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Thesis for the Degree of Doctor of Philosophy

Self-organizing Resource Allocation for 5Gcellular Networks

S. M. Ahsan Raza Kazmi

Department of Computer Science & EngineeringGraduate School

Kyung Hee UniversitySouth Korea

August 2017

Self-organizing Resource Allocation for 5Gcellular Networks

S. M. Ahsan Raza Kazmi

Department of Computer Science & EngineeringGraduate School

Kyung Hee UniversitySouth Korea

August 2017

Dedicated To

my beloved parents and wife for their never ending support.

Abstract

The modern mobile communication by incorporating novel bandwidth hungry applications has

revolutionized our life by empowering us in optimizing our daily life operations, economics and

health. These bandwidth hungry applications has evolved at a very rapid pace, thus, generating a

tsunami of mobile traffic on the existing mobile networks. Moreover, mobile users analyze, gather

and share a huge amount of information among different peers in the network. Thus, operators

are forced to keep up with the requirements of the mobile users and find novel technologies and

solutions to handle this tsunami of mobile traffic.

The existing network capacities requires significant enhancements to cope with the growing

demands of end users. In current mobile network architecture, the major bottleneck is the radio

access networks (RANs) which are typically wireless networks. The dynamic nature of wireless

communications makes these RANs highly uncertain and random. Therefore, the challenge for

the future mobile networks is to design high capacity RANs to handle the growing users’ demand.

However, this would require novel RAN access algorithms and will present novel challenges that

need to be addressed.

A number of challenges need to be addressed to bring the next generation RAN into fruition.

The biggest challenge in RAN pertains to the limited available wireless spectrum. The spectrum

suffers from congestion due to i) exponential increase in number of wireless devices such as smart

phones and tablets ii) novel and abundant bandwidth hungry applications such as online gaming,

high definition videos etc. Therefore, the main goal is to develop efficient RAN schemes that can

deal with scheduling, interference mitigation, resource allocation and power control in this limited

spectrum.

In this dissertation, we consider two 5G RAN enablers, i.e., dense small cell network and

i

ii

device to device network, each with its respective network optimization problem and challenges.

We design a self-organizing RAN access scheme for both these enabling technologies.

The first scheme is designed for heterogeneous mobile networks which involves solving a net-

work optimization problem that deals with resource allocation for dense networks. Small-cell base

stations have been proposed for the current and next generation cellular network to increase net-

work capacity and reduce the outage. The goal is to reuse the allocated resources in the cellular-tier

by protecting them from harmful interference. The challenge is to solve the classical problem in a

self-organizing or in an autonomous manner without heavy messages exchange. We propose two

schemes to solve this problem. The first scheme is developed by applying the duality-based op-

timization approach, which enables distributed implementation. The second scheme, that enables

coordination, is devised based on matching theory. Simulation results show that the proposed

duality-based scheme outperforms the greedy approach by 4% in terms of sum-rate whereas the

matching-based scheme with tier-coordination yields performance gains up to 17% compared with

the duality-based approach.

The second scheme is designed for dense device-to-device (D2D) communications over ex-

isting mobile cellular networks. Spectrum efficiency can be enhanced by enabling the D2D com-

munication, thus, enhancing the network throughput of existing networks. However, enabling

D2D communication in an underlay fashion poses a significant challenge pertaining to interfer-

ence management. We formulate our problem as a combinatorial problem in which the objective

is to maximize the network utility of all D2D pairs. To solve this problem, a learning framework

is proposed based on a problem-specific Markov chain. From the local balance equation of the

designed Markov chain, the transition probabilities are derived for distributed implementation.

Then, a novel two phase algorithm is developed to perform mode selection and resource allocation

in the respective phases. This algorithm converges to a near-optimal solution. Moreover, to reduce

the computation in the learning framework, two resource allocation algorithms based on matching

theory are proposed to output a specific and deterministic solution. The first algorithm employs the

one-to-one matching game approach, whereas, in the second algorithm, the one-to many matching

game with externalities and dynamic quota is employed. Simulation results show that the proposed

framework converges to a near optimal solution under all scenarios with probability one. More-

iii

over, our results show that the proposed matching game with externalities achieves a performance

gain of up to 35% in terms of the average utility compared to a classical matching scheme with no

externalities.

Acknowledgement

In the name of Allah, the Beneficent, the Merciful.

”Read! In the Name of your Lord, Who has created (all that exists), He has created man from

a clot (a piece of thick coagulated blood) Read! And your Lord is the Most Generous, Who has

taught (the writing) by the pen. He has taught man that which he knew not.”

(Quran: Chapter 96: Surah Al-Alaq (The Clot), verses 1-5.)

Above all, I thanks Almighty ALLAH for bestowing His blessings in every possible form upon

me. He gave me strength, courage, patience through which I was able to cope with all obstacles

during this PhD journey. Without His blessing, I could not have made any step forward.

I would like to offer my sincere gratitude to my honorable advisor, Professor Choong Seon

Hong who has spent an enormous deal of time and effort during my studies. I am extremely

grateful for the time, esteemed guidance and advice that helped me in shaping up my research and

achieving significant improvement in this dissertation. I would also like to thank to all my thesis

committee members for providing insightful and constructive comments to significantly improve

the quality of this dissertation.

Next, I would like to thank Dr. Nguyen H. Tran and Mr. Ho Manh Tai, who have helped

and given constructive criticism on my works. The insights provided by them have helped in

significantly improving my work. I also appreciate all the colleagues from Networking Lab for

their generous support that helped making my life in Korea easier.

Lastly, I have no words to express my gratitude to my family for their infinite love, encourage-

ment, and support, especially my parents, S. Azhar Ali Kazmi and S. Nafisa Azhar. I would like

to acknowledge their sacrifices.

S. M. Ahsan Kazmi

iv

Table of Contents

Abstract i

Acknowledgment iv

Table of Contents v

List of Figures viii

1 Introduction 1

1.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3.1 Resource Allocation in Heterogeneous Networks . . . . . . . . . . . . . 5

1.3.2 Resource Allocation in Device-to-Device Communications . . . . . . . . 6

1.4 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4.1 Resource Allocation in Heterogeneous Wireless Networks . . . . . . . . 7

1.4.2 Resource Allocation in Device-to-Device Communications . . . . . . . . 8

1.5 Structure of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Chapter 2 Resource Allocation in Heterogeneous Wireless Networks 12

2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2 Background and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 System Model and Problem Definition . . . . . . . . . . . . . . . . . . . . . . . 14

2.3.1 Resource Allocation and Link Models . . . . . . . . . . . . . . . . . . . 16

v

vi

2.3.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Optimization-based Resource Allocation . . . . . . . . . . . . . . . . . . . . . 17

2.4.1 Problem Relaxation and Dual Decomposition . . . . . . . . . . . . . . . 17

2.4.2 Algorithm Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Matching-based Resource Allocation . . . . . . . . . . . . . . . . . . . . . . . 21

2.5.1 Matching theory preliminaries . . . . . . . . . . . . . . . . . . . . . . . 21

2.5.1.1 Preferences of the players . . . . . . . . . . . . . . . . . . . . 21

2.5.1.2 Proposed algorithm . . . . . . . . . . . . . . . . . . . . . . . 25

2.5.1.3 Practical Implementation . . . . . . . . . . . . . . . . . . . . 26

2.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Chapter 3 Resource Allocation in underlay Device-to-Device Communications 38

3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2 Background and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3 System Model and Problem Definition . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.1 Resource Allocation and Link Model . . . . . . . . . . . . . . . . . . . 42

3.3.2 D2D Decision and Mode Selection model . . . . . . . . . . . . . . . . . 43

3.3.3 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.4 JMARA via Markov Approximation . . . . . . . . . . . . . . . . . . . . . . . . 46

3.4.1 Step 1: Log-sum-exp Approximation . . . . . . . . . . . . . . . . . . . 47

3.4.2 Step 2: Markov Chain (MC) . . . . . . . . . . . . . . . . . . . . . . . . 48

3.4.3 Learning Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.5 Resource Allocation via Matching . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5.1 Case 1: Partial-Reuse Mode . . . . . . . . . . . . . . . . . . . . . . . . 54

3.5.1.1 Matching Game Formulation . . . . . . . . . . . . . . . . . . 55

3.5.1.2 Preference Profiles of Players . . . . . . . . . . . . . . . . . . 55

3.5.1.3 Resource Allocation Algorithm . . . . . . . . . . . . . . . . . 57

3.5.2 Case 2: Full-Reuse mode . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5.2.1 Matching Game Formulation . . . . . . . . . . . . . . . . . . 61

vii

3.5.2.2 Preference Profiles of Players . . . . . . . . . . . . . . . . . . 62

3.5.2.3 Preferences and Externalities . . . . . . . . . . . . . . . . . . 63

3.5.2.4 Resource Allocation Algorithm . . . . . . . . . . . . . . . . . 64

3.5.3 Computation Complexity and Implementation . . . . . . . . . . . . . . . 70

3.5.4 Example Scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.5.4.1 Partial-Reuse Mode . . . . . . . . . . . . . . . . . . . . . . . 72

3.5.4.2 Full-Reuse Mode . . . . . . . . . . . . . . . . . . . . . . . . 72

3.5.4.3 Full-Reuse Mode without Handling Externalities . . . . . . . . 74

3.6 Simulation Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.6.1 Simulation Results for Learning . . . . . . . . . . . . . . . . . . . . . . 76

3.6.2 Simulation Results for Resource Allocation . . . . . . . . . . . . . . . . 83

3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Chapter 4 Conclusion and Future Directions 95

4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Bibliography 98

Appendix A List of Publications 110

List of Figures

1.1 Evolution of Hetnet architecture [3]. . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Future wireless architecture by enabling dense small cells and device to device

communication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Proposed system model. Solid line showing the downlink information links while

dotted line showing the cross tier interference. . . . . . . . . . . . . . . . . . . . 15

2.2 Two-sided Matching. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Two matchings µ and µ′. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Sequence diagram of Algorithm 2. . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.5 Flow diagram of Algorithm 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.6 Average Rate at Irmax = −60dBm. . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.7 Average Rate at Irmax = −100dBm. . . . . . . . . . . . . . . . . . . . . . . . . 34

2.8 Average number iterations of M-DRA vs O-DRA, for different number of users. . 35

2.9 Comparison of average sum rate. . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.1 A downlink D2D communication system. The solid line shows the information

links while the dashed line shows the interference links. . . . . . . . . . . . . . . 40

3.2 Block diagram of learning algorithm (LA). . . . . . . . . . . . . . . . . . . . . 53

3.3 Partial Reuse-mode Resource Allocation Algorithm. . . . . . . . . . . . . . . . 59

3.4 Full Reuse-mode Resource Allocation Algorithm. . . . . . . . . . . . . . . . . . 67

3.5 Real-time utility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.6 Real-time performance gap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

3.7 Standard deviation of real-time performance. . . . . . . . . . . . . . . . . . . . 79

viii

ix

3.8 Normalized performance gap. . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

3.9 Average Utility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.10 Average successfully joined D2Ds . . . . . . . . . . . . . . . . . . . . . . . . . 82

3.11 Average Stopping time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

3.12 Average utility under Irmax = −80 dBm . . . . . . . . . . . . . . . . . . . . . . 85



3.15 Average utility of the proposed FR-RA scheme under various tolerance levels with

K = 50. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.16 Average utility of the proposed PR-RA scheme under various tolerance levels with

K = 50. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3.17 Average number iterations vs. network size, for Irmax = −80 dBm . . . . . . . . 89





Chapter 1Introduction

This chapter provides a brief background of the future mobile networks, i.e., 5G networks and

its challenges. Then, we discuss about two 5G enablers, i.e., heterogeneous networks (HetNets)

and device to device (d2d) communication that can bring the 5G networks into fruition. The

motivation, contribution and related works for these two 5G enablers are also provided. Finally,

the organization of this dissertation is presented at the end of this chapter.

1.1 Background and Motivation

The proliferation of high-performance mobile devices, i.e., smart-phones and tablets [1] and band-

width hungry applications, i.e., high definition videos, multimedia etc [2] over the mobile network

have fundamentally changed the existing mobile networks. These bandwidth hungry applications

has evolved at a very rapid pace, thus, generating a tsunami of mobile traffic on the mobile net-

works. This growth of devices and applications has increased exponentially thus creating network

congestion. Thus, the existing network cannot cope with these requirements and will require novel

solutions to handle this tsunami of mobile traffic [3, 4].

A recent survey has fore-casted that mobile traffic will increase about seven-fold per month

from 2016 to 2021 and the number of connected devices is expected to grow from 8.0 billion in

2016 to 11.6 billion by 2021 [1]. This motivates the promotion of current mobile communication

technologies to achieve greater capacity and higher spectral efficiencies. In order to satisfy this in-

creasing traffic demand, both industry [5] and academia [6] are finding potential solutions to cope

with future mobile networks requirements, i.e., the fifth generation (5G) mobile networks. The

existing network capacities require significant enhancements to cope with the growing demands

of end users [4]. In current mobile network architecture, the major and apparent bottleneck is the

1

CHAPTER 1. INTRODUCTION 2

radio access networks (RANs) [4–7].

RAN are typically wireless networks which provide last hop wireless services to users. The

dynamic nature of wireless communications makes these last hop networks highly uncertain and

random. Therefore, the biggest challenge for the future mobile networks is to design high ca-

pacity RANs to handle the growing end users’ demand [8, 9]. However, this would require novel

RAN access algorithms and will present novel challenges that need to be addressed. The biggest

challenge pertains to the limited available wireless spectrum which falls in the resource manage-

ment of RANs. The spectrum suffers from congestion due to the exponential increase in number

of wireless devices and bandwidth hungry applications. Therefore, the main goal is to develop

efficient RAN schemes that can efficiently perform resource management.

The existing centralized resource management solutions are becoming extremely computation-

ally complex and also incur high communication overhead due to the tsunami of traffic generated

by these modern devices and applications. Thus, the traditional resource allocation schemes can-

not be suitable for the future mobile network, i.e., 5G networks [10]. Thus, the resource manage-

ment in 5G networks is migrating to self-organizing management solutions from the centralized

solutions.

To cope with the increasing tsunami of traffic, novel resource management schemes in RAN

are required with the following characteristics. The first requirement is that the RAN scheme

should be simple to implement. Second, the RAN schemes should be adaptable to the dynamic

wireless environment. Third, the RAN schemes should be able to operate in a distributed manner

so that it can scale according to network size. We aim to design novel resource allocation schemes

with these aforementioned characteristics to cope with the projected network growth. In this

dissertation, we consider to provide solutions for two novel 5G network enablers, i.e., dense small

cell networks and device to device (D2D) networks [4, 33]. The goal of this dissertation is to

achieve a self-organizing resource allocation scheme for these two enablers. Moreover, we apply

the analytical tools such as optimization theory, matching theory and Markov approximation to

handle the challenges of the existing works.

These analytical approaches have been widely adopted in the wireless resource allocation

problem. Optimization theory based solutions that are generally centralized can be applied to


Figure 1.1: Evolution of Hetnet architecture [3].

calculate the optimal results for the resource allocation problem. However, it may require heavy

message exchanges if not designed intelligently. Moreover, the optimization approach generally

yield significant overhead and complexity for a practical size of mobile network. This overhead

and complexity can increase exponentially when considering combinatorial problems which is the

case in resource allocation problem. We apply matching theory which is a practical framework

and has been successfully applied in many economic field problems. The main motivations to

apply matching theory for wireless resource allocation problem are the followings:

• It has the capability to capture various wireless communication features.

• Its ability to model complex wireless system requirements through preference relations.

• Its can be implemented in a distributed fashion and provide low-complexity and one sided

optimal solutions that are stable.

In this thesis, we provide an approach of applying the matching theory for the aforementioned

5G enablers. Furthermore, we also compare our proposed solutions with existing mathematical

solutions pertaining to resource allocation. Finally, we analyze both theoretical and numerical

benefits of our proposal over the existing solutions for these 5G enablers.


1.2 Challenges

The tsunami of traffic generated by the modern wireless devices and the emergence of novel net-

work paradigm has transformed the operations of modern wireless networks. In order to meet the

requirements of end users, a lot of novel paradigms such as heterogeneous networks [11–13],

large-scale D2D communications [14–16], cognitive radios [17–21], LTE-unlicensed [22–26],

large-scale multi-input and multi-output (MIMO) antennas [27–31] and many more have pro-

posed to operate within the current mobile networks [32–34]. In [3], the evolution of HetNet

architecture is presented. It is illustrated that dense small cell base stations along with the afore-

mentioned technologies will coexist with the existing HetNets to fulfill the requirements as shown

in Fig. 1.1. In this dissertation, we only focus and discuss on two enabling technologies, i.e., dense

heterogeneous networks [35] and large-scale D2D communications [36]. Both HetNets and d2d

communication can boost the spectrum utilization as well as the coverage of the existing mobile

networks. Enabling these technologies into the existing network will leads to the future wireless

architecture, as shown in Fig.1.2.

The centralized resource management schemes that have been successfully deployed in ex-

isting mobile networks are no longer able to cope with the requirements of the future networks

[37, 38]. In such complex environments a self-organizing solution would be more suitable. The

reason behind this shift from centralized to self-organizing is motivated by dense network users

and demand for low-latency communication.

Additionally, for resource management in the future multi-tiered heterogeneous wireless ar-

chitecture, there exist another important challenge pertaining to the interference management [39].

Interference management is one of the key requirements that need to be fulfilled through which

the resources can be shared among heterogeneous peers, i.e., macro-cell, small-cell and d2d users.

In order to share the resources, the incumbent tier needs to be protected from interference stem-

ming from other tiers. Moreover, if interference is not well-handled, the resource efficiency can

significantly degrade in such multi-tiered heterogeneous wireless architecture. Thus interference

management is also one of the fundamental challenges that need to be addressed. In this disserta-

tion, we provide self-organizing resource management schemes in the RAN that also addresses the

interference management issue. We present our solutions for two emerging 5G network enablers.


Introduction: Problem Statement 7/20

• Centralized Resource allocation can no longer cope with the

tsunami of heterogeneous demands and UEs.

• These systems are unable to scale due to lack of coordination.

• Self-organizing and decentralized resource allocation scheme taking

into account the coexistence of novel heterogeneous technologies

(i.e., 5G networks) that can ensure interference management.

• How to meet these heterogeneous demands with limited wireless

spectrum (channels) ?

• How to protect the incumbent UEs from interference?

• How to reduce the coordinate overhead?

Goals

Challenges

Resource Management

D2D Communication

Figure 1.2: Future wireless architecture by enabling dense small cells and device to device com-munication.

1.3 Contribution

In this dissertation, we consider two emerging 5G network enablers and present resource allocation

schemes for them. We consider their own respective network optimization problems. Due to their

different network environments, both problems have different kinds of constraints corresponding

to different underlying layers.

1.3.1 Resource Allocation in Heterogeneous Networks

In this research topic, we investigate the joint resource allocation (RA) and interference manage-

ment (IM) problem for dense small cell network underlay cellular network. We introduce two

novel algorithms for RA and IM. Both proposed self-organizing algorithms are designed to simul-

taneously enable protection for the macrocell tier and to operate in large-scale dense networks.

Furthermore, unlike existing algorithms such as in [40, 42], and [43], the proposed matching-

based approach achieves efficient coordination between network tiers with minimal message pass-

ing compared to previous works [40, 42]. Our main contributions can thus be summarized as

follows:

• We formulate the RA problem with the macro-tier protection as a mixed-integer optimiza-


tion problem.

• To solve this problem, we develop a duality-based RA algorithm that can achieve a near

optimal solution by uniformly assigning cross-tier interference budget for the SBSs. This

approach enables distributed implementation and affordable computational complexity.

• By exploiting non-uniform cross-tier interference using a tier-coordination approach, the

network performance can be improved. However, a duality-based approach with tier-

coordination induces heavy information exchange [43]. Therefore, based on matching the-

ory, we propose a second distributed approach with limited information exchange.

• Numerical results show that, the proposed duality-based algorithm outperforms the greedy

approach by 4% in terms of sum-rate and the use of matching theory can significantly im-

prove the overall network sum-rate. This performance advantage can reach up to 17% com-

pared to the duality-based optimization approach.

1.3.2 Resource Allocation in Device-to-Device Communications

In this research topic, we introduce a self-organizing scalable solution for a dense D2D network

by jointly addressing the problems of mode selection, resource allocation, and interference man-

agement aspects. We propose a novel learning framework based on Markov approximation to

address these issues. Unsupervised learning is used for mode selection and a two-sided matching

game is incorporated to address the resource allocation aspects. The proposed matching game is

shown to reduce the computation and configuration size in the framework while enabling a self-

organizing and distributed control. Furthermore, we consider a practical scenario in which a group

of D2D pairs reuse the same resource simultaneously if the cellular transmission protection can be

guaranteed. In summary, our key contributions include the following:

• First, we formulate the joint problem of mode selection, and resource allocation with an

objective to maximize the utility of all D2D pairs subject to interference protection for

cellular transmission. The formulated problem is a mixed-integer non-linear optimization

problem that is NP-hard and requires exponential computation efforts to obtain the optimal

solution.


• Second, to solve the joint problem, we propose a learning framework based on Markov

approximation. Furthermore, we design an ergodic Markov chain and the transition proba-

bilities, which makes the Markov chain converge to its stationary probabilities. Using these

transition probabilities, we propose a novel two phase algorithm to perform mode selec-

tion and resource allocation in the respective phases. This distributed algorithm eventually

converges to the near optimal solution in probability with a bounded performance gap.

• Third, in order to reduce the computation and configuration size in Markov approximation,

we propose two algorithms for resource allocation based on matching theory. Furthermore,

we prove the stability, convergence, and optimality of the matching based resource alloca-

tion algorithms.

• Simulation results show the convergence, optimality gap, and utility gains achieved using

the proposed framework. Results show that the framework converges to a near optimal

solution. Moreover, our results show that the proposed matching game with externalities

achieves a performance gain of up to 35% in terms of the average utility compared to a

classical matching scheme with no externalities.

1.4 Related Works

There has been many works on dense HetNets [37] and d2d communications [44]. Here, we

summarize and restrict the works relevant to the resource management in these enablers:

1.4.1 Resource Allocation in Heterogeneous Wireless Networks

The dense and pervasive deployment of wireless small cells can boost the performance of existing

macrocellular networks; however, it poses significant challenges pertaining to the cross-tier inter-

ference management. In this work, we consider the downlink resource allocation problem for an

underlay small cell network. In this network, the protection of the macrocell tier is achieved by

imposing cross-tier interference constraints in the resource allocation problem.

A centralized resource allocation approach using a greedy algorithm for RA has been pro-

posed in [40]; however, this requires heavy message passing and suffers from scalability issues


for densely deployed small cell base-station (SBSs). In next-generation 5G networks, the macro

base station (MBS) must serve a large coverage area with a high number of connected devices [4]

and an important challenge in deploying a large number of SBSs is to reduce the signaling and

communication overhead at the MBS. The main drawback is that this approach can require the

MBS to exchange various information continuously with all SBSs which increases the signaling

overhead and computational load for the MBS and becomes impractical for the dense deployment

of SBSs.

In [42], another distributed scheme has been proposed which achieves a sub-optimal RA so-

lution. However, this scheme may not be suitable for dense heterogeneous networks (HetNets)

because of high signaling overhead required to establish reference users for individual SBSs. A

distributed RA scheme with macro-tier protection is proposed in [43] which is shown to converge

to a centrally calculated solution. However, this approach has slow convergence, which may not

be desirable in dense small cell network. Note that a distributed approach with heavy message ex-

changes among network entities over the control channel such as in [42, 43] would again increase

signaling and communication overhead that is not suitable for dense networks.

1.4.2 Resource Allocation in Device-to-Device Communications

Resource allocation in D2D networks has attracted significant recent attention and a comprehen-

sive survey can be found in [44]. In particular, there has been a number of recent works [45–53],

that focused on underlay D2D networks. For instance, in [45], the authors optimize the through-

put over the shared D2D resources while meeting prioritized cellular service constraints. However,

this work is based on a centralized approach that requires significant overhead and is not tailored

to the dense nature of D2D networks. In [46], a practical and efficient interference-aware resource

allocation scheme is presented for D2D enabled networks. In [45] and [46] resource allocation in

D2D communication is completely base-station (BS) controlled. This centralized control can lead

to significant overhead for a dense D2D network [54]. Indeed, device-centric architectures are

more suitable for dense D2D networks in which a user device is at least able to control his action

based on its local information, thus distributing the control in the network [54].

A distributed scheme for resource allocation is studied in [47] to enable ad-hoc D2D networks


during uplink transmission of the cellular system. Despite the resulting improvement in the system

throughput, this approach requires significant message passing to operate in a distributed manner.

In [48], joint power control and reuse partner selection is investigated and shown to have im-

proved performance for D2D systems. Similarly, in [49], a tractable iterative solution is proposed

for improving the energy and resource usage in a D2D network, using fractional programming.

Moreover in [53], a comprehensive survey on the application of different game-theoretic models

for D2D resource allocation problem is demonstrated. In [50], a coalition game approach is pro-

posed to solve the joint power and channel allocation problem in which D2D and cellular links act

as the players. Similarly, in [51], a novel power and channel allocation scheme for a D2D enabled

system is studied using matching theory to improve cellular network throughput. However, the

works in [48–51] do not account for the presence of multiple D2D pairs on the same resource

block, which can improve the overall system resource utilization, particularly in dense networks.

Moreover, in existing works, such as in [47–51], uplink resources for the D2D communication

are considered due to ease of interference management. However, these existing works do not

directly extend to the downlink due to the different system dynamics and interference character-

istics. Furthermore, downlink is the dominating wireless traffic in 5G and beyond systems [55],

thus, novel approaches are needed for the downlink resource reuse in an underlay D2D commu-

nication. Moreover, in most of the aforementioned works (except [45, 48, 50]), a fixed resource

sharing approach for D2D communication is considered, which cannot cope with the dynamic

channel conditions and buffer status of D2D users.

The use of resource sharing can be an effective solution for interference mitigation in D2D

communications. In D2D systems, resource sharing includes mode selection along with resource

allocation. Using mode selection, the network can decide whether dedicated resources or shared

resources are used for D2D communication. In existing works such as [45, 48, 50] that consider

joint mode selection and resource allocation, it has been observed that the shared mode can pro-

vide significant improvement in terms of network throughput compared to the dedicated mode,

especially for dense networks. Moreover, a mixed mode approach in which D2D links can oper-

ate in multiple modes through resource multiplexing has also been studied in [52]. Typically, for

mode selection, a binary mode selection variable can be used, where the decisions for the mode


are taken at the BS subject to the D2D users’ channel conditions and buffer status information.

However, under dense deployment scenarios, this centralized control will incur excessive com-

plexity and overhead on the BS. Moreover, a centralized solution for the joint mode selection and

resource allocation in D2D enabled cellular systems is still an open issue. Therefore, distributed

approaches for such joint problems will be needed. In order to address these shortcomings, one

approach is to incorporate learning theory, which will be critical for future deployment of dense

networks.

In general, the use of a Markov approximation framework is suitable for solving a number of

combinatorial optimization problems with feasible learning features [56]. However, the solutions

produced by this framework require complete network information, which rises the scalability is-

sues [56], [57]. Therefore, the work in [58] and [59] presented a near optimal solution for a joint

problem (i.e., user association and resource allocation) in heterogeneous cellular networks. More-

over in [60–62], other learning approaches are applied to address the resource allocation problem

in D2D networks. These works achieved improved system performance by adding the learning

aspect to D2D networks. However, these works have ignored the mode selection aspect for D2Ds,

which can further improve network throughput performance.

1.5 Structure of the Dissertation

The rest of the dissertation is organized as follows: In Chapter 2, we discuss about the resource

allocation problem in an underlay heterogeneous wireless networks. Firstly, the system model is

described in Section 2.3. Secondly, our proposed optimization based resource allocation scheme

is given in Section 2.4. In Section 2.5, we present our second solution based on matching game in

which we derive its preferences and the solution. In Section 2.6, we present our simulation results,

and conclusion are given in Section 2.7. In Chapter 3, we investigate the joint mode selection

and resource allocation problem in D2D network underlay in a cellular networks. In Section 3.3,

we present our system model and formulate our optimization problem. We present our proposed

solution based on Markov approximation in Section 3.4. Then, the resource allocation problem

is formulated as a game in Section 3.5 and present two resource allocation solutions, i.e., partial-

reuse mode and full-reuse mode in Section 3.5.1 and Section 3.5.2, respectively. We present


our simulation results in Section 3.6, and we summarize this chapter in Section 3.7. Finally in

chapter 4, we conclude our dissertation and provide future works in section 4.1 and section 4.2,

respectively.

Chapter 2Resource Allocation in Heterogeneous Wireless Networks

2.1 Overview

The dense and pervasive deployment of wireless small cells can boost the performance of exist-

ing macrocellular networks; however, it poses significant challenges pertaining to the cross-tier

interference management. In next-generation 5G networks, the macro base station (MBS) must

serve a large coverage area with a high number of connected devices [4]. One important chal-

lenge in deploying a large number of small cell base stations (SBSs) is to reduce the signaling and

communication overhead at the MBS. A centralized resource allocation (RA) approach such as

in [4,60] can require the MBS to exchange various information continuously with all SBSs which

increases the signaling overhead and computational load for the MBS and becomes impractical for

the dense deployment of SBSs. Similarly, a distributed approach with heavy message exchanges

among network entities over the control channel such as in [42, 43] would again increase sig-

naling and communication overhead. In this work, the downlink resource allocation problem for

an underlay small cell network is studied and the protection of the macrocell tier is achieved by

imposing cross-tier interference constraints in the resource allocation problem.

In a nutshell, a distributed approach with minimum message passing would be more practical

and important for the proposed resource allocation problem, because of the reasons mentioned

above. To solve the underlying mixed-integer resource allocation problem, we propose two dif-

ferent algorithms. The first algorithm is developed by applying the duality-based optimization

approach for the relaxed problem, which enables distributed implementation. The second algo-

rithm which enables coordination is devised based on matching theory. Toward this end, we claim

that both solutions require minimal message passing.

Simulation results show that the proposed duality-based algorithm outperforms the greedy

12

CHAPTER 2. RESOURCE ALLOCATION IN HETEROGENEOUS WIRELESS NETWORKS 13

approach by 4% in terms of sum-rate whereas the matching-based algorithm with tier-coordination

yields performance gains up to 17% compared with the duality-based approach. Therefore, our

proposed solutions are novel and practical which are suitable for a large-scale dense networks of

SBSs.

2.2 Background and Contributions

One promising solution for improving the capacity of wireless networks is via the dense deploy-

ment of small cell base stations (SBSs) [64–67]. However, effective operation of such SBSs

requires meeting several technical challenges including resource allocation (RA) [68–72], inter-

ference management (IM) [73–76], and emerging network engineering issues.

A centralized approach using a greedy algorithm for RA has been proposed in [40]; how-

ever, this requires heavy message passing and suffers from scalability issues for densely deployed

SBSs. In [42], another distributed scheme has been proposed which achieves a sub-optimal RA

solution. However, this scheme may not be suitable for dense heterogeneous networks (HetNets)

because of high signaling overhead required to establish reference users for individual SBSs. A

distributed RA scheme with macro-tier protection is proposed in [43] which is shown to converge

to a centrally calculated solution. However, this approach has slow convergence, which may not

be desirable in dense small cell network.

We address these challenges by introducing two novel algorithms for RA and IM. Both pro-

posed distributed algorithms are designed to simultaneously enable protection for the macrocell

tier and to operate in large-scale dense networks. Furthermore, unlike existing algorithms such

as in [40, 42], and [43], the proposed matching-based approach achieves efficient coordination

between network tiers with minimal message passing compared to previous works. Our main

contributions can thus be summarized as follows:

• We formulate the RA problem with the macro-tier protection as a mixed-integer optimiza-

tion problem.

• To solve this problem, we develop a duality-based RA algorithm that can achieve a near

optimal solution by uniformly assigning cross-tier interference budget for the SBSs. This


approach enables distributed implementation and affordable computational complexity.

• By exploiting non-uniform cross-tier interference using a tier-coordination approach, the

network performance can be improved. However, a duality-based approach with tier-

coordination induces heavy information exchange [43]. Therefore, based on matching the-

ory, we propose a second distributed approach with limited information exchange.

• Numerical results show that, the proposed duality-based algorithm outperforms the greedy

approach by 4% in terms of sum-rate and the use of matching theory can significantly im-

prove the overall network sum-rate. This performance advantage can reach up to 17% com-

pared to the duality-based optimization approach.

The rest of this chapter is organized as follows. Section 2.3 presents the system model and

problem formulation. Section 2.4 describes our proposed optimization based resource allocation

scheme and its limitations. In Section 2.5, we present our second solution based on matching

game, we model the problem as a matching game and then derive its preferences and the solution.

In Section 2.6, we present our simulation results, and conclusion are given in Section 2.7.

2.3 System Model and Problem Definition

Consider a HetNet consisting of a set of SBSs, B = 1, 2, ..., J, located within the coverage of

one macrocell base station (MBS) as shown in Fig. 1. The set of macro-cell users (MUEs) and

small cell users (SUEs) are denoted by M = 1, 2, ...,M and S = 1, 2, ..., S, respectively.

The MBS and SBSs use the same set of orthogonal resources R = 1, 2, ..., R. 1 However,

for any given resource r ∈ R, a predefined interference threshold Irmax must be maintained for

protecting the MUEs.

1One resource corresponds to one subcarrier or subchannel of the LTE network [43].


Controller MBS

SBSSBS

MUE

SC user

SC user

SC user

SC user

MUE

: Interference links

: Information links

: Fiber backhaul links

Figure 2.1: Proposed system model. Solid line showing the downlink information links whiledotted line showing the cross tier interference.


2.3.1 Resource Allocation and Link Models

We assume that all SBSs transmit using a fixed power (e.g., any feasible power for each SBS

transmitter) [42]. However, each SBS can have its own, and different power budgets. In addition,

we assume that the transmit power of each SBS is equally divided among its resources and, thus,

the interference power on each resource is constant. For RA optimization, we introduce binary

variables xrj,k, as follows:

xrj,k =

1, if SUE k in SBS j is assigned resource r,

0, otherwise.

We always set xrj,k = 0 for any SUE k, which is not associated with SBS j. The received SINR

pertaining to the transmission of SBS j to SUE k over resource r with transmit power P rj is:

γrj,k =P rj g

rj,k

P rMgrM,k +

∑i∈Ωr,

P ri gri,k + σ2

, (2.1)

where P rM and P ri ,∀i ∈ Ωr, represent the transmit powers of the MBS and SBS, respectively, in

the set Ωr which are using resource r. The channel gain between SBS j and SUE k is grj,k whereas

grM,k and gri,k are, respectively, the channel gains from the MBS and other underlay SBSs i to SUE

k. The noise power is assumed to be σ2. Then, the data rate of user k associated with SBS j on

resource r is given by Rrj,k = W r log(1 + γrj,k) where W r is the bandwidth of resource r.

2.3.2 Problem Statement

Our objective is to maximize the sum rate of all SBSs by reusing the macrocell resources. The

data rate achieved by an SBS j over all allocated resources is:

Rj =∑

r∈R

∑k∈S

xrj,kWr log(1 + γrj,k). (2.2)

Moreover, the interference experienced by MUE m on resource r is given by Ir =∑j∈B

∑k∈S x

rj,kP

rj g

rj,m, where grj,m is the channel gain between SBS j and MUE m, on re-


source r. Note that the binary RA variables xrj,k ensure that we only account for the interference

created by SUEs that are assigned the same resource. The considered RA problem can be stated

as follows:

P1: maximizexrj,k∈X ,∀k,j,r

∑j∈B

Rj (2.3)

subject to∑

k∈Sxrj,k ≤ 1, ∀r ∈ R,∀j ∈ B, (2.4)

Ir ≤ Irmax, ∀r ∈ R. (2.5)

In P1, constraint (2.4) ensures that each resource can be allocated to at most one user in

each SBS to avoid strong intra-cell interference ; additionally, constraint (2.5) ensures the MUE

protection by keeping its aggregate interference below a predefined threshold. Problem P1 is

a non-convex, integer problem, which is difficult to solve for a practical setting with large sets

of users and resources [63]. Typically, solutions presented for problems similar to P1 requires

significant message exchanges [42], [43]. Therefore, by using optimization and matching theory,

we present two distributed novel and practical algorithms with minimal message passing (i.e., no

message exchange in Alg. 1 due to relaxation and only SBS proposals to MBS in Alg. 2) which

are suitable for a large-scale dense networks of SBSs.

2.4 Optimization-based Resource Allocation

2.4.1 Problem Relaxation and Dual Decomposition

To develop a practical distributed algorithm for the RA problem, we decompose the original prob-

lem into multiple problems which can be solved at individual SBSs. Toward this end, we relax

the coupled interference constraint (2.5) of P1 by dividing the interference threshold into J parts

corresponding to J SBSs [77]. This guarantees that each SBS is allocated the same cross-tier inter-

ference budget on each resource. Note that more complex designs can allocate different cross-tier

interference budgets for different SBSs; however, such design would require heavy message pass-

ing among SBSs, which is impractical in dense HetNets. Thus, the decomposed problem can be


stated as follows:

P2: maximizexrj,k∈X ,∀k,r

Rj (2.6)

subject to∑

k∈Sxrj,k ≤ 1, ∀r ∈ R,∑

k∈Sxrj,kP

rj g

rj,m ≤ Irmax/J, ∀r ∈ R.

The partial Lagrangian with respect to the interference constraint of P2 can be presented as

L(xrj,k, αrk) =∑

r∈R Lr(xrj,k, α

rk), where αrk represents the interference price, and Lr(xrj,k, α

rk)

is equal to:

∑k∈S

xrj,kWr log(1 + γrj,k)− αrk(

∑k∈S

xrj,kPrj g

rj,m −

Irmax

J).

The dual function g(.) is then given as

g(αrk) =

maximize

xrj,k∈0,1∀k,∀rL(xrj,k, α

rk)

subject to∑

k∈S xrj,k ≤ 1.

(2.7)

A dual based approach is a standard technique which has been used typically in finding a

decomposed solution [43, 60]. Finding the global optimal solution for P1 requires heavy mes-

sage exchange and centralized computation which may present several major limitations given the

limited capacity of control channels, latency of control message, and densely deployed network

entities [42]. The message exchanges are typically required to solve P1 while maintaining the

coupling constraint (2.5). Even by using other practical approaches to maintain the interference

constraints (2.5) such as reference user [42] or biased interference constraint which can achieve

a near optimal solution, some heavy message exchanges are required. For a large-scale dense

network of SBSs, as the number of network entities increases, these existing approaches will also

face the aforementioned limitations. Therefore, to alleviate these limitations, we equally divide

the coupled interference constraint (constraint (2.5)) and achieve the followings:

1. A practical and low complexity solution targeting the large-scale dense networks of SBSs.


2. A self-organizing solution which enables distributed operation for each SBS without any

message exchange between network entities.

3. A near optimal solution.

4. Fast convergence time, convergence is an important factor when targeting a large-scale

dense networks.

Furthermore, such an approach can be used as a benchmark for evaluating the performance

achieved by other approaches.

2.4.2 Algorithm Design

Based on the above analysis, we propose, in Alg. 1, an optimization-based distributed resource

allocation algorithm. In this algorithm, the updates of the interference price αrk(t) can be con-

ducted in a distributed way since these updates only require information on the channel gain grj,m,

which can be obtained from the underlying SBS via the MBS. This requires a relatively small

exchange of information compared to the previous works in [40, 42], and [43]. The convergence

can be proved using the gradient-based standard technique [63], and it converges to a near optimal

solution due to the simplified uniform allocation of the cross-tier interference budget [77].


Algorithm 1: Optimization-based distributed RA

1: initialize: t = 0, αrk(0) ≥ 0, step-size κr(0) > 0;

2: repeat

3: t← t+ 1

4: Each SBS j updates xrj,k for its SUEs k and αrk as follows:

• xrj,k(t+ 1) =

1, if r = r∗and k = k∗,

0, otherwise

where, r∗ = arg maxr∈R

(W r log(1 + γrj,k)− αrk(t)P rj grj,m),

k∗ = arg maxk∈S

(W r∗ log(1 + γr∗j,k)− αr

∗k (t)P r

∗j gr

∗j,m);

• αrk(t+ 1) = αrk(t)− κr(t)(∑k∈S

xrj,k(t)Prj g

rj,m − Irmax

/J),

where, κr(t) > 0 is a step-size.

5: if xrj,k = 1 and P rj grj,m > Irmax/J then

6: xrj,k = 0

7: end if

8: until αrk(t+ 1)− αrk(t) ≤ ε


2.5 Matching-based Resource Allocation

Although Algorithm 1 provides a low-complexity solution, it requires relaxing the interference

constraints to eliminate coordination between tiers and maintain the IM process. This can de-

grade the network performance. To improve it, a certain coordination between network tiers for

non-uniform cross-tier interference allocation is required. Hence, a central controller can be im-

plemented at the MBS to enable coordination among macro-SBS tiers [40,41] and to maintain the

interference limit Irmax. In the presence of coordination, we propose a second solution approach

based on matching theory [78–81].

2.5.1 Matching theory preliminaries

The RA problem can be formulated as a two-sided matching game. We assume each SUE can

use a single resource. However, different SBSs can use the same resource to improve the spec-

trum efficiency. Our design corresponds to a many-to-one matching [82] given by the tuple

(B,R, qr,B,R). Here, B , jj∈B and R , rr∈R represent the set of the pref-

erence relations of the SBSs and resources, respectively.

Definition 1 A matching µ is defined by a function from the set B ∪

R into the set of elements of B ∪ R such that: (i) |µ(j)| ≤ 1 and µ(j) ∈ R, (ii)

|µ(r)| ≤ qr and µ(r) ∈ B ∪ φ, where qr is the quota of r, and (iii) µ(j) = r if and only

if j is in µ(r).

2.5.1.1 Preferences of the players

Matching is performed on the basis of preference profiles that can be built by the SBSs Pj and

the controller Pr to rank potential matchings based on the local information. Note that, on each r,

each SBS j will choose its user k with highest data rate Rrj = maxk Rrj,k. Then, an SBS j ranks a

resource r based on the following preference function:

Uj(r) = Rrj . (2.8)


Similarly, for the controller side, each resource r also ranks the SBSs according to the following

preference function:

Ur(j) = Rrj − βIrj , (2.9)

where Irj = P rj grj,m represent interference produced by SBS j to the MUE assigned that resource.

The first term in (2.9), represents the achievable data rate on resource r, the second term accounts

for a penalty due to the interference produced by SBS j, and β represents a weight parameter.

The second term implies that the controller gives less utility to the SBSs which cause higher

interference to the MUE on resource r.

For the formulated two-sides, our goal is to seek a stable matching, which is a key solution

concept [84]. The deferred-acceptance algorithm can be employed [84]. Traditionally, in one-to-

many matching, a fixed, per player quota on one side is assumed according to which a fixed number

of players of the opposite side can be matched. However, our formulated matching game involves

a dynamic quota as the controller allows a number of SBSs (with heterogeneous interference)

to use each resource as long as the interference constraint on that resource is not violated. This

heterogeneous interference of SBSs and dynamic quota of resources introduces new challenges

that prevent the use of standard deferred-acceptance algorithm. Therefore, we formally define the

blocking pair for the formulated game as follows:

Definition 2 A pair (j, r) is a blocking pair for µ if:

a. Irres ≥ Irj , j r ∅ and r j µ(j),

b. Irres < Irj , Irres +

∑j′∈µ(r) Ij′

r ≥ Irj ,

j r j′ and r j µ(j),

where Irres = Irmax − Ir represent the residual of the interference tolerance (remaining quota) on

the resource r. The quota of a resource r ∈ R is filled when Irres < Irj for a requesting j ∈ B.

Definition 2 is based on the following intuition [85]. Whenever an SBS j prefers a resource r to

its assigned resource µ(j), if either: i) r has sufficient interference tolerance Irres and is willing to


admit j (i.e., j r ∅), or ii) its quota is filled but it is able to admit j by rejecting some accepted

SBSs which are ranked lower than j, then j and r can deviate from their assigned µ(j) and µ(r),

respectively. A matching is stable if no blocking pair exists.

In the following, we first explain the high level meaning of a “matching” in Definition 1, and

then explain the “blocking pair” in Definition 2.

SBS Resources

j1

j2

j3

r1

r2

Matching µ

SBS Resources

j1

j2

j3

r1

r2

Figure 2.2: Two-sided Matching.

Fig. 2.2 shows an example with two set of players, i.e., 3 SBSs and 2 resources. According

to Definition 1 (one to many matching). A matching µ is an assignment between the two set of

players such that:

1. Each SBS is assigned to at most one resource i.e., constraints (2.4) of problem P1. For

example, SBS j1 matched to resource r1. SBS j2 and SBS j3 are matched to resource r2.

2. No resource is oversubscribed i.e., constraints (2.5) of problem P1. For example, assume r1

and r2 have limited quota of 1 and 2 players respectively. Then, r1 can be matched to one

SBS only (j1) whereas r2 can support two SBSs, i.e., j2 and j3.

Next, we explain the idea of a blocking pair. Fig. 2.3 shows an example with two matchings

µ and µ′. Additionally, the quota of resources and preference profile for both sides, i.e., SBSs and

resources, is provided. Generally, if an SBS j prefers resource r more than its current matched

resource, and similarly resource r prefers SBS j more than its current matched SBS. Then, the

pair can deviate from the current matching in order to be matched to each other. This is called a

blocking pair [47]. In Fig. 2.3, according to the preference profile, it can be seen that the matching


SBS Resources

j1

j2

j3

r1

r2

Matching µ

SBS Resources

j1

j2

j3

r1

r2

Matching µ´

preferences of SBS

• j1: r

1> r

2• j

2: r

2> r

1• j

3: r

2> r

1

preferences of resources

• r1: j

1> j

3> j

2• r

2: j

2> j

3> j

1

Quota of resources

• r1: 2 SBSs

• r2: 2 SBSs

Figure 2.3: Two matchings µ and µ′.

produced by µ does not contain any blocking pair. However in µ′, SBS j2 is matched to resource

r1 but SBS j2 prefers resource r2 over resource r1 and similarly resource r2 also prefers SBS j2,

thus, a blocking pair exists, i.e., (j2, r2) in µ′, as both prefer to be matched to each other, over

their current partners.

Now, according to Definition 2, if any of the following two condition occur, then the matching

will have a blocking pair:

1. Irres ≥ Irj , j r ∅ and r j µ(j).

Whenever an SBS j prefers a resource r to its assigned resource µ(j) (can be φ, meaning it

is unassigned), and resource r has sufficient interference tolerance Irres and also prefers to

admit SBS j. Then, SBS j and resource r have a strong incentive to deviate from current

matching and form a new matching.

2. Irres < Irj , Irres +

∑j′∈µ(r) Ij′

r ≥ Irj , j r j′ and r j µ(j).


Whenever an SBS j prefers a resource r to its assigned resource µ(j), however, resource

r quota is filled but it is able to admit SBS j by rejecting some previously accepted SBSs

j′ which are ranked lower than SBS j according to the preference profile of resource r.

Then, SBS j and resource r can deviate from their assigned matching and block the current

matching.

2.5.1.2 Proposed algorithm

As a solution to this game, we propose a novel RA scheme to produce a stable matching in Alg.

2 which guarantees macro-tier protection captured in constraint (2.5). At each iteration t, each r

receives proposals from unassigned SBSs j that rank r as the highest in Pj(t)(lines 5-7). i) If r

has sufficient quota Irres(t) to admit j, it accepts the proposal and updates Irres

(t) and µ(r)(t)(lines

8-9). ii) Otherwise, if the quota of r is filled, then r finds all of its current matched j′ which have a

lower ranking than j according to Pr(t)(lines 10-11). Each least preferred SBS jlp ∈ P ′r(t) is then

sequentially rejected, and Irres(t), P ′r

(t), and jlp are updated until j can be admitted or there is no

additional j′ to reject (lines 12-16). After rejecting all j′ ∈ P ′r(t), if r still has an insufficient quota

to admit j, then j is rejected and j is set to the jlp (lines 17-20). Finally, the controller removes

jlp and its less preferred SBSs from the Pr(t), and similarly these SBSs also remove r from their

respective Pj(t)(lines 21-23). With this process, we guarantee that any less preferred SBS will

not be accepted by that resource even if it has sufficient quota to do so, which is crucial for the

matching stability of our design. This process is repeated until the matching converges (line 24).

The flow chat of Alg. 2 is also shown in Fig.2.5.

The output µ(t) of Alg. 2 can be transformed to a feasible allocation vector X of problem

P1 (line 25). Note that, the worst case running time complexity of Alg. 2 is linear in the size of

input preference profiles (i.e., O(JR) where J and R represent SBSs and resources, respectively)

similar to Alg. 1 which also has a linear complexity (i.e.,O(KR), whereK represents the number

of SUEs).

Note that, by using (2.9), each resource ranks all SBSs according to the utility they produce

which depends on the interference they produce on the resource (i.e., penalty term). For example,


if interference produced by an SBS j is higher compared to some other SBS j′ on resource r,

then SBS j will have a lower utility as compared to SBS j′. This implies that SBS j would be

ranked lower in the preference profile of resource r compared to SBS j′. Using this approach

every resource ranks all the SBSs in a non-increasing order of utility in its respective preference

profile Pr. The motivation behind (2.9) is to assign the resource to the SBS which produces the

highest utility. Furthermore, by using (2.9), we build the preference profile of r. This preference

profile is then used by Alg. 2 for rejecting lower ranked SBS, if the interference produced is higher

than the tolerance level. Second, to maintain constraint (2.5) in Alg. 2 the following procedure

is followed. Whenever a proposal is received for any resource r, the controller first evaluates the

proposal’s feasibility (i.e., constraint (2.5), line 8 of Alg. 2 in the manuscript). This is performed

to ensure that interference produced by assigning an SBS j over a resource r (Irj ) is always below

the available quota Irres (i.e., constraint (2.5)). This guarantees that any matched set of SBSs over

a resource will not violate the constraint (2.5). Moreover, the simulation section also validate the

macro-tier protection (constraint (2.5)) by the reduction in rate achieved by Alg. 2 as interference

protection constraint becomes stricter.

2.5.1.3 Practical Implementation

To elaborate this in detail, we discuss about the matching game algorithm and explain the required

overhead that needs to be communicated between the players and base station.

1. Initialization phase: Initially, the preference list is set up. Users/BS collect information lo-

cally, i.e., Interference, propagation gain, transmission rate, monetary offers and etc. How-

ever, in our case the maximum interference value on all resource blocks (RBs) is required by

each player. Such information can be sent to the players via the Physical Broadcast Channel

(PBCH) of LTE. PBCH carries part of the system information, required by the UE terminal

in order to access the network, specifically PBCH carries the Master Information Block of

24 bits which has the following information:

i. DL Bandwidth (3 bits) (i.e., 1.4MHz - 20 MHz)

ii. Physical HARQ Indicator Channel (PHICH) Configuration (3 bits)

iii. System Frame Number (8 bits)


iv. Spare bits (10 bits)

These spare bits can be used to transmit the maximum interference value required to build

the preference profile.

2. Proposing phase: Communication signals are sent from each players to BS for acquiring

resource blocks. This incurs an additional proposal overhead which is not currently sup-

ported by the 3GPP standard of LTE. However, this information can be sent via the Physical

Uplink control Channel (PUCCH) of each proposing transmitter. Typically, PUCCH carries

Uplink Control Information (UCI) which is basically bits and pieces of information that

eNB requires from UE in order to understand what UE (user equipment) needs and carries

other information like channel quality that UE is seeing in downlink. UCI is divided into

three main sub branches i.e. Channel State Information (CSI), Scheduling Requests (SR)

and HARQ ACK/NACK. To facilitate these functions, PUCCH has been categorized by

seven formats. We can adopt the format 1 and format 1a for sending the proposals. We can

see that the proposing message, i.e., scheduling request will be very small, i.e., 1 bit per

transmission time interval (TTI).

3. Accepting/rejecting phase: BS make decisions and send communication signals with re-

ject/accept overhead. Such information can be send via Physical Downlink Control Chan-

nel (PDCCH) where the set of accepted players will be allocated the RBs and the other

will wait. Typically, PDCCH is a physical channel that carries downlink control informa-

tion (DCI) that carries scheduling assignments and other control information for all network

users. There are four formats of PDCCH. The matched lists are then updated by both side of

players. Finally, termination takes place when there is no more RBs to propose or all play-

ers are matched with resources. This complete procedure is also shown via the sequence

diagram.


Figure 4: Sequence diagram of a matching based algorithm

Enhance future work by incorporating millimeter wave

communication for 5G networks.

Millimeter Wave (mmWave) is one proposal to achieve 1000 times network

capacity improvement goal of the fifth generation (5G) mobile network

specification. There are several advantages in moving to the mmWave

spectrum for cellular among which the major one is the channel bandwidth

available which is likely to be much larger (e.g., 500 MHz per channel or more

compared with 5–20 MHz in today’s microwave systems). Using these

mmWave networks in 5G especially for small cells can boost the available

capacity. However, intelligent and efficient resource management schemes

will be required and considered as future direction to deploy efficient

mmWave networks.

Figure 2.4: Sequence diagram of Algorithm 2.

Theorem 1 Alg. 2 converges to a stable allocation.

Proof We prove this theorem by contradiction. Assume that Alg. 2 produces a matching µ with

a blocking pair (j, r) by Definition 2. Since r j µ(j), j must have proposed to r and has

been rejected due to interference violation on r (lines 19-20). When j was rejected, then j′ was

rejected either before j (lines 13-16), or was made unable to propose because r is removed from

j′ preference list (lines 22-23). Thus, j′ /∈ µ(r), a contradiction.


Initialize:

set up preference lists (PLs)

Propose: Each user proposes to its most favorite resource; and

delete it from its PL;

Check: If all users’ all users are matched or PLs are empty?

Accept/reject: Each resource keeps the most favorite players w.r.t. its PL

and quota from the proposals; and reject the rest;

Terminate: A stable matching between users and

resources.

Yes

No

Figure 2.5: Flow diagram of Algorithm 2.


Algorithm 2: Matching-based distributed RA

1: input: Pj , Pr, ∀r, j.

2: initialize: t = 0, µ(t) , µ(j)(t), µ(r)(t)j∈B,r∈R = ∅, Irres(t) = Irmax, Kr(t) = ∅, Pj(0) = Pj ,

Pr(0) = Pr, ∀r, j.

3: repeat

4: t← t+ 1

5: for r ∈ R do

6: for j ∈ B with r as its most preferred in Pj(t) do

7: whilej /∈ µ(r)(t) and P(t)j 6= ∅ do

8: if Irres(t) ≥ Irj , then

9: µ(r)(t) ← µ(r)(t) ∪ j; Irres(t) ← Irres(t) − Irj ;

10: else

11: P ′(t)r = j′ ∈ µ(r)(t)|j r j′

12: jlp ← the least preferred j′ ∈ P ′(t)r ;

13: while(P ′(t)r 6= ∅) ∪ (Irres(t) < Irj ) do

14: µ(r)(t) ← µ(r)(t) \ j′; P ′(t)r ← P ′(t)r \ jlp;

15: Irres(t) ← Irres

(t) + Irj′;

16: jlp ← the least preferred j′ ∈ P ′r(t);

17: end while

18: if Irres(t) ≥ Irj , then


20: else

21: jlp ← j;

22: end if

23: Kr(t) = k ∈ Pr(t)|jlp r k ∪ jlp

24: for k ∈ Kr(t) do

25: Pk(t) ← Pk(t) \ r; Pr(t) ← Pr(t) \ k;


26: end for

27: end if

28: end while

29: end for

30: end for

31: until µ(t) = µ(t−1)

32: output: µ(t)

2.6 Numerical Results

In our simulations, we consider a network with 5 SBSs each of which supports 3 UEs, and 5

MUEs using 5 resources. All users are randomly located inside the coverage of an MBS which

has a radius of r1 = 1000 m, whereas the coverage distance of each small cell is r2 = 100 m. The

bandwidth of each resource W r is set equal to 1 and the weighting parameter β is set to a normal-

ized value of 1, whereas the background noise power is assumed to be −90 dBm. The channel

power gain is modeled as grj,k = 10(−L(dj,k))/10, where L(dj,k) represents the path loss and dj,k is

the distance between BS j and user k. We assume that L(dM,k) = 16.62 + 37.6 log10(dM,k) for

the channel gain from the MBS to UE k and L(dj,k) = 37 + 32 log10(dj,k) for the channel gain

from SBS j to UE k. The SBSs transmit with varying power over simulation runs ranging from 15

dBm to 23 dBm [83]. Moreover, we compare the proposed algorithms with a centralized greedy

scheme that sequentially allocates resources to users in each SBS until the interference constraint

is violated. All results are obtained by averaging over a large number of independent simulation

runs, each of which realizes random locations of base stations, users, and channel power gains.

Results corresponding to the optimization-based, matching-based, and greedy algorithms are de-

noted as “O-DRA”, “M-DRA”, and “Greedy”, respectively.

In Figs. 2.6 and 2.7, we compare the sum rate of SBSs achieved by different schemes for

two different interference thresholds Irmax = −60 and −100 dBm. It can be observed that both

proposed algorithms and greedy algorithm result in indistinguishable performance when Irmax =

−60 dBm. However, for decreased macro-tier interference threshold (Irmax = −100 dBm), lower


sum rate of the SBSs can be achieved since the interference protection constraint becomes stricter.

Moreover, the matching approach outperforms the optimization-based approach in terms of the

sum rate at this lower interference protection threshold. This is because the optimization approach

splits the interference budget Irmax uniformly among all SBSs and does not coordinate with the

macro-tier. Moreover, each SBS may prevent its UEs from using resource r if the uniformly

assigned interference limit is violated. On the other hand, in the matching-based approach, the

controller performs coordination between the network tiers and, thus, it only rejects the least pre-

ferred SBS-UE pair from the set of potential SBS-UE pairs.


50 1000

0.2

0.4

0.6

0.8

1

UEs sum rate (Mbps)

Cum

ulat

ive

dist

ribut

ion

M−DRAGreedyO−DRA

Figure 2.6: Average Rate at Irmax = −60dBm.


0 50 100 1500

0.2

0.4

0.6

0.8

1

UEs sum rate (Mbps)

Cum

ulat

ive

dist

ribut

ion

M−DRAO−DRAGreedy

Figure 2.7: Average Rate at Irmax = −100dBm.


0 5 10 15 20 25 300

2

4

6

8

10

12

Number of UEs

Itera

tions

M−DRAO−DRA

Figure 2.8: Average number iterations of M-DRA vs O-DRA, for different number of users.

Fig. 2.8 compares the average number of iterations required by both M-DRA and O-DRA

versus the number of users (i.e., network size) as Irmax = −80 dBm. It can be observed that the

number of iterations increase with the number of users. Moreover, M-DRA convergence time is

reasonable i.e., it is around 11 iterations with 5 resources. Moreover, for O-DRA, the maximum

number of iterations is smaller than 7 for all network sizes. This fast convergence time can be

achieved due to a completely distributed design of O-DRA with no message passing.

In Fig. 2.9, the average sum rate of all UEs versus the number of UEs is shown for the proposed

and greedy algorithms as Irmax = −80 dBm. Moreover, we use two benchmarks here, first, the

upper bound (UB) of problem P1 which is obtained by relaxing the binary indicator variable so

that it can take any value in the range [0, 1] and then we use the tier-aware approach in [43] as

our second benchmark. It can be inferred that the matching-based, optimization-based and Greedy

approaches achieve up to 96.8%, 82.6%, and 80.2% of the average sum rate obtained by the UB,

respectively for a network with 20 UEs. Thus, it is clear that the matching-based approach is

close to optimal. Furthermore, it can be observed that the sum rate increases with more UEs,


5 10 15 20 25 3030

60

90

120

Number of UEs

Ave

arge

sum

rat

e (M

bps)

M−DRAUBO−DRATier aware

Figure 2.9: Comparison of average sum rate.

which, however, saturates as the number of UEs becomes sufficiently large. This is because of the

limited number of resources at each SBS (r = 5). Additionally, the optimization-based approach

achieves a performance benefit up to 4% compared to the greedy approach while the matching-

based approach achieves 17% and 21% higher sum rate compared to the optimization-based and

greedy approaches, respectively for a network with 20 UEs.

2.7 Summary

In this work, we proposed two resource allocation algorithms for the two-tier heterogeneous net-

work, namely the optimization-based and matching-based algorithms. Distributed implementa-


tion of these algorithms have also been discussed in details. Numerical studies have shown that

the matching-based algorithm outperforms the optimization-based algorithm especially in the low

macro-tier interference limit. However, the performance of both algorithms is almost indistin-

guishable as the macro-tier interference limit becomes sufficiently large.

Chapter 3Resource Allocation in underlay Device-to-Device

Communications

3.1 Overview

Spectrum efficiency can be enhanced by enabling the D2D communication, thus, enhancing the

network throughput of existing networks. However, enabling D2D communication in an under-

lay fashion poses a significant challenge pertaining to interference management. In this research,

mode selection and resource allocation is studied for an underlay D2D network while providing

interference management. We formulate this problem as a combinatorial problem in which we

aim to maximize the utility of all D2D pairs. To solve this problem, a learning framework is pro-

posed based on a problem-specific Markov chain. From the local balance equation of the designed

Markov chain, the transition probabilities are derived for distributed implementation. Then, a

novel two phase algorithm is developed to perform mode selection and resource allocation in the

respective phases. This algorithm converges to a near-optimal solution. Moreover, to reduce the

computation in the learning framework, two resource allocation algorithms based on matching

theory are proposed to output a specific and deterministic solution. The first algorithm employs

the one-to-one matching game approach whereas in the second algorithm, the one-to many match-

ing game with externalities and dynamic quota is employed. Simulation results show that the

proposed framework converges to a near optimal solution under all scenarios with probability one.

Moreover, our results show that the proposed matching game with externalities achieves a perfor-

mance gain of up to 35% in terms of the average utility compared to a classical matching scheme

with no externalities.

38

CHAPTER 3. RESOURCE ALLOCATION IN UNDERLAY DEVICE-TO-DEVICE COMMUNICATIONS 39

3.2 Background and Contributions

To efficiently cope with the rapid increase in wireless traffic, device-to-device (D2D) communica-

tions over wireless cellular networks has emerged as a promising technique to boost the capacity

and coverage of tomorrow’s 5G systems [54, 86, 87]. Using D2D communication, a D2D trans-

mitter can directly transmit to the D2D receiver without routing its traffic through the cellular base

station (BS). The use of D2D communications over cellular networks can significantly improve

the network performance in terms of data offload [54, 88], content sharing/dissemination [89, 90],

energy efficiency [92], coverage extension [54], and improved spectrum efficiency [44, 93, 94].

However, reaping the benefits of D2D communications requires meeting significant challenges in

terms of resource allocation and interference management [45–47].

One of the most critical challenges in D2D is to manage the interference stemming from the

reuse of spectrum resources [86]. D2D links can use either the unlicensed spectrum (i.e, out-

band) [94] or the licensed spectrum (i.e., in-band) [45] for transmission. In both cases due to

spectrum reuse, the D2D transmission links can cause interference to other users in the network.

We focus on the use of in-band spectrum (i.e., cellular resources) for D2D communication, as

in-band D2D communication can provide better quality of service guarantees compared to the

out-band spectrum [44]. Furthermore, in an in-band D2D communication, cellular resources can

be allocated to D2D links in either an orthogonal manner, i.e., the D2D connections use reserved

resources (the dedicated mode or overlay), or in a non-orthogonal manner, i.e., the D2D connec-

tions use same resources as the cellular connections (the shared mode or underlay). In this work,

we adopt the underlay (shared) mode since it provides a much better spectral efficiency than the

dedicated mode, particularly in dense networks.

Then, our challenge is to manage the interference stemming from the reuse of cellular re-

sources between D2D links and regular cellular links. In such a D2D enabled network, both cross

tier (i.e., between a D2D pair and cellular user) and co-tier (i.e., between two D2D pairs when in

close proximity) interference can occur, which significantly degrades the network performance.

Moreover, unlike classical approaches for resource allocation, in a D2D enabled system, the num-

ber of choices for allocating resources exponentially increase as D2D pairs in network increase.

Thus, centralized solutions [45, 46] are not suitable which can incur massive overhead in terms of


CU 1CU 2

Cellular BS

D2D pair 1

D2D pair 2

D2D p

air 4

CU 3

D2D pair 3

D2D p

air 5

Figure 3.1: A downlink D2D communication system. The solid line shows the information linkswhile the dashed line shows the interference links.

required computation and signaling. Therefore, an efficient resource allocation scheme is required

that guarantees interference protection to cellular links and operates in a distributed fashion.

The main contribution of this research is to introduce a distributed scalable solution for a

dense D2D network by jointly addressing the problems of mode selection, resource allocation,

and interference management aspects. We propose a novel learning framework based on Markov

approximation to address these issues. Unsupervised learning is used for mode selection and a

two-sided matching game is incorporated to address the resource allocation aspects. The proposed

matching game is shown to reduce the computation and configuration size in the framework while

enabling a self-organizing and distributed control. Furthermore, we consider a practical scenario

in which a group of D2D pairs reuse the same resource simultaneously if the cellular transmission

protection can be guaranteed. In summary, our key contributions include the following:

• First, we formulate the joint problem of mode selection, and resource allocation with an

objective to maximize the utility of all D2D pairs subject to interference protection for

cellular transmission. The formulated problem is a mixed-integer non-linear optimization


problem that is NP-hard and requires exponential computation efforts to obtain the optimal

solution.

• Second, to solve the joint problem, we propose a learning framework based on Markov

approximation. Furthermore, we design an ergodic Markov chain and the transition proba-

bilities, which makes the Markov chain converge to its stationary probabilities. Using these

transition probabilities, we propose a novel two phase algorithm to perform mode selec-

tion and resource allocation in the respective phases. This distributed algorithm eventually

converges to the near optimal solution in probability with a bounded performance gap.

• Third, in order to reduce the computation and configuration size in Markov approximation,

we propose two algorithms for resource allocation based on matching theory. Furthermore,

we prove the stability, convergence, and optimality of the matching based resource alloca-

tion algorithms.

• Simulation results show the convergence, optimality gap, and utility gains achieved using

the proposed framework. Results show that the framework converges to a near optimal

solution. Moreover, our results show that the proposed matching game with externalities

achieves a performance gain of up to 35% in terms of the average utility compared to a

classical matching scheme with no externalities.

The rest of this chapter is organized as follows. In Section 3.3, we present our system model and

formulate our optimization problem. Section 3.4 describes in detail how we map the proposed

optimization problem into the learning framework and derive a distributed algorithm. Then, we

formulate the resource allocation problem as a matching game in Section 3.5 and present two

resource allocation solutions, i.e., partial-reuse mode and full-reuse mode in Section 3.5.1 and

Section 3.5.2, respectively. We present our simulation results in Section 3.6, and we summarize

this chapter in Section 3.7.


3.3 System Model and Problem Definition

Consider the downlink of a cellular network consisting of a single BS and a set K of K D2D pairs

located under its coverage, as shown in Fig. 1. The choice of downlink reflects the worst case

interference scenario.1 We use the index k0 to indicate the BS. We let set C be the set of C cellular

users. The BS and D2D pairs use the same setR ofR orthogonal resource blocks (RBs).2 For any

given RB r ∈ R, a predefined interference threshold Irmax must be maintained for protecting the

cellular users. Our system model is focused on a dense communication environment in which the

density of the users is higher than the number of connections that a given BS can support (e.g., a

football stadium). Typically, in such an environment, congestion occurs due to the high number of

connections. Therefore, D2D communication can be used to improve the area spectral efficiency

and increase the number of connected devices per shared RBs.

3.3.1 Resource Allocation and Link Model

In our model, the D2D transmissions are synchronized to the cellular transmissions. We assume

that all transmitters (BS and D2D pairs) transmit using a fixed power within the RB duration.

However, each transmitter can have its individual value for the power budget. In addition, we

assume that the transmit power of each transmitter is equally divided among its RBs and thus, the

interference power is constant. The D2D pairs at each time slot need to determine which RB is

feasible in order to maximize the utility of the system while protecting the cellular users. For RB

allocation, we introduce the binary variables xrk:

xrk =

1, if D2D pair k is assigned RB r,

0, otherwise.(3.1)

The received signal to interference noise ratio (SINR) pertaining to the transmission of the1The developed methodology can also be applied to the uplink case by simply considering the protection of cellular

BS.2One resource block can correspond to one sub-carrier of the OFDM-based LTE network.


D2D pair k over RB r with transmit power P rk is:

γrk =xrkP

rk g

rk

P rk0grk0,k

+∑

i∈Ωr,i 6=k xriP

ri g

ri,k + σ2

, (3.2)

where the RB gain over the link of D2D pair k is grk, gri,k represents the RB gain between D2D

pair i and D2D pair k, and grk0,k is the RB gain from the BS to D2D pair k. P rk0 and P ri , ∀i ∈ Ωr,

represent the transmit powers of the BS and the other D2D pairs, respectively, and Ωr is the set

of D2D pairs which are using RB r. Note that, the set of D2D pairs Ωr using RB r is updated

dynamically. The noise power is assumed to be σ2. Similarly, the SINR of cellular user c over RB

r is given as:

γrc =P rk0g

rk0,c∑

i∈ΩrxriP

ri g

ri,c + σ2

, (3.3)

where grk0,c and gri,c represent the RB power gains from the BS to cellular user c and D2D pair

i to cellular user c, respectively. Note that∑

i∈ΩrxriP

ri g

ri,c is the interference experienced by

the cellular user c from a set of D2D pairs Ωr that use RB r. Then, the data rate of any user

u ∈ K \ k0 ∪ C on RB r is represented as follows:

Rru = W r log(1 + γru), (3.4)

where W r is the bandwidth of RB r.

3.3.2 D2D Decision and Mode Selection model

Next, we present the models for D2D decision and mode selection used in our system. In the D2D

decision model, each D2D pair acts based on its achieved utility. The action here represents the

D2D decision to use a given mode or not. We assume that each D2D pair selfishly and rationally

acts in a way that maximizes its utility. Moreover, each D2D pair has knowledge of its own utility

functions. Therefore, each D2D pair only acts to maximize its own utility. A decision variable αk


is used to indicate if D2D pair k will follow a specific mode, as follows:

αk =

1, if D2D pair k uses the mode,

0, otherwise.

This D2D decision model assists the BS in the mode selection process. For mode selection,

we consider two modes that can be selected for RB allocation for the D2D pairs. Motivated by

the resource utilization gain achieved by the reuse mode, we only employ the reuse mode in our

model. However, we propose to classify the reuse mode for our network into two modes:

• Partial reuse mode: Only one D2D pair can be allocated to an RB currently in use by a

cellular user, only if the interference is below a pre-defined threshold. By using this mode,

there exists no co-tier interference (i.e., between D2D pairs). This mode is suitable for

scenarios in which the number of D2D pairs is limited compared to the RBs or the D2D

pairs are in close proximity with each other.

• Full reuse mode: A group of D2D pairs can share an RB only if the interference produced

by this group is below the predefined threshold for protecting the cellular tier. However, by

using this mode, co-tier interference will also occur. This mode is preferred in the scenario

where there exist a large number of D2D pairs compared to RBs. Moreover, this mode can

further enhance the RB efficiency, if co-tier interference is well handled.

However, in any given time slot only one mode will be activated for use in the network [52]. A

binary variable y is defined to represent the two modes, controlled by the BS:

y =

1, partial-reuse mode,

0, full-reuse mode.

In contrast to previous works [45, 48, 50] and [52], in our model, the BS does not choose a mode

for individual D2D pairs based on their channel conditions and buffer status. Here, the BS chooses

a mode depending upon the utility achieved by the network. This significantly reduces the com-

putational load since the BS will only need to calculate the network utility. However, to obtain the


utility for the network, the D2D pairs and BS need to respectively learn which D2D users can be

successfully admitted under which mode such that the global network utility is maximized.

3.3.3 Problem Formulation

Our goal is to maximize a utility function that captures the sum rate of the D2D pairs by selecting

the optimal mode for communication, admitting the best D2D pairs, and properly reusing the RBs

already occupied by the cellular tier. Therefore, we define the utility function of the D2D network

as follows:

U(y,α, x) =∑

k∈K

∑r∈R

[yαkRrk + (1− y)αkR

rk]. (3.5)

Here, we note that a D2D pair can only use a given RB if the interference level is less than

the predefined interference threshold Irmax set by the BS on each r. Moreover, the interference

experienced by cellular user c over RB r from a D2D pair k is given by Irk = αkxrkP

rk g

rk,c. Note

that the binary D2D decision αk and RB allocation variables xrk ensure that we only account for

the interference created by the D2D pair that use the given mode and is assigned the same RB.

Then our considered joint mode selection and RB allocation (JMARA) problem can be stated as

follows:

JMARA: maximizey,α,x

U(y,α, x) (3.6)

s.t.∑

r∈Rxrk ≤ 1, ∀k ∈ K, (3.7)

yαkIrk +

|Ωr|∑k=1

(1− y)αkIrk ≤ Irmax, ∀r ∈ R, (3.8)

xrk ∈ 0, 1 , ∀k ∈ K, ∀r ∈ R, (3.9)

αk ∈ 0, 1 , ∀k ∈ K, (3.10)

y ∈ 0, 1 . (3.11)

In JMARA, the first constraint (3.7) ensures that each D2D transmitter can be allocated to only

one RB. The condition in (3.7) is used to better manage the interference stemming from D2D


communications. The second constraint (3.8) ensures the protection of cellular user by keeping the

interference produced by D2D transmitters below a predefined threshold under either partial-reuse

mode (y = 1) or full-reuse mode (y = 0). Finally, the binary indicator variables for RB allocation

xrk, D2D decision αk, and mode selection y are represented by constraints (3.9), (3.10) and (3.11),

respectively. The problem JMARA is a non-convex, integer problem, which is difficult to solve in

practical settings with a large set of D2D pairs and RBs [63]. Thus, Markov approximation [56,57]

framework is used to find a solution for JMARA as it possess the capability to solve combinatorial

problems, which will be presented in the next section.

3.4 JMARA via Markov Approximation

Our proposed solution framework is composed of two steps. The first step is to create a log-sum-

exp approximation and the second step is to derive the Markov chain for our problem.

We let f = y,α, x be a network configuration and F be the set of all F feasible configura-

tions defined by constraints (3.7) and (3.8). We let Uf = U(y,α, x). Therefore, JMARA can be

written as

maxf∈F

Uf . (3.12)

However, Uf in not differentiable. Thus, we transform (3.12) from a discrete function of f to

an equivalent continuous function of pf (i.e., an equivalent maximum weight independent set

problem) as:

maxp≥0

∑f∈F

pfUf

s.t.∑f∈F

pf = 1,(3.13)

where pf represents the probability of choosing configuration f , i.e., the weight of the configura-

tion. pf can be viewed as the fraction of the time a configuration f is activated. Note that, both

problems given in (3.12) and (3.13) have the same optimal value [56]. However, (3.13) is still chal-

lenging to solve due to the combinatorial nature of the variables. Next, to solve this combinatorial


problem, we use the Log-sum-exp Approximation.

3.4.1 Step 1: Log-sum-exp Approximation

The Log-sum-exp function is a convex and closed function [56] mainly used by machine learning

algorithms as a smooth approximation of the max function. Therefore, we interpreted it as a

differentiable approximation of the max function given in (3.12) [63, pp. 72]. Hence, we have:

maxf∈F

Uf ≈ gβ(Uf ) =1

βlog

∑f∈F

exp(βUf )

, (3.14)

where β is a positive constant. Furthermore, the approximation gap is upper-bounded by F , where

F is the size of the set F , and Umax = maxf∈F

Uf , and then the approximation accuracy will be [63]:

0 ≤ |Umax − gβ(Uf )| ≤ 1

βlogF. (3.15)

Clearly, as β →∞, 1β logF → 0, which renders the approximation exact. The following problem

is equivalent to solving the log-sum-approximation in (3.14) [56, 63]:

maxp≥0

∑f∈F

pfUf −1

β

∑f∈F

pf log pf

s.t.∑

f∈Fpf = 1,

(3.16)

where the first term in (3.16) represents the MWIS objective and the second term represents the

entropy term. We can obtain the optimal probability distribution p∗ by solving the Karush-Khun-

Tucker (KKT) condition for the above problem [63], given as follows ∀f ∈ F :

p∗f (Uf ) =exp(βUf )∑

f ′∈Fexp(βUf ′)

=1∑

f ′∈Fexp(β(Uf ′ − Uf ))

, (3.17)

where (Uf ′ − Uf ) is the difference in utilities. The optimal solution in (3.17) presents an implicit

solution for (3.16) that differs from (3.13) by an entropy term − 1β

∑f∈F pf log pf . Furthermore,


the solution to (3.16) requires complete information of F . Thus, to find F , a computationally

exhaustive approach is needed, which is not practical.

3.4.2 Step 2: Markov Chain (MC)

The solution given in (3.17) is not practical since complete information on all feasible configu-

rations F is required, which is not possible as discussed in Section 3.1. Hence, we view (3.17)

as a Markov chain. To this end, each configuration f corresponds to a state with (3.17) being

its stationary distribution. Then, the goal is to derive the Markov chain for the problem given

in (3.16) and reach to the optimal stationary distribution given in (3.17) that represents its solu-

tion. From [56], it is shown that there exists at least one continuous-time time-reversible ergodic

Markov chain with stationary distribution p∗f (Uf ) for any probability distribution of the product

form p∗f (Uf ) presented in (3.17).

In order to construct a time-reversible Markov chain with stationary distribution p∗f (Uf ), we

let configuration f , f ′ ∈ F be the states of a time-reversible ergodic Markov chain and let q(f→f ′)

and q(f ′→f) denote the nonnegative transition rates from states f → f ′ and f ′ → f , respectively.

Then, the following two conditions are sufficient for the Markov chain design [56]:

• any two states are accessible from each other.

• the local balanced equation satisfies (3.18), ∀f, f ′ ∈ F ,

p∗f (Uf ) q(f→f ′) = p∗f ′(Uf ′)q(f ′→f),

exp(βUf )q(f→f ′) = exp(βUf ′)q(f ′→f).(3.18)

These equation are useful because they eliminates the need for all information of the complete

configurations space F . Any q(f→f ′) and q(f ′→f) values for the design of the algorithm can

be adopted as long as (3.18) is satisfied. Therefore, we limit the number of configurations to

f and f ′, i.e., F = f, f ′. We set the conditional probabilities as the transition rates, i.e.,

q(f ′→f) = p∗f |f,f ′(Uf ) and q(f→f ′) = p∗f ′|f,f ′(U′f ). Hence, we obtain

p∗f |f,f ′(Uf ) + p∗f ′|f,f ′(U′f ) = 1,

q(f ′→f) + q(f→f ′) = 1.(3.19)


Thus, by solving (3.18) and (3.19) we obtain the transition probabilities as a logistic function of

utility difference as

q(f→f ′) = (1 + exp[β(Uf − Uf ′)])−1, (3.20)

q(f ′→f) = (1 + exp[β(Uf ′ − Uf )])−1. (3.21)

These transition probabilities are used to derive the Markov chain towards the optimal solution

in (16). However, we cannot design a distributed and scalable algorithm using (3.20) and (3.21),

which use the global utility, i.e., Uf . As we know that the network is distributed in nature, a player

k is only aware of its own individual local utility Ufk without additional signaling and overhead.

Therefore, we define Uk,fk = Uk(m,αk, xk) as the local utility for each player k. Then, we

substitute the local utilities in (3.20) and (3.21) to obtain

q(fk→f ′k) = (1 + exp[βk(Uk,fk − Uk,f ′k)])−1, (3.22)

q(f ′k→fk) = (1 + exp[βk(Uk,f ′k − Uk,fk)])−1. (3.23)

Hence, the Markov chain based on using these local utilities converges to a distribution pf (Uf )

instead of p∗f (Uf ) given in (3.17). However, the gap between this distribution pf (Uf ) and the

optimal p∗f (Uf ) is also bounded [57, 58].


Algorithm 3: Learning Algorithm (LA)

1: initialize: i[1] ← 0, y[1] ← rand ∈ 0, 1,

Υk(1)← 0, ωk ← 1, βk(1)← 1, ∀k.

αk[1] , [∅]k∈K, xk [1] , [∅]k∈K.

2: while t 6= T and D 6= ∅ and ω0 > 0 do

Phase 1: Mode Selection

3: if i[t] 6= 1 then

4: y, α[t+1]k ←

randy, αk with prob. ωk,

y, α[t]k with prob. 1− ωk.

5: else

6: Calculate ν ← q(fk→fk′) using (3.22).

7: y, α[t+1]k ←

y, α[t−1]

k with prob. ν,

y, α[t]k with prob. 1− ν.

8: βk(n+ 1)← βk(n) ∗ βstep.

9: Υk(n− 1)← Υk(n).

10: Υk(n)← y, α[t+1]k .

11: if Υk(n− 1) = Υk(n) then

12: ωk ← max0, ωk − ωstep

13: i[t+1] ← 1− i[t]

Phase 2: Resource Allocation:

14: if y[t+1] = 1 then

15: Run Alg. 4 for α[t+1] to obtain x[t+1].

16: else

17: Run Alg. 5 for α[t+1] to obtain x[t+1].

18: Calculate utility U [t+1]k,fk

,∀D.

Phase 3: Update:



20: if ωk = 0 then

21: D ← D \ k.

3.4.3 Learning Algorithm

Next, based on the analysis of the Markov chain in Section 3.4.2, we present the learning algorithm

shown in Alg. 3 for solving the modeled Markov chain. The algorithm consists of three phases:

(i) the mode selection phase (lines 3-13), (ii) resource allocation phase (lines 14-18), and (iii)

update phase (line 19-21) as illustrated in Fig. 3.2. In Phase 1, we use unsupervised learning

using the logistic equations given by (3.22) and (3.23). The learning approach uses properties

from log-linear learning [95] and simulated annealing [96] for selection of the control variables

action (i.e., y and α). For our scenario, the BS chooses the mode action and all D2D pairs choose

their admission action. In Phase 2, resource allocation (i.e., x) is performed (details of resource

allocation are presented in Sec. 3.5), for the given mode and D2D pairs that decide to use this

mode. Once the first two phases are executed, all control variables are updated in Phase 3.

In line 1 of Alg. 1, all the control variables and the auxiliary variables are initialized. We intro-

duce the auxiliary variables as Υk = [Υ1, ...,Υ|n|], i[t], βk and ωk. Here, these auxiliary variables

are used to control the mixing characteristics and stopping time for the underlying Markov chain.

The vector Υk is used for convergence analysis, and i[t] is an experimentation indicator that indi-

cates whether or not experimentation takes place at time slot t. βk controls the gap given in (3.15)

and ωk balances between exploration and exploitation rates. As explained earlier, as βk →∞, the

gap 1βk

logFk → 0 and the βk update control the mixing of the Markov chain, which can be either

linear or geometric. We implement the geometric update (line 8), which gradually yields zero gap.

The learning algorithm starts by the BS (i.e., k0) selecting a random mode y[1] (i.e., partial or

full-reuse mode) when there exists no configuration (line 1). In Phase 1, the set of players D ⊆ K

either performs experimentation or consolidation. In experimentation, for time slot t + 1, each

player executes one of the two actions, i.e., a new random configuration is chosen (exploration)

or it stays with the current configuration (exploitation) with probability ωk or 1−ωk, respectively

(line 4). During consolidation, the current utility obtained at time slot t is compared with the

previously achieved utility at time slot t−1 by all players. Then, each player probabilistically (i.e.


with probability ν) chooses its action for time slot t+ 1. Furthermore, the actions that achieve the

maximum utility have a higher probability to be chosen (lines 5-7). Furthermore, as the Markov

chain moves towards convergence (line 11), we reduce the exploration rate by a constant step

size (line 12). Note that all players are aware of the their own utility received, the configuration

employed for the last two time slots, and whether or not they experimented in the last time slot.

After Phase 1 is completed for time slot t + 1, Phase 2 starts. In this phase (details of this

phase are presented in Section 3.5), based on the players actions, a resource allocation algorithm

is executed to obtain the resource allocation vector x[t+1] (lines 14-17). Then, the utility of con-

figuration U [t+1]k,fk

is evaluated for all players D.

Finally, we update both the the control variables in Phase 3 for the next time slot. Moreover, as

the exploration rate ωk approaches zero, we remove the player from learning, as it operates in the

best configuration (lines 20-21). These three phases are repeated until convergence (line 2), i.e.,

the Markov chain reaches the stationary state. Moreover, in our learning framework, the matching

algorithm outputs a specific and deterministic solution for resource allocation. This matching

outcome is then used in the learning framework as a joint configuration with D2D decision and

mode selection. Since, the overall framework is based on an ergodic Markov chain, after sufficient

time slots T , converges to a near optimal solution is achieved in probability [56], [58] and [59].


Experimentation Consolidation

If experimented

at tTrue

False

Phase 1: Mode Selection

Phase 2: Resource Allocation

If

Choose randomly

True Flase

Choose configuration at

time (t-1)

Calculate transition

probability using (21),

Generate a random

number

IfTrue

Choose flow

configuration at time (t)

Flase

( )k t

[ 1] , , t

k ky rand y

( )t

0 1

( )t

[ 1] [ ] , , t t

k ky y[ 1] [ 1] , , t t

k ky y

Phase 3: Update[ 1] [ 1] [ 1], ,t t t

k ky x

If[ 1] 1ty

Full Reuse Mode: Partial Reuse Mode[ 1]t

kx[ 1]t

kx

Start

If

False

TrueStop0k

[ ]i 1t

Generate a random

number

0 1

Choose flow

configuration at time (t)

[ 1] [ ] , , t t

k ky y

TrueFalse

Figure 3.2: Block diagram of learning algorithm (LA).


3.5 Resource Allocation via Matching

Once Phase 1 of Alg. 3 is executed, we obtain the mode y as well as the D2D pairs α that use

the selected mode at time slot t + 1. The next goal here is to perform RB allocation for the

given mode and D2D pairs. For a given mode selection variable y, problem JMARA can be

divided into two combinatorial problems, depending upon the value of y. In this section, we apply

matching theory for solving these problems under two cases: the partial-reuse or the full-reuse

modes. The motivation to apply matching theory for the RB allocation problem is its ability to

tackle combinatorial problems and achieve a distributed solution [81,98]. The benefits of matching

theory come from the distributed nature of control in the system. Furthermore, matching theory

allows each player (i.e., D2D pairs and RBs) to define its individual utilities depending upon its

local information.

3.5.1 Case 1: Partial-Reuse Mode

In the partial reuse mode, i.e., y = 1, only one D2D pair can use an RB if the interference level is

less than the predefined interference threshold Irmax set by the BS. Then, we can state the following

problem, as derived directly from JMARA:

PR: maximizexrk∈x

∑r∈R

∑k∈K

Rrk (3.24)

subject to (3.7), (3.9),

Irk ≤ Irmax, ∀r ∈ R. (3.25)

In PR, the objective is reduced to maximizing the sum-rate of all D2D pairs by assigning the RBs.

The constraint given by (3.25) ensures the protection of cellular users by keeping the interference

produced by the D2D transmitter below a predefined threshold. This allows the re-usability of an

RB r to increase RB efficiency if the interference constraint can be maintained. Problem PR is still

a combinatorial problem, and finding the solution becomes NP-hard, for a large set of D2D pairs

and RBs in a practical amount of time [63]. Note that PR is desired to be solved in a distributed


manner by each D2D pair such that it maximizes its own rate. Therefore, we use matching theory

to map the problem PR into a matching game and then discuss the details of the solution in the

following subsections.

3.5.1.1 Matching Game Formulation

Next, the RB allocation problem is formulated as a two-sided matching game, then we define the

utility and finally present a matching algorithm that achieve a stable solution.

We assume each D2D pair forms a set that can use a single RB. However, to use this RB, the

interference produced by D2D pairs to RBs should be under the tolerable predefined interference

level, i.e., constraint (3.25). Similarly, every RB also forms a set to accommodate a D2D pair

among all the pairs. Therefore, our design corresponds to a one-to-one matching given by the

tuple (K,R,K,R). Here,K , kk∈K andR , rr∈R represent the set of preference

relations of D2D pairs and RBs, respectively. Formally, we define the matching as follows:

Definition 3 A matching µ is defined by a function from the set K ∪

R into the set of elements of K ∪R such that k = µ(r) if and only if r = µ(k).

3.5.1.2 Preference Profiles of Players

Matching is performed by the two sets of players using preference profiles. For each player, the

preference profile is used to rank the players of the opposite side. In the proposed game, the two

sides, D2D pairs and RBs, will build their preference profiles by utilizing local information avail-

able at each side. The preference profile for the D2D pairs is based on the following preference

function of the achievable data rate on RB r:

Uk(r) = W r log(1 + γrk). (3.26)

The intuition for such a preference function comes from the objective of problem PR, where each

D2D pair wants to maximize its sum rate. Hence, each D2D pair ranks all the RBs r in a non-

increasing order in its preference profile represented by Pk. Note that an RB r ∈ R that produces

a higher utility (consequently the data rate achieved by using the more preferred RB is higher)


according to (3.26) will be preferred over an RB r′ ∈ R by a D2D pair k, i.e., r k r′, for

carrying out its transmission and will thus be placed higher in its preference profile.

Similarly, each RB r also needs to have a preference profile that ranks all the D2D pairs k ∈ K

according to its preference function. By using a two-sided matching game for our problem so

we can guarantee cellular tier protection by the RB defined preferences. This is important for the

proposed game to guarantee (3.25). This is one of the main motivations for using a two-sided

matching game for our problem. Moreover, the preference list for each RB is formed by the

BS. The information required at the BS includes the power level of the D2D transmitters pk, the

predefined maximum interference threshold Irmax for each RB, and the RB power gain between the

D2D transmitter and cellular user grk,c. The preference function is given by:

Ur(k) = max (Irmax − Irk , 0). (3.27)

According to this preference function, an RB gives less utility to a D2D pair k, which creates

more interference. Additionally, all D2D pairs that violate (3.25) receive a zero utility and are

ranked as the lowest in the preference profile of r. Furthermore, to calculate the ranking of each

D2D pair, the BS for each r needs to calculate the interference Irk induced by the D2D pair k if an

RB r is in use. As we assume the power levels of the D2D pair are fixed and known to the BS, the

calculation of Irk only depends on the RB gain grk,c.

Here, we note that RB power gain grk,c can be estimated by cellular users and sent back to the

BS by using the pilot signal or any standard RB estimation technique. The total interference for

each cellular user can be estimated as follows. All cellular users estimate the total received power

and send this value to the BS. The BS can then calculate the interference induced by the D2D pair

on RB r. Therefore, calculation of the interference only requires the standard RB estimation of

grk,c. In addition, signaling is only involved in sending these values from the cellular user to the

BS, which only occurs once during the initialization phase. Once this information is acquired,

Irk is calculated and the BS ranks each D2D pair k for each RB r in the preference profile of r

represented by Pr.


3.5.1.3 Resource Allocation Algorithm

We present the RB allocation algorithm based on the proposed matching game. The aim of this

algorithm is to find a stable allocation that is a key solution concept in matching theory [84, 99]

and can be defined as follows:

Definition 4 A matching µ is stable if there exists no blocking pair (k, r), where k ∈ K, r ∈ R,

such that r k µ(k) and k r µ(r), where µ(k) and µ(r) represent, the current matched partners

of k and r, respectively.

In our game, a stable solution ensures that no matched D2D pair would benefit from deviating

from their assigned RB r with a new RB r′. The output of our algorithm is the RB allocation vector

x of D2D pairs that maximizes the objective of the optimization problem PR, and the pseudo code

is given in Alg. 4. The presented algorithm converges to a stable allocation as it is a variant of the

well-known deferred acceptance algorithm [84].

Alg. 4 has three phases namely, the initialization phase, the matching phase and the RB alloca-

tion phase. In the initialization phase, information on the active D2D pairsα and local information

required is attained to build the preference profiles (lines 1-3).

In the second phase matching, each unassigned D2D pair k proposes to its most preferred

RB r according to Pk (lines 7-8). The BS determines the interference Irk produced and evaluates

(3.25). If (3.25) is violated, the D2D pair k is rejected. Otherwise, the BS checks the preference

ranking of the resource r. If ranked higher than the current match (µ(r)t), the D2D pair k will

be accepted. Otherwise, it will be rejected. Finally, all the rejected D2D pairs at iteration t, i.e.,

the set Lr(t), are removed by both sides in order to update their preference profiles. The matching

process is carried out iteratively until a stable match is found between both sides. The process will

terminate when all the D2D pairs that can maintain the interference tolerance level are assigned to

RBs or there are no more RBs to propose. The algorithm will converge when the matching of two

consecutive iterations t remains unchanged (lines 4-22) [84]. The final stage is the RB allocation

phase in which the matched D2D pairs are allowed to transmit on the matched RBs (lines 23-24).


Algorithm 4: Partial Reuse-mode Resource Allocation Algorithm

1: Phase 1: Initialization:

2: input: α, Pk, Pr, ∀r, k.

3: initialize: t = 0, µ(t) , µ(k)(t), µ(r)(t)k∈K,r∈R = ∅, Lr(t) = ∅ Pk(0) = Pk, Pr(0) = Pr,

Irmax, ∀r, k.

4: Phase 2: Matching:

5: repeat

6: t← t+ 1.

7: for k ∈ K, propose r according to Pk(t) do

8: while k /∈ µ(r)(t) and P(t)k 6= ∅ do

9: if Irmax ≥ Irk then

10: if k r µ(r)(t) then

11: µ(r)(t) ← µ(r)(t) \ k′.

12: µ(r)(t) ← k.

13: P ′(t)r = k′ ∈ µ(r)(t)|k r k′.

14: else

15: P ′′(t)r = k ∈ K|µ(r)(t) r k.

16: else

17: P ′′′(t)r = k ∈ K|Irmax ≤ Irk.

18: Lr(t) = P ′(t)r ∪ P ′′(t)r ∪ I ′

(t)r .

19: for l ∈ Lr(t) do

20: Pl(t) ← Pl(t) \ r.

21: Pr(t) ← Pr(t) \ l

22: until µ(t) = µ(t−1). Phase 3: Update:

23: output: µ(t).


Initialize:


Propose: Each user proposes to its most favorite resource


Accept/reject: Each resource keeps the most favorite users w.r.t. its PL

from the proposals; and reject the rest;

Terminate: A stable matching between users and

resources.

Yes

No

Figure 3.3: Partial Reuse-mode Resource Allocation Algorithm.


Theorem 2 The stable solution resulting from Alg. 4 is also a local maximum of the PR problem.

Proof We prove that the stable point produced as an outcome by Alg. 4 is also a local maximum

for the PR problem. As the objective function of PR is used to maximize the utility of all the D2D

pairs, then the outcome of Alg. 4 at each iteration t can be mapped to the RB allocation vector x

as follows:

µ(t) 7→ x(t). (3.28)

Note that the utility for an RB allocation vector x for all D2D-RB pairs can be represented as

follows:

U(x) =∑r∈R

∑k∈K

Rrk(x). (3.29)

Then, based on the reject/accept operation at each iteration t in Alg. 4, the matching µ cap-

tures the value of∑

r∈R∑

k∈KRrk(x), in which the matching at the t-th iteration guarantees that∑

r∈R∑

k∈KRrk(x)(t) ≥

∑r∈R

∑k∈KR

rk(x)(t−1). This gives us the following relation:

U(x(t)) ≥ U(x(t−1)). (3.30)

Thus, we can see that the objective function of problem PR is captured using a non-decreasing

function with the binary variable x in the reject/accept operation of Alg. 4. Then, the matching

algorithm converges to a local maximal value of the problem PR.

3.5.2 Case 2: Full-Reuse mode

In the full-reuse mode, i.e., y = 0, the BS allows a set of D2D pairs to reuse the RB with a cellular

user in such a manner that this allocation does not violate the interference constraint, i.e., Irmax set


by the BS. Then, we can state the following problem:

FR: maximizexrk∈x

∑r∈R

∑k∈K

Rrk (3.31)

subject to (3.7), (3.9),∑|Ωr|

k=1xrkP

rk g

rk,c ≤ Irmax . (3.32)

Similar to problem PR, the objective in FR is to maximize the sum rate of all D2D pairs. However,

in FR, the constraint given by (3.32) reflects reuse of the same RB by a set of D2D pairs Ωr only

if the interference is not violated (i.e., Irmax) over RB r. The formulated problem FR is also a

combinatorial problem and solving FR is an NP-hard problem, i.e., the complexity of FR will

remain intractable for a sufficiently large set of RBs and D2D pairs. This motivates the use of

matching theory.

3.5.2.1 Matching Game Formulation

Similar to the partial-reuse mode, in the full-reuse mode there are also two disjoint sets of agents,

the set of RBs, R, and the set of D2D pairs, K. Each RB r has a strict, transitive, and complete

preference profile Pr defined over D2D pairs, i.e., 2K. Note that under the full-reuse mode, D2D

pairs can operate on the same RB, which can cause severe interference to cellular users as well

as other D2D pairs operating on the same RBs. This can be observed from (3.2), the SINR of a

D2D pair k. From (3.7), it is given that each D2D pair can use a single RB. However, different

D2D pairs can use the same resource to improve RB efficiency. Therefore in full-reuse mode, the

preference profile Pk of D2D pairs is defined over the RBs, i.e., R. Note that, other D2D pairs

k′ operating on that RB implicitly affect the preference ranking of the D2D pair k. Therefore,

our design corresponds to the one-to-many matching given by the tuple (K,R,K,R). Here,

K , kk∈K and R , rr∈R represent the set of preference relations of the D2D pairs

and RBs, respectively. Formally, we define the matching as follows:

Definition 5 A matching µ is defined on the set K ∪R, which satisfies for all r ∈ R and k ∈ K:

1. |µ(k)| ≤ 1 and µ(k) ∈ R ∪ φ,


2. |µ(r)| ≤ qr and µ(r) ∈ 2K ∪ φ,

3. If k ∈ µ(r) then µ(k) = r,

4. If µ(k) ∈ r for RB r then µ(r) =M,

where qr denotes the quota of RB r,M ⊂ K denotes the set of acceptable D2D pairs who prefer

r, and |µ(.)| denotes the cardinality of the matching outcome µ(.). Then, the first two conditions

here represent constraints given by (3.7) and (3.32), respectively, where qr represents the total

tolerable interference Irmax of RB r. Note that, by using qr, which represents the total tolerable

interference, we can make a decision on the number of D2D pairs that can be allocated a given

RB r without violating condition (3.32). Here, µ(k) = φ means that k is not matched to any RB.

Similarly, if µ(r) = φ, then there are no D2D pairs matched to RB r.

3.5.2.2 Preference Profiles of Players

Similar to the partial-reuse mode in the full-reuse mode, the agents on both sides need to rank each

other using the preference profile. However, the preference profiles of D2D pairs here depend on

the RBs as well as other D2D pairs assigned to that RB. externalities are such relationships which

are interdependent [81]. Due to these externalities, an agent changes its preference order based on

matching formation of other agents and thus agents may never reach to a final RB allocation.

In order to build the preference profile of D2D pairs, each D2D pair calculates the achievable

data rate for each RB and then ranks them in a descending order. The following preference function

is used by each D2D pair:

Uk(r, µ) = W r log(1 + γrk). (3.33)

Note that, channel gains in LTE-A system are acquired for sub-bands (i.e., group of RBs) rather

than for each RB [100]. Then, each D2D pair k will have the same preference over that group

of RBs, i.e., the RBs with same gains will result in the same achievable rate, thus, creating ties

among these RBs in D2D’s preference list. We can simply break all such ties in any arbitrary way

and rank them in a strict order to achieve a stable allocation [101]. Thus, for any D2D pair k, a


preference relationk is defined over the set of RBsR such that, for any two RBs i, j ∈ R, i 6= j,

and two matchings µ and µ′ ∈ K ×R, i = µ(k), j = µ′(k),

(i, µ) k (j, µ′)⇔ Uk(i, µ) > Uk(j, µ′). (3.34)

Similarly, each RB r creates its preference profile by using the following preference function:

Ur(M, µ) = maxi|Mi| : IrMi

≤ Irmax. (3.35)

According to (3.35), each RB r chooses a subset of D2D pairs M such that the interference

produced by M is less than the tolerable interference threshold Irmax. This preference function

maximizes the number of elements inM, i.e., it maximizes the D2D pairs. Note that this allows

the D2D pairs that produce the lowest interference to be preferred by RB r. The subset with

the highest number of elements is the most preferred among all the feasible subsets and ranked

accordingly. Moreover, for any RB r, a preference relation r is defined such that for any two

subsets of D2D pairsM,N ∈ K, whereM 6= N , andM = µ(r),N = µ′(r):

(M, µ) r (N , µ′)⇔ Ur(M, µ) > Ur(N , µ′). (3.36)

Once the matching game and preference profile of both agent sides have been defined, we now aim

to find a stable RB allocation scheme for the proposed game. However, it is evident from (3.33)

and (3.35) that our preferences are a function of the existing matching µ, and from (3.2), it is clear

that the D2D pairs affect each others performance through co-tier interference. Therefore, in the

next subsection, we present a novel approach adopted to handle such externalities.

3.5.2.3 Preferences and Externalities

Next, we develop a novel approach to handle externalities in the proposed game and analyze its so-

lution. In the proposed game, if D2D pair k is assigned to a RB r, it will produce interference with

the cellular user as well as with the neighboring D2D pairs using the same RB r. Consequently,

an agent (D2D pair) may change its preference order with regards to a given RB r in response to


the action of other agents, i.e., D2D pairs k′ that have been assigned to RB r. This may lead to a

situation in which agents never reach a final allocation.

Therefore, to build D2D pair preferences that can also handle the externalities, we represent the

initial D2D network as an interference graph. To deal with the externalities caused by neighboring

D2D pairs, we use an approach similar to [102], [103]. In a graph, the nodes represent D2D pairs,

and the edges indicate the interference between connected nodes. We assume that each D2D pair

first evaluates its interfering neighboring D2D pairs. This can be done by assuming two D2D pairs

i and k are connected by an edge that satisfies the following condition, i.e., the required signal

ratio to the interference signal is below a threshold ζk:

Pkgrk

Pigri,k≤ ζk.

Here, ζk is the predefined thresholds of D2D pair k selected to determine the severity of the

interference. This indicates that D2D pair k cannot share the same RB with D2D pair i if an edge

exists. Once all the interfering D2D pairs are identified for each D2D pair, the D2D pairs send this

set to the BS. We call this set as a conflict set for a D2D pair k and denote it as follows:

Ck =

k′ ∈ K :

Pkgrk

Pigri,k≤ ζk

. (3.37)

The main idea here is to restrict the reuse of RBs between D2D pairs who are very close to each

other, as this will cause instability and will have an adverse effect on the network.

3.5.2.4 Resource Allocation Algorithm

In order to find a stable RB allocation scheme, first, we need to define the blocking pair. However,

in our formulated game there is an additional challenge of dynamic quota, i.e., the BS allows a

number of D2D pairs (with heterogeneous interference) to use each RB as long as the interference

constraint on that RB is not violated. This heterogeneous interference of D2D pairs and dynamic

quota of resources introduces new challenges in the game similar to [85]. Moreover, our formu-

lated game has the additional challenge of externalities, which is not addressed in [85]. Therefore,

the blocking pair for the formulated game with dynamic quota and externalities is defined as fol-


lows:

Definition 6 A matching µ is said to be stable if there exists no blocking pair (k, r) such that:

a. Irres ≥ Irk , k r ∅, r k µ(k), and µ(r) /∈ Ck,

b. Irres < Irk , Irres +

∑k′∈µ(r) Ik′

r ≥ Irk , k r k′, r k µ(k), and µ(r) /∈ Ck,

where Irres = Irmax −∑

k∈µ(r) Irk represents the residual of the interference tolerance (remaining

quota) on RB r. The quota of an RB r ∈ R is filled when Irres < Irk for a requesting k ∈ K.

Definition 6 is based on the following intuition. Whenever a D2D pair k prefers an RB r over its

assigned RB µ(k) that does not contain a conflicting D2D pair (i.e., µ(r) /∈ Ck), if either: i) r

has sufficient interference tolerance Irres and is willing to accept k (i.e., k r ∅), or ii) its quota

is filled but it is able to accept k by rejecting some accepted D2D pairs which are ranked lower

than k, then k and r can deviate from their assigned matching to form a blocking pair. A stable

matching represents a matching if no blocking pairs exist.

In contrast to the partial reuse mode, here, the preference profile of the D2D pairs are interde-

pendent through the interference terms, as seen in (3.2). Therefore, to achieve stability, a sufficient

condition is that the formation of any new D2D-RB pair does not undermine the stability of ex-

isting matched D2D-RB pairs. By employing such a condition, the preference profile of currently

matched D2Ds on an RB will remain unaltered even after this new pair formation. Stability in our

solution ensures that after RB allocation, no matched pair (D2D-RB) in the network would deviate

from their assigned RB with a new better RB and vice versa.

Algorithm 5: Full Reuse-mode Resource Allocation Algorithm

1: input: α, P(t)k , P(t)

r , Ck, ∀r, k.

2: initialize: t = 0, µ(1) , µ(k)(1), µ(r)(1)k∈K,r∈R = ∅, Irres(1) = Irmax, Jr(1) = ∅, C(1)r = ∅,

∀r, k.

3: t← t+ 1.

4: Update ∀k, Pk(t) for given µ(r)(t−1).

5: ∀k ∈ K with r as its most preferred in P(t)k


6: while k /∈ µ(r)(t) and P(t)k 6= ∅ do

7: if Irres(t) < Irj , then

8: P ′(t)r = k′ ∈ µ(r)(t)|k r k′.

9: jlp ← the least preferred k′ ∈ P ′(t)r .

10: while (P ′(t)r 6= ∅) ∪ (Irres(t) < Irj ) do

11: µ(r)(t) ← µ(r)(t) \ jlp, P ′(t)r ← P ′(t)r \ jlp.


(t) + Irjlp .

13: if Irres(t) < Irj , then

14: jlp ← k

15: else

16: if C(t)r = k′ ∈ µ(r)(t) ∪ Ck = ∅, then

17: µ(r)(t) ← µ(r)(t) ∪ k, Irres(t) ← Irres

(t) − Irk .

18: else

19: D(t)r = k′ ∈ C(t)

r |k r k′.

20: for jlp ∈ D(t)r do

21: µ(r)(t) ← µ(r)(t) \ jlp.


(t) + Irjlp .

23: if C(t)r = k′ ∈ µ(r)(t) ∪ Ck = ∅, then

24: µ(r)(t) ← µ(r)(t) ∪ k, Irres(t) ← Irres

(t) − Irk .

25: else

26: jlp ← k.

27: Jr(t) = j ∈ Pr(t)|jlp r j ∪ jlp.

28: for j ∈ Jr(t) do

29: Pj(t) ← Pj(t) \ r, Pr(t) ← Pr(t) \ j

30: output: µ(t).


Initialize:


Propose: Each user proposes to its most favorite resource; and

delete it from its PL;


Accept/reject: Each resource keeps the most favorite users w.r.t. its PL,

Conflict graph and quota from the proposals; and reject the rest;

Terminate: When two matching are same, it

converges

Yes

Up

dat

e P

refe

ren

ce b

ased

on

pre

vio

us

mat

chin

g

Figure 3.4: Full Reuse-mode Resource Allocation Algorithm.


Next, we present a novel and stable RB allocation algorithm. The algorithm starts by using the

local information to build the preference profiles (lines 1-3) similar to Alg. 4. At each iteration t,

each D2D pair k, first calculates its utility and ranks all the RBs based on the previous matching

µ(r)(t−1) (line 4). Then, each D2D pair k proposes to the most preferred r, which can result in

either of the two following cases.

The first case is when r does not have sufficient quota Irres(t) to accept k, and so r then finds the

current matched D2D pairs that rank lower than D2D pair k according to Pr(t) (lines 7-9). Each

of the least preferred D2D pairs k′ is sequentially rejected until either k can be accepted or there

is no additional k′ to reject (lines 10-12). If sufficient quota to accept k is not created, then k is

also rejected and considered as the least preferred D2D pair represented by jlp (lines 13-14).

The second case is when the quota of r is enough to accommodate k, in which it then checks the

conflict set Ck. If the conflict set is empty, the D2D pair k is accepted (lines 15-17). Otherwise, it

removes all lower ranked conflicting D2D pairs compared to D2D pair k from its current matching

(lines 18-22). If the conflict set is still non-empty, the D2D pair k is rejected and is considered as

the least preferred jlp (lines 23-26).

Finally, the least preferred D2D pair jlp and all D2D pairs ranked lower than jlp are removed from

Pr(t), and similarly these D2D pairs also remove r from their respective Pk(t) (lines 27-29). With

this process, we guarantee that any less preferred D2D pair will not be accepted by that RB even

if it has sufficient quota to do so, which is crucial for the matching stability of our design. This

process is repeated until the matching converges. The algorithm will converge when the matching

of two consecutive iterations t remains unchanged.

Theorem 3 Alg. 5 converges to a stable allocation.

Proof We prove this theorem by contradiction. In any iteration t, assume that Alg. 5 produces a

matching µ(t) with a blocking pair (k, r) according to Definition 4. Then, we have, k r(t) µ(r)

and r k(t) µ(k) at iteration t. Therefore, we prove that these two conditions k r(t) µ(r) and

r k(t) µ(k) cannot hold simultaneously.

Assuming r k(t) µ(k), this implies that D2D pair k must have proposed to RB r according to the

Alg. 5. However, the matching result µ(k)(t) 6= r represents that r prefers µ(r) to k at iteration

t, i.e., µ(r) r(t) k. According to Alg. 5, a proposing pair k can be rejected due to the following


two reasons:

1. D2D pair k gets rejected due to the quota limitation, i.e., Irres < Ik (lines 7-14 of Alg. 5).

This can only occur when φ r k. This implies RB r remains unmatched rather than

accommodating D2D pair k. Furthermore, when k was rejected, any lower ranked D2D pair

k′ was also either rejected before D2D pair k (lines 10-12 of Alg. 5) or was made unable to

propose because r is removed from all lower ranked D2D pairs preference list (lines 27-29

of Alg. 5).

2. D2D pair k gets rejected due to the current matched D2D pair, µ(r) (lines 18-26 of Alg. 5).

This states that RB r has sufficient quota to accommodate D2D pair k, but it also belongs

to the conflict set of current matched D2D pair (i.e., k ∈ Cµ(r)) and satisfies µ(r) r(t) k,

i.e., the current matched D2D pair µ(r) is ranked higher than the proposing pair k in the

preference profile of RB r (Pr).

Despite that k prefers to be matched with r rather than µ(r), r still prefers to be matched with

µ(r) rather than k, i.e., the condition k r(t) µ(r) does not hold when r k(t) µ(k). Similarly,

we can prove that the condition r k(t) µ(k) does not hold if k r(t) µ(r). Hence, D2D pair k

and RB r cannot form a blocking pair, and the matching obtained at each iteration t by Alg. 5 is

stable.

The optimality property of the stable matching approach can be observed using the definition of

weak Pareto optimality [104]. Let U(µ) denote the utility obtained by matching µ. A matching

µ is weak Pareto optimal if there is no other matching µ′ that can achieve a better utility, i.e.,

U(µ′) u∑

r∈R∑

k∈KRrk(µ′) ≥ U(µ) u

∑r∈R

∑k∈KR

rk(µ′). Formally, we state this as

follows:


Definition 7 A matching µ is weak Pareto optimal (PO) if there is no other matching µ′ with

U(µ′) ≥ U(µ) [104].

Theorem 4 Alg. 5 produces a weak PO solution for the FR problem.

Proof Let us consider µ(t) to be the stable match obtained by Alg. 5 at iteration t. Assume µ′(t)

be a new arbitrary unstable matching that is better than µ(t) in that it achieves a higher utility for

all D2D-RB pairs, i.e., U(µ′) u∑

r∈R∑

k∈KRrk(µ′(t)) ≥ U(µ) u

∑r∈R

∑k∈KR

rk(µ

(t)).

Since µ′ is unstable, then, there exists at least one blocking pair. Let D2D-RB pair, i.e., (k, r)

be a blocking pair. Then, from Definition 5, we have two cases:

1. Irres ≥ Irk , k r ∅, r k µ(k)′, and µ(r) /∈ Ck.

For case 1, Alg. 5 will construct a new stable matching µ by assigning RBs r to D2D pair k instead

of the currently assigned RB µ(k)′. This increases the utility compared to the current match µ′,

i.e., since all other utilities are left unchanged in µ′, this shows that U(µ) ≥ U(µ′).

2. Irres < Irk , Irres +

∑k′∈µ(r) Ik′

r ≥ Irk ,

k r k′, r k µ(k), and µ(r) /∈ Ck.

For case 2, Alg. 5 will construct a new stable matching µ by removing low ranked D2D pairs

k′ from RB r, and then assigning RB r to D2D pair k. Since a lower ranked D2D pair k′ is

replaced with a higher ranked D2D pair k, the utility obtained by µ will be grater than µ′, i.e.,

U(µ) ≥ U(µ′). Hence, under both cases, the unstable matching µ′ is replaced by the new matching

µ. Thus, from the above arguments, we conclude there is no unstable matching µ′ that can achieve

better utility compared to a stable matching µ. Then, based on Definition 5, µ produced by Alg. 5

is a stable outcome and a weak PO allocation for the problem FR.

3.5.3 Computation Complexity and Implementation

In order to quantify the computational complexity of Alg. 4 and Alg. 5, first, we discuss the

complexity of building the preference profile by both set of players (i.e., D2D pairs and RBs) that

are the input to Alg. 4 and Alg. 5. Then, we discuss the running time of both algorithms.


For each D2D pair k, the complexity of building the preference profile using any standard

sorting algorithm is O(R log(R)). Similarly the complexity of building the preference profile at

the central BS for all RBs R is O(KR log(KR)), where R and K represent the total number of

RBs and D2D pairs, respectively. So, the input to Alg. 2 is η =∑

k∈K |Pk|+∑

r∈R |Pr| = 2KR,

where |P| denote the size of preference profile P . Moreover, Alg. 2 terminates after a finite

number of iterations [84]. Under the worst case, when the preferences of all D2D pairs for all

RBs are the same, it can be seen that the time complexity is linear in the size of input preference

profiles (i.e., O(η) = O(KR)) [105].

In Alg. 5 to handle the externalities, at each iteration, all D2D pairs update their preference list

(i.e., O(R log(R))) based on the current matching. This is different from Alg. 4 whose preference

list is updated only once during the initialization phase. Moreover, an additional input vector of

the conflict set Ck will be added as an input with maximum size of K − 1 (i.e., the worst case

occurs when all D2D pairs are a member of the conflict set of all other D2D pairs). However, in

general, the size of Ck will be far smaller than the total number (K) of D2D pairs in the network.

Then, Alg. 5 input is equal to η=∑

k∈K |Pk|+∑

r∈R |Pr|+∑

k∈K |Ck| = 2KR+K(K− 1)/2.

From Theorem. 1, we state that Alg. 5 terminates after a finite number of iterations. Then it can be

stated that under worst case, the time complexity of Alg. 5 is also linear with respect to the size of

input preference profiles (i.e., O(η) = O(KR+ K2−K2 )). Thus, both algorithms show reasonable

computational complexity for practical implementation.

3.5.4 Example Scenario

In this subsection, we provide a detailed discussion supported with examples for the RB allocation

schemes. First, RB allocation using the partial reuse mode is discussed, i.e., Alg. 4. Then, we

discuss the RB allocation process for the full-reuse mode i.e., Alg. 5. Moreover, we elaborate in

detail the effect of externalities and their consequences if not well handled.

We consider Fig. 3.1 as our example for a D2D enabled system, where the dashed lines repre-

sent the interfering links. Note that the BS interferes with all D2D pairs, which is not shown in the

figure. From Fig. 1, we consider that all D2D pairs choose to use the given mode (i.e., controlled

by the vector α) so the two sides are K = k1, k2, k3, k4, k5, and R = r1, r2, r3. Let PK and


PR, represent the preference profile of all players as follows:

Pk1 = Pk5 = r1, r3, r2, Pr1 = k1, k2, k5, k4, k3, qr1 = 1,

Pk2 = r3, r1, r2, Pr2 = k5, k4, k2, k1, k3, qr2 = 3,

Pk3 = Pk4 = r2, r3, r1, Pr3 = k4, k2, k5, k1, k3, qr3 = 1.

3.5.4.1 Partial-Reuse Mode

We first check the case when the partial-reuse mode (i.e., y = 1) is activated. Under this mode,

there is no co-tier interference (no externalities among D2D pairs), thus we have a one-to-one

matching scenario. From Alg. 4, all five D2D pairs propose to their respective preferred RBs

simultaneously. Note that the BS manages the RBs preference profiles. From the preference

profiles, we can see that k1 and k5 propose to r1, k2 proposes to r3, and k3 and k4 propose to r2 at

time instant t. At t, we have:

µ(r1) = k1, µ(r2) = k4, µ(r3) = k2.

Now at time instant t+1, the rejected D2D pairs k3 and k5 will update the preference by removing

the RBs that have rejected them and then propose to the next best option, i.e., r3 for both rejected

D2D pairs. On receiving these proposals, r3 compares its current match with the new proposals.

It chooses the best among them (i.e., k2) and rejects the rest (i.e., k3, k5). Now, the rejected pairs

again update and propose until there are no more RBs to propose or all D2D pairs are matched.

Finally, we have the following matching:

µ(r1) = k1, µ(r2) = k5, µ(r3) = k2.

3.5.4.2 Full-Reuse Mode

Now consider the second case, i.e., the full-reuse mode (y = 0). As stated earlier, this is a one-

to many matching. For ease of understanding, we assume each pair has a uniform interference

(opposed to dynamic interference) on all RBs and a predefined quota for RBs (i.e., qr1 = 1, qr2 =

3, qr3 = 1). Under this scenario, each D2D pair first identifies its conflict set and sends it to the


BS. Note that this is done only once in the initialization phase. Additionally, this is important for

handling the externalities as explained in Sec. 3.5.2.3. Considering Fig. 1, the conflict set using

(3.37) is Ck1 = φ, Ck2 = k3, k4, Ck3 = k2, k4, Ck4 = k2, k3, and Ck5 = φ.

Similar to the first scenario, all D2D pairs propose to the most preferred RBs at time instant t

and we obtain

µ(r1) = k1, µ(r2) = k4, µ(r3) = k2.

This information is broadcast in the network by the BS. Note that, k5 is rejected by r1 due to the

quota limitation qr1 = 1, but k3 is rejected by r2 because k3 ∈ Ck4 (i.e., k3 exists in the conflict

set of a D2D pair k4) and from Pr2 , we have k4 r2 k3. After receiving the current matching of all

D2D pairs, we recalculate their respective utilities using (3.33) and re-rank all the RBs according

to their utility. In this example, k3 and k4 change their preferences from r3 ki r1 to r1 ki r3

because µ(r3) = k2 and k2 ∈ Cki , where i = 3, 4. Hence, the new preference list, at time instant

t+ 1 is as follows:

Pk1 = r1, r3, r2, Pr1 = k1, k2, k4, k3, qr1 = 0,

Pk2 = r3, r1, r2, Pr2 = k4, k2, k1, k5, qr2 = 2,

Pk3 = r1, r3, Pr3 = k4, k2, k5, k1, k3, qr3 = 0,

Pk4 = r2, r1, r3,

Pk5 = r3, r2.

Now the rejected pairs, i.e., k3 and k5, propose to r1 and r3, respectively; k3 and k5 are rejected

by r1 and r3 because µ(r1) r1 k3 and µ(r3) r3 k5 with qr = 0. Again, all pairs update the

preference profiles accordingly. k3 and k5 again propose at time instant t + 2 with the update

preference list to r3 and r2, respectively. k3 is again rejected because µ(r3) r3 k3 and qr3 = 0,

but k5 is accepted because qr2 = 2 and k5 /∈ Cµ(r2). Therefore, the final matching from Alg. 5 is

µ(r1) = k1, µ(r2) = k4, k5 µ(r3) = k2.

Note that k3 has no more RBs to propose to and all the other D2D pairs are matched. Thus, the


algorithm stops. Furthermore, we can observe that the spectral efficiency is improved by reusing

the resources more in Alg. 5 (4 D2D pairs on 3 RBs) compared to Alg. 4 (3 D2D pairs on 3 RBs).

However, Alg. 5 has an additional overhead due to coordination (i.e., conflict set information and

matching update) compared to Alg. 4.

3.5.4.3 Full-Reuse Mode without Handling Externalities

Now consider the case where externalities are not handled. This means there is no conflict sets

information available. Under this scenario, with the same initial quota information, k1 and k5

propose to r1, k2 proposes to r3, and k3 and k4 propose to r2 at time instant t. We obtain the

following matching:

µ(r1) = k1, µ(r2) = k3, k4 µ(r3) = k2.

With this matching, the problem arises with µ(r2), as both pairs when assigned to r2 interfere with

each other. This can reduce their actual utilities when compared to other RBs. Thus, they may be

willing to switch to a new RB that provides them a higher utility. Assuming their second choice is

better than their current match, then at time instant t+ 1, the rejected pair k5 and both unsatisfied

pairs k3 and k4 propose once more to their best choices; they apply to r3 in this example, and r3

chooses k4 due to the quota limitation. We then have

µ(r1) = k1, µ(r2) = φ µ(r3) = k4.

With this assignment, we can see that both k3 and k4 prefer r2 and that r2 also prefers them to its

current match. Both pairs will propose again in the next time instant and will be accepted. This

brings us back to the initial case. Thus, under the case where externalities are not handled, these

D2D pairs will always switch between their preferences and will never be able to converge to a

stable allocation.


Table 3.1: Default Simulation ParametersSimulation Parameters ValuesRadius of MBS 500 mCarrier frequency (f ) 2 GHzFrame Structure Type 1 (FDD)Transmission Time Interval (TTI) 1 msTotal transmit power of BS 46 dBmTotal transmit power of D2Ds 23 dBmSystem bandwidth 3 MHzBandwidth of each RB (W ) 180 kHzNumber of subcarriers per RB 12Neighboring subcarrier spacing 15 kHzModulation and coding scheme (MCS) [106] QPSK: 1/12, 1/9, 1/6, 1/3, 1/2, 3/5

16QAM: 1/3, 1/2, 3/5Path loss (cellular link) 128.1 + 37.6 log(d), d[km]Path loss (D2D links) [107] 32.45 + 20 log(f) + 20 log(d), f[MHz]Shadow fading standard deviation [107] 3 dBProximity of D2Ds (R2) random 20 ∼ 30 mThermal noise for 1 Hz at 20 ˙C −174 dBm


3.6 Simulation Results and Analysis

We consider a downlink system in which the BS is assumed to be deployed at a fixed location, and

we randomly deploy C cellular users and K D2D pairs following a homogeneous Poisson point

process (PPP). We assume the system bandwidth to be 3 MHz3 which is occupied by theC cellular

users. Moreover, we consider a full buffer model for all K D2D pairs. The main parameters

used in our simulations are shown in Table 3.1 unless stated otherwise. These parameters are

chosen according to the system model guidelines in [106–108]. Note that, all statistical results are

averaged over 100 runs of random locations of D2D pairs, cellular users, and RB gains.

3.6.1 Simulation Results for Learning

In this subsection, we perform simulations to evaluate our proposed learning scheme. For this

simulation, we first generate an instance of network with K = 20 D2D pairs. We then evaluate

the following aspects of the learning scheme: the convergence of the learning scheme and the nor-

malized performance gap. Second, we generate instances of the network starting from K = 5 to

K = 50. For this simulation, we run each instance 100 times to obtain the sample average of util-

ity, the average number of successfully joined4 D2D pairs in the system, and the average stopping

time for convergence. Note that for these simulations, we assume the cellular-tier interference tol-

erance level to be fixed at Irmax = −80 dBm for all RBs. Finally, to evaluate our learning scheme,

we define the normalized performance gap as follows:

ε(t) = 1− U(t)

Umax, (3.38)

where U(t) is the utility at time-slot t, and Umax = maxf∈F Uf . We use the built-in simulated

annealing functions in MATLAB to obtain optimal solution Umax.

Fig. 3.5 shows the real-time utility values calculated using (3.5) along with its time average

values, which are obtained by means of a sliding window. We observe that as the time slot in-3The methodologies developed in this research can also be applied to any value of system bandwidth. The motivation

for our choice (i.e., 3 MHz) is to analyze the performance under dense environment with peak network traffic and forthe sake of simulation simplicity.

4Successfully joined D2D pairs represent the D2D pairs which choose to use the given mode and are also allocatedRBs.


creases, each D2D pair learns its possible configurations and chooses high utility configurations

with high probabilities. Despite the fluctuations of the utility, the time average values show an in-

creasing trend in Fig. 3.5. This shows that the learning scheme converges in probability. However

once the convergence is achieved, the configurations do not change, i.e., after time-slot 184.

In Fig. 3.6, we can see the corresponding performance gap calculated using (3.38), which

has a descending trend with time. Furthermore, after a very short time-period (less than 20), we

observe that the ε(t) values becomes less than ε0, where ε0 = 1 − 1/e, which is the typical gap

for randomized greedy algorithms [109].

50 100 150 200 250

1

2

3

← t =184

Util

ity (

Mbp

s)

Time slot (ms)

UmaxUlearning Uavg

Figure 3.5: Real-time utility.


50 100 150 200 2500

0.2

0.4

0.6

0.8

ε(t)

Time slot (ms)

← t =184

1 − 1/e

ε0 ε(t)

Figure 3.6: Real-time performance gap.


1 1.5 2 2.50

20

40

Average utiliy for interval 1−75 ms, Std: 0.44.

1 1.5 2 2.50

20

40


1 1.5 2 2.50

20

40


Figure 3.7: Standard deviation of real-time performance.


In Fig. 3.7, we calculate the standard deviation of the real-time performance. Here, we take

three intervals, i.e., 1 − 75 ms, 75 − 150 ms, and 150 − 250 ms. We observe that as the time

increases, all players learn their optimal actions and move towards the convergence. Thus, the

standard deviation reduces for the next interval and finally the solution converges to the stationary

distribution when all players stop learning.

Next, we test the normalized performance gap under three cases, K = 20, K = 30, and

K = 40. It is observed that under all cases, the learning scheme converges to a near optimal

solution. Additionally, when the ratio of the available RBs (i.e., 15 RBs with system bandwidth

3 MHz) to the number of D2D pairs satisfies (RK ≥ 0.5), the mode selection does not affect the gap

and the normalized performance gap is below the randomized greedy algorithm gap (ε0). However,

if the ratio of available RBs to the number of D2D pairs is less than 0.5, (i.e., RK < 0.5) (e.g., the

K = 40 case), the impact of mode selection becomes apparent and increases the performance gap

from the optimal. Still, as shown in Fig. 3.8, Prε ≤ ε0 > 0.9 for the majority of the time. This

shows that the learning scheme selects the best mode of operation according to the network size

the majority of the time, i.e., for a large network size (K = 40), the full-reuse mode is selected.

Hence, we can infer that the network operates under the best configurations for most of the time.


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Normalized performance gap, ε

Pr

(ε≤

ε0)

Emprical CDF

← 1 − 1/e

εK=40

εK=30

εK=20

Figure 3.8: Normalized performance gap.

Figs. 3.9 and 3.10 show the average utility achieved and fraction of successful joined D2D

pairs for different network sizes, K. We observe that the utility increases with the network size

despite a fixed number of RBs, i.e., R = 15. This is because according to the network size, the

learning algorithm switches to the best suited mode, i.e., the partial-reuse mode for a small network

size or the full-reuse mode for a larger network size. However, as the network size becomes larger

(K ≥ 40), the average utility approaches a saturation state due to limited RBs and the predefined

Irmax values. This trend is also evident in Fig. 3.10, where the fraction of successfully joined

D2D pairs decrease drastically after the saturation point (i.e., K ≥ 40). In Fig. 3.11, we evaluate

the average stopping time for our learning scheme. It can be seen that for all network sizes, the

learning scheme has a reasonable stopping time that increases sub-linearly with the network size.

Moreover, it is observed that the stopping time has high confidence intervals which are a result of

the mixing characteristic of the underlying Markov chain.


10 20 30 40 500

1

2

3

4

5A

vera

ge U

tility

(M

bps)

Network Size (K)

Figure 3.9: Average Utility

10 20 30 40 5050

60

70

80

90

100

Join

ed D

2Ds

(%)

Network size (K)10 20 30 40 50

0

10

20

30

40

50

No.

of j

oine

d D

2Ds

Figure 3.10: Average successfully joined D2Ds


10 20 30 40 50100

150

200

250

300

350S

topp

ing

time

(ms)

Network Size (K)

Figure 3.11: Average Stopping time

3.6.2 Simulation Results for Resource Allocation

In order to evaluate the performance of the RB allocation schemes, first, we show the comparison

in terms of average utility achieved by enabling the full-reuse and partial-reuse mode schemes

under different network sizes (i.e., the number of Joined D2D users, K). Second, we evaluate

the average utility for four different system bandwidth values, i.e., 1.4 MHz, 3 MHz, 5 MHz, and

10 MHz for a fixed network size, i.e., K = 50. Finally, we show the average number of iterations

resulting for different network sizes. Note that, the performance of the RB allocation scheme

depends upon the predefined max interference level Irmax of the RB r. Therefore, we analyze

the performance of RB allocation schemes with respect to three different maximum interference

tolerance thresholds set by the cellular tier, Imax = −120,−100, and −80 dBm [43, 98]. In our

simulations for all D2D pairs K, we set the co-tier interference threshold to ζk = 10 dB (i.e.,

between two D2D pairs).

We compare our proposed approaches with two other approaches: 1) The first approach (Base-

line 1) is a distributed algorithm that is based on the one-to-many matching game, similar to our

proposed algorithm for the full-reuse mode; however, no inter-tier interference among the D2D


pairs is incorporated (i.e., without externalities). This approach aims to maximize the network

utility while providing cellular tier interference protection. However, this approach is unstable

due to the reasons discussed in Sec. 3.5.4.3. This benchmark algorithm is in line with some ex-

isting works used for RB allocation such as [98, 110], 2) The second is a centralized approach

(Baseline 2) that uses the Hungarian assignment method for RB allocation [112]. Results corre-

sponding to the full-reuse mode and partial-reuse mode algorithms are denoted as FR-RA, and

PR-RA, respectively.

First, the achievable utility by D2D pairs is shown with respect to three different Irmax values

for system bandwidth value of 3 MHz (i.e., 15 RBs). In this simulation, we increase the network

size (D2D pairs) and observed the average utility. First, we find that for the FR-RA and Baseline

1 schemes, the average utility increases as the network size grows. However, for Baseline 1,

after the network size is sufficiently large (above 30 D2D pairs and higher), the utility starts to

degrade. The reason for this performance degradation is as the network size increases, the inter-

D2D interference also increases, which degrades the performance. A performance gain in terms of

average utility up to 35%, 27%, and 13% under Irmax = −80, −100, and −120 dBm, respectively

is observed by the FR-RA when compared to Baseline 1 for a network of 50 D2D pairs.

Second, the utility saturates as the network grows when Irmax = −80 and −100 dBm for the

PR-RA and the Baseline 2 schemes. This is because of the limited amount of RBs (i.e., 15 in

3 MHz of bandwidth) in the simulation, and both schemes allow a single D2D pair on an RB.

Therefore, only the best one is allocated to the RB. Moreover, the performance of the PR-RA

scheme and Baseline 2 is indistinguishable under all scenarios.

Third, it is observed from Figs. 3.12, 3.13, and 3.14 that the FR-RA scheme is highly affected

by different Irmax thresholds compared to the PR-RA scheme (i.e., at Irmax = −120 dBm, the utility

drops to up to 52% of the utility obtained at Irmax = −80 dBm). This is mainly because the

interference protection constraint becomes stricter and a smaller number of users can reuse the

RBs in the FR-RA scheme, whereas in the PR-RA scheme, only one D2D pair is using the RB.

Moreover, for a loose protection threshold (i.e., Irmax = −80 and −100 dBm), the FR-RA scheme

yields a performance benefit of up to 158% and 123% compared to the PR-RA scheme, whereas

for a tighter protection threshold, Irmax = −120 dBm, the performance gain is reduced to 36%.


Finally, we can infer that for a network size of less than 15 D2D pairs, the performance of all the

schemes are indistinguishable.

10 20 30 40 500

2

4

6

Network Size (K)

Ave

rage

Util

ity (

Mbp

s)

FR−RA PR−RA Baseline 1 Baseline 2

Figure 3.12: Average utility under Irmax = −80 dBm


10 20 30 40 500

1

2

3

4

5

Network Size (K)

Ave

rage

Util

ity (

Mbp

s)



10 20 30 40 500

1

2

3

4

5

Network Size (K)

Ave

rage

Util

ity (

Mbp

s)




Fig. 3.15 and Fig. 3.16 compares the performance of the proposed FR-RA and PR-RA

schemes. In this simulation, we fix the network size to 50 D2D pairs for four different system

bandwidth values, i.e., 1.4 MHz (6 RBs), 3 MHz (15 RBs), 5 MHz (25 RBs), and 10 MHz (50

RBs) under different Irmax values. It can be observed that under all Irmax values, the average utility

of the PR-RA scheme increases. This is because the unassigned D2D pairs are able to acquire RBs

as the RBs in the system are increased. Moreover, we find that, the average utility for the FR-RA

scheme almost saturates as the number of RBs increases in the system. The main reason for such

an action is that under loose interference thresholds ranging from Irmax = −80 to−100 dBm, most

of the D2D pairs get RBs assigned and under tight interference thresholds Irmax = −120 dBm, a

few D2D pairs are allocated RBs while the rest are rejected.

1020

3040

50

−120

−100

−801

2

3

4

5

6

Number of RBs (R)Ir

max(dBm)

Ave

rage

Util

ity (

Mbp

s)

Figure 3.15: Average utility of the proposed FR-RA scheme under various tolerance levels withK = 50.


1020

3040

50

−120

−100

−800

2

4

6

Number of RBs (R)Ir

max (dBm)

Ave

rage

Util

ity (

Mbp

s)

Figure 3.16: Average utility of the proposed PR-RA scheme under various tolerance levels withK = 50.

Finally, the average iterations versus the network size for two different system bandwidth val-

ues, i.e., 1.4 MHz, and 3 MHz are compared. It can be observed that for a loose interference

tolerance threshold level Irmax = −80 dBm (Fig. 3.17), the proposed FR-RA scheme has a re-

markable convergence time and is around 5 and 7 iterations for both 1.4 MHz, and 3 MHz cases,

respectively. This fast convergence time can be achieved due to the loose tolerance threshold level,

as most of the D2D pairs are accepted at their initial proposals (line 15 of Alg. 5). Additionally,

the average iterations increase with the network size because of the increase in inter D2D interfer-

ence (i.e., less than 3 average iterations for a network size of 10 compared to 7 average iterations

for a network size 50). However, the use of the PR-RA scheme under Irmax = −80 has a higher

number of average iterations for both the 1.4 MHz (less than 6) and 3 MHz (less than 8) cases

compared to the FR-RA scheme for all network sizes. In the PR-RA scheme, for a relatively loose

Irmax value, all the users meet the interference constraint (line 9 of Alg. 4). Then, to assign an RB


0 10 20 30 40 500

5

10

15

Network Size (K)

Ave

rage

iter

atio

ns

FR−RA, 3 MHzPR−RA, 3 MHzFR−RA, 1.4 MhzPR−RA, 1.4 MHz

Figure 3.17: Average number iterations vs. network size, for Irmax = −80 dBm

to a D2D pair, all low ranked D2D pairs have to be analyzed and rejected (lines 10-15 of Alg. 4).

This increases the average iterations even for a small network size (i.e., less than 15). However

for a tighter Irmax value (Fig. 3.18 and Fig. 3.19), a number of D2D pairs will be initially rejected

due to tighter interference constraint (line 9 of Alg. 4), which reduces the average iterations for

a small network size. In the FR-RA scheme, at a tighter interference tolerance threshold level of

Irmax = −100 dBm (Fig. 3.18), the iterations increases with network size increase, but is around 6

and 9 iterations with 1.4 MHz and 3 MHz bandwidth, respectively. Moreover, under Irmax = −120

dBm (Fig. 3.19), the average iteration converges to 14 and 6 iterations for even a small network

size (i.e., less than 5 D2D pairs) when bandwidth values of 3 MHz and 1.4 MHz are considered,

respectively. This is because most of the D2D pairs are rejected by RBs due to the tight Irmax (line

7 of Alg. 5. This then forces the pairs to propose to the next RBs, and consequently most of the

D2D pairs re-propose until they are either accepted or rejected by all RBs in the system. Note that

under all cases, the average number of iterations will always be less than the number of RBs. This

can be achieved due to a completely distributed design of the FR-RA and PR-RA schemes.


0 10 20 30 40 500

5

10

15

Network Size (K)

Ave

rage

iter

atio

ns FR−RA, 3 MHz

PR−RA, 3 MHzFR−RA, 1.4 MhzPR−RA, 1.4 MHz



0 10 20 30 40 500

5

10

15

Network Size (K)

Ave

rage

iter

atio

ns FR−RA, 3 MHzPR−RA, 3 MHzFR−RA, 1.4 MhzPR−RA, 1.4 MHz



Finally, the achievable utility by D2D pairs is compared with respect to system bandwidth

value of 3MHz (i.e., 15 RBs). In this simulation, we increase the network size (D2D pairs) and

observed the average utility. First, we find that for all the schemes, the average utility increases as

the network size grows. However, for traditional matching, after the network size is sufficiently

large (above 30 D2D pairs and higher), the utility starts to degrade. The reason for this perfor-

mance degradation is as the network size increases, the inter-D2D interference also increases,

which degrades the performance. A performance gain in terms of average utility up to 35% is

observed by the FR-RA when compared to traditional matching for a network of 50 D2D pairs.

Moreover, both proposed and swap matching have indistinguishable performances. Second, the

utility saturates as the network grows. This is because of the limited amount of RBs (i.e., 15 in

3MHz of bandwidth) in the simulation.

Then, we compare the average iterations required to converge to a stable solution for both the

proposed matching and swap matching schemes. Here, we increase the network size to study the

effect of average iterations. As the network size grows, more number of users need to propose to

the RBs and the average iterations increase. However, for the proposed scheme, fast convergence

time can be achieved due to updating and removing the rejected players from the preference list.

However, in case of swap matching the converge time almost increases sub-linearly with network

size due to more number of users and accept-reject procedure of swap matching. In swap matching,

all the players make appropriate swaps until there exist no swap such that the utility of the network

can increase. Thus it has a very high converge time compared to the proposed scheme which is

not suitable for many 5G bandwidth hungry applications.


network grows. This is because of the limited amount of RBs (i.e., 15 in 3MHz of

bandwidth) in the simulation.”

Figure 2: Comparison of average utility

“In figure 3, we compare the average iterations required to converge to a stable

solution for both the proposed matching and swap matching schemes. Here, we

increase the network size to study the effect of average iterations. As the network

size grows, more number of users need to propose to the RBs and the average

iterations increase. However, for the proposed scheme, fast convergence time can

be achieved due to updating and removing the rejected players from the

preference list. However, in case of swap matching the converge time almost

increases sub-linearly with network size due to more number of users and accept-

reject procedure of swap matching. In swap matching, all the players make

appropriate swaps until there exist no swap such that the utility of the network can


3.7 Summary

In this work, we designed a resource allocation framework for D2D communication over cellular

networks by using Markov approximation and matching-game approaches. We considered two

important aspects: mode-selection and resource block allocation for the performance of the D2D

network. We used a learning framework based on Markov approximation in which we have de-

signed a problem specific Markov chain that converges close to an optimal solution with probabil-

ity one. Furthermore, we proposed novel resource allocation algorithms based on matching theory

that can work within the proposed learning framework. These resource allocation algorithms help

us obtain a stable resource allocation that is a locally optimal solution of an NP-hard resource allo-

cation problem at each time slot of the Markov approximation process. Our framework has shown


increase. Thus it has a very high converge time compared to the proposed scheme

which is not suitable for many 5G bandwidth hungry applications.’’

Figure 3: Comparison of average iterations

References

[1] A. Abdelnasser, E. Hossain, and D. I. Kim, “Tier-aware resource allocation in ofdma macrocell-

small cell networks,” IEEE Trans. Commun., vol. 63, no. 3, pp. 695-710, Mar. 2015.

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that it achieves a stable, distributed and scalable solution for the network. Simulation results have

shown that the proposed framework convergence in probability, achieves interference protection

and closely approaches the optimal solution. Furthermore, we have also validated the stability and

convergence of the resource allocation algorithm.

Chapter 4Conclusion and Future Directions

This final chapter summarizes the major contributions of the dissertation and highlights the future

research topic.

4.1 Conclusion

In this dissertation, we have investigated two network optimization problems for two novel radio

access technologies that will enable the 5G paradigm. Each network optimization problem has its

own objective and constraints due to the underlying characteristics of the corresponding network

environment.

For the first optimization problem, we have proposed two novel approaches for resource allo-

cation in underlay small cells while protecting the macro tier. In the first approach, we relax the

original problem and present a self-organizing approach using the optimization theory. Then, for

the second approach, we formulated the resource allocation problem as a many-to-one matching

game in which a BS builds the preference profile on behalf of all channels and each SBSs build

their own preference profile for each channel using local conventional rate maximization param-

eter. Through these preference profiles each set of players can evaluate each other based on their

defined utilities. In order to solve the problem, we proposed a novel resource allocation algo-

rithm which guarantees macro tier protection and a stable match for the underlay SCs. Both our

proposed schemes can be implemented distributively, thus, a self-organizing solution. Simulation

results presented for the proposal showed the interference protection for macro tier, convergence

of algorithm in terms of rate and stable matching for underlay SC network.

Second, we studied the advantages of enabling D2D communication that can coexist with the

traditional cellular system. To solve this problem, we designed a resource allocation framework for

95

CHAPTER 4. CONCLUSION AND FUTURE DIRECTIONS 96

D2D communication over cellular networks by using Markov approximation and matching-game

approaches. We considered two important aspects: mode-selection and resource block allocation

for the performance of the D2D network. We used a learning framework based on Markov ap-

proximation in which we have designed a problem specific Markov chain that converges close to

an optimal solution with probability one. Furthermore, we proposed novel resource allocation al-

gorithms based on matching theory that can work within the proposed learning framework. These

resource allocation algorithms help us obtain a stable resource allocation that is a locally optimal

solution of an NP-hard resource allocation problem at each time slot of the Markov approximation

process. Our framework has shown that it achieves a stable, distributed and scalable solution. The

proposed framework convergence in probability, achieves interference protection and closely ap-

proaches the optimal solution. Furthermore, we have also validated the stability and convergence

of the resource allocation algorithm both analytically and via extensive simulation.

All algorithms proposed in this dissertation are self-organizing, scalable and can be imple-

mented distributively in the cellular network.

4.2 Future Directions

Novel network application and services are being developed and incorporated in the current net-

work at a very rapid pace, thus requiring solutions to a number of potential challenges. This is

creating new network optimization problems that need to be addressed. The followings are some

open issues and future directions.

1. Due to the proliferation of smart mobiles devices, there has been a great diversity both in

the contents as well as the devices. These factors need to be taken into account by adding the user

QoS based on its capability. By incorporating the device heterogeneity along with its demand, it

is expected that we can even support delay-sensitive traffic based on prioritizing the traffic.

2. Multi-point connectivity is also among one proposal to meet the users QoS requirements.

Using multi-point approach, a user device can maintain multiple connections with multiple re-

ceivers based on its application. Thus, intelligent and efficient resource management schemes will

be required in such multi-point systems.

3. Millimeter Wave (mmWave) is also a proposal that can meet the future network require-

CHAPTER 4. CONCLUSION AND FUTURE DIRECTIONS 97

ments. Using these mmWave networks in 5G especially for small cells can boost the available

capacity. However, intelligent and efficient resource management schemes will be required to

deploy efficient mmWave networks.

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Appendix AList of Publications

International Journal Papers:

[1] S. M. Ahsan Kazmi, Nguyen H. Tran, Walid Saad, Long Bao Le, Tai Manh Ho, Choong

Seon Hong, Optimized Resource Management in Heterogeneous Wireless Networks, IEEE

Communications Letters, Vol.20, No.7, July 2016. (SCI, IF: 1.291).

[2] S. M. Ahsan Kazmi, Nguyen H. Tran, Walid Saad, Zhu Han, Tai Manh Ho, Thant Zin Oo,

Choong Seon Hong, Mode Selection and Resource Allocation in Device-to-Device Commu-

nications: A Matching Game Approach, IEEE Transactions on Mobile Computing, 2017 (in

press). (SCI, IF: 2.456)

[3] S.M. Ahsan Kazmi, Nguyen H. Tran, Tai Manh Ho, Choong Seon Hong, Hierarchical

Matching Game for Wireless Network Virtualization, IEEE Communications Letters, 2017

(in press). (SCI, IF: 1.291).

[4] Tai Manh Ho, Nguyen H. Tran, Cuong T. Do, S.M Ahsan Kazmi, Eui-Nam Huh and Choong

Seon Hong, ”Power Control for Interference Management and QoS Guarantee in Hetero-

geneous Networks,” IEEE Communications Letters, pp.1402-1405, VOL.19, NO.8, AUG.

2015. (SCI, IF: 1.291).

[5] VanDung Nguyen, S.M. Ahsan Kazmi, and Choong Seon Hong, ECCT: An Efficient-

Cooperative ADHOC MAC for Cluster-Based TDMA System in VANETs, International

Journal of Distributed Sensor Networks, Volume 2015 (2015), Article ID 746438, 12 pages,

July, 2015. (SCIE, IF: 0.906)

110

LIST OF PUBLICATIONS 111

[6] Tai Manh Ho, Nguyen H. Tran, Long Bao Le, Walid Saad, S.M. Ahsan Kazmi and Choong

Seon Hong, Coordinated Resource Partitioning and Data Offloading in Wireless Heteroge-

neous Networks, IEEE Communications Letters, Vol.20, No.5, May 2016. (SCI, IF: 1.291).

[7] Seungil Moon, Than Zin Oo, S.M. Ahsan Kazmi, Bang Ju PARK, Choong Seon Hong,

SDN-based Self-Organizing Energy Efficient Downlink/Uplink Scheduling in Heterogeneous

Cellular Networks IEICE TRANSACTIONS on Information and Systems, vol.100, no. 5,

2017. (SCIE, IF: 0.245).

[8] Dai H. Tran, Nguyen H. Tran, Chuan Pham, S.M. Ahsan Kazmi, Eui-Nam Huh, Choong

Seon Hong,“ OaaS: offload as a service in fog networks Computing, 2017 (in press). (SCI,

IF: 0.872).

[9] Tai M. Ho, Nguyen H. Tran, S.M. Ahsan Kazmi, , Choong Seon Hong, Wireless Virtu-

alization Design with Dynamic Isolation Provisioning and Energy Efficiency Optimization

for Wireless Heterogeneous Networks, IEEE Transactions on Mobile Computing, (under-

review). (SCI, IF: 2.456).

International Conference Papers:

[10] S. M. Ahsan Kazmi, Nguyen H. Tran, Tai Ho, Thant Zin Oo, Choong Seon Hong, Tuan

Le, Seungil Moon, ”Resource Management in Dense Heterogeneous Networks,” The 17th

Asia-Pacific Network Operations and Management Symposium(APNOMS 2015), Aug 19-

21, 2015, Busan, Korea.

[11] S. M. Ahsan Kazmi, Nguyen H. Tran, Tai Manh Ho, Dong Kyu Lee, and Choong Seon

Hong, ”Decentralized Spectrum Allocation in D2D Underlying Cellular Networks” The 18th

Asia-Pacific Network Operations and Management Symposium (APNOMS 2016), Oct. 5-7,

2016, Kanazawa, Japan.

[12] S. M. Ahsan Kazmi, Choong Seon Hong, ”A matching game approach for resource alloca-

tion in wireless network virtualization”, The International Conference on Ubiquitous Infor-

mation Management and Communication (IMCOM 2017), Jan. 05-07, 2017, Beppu, Japan.


[13] Choong Seon Hong , S. M. Ahsan Kazmi, Seungil Moon, Nguyen Van Mui, SDN Based

Wireless Heterogeneous Network Management, the 2nd International Conference Advanced

Engineering - Theory and Applications 2015(AETA 2015), Dec 9-11, Ho Chi Minh city,

Vietnam.

[14] Tai Manh Ho, Tuan LeAnh, S. M. Ahsan Kazmi, Choong Seon Hong, ”Opportunistic Re-

source Allocation via Stochastic Network Optimization in Cognitive Radio Networks,” The

16th Asia-Pacific Network Operations and Management Symposium (APNOMS 2014), Sep

17-19(18), 2014, Hsinchu, Taiwan.

[15] Tuan LeAnh, Nguyen H. Tran, S. M. Ahsan Kazmi, Thant Zin Oo, Choong Seon Hong,

”Joint Pricing and Power Allocation for Uplink Macrocell and Femtocell Cooperation,” The

International Conference on Information Networking(ICOIN 2015), Jan 12-14(13), 2015,

Siem Reap, Cambodia.

[16] Tai Manh Ho, Nguyen H. Tran, Long Bao Le, S. M. Ahsan Kazmi, Seung Il Moon, Choong

Seon Hong, ”Network Economics Approach to Data Offloading and Resource Partitioning in

Two-Tier LTE HetNets,” 2015 IFIP/IEEE International Symposium on Integrated Network

Management(IM 2015), Ottawa, Canada, May 11-15. 2015.

[17] Thant Zin Oo, Nguyen H. Tran, Tuan Le, S. M. Ahsan Kazmi, Tai Ho, Choong Seon Hong,

”Traffic Offloading under Outage QoS Constraint in Heterogeneous Cellular Networks,” The

17th Asia-Pacific Network Operations and Management Symposium(APNOMS 2015), Aug

19-21, 2015, Busan, Korea.

[18] Tai Manh Ho, Nguyen H. Tran, Cuong T. Do, S. M. Ahsan Kazmi, Tuan LeAnh, Choong

Seon Hong, ”Data Offloading in Heterogeneous Cellular Networks: Stackelberg Game Based

Approach,” The 17th Asia-Pacific Network Operations and Management Symposium (AP-

NOMS 2015), Aug 19-21, 2015, Busan, Korea.

[19] Tuan LeAnh, Nguyen H.Tran, S. M. Ahsan Kazmi, Thant Zin Oo, Kyi Thar, Tai Manh Ho,

Choong Seon Hong, ”Load-Sharing based on Relay-aided Cooperative Modeling in Uplink


Two-Tier Cellular Networks,” The 17th Asia-Pacific Network Operations and Management

Symposium(APNOMS 2015), Aug 19-21, 2015, Busan, Korea.

[20] Seungil Moon,Tuan Le, S. M. Ahsan Kazmi, Thant Zin Oo, Choong Seon Hong, ”SDN

Based Optimal User Association and Resource Allocation in Heterogeneous Cognitive Net-

works ,” The 17th Asia-Pacific Network Operations and Management Symposium(APNOMS

2015), Aug 19-21, 2015, Busan, Korea.

[21] Tai Manh Ho, Nguyen H. Tran,S. M. Ahsan Kazmi, Seung Il Moon, Choong Seon Hong,

”Distributed Pricing Power Control for Downlink Co-tier Interference Coordination in Two-

Tier Heterogeneous Networks”, International Conference on Ubiquitous Informing Manage-

ment and Communication(ACM IMCOM 2016), Jan 4-6, 2016, Danang, Vietnam.

[22] Tri Nguyen Dang, S. M. Ahsan Kazmi, Tai Manh Ho, Nguyen H. Tran, Choong Seon Hong,

”A Double-Auction Mechanism for Wireless Charging Networks” The 18th Asia-Pacific Net-

work Operations and Management Symposium(APNOMS 2016), Oct. 5-7, 2016, Kanazawa,

Japan.

[23] Tai Manh Ho, Nguyen H. Tran, S. M. Ahsan Kazmi, Do Hyun Kim and Choong Seon

Hong, ”Distributed Resource Allocation for Interference Management and QoS Guarantee

in Underlay Cognitive Femtocell Networks” The 18th Asia-Pacific Network Operations and

Management Symposium(APNOMS 2016), Oct. 5-7, 2016, Kanazawa, Japan.

[24] Tai Manh Ho, Nguyen H. Tran, S. M. Ahsan Kazmi, Choong Seon Hong, ”Dynamic Pric-

ing for Resource Allocation in Wireless Network Virtualization: A Stackelberg Game Ap-

proach”, The International Conference on Information Networking (ICOIN 2017), Jan. 11-

13, 2017, Da Nang, Vietnam.

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