performance analysis of fractional frequency reuse schemes

University of Calgary

PRISM: University of Calgary's Digital Repository

Graduate Studies The Vault: Electronic Theses and Dissertations

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Multi-Relay Multi-Cell OFDMA and NOMA Cellular Networks (Unpublished doctoral thesis).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

University of Calgary graduate students retain copyright ownership and moral rights for their

thesis. You may use this material in any way that is permitted by the Copyright Act or through

licensing that has been assigned to the document. For uses that are not allowable under

copyright legislation or licensing, you are required to seek permission.

Downloaded from PRISM: https://prism.ucalgary.ca

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



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



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


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


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)


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)


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


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)


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


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)


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)


Inner zone (FRF=1)


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


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)


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


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)


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


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) [61]

Non-Coop, (1,7/4) [61]


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) [61]

Non-Coop, (1,7/4) [61]


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) [61]

Coop, (1,3) [71]


Non-Coop, (1,7/3) [61]

Non-Coop, (1,3) [64]


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) [61]

Non-Coop, (1,7/4) [61]


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


0

5

10

15

20

25

30

35

40

45

Av

erg

e S

E [

b/s

/Hz]



Coop, (1,7/4) [61]

Coop, (1,7/3) [61]

Coop, (1,3) [71]


Figure 3.12: Average SE with relays for the main cluster with two tiers of the proposed


42

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


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) [61]

Coop, (1,7/3) [61]

Coop, (1,3) [71]


Figure 3.13: Average EE with relays for the main cluster with two tiers of the proposed


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

.


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



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+ +

_


ny Decoder

Decoder

0 ,B mx

nhX

0 0 0, , ,( )B n B m B n nh x x w+ +

_


ny Decoder

Decoder

0 ,B mx

nhX

0 0 0, , ,( )B n B m B n nh x x w+ +

_


ny Decoder

Decoder

0 ,B mx

nhX

0 0 0, , ,( )B n B m B n nh x x w+ +

_


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+ +

_



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+ +

_



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+ +

_



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+ +

_


Decoder

Decoder

0 ,B mx

nhX

0 0 0, , ,( )B n B m B n nh x x w+ +

_


ny Decoder

Decoder

0 ,B mx

nhX

0 0 0, , ,( )B n B m B n nh x x w+ +

_


ny Decoder

Decoder

0 ,B mx

nhX

0 0 0, , ,( )B n B m B n nh x x w+ +

_


ny Decoder

Decoder

0 ,B mx

nhX

0 0 0, , ,( )B n B m B n nh 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+ +

_



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+ +

_



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+ +

_



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+ +

_



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.


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


Parameters Values



BS-MS minimum distance 100m


Path-loss exponent ρ 2


Data modulation BPSK

SIC receiver’s detection threshold λth 2

Number of sub-carriers 35

Bandwidth of a subcarrier 30 KHz


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 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 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


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



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

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).



mi+ CNOMA

ni,imperf; (5.25)



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

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.



mo+ CNOMA

no,imperf ; (5.37)



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


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) + 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


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



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) + 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.


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.


Parameters Values



BS-MS Minimum distance 100m


Path-loss exponent ρ 2


Data modulation BPSK

SIC receiver’s detection threshold λth 2

Number of sub-carriers 35

Bandwidth of a subcarrier 30 KHz


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)


Perfect Proposed UP


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)



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 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.


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.


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

Bibliography

[1] K. Cheung, S. Yang, and L. Hanzo, “Achieving maximum energy-efficiency in multi-

relay ofdma cellular networks: A fractional programming approach,” IEEE Transac-

tions on Communications, vol. 61, no. 7, pp. 2746–2757, July 2013.

[2] S. Huang, H. Chen, J. Cai, and F. Zhao, “Energy efficiency and spectral-efficiency

tradeoff in amplify-and-forward relay networks,” IEEE Transactions on Vehicular

Technology, vol. 62, no. 9, pp. 4366–4378, Nov 2013.

[3] E. Katranaras, J. Tang, and M. Imran, “Energy and spectral efficient inter base station

relaying in cellular systems,” in IEEE 77th Vehicular Technology Conference (VTC

Spring), June 2013, pp. 1–5.

[4] G. Li, Z. Xu, C. Xiong, C. Yang, S. Zhang, Y. Chen, and S. Xu, “Energy-efficient

wireless communications: tutorial, survey, and open issues,” IEEE Wireless Commu-

nications, vol. 18, no. 6, pp. 28–35, December 2011.

[5] D. Feng, C. Jiang, G. Lim, J. Cimini, L.J., G. Feng, and G. Li, “A survey of energy-

efficient wireless communications,” IEEE Communications Surveys Tutorials, vol. 15,

no. 1, pp. 167–178, Jan 2013.

[6] C. e Souza, A. Ricieri, J. R. Almeida Amazonas, and T. Abrao, “Energy-efficiency

maximisation for cooperative and non-cooperative ofdma cellular networks—a survey,”

Transactions on Emerging Telecommunications Technologies, 2014.

[7] Y. Li and Z. Zheng, “Energy-efficient power allocation for two-hop relay networks,”

Electronics Letters, vol. 50, no. 2, pp. 123–125, January 2014.

[8] A. Mahmud and K. Hamdi, “A unified framework for the analysis of fractional fre-

quency reuse techniques,” Communications, IEEE Transactions on, vol. 62, no. 10,

112

pp. 3692–3705, Oct 2014.

[9] M. Yassin, M. A. AboulHassan, S. Lahoud, M. Ibrahim, D. Mezher, B. Cousin, and

E. A. Sourour, “Survey of icic techniques in lte networks under various mobile envi-

ronment parameters,” Wireless Networks, vol. 23, no. 2, pp. 403–418, 2017.

[10] M. Shipon Ali, H. Tabassum, and E. Hossain, “Dynamic user clustering and power

allocation for uplink and downlink non-orthogonal multiple access (noma) systems,”

arXiv preprint arXiv:1608.01081, 2016.

[11] M. B. Shahab and S. Y. Shin, “User pairing and power allocation for non-orthogonal

multiple access: Capacity maximization under data reliability constraints,” Physical

Communication, vol. 30, pp. 132–144, 2018.

[12] A. Benjebbovu, A. Li, Y. Saito, Y. Kishiyama, A. Harada, and T. Nakamura, “System-

level performance of downlink noma for future lte enhancements,” in 2013 IEEE Globe-

com Workshops (GC Wkshps), Dec 2013, pp. 66–70.

[13] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-

orthogonal multiple access (noma) for cellular future radio access,” in 2013 IEEE 77th

Vehicular Technology Conference (VTC Spring), June 2013, pp. 1–5.

[14] Z. Ding, P. Fan, and H. V. Poor, “Impact of user pairing on 5g nonorthogonal multiple-

access downlink transmissions,” IEEE Transactions on Vehicular Technology, vol. 65,

no. 8, pp. 6010–6023, 2016.

[15] S. Timotheou and I. Krikidis, “Fairness for non-orthogonal multiple access in 5g sys-

tems,” IEEE Signal Processing Letters, vol. 22, no. 10, pp. 1647–1651, Oct 2015.

[16] V. Donald, “Advanced mobile phone service: The cellular concept,” Bell System Tech-

nical Journal, vol. 58, no. 1, pp. 15–41, Jan 1979.

113

[17] K. Fu, K. Chou, Y.-S. Chen, and P. Cheng, “Adaptive frequency reuse for interference

management in ieee 802.16m system,” HsinChu,Taiwan, Tech. Rep., 2008.

[18] A. Grami, Introduction to Digital Communications. Academic Press, 2016.

[19] T. S. Rappaport, Wireless communications: principles and practice. prentice hall

PTR New Jersey, 2002, vol. 2.

[20] K. Samdanis, P. Rost, A. Maeder, M. Meo, and C. Verikoukis, Green Communications:

Principles, Concepts and Practice. John Wiley & Sons, 2015.

[21] A. Pott, P. V. Kumar, T. Helleseth, and D. Jungnickel, Difference sets, sequences and

their correlation properties. Springer Science & Business Media, 2012, vol. 542.

[22] S. W. Halpern, “Reuse partitioning in cellular systems,” in 33rd IEEE Vehicular Tech-

nology Conference, vol. 33, May 1983, pp. 322–327.

[23] J. Zander and M. Frodigh, “Capacity allocation and channel assignment in cellular

radio systems using reuse partitioning,” Electronics Letters, vol. 28, no. 5, pp. 438–

440, Feb 1992.

[24] A. Sharma, P. Sharma, R. Chaki, and U. Bhattacharya, “Reducing call blocks in

cellular network with non-uniform traffic conditions,” Foundations of Computing and

Decision Sciences, vol. 39, no. 4, pp. 301–318, 2014.

[25] Z. Naseem, I. Nausheen, and Z. Mirza, “Propagation models for wireless communica-

tion system,” IRJET, vol. 5, no. 01, 2018.

[26] D. Tse and P. Viswanath, Fundamentals of wireless communication. Cambridge uni-

versity press, 2005.

[27] F.-L. Luo and C. J. Zhang, Signal processing for 5G: algorithms and implementations.

John Wiley & Sons, 2016.

114

[28] T.-D. Chiueh and P.-Y. Tsai, OFDM baseband receiver design for wireless communi-

cations. John Wiley & Sons, 2008.

[29] Y. Tao, L. Liu, S. Liu, and Z. Zhang, “A survey: Several technologies of non-orthogonal

transmission for 5g,” China communications, vol. 12, no. 10, pp. 1–15, 2015.

[30] Y. Liu, Z. Qin, M. Elkashlan, Z. Ding, A. Nallanathan, and L. Hanzo, “Non-orthogonal

multiple access for 5g and beyond,” arXiv preprint arXiv:1808.00277, 2018.

[31] M. Aldababsa, M. Toka, S. Gokceli, G. K. Kurt, and O. Kucur, “A tutorial on

nonorthogonal multiple access for 5g and beyond,” Wireless Communications and Mo-

bile Computing, 2018.

[32] Z. Ding, X. Lei, G. K. Karagiannidis, R. Schober, J. Yuan, and V. K. Bhargava, “A

survey on non-orthogonal multiple access for 5g networks: Research challenges and

future trends,” IEEE Journal on Selected Areas in Communications, vol. 35, no. 10,

pp. 2181–2195, 2017.

[33] K. Lu, Z. Wu, and X. Shao, “A survey of non-orthogonal multiple access for 5g,” in

IEEE 86th Vehicular Technology Conference (VTC-Fall), 2017, pp. 1–5.

[34] L. Dai, B. Wang, Y. Yuan, S. Han, C. I, and Z. Wang, “Non-orthogonal multiple

access for 5g: solutions, challenges, opportunities, and future research trends,” IEEE

Communications Magazine, vol. 53, no. 9, pp. 74–81, Sep. 2015.

[35] S. R. Islam, M. Zeng, O. A. Dobre, and K.-S. Kwak, “Non-orthogonal multiple access

(noma): How it meets 5g and beyond,” Wiley 5G, pp. 1–28, 2019.

[36] M. Mohammadkarimi, M. A. Raza, and O. A. Dobre, “Signature-based nonorthogonal

massive multiple access for future wireless networks: Uplink massive connectivity for

machine-type communications,” IEEE vehicular technology magazine, vol. 13, no. 4,

pp. 40–50, 2018.

115

[37] S. M. R. Islam, N. Avazov, O. A. Dobre, and K. Kwak, “Power-domain non-orthogonal

multiple access (noma) in 5g systems: Potentials and challenges,” IEEE Communica-

tions Surveys Tutorials, vol. 19, no. 2, pp. 721–742, Secondquarter 2017.

[38] S. R. Islam, M. Zeng, O. A. Dobre, and K.-S. Kwak, “Resource allocation for downlink

noma systems: Key techniques and open issues,” IEEE Wireless Communications,

vol. 25, no. 2, pp. 40–47, 2018.

[39] L. Zhu, J. Zhang, Z. Xiao, X. Cao, and D. O. Wu, “Optimal user pairing for down-

link non-orthogonal multiple access (noma),” IEEE Wireless Communications Letters,

vol. 8, no. 2, pp. 328–331, April 2019.

[40] D. Tse and P. Viswanath, Fundamentals of wireless communication. Cambridge uni-

versity press, 2005.

[41] K. Higuchi and A. Benjebbour, “Non-orthogonal multiple access (noma) with succes-

sive interference cancellation for future radio access,” IEICE Transactions on Commu-

nications, vol. 98, no. 3, pp. 403–414, 2015.

[42] Z. Wei, J. Yuan, D. W. K. Ng, M. Elkashlan, and Z. Ding, “A survey of downlink non-

orthogonal multiple access for 5g wireless communication networks,” arXiv preprint

arXiv:1609.01856.

[43] A. Yahya, “Lte-a cellular networks,” MULTI-HOP RELAY FOR COVERAGE, CA-

PACITY AND PERFORMANCE ENHANCEMENT, 2016.

[44] E. Hossain, D. I. Kim, and V. K. Bhargava, Cooperative cellular wireless networks.

Cambridge University Press, 2011.

[45] I. F. Akyildiz, D. M. Gutierrez-Estevez, and E. C. Reyes, “The evolution to 4g cellular

systems: Lte-advanced,” Physical communication, vol. 3, no. 4, pp. 217–244, 2010.

116

[46] H. Nafea, F. Zaki, and H. Moustafa, “Studies on relay modes and system capacity

in wimax ieee 802.16m multi-hop relay networks,” in 31st National Radio Science

Conference (NRSC), April 2014, pp. 184–193.

[47] X. Gao, X. Wang, and V. C. Leung, “A two-hop equalize-and-forward relay scheme

in ofdm-based wireless networks over multipath channels,” Wireless Communications

and Mobile Computing, vol. 16, no. 7, pp. 778–793, 2016.

[48] M. Pejanovic-Djurisic, E. Kocan, and R. Prasad, OFDM based relay systems for future

wireless communications. River Publishers, 2012.

[49] N. Shende, O. Gurbuz, and E. Erkip, “Half-duplex or full-duplex relaying: A capacity

analysis under self-interference,” in 47th Annual Conference on Information Sciences

and Systems (CISS), March 2013, pp. 1–6.

[50] S.-N. Hong and G. Caire, “Virtual full-duplex relaying with half-duplex relays,” IEEE

Transactions on Information Theory, vol. 61, no. 9, pp. 4700–4720, Sept 2015.

[51] H. Lin, D. Gu, W. Wang, and H. Yang, “Capacity analysis of dedicated fixed and

mobile relay in lte-advanced cellular networks,” in IEEE International Conference on

Communications Technology and Applications, ICCTA, Oct 2009, pp. 354–359.

[52] S. Peters and R. Heath, “The future of wimax: Multihop relaying with ieee 802.16j,”

IEEE Communications Magazine, vol. 47, no. 1, pp. 104–111, January 2009.

[53] A. Daeinabi, K. Sandrasegaran, and X. Zhu, “Survey of intercell interference mitigation

techniques in lte downlink networks,” in Australasian Telecommunication Networks and

Applications Conference (ATNAC), Nov 2012, pp. 1–6.

[54] X. Zhang, C. He, L. Jiang, and J. Xu, “Inter-cell interference coordination based

on softer frequency reuse in ofdma cellular systems,” in International Conference on

Neural Networks and Signal Processing, NNSP, June 2008, pp. 270–275.

117

[55] M. Porjazoski and B. Popovski, “Analysis of intercell interference coordination by

fractional frequency reuse in lte,” in International Conference on Software, Telecom-

munications and Computer Networks (SoftCOM), Sept 2010, pp. 160–164.

[56] J. Liu, D. Wang, J. Pang, D. Wang, and G. Shen, “Inter-cell interference coordination

based on soft frequency reuse for relay enhanced cellular network,” in IEEE 21st Inter-

national Symposium on Personal Indoor and Mobile Radio Communications (PIMRC),

Sept 2010, pp. 2304–2308.

[57] A. Hamza, S. Khalifa, H. Hamza, and K. Elsayed, “A survey on inter-cell interference

coordination techniques in ofdma-based cellular networks,” IEEE Communications

Surveys Tutorials, vol. 15, no. 4, pp. 1642–1670, Fourth 2013.

[58] S.-E. Elayoubi, O. Ben Haddada, and B. Fourestiee, “Performance evaluation of fre-

quency planning schemes in ofdma-based networks,” IEEE Transactions on Wireless

Communications, vol. 7, no. 5, pp. 1623–1633, May 2008.

[59] Q. Li, Z. Wang, and F. Ma, “Inter-cell interference coordination research for lte,” in

IEEE 4th International Symposium on Microwave, Antenna, Propagation, and EMC

Technologies for Wireless Communications (MAPE), Nov 2011, pp. 695–700.

[60] M. Yassin, M. A. AboulHassan, S. Lahoud, and M. Ibrahim, “Survey of icic techniques

in lte networks under various mobile environment parameters,” pp. 403–418, 2017.

[61] A. Najjar, N. Hamdi, and A. Bouallegue, “Fractional frequency reuse scheme in co-

operative relaying for multi-cell ofdma systems.” in MACOM. Springer, 2010, pp.

199–210.

[62] ——, “Fractional frequency reuse scheme with two and three regions for multi-cell

ofdma systems,” in 17th Telecommunication forum Telfor, November 2009, pp. 319–

322.

118

[63] Y.-J. Choi, C. S. Kim, and S. Bahk, “Flexible design of frequency reuse factor

in ofdma cellular networks,” in IEEE International Conference on Communications

(ICC), vol. 4, June 2006, pp. 1784–1788.

[64] A. Najjar, N. Hamdi, and A. Bouallegue, “Efficient frequency reuse scheme for multi-

cell ofdma systems,” in IEEE Symposium on Computers and Communications (ISCC),

July 2009, pp. 261–265.

[65] H. Lei, X. Zhang, and D. Yang, “A novel frequency reuse scheme for multi-cell ofdma

systems,” in IEEE 66th Vehicular Technology Conference, VTC-Fall, Sept 2007, pp.

347–351.

[66] R.-. TSG RAN WG1, “Interference mitigation by partial frequency reuse,” Siemens,

London, UK, Tech. Rep., 2006.

[67] Y. Xiang, J. Luo, and C. Hartmann, “Inter-cell interference mitigation through flexible

resource reuse in ofdma based communication networks,” in European wireless, 2007,

pp. 1–4.

[68] A. M. Saleh, N. T. Le, and A. B. Sesay, “Inter-cell interference coordination using

fractional frequency reuse scheme in multi-relay multi-cell ofdma systems,” in IEEE

31st Canadian Conference on Electrical and Computer Engineering (CCECE), 2018.

[69] A. M. Saleh, N. T. Le, and A. B. Sesay, “Fractional frequency reuse (ffr) scheme

for inter-cell interference (ici) mitigation in multi-relay multi-cell ofdma systems,” in

IEEE 9th Annual Information Technology, Electronics and Mobile Communication

Conference (IEMCON), Nov 2018, pp. 358–364.

[70] H. Lei, X. Zhang, and D. Yang, “A novel frequency reuse scheme for multi-cell ofdma

systems,” in IEEE VTC-Fall, 2007, pp. 347–351.

119

[71] A. Najjar, N. Hamdi, and A. Bouallegue, “Efficient frequency reuse scheme in cooper-

ative relaying for multi-cell ofdma systems,” in MELECON, 2010, pp. 466–469.

[72] R. Patil and R. Patane, “Inter-cell interference mitigation reduction in lte using fre-

quency reuse scheme,” IJSR Publications, 2015.

[73] M. V. V. Reddy, E. Vivier, and F. Z. Kaddour, “Joint benefits of fractional frequency

reuse and relays in lte networks,” Oct 2013, pp. 127–131.

[74] Y. Zhao, X. Fang, X. Hu, Z. Zhao, and Y. Long, “Fractional frequency reuse schemes

and performance evaluation for ofdma multi-hop cellular networks,” April 2009, pp.

1–5.

[75] T. Hellesth, D. Jungnickel, A. Pott, and P. Kumar, “Difference sets, sequences and

their correlation properties,” 1998.

[76] M. Hata, “Empirical formula for propagation loss in land mobile radio services,” IEEE

VTC trans., pp. 317–325, 1980.

[77] A. M. Saleh and A. B. Sesay, “Sum rate maximization for ffr schemes with inter-cell

interference in downlink multi-cell noma-based networks.” under revision.

[78] I. A. Mahady, E. Bedeer, S. Ikki, and H. Yanikomeroglu, “Sum-rate maximization of

noma systems under imperfect successive interference cancellation,” IEEE Communi-

cations Letters, vol. 23, no. 3, pp. 474–477, 2019.

[79] M. B. Shahab, M. Irfan, M. F. Kader, and S. Young Shin, “User pairing schemes for

capacity maximization in non-orthogonal multiple access systems,” Wireless Commu-

nications and Mobile Computing, vol. 16, no. 17, pp. 2884–2894, 2016.

[80] J. Zhu, J. Wang, Y. Huang, S. He, X. You, and L. Yang, “On optimal power allocation

for downlink non-orthogonal multiple access systems,” IEEE Journal on Selected Areas

in Communications, vol. 35, no. 12, pp. 2744–2757, 2017.

120

[81] K. Senel and S. Tekinay, “Optimal power allocation in noma systems with imperfect

channel estimation,” in IEEE Global Communications Conference, 2017, pp. 1–7.

[82] J.-M. Kang and I.-M. Kim, “Optimal user grouping for downlink noma,” IEEE Wire-

less Communications Letters, vol. 7, no. 5, pp. 724–727, 2018.

[83] X. Zhang, J. Wang, J. Wang, and J. Song, “A novel user pairing in downlink non-

orthogonal multiple access,” in IEEE International Symposium on Broadband Multi-

media Systems and Broadcasting (BMSB), 2018, pp. 1–5.

[84] J. He, Z. Tang, and Z. Che, “Fast and efficient user pairing and power allocation

algorithm for non-orthogonal multiple access in cellular networks,” Electronics Letters,

vol. 52, no. 25, pp. 2065–2067, 2016.

[85] D. Wan, M. Wen, Y. Liu, F. Ji, H. Yu, and F. Chen, “User pairing strategy: A novel

scheme for non-orthogonal multiple access systems,” in IEEE Globecom Workshops

(GC Wkshps), 2017, pp. 1–6.

[86] C.-L. Wang, J.-Y. Chen, and Y.-J. Chen, “Power allocation for a downlink non-

orthogonal multiple access system,” IEEE wireless communications letters, vol. 5, no. 5,

pp. 532–535, 2016.

[87] J. A. Oviedo and H. R. Sadjadpour, “A new noma approach for fair power alloca-

tion,” in IEEE Conference on Computer Communications Workshops (INFOCOM

WKSHPS), 2016, pp. 843–847.

[88] Z. Q. Al-Abbasi and D. K. So, “User-pairing based non-orthogonal multiple access

(noma) system,” in IEEE 83rd Vehicular Technology Conference (VTC-Spring), 2016,

pp. 1–5.

[89] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li, and K. Higuchi, “Non-

orthogonal multiple access (noma) for cellular future radio access,” in IEEE 77th ve-

121

hicular technology conference (VTC-Spring), 2013, pp. 1–5.

[90] Z. Wei, J. Yuan, D. W. K. Ng, M. Elkashlan, and Z. Ding, “A survey of downlink non-

orthogonal multiple access for 5g wireless communication networks,” arXiv preprint

arXiv:1609.01856, 2016.

[91] L. Dai, B. Wang, Z. Ding, Z. Wang, S. Chen, and L. Hanzo, “A survey of non-

orthogonal multiple access for 5g,” IEEE communications surveys & tutorials, vol. 20,

no. 3, pp. 2294–2323, 2018.

[92] W. Shin, M. Vaezi, B. Lee, D. J. Love, J. Lee, and H. V. Poor, “Non-orthogonal

multiple access in multi-cell networks: Theory, performance, and practical challenges,”

IEEE Communications Magazine, vol. 55, no. 10, pp. 176–183, 2017.

[93] Z. Xu, G. Y. Li, C. Yang, and X. Zhu, “Throughput and optimal threshold for ffr

schemes in ofdma cellular networks,” IEEE Transactions on Wireless Communications,

vol. 11, no. 8, pp. 2776–2785, August 2012.

[94] J. G. Proakis and M. Salehi, Digital communications, 2014, vol. 5.

[95] Z. Ding, M. Peng, and H. V. Poor, “Cooperative non-orthogonal multiple access in 5g

systems,” IEEE Communications Letters, vol. 19, no. 8, pp. 1462–1465, Aug 2015.

[96] J. Kim and I. Lee, “Capacity analysis of cooperative relaying systems using non-

orthogonal multiple access,” IEEE Communications Letters, vol. 19, no. 11, pp. 1949–

1952, Nov 2015.

[97] R. Jiao, L. Dai, J. Zhang, R. MacKenzie, and M. Hao, “On the performance of noma-

based cooperative relaying systems over rician fading channels,” IEEE Transactions

on Vehicular Technology, vol. 66, no. 12, pp. 11 409–11 413, Dec 2017.

122

[98] M. B. Uddin, M. F. Kader, and S. Y. Shin, “Cooperative amplify-and-forward relaying

in noma,” Journal of the Korean Institute of Communication Sciences, pp. 385–386,

2018.

[99] J. Kim, J. Lee, D. Kim, and Y. Choi, “System-level performance evaluation for non-

orthogonal multiple access in coordinated direct and relay transmission,” in 2017 In-

ternational Conference on Information and Communication Technology Convergence

(ICTC), Oct 2017, pp. 1296–1298.

[100] M. Yang, J. Chen, L. Yang, L. Lv, B. He, and B. Liu, “Design and performance analysis

of cooperative noma with coordinated direct and relay transmission,” IEEE Access,

vol. 7, pp. 73 306–73 323, June 2019.

[101] O. Abbasi, A. Ebrahimi, and N. Mokari, “Noma inspired cooperative relaying system

using an af relay,” IEEE Wireless Communications Letters, vol. 8, no. 1, pp. 261–264,

Feb 2019.

[102] Q. Liu, T. Lv, and Z. Lin, “Energy-efficient transmission design in cooperative relaying

systems using noma,” IEEE Communications Letters, vol. 22, no. 3, pp. 594–597,

March 2018.

[103] D. Do, M. Vaezi, and T. Nguyen, “Wireless powered cooperative relaying using noma

with imperfect csi,” in IEEE Globecom Workshops (GC Wkshps), Dec 2018, pp. 1–6.

[104] H. Liu, Z. Ding, K. J. Kim, K. S. Kwak, and H. V. Poor, “Decode-and-forward relay-

ing for cooperative noma systems with direct links,” IEEE Transactions on Wireless

Communications, vol. 17, no. 12, pp. 8077–8093, 2018.

[105] D. B. da Costa and M. D. Yacoub, “Outage performance of two hop af relaying systems

with co-channel interferers over nakagami-m fading,” IEEE Communications Letters,

vol. 15, no. 9, pp. 980–982, Sep. 2011.

123

[106] J. C. S. S. Filho and M. D. Yacoub, “Nakagami-m approximation to the sum of m non-

identical independent nakagami-m variates,” Electronics Letters, vol. 40, pp. 951–952,

July 2004.

[107] M. K. Simon and M.-S. Alouini, Digital communication over fading channels. John

Wiley & Sons, 2005, vol. 95.

[108] D. B. d. Costa, H. Ding, and J. Ge, “Interference-limited relaying transmissions in dual-

hop cooperative networks over nakagami-m fading,” IEEE Communications Letters,

vol. 15, no. 5, pp. 503–505, 2011.

[109] I. Gradshteyn, I. Ryzhik, and A. Jeffrey, Table of integrals series and products. Aca-

demic Press, 2007.

[110] I. Krikidis, J. S. Thompson, S. McLaughlin, and N. Goertz, “Max-min relay selec-

tion for legacy amplify-and-forward systems with interference,” IEEE Transactions on

Wireless Communications, vol. 8, no. 6, pp. 3016–3027, 2009.

[111] A. Papoulis and S. U. Pillai, Probability, random variables, and stochastic processes.

McGraw-Hill, 2002.

[112] V. Adamchik and O. Marichev, “The algorithm for calculating integrals of hyperge-

ometric type functions and its realization in reduce system,” in Proceedings of the

international symposium on Symbolic and algebraic computation. ACM, 1990, pp.

212–224.

124

performance analysis of fractional frequency reuse schemes

Documents