achieves high SINR at the users’ receivers by combining their signals
in the two time slots [35, 44].
16
2.6.1 Classification of Relays
Depending on the functionality of the relays, a variety of classifications have been used in
LTE-A and 3GPP standardizations [45].
2.6.1.1 AF and DF Relays
Depending on how a signal is processed, relays can be classified as amplify-and-forward (AF)
relays and decode-and-forward (DF) relays [6, 44, 46].
Amplify-and-forward (AF) Relays amplify the signal from the BS and re-transmit
it to the destination. The disadvantage of the AF relay is that the received signal may
contain both interference and noise, which are also amplified. Nevertheless, the AF provides
performance improvements that cannot be achieved by the DF relay. For example, the
transmitted signal in the AF type of relays can be received from the source and relay either
in different time slots or in the same time slot, thereby increasing the diversity order to two.
Decode-and-forward (DF) Relays decode the received signal, encode it again and
then retransmit it to the destination. Here, there is no diversity, and there is performance
degradation when the relay decodes the received signal incorrectly.
There are some other relays that compress and forward the received signal, referred to
as compress-and-forward (CF). However, AF and DF relays are the most common protocols
that have been used in cooperative wireless communications.
The AF relay is proposed because it provides a higher diversity order than the DF and
due to its flexibility to work in the time domain or the frequency domain [47, 48]. The AF
requires an amplifying repeater to relay the BS transmitted signal, while the DF requires
an analogue-to-digital (A/D) block, digital-to-analogue (D/A) block, decoder, and encoder
(long processing latency). Therefore, due to the simplicity of its implementation, its low
computation operations, and the diversity gain, this thesis proposes utilizing the AF as
a relaying protocol in the solutions for relay-based FFR schemes in OFDMA and NOMA
networks.
17
2.6.1.2 Half-Duplex and Full-Duplex Relays
Relays can also be classified into half-duplex (HD) and full-duplex (FD) relays [49, 50].
Half-duplex (HD) Relays operate either in two orthogonal time slots or two different
frequency bands to establish the connection between source and destination.
Full-duplex (FD) Relays can be used when the BS and RS can share the same time
slot or frequency band to communicate with the MS. The disadvantage of the FD relay is that
when it is retransmitting while receiving new data, self-interference between the transmitting
and receiving antennas occurs. This issue makes the practice implementation difficult.
In this thesis, the HD RSs are considered to avoid the above-mentioned issues in FD
relays.
2.6.1.3 Fixed and Mobile Relays
According to the deployment and mobility properties, relays can be classified into fixed relay
stations (FRSs) and mobile relay stations (MRSs) [6, 51].
Fixed relay stations (FRSs) are deployed in each cell in fixed locations to give data
rate coverage uniformly for all users in each sector as well as to extend the cell coverage.
The advantages of using FRSs are that they can be installed in a planned way to provide
better coverage for the shadowing area or hot spot and have lower cost and low transmit
power compared with BSs. This thesis considers the FRSs type.
Mobile relay stations (MRSs) are movable and can be either a network element
(e.g., traditional relays) or a mobile user serving as a relay for other users.
2.6.1.4 Non-Transparent and Transparent Relays
Two relay classifications are used in 3GPP standardization [52]: Type I (Non-Transparent)
and Type II (Transparent) as shown in Figure 2.4. Type I is referred to as non-transparent
because there is no direct link between the BS and MS. Type I relay needs to transmit a
common reference signal and control information for the base station, and it is used for
coverage extension.
18
Type II is referred to as transparent because there is a direct link between the BS and
MS. It does not need to transmit a common reference signal and control information, and it
is used to provide diversity and improve overall system capacity.
BSRS MSMSRS
Type II (Transparent) Type I (Non-Transparent)
Figure 2.4: Layout of type I and type II.
2.7 Inter-Cell Interference Mitigation Approaches in OFDMA-Besed Cellu-
lar Networks
Three approaches are available in the literature for mitigating ICI in cellular networks: inter-
cell interference randomization, inter-cell interference cancellation, and inter-cell interference
coordination or avoidance [53, 54]. The first technique does not reduce the interference;
rather, it distributes the interference over all users randomly so the outer zone users will not
always suffer from strong ICI within the transmission period.
Inter-cell interference cancellation only cancels the dominant interference by subtracting
it from the received signal, which involves long signal processing and extra complexity. Inter-
cell interference coordination is used with some restrictions on frequency or power (frequency
reuse schemes or power control schemes) to improve the outer zone throughput without
degradation to the inner zone throughput. The Release 8 in LTE supports ICIC techniques
[53, 55, 56]. This thesis considers the inter-cell interference coordination to minimize ICI,
especially for outer zone users.
19
2.7.1 ICIC using Frequency Reuse Schemes in Cellular Networks
ICIC using frequency reuse schemes is proposed the literature to reduce the effect of ICI on
the system performance and improve the throughput of the system, especially for outer zone
users by coordinating (reusing) the downlink frequency resources between the cells.
2.7.1.1 Conventional Frequency Reuse Scheme for Multi-Cell OFDMA Systems
Due to limitations and cost of the available bandwidth, each sub-band allocated for the
cellular system can be reused in different clusters. In the conventional frequency reuse
scheme, the frequency reuse factor is 1 (FRF=1). In FRF=1, the entire available frequency
band (f) is reused in each cell with the same transmit power, as illustrated in Figure 2.5.
The main cluster (in boldface) consists of only one cell, which is repeated to tile the whole
plane (two tiers).
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
Power
FrequencyB WB W
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
f
Power
FrequencyB W
f
Figure 2.5: Layout of frequency reuse factor of 1 (FRF=1).
This scheme is simple and has a high data rate; however, the MS users suffer from high
ICI from adjacent cells. For example, if the mth user is located in the reference cell (i.e., in
the center of the two tiers), ICI would come from 18 adjacent cells. The received SINR at a
user m can be calculated by
ΓB0,m =PB0|hB0,m|2
IC +N0
, (2.1)
where PB0 is the transmit power of the serving BS B0, |hB0,m|2 is the channel gain of the link
20
between the serving BS B0 and user m, N0 is Additive white gaussian noise (AWGN), and
IC is comprised of inter-cell interference and intra-cell interference of a user m as follows
IC = I + Iintra. (2.2)
In this scheme, Iintra = 0 because there is only one BS in each cell. The I is produced from
each of 18 BSs within the first two tiers,
I =19∑j=2
PBj|hBj ,m|2. (2.3)
where |hBj ,m|2 is the channel gain of the link between the interfering BS Bj and user m.
High ICI would cause a low received SINR as in (2.1) and a high outage probability for user
m, which leads to the degradation of m user’s performance [53, 57].
2.7.1.2 Frequency Reuse Factor of 3 (FRF=3) Scheme for Multi-Cell OFDMA Systems
To reduce ICI in the conventional frequency reuse scheme, FRF=3 is used. In this scheme,
the available frequency spectrum is divided into three orthogonal sub-bands with the same
transmit power. Every three adjacent cells in a cell cluster are allocated different sub-bands,
as illustrated in Figure 2.6. The main cluster (in boldface) consists of three cells, and is
repeated to tile the whole plane (two tiers).
3
4
Cell 1 17
5
2
6
11
7
14
15
16
18
199
10
12
13
8
Frequency
Power
Cell 1
Cell 2
Cell 3
B W
Figure 2.6: Layout of frequency reuse factor of 3 (FRF=3).
For an MS mth located in cell 1, ICI comes only from the six adjacent cells within the
first two tiers compared to 18 for the conventional scheme (FRF=1), which can be calculated
21
as
I =9∑j=4
PB2j+1|hB2j+1,m|2. (2.4)
Thus, the trade-off is a reduction in bandwidth utilization by a factor of 3 (i.e., the spectrum
efficiency of each cell is reduced by one-third of the available bandwidth) [53, 58].
2.7.1.3 Fractional Frequency Reuse Schemes for Multi-Cell OFDMA Systems
Generally speaking, the purpose of FFR design is to deploy frequency patterns (sets) in a
way that an MS user can avoid interfering or being interfered with by non-serving cells in
its reuse set [59]. The FFR scheme has been proposed as an ICIC technique to minimize the
effect of ICI in OFDMA-based fourth generation (4G) wireless standards [60], such as IEEE
802.16m, 3GPP LTE/LTE-A Release 8 and above [7]. Moreover, it can be used to achieve
a balance between the need for a high system throughput and sufficient outer zone spectral
efficiency.
The basic idea of the FFR scheme is to assign a low frequency reuse factor or even unity
FRF to users near the serving BS (inner zone users), whereas the users far away from the
serving BS (outer zone users) are assigned a higher FRF [61, 62, 63].
Hybrid Frequency Reuse Scheme
To further reduce ICI, a combination of FRF=1 and FRF=3 (i.e., FRF=(1,3)) is used to
utilize the advantages of both schemes. Each cell is divided into an inner zone and an outer
zone, as shown in Figure 2.7. The inner zone uses an FRF=1, while each outer zone uses
an FRF=3. The sub-band frequency for the outer zone is divided into three orthogonal
sub-bands corresponding to three sectors, as illustrated in Figure 2.7 [64, 65].
22
22
11
77
66
55
1515
33
44
1313
1414
1616
1717
1818
1919
88
99
1212
1111
1010
FRF=1
FRF=3
FRF=1
FRF=3
Frequency
Power
Frequency
FRF=1 for inner zones
FRF=3 for outer zones
B WB W
2
1
7
6
5
15
3
4
13
14
16
17
18
19
8
9
12
11
10
FRF=1
FRF=3
Frequency
Power
Frequency
FRF=1 for inner zones
FRF=3 for outer zones
B W
Figure 2.7: A hybrid frequency reuse FRF=(1,3) scheme for multi-cell OFDMA systems.
From Figure 2.7, when the MS is located in the inner zone of cell 1, it receives ICI from
18 adjacent cells. When an MS located in the outer zone of cell 1 (for example, in the orange
sector of cell 1), it will experience ICI from only seven cells (ICI comes from cells 4, 5, 11, 12,
13, 14, and 15). This scheme has been shown to decrease interference for outer zone users
with the trade-off of the reducing data rate because they utilize only one-third of the entire
spectrum.
FFR Schemes in Cooperative Relaying
Cooperative relaying FFR schemes have been proposed in [61, 62, 63] to improve the system
performance of FRF of 1 and FRF of 3. Cooperative relaying FFR is based on dividing the
entire cell into inner zones with FRF=1 and outer zones with FRF between 1 and 3.
In this thesis, two cooperative FFR schemes are proposed with a new formula to allocate
seven sub-bands between three-sectors in the FRF=(1,7/3) scheme or between four-sectors
in the FRF=(1,7/4) scheme to minimize the number of interfering sectors from the first two
tiers. The FRF=(1,7/3) scheme with a difference set of (7,3,1) and FRF=(1,7/4) scheme
with a difference set of (7,4,2) with cooperative relaying utilize AF fixed relays (more details
on these two schemes can be found in Chapter 3 of this thesis). The advantage of this
23
scheme is a reduction in ICI compared to the hybrid frequency reuse scheme FRF=(1,3).
Consequently, whenever the frequency reuse factor is increased, the ICI is reduced (FRF=
1, 3, 4, 7, 9 and 12) [18].
Partial Frequency Reuse (PFR) Scheme
The PFR scheme was first proposed in [66] and is also referred to as fractional frequency
reuse with full isolation (FFR-FI) [57]. The main idea, as illustrated in Figure 2.8 of the
PFR scheme,is to divide the whole available bandwidth into four groups. The first group
is assigned to inner zone users with FRF=1 and reduced transmit power. The other three
groups are assigned to outer zone users with FRF=3 and amplified transmit power, assuming
that the total transmitting power is fixed [53, 57, 67].
This scheme improves SINR in the outer zones and maintains an acceptable level of
spectral efficiency due to the FRF being greater than 1 in the outer zones. The PFR also
reduces ICI due to the orthogonality between the outer zone sub-bands and the inner zone
sub-bands of neighbouring cells.
Cell 2
Cell 3
Cell 1
Power
Frequency
Cell 2
Power
Frequency
Cell 1
Power
Frequency
Cell 3
B W
Figure 2.8: Partial frequency reuse scheme for multi-cell OFDMA systems.
24
Chapter 3
Performance Analysis of Fractional Frequency Reuse
Schemes in Multi-Relay Multi-Cell OFDMA Systems 1
3.1 Chapter Overview
In this chapter, new frequency patterns are proposed for an FRF=(1,7/3) scheme using a
difference set of (7,3,1) and for an FRF=(1,7/4) scheme using a difference set of (7,4,2) based
on the work in [61]. The proposed frequency patterns are deployed with AF-fixed relays to
minimize the effect of ICI on the system performance. Furthermore, the proposed scheme
is applied in each cell within a 19-cell structure (two tiers) to improve system performance
indices such as SINR, SE, EE, CDF of the SINR of the received signal, and OP. System
performances with these metrics are evaluated for each cell in the main cluster (7-cells) with
18 surrounding cells, and then the average is taken to tile the whole plane. The authors in
[61] calculated similar analysis; however, they only take into account one cell within two tiers.
Relaying and OFDMA are potentially two efficient techniques to use to meet the growing
demands for reliable high data rates, to improve SE, and to meet QoS requirements, especially
for outer zone users. There are several benefits of deploying outer zone AF relays compared
to using only one BS. For instance, low-cost RSs, do not need to connect via ordinary cables
1The content of this chapter has generated two published conference papers [68]. Saleh, Ali M. and T.
Le, Ngon and Sesay, Abu B., ”Inter-Cell Interference Coordination using Fractional Frequency Reuse Scheme
in Multi-Relay Multi-Cell OFDMA Systems”, 2018 IEEE 31th Canadian Conference on Electrical and Com-
puter Engineering (CCECE). [69]. Saleh, Ali M. and T. Le, Ngon and Sesay, Abu B., ”Fractional Frequency
Reuse (FFR) Scheme for Inter-Cell Interference (ICI) Mitigation in Multi-Relay Multi-Cell OFDMA Sys-
tems”, 2018 IEEE 9th Annual Information Technology, Electronics and Mobile Communication Conference
(IEMCON).
25
for backhaul networks. Fixed AF-RSs are placed at the outer zone to increase capacity and
extend cell coverage. These relays reduce the impact of path-loss due to the resulting shorter
transmission range and spatial diversity.
The remainder of this chapter is organized as follows. Related work is discussed in
Section 3.2. The system model is presented in Section 3.3. The difference set definition and
the proposed scheme are discussed in Section 3.4. In Section 3.5, the performance analysis of
FRF=(1,7/3) and FRF=(1,7/4) schemes is provided. In Section 3.6, the SINR, SE, EE, CDF
of the SINR of the received signal, and OP are analyzed. Finally, the chapter is concluded
in Section 3.7.
3.2 Related Work
Several FFR schemes, with and without relays, have been proposed in the literature with
the analysis of system performance with an emphasis on outer zone users. In [64, 70], the
authors propose an FRF=1 in the inner zone and FRF=3 in the outer zone without relays.
They analyze the system performance such as the SINR, CDF of the SINR of the received
signal, and cell throughput. They use two criteria for switching between the inner zone and
the outer zone: distance and SINR threshold. The authors in [71] propose the use of FRF=1
and FRF=3 in the inner and outer zones, respectively, with relays. The authors in [72]
propose a cluster-aware soft frequency reuse (CASFR) scheme without relays to mitigate
the ICI in LTE femtocell networks.
Cooperative relaying in cellular networks has gained attention due to its spatial diversity
property. The authors in [61] propose a cooperative FFR scheme to enhance the QoS of a
non-cooperative FFR scheme. However, they consider only one cell within a 19-cell struc-
ture. In [73], the authors propose a frequency and power planning with relays to minimize
ICI. However, intra-cell interference is not taken into account. The authors in [74] investi-
gate the throughput and interference suppression factor for the inner zone in a cooperative
26
FFR scheme. However, the outer zone bandwidth is divided into three sub-bands and they
consider only one cell within a 19-cell structure. The authors in [63] investigate the cell data
rate for both schemes (FRF=(1,7/3) and FRF=(1,7/4)) without relays as well as without
sectorization. Inspired by [61], this thesis proposes a new formula for allocating the frequency
patterns for both FRF=(1,7/3) and FRF=(1,7/4) schemes. The system performance is then
analyzed for each cell within the main cluster with 18 surrounding cells.
3.3 System Model
The layout of each cell with three and four sectors, in the proposed schemes is illustrated in
Figure 3.1 and Figure 3.2, respectively.
In both figures (Figure 3.1 and Figure 3.2), the relay is assumed to operate in two equal
time slots (TSs). In the first time slot (TS1), the BS broadcasts the signal to the inner zone
users with an omnidirectional antenna and uses FRF= 1. Also, in the first time slot, the
BS broadcasts to the relay and to the outer zone users with directional antennas and uses
FRF=7/3 with three sectors or FRF=7/4 with four sectors.
BS
MSOuter zone
Inner zone
RS
transmission link in TS1
transmission link in TS2
Figure 3.1: Transmission link with relays in each 3-sectored cell.
In the second time slot (TS2), each RS in both schemes amplifies the received signal and
re-transmits it to the destination with a directional antenna.
27
BS
MS Outer zone
Inner zone
RS transmission link in TS1
transmission link in TS2
Figure 3.2: Transmission link with relays in each 4-sectored cell.
The layout of a 36 multi-cell OFDMA downlink cellular system for both schemes with
the proposed frequency patterns are shown in Figure 3.3 and Figure 3.4, respectively.
First, the proposed frequency patterns are assigned to the boldface main cluster cells.
These patterns are allocated in such a way that the average number of interfering sectors
from the first two tiers for the outer zone users is reduced. The main cluster is copied to
generate the entire system, as illustrated in Figure 3.3 and Figure 3.4, respectively.
7
4
6
6
5
3
1
5
7
4
3
1 Cell 0
6
1
2
2
5
4
2
7
3
7
4
6
6
5
3
1
5
74
3
1
2
7
3
6
1
2
2
7
3
6
5
3
2
5
4
4
3
1
7
4
6
6
5
31
5
7
4
3
1
6
1
2
2
5
4
2
7
3
2
7
3
6
5
3
7
4
6
1
5
7
2
5
4
7
4
6
4
3
1
6
1
2
4
3
1
2
5
4
6
1
2
4
3
1
1
5
7
Inner zone (FRF=1)
Outer zone (FRF=7/3)
Figure 3.3: The layout of 36-cell structure for the FRF =(1,7/3) proposed scheme.
28
Inner zone (FRF=1)
Outer zone (FRF=7/4)
1
7
5
Cell 0
2
6
1
7
4
2
6
3
1
3
5
4
17
3
2
4
6
7
3
5 2
5
4
6
1
7
5
2 2
6
3
1
7
3
2
4
6
7
3
5 2
5
4
6
1
7
5
2
3
5
4
17
3
2
4
6
7
3
5 2
5
4
6
1
7
5
2
6
1
7
4
3
5
4
17
3
2
4
6
7
3
5
1
7
5
2
6
1
7
4
2
6
3
1
3
5
4
17
3
2
4
1
7
5
2
6
1
7
4
2
6
3
1
3
5
4
1
2
5
4
6
1
7
5
2
6
1
7
4
2
6
3
1
6
7
3
5 2
5
4
6
Figure 3.4: The layout of 36-cell structure for the FRF =(1,7/4) proposed scheme.
3.4 The Difference Set Definition and the Proposed Scheme
To understand how to allocate the seven sub-bands between all sectors of the main cluster
in both schemes, the idea of the difference set is used [75]. The difference set denoted as
(N ,S,Z) is defined as follows: N is the number of cells in one cluster, S is the number of
sectors in each cell, and Z is the number of common sub-channels between any adjacent
cells.
Let us consider Disub as a set of indices of the sub-bands for the ith cell. The proposed
formula for Disub can be expressed as
Disub = D0
sub + 2i (mod N), i ∈ ϕ. (3.1)
where ϕ = {0, 1, 2, ...., N − 1}.
For a difference set of (7, 3, 1), D0sub is chosen to be (1, 3, 4) for cell 0, as illustrated in
29
Figure 3.5, and there is only one common sub-channel between any adjacent cells.
For a difference set of (7, 4, 2), D0sub is chosen to be (1, 2, 5, 7) for cell 0, as illustrated in
Figure 3.6, and there are only two common sub-channels between any adjacent cells. After
that, to obtain the frequency patterns of surrounding cells, the proposed formula is applied
to obtain six other sets around cell 0 as described in APPENDIX A.
3.5 Performance Analysis of FRF = (1,7/3) and FRF=(1,7/4) Schemes
The performance indices analyzed in this section include SINR, SE, EE, CDF of the SINR
of the received signal, and OP. These performance indices are impacted by the ICI. Consider
cell 0 in Figures 3.5 or 3.6 as the desired cell. There are 18 surrounding cells that generate
ICI.
In both schemes (FRF=(1,7/3) and FRF=(1,7/4)), the available frequency spectrum is
divided into two sub-bands corresponding to the two zones, and the outer zone bandwidth
is divided into seven sub-channels with equal transmitted power as illustrated in Figure 3.5
and Figure 3.6, respectively. The advantage of this scheme is a reduction in ICI compared
to that of the FRF=(1,3) scheme.
30
First sub-band frequency for inner zone with FRF=1
Se
cond
sub-b
and
frequ
ency for outer zo
ne with
FRF=7/3
Power
Frequency
B W
1 2 3 4 6 75
5 63
51 7
2 3 7
2 4 5
4 6 7
1 2 6
4 Cell 0311
Inner zone (FRF=1)
Outer zone (FRF=7/3)
4
3
1 Cell 0
6
5
36
1
2
7
4
62
5
4
1
5
7
2
7
3
2
7
37
4
62
5
4
6
1
2
7
4
66
5
36
1
2
1
5
7
6
5
3
2
7
3
1
5
7
2
5
4
First sub-band frequency for inner zone with FRF=1
Se
cond
sub-b
and
frequ
ency for outer zo
ne with
FRF=7/3
Power
Frequency
B W
1 2 3 4 6 75
5 63
51 7
2 3 7
2 4 5
4 6 7
1 2 6
4 Cell 031
Inner zone (FRF=1)
Outer zone (FRF=7/3)
4
3
1 Cell 0
6
5
36
1
2
7
4
62
5
4
1
5
7
2
7
3
2
7
37
4
62
5
4
6
1
2
7
4
66
5
36
1
2
1
5
7
6
5
3
2
7
3
1
5
7
2
5
4
First sub-band frequency for inner zone with FRF=1
Se
cond
sub-b
and
frequ
ency for outer zo
ne with
FRF=7/3
Power
Frequency
B W
1 2 3 4 6 75
5 63
51 7
2 3 7
2 4 5
4 6 7
1 2 6
4 Cell 031
Inner zone (FRF=1)
Outer zone (FRF=7/3)
4
3
1 Cell 0
6
5
36
1
2
7
4
62
5
4
1
5
7
2
7
3
2
7
37
4
62
5
4
6
1
2
7
4
66
5
36
1
2
1
5
7
6
5
3
2
7
3
1
5
7
2
5
4
Figure 3.5: Proposed two-tiers structure for FRF=(1,7/3) scheme with one common sub-
channel.
Inner zone (FRF=1)
Outer zone (FRF=7/4)
Inner zone (FRF=1)
Outer zone (FRF=7/4)
1
7
5
Cell 0
2
1
7
5
Cell 0
2
3
5
4
1
3
5
4
1 6
1
7
4
6
1
7
4
2
6
3
1
2
6
3
12
5
4
6
2
5
4
6
6
7
3
5
6
7
3
5
7
3
2
4
7
3
2
4
2
5
4
6
2
5
4
6
6
7
3
5
6
7
3
52
6
3
1
2
6
3
12
5
4
6
2
5
4
6
6
1
7
4
6
1
7
4
2
6
3
1
2
6
3
1 3
5
4
1
3
5
4
1 6
1
7
4
6
1
7
4
7
3
2
4
7
3
2
4
3
5
4
1
3
5
4
1
6
7
3
5
6
7
3
5
7
3
2
4
7
3
2
4
Power
FrequencyFrequency
B WB W
1 2 3 4 6 751 2 3 4 6 75
Cell 0511
First sub-band frequency for inner zone with FRF=1
Second su
b-b
and
frequ
ency for outer zo
ne with
FRF=7
/4
2 7
32 74
4 51 3
2 654
63 5 7
1 4 6 7
1 62 3
Inner zone (FRF=1)
Outer zone (FRF=7/4)
1
7
5
Cell 0
2
3
5
4
1 6
1
7
4
2
6
3
12
5
4
6
6
7
3
5
7
3
2
4
2
5
4
6
6
7
3
52
6
3
12
5
4
6
6
1
7
4
2
6
3
1 3
5
4
1 6
1
7
4
7
3
2
4
3
5
4
1
6
7
3
5
7
3
2
4
Power
Frequency
B W
1 2 3 4 6 75
Cell 051
First sub-band frequency for inner zone with FRF=1
Second su
b-b
and
frequ
ency for outer zo
ne with
FRF=7
/4
2 7
32 74
4 51 3
2 654
63 5 7
1 4 6 7
1 62 3
Inner zone (FRF=1)
Outer zone (FRF=7/4)
1
7
5
Cell 0
2
3
5
4
1 6
1
7
4
2
6
3
12
5
4
6
6
7
3
5
7
3
2
4
2
5
4
6
6
7
3
52
6
3
12
5
4
6
6
1
7
4
2
6
3
1 3
5
4
1 6
1
7
4
7
3
2
4
3
5
4
1
6
7
3
5
7
3
2
4
Power
Frequency
B W
1 2 3 4 6 75
Cell 051
First sub-band frequency for inner zone with FRF=1
Second su
b-b
and
frequ
ency for outer zo
ne with
FRF=7
/4
2 7
32 74
4 51 3
2 654
63 5 7
1 4 6 7
1 62 3
Figure 3.6: Proposed two-tiers structure for FRF=(1,7/4) scheme with one common sub-
channel.
31
In desired cell 0, the received signal at MS m in the first time slot can be written as
y(1)m (t) =
L−1∑l=0
hlB0,msB0,m(t− vlB0,m
) +I∑j=1
L−1∑l=0
hlBj ,msBj ,m(t− vlBj ,m
) + w(1)B0,m
(t), (3.2)
where
hlB0,mand hlBj ,m
are the impulse responses of the channel for the lth path between the serving
BS B0 and interfering BS Bj, respectively, and the MS m (i.e., B0-MS and Bj-MS) links;
sB0,m and sBj ,m are the transmit symbols of the B0-MS and Bj-MS links, respectively;
vlB0,mand vlBj ,m
are the time delays of the lth path of B0-MS and Bj-MS links, respectively;
w(1)B0,m
(t) is the AWGN of B0-MS link in the first time slot;
I is the number of interfering cells (Bj’s) surrounding B0 (ICI) in either cases (Iinn for
the inner zone case and Iout for the outer zone case) for both schemes (FRF=(1,7/3) and
FRF=(1,7/4)).
The hlB0,mand hlBj ,m
can be written, respectively, as
h(1)B0,m
(t) =L−1∑l=0
hlB0,mδB0,m(t− vlB0,m
), (3.3)
h(1)Bj ,m
(t) =L−1∑l=0
hlBj ,mδBj ,m(t− vlBj ,m
). (3.4)
The transfer function of h(1)B0,m
(t) and h(1)Bj ,m
(t) for MS m on subcarrier k can be expressed as
Hk,(1)B0,m
=L−1∑l=0
hlB0,mexp(−2πjk∆fvlB0,m
), (3.5)
Hk,(1)Bj ,m
=L−1∑l=0
hlBj ,mexp(−2πjk∆fvlBj ,m
), (3.6)
where ∆f is the subcarrier spacing.
The received signal at the serving RS R0 and at the interfering RS Rj in the first time
slot can be expressed, respectively, as
y(1)R0
(t) =L−1∑l=0
hlB0,R0sB0,m(t− vlB0,R0
) +I∑j=1
L−1∑l=0
hlBj ,R0sBj ,m(t− vlBj ,R0
) + w(1)B0,R0
(t), (3.7)
32
y1Rj
(t) =L−1∑l=0
hlBj ,RjsBj ,m(t− vlBj ,Rj
) + w(1)Bj ,Rj
(t), (3.8)
where I represents the number of interfering cells (ICI) around the desired cell. The path-
loss and shadow in dB of MS m can be calculated using the COST-Hata model [76] at the
distance dB0,m as follows
PLdB(dB0,m) = 46.3 + 33.9 log10(fc)− 13.82 log10(hb)− a(hm)
+ (44.9− 6.55 log10(hb)) log10(dB0,m) + SHσ(dB), (3.9)
where fc is the carrier frequency in (MHz), hb is the height of the BS’s antenna in (m), hm
is the height of the MS’s antenna in (m), and a(hm) is the correction factor of the MS’s
antenna height, which is given by
a(hm) = [1.1 log10(fc)− 0.7]hm − (1.56 log10(fc)− 0.8), (3.10)
and the term SHσ(dB) in (3.9) represents a shadowing effect, which follows a log-normal
distribution with zero mean and standard deviation σ.
Using (3.5), (3.6), and (3.9), the channel gain for the B0-MS link in terms of small scale
fading and large scale fading can be expressed as
Gk,(1)B0,m
= 10−PLdB(dB0,m) |Hk,(1)
B0,m|2 (3.11)
in the desired cell 0, and for the Bj-MS link from the interfering cell j can be expressed as
Gk,(1)Bj,m = 10−PLdB(dBj,m
) |Hk,(1)Bj ,m|2. (3.12)
The instantaneous received SINR of the inner zone user mi and outer zone user mo in the
first time slot can be written, respectively, as
Γk,(1)mi
=Pk,(1)B0,mi
Gk,(1)B0,mi
Iinn∑j=1
Pk,(1)Bj ,mi
Gk,(1)Bj ,mi
+ ∆fNo
, (3.13)
33
Γk,(1)mo
=Pk,(1)B0,mo
Gk,(1)B0,mo
Iout∑j=1
Pk,(1)Bj ,mo
Gk,(1)Bj ,mo
+ ∆fNo
, (3.14)
where Pk,(1)B0,m
, Pk,(1)Bj ,m
are the transmit powers of the B0 and Bj in the first time slot; re-
spectively, either user m is in the inner zone or in the outer zone. Iinn and Iout represent
the ICI for the inner and outer zone users, respectively, either for FRF=(1,7/3) scheme or
FRF=(1,7/4) scheme. No is the white noise power density.
In the second time slot, the received signal at the user m located in the outer zone from
the corresponding relay can be expressed as
y(2)m (t) =
L−1∑l=0
βR0,m hlR0,m
y(1)R0
(t−vlR0,m)+
I∑j=1
L−1∑l=0
βRj ,m hlRj ,m
y(1)Rj
(t−vlRj ,m)+w
(2)R0,m
(t), (3.15)
where y(1)R0
(t) and y(1)Rj
(t) are given in (3.7) and (3.8), respectively, and βR0,m and βRj ,m are
the amplifier gains of the R0-MS and Rj-MS links, respectively, which can be written as [71]
βR0,m =
√√√√√ PR0
PB0
L−1∑l=0
|hlB0,R0|2 + ∆fNo
, (3.16)
βRj ,m =
√√√√√ PRj
PBj
L−1∑l=0
|hlBj ,Rj|2 + ∆fNo
. (3.17)
The transfer function for y(2)m (t) in (3.15) can be expressed as
Y (2)m = H
k,(2)R0,m
sk,(2)B0,m
+Iout∑j=1
Hk,(2)Rj ,m
sk,(2)Bj ,m
+W(2)R0,m
, (3.18)
where
Hk,(2)R0,m
= βR0,mHB0,R0HR0,m, (3.19)
Hk,(2)Rj ,m
= βR0,mHR0,m + βRj ,mHRj ,m + βRj ,mHBj ,RjHRj ,m, (3.20)
34
where
HB0,R0 =L−1∑l=0
hlB0,R0exp(−2πjk∆fvlB0,R0
), (3.21)
HR0,m =L−1∑l=0
hlR0,mexp(−2πjk∆fvlR0,m
), (3.22)
HRj ,m =L−1∑l=0
hlRj ,mexp(−2πjk∆fvlRj ,m
), (3.23)
HBj ,Rj=
L−1∑l=0
hlBj ,Rjexp(−2πjk∆fvlBj ,Rj
). (3.24)
The channel gains between the serving RS (R0), interfering RS (Rj) and the user mth in
the second time slot in terms of small scale fading and large scale fading can be written,
respectively, as
Gk,(2)R0,m
= 10−PLdB(dR0,m) |Hk,(2)
R0,m|2, (3.25)
Gk,(2)Rj ,m
= 10−PLdB(dRj,m) |Hk,(2)
Rj ,m|2. (3.26)
The instantaneous received SINR of the outer zone user mo in the second time slot can be
expressed as
Γk,(2)mo
=Pk,(2)R0,mo
Gk,(2)R0,mo
Iout∑j=1
Pk,(2)Rj ,mo
Gk,(2)Rj ,mo
+ ∆fNo
, (3.27)
where Pk,(2)R0,mo
, Pk,(2)Rj ,mo
are the transmit powers of the serving RS R0 and interfering RS Ri,
respectively, in the second time slot. Iout represents the number of interfering cells (ICI) for
the outer zone users in the second time slot.
Consequently, using maximum ratio combining (MRC), the total SINR at the outer zone
user mo receiver on subcarrier k, in the first time slot as in (3.14) and second time slot as in
(3.27) can be calculated as follows
Γkmo,total = Γk,(1)mo
+ Γk,(2)mo
. (3.28)
35
The achievable rate for user m on subcarrier k can be computed using Shannon’s formula as
Ckm =
1
2log2(1 + Γkm), (3.29)
where Γkm = Γk,(1)mi for the inner zone user mi as in (3.13) and Γkm = Γkmo,total
for the outer
zone user mo as in (3.28). The factor1
2indicates that two time slots are required for two-hop
AF transmissions.
The achievable EE for user m on subcarrier k is defined as the ratio of the achievable
rate to the total power consumption PT as follows
ηm,kEE =Ckm
PT, (3.30)
where PT can be calculated as PT = Pc + Pamp, Pc denotes the circuit power consumption
while Pamp is the amplifier power consumption at the source (i.e., Pamp = PB0ζB0) and at
the relay (i.e., Pamp = PR0ζR0). ζB0 and ζR0 are the drain efficiencies of the amplifiers at BS
and RS, respectively. PB0 and PR0 are the transmit powers of the BS and RS, respectively.
The Outage Probability Pout(Γth) is defined as the probability that the SINR (Γkm) falls
below a given threshold Γth, that is,
Pout(Γth) = Pr(Γkm < Γth). (3.31)
3.6 Simulation Results
In this section, the performance of the proposed schemes is analyzed and compared to other
schemes with and without relays. Performance includes the SINR, CDF of the SINR of
the received signal, the OP with varying SINR thresholds, and the average of spectral and
energy efficiencies as functions of the distance from the BS.
All the simulation results in these figures are the average performance of over 106 user
distributions and channel realizations. The users are assumed to be uniformly distributed in
36
the desired cell. The distance threshold for switching between the inner zone and the outer
zone is assumed to be 0.6 km. The simulation parameters are given in Table 3.1.
Table 3.1: Chapter 3 simulation parameters
Parameters Values
The cell radius 1000m
The inner zone radius 600m
BS-MS minimum distance dB0,m 100m
BS’s antenna height hb 32m
MS’s antenna height hm 1.5m
White noise power density No -174 dBm/Hz
Fast fading model Cost 231-Hata model
Standard deviation of shadowing σ=3dB
Channel bandwidth 10 MHz
Number of subcarriers K 350
Subcarrier spacing ∆f 15 KHz
Carrier frequency fc 2500 MHz
Reciprocal of the BS and RS power amplifier’s drain efficiency ζB0 and ζR0 2.6
Fixed circuit power consumption of the BS and RS Pc 20 dBm
Fixed transmit power of BS PB0 43 dBm
fixed transmit power of RS PR0 33 dBm
Monte Carlo simulation iterations 106
The received SINR in (dB) for the main cluster, with two tiers for each cell, against
the distance from the BS for both proposed schemes (FRF=(1,7/3) and FRF=(1,7/4)) and
other schemes are presented in Figure 3.7 and 3.8, respectively. The Figures demonstrate
that the SINR of the proposed schemes (FRF=(1,7/3) and FRF=(1,7/4)) is greater than
those in [61], [64], and [71], for the outer zone users with cooperative and non-cooperative
relaying. This is because the average number of interfering cells is reduced with the proposed
frequency reuse patterns.
37
In the inner zone, all schemes have similar SINR because they utilize an FRF=1. In
each cell, as the user m moves away from the serving BS B0, the SINR decreases, because of
increasing dB0,m, until it reaches the outer zone boundary, then the SINR increases because
of the utilization of relays.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance to BS [km]
5
10
15
20
25
30
35
40
45
SIN
R (
dB
)
Coop, (1,7/3) Proposed
Coop, (1,7/3) [61]
Coop, (1,3) [71]
Non-Coop, (1,7/3) Proposed
Non-Coop, (1,7/3) [61]
Non-Coop, (1,3) [64]
Conv. Scheme (FRF=1) [71]
Figure 3.7: SINR for the main cluster with two tiers for the proposed scheme FRF=(1,7/3)
and other schemes.
Figure 3.8 shows that the SINR performance of the proposed FRF=(1,7/4) scheme out-
performs the FRF=(1,7/3) scheme. However, this is at the expense of the increase in the
number of sectors, which increases the number of RSs. Also, it is seen that the proposed
FRF=(1,7/4) scheme at a distance threshold of 0.6 km, for example, achieves SINR gains of
about 3.21 dB in the cooperative relaying and 4.19 dB in the non-cooperative relaying case
compared to FRF=(1,7/4) in [61]. From Figure 3.7, the proposed FRF=(1,7/3) scheme at
a distance threshold of 0.6 km, for example, achieves SINR gains of about 5.62 dB in the
38
cooperative relaying and 7.56 dB in the non-cooperative case compared to the FRF=(1,3)
scheme in [71] and [64], respectively.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance from BS [km]
5
10
15
20
25
30
35
40
45
SIN
R (
dB
)
Coop, (1,7/4) Proposed
Coop, (1,7/3) Proposed
Non-Coop, (1,7/4) Proposed
Non-Coop, (1,7/3) Proposed
Coop, (1,7/4) [61]
Non-Coop, (1,7/4) [61]
Conv. Scheme (FRF=1) [71]
Figure 3.8: Comparison of the received SINR of the proposed schemes FRF=(1,7/4),
FRF=(1,7/3) and other schemes.
Figure 3.9 illustrates the CDF of the SINR of the received signal of the proposed schemes
and other schemes for both cases, cooperative and non-cooperative relaying. From this
Figure, the proposed FRF=(1,7/4) scheme with and without relays outperforms the scheme
proposed in [61]. For example, our proposed scheme exhibits gains of 2.4 dB at a CDF of
0.41 in the cooperative relaying case and gains of 2.6 dB for the non-cooperative relaying at
a CDF of 0.58 compared to the scheme in [61].
39
-20 -10 0 10 20 30 40 50SINR [dB]
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD
F
Coop, (1,7/4) Proposed
Coop, (1,7/3) Proposed
Non-Coop, (1,7/4) Proposed
Non-Coop, (1,7/3) Proposed
Coop, (1,7/4) [61]
Non-Coop, (1,7/4) [61]
Conv. Scheme (FRF=1) [71]
Figure 3.9: CDF of the received SINR for the main cluster with two tiers of the proposed
schemes and other schemes.
Figures 3.10 and 3.11 depict the outage probability of the received SINR varying with
threshold Γth (dB) for both proposed schemes (FRF=(1,7/3) and FRF=(1,7/4)) and other
schemes in [61], [64], and [71]. From these Figures, it is obvious that the Poutage performance
of the proposed schemes outperforms those of the previous schemes, which indicates that
the ICI for the proposed schemes is less than those in the other schemes, especially for the
outer zone users. Also, it is clear that the worst scheme is the conventional scheme (FRF=1)
because it has high ICI compared to other schemes and there are no relays in this scheme.
40
-10 -5 0 5 10 15 20 25 30 35
th
(dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Po
uta
ge
Coop, (1,7/3) Proposed
Coop, (1,7/3) [61]
Coop, (1,3) [71]
Non-Coop, (1,7/3) Proposed
Non-Coop, (1,7/3) [61]
Non-Coop, (1,3) [64]
Conv. Scheme (FRF=1) [71]
Figure 3.10: Outage probability of the received SINR for the proposed FRF=(1,7/3) scheme
and other schemes versus the threshold Γth (dB).
-10 -5 0 5 10 15 20 25 30 35
th
(dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pouta
ge
Coop, (1,7/4) Proposed
Coop, (1,7/3) Proposed
Non-Coop, (1,7/4) Proposed
Non-Coop, (1,7/3) Proposed
Coop, (1,7/4) [61]
Non-Coop, (1,7/4) [61]
Conv. Scheme (FRF=1) [71]
Figure 3.11: Outage probability of the received SINR for both proposed schemes and other
schemes versus the threshold Γth (dB).
The average spectral and energy efficiencies with relays are evaluated versus the distance
41
from the BS in Figure 3.12 and Figure 3.13, respectively. From these Figures, when user m
moves away from the serving BS B0, the average SE and EE decay until the user reaches the
outer zone boundary. When the MS enters the outer zone, the proposed scheme outperforms
the other schemes in [61] and [71] because of the reduction in ICI.
As illustrated in Figure 3.12, with relays at a distance threshold of 0.6 km, for example,
we observe SE gains of 3.97 b/s/Hz and 2.03 b/s/Hz with FRF=(1,7/4) and FRF=(1,7/3),
respectively, compared to both schemes in [61]. Furthermore, it can be seen that the increase
in the number of sectors, which increases the number of relays leads, to improvements in the
system performance such as SE and EE as shown in Figure 3.12 and Figure 3.13, respectively.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance from BS [km]
0
5
10
15
20
25
30
35
40
45
Av
erg
e S
E [
b/s
/Hz]
Coop, (1,7/4) Proposed
Coop, (1,7/3) Proposed
Coop, (1,7/4) [61]
Coop, (1,7/3) [61]
Coop, (1,3) [71]
Conv. Scheme (FRF=1) [71]
Figure 3.12: Average SE with relays for the main cluster with two tiers of the proposed
schemes and other schemes.
42
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance from BS [km]
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Av
erg
e E
E [
b/s
/J]
Coop, (1,7/4) Proposed
Coop, (1,7/3) Proposed
Coop, (1,7/4) [61]
Coop, (1,7/3) [61]
Coop, (1,3) [71]
Conv. Scheme (FRF=1) [71]
Figure 3.13: Average EE with relays for the main cluster with two tiers of the proposed
schemes and other schemes.
3.7 Conclusion
In this chapter, a frequency reuse pattern formula is proposed to minimize the number
of interfering cells for both schemes (FRF=(1,7/3) and FRF=(1,7/4)) compared to other
schemes, especially for outer zone users. The proposed patterns are applied for each cell
within the main cluster with two tiers around each cell. Also, the performance analysis
takes into account the effect of ICI for cooperative AF relaying and non-cooperative relaying
in downlink OFDMA multi-cell systems is provided to evaluate the SINR, CDF of the SINR
of the received signal, Poutage with a varying SINR threshold, and the average of spectral
and energy efficiencies versus the distance from the BS.
Simulation results show that the proposed schemes achieve a significant reduction in ICI
43
for the outer zone users compared to those of previous works. The benefits of AF relays
on the system performance such as increasing the cell capacity and decreasing the outage
probability due to the reduction in the distance between the transmitter and the outer zone
users have been demonstrated. Since each relay only transmits to the outer zone users within
the second time slot, there is a potential energy/battery-saving benefit.
44
Chapter 4
Sum Rate Maximization for FFR Schemes with
Inter-Cell Interference in Downlink Multi-Cell
NOMA-Based Networks 1
.
4.1 Chapter Overview
In this chapter, the achievable sum-rate (ASR) is optimized in NOMA under a PA, efficient
SIC, and minimum QoS requirements constraints for FFR schemes in perfect and imperfect
SIC conditions. A UP algorithm with the obtained optimal PA is proposed to maximize
ASR in the FFR scheme while considering the impact of ICI on the system performance.
Furthermore, the proposed PA and UP are applied for an FRF =(1,3) FFR scheme to analyze
the ASR, the CDF of the SINR of the received signal, and OP in the interested cell with 18
surrounding cells. A new formula is derived to calculate the SIC error factor Fc at the closer
user receiver in the imperfect SIC case.
To fully reap the advantages of NOMA, we need appropriate PA and UP techniques.
The key idea of PA is to multiplex multiple users at different power levels but at the same
sub-band frequency. PA is implemented by varying the transmit power coefficients between
the users in each pair, which in turn varies the throughput of each user (i.e., the throughput
is influenced by the PA coefficients). The procedure for grouping a number of users and
1The content of this chapter has been submitted as a journal paper [77] to IEEE Transaction on Wireless
Communications. Saleh, Ali M. and and Sesay, Abu B., ”Sum Rate Maximization for FFR Schemes with
Inter-Cell Interference in Downlink Multi-Cell NOMA-Based Networks”.
45
assigning a common sub-band frequency to them is known as UP. The objective of UP is to
divide the total number of users M into multiple pairs in a way that maximizes the sum-rate
of that pair. In this thesis, the proposed UP algorithm keeps the difference between the
indices of channel gains of paired users always constant. A decoding error for a particular
user’s signal might occur when the number of users in each pair is increased. This affects
the decoding of all the other users’ signals, resulting in system performance degradation.
Therefore, the number of users in each pair should be as small as possible so as to eliminate
the impact of error propagation.
SC at the transmitter and SIC at the receiver are key technologies of NOMA schemes.
The basic idea of NOMA is to allocate non-orthogonal sub-carriers to multiple users at the
same time via superposition transmission.
Currently, FFR schemes are the most reliable approaches used to eliminate ICI in OFDMA
systems, especially for outer zone users. In NOMA, appropriate UP and PA between users
are the main metrics for achieving high spectral efficiency (serving multiple users simul-
taneously with the same sub-band frequency and reducing interference through SIC) and
improved user fairness (power control between near and far users). The objective of this
Chapter is to investigate the advantages of FFR schemes and NOMA under perfect and
imperfect SIC situations. The proposed PA and UP are used in an FRF =(1,3) FFR scheme
to analyze the ASR, the CDF of the SINR of the received signal, and OP in the interested
cell with 18 surrounding cells generating ICI.
The remainder of this chapter is organized as follows. Section 4.2 describes the related
work. In Section 4.3, the system and channel models are presented. The spectral efficiency
and outage probability for the FFR scheme in NOMA are analyzed in Section 4.4. In Section
4.5, the proposed power allocation algorithm with an SIC constraint to maximize ASR is
presented. ASR with a proposed SIC error factor at the closer user receiver is addressed
in section 4.6. Generalization of the proposed UP algorithm to maximize ASR in the FFR
46
scheme is described in Section 4.7. The system performance of the proposed UP in terms of
ASR, the CDF of the SINR of the received signal, and the OP is analyzed in Section 4.8.
Finally, the chapter is concluded in Section 4.9.
4.2 Related Work
In new NOMA schemes, many studies have been done on sum-rate maximization considering
PA, UP, and energy-efficient resource allocation. In [39], PA and UP are investigated to
maximize the ASR in NOMA for only perfect SIC in a 2-user case. The authors generalize
the solution for a specific distance between BS and MS in a single cell. The sum-rate of a
2-user case in a NOMA with imperfect SIC and fixed transmit power in one cell is optimized
in [78]. In [79], the authors investigate the effect of UP on the system performance in one
cell with fixed PA coefficients only.
The authors in [11] investigate the effect of UP and PA in the pair sum capacity and bit
error rate (BER) of users in perfect and imperfect SIC situations. Also, they maximize the
pair sum capacity under a data reliability constraint. All their work have been done for a
single cell with 2 users only. In [14], the authors investigate the impact of UP on fixed PA
in NOMA and cognitive-radio-inspired NOMA but for only perfect SIC case and in one cell
only.
PA in NOMA is investigated in [80] to optimize the sum-rate, maximin fairness, and
energy efficiency with weights or QoS constraints for perfect SIC in a single cell only. Opti-
mization of individual data rates using two PA algorithms under an imperfect SIC condition
in a single cell is investigated in [81]. The sum-rate in a cell is optimized in [10] in terms
of user clustering and PA for a perfect SIC condition. In [82] and [83], the authors inves-
tigate user grouping to optimize the sum-rate with a fixed transmit power and perfect SIC
condition in one cell.
The authors in [84] propose a fast and simple UP algorithm to obtain a maximum pro-
47
portional fairness metric with a fixed PA in one cell. In [85], the authors propose a novel UP
to pair one of the two center cell users with a user of the cell edge in a single cell to achieve
a better throughput for the cell-edge user in a perfect SIC case and a fixed PA manner. The
PA is investigated in [86, 87, 88] to optimize the sum-rate of a 2-user case with only total
power and minimum QoS requirement constraints in a perfect SIC condition and a single
cell.
To the best of the author’s knowledge and comparing with the existing work in the
literature, there are no publications that aim to optimize the ASR in NOMA under a PA,
efficient SIC, and minimum QoS requirement constraints for FFR schemes in perfect and
imperfect SIC scenarios.
4.3 System and Channel Models
The layout of the downlink OFDMA multi-cell system with FRF=(1,3) FFR scheme is
illustrated in Figure 4.1.
48
FRF=1
FRF=3
Frequency
FRF=1 for inner zones
FRF=3 for outer zones
B W
Frequency
Power
Cell 0
BS
Figure 4.1: Network structure for the FRF=(1,3) FFR scheme in OFDMA system.
In this scheme, each cell is partitioned into two zones; inner and outer zones. Then, the
available bandwidth (BW) is split into two parts corresponding to two zones. The first part
is utilized in the inner zone with the conventional scheme (i.e., FRF=1) and the other part
is partitioned into three orthogonal sub-bands corresponding to three sectors in the outer
zone (i.e., FRF=3) as illustrated in Figure 4.1.
The system model for the two cases (inner and outer zones) of two users m and n downlink
NOMA with SIC is illustrated in Figure 4.2 and 4.3, respectively. In this model, all the users
in the inner zone and in the outer zone are paired separately.
49
User n
User m
0 ,B mh
0 ,B nh
User n
User m
0 ,B mh
0 ,B nh
0BBS0BBS
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
User n
User m
0 ,B mh
0 ,B nh
0BBSny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
User n
User m
0 ,B mh
0 ,B nh
0BBSny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
User n
User m
0 ,B mh
0 ,B nh
0BBSny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
Figure 4.2: Two users downlink NOMA with the SIC model for inner zone users.
User n
User m
0 ,B mh
0 ,B nh
User n
User m
0 ,B mh
0 ,B nh
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
0BBS
User n
User m
0 ,B mh
0 ,B nh
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
0BBS
User n
User m
0 ,B mh
0 ,B nh
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
0BBS
User n
User m
0 ,B mh
0 ,B nh
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
0BBS
User n
User m
0 ,B mh
0 ,B nh
ny Decoder
Decoder
0 ,B mx
nhX
0 0 0, , ,( )B n B m B n nh x x w+ +
_
0 0, ,B n B n nh x w+nx
Decoder0 ,B mx0 0 0, , ,( )B m B m B n mh x x w+ +
my
Frequency
Power
. . . .. . . .
0 ,B mP
0 ,B nP
0BBS
Figure 4.3: Two users downlink NOMA with the SIC model for outer zone users.
From both Figures 4.2 and 4.3, there are two users, m and n, sharing the same sub-band
with channel gains |hB0,m|2 and |hB0,n|2; respectively, where B0 represents the serving BS.
User n is the near user who has the highest channel gain (i.e., |hB0,n|2 > |hB0,m|2); therefore,
it needs less transmit power than that of the user m from the base station (downlink) (i.e.,
PB0,n < PB0,m).
In NOMA, the user who needs less transmit power will receive more interference from
50
the user who needs more transmit power; however, it can decode its signal easily using SIC.
On the other hand, the user who needs more transmit power will consider the interference
from the user who needs less transmit power as noise [89, 90, 91].
The BS transmits the superimposed signal as
x =√αB0,mPB0 xB0,m +
√αB0,nPB0 xB0,n, (4.1)
where αB0,m and αB0,n are the PA coefficients of user m and n, respectively. Furthermore,
αB0,m and αB0,n must satisfy the condition of αB0,m + αB0,n = 1. This is equivalent to
αB0,m = (1− αB0,n) for the 2-user case.
At the m and n users’ receiver, the received signal can be expressed as
ym = hB0,m xB0,m +I∑j=1
hBj ,m xBj ,m + wm;
yn = hB0,n xB0,n +I∑j=1
hBj ,n xBj ,n + wn, (4.2)
where x is given by (4.1) either from the serving BS B0 (xB0,m or xB0,n) or from interfering BS
Bj (xBj ,m or xBj ,n). hB0,m, hB0,n, hBj ,m, and hBj ,n represent the channel coefficients between
the serving BS, interfering BS and users m and n; respectively, which include a path-loss
and small-scale fading. The components wm ∼ CN(0, σ2m) and wn ∼ CN(0, σ2
n) are AWGN.
The second term on the right-hand side of (4.2) is the ICI from the adjacent cells to users
m and n (for the inner zone case I = Iinn = 18 or I = Iout = 7 for the outer zone case).
Assume, in the downlink NOMA links, the decoding order is in descending order of the
channel gains (i.e., |hB0,n|2 > |hB0,m|2). Therefore, the user n will decode user m’s signal
first, then remove the interference from user m by subtracting m’s signal and then decoding
its own signal. User m can decode its own signal successfully with interference from user n
considered as a noise [92].
51
The path-loss of the m and n users can be modelled as
PL(dBj ,m) = d−ρBj ,m;
PL(dBj ,n) = d−ρBj ,n, (4.3)
where dBj ,m and dBj ,n denote the distances from the serving BS (B0, j = 0) or from interfering
BSs (Bj, j 6= 0) to users m and n, respectively. The parameter ρ represents the path-loss
exponent (ρ= 2 to 4 in dense urban areas). In addition, Rayleigh fast fading is represented
as a small-scale fading for both users m and n with exponential PDF fSF (x) = e−x, x > 0
[93].
4.4 Spectral Efficiency and Outage Probability for an FFR Scheme in NOMA
The maximum amount of data that can be transmitted over a given bandwidth is defined
as SE. The probability that the SINR drops below a given threshold (Γth) is defined as the
OP. The SE and OP are derived for the entire cell (inner and outer zone) in the next two
subsections.
4.4.1 Spectral Efficiency and Outage Probability for Inner Zone Users
At the center of each cell, there is a BS equipped with an omni-directional antenna to cover
the inner zone area. In this case, the number of interfering cells is Iinn = 18 for a two-tier
structure.
Let ΓNOMAmi
and ΓNOMAni
denote the SINR for both users mi and ni, respectively. Then, the
achievable rates of both users mi and ni in NOMA for the imperfect SIC case are evaluated,
respectively, as
CNOMAmi
= log2(1 + ΓNOMAmi
) = log2(1 +(1− αB0,ni
)|hB0,mi|2
αB0,ni|hB0,mi
|2 +Iinn∑j=1
|hBj ,mi|2 + γ−1
), (4.4)
52
CNOMAni,imperf
= log2(1+ΓNOMAni,imperf
) = log2(1+αB0,ni
|hB0,ni|2
4(1− αB0,ni)|hB0,ni
|2 +Iinn∑j=1
|hBj ,ni|2 + γ−1
), (4.5)
CNOMAni,perf
= log2(1 + ΓNOMAni,perf
) = log2(1 +αB0,ni
|hB0,ni|2
Iinn∑j=1
|hBj ,ni|2 + γ−1
), (4.6)
where γ represents the SNR (γ =PB0
N0
) of each user.
For OMA, the achievable rates of both users mi and ni are evaluated, respectively, as
COMAmi
=1
2log2(1 +
|hB0,mi|2
Iinn∑j=1
|hBj ,mi|2 + γ−1
), (4.7)
COMAni
=1
2log2(1 +
|hB0,ni|2
Iinn∑j=1
|hBj ,ni|2 + γ−1
), (4.8)
where the factor (1/2) represents the assigned bandwidth for each user.
The outage probability of the SINR of the inner user ni can be calculated by
Pout = Pr(ΓNOMAni
< Γth). (4.9)
4.4.2 Spectral Efficiency and Outage Probability for Outer Zone Users
In order to cover each sector, the BS is equipped with a directional antenna (i.e., with 120o
angle). In this case, the number of interfering cells is reduced to Iout = 7 compared to the
inner zone case (Iinn = 18) for a two-tier structure.
Let ΓNOMAmo
and ΓNOMAno
denote the SINR for both users mo and no, respectively. Then,
the achievable rates of both users mo and no in NOMA for the imperfect SIC case are
evaluated, respectively, as
CNOMAmo
= log2(1 + ΓNOMAmo
) = log2(1 +(1− αB0,no)|hB0,mo |2
αno|hB0,mo|2 +Iout∑j=1
|hBj ,mo|2 + γ−1
), (4.10)
53
CNOMAno,imperf = log2(1 + ΓNOMA
no,imperf ) = log2(1 +αB0,no |hB0,no |2
4(1− αB0,no)|hB0,no |2 +Iout∑j=1
|hBj ,nout|2 + γ−1
),
(4.11)
CNOMAno,perf = log2(1 + ΓNOMA
no,perf ) = log2(1 +αB0,no |hB0,no |2
Iout∑j=1
|hBj ,no |2 + γ−1
). (4.12)
For OMA, the achievable rates of both users mo and no are evaluated, respectively, as
COMAmo
=1
2log2(1 +
|hB0,mo|2Iout∑j=1
|hBj ,mo|2 + γ−1
), (4.13)
COMAno
=1
2log2(1 +
|hB0,no|2Iout∑j=1
|hBj ,no |2 + γ−1
). (4.14)
The outage probability of the SINR of the outer user nout can be calculated by
Pout = Pr(ΓNOMAno
< Γth). (4.15)
4.5 Proposed Power Allocation Algorithm with SIC Constraint to Maximize
Achievable Sum-Rate
An optimization problem is formulated to maximize the ASR for the case of more than two
users. As well, lower and upper bounds are obtained for the optimal PA coefficient in a
2-user case.
4.5.1 Problem Formulation
Let us introduce a binary variable bm,n to define the pairing relationship between any two
users m and n as follows
bm,n =
1, if m pairs n;
0, otherwise.
(4.16)
54
Then, the optimization problem to maximize the ASR is formulated as
maxαB0,n
, bm,n
2U∑m=1
2U∑n=m+1
bm,n(C(m,n)m + C(m,n)
n )
s.t. C(m,n)m ≥ bm,nC
OMAm ,
C(m,n)n ≥ bm,nC
OMAn ,
(1− αB0,n)|hB0,n|2
αB0,n|hB0,n|2 + γ−1≥ λth
⇒ αB0,n ≤|hB0,n|2 − λthγ−1
|hB0,n|2(1 + λth),
0 < αB0,n < 1,∀ 1 ≤ n ≤ 2U,
bm,n ∈ {0, 1}, ∀ 1 ≤ m,n ≤ 2U,
bm,n = bn,m,∀ 1 ≤ m,n ≤ 2U,
bm,m = 0,∀ 1 ≤ m ≤ 2U,
2U∑m=1
bm,n = 1,∀ 1 ≤ n ≤ 2U,
2U∑n=1
bm,n = 1,∀ 1 ≤ m ≤ 2U,
(4.17)
where U represents the number of pairs (groups). To provide an insight into the solution to
this problem, we shall consider a 2-user case.
The above optimization problem (i.e., (4.17)) for the 2-user case reduces to the following
maxαB0,n
CNOMAm + CNOMA
n
s.t. C(m,n)m ≥ COMA
m ,
C(m,n)n ≥ COMA
n ,
(1− αB0,n)|hB0,n|2
αB0,n|hB0,n|2 + γ−1≥ λth
⇒ αB0,n ≤|hB0,n|2 − λthγ−1
|hB0,n|2(1 + λth),
0 < αB0,n < 1,
(4.18)
55
where λth is a minimum threshold of the ratio between the allocated power of both users
to guarantee the SIC will decode correctly. The first two constraints in (4.18) are satisfied
with the achievable rate of each user in NOMA being higher than that in the OMA. The
third constraint represents efficient SIC. The last constraint guarantees that the summation
of αB0,n and (1− αB0,n) does not exceed one.
From the first two constraints, in general case (either in the inner or outer zone), we can
obtain a range of αB0,n for a perfect SIC case as follows:
CNOMAm ≥ COMA
m
⇔ log2(1 +(1− αn)|hB0,m|2
αn|hB0,m|2 +I∑j=1
|hBj ,m|2 + γ−1
) ≥ 1
2log2(1 +
|hB0,m|2I∑j=1
|hBj ,m|2 + γ−1
)
⇒ αB0,n ≤Am(Bm − Am)
Em,
(4.19)
where Tm =I∑j=1
|hBj ,m|2, Em = |hB0,m|2, Am =√Tm + γ−1, Bm =
√Tm + γ−1 + Em, and I
represents the number of interfering cells (ICI) around the desired cell.
CNOMAn ≥ COMA
n
⇔ log2(1 +αn|hB0,n|2
I∑j=1
|hBj ,n|2 + γ−1
) ≥ 1
2log2(1 +
|hB0,n|2I∑j=1
|hBj ,n|2 + γ−1
),
⇒ αB0,n ≥An(Bn − An)
En,
(4.20)
where Tn =I∑j=1
|hBj ,n|2, En = |hB0,n|2, An =√Tn + γ−1, Bn =
√Tn + γ−1 + En, and I
represents the number of interfering cells (ICI) around the desired cell.
Given the upper bound for αB0,n in (4.18) and (4.19), the optimal solution of αB0,n will
be the minimum value of (4.18) and (4.19).
56
4.6 Achievable Sum-Rate with Proposed SIC Error Factor at the Closer
User Receiver
Assume that the transmitted signals are modulated as binary phase-shift keying (BPSK)
modulation and we are interested in the process of SIC at the close user n. Since the signal
collected at the receiver of user n is given by
yn =√
(1− αB0,n)PB0 xmhB0,n +√αB0,nPB0 xnhB0,n + wn (4.21)
The BER for BPSK modulation over a Rayleigh fading channel hB0,n is given by [94]
Pe = Q
√|hB0,n|2d2min
4No
, (4.22)
where dmin = 2A1 for detecting the symbol xn = −1 while the symbol xm = 1 is transmitted
and dmin = 2A2 for detecting the symbol xn = 1 while the symbol xm = 1 is transmitted.
A1 =√
(1− αB0,n)PB0 −√αB0,nPB0 and A2 =
√(1− αB0,n)PB0 +
√αB0,nPB0 as illustrated
in Figure 4.4.
2A2A
1A1A
1nx =1nx = 1nx = −1nx = −1mx = − 1mx =0
0 0,B n BP0 0,(1 )B n BP−
0 0,(1 )B n BP−0 0,B n BP
Figure 4.4: BPSK Constellation.
In the next theorem, the SIC error factor Fc is defined as the average probability of error.
Theorem 1. The SIC error factor Fc in a NOMA scheme with 2-user is defined as
Fc = Pe =1
2Q
(√γ|hB0,n|(
√(1− αB0,n)−√αB0,n)
)+
1
2Q
(√γ|hB0,n|(
√(1− αB0,n) +
√αB0,n)
), (4.23)
57
where Fc is a function of channel coefficient (|hB0,n|), SNR (γ), and the transmit power
coefficient (αB0,n).
Proof : See APPENDIX B.
In the imperfect SIC case, the achievable rate at the user n is calculated by
CNOMAn,imperf = Fc log2(1 +
αB0,n|hB0,n|2
4(1− αB0,n)|hB0,n|2 +I∑j=1
|hBj ,n|2 + γ−1
)
+ (1− Fc) log2(1 +αB0,n|hB0,n|2
I∑j=1
|hBj ,n|2 + γ−1
), (4.24)
Thus, the total achievable sum-rate for imperfect SIC is given by
CNOMAtot,imperf = CNOMA
m + CNOMAn,imperf ; (4.25)
whereas, for perfect SIC is given by
CNOMAtot,perf = CNOMA
m + CNOMAn,perf , (4.26)
where CNOMAm for inner zone user is in (4.4) and for outer zone user is in (4.10), while
CNOMAn,perf =
αB0,n|hB0,n|2I∑j=1
|hBj ,n|2 + γ−1
, where I represents the number of interfering cells; either for
inner zone (Iinn) case or outer zone (Iout) case.
4.7 Generalization of Proposed User Paring Algorithm to Maximize Achiev-
able Sum-Rate in FFR Scheme
The authors in [14, 89] show that the greater the channel gain difference for paired users, the
higher the sum-rate for NOMA can be achieved compared to OMA. The authors in [39] do
not consider the effect of the channel gain differences between paired users since they assume
a perfect SIC. On the other hand, in the imperfect SIC case, this assumption will negatively
affect the system performance due to the users being so close to each other resulting in a
very high inter-user interference.
58
To overcome the issues mentioned above, in this thesis, a UP that keeps the difference
between the indices of channel gains of paired users always constant is proposed.
The proposed UP algorithm is given in Algorithm 1.
Algorithm 1 :Proposed UP Algorithm
1: Sort and number all the users channel gains in ascending order
|h1|2, |h2|2, ..., |hM2|2, |hM
2+1|2, ..., |hM |2,
where M is the total number of users.
2: If M is even, then we need to classify all users into two groups: AL for low channel gains
and AH for high channel gains which can be expressed as
AL = {|h1|2, |h2|2, ..., |hM2|2},
AH = {|hM2
+1|2, |hM2
+2|2..., |hM |2},
then the users will be paired as follows
g1 = {|h1|2, |hM2
+1|2},
g2 = {|h2|2, |hM2
+2|2},... gM
2= {|hM
2|2, |hM |2}.
3: If M is odd, then we need to find the median of M users which is |hM+12|2 and then AL
represents the group before the median and AH represents after the median.
AL = {|h1|2, |h2|2, ..., |hM−12|2} ,
AH = {|hM+12
+1|2, |hM+12
+2|2..., |hM |2},
then users will be paired as follows
g1 = {|h1|2, |hM+12
+1|2},
g2 = {|h2|2, |hM+12
+2|2},...
gM−12
= {|hM−12|2, |hM |2}.
The last user will be alone and will uses a whole subcarrier as in OMA systems.
4: If M is a single user, then we do not need the pairing; the user will use the entire
bandwidth.
59
Consequently, the mechanism of the proposed algorithm can be written as
gu =
{|hu|2, |hu+M2|2}, ∀ 1 ≤ u ≤ M
2if M is even
{|hu|2, |hu+M+12|2}, ∀ 1 ≤ u < M+1
2if M is odd.
(4.27)
In (4.27), it is observed that the difference between the indices of the channel gains of
any paired users is constant and this process is continued until complete pairing all of the
users. Also, it can be observed that the proposed algorithm is working efficiently even for
many users.
4.8 Simulation Results
The performance of the proposed UP scheme with optimal PA coefficients is analyzed and
compared with random UP, near-far UP proposed in [39], and OMA system. All the simula-
tion results in these Figures are the average performance of over 106 user distributions and
channel realizations. In a downlink NOMA, the ASR of the proposed scheme is evaluated
and compared to other schemes for perfect and imperfect SIC. However, the CDF of the
SINR of the received signal, the gain of ASR when the SIC constraint in the optimization
problem is included and without that constraint, and the OP versus SINR threshold are
evaluated and compared to other schemes for imperfect SIC (practical SIC) only.
The distribution of users is assumed to be uniform within the entire interested cell.
TABLE 1 shows the main simulation parameters.
60
Table 4.1: Chapter 4 simulation parameters
Parameters Values
The inner zone radius 600m
The cell radius 1000m
BS-MS minimum distance 100m
White noise power density No -174 dBm/Hz
Path-loss exponent ρ 2
Channel bandwidth 10 MHz
Data modulation BPSK
SIC receiver’s detection threshold λth 2
Number of sub-carriers 35
Bandwidth of a subcarrier 30 KHz
Monte Carlo simulation iterations 106
Figure 4.5 plots the ASR versus SNR (dB) in FFR scheme for various schemes including
the proposed scheme, near-far UP proposed in [39], random UP , and OMA in a perfect and
imperfect SIC situations.
61
-20 -10 0 10 20 30 40
SNR (dB)
0
50
100
150
200
250
300
Av
erag
e S
um
Rat
e (b
ps/
Hz)
Imperfect Proposed UP
Perfect Proposed UP
Imperfect UP in [39]
Perfect UP in [39]
Imperfect Random UP
Perfect Random UP
OMA
Figure 4.5: ASR for an FFR scheme in NOMA of perfect and imperfect SIC with 70 users.
Figure 4.5 shows that the ASR of the proposed scheme in NOMA is greater than that of
OMA, which is satisfying the first two constraints in the optimization problem as in (4.17).
Also, Figure 4.5 shows that in the perfect SIC case, the ASR of the near-far UP scheme
in [39] is slightly greater than the proposed UP scheme at low SNR because the difference
between the channel gains, which they do not take into account, will not affect the ASR in
this case. However, at high SNR, the performance of the proposed UP which considers the
deference in the channel gains outperforms those of the other schemes.
In addition, Figure 4.5 shows that as SNR (dB) increases, the ASR of perfect and im-
perfect SIC of the proposed scheme converge. This is because increasing the transmit power
of the far user aids detection of its signal more efficiently at the close user receiver. For
the imperfect SIC case (more practical), Figure 4.6 illustrates the proposed UP scheme in
NOMA outperforms the other schemes and OMA.
62
-20 -10 0 10 20 30 40
SNR (dB)
0
50
100
150
200
250
300
Av
erag
e S
um
Rat
e (b
ps/
Hz)
Imperfect Proposed UP
Imperfect UP in [39]
Imperfect Random UP
OMA
Figure 4.6: ASR for an FFR scheme in NOMA of imperfect SIC (practical SIC) with 70
users.
The ASR comparison of the proposed scheme with and without efficient SIC constraint
is provided in Figure 4.7, which shows that the SIC constraint ensures that the far user’s
signal is decoded by the close user correctly.
63
-20 -10 0 10 20 30 40
SNR (dB)
0
50
100
150
200
250
300
Av
erag
e S
um
Rat
e (b
ps/
Hz)
Imperfect proposed UP with SIC Constraint
Imperfect proposed UP without SIC Constraint
Imperfect UP in [39] with SIC Constraint
Imperfect UP in [39] without SIC Constraint
Imperfect Random UP with SIC Constraint
Imperfect Random UP without SIC Constraint
OMA
Figure 4.7: ASR for an FFR scheme in NOMA with and without SIC constraint for the
proposed UP scheme, other pairing schemes, and OMA system.
In Figure 4.8, the ASR for the FFR scheme in imperfect SIC condition is evaluated
against the number of users, which depicts a linear relationship of the ASR with the number
of users. Also, the Figure shows that the proposed UP scheme outperforms the other schemes
including OMA as the number of users increases (i.e., the proposed UP scheme is working
efficiently even with a large number of users, either even or odd number).
64
15 20 25 30 35 40 45 50 55 60
No. of Users
0
50
100
150
200
250
Av
erag
e S
um
Rat
e (b
ps/
Hz)
Imperfect Proposed UP
Imperfect UP in [39]
Imperfect Random UP
OMA
Figure 4.8: ASR for an FFR scheme in NOMA of imperfect SIC with SNR=100 dB of the
proposed UP scheme, other pairing schemes, and OMA system.
Figure 4.9 depicts a comparison between the CDF of the SINR versus SINR in (dB) of
the proposed UP scheme with other schemes in imperfect SIC case for the inner and outer
zone users.
65
-30 -20 -10 0 10 20 30
SINR (dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CD
F
Proposed UP - Inner Zone
Proposed UP - Outer Zone
UP in [39] - Inner Zone
UP in [39] - Outer Zone
Random UP - Inner Zone
Random UP - Outer Zone
Figure 4.9: CDF of the SINR for inner and outer zone users when the number of users =24
in imperfect SIC case.
Figure 4.10 illustrates a comparison of the OP of the SINR versus the threshold Γth (dB)
of the proposed UP scheme with other schemes in imperfect SIC case for the inner and outer
zone users.
66
-15 -10 -5 0 5 10 15 20 25
th
(dB)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Pouta
ge
Proposed UP - Inner Zone
Proposed UP - Outer Zone
UP in [39] - Inner Zone
UP in [39] - Outer Zone
Random UP - Inner Zone
Random UP - Outer Zone
Figure 4.10: Outage probability of the SINR versus the threshold Γth (dB) for inner and
outer zone users when the number of users =24 in imperfect SIC case.
Both Figures 4.9 and 4.10 show that the performance of the proposed UP scheme out-
performs those of the other schemes for both inner and outer zone users. In addition, due to
the mitigation in ICI in the proposed FFR scheme, the performance of the outer zone users
outperforms those of the inner zone users.
4.9 Conclusion
In this chapter, an optimization problem is formulated to maximize the ASR in a downlink
NOMA under PA, efficient SIC, and minimum QoS requirement constraints. The optimal PA
coefficient expression has been derived for a two user case that satisfies all given constraints
simultaneously. Also, an UP scheme with the resulting optimal PA in the FFR scheme for
perfect and imperfect SIC scenarios is proposed. In addition, an expression to calculate a
67
cancellation error factor for the imperfect SIC (practical SIC) case is derived. The proposed
scheme’s performance is analyzed in terms of ASR, the CDF of the SINR of the received
signal, and the outage probability for an FFR scheme taking into account the impact of ICI
in the system performance.
Furthermore, simulation results depict the efficiency of the proposed scheme over other
schemes, especially for the imperfect SIC condition (i.e., more practical scenario) and outer
zone users.
68
Chapter 5
Sum Rate Maximization for FFR Schemes with
Inter-Cell Interference in Downlink Multi-Relay
Multi-Cell NOMA-Based Networks
5.1 Chapter Overview
In this chapter, the instantaneous SINR expressions for inner and outer zone users are derived
in a cooperative AF-fixed relaying in the first and second time slots. Then, the total received
SINR at the outer zone users in the first and second time slots are combined using MRC.
The achievable rates are derived for inner and outer zone pairs in perfect and imperfect
SIC situations. An achievable sum-rate is optimized in each pair in the cooperative relaying
NOMA under PA, efficient SIC, and minimum QoS requirement constraints for FFR schemes
in a perfect SIC scenario. An upper and lower bound of the PA coefficient expressions are
derived in the first and second time slots while considering the effect of ICI in perfect SIC
scenarios. The proposed UP in this Chapter is the same as in Chapter 4. System performance
in terms of ASR with respect to SNR in (dB) and the number of users is analyzed for an
FRF=(1,3) FFR scheme while accounting for the impact of ICI in perfect and imperfect SIC
conditions. Furthermore, the OP expression is derived for each inner and outer zone’s pairs
in a perfect SIC case under Nakagami-m fading and path-loss fading channel conditions.
NOMA is combined with cooperative relaying transmission (cooperative NOMA trans-
mission) to improve the performance of outer zone users since they have poor channel con-
ditions due to long distance transmission from the serving BS. Also, cooperative NOMA
transmission can potentially extend the service coverage, reduce channel impairments, and
achieve maximum diversity gain (i.e., it needs an additional time slot for relay transmission)
69
for all multiplexed users compared to non-cooperative NOMA and OMA schemes. Therefore,
this thesis proposes an AF-fixed relays in NOMA-based cooperative relaying to improve the
ASR and OP of outer zone users while taking into account the effect of ICI and perfect and
imperfect SIC for an FFR scheme in downlink multi-cell networks.
To reduce practical implementation issues (i.e., the system complexity) of the cooperative
NOMA, UP and the number of users in each pair are important concerns. Therefore, this
thesis considers an OMA scheme between each pair to mitigate inter-pair interference as well
as NOMA scheme within each pair to maximize capacity and consider two users in each pair.
The remainder of this chapter is organized as follows. Related work is presented in
Section 5.2. In Section 5.3, the system model is provided. The instantaneous SINR at inner
zone users in the first time slot is analyzed in Section 5.4. In Section 5.5, the instantaneous
SINR at outer zone users in the first time slot is analyzed. The instantaneous SINR at outer
zone users in the second time slot is analyzed in Section 5.6. The achievable rate for the
inner zone group is evaluated in Section 5.7. In Section 5.8, the achievable rate for the outer
zone group is evaluated. The outage probability analysis is presented in Section 5.9. The
system performance of the proposed UP scheme in terms of ASR with respect to SNR in
(dB) and the number of users and the comparison between cooperative and non-cooperative
proposed schemes are analyzed in Section 5.10. Finally, the chapter is concluded in Section
5.11.
5.2 Related Work
The first cooperative NOMA technique was proposed in [95] while having the strong users
(close to the BS) as relays to improve the system performance of the weak users (far from the
BS). The authors investigate the effect of user pairing on the cooperative and non-cooperative
NOMA systems. In addition, they analyze the OP for three schemes: OMA, cooperative
NOMA, and non-cooperative NOMA systems. However, their work only examined a single
70
cell with two users (no user pairing) with an FPA scheme and only in a perfect SIC condition.
The authors in [96] propose a DF-cooperative relaying scheme in NOMA to enhance the
spectral efficiency assuming independent Rayleigh fading channels. However, they analyze
the system performance only in one cell with an FPA scheme and in a perfect SIC case.
The same work as in [96] has been done in [97] but on Rician fading channels. The AF-
relaying cooperative scheme in a NOMA system is proposed in [98] to improve the ergodic
sum capacity with an FPA scheme in a single cell and only two-users (no user pairing). In
[99], the system-level performance of NOMA in a coordinated direct and relay transmission
is investigated and compared to a non-coordinated direct and relay transmission scheme.
However, the authors did not consider user pairing and considered only one cell without a
direct link from the serving BS to far users. They also show the simulation results in tables
(no analytical part) to describe the gain between coordinated and non-coordinated NOMA
schemes.
The OP is investigated in coordinated direct and relay transmission with a dynamic
detection in [100] for a single relay and multiple relay scenarios. However, the authors ignored
user pairing and completed their work only for one cell without a direct link between the
serving BS and far users and in a perfect SIC condition with an FPA scheme.
The authors in [101] propose a NOMA-based cooperative relaying system using AF relay
only in a single cell with an FPA scheme in a perfect SIC situation. They analyze the OP and
ergodic sum-rate for an AF-relay and show that the performance with AF-relay outperforms
DF-relay. However, there is no user pairing since the AF-relay acts as the second user. The
transmit power is optimized at the source and DF-relay in [102] to maximize the global
energy efficiency (GEE) of the system only in one cell and two users (no user pairing) in a
perfect SIC condition. In addition, the authors propose two strategies at the relay to decode
the transmit symbols with no direct link to the users from the serving BS.
The authors in [103] investigate the impact of imperfect channel state information (CSI)
71
in an energy harvesting cooperative NOMA network in terms of OP with no direct link
between the serving BS and two users. The simulation results show that the system per-
formance for the close user with an FPA outperforms dynamic power allocation (DPA) but
with poor fairness. A good OP for the far user with a DPA scheme than FPA with a better
fairness. Their work was done only on a single cell and there was no direct link between the
serving BS and two users (no user pairing).
OP and throughput are analyzed in [104] with selective and incremental DF relays in
NOMA-based with a direct link to the far two users (no user pairing) in a single cell and
FPA scheme.
To the best of the author’s knowledge and compared with the existing work in the litera-
ture, no publications aim to optimize the ASR in NOMA-based cooperative relaying under a
PA, efficient SIC, and minimum QoS requirement constraints for FFR schemes in perfect and
imperfect SIC scenarios with a direct link between the serving BS and far users (outer zone
users). In addition, there is no closed form for OP under Nakagami-m fading and path-loss
fading for an FFR scheme while considering the effect of ICI and perfect SIC scenarios in a
NOMA-based downlink multi-relay multi-cell network.
5.3 System Model
The layout of downlink OFDMA multi-cell multi-relay system with FRF=(1,3) FFR scheme
is illustrated in Figure 5.1.
72
FRF=1
FRF=3
Frequency
FRF=1 for inner zones
FRF=3 for outer zones
B W
Frequency
Power
Cell 0RS
BS
Figure 5.1: Network structure for the FRF=(1,3) FFR scheme in OFDMA system
In this scheme, each cell is partitioned into two zones; inner and outer zones. Then, the
available bandwidth is split into two parts corresponding to the two zones. The first part
is utilized in the inner zone with the conventional scheme (i.e., FFR=1) and the other part
is partitioned into three orthogonal sub-bands corresponding to three sectors in the outer
zone (i.e., FFR=3). At the boundary between inner and outer zones of each sector, there is
an AF-fixed relay equipped with a directional antenna to cover each sector as illustrated in
Figure 5.1.
Fig 5.2 illustrates the communication between the BS and inner zone users mi and ni as
well as with outer zone users mo and no and the relays in the first time slot. In the second
time slot, the RS amplifies the received signal and retransmit it to the outer zone users mo
and no.
73
BS
RS First time slot
Second time slot
BS
im
om
on
in
mP
nP
Frequency
Power
. . . .. . . .
One group
Figure 5.2: Cooperative NOMA relaying with a direct link in two time slots
5.4 Instantaneous SINR at Inner Zone Users in the First Time Slot
As depicts in Figure 5.2, the BS transmits the superimposed signal xB0,inn =√αB0,ni
PB0xB0,ni+√
αB0,miPB0xB0,mi
to the inner zone users for every new time slot, where αB0,niand αB0,mi
are the power allocation coefficients between the serving BS B0 and inner zone users mi and
ni; αB0,ni+ αB0,mi
= 1 and αB0,mi> αB0,ni
. E{|xB0,ni|2} = E{|xB0,mi
|2} = 1 and PB0 is the
total transmit power of the serving BS B0.
The received signal at the inner zone user ni can be expressed as
yni= hB0,ni
xB0,inn +
Iinn∑j=1
hBj ,nixBj ,inn + wni
= hB0,ni
(√αB0,ni
PB0xB0,ni+√αB0,mi
PB0xB0,mi
)(5.1)
+
Iinn∑j=1
hBj ,ni
(√αBj ,ni
PBjxBj ,ni
+√αBj ,mi
PBjxBj ,mi
)+ wni
,
where the second term in (5.1) (i.e.,∑Iinn
j=1 hBj ,nixBj ,inn) represents ICI from the adjacent
cells within two tiers. The parameters hB0,niand hBj ,ni
are the channel coefficients between
the serving BS B0, interfering BS Bj and user ni, respectively. All the channel coefficients
are subjected to Rayleigh fast fading and path-loss fading.
Following the same procedure for the inner zone user mi, the received signal can be
74
expressed as
ymi= hB0,mi
xB0,inn +
Iinn∑j=1
hBj ,mixBj ,inn + wmi
= hB0,mi
(√αB0,ni
PB0xB0,ni+√αB0,mi
PB0xB0,mi
)(5.2)
+
Iinn∑j=1
hBj ,mi
(√αBj ,ni
PBjxBj ,ni
+√αBj ,mi
PBjxBj ,mi
)+ wmi
.
Assume the transmit powers of the serving BS PB0 and interfering BSs PBjare equal (i.e.,
PB0 = PBj= P ) and the decoding order is in descending order (i.e., |hB0,ni
|2 > |hB0,mi|2).
The near user ni decodes xB0,mifirst and then uses SIC to remove the interference from user
mi, by subtracting mi’s signal, then decodes its own signal xB0,ni.
The instantaneous received SINR at the inner zone’s near user ni when decoding xmiand
xniin the first time slot with imperfect SIC can be expressed, respectively, as
Γ(1),xmiB0,ni
=αB0,mi
P |hB0,ni|2
αB0,niP |hB0,ni
|2 + P∑Iinn
j=1 |hBj ,ni|2 + σ2
, (5.3)
Γ(1),xniB0,ni,dec−wrong =
αB0,niP |hB0,ni
|2
4αB0,miP |hB0,ni
|2 + P∑Iinn
j=1 |hBj ,ni|2 + σ2
, (5.4)
Γ(1),xniB0,ni,dec−right =
αB0,niP |hB0,ni
|2
P∑Iinn
j=1 |hBj ,ni|2 + σ2
, (5.5)
where Iinn is the number of interfering BSs (Bj) from adjacent cells (Iinn = 18 within two
tiers).
Assume γ =P
σ2(represents SNR), then (5.3), (5.4), and (5.5) become
Γ(1),xmiB0,ni
=αB0,mi
γ|hB0,ni|2
αB0,niγ|hB0,ni
|2 + γ∑Iinn
j=1 |hBj ,ni|2 + 1
, (5.6)
Γ(1),xniB0,ni,dec−wrong =
αB0,niγ|hB0,ni
|2
4αB0,miγ|hB0,ni
|2 + γ∑Iinn
j=1 |hBj ,ni|2 + 1
, (5.7)
Γ(1),xniB0,ni,dec−right =
αB0,niγ|hB0,ni
|2
γ∑Iinn
j=1 |hBj ,ni|2 + 1
. (5.8)
75
Similarly, the instantaneous received SINR at the inner zone’s far user mi to decode xmiin
the first time slot can be expressed as
Γ(1),xmiB0,mi
=αB0,mi
γ|hB0,mi|2
αB0,niγ|hB0,mi
|2 + γ∑Iinn
j=1 |hBj ,mi|2 + 1
. (5.9)
5.5 Instantaneous SINR at Outer Zone Users in the First Time Slot
As shows in Figure 5.2, the BS transmits the superimposed signal xB0,out =√αB0,noPxB0,no+√
αB0,moPxB0,mo to the outer zone users. Using the same assumptions for the inner zone
users (i.e., near user no and far user mo), the instantaneous received SINR at the outer
zone’s near user no to decode xmo and xno in the first time slot with imperfect SIC can be
expressed, respectively, as
Γ(1),xmoB0,no
=αB0,moγ|hB0,no |2
αB0,noγ|hB0,no|2 + γ∑Iout
j=1 |hBj ,no |2 + 1, (5.10)
Γ(1),xnoB0,no,dec−wrong =
αB0,noγ|hB0,no|2
4αB0,moγ|hB0,no |2 + γ∑Iout
j=1 |hBj ,no |2 + 1, (5.11)
Γ(1),xnoB0,no,dec−right =
αB0,noγ|hB0,no |2
γ∑Iout
j=1 |hBj ,no |2 + 1. (5.12)
Similarly, the instantaneous received SINR at the outer zone’s far user mo to decode xmo
in the first time slot can be expressed as
Γ(1),xmoB0,mo
=αB0,moγ|hB0,mo |2
αB0,noγ|hB0,mo|2 + γ∑Iout
j=1 |hBj ,mo|2 + 1, (5.13)
where Iout = 7 in this case, which is due to a reduction in ICI compared to the inner zone
users.
76
The received signal at the serving relay R0 in the first time slot can be expressed as
yR0 = hB0,R0xB0,out +Iout∑j=1
hBj ,R0xBj ,out + wR0
= hB0,R0(√αB0,noPxB0,no +
√αB0,moPxB0,mo) (5.14)
+Iout∑j=1
hBj ,R0
(√αBj ,noPxBj ,no +
√αBj ,moPxBj ,mo
)+ wR0 .
Assume AF-relay, the relay amplifies the received signal by amplifier gain β and then
retransmits to the outer zone users, where β =
√PR0
PB0|hB0,R0 |2 +∑Iout
j=1 PBj|hBj ,R0|2 + σ2
[105]. For simplicity, PB0 = PBj= PR0 = P is assumed, then
β =
√γ
γ|hB0,R0 |2 + γ∑Iout
j=1 |hBj ,R0|2 + 1.
5.6 Instantaneous SINR at Outer Zone Users in the Second Time Slot
As illustrates in Figure 5.2, the outer zone users no and mo will receive the amplified signal
from the relay. The received signal at no and mo in the second time slot can be expressed,
respectively, as
y(2)R0,no
= βhR0,noyR0 + w(2)no
= βhR0,no
(hB0,R0(
√αB0,noPxB0,no +
√αB0,moPxB0,mo)
)(5.15)
+ βhR0,no
(Iout∑j=1
hBj ,R0(√αBj ,noPxBj ,no +
√αBj ,moPxBj ,mo)
)+ βhR0,nowR0 + w(2)
no;
y(2)R0,mo
= βhR0,moyR0 + w(2)mo
= βhR0,mo
(hB0,R0(
√αB0,noPxB0,no +
√αB0,moPxB0,mo)
)(5.16)
+ βhR0,mo
(Iout∑j=1
hBj ,R0(√αBj ,noPxBj ,no +
√αBj ,moPxBj ,mo)
)+ βhR0,mowR0 + w(2)
mo;
Thus, the instantaneous received SINR at the outer zone’s near user no to decode xmo
77
and xno in the second time slot with imperfect SIC can be expressed, respectively, as
Γ(2),xmoR0,no
=γ2αB0,mo|hR0,no |2|hB0,R0|2
γ2αB0,no|hR0,no |2|hB0,R0|2 + γ2|hR0,n0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,no|2 + |hB0,R0|2+
∑Ioutj=1 |hBj ,R0|2) + 1
,
(5.17)
Γ(2),xnoR0,no,
dec−wrong=
γ2αB0,no |hR0,no|2|hB0,R0 |2
4γ2αB0,mo |hR0,no |2|hB0,R0|2 + γ2|hR0,n0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,no|2 + |hB0,R0|2+
∑Ioutj=1 |hBj ,R0|2) + 1
,
(5.18)
Γ(2),xnoR0,no,dec−right =
γ2αB0,no|hR0,no |2|hB0,R0|2
γ2|hR0,n0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,no|2 + |hB0,R0|2 +∑Iout
j=1 |hBj ,R0|2) + 1.
(5.19)
Similarly, the instantaneous received SINR at the outer zone’s far user mo to decode xmo in
the second time slot can be expressed as
Γ(2),xmoR0,mo
=γ2αB0,mo|hR0,mo|2|hB0,R0|2
γ2αB0,no |hR0,mo|2|hB0,R0|2 + γ2|hR0,m0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,mo |2 + |hB0,R0|2+
∑Ioutj=1 |hBj ,R0|2) + 1
.
(5.20)
5.7 Achievable Rate for the Inner Zone Group
The achievable rate for the inner zone user mi can be expressed using Shannon’s formula as
CNOMAmi
= log2(1 + Γ(1),xmiB0,mi
) = log2(1 +αB0,mi
γ|hB0,mi|2
αB0,niγ|hB0,mi
|2 + γ∑Iinn
j=1 |hBj ,mi|2 + 1
). (5.21)
Two cases of the achievable rate for the inner zone user ni are considered, perfect and
imperfect SIC, respectively, as follows
CNOMAni,perf
= log2(1 + Γ(1),xniB0,ni,dec−right) = log2(1 +
αB0,niγ|hB0,ni
|2
γ∑Iinn
j=1 |hBj ,ni|2 + 1
); (5.22)
78
CNOMAni,imperf
= Fc log2(1 + Γ(1),xniB0,ni,dec−wrong) + (1− Fc) log2(1 + Γ
(1),xniB0,ni,dec−right)
= Fc log2(1 +αB0,ni
γ|hB0,ni|2
4αB0,miγ|hB0,ni
|2 + γ∑Iinn
j=1 |hBj ,ni|2 + 1
) (5.23)
+ (1− Fc) log2(1 +αB0,ni
γ|hB0,ni|2
γ∑Iinn
j=1 |hBj ,ni|2 + 1
),
where Fc represents the SIC error factor, which is defined as the average probability of error.
From Theorem 1 in Chapter 4, the Fc can be expressed as
Fc = Pe =1
2Q
(√γ|hB0,ni
|(√
(1− αB0,ni)−√αB0,ni
)
)+
1
2Q
(√γ|hB0,ni
|(√
(1− αB0,ni) +√αB0,ni
)
), (5.24)
where Fc is a function of channel coefficient (|hB0,ni|), SNR (γ), and the transmit power
coefficient (αB0,ni).
Thus, the total achievable sum-rate for imperfect SIC is given by
CNOMAtot,imperf = CNOMA
mi+ CNOMA
ni,imperf; (5.25)
whereas, for perfect SIC is given by
CNOMAtot,perf = CNOMA
mi+ CNOMA
ni,perf, (5.26)
where RNOMAmi
for the inner zone user mi is given in (5.21).
Since, the expression for the throughput of each inner zone pair (Cmi, Cni
) is obtained,
an optimization problem is formulated. The objective function of the optimization problem
is to maximize the sum-rate of each pair subject to transmit power coefficient αni. Since
αni+αmi
= 1, the lower and upper bounds for αniare obtained and then set αmi
= 1−αni.
79
5.7.1 Problem Formulation for Inner Zone Group
maxαni
CNOMAmi
+ CNOMAni
s.t. C(mi,ni)mi
≥ COMAmi
,
C(mi,ni)ni
≥ COMAni
,
(1− αni)γ|hni
|2
αniγ|hni
|2 + 1≥ λth
⇒ αni≤ γ|hn|2 − λthγ|hn|2(1 + λth)
,
0 < αni< 1
(5.27)
where λth is the minimum threshold of the ratio between the allocated power of both users
to guarantee the SIC will decode correctly. The first two constraints in (5.27) ensure that
the throughputs of the inner zone users in NOMA should be greater than that in OMA.
From these constraints, an upper and lower bounds of αnican be determined and then
αmi= 1− αni
for perfect SIC situation as follows
CNOMAmi
≥ COMAmi
⇔ log2(1 +(1− αB0,ni
)γ|hB0,mi|2
αB0,niγ|hB0,mi
|2 + γ∑Iinn
j=1 |hBj ,mi|2 + 1
) ≥ 1
2log2(1 +
γ|hB0,mi|2
γIinn∑j=1
|hBj ,mi|2 + 1
)
⇒ αni≤ Ami
(Bmi− Ami
)
Emi
,
(5.28)
where Tmi= γ
Iinn∑j=1
|hBj ,mi|2, Emi
= γ|hB0,mi|2, Ami
=√Tmi
+ 1, andBmi=√Kmi
+ Cmi+ 1.
80
RNOMAni
≥ ROMAni
⇔ log2(1 +αB0,ni
γ|hB0,ni|2
γ∑Iinn
j=1 |hBj ,ni|2 + 1
) ≥ 1
2log2(1 +
γ|hB0,ni|2
γIinn∑j=1
|hBj ,ni|2 + 1
)
⇒ αni≥ Ani
(Bni− Ani
)
Eni
,
(5.29)
where Tni= γ
Iinn∑j=1
|hBj ,ni|2, Eni
= γ|hB0,ni|2, Ani
=√Tni
+ 1, Bni=√Tni
+ Eni+ 1, and
Iinn represents the number of interfering cells (ICI) around the desired cell.
Given the upper bound for αniin (5.27) and (5.28), the optimal solution of αni
will be
the minimum value of αniin (5.27) and (5.28).
5.8 Achievable Rate for the Outer Zone Group
In order to decode xmo at user mo for the two-time slots, the MRC can be applied to combine
their SINR (i.e., (5.13) and (5.20)) as fallows
Γxmomo,total
= Γ(1),xmoB0,mo
+ Γ(2),xmoR0,mo
=αB0,moγ|hB0,mo |2
αB0,noγ|hB0,mo |2 + γ∑Iout
j=1 |hBj ,mo |2 + 1
+γ2αB0,mo|hR0,mo |2|hB0,R0|2
γ2αB0,no |hR0,mo|2|hB0,R0 |2 + γ2|hR0,m0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,mo|2 + |hB0,R0 |2+
∑Ioutj=1 |hBj ,R0 |2) + 1
.
(5.30)
The achievable rate for the outer zone user mo can be expressed as
Cmo =1
2log2(1 + Γ
xmomo,total
). (5.31)
81
Also with the perfect SIC situation to decode xno for user no, MRC combines their SINR
for the two time slots (i.e., (5.12) and (5.19)) as fallows
Γxnono,total,dec−right = Γ
(1),xnoB0,no,dec−right + Γ
(2),xnoR0,no,dec−right
=αB0,noγ|hB0,no|2
γ∑Iout
j=1 |hBj ,no|2 + 1(5.32)
+γ2αB0,no |hR0,no|2|hB0,R0 |2
γ2|hR0,n0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,no|2 + |hB0,R0|2 +∑Iout
j=1 |hBj ,R0|2) + 1.
The achievable rate for the outer zone user no to decode xno with perfect SIC can be expressed
as
Cno,perf =1
2log2(1 + Γ
xnono,total,dec−right). (5.33)
Proceeding similarly, with imperfect SIC to decode xno for user no, MRC combines their
SINR for the two time slots (i.e., (5.11) and (5.18)) as fallows
Γxnono,total,
dec−wrong= Γ
(1),xnoB0,no,dec−wrong + Γ
(2),xnoR0,no,dec−wrong
=αB0,noγ|hB0,no|2
4αB0,moγ|hB0,no|2 + γ∑Iout
j=1 |hBj ,no|2 + 1
+γ2αB0,mo |hR0,no|2|hB0,R0|2
4γ2αB0,no|hR0,no |2|hB0,R0|2 + γ2|hR0,n0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,no|2 + |hB0,R0|2+
∑Ioutj=1 |hBj ,R0|2) + 1
.
(5.34)
The achievable rate for the outer zone user no to decode xno with imperfect SIC can be
expressed as
Cno,imperf =1
2Fc log2(1 + Γ
xnono,total,dec−wrong) +
1
2(1− Fc) log2(1 + Γ
xnono,total,dec−right), (5.35)
where Fc represents the SIC error factor, which is defined as the average probability of error.
From Theorem 1 in Chapter 4 and follow the same procedure but here with considering
an AF-fixed relay cooperation. Thus, after some algebraic manipulations, the Fc can be
82
expressed as
Fc = Pe =1
2Q
(√γβ|hB0,R0 ||hR0,no |(
√(1− αB0,no)−
√αB0,no)
)+
1
2Q
(√γβ|hB0,R0||hR0,no |(
√(1− αB0,no) +
√αB0,no)
), (5.36)
where Fc is a function of channel coefficients (|hB0,R0|, |hR0,no |), SNR (γ), the transmit power
coefficient (αB0,no), and the amplifier gain β.
Thus, the total achievable sum-rate for imperfect SIC is given by
CNOMAtot,imperf = CNOMA
mo+ CNOMA
no,imperf ; (5.37)
whereas, for perfect SIC is given by
CNOMAtot,perf = CNOMA
mo+ CNOMA
no,perf , (5.38)
where CNOMAmo
for the outer zone user mo is given in (5.31).
Since, the expression for the throughput of each outer zone pair (Cmo , Cno) is obtained,
an optimization problem is formulated. The objective function of the optimization problem
is to maximize the sum-rate of each pair subject to transmit power coefficient αno . Since
αno +αmo = 1, the lower and upper bounds for αno are obtained and then set αmo = 1−αno .
5.8.1 Problem Formulation for Outer Zone Group
maxαno
CNOMAmo
+ CNOMAno
s.t. C(mo,no)mo
≥ COMAmo
,
C(mo,no)no
≥ COMAno
,
(1− αno)γ|hno |2
αnoγ|hno |2 + 1≥ λth
⇒ αno ≤γ|hn|2 − λthγ|hn|2(1 + λth)
,
0 < αno < 1
(5.39)
83
From the first constraint in (5.39), an upper and lower bounds of αno can be determined
and then αmo = 1− αno for perfect SIC situation as follows
CNOMAmo
≥ COMAmo
⇔ 1
2log2(1 +
(1− αB0,no)γ|hB0,mo|2
αB0,noγ|hB0,mo |2 + γ∑Iout
j=1 |hBj ,mo |2 + 1+
γ2(1− αB0,no)|hR0,mo|2|hB0,R0 |2
γ2αB0,no |hR0,mo |2|hB0,R0|2 + γ2|hR0,m0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,mo |2 + |hB0,R0|2 +∑Iout
j=1 |hBj ,R0 |2) + 1)
≥ 1
4log2(1 +
γ|hB0,mo |2
γIout∑j=1
|hBj ,mo |2 + 1
+γ2|hB0,R0|2|hR0,mo|2
γ(|hR0,mo|2 + |hB0,R0 |2) + 1).
(5.40)
From this constraint, a quadratic equation is obtained in terms of αno (i.e., aα2no
+bαno +c =
0). Solving this equation; the upper and lower bounds of αno can be expressed as
−b−√b2 − 4ac
2a≤ αno ≤
−b+√b2 − 4ac
2a; if a 6= 0, b > 0. (5.41)
From the second constraint in (5.39), the lower bound of αno can be determined for
perfect SIC situation as follows
CNOMAno
≥ COMAno
⇔ 1
2log2(1 +
αB0,noγ|hB0,no|2
γ∑Iout
j=1 |hBj ,no |2 + 1
+γ2αB0,no|hR0,no|2|hB0,R0|2
γ2|hR0,n0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,no|2 + |hB0,R0|2 +∑Iout
j=1 |hBj ,R0|2) + 1)
≥ 1
4log2(1 +
γ|hB0,no|2
γIout∑j=1
|hBj ,no|2 + 1
+γ2|hB0,R0|2|hR0,no|2
γ(|hR0,no |2 + |hB0,R0|2) + 1)
⇒ αno ≥(TBj ,no + 1)(W +QR0,noLBj ,R0 + LBj ,R0)(Sq − 1)
EB0,no(W +QR0,noLBj ,R0 + LBj ,R0) + AB0,R0QR0,no(TBj ,no + 1),
(5.42)
84
where TBj ,no = γIout∑j=1
|hBj ,no|2, EB0,no = γ|hB0,no |2, AB0,R0 = γ|hB0,R0|2, QR0,no = γ|hR0,no|2,
LBj ,R0 = γIout∑j=1
|hBj ,R0|2, W = AB0,R0 + QR0,no + 1, Iout represents the number of interfering
cells (ICI) around the desired cell, and
Sq =
√W (TBj ,no + 1) + EB0,noW + AB0,R0QR0,no(TBj ,no + 1)
W (TBj ,no + 1).
Now there are two lower bounds of αno as in (5.41) and (5.42); therefore, the lower bound
for αno will be the maximum value of αno between (5.41) and (5.42) as follows
αno ≥ max
{−b−
√b2 − 4ac
2a, αlow2
}, (5.43)
where αlow2 =(TBj ,no + 1)(W +QR0,noLBj ,R0 + LBj ,R0)(Sq − 1)
EB0,no(W +QR0,noLBj ,R0 + LBj ,R0) + AB0,R0QR0,no(TBj ,no + 1).
The upper bound for αno is given by
αno ≤−b+
√b2 − 4ac
2a. (5.44)
5.9 Outage Probability Analysis
Outage probability Pout is defined as the probability that the received SINR falls below the
certain threshold Γth. In this section, the closed form of the OP is derived for the inner zone
pairs (mi, ni) and outer zone pairs (mo, no).
5.9.1 Outage Probability for Inner Zone User mi
The SINR ΓxmiB0,mi
for the inner zone user mi is given in (5.9) as
Γ(1),xmiB0,mi
=αB0,mi
γ|hB0,mi|2
αB0,niγ|hB0,mi
|2 + γ∑Iinn
j=1 |hBj ,mi|2 + 1
. (5.45)
85
Let us denote γ1 = γ|hB0,mi|2, γj = γ
∑Iinn
j=1 |hBj ,mi|2, γ1 = E{γ|hB0,mi
|2} = γE{|hB0,mi|2} =
γψ1, and γj = E{γ∑Iinn
j=1 |hBj ,mi|2} = γψj. Then, (5.45) can be rewritten as
Γ(1),xmiB0,mi
=αB0,mi
γ1
αB0,niγ1 + γj + 1
=aγ1
bγ1 + cγj + 1, (5.46)
where a = αB0,mi, b = αB0,ni
, and c = 1.
Assuming all the channels are subjected to Nakagami-m fading, γj which is a summation
of interfering signals is approximated as a single Gamma random variable (RV) [106]. The
PDF and CDF of γ1 and γj have a general forms as [107]
fY (y) =mmym−1
Γ(m)γmexp
(−my
γ
); (5.47)
FY (y) = 1− Γ(m,my/γ)
Γ(m), (5.48)
where (a) when y = γ1, then m , m1 and γ , γ1 = γψ1; (b) when y = γj, then m , mj
and γ , γj = γψj. In order to evaluate the PDF and CDF in (5.47) and (5.48), the Gamma
parameters m1, mj, γ1, and γj need to be calculated.
After applying an accurate approximation, the parameters mj, and γj can be calculated
using the moment-based estimators [106, 108]. Let us denote φ =∑Iinn
j=1 |hBj ,mi|2, then
moment-based estimators can be expressed from the exact moments of φ as
ψj = E[φ], (5.49)
mj =ψ2j
E[φ2]− ψ2j
. (5.50)
To obtain the exact moment E[φ2], a multinomial expansion can be used [106] as follows
E [φr] =r∑
r1=0
r1∑r2=0
...
rIinn−2∑rIinn−1=0
(r
r1
)(r1
r2
)...
(rIinn−2
rIinn−1
)
x E[|h1|2(r−r1)
]E[|h2|2(r1−r2)
]... E
[|hIinn
|2(rIinn−1)], (5.51)
86
where
E [|hj|r] =Γ(mj + (r/2))
Γ(mj)
(ψjmj
)r2. (5.52)
Thus, OP for user mi can be obtained as follows
Pout,mi= Pr(Γ
(1),xmiB0,mi
≤ Γth) = Pr
(aγ1
bγ1 + cγj + 1≤ Γth
)= Pr
(γ1 ≤
Γth(cγj + 1)
a− bΓth
)= 1−
∫ ∞0
Pr
(γ1 ≥
Γth(cy + 1)
a− bΓth
)fγj(y) dy
= 1−∫ ∞
0
Fγ1
(Γth(cy + 1)
a− bΓth
)fγj(y) dy, (5.53)
where Fγ1
(Γth(cy + 1)
a− bΓth
)is the complementary CDF (CCDF) of γ1, which can be evaluated
at
(Γth(cy + 1)
a− bΓth
)using (5.48), and the PDF of γj can be obtained using (5.47) (i.e., fγj(y) =
mmj
j ymj−1
Γ(mj)γjexp
(−mjy
γj
). The CCDF of γ1, assuming positive integer values of m1 in (5.48)
and relying on [109, Eq. (8.352.2) and Eq. (1.111)], and after some algebraic manipulations
can be expressed as
Fγ1
(Γth(cy + 1)
a− bΓth
)= exp
(−m1
γ1
(u(Γth)y + v(Γth))
)m1−1∑n=0
n∑k=0
1
n!
(n
k
)mn
1u(Γth)kv(Γth)
n−kyk
γn1,
(5.54)
where u(Γth) =cΓth
a− bΓthand v(Γth) =
Γtha− bΓth
, which, hereinafter will be denoted as u and
v only for simplicity. Substituting fγj(y) and (5.54) into (5.53) yields
Pout,mi= 1− 1
Γ(mj)exp
(−m1v
γ1
)m1−1∑n=0
n∑k=0
k1
n!
(n
k
)(mj
γj
)mj
x
∫ ∞0
yk+mj−1 exp
(−y(mj
γj+m1u
γ1
))dy︸ ︷︷ ︸
Ij
, (5.55)
where k1 =mn
1ukvn−k
γn1. Evaluating the integral in (5.55), the result can be expressed as
Ij = Γ(mj + k)
(γjmj
)mj+k (1 +
m1uγjγ1mj
)−mj−k
. (5.56)
87
Now, to obtain the final closed form of the OP for the inner user mi, substitute (5.56) in
(5.55) which yields
Pout,mi= 1− 1
Γ(mj)exp
(−m1v
γ1
)m1−1∑n=0
n∑k=0
k1Γ(mj + k)
n!
(n
k
)(γjmj
)k (1 +
m1uγjγ1mj
)−mj−k
,
(5.57)
where a = αB0,mi, b = αB0,ni
, c = 1, u =cΓth
a− bΓth, v =
Γtha− bΓth
, and k1 =
(m1v
γ1
)n (uv
)k.
5.9.2 Outage Probability for Inner Zone User ni
The SINR Γ(1),xniB0,ni,dec−right for the inner zone user ni with perfect SIC is given in (5.8) as
Γ(1),xniB0,ni,dec−right =
αB0,niγ|hB0,ni
|2
γ∑Iinn
j=1 |hBj ,ni|2 + 1
. (5.58)
Let us denote γ2 = γ|hB0,ni|2, γj2 = γ
∑Iinn
j=1 |hBj ,ni|2, γ2 = E{γ|hB0,ni
|2} = γE{|hB0,ni|2}
= γψ2, and γj2 = E{γ∑Iinn
j=1 |hBj ,ni|2} = γψj2 . Then (5.58) can be rewritten as
Γ(1),xniB0,ni
=αB0,ni
γ2
γj2 + 1=
aγ2
bγj2 + 1, (5.59)
where a = αB0,ni, b = 1.
Pout,ni= Pr(Γ
xniB0,ni
≤ Γth) = Pr
(aγ2
bγj2 + 1≤ Γth
)= Pr
(γ2 ≤
Γth(bγj2 + 1)
a
)= 1−
∫ ∞0
Pr
(γ2 ≥
Γth(bw + 1)
a
)fγj2 (w) dw
= 1−∫ ∞
0
Fγ2
(Γth(bw + 1)
a
)fγj2 (w) dw. (5.60)
Following the same procedure as in inner zone user mi, the CCDF of γ2 can be obtained
as in (5.54) which yields
Fγ2
(Γth(bw + 1)
a
)= exp
(−m2
γ2
(uw + v)
)m2−1∑n=0
n∑k=0
1
n!
(n
k
)mn
2ukvn−kwk
γn2, (5.61)
where u =bΓtha
, v =Γtha
. The Gamma parameters can be calculated as in (5.49)-(5.52)
where φ =∑Iinn
j=1 |hBj ,ni|2.
88
Substituting fγj2 (w) =mmj2j2
wmj2−1
Γ(mj2)γj2exp
(−mj2w
γj2
)and (5.61) into (5.60) yields
Pout,ni= 1− exp
(−m2v
γ2
)m2−1∑n=0
n∑k=0
1
n!
(n
k
)k2
Γ(mj2)
(mj2
γj2
)mj2
x
∫ ∞0
wk+mj2−1 exp
(−w
(mj2
γj2+m2u
γ2
))dw︸ ︷︷ ︸
Ij2
, (5.62)
where k2 =mn
2ukvn−k
γn2. Evaluating the integral in (5.62), the result can be expressed as
Ij2 = Γ(mj2 + k)
(γj2mj2
)mj2+k (
1 +m2uγj2γ2mj2
)−mj2−k
. (5.63)
To obtain the final closed form of the OP for the inner zone user ni, substitute (5.63)
into (5.62) yields
Pout,ni= 1− 1
Γ(mj2)exp
(−m2v
γ2
)m2−1∑n=0
n∑k=0
k2Γ(mj2 + k)
n!
(n
k
)(γj2mj2
)kx
(1 +
m2uγj2γ2mj2
)−mj2−k
, (5.64)
where a = αB0,ni, b = 1, u =
bΓtha
, v =Γtha
, and k2 =
(m2v
γ2
)n (uv
)k.
5.9.3 Outage Probability for Outer Zone User mo
The SINR Γxmomo,total
for the outer zone user mo is given in (5.30) as
Γxmomo,total
= Γ(1),xmoB0,mo
+ Γ(2),xmoR0,mo
=αB0,moγ|hB0,mo |2
αB0,noγ|hB0,mo |2 + γ∑Iout
j=1 |hBj ,mo |2 + 1
+γ2αB0,mo|hR0,mo |2|hB0,R0|2
γ2αB0,no |hR0,mo|2|hB0,R0 |2 + γ2|hR0,m0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,mo|2 + |hB0,R0 |2+
∑Ioutj=1 |hBj ,R0 |2) + 1
,
(5.65)
Let us denote γ3 = γ|hB0,mo|2, γj3 = γ∑Iout
j=1 |hBj ,mo|2, γ4 = γ|hB0,R0|2, γ5 = γ|hR0,mo|2,
γj4 = γ∑Iout
j=1 |hBj ,R0 |2, γ3 = E{γ|hB0,n0|2} = γE{|hB0,n0|2} = γψ3, γ4 = E{γ|hB0,R0|2} =
89
γE{|hB0,R0|2} = γψ4, γj3 = E{γ∑Iout
j=1 |hBj ,n0 |2} = γψj3 , and γj4 = E{γ∑Iout
j=1 |hBj ,R0|2} =
γψj4 . Then, (5.65) can be rewritten as
Γxmomo,total
=αB0,moγ3
αB0,noγ3 + γj3 + 1+
αB0,moγ4γ5
αB0,noγ4γ5 + γ5γj4 + γ4 + γ5 + γj4 + 1
=aγ3
bγ3 + cγj3 + 1+
aγ4γ5
bγ4γ5 + cγ5γj4 + dγ4 + eγ5 + fγj4 + 1
= Γ(1),xmoB0,mo
+ Γ(2),xmoR0,mo
, (5.66)
where a = αB0,mo , b = αB0,no , c = d = e = f = 1.
Now, the CDF of the first and second term in (5.66) is needed to obtain separately.
Following the same procedure of inner zone user mi to obtain the CDF for mo, the CDF of
Γ(1),xmoB0,mo
can be expressed as
FΓ(1),xmoB0,mo
(Γth) = 1− 1
Γ(mj3)exp
(−m3v
γ3
)m3−1∑n=0
n∑k=0
k3Γ(mj3 + k)
n!
(n
k
)(γj3mj3
)kx
(1 +
m3uγj3γ3mj3
)−mj3−k
, (5.67)
where a = αB0,mo , b = αB0,no , c = 1, u =cΓth
a− bΓth, v =
Γtha− bΓth
, k3 =
(m3v
γ3
)n (uv
)k. The
Gamma parameters in this case can be calculated as in (5.49)-(5.52) where φ =∑Iout
j=1 |hBj ,mo|2.
The second term in (5.66) is give as
Γ(2),xmoR0,mo
=aγ4γ5
bγ4γ5 + cγ5γj4 + dγ4 + eγ5 + fγj4 + 1. (5.68)
To obtain the closed form of the CDF of Γ(2),xmoR0,mo
, an asymptotic CDF in a high SNR
regimes is considered. Using (bE{γ4}E{γ5}+cE{γ5}E{γj4} � dE{γ4}+eE{γ5}+fE{γj4}+
1) [110], where E{} denotes the mathematical expectation operation. Thus, the (5.68) can
be rewritten as
Γ(2),xmoR0,mo
' aγ4γ5
bγ4γ5 + cγ5γj4' aγ4
bγ4 + cγj4. (5.69)
90
The asymptotic CDF of Γ(2),xmoR0,mo
can be obtained as
FΓ(2),xmoR0,mo
(Γth) = Pr
(aγ4
bγ4 + cγj4≤ Γth
)= Pr
(γ4 ≤
Γthcγj4a− bΓth
)= 1−
∫ ∞0
Pr
(γ4 ≥
Γthcz
a− bΓth
)fγj4 (z) dz
= 1−∫ ∞
0
Fγ4
(Γthcz
a− bΓth
)fγj4 (z) dz. (5.70)
Following the same procedure as before, the CCDF of γ4 is obtained as in (5.54), which
yields
Fγ4
(Γthcz
a− bΓth
)= Fγ4 (uz) = exp (−k4z)
m4−1∑n=0
1
n!(k4z)n , (5.71)
where u =cΓth
a− bΓth, k4 =
m4u
γ4
. The Gamma parameters in this case can be calculated as
in (5.49)-(5.52) where φ =∑Iout
j=1 |hBj ,R0 |2.
Substituting fγj4 (z) =mmj4j4
zmj4−1
Γ(mj4)γj4exp
(−mj4z
γj4
)and (5.71) into (5.70) yields
FΓ(2),xmoR0,mo
(Γth) = 1− 1
Γ(mj4)
(mj4
γj4
)mj4m4−1∑n=0
kn4n!
∫ ∞0
zn+mj4−1 exp
(−z(k4 +
mj4
γj4
))dz︸ ︷︷ ︸
Ij4
.
(5.72)
Evaluating the integral in (5.72) yields
Ij4 = Γ(mj4 + n)
(γj4mj4
)mj4+n(
1 +k4γj4mj4
)−mj4−n
. (5.73)
To obtain the final closed form of the CDF for Γ(2),xmoR0,mo
, substitute (5.73) into (5.72) yields
FΓ(2),xmoR0,mo
(Γth) = 1− 1
Γ(mj4)
m4−1∑n=0
kn4 Γ(mj4 + n)
n!
(γj4mj4
)n(1 +
k4γj4mj4
)−mj4−n
, (5.74)
where a = αB0,mo , b = αB0,no , c = 1, u =cΓth
a− bΓth, and k4 =
m4u
γ4
.
The CDF of the sum of two SINRs as in (5.66) will be a convolution of their densities
[111] as follows
FZ(z) =
∫ ∞−∞
FY (z − x) fX(x) dx =
∫ ∞−∞
FX(z − y) fY (y) dy, (5.75)
91
where Z = X+Y , X, Y are two independent random variables. Thus, the asymptotic closed
form for Pout of the outer zone user mo is obtained.
5.9.4 Outage Probability for Outer Zone User no
The SINR Γxnono,total,dec−right for the outer zone user no with perfect SIC is given in (5.32) as
Γxnono,total,dec−right = Γ
(1),xnoB0,no,dec−right + Γ
(2),xnoR0,no,dec−right
=αB0,noγ|hB0,no|2
γ∑Iout
j=1 |hBj ,no|2 + 1(5.76)
+γ2αB0,no |hR0,no|2|hB0,R0 |2
γ2|hR0,n0|2∑Iout
j=1 |hBj ,R0|2 + γ(|hR0,no|2 + |hB0,R0|2 +∑Iout
j=1 |hBj ,R0|2) + 1.
Let us denote γ5 = γ|hB0,no|2, γj5 = γ∑Iout
j=1 |hBj ,2o |2, γ4 = γ|hB0,R0|2, γ6 = γ|hR0,no|2,
γj4 = γ∑Iout
j=1 |hBj ,R0|2, γ5 = E{γ|hB0,n0|2} = γE{|hB0,n0|2} = γψ5, γ4 = E{γ|hB0,R0 |2} =
γE{|hB0,R0|2} = γψ4, γj5 = E{γ∑Iout
j=1 |hBj ,n0|2} = γψj5 , and γj4 = E{γ∑Iout
j=1 |hBj ,R0|2} =
γψj4 . Then, (5.76) can be rewritten as
Γxnono,total
=αB0,noγ5
γj5 + 1+
αB0,noγ4γ6
γ6γj4 + γ4 + γ6 + γj4 + 1
=aγ5
bγj5 + 1+
aγ4γ6
bγ6γj4 + cγ4 + dγ6 + eγj4 + 1
= Γ(1),xnoB0,no
+ Γ(2),xnoR0,no
, (5.77)
where a = αB0,no , b = c = d = e = 1.
To obtain the CDF of Γ(1),xnoB0,no
and Γ(2),xnoR0,no
, the same procedure for the inner zone user ni
is followed. The CDF of Γ(1),xnoB0,no
can be expressed as
FΓ(1),xnoB0,no
(Γth) = 1− exp
(−m5v
γ5
)m5−1∑n=0
n∑k=0
1
n!
(n
k
)k5
Γ(mj5)
(mj5
γj5
)mj5
x
∫ ∞0
tk+mj5−1 exp
(−t(mj5
γj5+m5u
γ5
))dt︸ ︷︷ ︸
Ij5
, (5.78)
Evaluating the integral in (5.78) as
Ij5 = Γ(mj5 + k)
(γj5mj5
)mj5+k (
1 +m5uγj5γ5mj5
)−mj5−k
︸ ︷︷ ︸I5
. (5.79)
92
Based on [112, Eq.(10)], the term I5 in (5.79) can be expressed in terms of Meijer’s
G-function as
I5 =1
Γ(mj5 + k)G1,1
1,1
γ5mj5
m5uγj5
∣∣∣∣ 1
mj5 + k
. (5.80)
Substituting (5.80) in (5.79) yields
Ij5 =
(γj5mj5
)mj5+k
G1,11,1
γ5mj5
m5uγj5
∣∣∣∣ 1
mj5 + k
. (5.81)
Substituting (5.81) into (5.78) yields
FΓ(1),xnoB0,no
(Γth) = 1− 1
Γ(mj5)exp
(−m5v
γ5
)m5−1∑n=0
n∑k=0
k5
n!
(n
k
)(γj5mj5
)kG1,1
1,1
γ5mj5
m5uγj5
∣∣∣∣ 1
mj5 + k
,(5.82)
where a = αB0,no , b = c = d = e = 1, u =bΓtha
, v =Γtha
, k5 =
(m5v
γ5
)n (uv
)k. The Gamma
parameters in this case can be calculated as in (5.49)-(5.52) where φ =∑Iout
j=1 |hBj ,no|2.
The second term in (5.77) is give as
Γ(2),xnoR0,no
=aγ4γ6
bγ6γj4 + cγ4 + dγ6 + eγj4 + 1. (5.83)
To obtain the closed form of the CDF of Γ(2),xnoR0,no
, an asymptotic CDF in a high SNR
regimes is considered. Based on [110] (b E {γ6}E{γj4} � d E{γ6} + e E{γj4} + 1). Thus,
the (5.83) can be rewritten as
Γ(2),xnoR0,no
' aγ4γ6
bγ6γj4 + cγ4
. (5.84)
The asymptotic CDF of Γ(2),xnoR0,no
can be obtained as
FΓ(2),xnoR0,no
(Γth) = Pr
(aγ4γ6
bγ6γj4 + cγ4
≤ Γth
)= Pr
(γj4 ≥
aγ4γ6 − cγ4Γthbγ6Γth
)=
∫ ∞0
∫ ∞0
Pr
(γj4 ≥
axy − cyΓthbxΓth
)fγ6(x) fγ4(y) dx dy
=
∫ ∞0
∫ ∞0
Fγj4
(axy − cyΓth
bxΓth
)fγ6(x) fγ4(y) dx dy. (5.85)
93
Following the same procedure as before, the CCDF of γj4 is obtained as follows
Fγj4
(axy − cyΓth
bxΓth
)= exp
(−y(k6 −
k7
x)
)mj4−1∑
n=0
n∑k=0
1
n!
(n
k
)k8y
nxk−n, (5.86)
where u4 =a
bΓth, v4 =
c
b, k6 =
mj4u4
γ4
, k7 =−mj4v4
γ4
, k8 = kk6 kn−k7 . The Gamma parameters
in this case can be calculated as in (5.49)-(5.52) where φ =∑Iout
j=1 |hBj ,R0 |2.
Substituting fγ6(x) =mm6
6 xm6−1
Γ(m6)γ6
exp
(−m6x
γ6
), fγ4(y) =
mm44 ym4−1
Γ(m4)γ4
exp
(−m4y
γ4
), and
(5.86) into (5.85) yields
FΓ(2),xnoR0,no
(Γth) =1
Γ(m4)Γ(m6)
(m4
γ4
)m4(m6
γ6
)m6mj4−1∑
n=0
n∑k=0
k8
n!
(n
k
)x
∫ ∞0
∫ ∞0
yn+m4−1 exp
(−y(k6 −
k7
x+m4
γ4
)
)dy︸ ︷︷ ︸
I4
xk−n+m6−1 exp
(−m6
γ6
x
)dx.
(5.87)
Evaluating the integral in (5.87) yields
I4 = Γ(m4 + n)
(γ4
m4
)m4+n(1 +
γ4(k6x− k7)
m4x
)−m4−n
︸ ︷︷ ︸I
. (5.88)
Based on [112, Eq.(10)], the term I in (5.88) can be expressed in terms of Meijer’s G-
function as
I =1
Γ(m4 + n)G1,1
1,1
m4x
γ4(k6x− k7)
∣∣∣∣ 1
m4 + n
, (5.89)
Substituting I into (5.88), I4 into (5.87), and express exp
(−m6
γ6
x
)in terms of Meijer’s
G-function using [112, Eq. (11)], then (5.87) can be rewritten as
FΓ(2),xnoR0,no
(Γth) =1
Γ(m4)Γ(m6)
(m6
γ6
)m6mj4−1∑
n=0
n∑k=0
k8
n!
(n
k
)(γ4
m4
)n
x
∫ ∞0
xW G1,00,1
m6
γ6
x
∣∣∣∣−0
G1,11,1
m4x
γ4(k6x− k7)
∣∣∣∣ 1
m4 + n
dx
︸ ︷︷ ︸I6
, (5.90)
94
where W = k−n+m6−1 and using [112, Eq.(21)] to evaluate the integral of the product of
two Meijer’s G-functions, which is also Meijer’s G-function. Thus, the result of evaluating
I6 can be expressed as
I6 = G1,22,1
γ6m4
m6γ4(k6 − k7)
∣∣∣∣1, 1− k −m6 + n
m4 + n
. (5.91)
Substituting I6 into (5.90), the asymptotic CDF of Γ(2),xnoR0,no
can be expressed as
FΓ(2),xnoR0,no
(Γth) =1
Γ(m4)Γ(m6)
(m6
γ6
)m6mj4−1∑
n=0
n∑k=0
k8
n!
(n
k
)(γ4
m4
)n
x G1,22,1
γ6m4
m6γ4(k6 − k7)
∣∣∣∣1, 1− k −m6 + n
m4 + n
, (5.92)
where u4 =a
bΓth, v4 =
c
b, k6 =
mj4u4
γ4
, k7 =−mj4v4
γ4
, k8 = kk6 kn−k7 .
The CDF of the sum of two SINRs as in (5.76) will be a convolution of their densities
[111] as follows
FZ(z) =
∫ ∞−∞
FY (z − x) fX(x) dx =
∫ ∞−∞
FX(z − y) fY (y) dy, (5.93)
where Z = X+Y , X, Y are two independent random variables. Thus, the asymptotic closed
form for Pout of the outer zone user no is obtained.
5.10 Simulation Results
The performance of the proposed UP scheme with optimal PA coefficients for an FFR scheme
with AF-fixed relays while taking into account the impact of ICI and perfect and imperfect
SIC cases is analyzed and compared with random UP and near-far UP proposed in [39].
All the simulation results in these Figures are the average performance of over 106 user
distributions and channel realizations. The system performance includes the ASR with
respect to SNR in (dB) for perfect and imperfect SIC scenarios and ASR with respect to the
95
number of users for imperfect SIC (practical SIC) only. Also, there is a comparison of ASRs
between a cooperative and non-cooperative proposed UP algorithms for an FFR scheme is
analyzed.
Table 5.1: Chapter 5 simulation parameters
Parameters Values
The inner zone radius 600m
The cell radius 1000m
BS-MS Minimum distance 100m
White noise power density No -174 dBm/Hz
Path-loss exponent ρ 2
Channel bandwidth 10 MHz
Data modulation BPSK
SIC receiver’s detection threshold λth 2
Number of sub-carriers 35
Bandwidth of a subcarrier 30 KHz
Monte Carlo simulation iterations 106
Figure 5.3 depicts the ASR as a function of SNR in (dB) for the proposed UP, near-far
UP in [39], and random UP of an FFR scheme in cooperative relaying while taking into
account the effect of ICI in perfect and imperfect SIC situations.
96
-20 -10 0 10 20 30 40
SNR (dB)
0
50
100
150
200
250
300
350
Avera
ge S
um
Rate
(bps/H
z)
Imperfect Proposed UP
Perfect Proposed UP
Imperfect UP in [39]
Perfect UP in [39]
Imperfect Random UP
Perfect Random UP
Figure 5.3: ASR for an FFR scheme in cooperative relaying NOMA-based of perfect and
imperfect SIC with 70 users.
Figure 5.3 shows that in a perfect SIC case, the ASR of the proposed UP scheme (taking
into account the difference of channel gains) is greater than the other UP schemes at high
SNR. However, at low SNR, the near-far UP scheme (not taking into account the difference of
channel gains) is slightly greater than the proposed UP scheme. This is because the effect of
the difference of channel gain at low SNR will not affect the ASR in a perfect SIC situation.
For imperfect SIC (practical SIC), the proposed UP scheme outperforms the other schemes
for all SNR values, as illustrated in Figure 5.4.
97
-20 -10 0 10 20 30 40
SNR (dB)
0
50
100
150
200
250
300
350
Avera
ge S
um
Rate
(bps/H
z)
Imperfect Proposed UP
Imperfect UP in [39]
Imperefect Random UP
Figure 5.4: ASR for an FFR scheme in cooperative relaying NOMA-based of imperfect SIC
(practical SIC) with 70 users.
The ASR comparison of the cooperative and non-cooperative proposed UP scheme in a
perfect and imperfect SIC situations is presented in Figure 5.5.
98
-20 -10 0 10 20 30 40
SNR (dB)
0
50
100
150
200
250
300
350
Avera
ge S
um
Rate
(bps/H
z)
Coop, Imperfect Proposed UP
Coop, Perfect Proposed UP
Non-Coop, Imperfect Proposed UP
Non-Coop, Perfect Proposed UP
Figure 5.5: Comparison of ASRs between cooperative and non-cooperative relaying of pro-
posed UP for an FFR scheme NOMA-based of perfect and imperfect SIC with 70 users.
Figure 5.5 shows that the performance of the cooperative proposed scheme outperforms
those of the non-cooperative scheme either in perfect or imperfect SIC scenarios, which
confirms the benefits of relays for reducing the effect of path-loss (shorter transmission range)
and increasing the spatial diversity for outer zone users. Also, Figure 5.5 illustrates that the
ASR of perfect and imperfect SIC of cooperative and non-cooperative proposed schemes
converge as the SNR in (dB) increases. This is due to the high SNR (high transmit power)
of the far user, resulting in a correct detection of its signal at the close user (i.e., perfect and
imperfect cases are almost the same).
Figure 5.6 plots the ASR versus the number of users for a cooperative relaying FFR
scheme while taking into account the impact of ICI in imperfect SIC (more practical) con-
ditions.
99
15 20 25 30 35 40 45 50 55 60
No. of Users
0
50
100
150
200
250
300
Avera
ge S
um
Rate
(bps/H
z)
Imperfect Proposed UP
Imperfect UP in [39]
Imperfect Random UP
Figure 5.6: ASR for an FFR scheme in cooperative relaying NOMA-based of imperfect SIC
with SNR=100 dB of the proposed UP scheme, other pairing schemes.
Figure 5.6 shows that the proposed UP scheme outperforms the other schemes. Also,
the ASR increases linearly with the number of users, which depicts that the proposed UP
scheme is working efficiently, even with a large number of users.
Figure 5.7 illustrates the ASR against the number of users of a cooperative and non-
cooperative FFR scheme while accounting for the effect of ICI in an imperfect SIC situation
for the proposed UP scheme and other schemes.
100
15 20 25 30 35 40 45 50 55 60
No. of Users
0
50
100
150
200
250
300
Avera
ge S
um
Rate
(bps/H
z)
Coop, Imperfect Proposed UP
Coop, Imperfect UP in [39]
Coop, Imperfect Random UP
Non-Coop, Imperfect Prposed UP
Non-Coop, Imperfect UP in [39]
Non-Coop, Imperfect Random UP
Figure 5.7: ASR for an FFR scheme in cooperative and non-cooperative relaying NOMA-
based of imperfect SIC with SNR=100 dB of the proposed UP scheme, other pairing schemes.
Figure 5.7 shows that the proposed UP scheme outperforms the other schemes in coop-
erative and non-cooperative schemes. In addition, Figure 5.7 shows that the cooperative
performance outperforms non-cooperative schemes due to the benefits of relays, such as
less interference due to the low transmission power of relays, two or more hops (increasing
diversity order), and extended cell coverage.
5.11 Conclusion
In this chapter, an optimization problem is formulated to maximize the ASR in a cooperative
AF-fixed relaying downlink NOMA FFR scheme under PA, efficient SIC, and minimum QoS
requirement constraints in a perfect SIC case. The upper and lower bounds of the PA
coefficient expressions are derived for a two user case that satisfies all given constraints
101
simultaneously. Also, an UP scheme with the resulting optimal PA in the FFR scheme for
perfect and imperfect SIC scenarios is proposed. In addition, an expression of the SIC error
factor for the imperfect SIC (practical SIC) case is derived in a cooperative relaying scheme.
The proposed UP scheme’s performance is analyzed in terms of ASR with respect to SNR in
(dB) and the number of users for an FRF=(1,3) FFR scheme while considering the impact
of ICI in perfect and imperfect SIC cases. Also, the comparison between the cooperative and
non-cooperative of the proposed scheme and other schemes is shown. The outage probability
expression is derived for each inner and outer zone pairs in an FRF=(1,3) FFR scheme while
taking into account the impact of ICI in a perfect SIC case under Nakagami-m fading and
path-loss fading channel conditions.
Simulation results show the efficiency of the proposed scheme over other schemes, espe-
cially for the imperfect SIC condition (i.e., more practical scenario) and outer zone users.
Also, the simulation results are shown the proposed cooperative relaying scheme outperforms
a non-cooperative scheme for an FRF=(1,3) FFR scheme while accounting the effect of ICI
in perfect and imperfect SIC scenarios. This is because of the benefits of relays on the system
performance such as increasing the cell throughput, spatial diversity of the outer zone users,
and less interference due to the low transmission power of relays.
102
Chapter 6
Summary, Conclusions and Future Work
In Section 6.1, a summary of the work in this thesis is presented along with the conclusions.
In Section 6.2, suggested future work is presented.
6.1 Thesis Summary and Conclusions
The main objectives of this thesis are to reduce the effect of ICI in FFR schemes downlink
OFDMA and NOMA multi-relay multi-cell wireless networks and maximize the sum-rate of
the paired users in cooperative and non-cooperative FFR schemes downlink NOMA multi-
cell wireless networks. To accomplish these objectives, a frequency reuse patterns formula
was developed for FRF=(1,7/3) and FRF=(1,7/4) in cooperative and non-cooperative re-
laying OFDMA FFR schemes to minimize the number of interfering adjacent cells (i.e., ICI),
especially for outer zone users. In a cooperative and non-cooperative relaying NOMA, the
PA and UP algorithms are also developed to maximize the sum-rate of each group either
in the inner zone or outer zone for FFR schemes while taking into account the effect of ICI
on the system performance. Finally, the proposed algorithms of the PA and UP are used to
derive the outage probability expression after determining the SINR in the first and second
time slots.
In Chapter 3, frequency reuse patterns using difference sets are developed to improve
the SE, EE, the CDF of the SINR of the received signal, and the OP for FFR schemes in
OFDMA systems. The developed formula exploits the benefits of RSs, which are placed
at the cell-edge boundary to enhance the outer zone users’ performance. Moreover, the
proposed algorithm is used in each cell within the main cluster, taking into account the
impact of ICI from two tiers around the desired cell and comparisons to previous works.
103
The main contributions of Chapter 3 are summarized below:
1. The development of a frequency reuse pattern to reduce the effect of ICI on the sys-
tem performance, especially for outer zone users for an FRF=(1,7/3) FFR scheme in
cooperative and non-cooperative relaying downlink OFDMA cellular networks.
2. The proposed frequency reuse pattern formula is used to minimize the impact of ICI on
the system performance, especially for outer zone users for an FRF=(1,7/4) FFR scheme
in cooperative and non-cooperative relaying downlink OFDMA cellular networks.
3. The proposed algorithm is applied in each cell within the main cluster while considering
two tiers around the reference cell.
The proposed schemes achieve a significant reduction in ICI for the outer zone users
compared to previous schemes. The system performance of the FRF=(1,7/4) scheme out-
performs the FRF=(1,7/3) scheme at the expense of the increase in the number of sectors,
which increases the number of relay stations. The advantages of the use of relays such as
increasing the cell capacity and decreasing the outage probability due to shorter transmission
range are demonstrated.
In Chapter 4, power allocation and user pairing algorithms are developed to maximize
ASR in an FFR scheme downlink NOMA-based multi-cell network while taking into account
the impact of ICI on the system performance. Based on the proposed algorithms, the system
performance is analyzed in perfect and imperfect SIC scenarios. An analytical expression
for the SIC error factor at the closer user is derived.
The main contributions of Chapter 4 are summarized below:
1. The derived analytical expression for the SE of both zones in an FFR scheme downlink
NOMA-based multi-cell network. This expression facilitates the investigation of the effect
of ICI and an imperfect SIC case on the system performance, especially for outer zone
users.
2. The derived analytical expression for the upper and lower bounds of the power allocation
104
coefficients to maximize ASR while taking into account the impact of ICI and perfect SIC
scenarios.
3. A UP algorithm is developed based on the condition that the difference between the
indices of channel gains of paired users is always constant to maximize the ASR with an
optimal PA scheme.
4. The derived analytical expression for the SIC error factor at the near user for the imperfect
SIC condition. This expression is used to evaluate the overall sum-rate of the system.
The proposed UP scheme in NOMA outperforms the other schemes and OMA schemes
in imperfect SIC case (more practical). The proposed UP scheme is working efficiently even
with a large number of users, either even or odd number. The performance of the proposed
UP scheme outperforms those of the other schemes for both inner and outer zone users. In
addition, due to the mitigation in ICI in the proposed FFR scheme, the performance of the
outer zone users outperforms those of the inner zone users.
In Chapter 5, power allocation and user pairing algorithms are developed to maximize
ASR in a cooperative relaying for an FFR scheme downlink NOMA-based multi-cell network
while taking into account the impact of ICI on the system performance. An analytical
framework is developed to evaluate the SINR for inner and outer zone users in the first and
second time slots. This framework is used to assess the ASR for both zone users while taking
into account the effect of ICI and imperfect SIC conditions. Based on the developed SINR
expressions in the two time slots, the OP expression is derived under Nakagami-m fading
and path-loss fading.
The main contributions of Chapter 5 are summarized below:
1. The instantaneous SINR analytical expression is derived for inner and outer zone users
in cooperative relaying for an FFR scheme NOMA-based downlink multi-cell networks
while taking into account the impact of ICI and imperfect SIC scenarios. This expression
is used for evaluating the rates for inner and outer zone paired users.
105
2. The analytical framework is developed to maximize the ASR for inner and outer zone
paired users in a cooperative relaying for an FFR scheme NOMA-based multi-cell system
in perfect SIC cases.
3. The derived analytical expression for the OP for both zones when all transmission paths
are subject to Nakagami-m fading and path-loss fading.
The performance of the cooperative proposed scheme outperforms those of the non-
cooperative scheme either in perfect or imperfect SIC scenarios. The advantages of the use
of relays such as reducing the effect of path-loss (shorter transmission range), increasing the
spatial diversity for outer zone users, and increasing the cell coverage are demonstrated.
6.2 Suggestions for Future Work
The work presented in this thesis can be extended in many directions. Some suggestions for
future work are listed below:
1. The proposed frequency reuse pattern formula may also be applied to cells with six sectors
and compared to those with three and four sectors.
2. This work can be investigated with other relaying protocols such as DF relays or CF
relays.
3. This work can be used to investigate the effects of an imperfect CSI along with the
imperfect SIC on the overall performance.
4. This work can be extended to other frequency reuse schemes, such as soft frequency reuse
schemes, adaptive reuse schemes, and full frequency reuse schemes.
5. This work can be extended to MIMO-based NOMA networks.
6. The validation of the derived analytical expression of the OP for inner and outer zone users
considering all channels undergo Nakagami-m fading and path-loss fading via Monte-Carlo
simulations can be extended as future work.
106
Appendix A
How to Generate the Proposed Frequency Patterns
The proposed formula in Chapter 3 is given as:
Disub = D0
sub + 2i (mod N), i ∈ ϕ, (A.1)
ϕ = {0, 1, 2, ...., N − 1}, N = 7.
As an example for a difference set of (7, 3, 1) for the FRF=(1,7/3) scheme and D0sub=
(1,3,4) for the cell 0, the six subsets for adjacent cells (main cluster) can be generated as
follows
Disub = D0
sub + 2i (mod N)
i = 1 :
= 1 + 2 mod 7 = 3 mod 7 = 3;
= 3 + 2 mod 7 = 5 mod 7 = 5;
= 4 + 2 mod 7 = 6 mod 7 = 6;
i = 2 :
= 1 + 4 mod 7 = 5 mod 7 = 5;
= 3 + 4 mod 7 = 7 mod 7 = 0 = 7;
= 4 + 4 mod 7 = 8 mod 7 = 1;
i = 3 :
= 1 + 6 mod 7 = 7 mod 7 = 0 = 7;
= 3 + 6 mod 7 = 9 mod 7 = 2;
= 4 + 6 mod 7 = 10 mod 7 = 3;
i = 4 :
= 1 + 8 mod 7 = 9 mod 7 = 2;
107
= 3 + 8 mod 7 = 11 mod 7 = 4;
= 4 + 8 mod 7 = 12 mod 7 = 5;
i = 5 :
= 1 + 10 mod 7 = 11 mod 7 = 4;
= 3 + 10 mod 7 = 13 mod 7 = 6;
= 4 + 10 mod 7 = 14 mod 7 = 0 = 7;
i = 6 :
= 1 + 12 mod 7 = 13 mod 7 = 6;
= 3 + 12 mod 7 = 15 mod 7 = 1;
= 4 + 12 mod 7 = 16 mod 7 = 2.
Then the main cluster is repeated to cover the whole plane as shown in Figure 3.3.
Also, for a difference set of (7, 4, 2) for the FRF=(1,7/4) scheme and D0sub=(1,2,5,7) for
cell 0, the six subsets for adjacent cells (main cluster) can be generated as follows
Disub = D0
sub + 2i (mod N)
i = 1 :
= 1 + 2 mod 7 = 3 mod 7 = 3;
= 2 + 2 mod 7 = 4 mod 7 = 4;
= 5 + 2 mod 7 = 7 mod 7 = 0 = 7;
= 7 + 2 mod 7 = 9 mod 7 = 2;
i = 2 :
= 1 + 4 mod 7 = 5 mod 7 = 5;
= 2 + 4 mod 7 = 6 mod 7 = 6;
= 5 + 4 mod 7 = 9 mod 7 = 2;
= 7 + 4 mod 7 = 11 mod 7 = 4;
i = 3 :
= 1 + 6 mod 7 = 7 mod 7 = 0 = 7;
108
= 2 + 6 mod 7 = 8 mod 7 = 1;
= 5 + 6 mod 7 = 11 mod 7 = 4;
= 7 + 6 mod 7 = 13 mod 7 = 6;
i = 4 :
= 1 + 8 mod 7 = 9 mod 7 = 2;
= 2 + 8mod 7 = 10 mod 7 = 3;
= 5 + 8 mod 7 = 13 mod 7 = 6;
= 7 + 8 mod 7 = 15 mod 7 = 1;
i = 5 :
= 1 + 10 mod 7 = 11 mod 7 = 4;
= 2 + 10 mod 7 = 12 mod 7 = 5;
= 5 + 10 mod 7 = 15 mod 7 = 1;
= 7 + 10 mod 7 = 17 mod 7 = 3;
i = 6 :
= 1 + 12 mod 7 = 13 mod 7 = 6;
= 2 + 12 mod 7 = 14 mod 7 = 0 = 7;
= 5 + 12 mod 7 = 17 mod 7 = 3;
= 7 + 12 mod 7 = 19 mod 7 = 5.
Then the main cluster is repeated to cover the whole plane as shown in Figure 3.4.
109
Appendix B
SIC Error Factor (Fc) Formula
In this Appendix, the formula of SIC error factor Fc is derived for imperfect SIC case at the
receiver of close user n. The constellation of BPSK modulation is illustrated in Figure B.1.
2A2A
1A1A
1nx =1nx = 1nx = −1nx = −1mx = − 1mx =0
0 0,B n BP0 0,(1 )B n BP−
0 0,(1 )B n BP−0 0,B n BP
Figure B.1: BPSK constellation.
From the Figure B.1, dmin = 2A1 for detecting the symbol xn = −1 while the symbol
xm = 1 is transmitted and dmin = 2A2 for detecting the symbol xn = 1 while the symbol
xm = 1 is transmitted. A1 =√
(1− αB0,n)PB0 −√αB0,nPB0 and A2 =
√(1− αB0,n)PB0 +√
αB0,nPB0 .
The average probability of error for defecting both symbols xn = −1 and xn = 1 can be
computed as
Pe = P (xm = −1|xm = 1, xn = −1)P (xn = −1) + P (xm = −1|xm = 1, xn = 1)P (xn = 1)
+ P (xm = 1|xm = −1, xn = −1)P (xn = −1) + P (xm = 1|xm = −1, xn = 1)P (xn = 1),
(B.1)
where P (xn = 1) = P (xn = −1) =1
2, and due to the symmetric property for the transmitted
symbols xm = 1 and xm = −1 as shown in Figure B.1, the (??) can be expressed as
Pe = P (xm = −1|xm = 1, xn = −1)P (xn = −1) + P (xm = −1|xm = 1, xn = 1)P (xn = 1).
(B.2)
110
Consequently, the SIC error factor Fc as the average probability of error can be expressed
as
Fc = Pe =1
2Q
√|hB0,n|2(2A1)2
4No
+1
2Q
√|hB0,n|2(2A2)2
4No
=
1
2Q
(√γ|hB0,n|(
√(1− αB0,n)−√αB0,n)
)+
1
2Q
(√γ|hB0,n|(
√(1− αB0,n) +
√αB0,n)
).
(B.3)
111
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