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ENABLING TECHNOLOGIES FOR NEXT-GENERATION WIRELESS NETWORKS
By
YUN ZHU
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2017
© 2017 Yun Zhu
Dedicate to my parents
ACKNOWLEDGMENTS
In my research, I have received assistance from many people. First, I would like to
thank my advisor, Dr. Dapeng Oliver Wu for his support, advice, guidance, and good
wishes. Dr. Wu has had a profound influence not only as my graduate advisor in UF, but
also on my life. His availability at all times including weekends, dedication towards work
and family, professional integrity, and pursuit of perfection helped me become a better
individual. Dr. Wu has made it his responsibility to make sure that I, as well as all of his
other students, have had the financial support we need to accomplish our goals. I am
grateful to him for the freedom and flexibility he gave me throughout my Ph. D. study.
My gratitude goes to the committee members (in alphabetical order), Dr. Ahmed
Helmy, Dr. Janise McNair and Dr. Yuguang Michael Fang, for their invaluable comments,
productive suggestions, and the time for reading the draft of my thesis.
During the course of my research, I have submitted several papers to peer reviewed
conferences and journals. The anonymous reviewers have provided valuable insights,
pointers to literature, and criticisms that I have used to make my research stronger.
I would like to thank my parents for their continuous support on my research path.
They are the source of my strength.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
CHAPTER
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.1 Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.1.1 Exploration of the Diversity Gain . . . . . . . . . . . . . . . . . . . . 141.1.2 Scheduling for MmWave Backhual . . . . . . . . . . . . . . . . . . 141.1.3 The Selection of Network on the Terminals . . . . . . . . . . . . . . 15
1.2 Solutions and Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 161.2.1 Miss and Forward: Exploiting Diversity with Intra-session Network
Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161.2.2 Regret Benefit Ratio Link Scheduler for Wireless Backhaul with
Directional Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . 171.2.3 Game Theoretic Approach for Network Access Control in Hetero-
geneous Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.3 Organizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2 MISS AND FORWARD: EXPLOITING DIVERSITY WITH INTRA-SESSIONNETWORK CODING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.2 Scheme Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Source Coding of MF . . . . . . . . . . . . . . . . . . . . . . . . . . 222.2.1.1 Precoding of MF . . . . . . . . . . . . . . . . . . . . . . . 232.2.1.2 Outer code of MF . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Relay Recoding of MF . . . . . . . . . . . . . . . . . . . . . . . . . 232.2.3 Helper Recoding of MF . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.3.1 Receiving batch . . . . . . . . . . . . . . . . . . . . . . . 242.2.3.2 Recoding and sending . . . . . . . . . . . . . . . . . . . . 252.2.3.3 Coordination with the relay . . . . . . . . . . . . . . . . . 252.2.3.4 Logical flow of the helper . . . . . . . . . . . . . . . . . . 25
2.2.4 Decoding of MF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3 Throughput Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Degree Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.3.2 Achievable Throughput Analysis . . . . . . . . . . . . . . . . . . . . 282.3.3 Rank Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5
2.3.3.1 Transfer matrix of MF . . . . . . . . . . . . . . . . . . . . 292.3.3.2 Derivative formula for two-Hop network . . . . . . . . . . 302.3.3.3 Comparison with BATS . . . . . . . . . . . . . . . . . . . 31
2.4 Practical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4.1 Packet Structure of MF . . . . . . . . . . . . . . . . . . . . . . . . . 342.4.2 Helper Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4.2.1 Relay beaconing . . . . . . . . . . . . . . . . . . . . . . . 352.4.2.2 Candidates responding . . . . . . . . . . . . . . . . . . . 352.4.2.3 Relay confirming . . . . . . . . . . . . . . . . . . . . . . . 36
2.4.3 Rank Distribution Estimation . . . . . . . . . . . . . . . . . . . . . . 362.4.4 Overhead Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.5.1 Numerical Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.5.1.1 Rank distribution . . . . . . . . . . . . . . . . . . . . . . . 382.5.1.2 Achievable throughput . . . . . . . . . . . . . . . . . . . . 38
2.5.2 Experimental Results: Two-hop Network . . . . . . . . . . . . . . . 392.5.2.1 Under different channel condition . . . . . . . . . . . . . . 402.5.2.2 Under unexpected loss . . . . . . . . . . . . . . . . . . . 412.5.2.3 Under blockage channel . . . . . . . . . . . . . . . . . . . 42
2.5.3 Experimental Results: Multi-hop TDMA Network . . . . . . . . . . . 432.5.3.1 Under different hops and loss rate . . . . . . . . . . . . . 442.5.3.2 With different number of helpers . . . . . . . . . . . . . . 45
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 REGRET BENEFIT RATIO LINK SCHEDULER FOR WIRELESS BACKHAULWITH DIRECTIONAL ANTENNAS . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.3 System Model and Assumption . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.1 MAC Layer Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 503.3.2 Physical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.4 RBRS under Slot based MAC . . . . . . . . . . . . . . . . . . . . . . . . . 523.4.1 Problem Formulation And Analysis . . . . . . . . . . . . . . . . . . 523.4.2 Heuristic Algorithm Design . . . . . . . . . . . . . . . . . . . . . . . 54
3.4.2.1 Contention graph . . . . . . . . . . . . . . . . . . . . . . 543.4.2.2 QoS-aware priority . . . . . . . . . . . . . . . . . . . . . . 553.4.2.3 Regret Benefit Ratio for each link . . . . . . . . . . . . . . 563.4.2.4 Find concurrent set . . . . . . . . . . . . . . . . . . . . . 563.4.2.5 Admission control . . . . . . . . . . . . . . . . . . . . . . 573.4.2.6 Overall scheduler design . . . . . . . . . . . . . . . . . . 58
3.4.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 593.5 D-RBRS under CSMA/CA based MAC . . . . . . . . . . . . . . . . . . . . 61
3.5.1 Contention Window and Regret Benefit Ratio . . . . . . . . . . . . 613.5.2 Neighborhood Detection . . . . . . . . . . . . . . . . . . . . . . . . 62
6
3.5.3 Window Prioritization . . . . . . . . . . . . . . . . . . . . . . . . . . 633.5.4 Coarse-to-Fine Window Mapping Algorithm . . . . . . . . . . . . . 64
3.5.4.1 Coarse phase . . . . . . . . . . . . . . . . . . . . . . . . 653.5.4.2 Fine phase . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.5.5 Inner Competition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.5.6 Admission Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.6.1 Experiment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.6.2 Performance Evaluation for RBRS under slotted MAC . . . . . . . . 69
3.6.2.1 Effects of number of links . . . . . . . . . . . . . . . . . . 693.6.2.2 Effects of number of slots . . . . . . . . . . . . . . . . . . 713.6.2.3 Effect of beam width of the antenna . . . . . . . . . . . . 713.6.2.4 Theoretical bound evaluation . . . . . . . . . . . . . . . . 72
3.7 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 733.7.1 Development of Simulators . . . . . . . . . . . . . . . . . . . . . . . 733.7.2 Performance Evaluation for D-RBRS under CSMA/CA . . . . . . . 74
3.7.2.1 Effects of number of links . . . . . . . . . . . . . . . . . . 743.7.2.2 Effects of number of packets in each link . . . . . . . . . 753.7.2.3 Effects of beam width of the antenna . . . . . . . . . . . . 76
3.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4 GAME THEORETIC APPROACH FOR NETWORK ACCESS CONTROL INHETEROGENEOUS NETWORKS . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.3 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.4 Repeated Stochastic Game and Problem Formulation . . . . . . . . . . . 82
4.4.1 Repeated Stochastic Game – An Overview . . . . . . . . . . . . . . 824.4.2 Game Formulation of the Network Selection Problem . . . . . . . . 844.4.3 Optimization objective . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.5 Implementation of the Network Selection Algorithms . . . . . . . . . . . . 874.6 Experiment Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6.1 Experiment Settings . . . . . . . . . . . . . . . . . . . . . . . . . . 914.6.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.6.2.1 With different network capacity . . . . . . . . . . . . . . . 934.6.2.2 With different number of users . . . . . . . . . . . . . . . 954.6.2.3 With network turbulence . . . . . . . . . . . . . . . . . . . 96
4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.8 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7
LIST OF TABLES
Table page
2-1 Some parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2-2 Slope comparison under 0.1 loss channel . . . . . . . . . . . . . . . . . . . . . 43
2-3 Throughput under different number of helpers exploited . . . . . . . . . . . . . 45
3-1 Mathematical notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3-2 Contention Window Prioritization . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3-3 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4-1 Mathematical notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8
LIST OF FIGURES
Figure page
2-1 Overhearing opportunity in ultra dense network . . . . . . . . . . . . . . . . . . 21
2-2 The logical flow of Helper l : store batch of packets and send them by examin-ing the information in packet header. . . . . . . . . . . . . . . . . . . . . . . . . 26
2-3 Comparison of transfer matrices: due to the diversity brought by the helper,the rank loss for MF is less that of BATS codes. Thus the overall rank of MF’send-to-end transfer matrix is higher, which leads to a higher throughput. . . . . 33
2-4 The header structure of a MF packet . . . . . . . . . . . . . . . . . . . . . . . . 34
2-5 The rank distribution of 9 hops under loss rate 0.2 . . . . . . . . . . . . . . . . 38
2-6 Achievable throughput of MF and BATS under different loss rate . . . . . . . . 39
2-7 Two hop settings in cellar network . . . . . . . . . . . . . . . . . . . . . . . . . 40
2-8 Throughputs for different coding scheme . . . . . . . . . . . . . . . . . . . . . . 41
2-9 The throughput under unexpected loss ratio . . . . . . . . . . . . . . . . . . . . 42
2-10 Throughputs for different coding scheme . . . . . . . . . . . . . . . . . . . . . . 43
2-11 Throughputs for different coding scheme . . . . . . . . . . . . . . . . . . . . . . 44
3-1 The mesh backhaul network in the small cells densely deployed scenario. . . . 47
3-2 Performance under different number of links . . . . . . . . . . . . . . . . . . . . 70
3-3 Performance under different number of slots . . . . . . . . . . . . . . . . . . . . 71
3-4 Performance under different beam width . . . . . . . . . . . . . . . . . . . . . . 72
3-5 The lower bound of total priority . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3-6 Performance under different number of links . . . . . . . . . . . . . . . . . . . . 75
3-7 Performance under different number of links . . . . . . . . . . . . . . . . . . . . 76
3-8 Performance under different beam width . . . . . . . . . . . . . . . . . . . . . . 77
4-1 The typical heterogeneous network and backbone communication . . . . . . . 79
4-2 From a wireless terminal to a wired terminal: the impact of total capacity . . . . 92
4-3 From a wireless terminal to a wireless terminal: the impact of total capacity . . 93
4-4 From a wireless terminal to a wired terminal: the impact of the number of users 94
9
4-5 From a wireless terminal to a wireless terminal: the impact of the number ofusers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4-6 From a wireless terminal to a wired terminal: one access point under randomfailures/attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4-7 From a wireless terminal to a wired terminal: two access points under ran-dom failures/attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4-8 From a wireless terminal to a wired terminal: three access points under ran-dom failures/attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4-9 From a wireless terminal to a wireless terminal: three access points underrandom failures/attacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4-10 From a wireless terminal to a wired terminal: impact of capacity under failureor attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
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Abstract of Dissertation Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy
ENABLING TECHNOLOGIES FOR NEXT-GENERATION WIRELESS NETWORKS
By
Yun Zhu
August 2017
Chair: Dapeng Oliver WuMajor: Electrical and Computer Engineering
Mobile data demand is growing explosively. Some industry and academic experts
predict a 1000-fold demand increase by 2020. The traditional tower-mounted BSs,
which are called macrocells, are not capable to meet the “capacity crunch”, and a new
types of networks, Ultra-dense Heterogeneous Small Cell Networks (HetSNets), is
emerging and regarded as the solution for the next generation wireless network.
HetSNets raises new opportunity as well as challenges: 1) The massive relays un-
der HetSNets give much opportunity for space diversity. Traditional cooperative diversity
techniques require complex scheduler on the physical layer and tight synchronization.
A new type of diversity is desired to be invented. 2) The mmWave communication is
drawing more and more attention and could be potentially exploited in the HetSNets net-
works, especially for the backbaul network. In a scenario where small cells are densely
deployed, effective and efficient backhaul scheduling schemes need to be designed with
the characteristics of mmWave communications taken into account. 3) Under HetSNets,
mobile terminals can be equipped with several Network Interface Cards (NICs), thus
allowing the terminal to connect to different wireless networks. Users are required to find
the best available network access point to connect with, according to some common
rules. And finding such rules is another big challenge.
In this dissertation, I propose the above three challenges are addressed with three
independent solutions. First of all, to exploit the diversity gain, a novel intra-session
11
network coding scheme is proposed. Secondly, a contention and QoS aware link
scheduler is designed for the mmWave backhual. Lastly, a game theoretical network
selection approach is to control the heterogeneous network access.
12
CHAPTER 1INTRODUCTION
Mobile data demand is growing explosively. A quick look into recent wireless
network statistics reveal that global mobile traffic experienced around 70% growth in
2014. Ciscos Visual Networking Index (VNI) forecasts that mobile networks will have
more than half of connected devices as smart devices by 2019. Some industry and
academic experts predict a 1000-fold demand increase by 2020 Qua (2015).
The traditional tower-mounted BSs, which are called macrocells, are just a single
type of BS, albeit the backbone that has enabled cellulars success to date. However, in
many important markets, adding further macrocells is not viable due to cost and the lack
of available sites; for example, many cities or neighborhood associations are simply not
very cooperative about opening up new tower locations. The problem facing operators is
not coverage but capacity. There are just too many mobile users demanding too much
data.
Adding BSs has been by far the most important factor historically for increasing
capacity. When BSs are added, each user competes with an ever smaller number of
users for a BSs bandwidth and backhaul connection: it may even have one or more BSs
to itself. More base stations than cell phones is where cellular technology is headed
in 1020 years Andrews (2013). Besides, WiFi is rapidly integrating with the cellular
network, and roaming between cellular and WiFi will become increasingly transparent
to end users. It can be envisioned that more type of networks will be integrated, too.
Following these ideas, a new form of network, Ultra-dense Heterogeneous Small Cell
Networks (HetSNets), is emerging and regarded as the solution for the next generation
wireless network. There are several advantages of this approach over macro-cell
enhancements Hwang et al. (2013).
1. The cost of deployment in HetSNets is much lower than that of macrocells. Unlikea macrocell, where a significant portion of the recurring cost comes from fiber to
13
each cell site, power usage, and real estate, there is no big operating cost in userdeployed HetSNets.
2. HetSNets are energy efficient as they can be utilized intelligently and opportunisti-cally. Depending on the traffic demand, small cells can be in dormant state, so theenergy consumption and interference can be minimized.
3. HetSNets can realize the always best connected principle by seamless handoverand smart offloading. Proximity-based over-the-air congestion control and fastinter-cell load balancing in HetSNets increase the overall spatial reuse.
1.1 Challenges
This new form of networks brings much challenges. In my thesis, I will focus on
three unique challenges for this next generation wireless networks.
1.1.1 Exploration of the Diversity Gain
Densely deployed as fixed entities and owned by infrastructure providers, the small
cells could serve as relays for the traffic between user and backbone in the wireless
backhaul. Those relays, located in street and on the roofs, may be faced with severe
channel conditions. However, as they are massive, there is much opportunity to exploit
space diversity in such settings.
Cooperative communication (CC) Nosratinia et al. (2004) could be a primary
approach to fit this role. Exploiting the broadcast nature of wireless communication, it
enjoys the diversity gain by allowing intermediate nodes to assist in the transmission of
information from a source to destination node. Based on different forwarding strategy,
CC can be categorized into amplify-and-forward, decode-and-forward, and decode
and re-encode Nosratinia et al. (2004). However, those technologies require complex
scheduler on the physical layer and tight synchronization Dohler and Li (2010).
It is desired that a new form of cooperative diversity could be invented that can fully
utilize the ultra dense feature, but without the drawback of those traditional approaches.
1.1.2 Scheduling for MmWave Backhual
The mmWave communication is drawing more and more attention and could be
potentially exploited in the HetSNets networks, especially for the backbaul network Ge
14
et al. (2016). With huge bandwidth available, wireless backhaul in mmWave bands, such
as the 60 GHz band and E-band (71–76 GHz and 81–86 GHz), provides several-Gbps
data rates and can be a promising backhaul solution for small cells.
On the other hand, unlike existing communication systems using lower carrier
frequencies (e.g., from 900 MHz to 5 GHz), mmWave communications suffer from
high propagation loss. To combat severe channel attenuation, directional antennas are
utilized at both the transmitter and receiver for high antenna gain. With the beamforming
technique, the transmitter and the receiver are able to direct their beams towards each
other for the directional communication Wang (2009). The directional communication
reduces the interference between links, and concurrent transmissions (spatial reuse)
can be exploited to greatly improve network capacity. In a scenario where small cells
are densely deployed, effective and efficient backhaul scheduling schemes need to be
designed with the characteristics of mmWave communications taken into account.
1.1.3 The Selection of Network on the Terminals
The nature of HetSNets allows multiple types of network to co-exist. Nowadays,
various mobile terminals such as smartphones and tablets are equipped with several
Network Interface Cards (NICs), thus allowing the terminal to connect to different wire-
less networks like GSM, LTE or 802.11, etc. Moreover, there are various standardization
groups that aim at integrating multiple heterogeneous networks over an Internet Protocol
(IP) backbone. For example, the 3rd Generation Partnership Project (3GPP), 3GPP2,
and the IEEE 802.21 Media Independent Handover (MIH) Working Groups have pro-
posed their standard to provide seamless mobility and session continuity for terminals
with multiple network interfaces.
Multipath TCP MPTCP Paasch et al. (2012) is a promising solution faced with
this new heterogeneous networks. As an evolution of TCP, it is able to use multiple
interfaces simultaneously under one single connection. In the meanwhile, it shows a
standard TCP socket API to the upper layer. By taking advantage of the multiple paths,
15
the user terminal can send the data stream to different paths in different time slots
according to the current network situation and thus optimize its own utility. Raiciu, et
al shows that MPTCP enables smooth handovers between WiFi and 3G Raiciu et al.
(2011). Leveraging diversities of connection under the dynamic environments, MPTCP
provides more reliable and faster connections for mobile devices and is so promising
In January 2013, the Multipath specification has been published by the IETF as an
Experimental standard Ford et al. (2013).
Under such setting, users are desired to find the best available network access
point to connect with, according to some common rules. Finding the rules is another big
challenge under HetSNets.
1.2 Solutions and Contributions
In this section, our proposed solutions are introduced based on the challenges
mentioned before.
1.2.1 Miss and Forward: Exploiting Diversity with Intra-session Network Coding
The ultra-dense setting introduces new opportunities for space diversity. In this
thesis, we propose Miss-and-Forward (MF), a new paradigm for intra-session network
coding, in which a special relay called “helper” is assigned to exploit the rich diversity.
In accordance, a network coding based scheme is designed which has the ability to
restore the “missed” information and in the meanwhile retains the benefit of state-of-
the-art batched sparse coding. Mathematically, we show that the source of throughput
gain is the higher ranked end-to-end transfer matrix. Besides, we provide a systematical
design to address some practical issues such as helper selection and rank distribution
estimation. Both numerical and simulation results show that our method significantly
outperforms fountain codes and existing network coding schemes.
16
1.2.2 Regret Benefit Ratio Link Scheduler for Wireless Backhaul with DirectionalAntennas
With huge bandwidth available in the mmWave band, wireless backhaul at mmWave
frequencies can be a promising backhaul solution for small cells densely deployed
underlying the homogeneous macrocells. With multiple links under such mmWave
wireless network, it is desired to have a scheduling mechanism that can effectively
improve the capacity of network with Quality of Service (QoS) considered. In this thesis,
we propose the Regret Benefit Ratio Scheduler (RBRS) that is able to maximize the
number of links with their QoS requirements satisfied. Our proposed indicator, called
Regret Benefit Ratio (RBR), allows us to simultaneously maximize the QoS benefit and
minimize contention among links under directional antennas. we design RBRS for a
time slot based centralized control mmWave network in which we utilize RBR to find
a suitable concurrent transmission links for every single time slot. Furthermore, we
also propose a distributed scheme under CSMA/CA, which implements the RBR by
prioritizing MAC contention window to provide better concurrent transmission support
while achieving QoS-aware capability. Simulations in the 73 GHz band are conducted to
demonstrate the superior performance of our algorithm under different criteria.
1.2.3 Game Theoretic Approach for Network Access Control in HeterogeneousNetworks
Nowadays most mobile devices are equipped with multiple network interfaces
and these terminals are able to gain benefits from integrating various heterogeneous
networks. On the other hand, the network resources utilized by the user are determined
by the network congestion status. The most challenge issue under this scenario is
the mechanism of an access network selection at each given time to provide 1) best
user experience and 2) improve network fairness. In this thesis, we proposed a game
theocratic approach to control the network access. With the goals of maximizing total
utility and achieving maximum proportional fairness among all users in the service area,
we formulated the problem as a repeated stochastic game. The Lyapunov optimization
17
algorithm is used to compute the optimized suggested actions for each user from the
game manager. Experiments show that our proposed approach can achieve much
higher utility while retains good fairness.
1.3 Organizations
Chapter 2 introduces the Miss and Forward, a novel intra-session network coding
scheme that exploits diversity.
Chapter 3 describes the Regret Benefit Ratio Scheduler, which schedule the
mmWave links in both TDMA and CSMA/CA manner.
Chapter 4 presents our game theoretical approach for network selection.
Chapter 5 concludes this thesis.
18
CHAPTER 2MISS AND FORWARD: EXPLOITING DIVERSITY WITH INTRA-SESSION NETWORK
CODING
2.1 Introduction
As we have mentioned in Chapter 1, traditional cooperative communications
suffers from many problem. The relative new method to exploit space diversity is
network coding. According to the number of flows, it can be categorized into two
approach. The first one is based on inter-session network coding Katti et al. (2006),
where multiple flows may perform XOR at relays Chen et al. (2006); Ding et al. (2009).
The second one is based on intra-session network coding, which aims at single flow.
This approach can also be called as opportunistic routing, in which relays broadcast
packets without predetermined next hops and delays forwarding decisions to exploit
channel diversity Biswas and Morris (2005). To avoid duplicate packet transmissions,
random linear network coding (RLNC) is exploited in the routing Chachulski et al.
(2006); Koutsonikolas et al. (2011). In these schemes, each relay makes a new linear
combination using the incoming packet and the packets in the relay’s buffer, finally
transmitting the coded packet. As long as the number of combined packets is large
enough, the above mentioned random linear network coding can achieve an end-to-end
throughput of 1 − ϵ for the same L-hop lossy network Yang and Yeung (2014). But
coexisted with the throughput gain are the computational complexity and the excessive
coefficient overhead Yang et al. (2014). Besides, although the opportunistic routing
naturally exploits the benefits of multiple routes by providing a new routing protocol for
network coding, it is not compatible with existing routing protocols in mesh networks,
which can become a barrier for its widespread deployment.
On the other hand, new techniques of network coding have been proposed to
address the limitation for RLNC, which partitions a file into subsets (or segment Wang
and Li (2007), generation Chou et al. (2003), block Park et al. (2006), batch Chachulski
et al. (2007), trunk Heidarzadeh and Banihashemi (2010); Tang et al. (2012)). More
19
recently, joint fountain coding and network coding schemes have been proposed Feizi
et al. (2012, 2014); Lun et al. (2008); Yang and Yeung (2014); Huang et al. (2014).
Batched Sparse (BATS) codes Yang and Yeung (2014), as the state-of-art coding
scheme among them, has the best ability to achieve the balance between throughput
and lower complexity/overhead. Although those techniques greatly improve throughput
by recoding, it suffers from a fundamental limitation. Consider the situation in Fig 2-1,
where S intends to send K naive packets to D. With recoding, those K native packets
are coded into N packets and transmitted to D over a lossy channel. In the case of less
than N − K packet losses, D can fully compensate by recoding the received packets into
N packets without any loss of source information. However, in the case of more than
N − K packet losses, certain packets are permanently lost no matter how R recodes
its received packets. We call these permanently lost packets “missed packets” to
distinguish them from the lost ones in the first case. Here, a key limitation is that these
missed packets cannot be compensated by R by any means, but only through the “help”
from other nodes.
Thanks to the dense deployments of next-generation wireless networks Perera
et al. (2014); Asadi et al. (2014), the aforementioned “help” is readily available and
should be properly exploited. As shown in Fig 2-1, under the dense network assump-
tion, it is quite possible that there exists another relay node H, that overhears these
“missed” packets and helps to “forward” them directly to D. From the perspective of D,
the packets received from H provide the remedy to the ones received from R. Rather
than having R1 transmit all N recoded packets, the more efficient way is to let H share
R’s task by recoding and forwarding the missed packets. Although the same amount
of redundancy can also be transmitted by R, it is less efficient as it cannot compen-
sate for the missed packets. The underlying reason is that the packets received by
R1 and H1 went through independent fading channels, and the packets lost in H may
20
be different from those in R. This wireless channel diversity has been exploited by the
above-mentioned idea of “Miss-and-Forward”.
S
R
D
H
Figure 2-1. Overhearing opportunity in ultra dense network
To better combat the lossy channel as well as taking advantage of the ultra dense
scenario, in this paper, we propose Miss-and-Forward (MF), a new intra-session
network coding approach that exploits rich diversity. Different from opportunistic routing,
this scheme can co-exist with existing routing protocols. And with batch wise coding
exploited Yang and Yeung (2014), low decoding complexity could be achieved. MF
is based on a logical topology as shown in Fig 2-1, in which the unexploited relay in
vicinity, called “helper”1 , is chosen to be coupled with the relay. As far as we know, our
work should be the first one to bridge the state of art intra-session network coding with
space diversity exploitation. The contributions of this chapter are as follows:
• We design and implement a delicate network coding protocol that is able tosupport the idea described above and in the meanwhile retain the benefit oflow complexity and high throughput of BATS codes Yang and Yeung (2014).Specifically, the batched sparse codes, generated from the source node, arerecoded by the relay and its corresponding helper in a cooperative fashion wherethe helper node captures missed information and provides the remedy.
• To optimize MF, we analyze the throughput of it from the decoding perspective.First, we show the upper bound of final throughput is directly decided by the rankdistribution. Based on that, we illustrate the advantage of MF over BATS codes bycomparing their rank distributions. To achieve the upper bound, we estimate therank distribution numerically and compute the theoretical throughput of MF. Results
1 To distinguish the helper with the usual relay, the word “relay” in this paper denotesthe intermediate node in the main path if not otherwise indicated.
21
show that compared with BATS codes, MF has a more preferable rank distribution,which results in 5%− 30% throughput gain.
• We propose a systematic design for MF and discuss some practical issuesincluding packets structure, helper selection, and runtime rank estimation. Wesimulate the proposed design, along with several reference designs such as BATScodes, fountain codes and RLNC, in a TDMA multi-hop network. Our methods areshown to achieve significant gain over fountain codes and existing network codingschemes. More importantly, the achieved throughput is only 5% lower than thetheoretical upper bounds calculated under the optimal operating condition.
This chapter is organized as follows: The coding scheme of MF framework is
presented in section 2.2, followed by mathematical analysis in section 2.3; We address
some practical issues in section 2.4; The performance evaluation will be in section 2.5;
Finally, we conclude this paper in section 2.6.
2.2 Scheme Description
In this section, we introduce the framework Miss-and-Forward. From the coding
perspective, MF can be seen as a derivate of BATS codes Yang and Yeung (2014). As
a state-of-the-art intra-session coding scheme, BATS codes achieve both low decoding
complexity and high resistance to the channel loss. MF extends the original BATS codes
to better exploit the massive relays in ultra-dense networks. Compared with BATS codes
whose recoding process is carried out by a single relay, MF relies on a pair of relay and
helper nodes to perform cooperative recoding.
2.2.1 Source Coding of MF
Assume a source (Node 1) wants to transmit a file consisting of K native packets to
a destination (Node L+ 1) over L hops. Each packet, denoted by a column vector in FTq ,
has T symbols in a finite field Fq, where q is the field size. The set of K native packets
is denoted by the following matrix
B = [b1, b2, · · · , bK ] , (2–1)
where bi is the i -th native packet. With an abuse of notation, when treating packets as
elements of a set, we write bi ∈ B.
22
The precoding, outer code, inner code are described in the following.
2.2.1.1 Precoding of MF
At a source node, precoding is performed, similar to RaptorQ (RQ) code Shokrollahi
(2006). The precoding can be achieved by a traditional erasure code such as LDPC and
Reed-Solomon code. After precoding, the output packets are further encoded by the
outer encoder of MF.
2.2.1.2 Outer code of MF
The outer code of MF is the same as the outer code of a BATS codes. Specifically,
a source node encodes the K native packets into a potentially unlimited number of
batches, each containing M coded packets. The i -th batch Xi is generated from a
subset Bi ⊂ B (B ∈ FT×Kq ) by the following operation
Xi = BiGi , (2–2)
where Gi ∈ Fdi×Mq is called the generator matrix of the i -th batch; Bi ∈ FT×diq ; Xi ∈ FT×M
q .
Similar to fountain codes, Bi is randomly generated by two steps: 1) sample a given
degree distribution Ψ = (Ψ1,Ψ2, · · · , ΨK) and obtain a degree di with probability Ψdi ;
2) uniformly and randomly choose di packets from B to form Bi . Matrix Gi is randomly
generated, with all entries independently and identically chosen from Fq according to a
uniform distribution.
2.2.2 Relay Recoding of MF
After receiving packets from both previous relay and helper, the relay node encodes
them properly and sends them to the next one. In MF, the relay recoding differs that
of BATS codes in that the recoding process will not generate a full batch with size M.
If the packet loss is severe at the previous hop, recoding to a full batch may bring too
much unwanted redundancy which impairs the efficiency. Thus instead, less than M
packets will be recoded and sent by the relay in MF, leaving the remaining part to the
23
helper. We use mRi ,l to denote the number of recoded packets in the i -th batch at Relay l .
Accordingly, the recoding matrix is given as HRi ,l ∈ FM×mRi ,lq .
Denote by YRi ,l+1 the set of packets in the i -th batch that is correctly received by
Relay l + 1 from Relay l , and Yi ,l the set of packets totally received at Relay l , the
recoding behavior of the Relay l can be summarized as the following formula:
YRi ,l+1 =
XiEti ,1, l = 1,
Yi ,lHRi ,lE
ti ,l , l > 1,
(2–3)
where Eti ,l is an mRi ,l ×mRi ,l diagonal matrix whose entry is one if the corresponding packet
is correctly received by Relay l + 1, and is zero otherwise. Eqa. (2–3) indicates MF
follows batch-wise transmission.
2.2.3 Helper Recoding of MF
The helper is the critical part in the MF that distinguishes our scheme from existing
ones. It is responsible for three major tasks during data transmission: 1) overhearing
from the previous relay and storing packets in a batch; 2) coordinating with its coupled
relay to know how it should recode; and 3) recoding and sending remedies to the next
one. We first present above tasks individually with the mathematical formula. After that,
we will demonstrate how the helper node accomplishes them smoothly with its logical
flow.
2.2.3.1 Receiving batch
Denote by Zi ,l+1 the set of packets in the i -th batch that are correctly overheard by
Helper l + 1, the flow evolves as follows:
Zi ,l+1 =
XiEui ,1, l = 1,
Yi ,lHRi ,lE
ui ,l , l > 1,
(2–4)
where Eui ,l is the erasure matrix for the hop from Relay l to Helper l + 1. Note that it
shares the same form as (3), with the only difference in its erasure matrix.
24
2.2.3.2 Recoding and sending
We denote YHi ,l+1 as the set of packets that are correctly received by Relay l+1 from
Helper l . Different from Zi ,l+1 in (2–4), YHi ,l+1 focuses on transmission from the helper to
the relay. Their relationship is given as follows:
YHi ,l+1 = Zi ,lHHi ,lE
di ,l , (2–5)
where HHi ,l ∈ FmRi ,l−1×m
Hi ,l
q is the recoding matrix of an RLNC for the i -th batch at Helper
l , and Edi ,l is the corresponding erasure matrix for the hop from Helper l to Relay l + 1.
Together with YRi ,l+1 in (2–3), we can have
Yi ,l+1 = [YRi ,l+1,Y
Hi ,l+1] (2–6)
at the receiving side. Yi ,l+1 then becomes the input for relay recoding as shown in (2–3).
2.2.3.3 Coordination with the relay
A key problem that hasn’t been addressed is how to choose the dimension of
recoding matrix for the relay and the helper, i.e. how to choose the parameters mRi ,l and
mHi ,l . As we have mentioned, we would like to let the helper become a smart node which
only sends the extra part that brings missed information. To achieve this, we choose the
mRi ,l to be the number of successfully received packets at Relay l . Note that this value
mathematically equals M minus the number of zero columns in Yi ,l . Since the recoding
at relay side does not change the number of packets, the helper can simply compute mHi ,l
as follows:
mHi ,l = M −mRi ,l . (2–7)
In this way, MF does not require extra channel use.
2.2.3.4 Logical flow of the helper
To accomplish tasks described above in a methodical manner, Helper l should
overhear packets sent from both Relay l−1 and Relay l and deal with different situations
accordingly.
25
On the one hand, it stores all the correctly received packets in a batch from Relay
l − 1 in its local buffer as described in (2–4), expecting them missed at Relay l . On
the other hand, when Relay l recodes and sends the current batch, Helper l overhears
those packets and regards them as a commend to start to recode and send its own.
Note that mRi ,l , the number of recoded packets sent by Relay l , is contained in the field
“Sent Num” in the packet header, so Helper l knows how to recode according to (2–5)
and (2–7).
With sequentially incoming batches, Helper l should also keep a local variable
Ncurrent to denote the ID of its currently processing batch. If the overheard packet does
not belong to the batch it holds, it will ignore this packet. The detailed logical flow of
Helper l is shown in Fig 2-2, where Npacket is the batch ID of the incoming packet.
A packet comes N_packet=N_current
From which
N_current++
Read Sent Num in the header
YES
Source
Wait for packet
NO
othersRelay
Local buffer
Recode and send
Drop the packet
Figure 2-2. The logical flow of Helper l : store batch of packets and send them byexamining the information in packet header.
To summarize, the intelligence of the helper node resides in two aspects. Firstly, the
helper contains innovative packets out of diversity, so it brings the missed information
back to the data stream; Secondly, the number of packets it sends is dynamically
changed according to the demand, which is just to the point to make a full batch.
26
2.2.4 Decoding of MF
Decoding is performed at the end Node L + 1, to recover the K native packets.
Similar to a raptor code, belief propagation (BP) is used to decode the outer code and
inner code of MF.
2.3 Throughput Analysis
In this section, we discuss the throughput of MF from the decoding perspective. We
first theoretically derive the relationship between upper bound of throughput and rank
distribution; Then, we focus on the rank distribution of MF and prove it is preferable than
that of BATS codes.
2.3.1 Degree Distribution
Similar to fountain codes, a good degree distribution design is crucial to the per-
formance of MF scheme. For Miss and Forward, the optimization of the outer code
is similar to that of BATS codes. In order to recover η · K native packets with linear
complexity, the optimal degree distribution Ψ∗ is obtained by solving the following
optimization problem Yang and Yeung (2014)
maxΨ
Kn
s.t. Ω (x ,h,Ψ) + Knln (1− x) ≥ 0, 0 ≤ x ≤ η,∑
d
Ψ(d) = 1, Ψ(d) ≥ 0,∀d ,
(2–8)
where n is number of received batches required for decoding, h ≜ hr ,L, r = 0, · · · ,M
is the rank distribution of transfer matrix, Ψ is the degree distribution to be optimized,
and Ω(x , h,Ψ) is defined in (Yang and Yeung, 2014, Eq.(19)) and is a linear function of
both h and Ψ. To fully recover a file, η is usually set to be the precoding rate.
27
2.3.2 Achievable Throughput Analysis
Denote by n∗ the numbers of batches required to recover the original file under
perfect, its respective normalized throughputs are
T ∗ = Kn∗·M ,
(2–9)
Clearly, once n∗ is determined, the theoretical throughput of MF can be computed.
In this part, we prove that n∗ can be calculated from the optimal degree distribution Ψ∗
according to the sufficient conditions for successful decoding Yang and Yeung (2014),
First, we define a condition function below
f (n′,α, η,K ,h,Ψ) ≜ ρ0
(α · η · Kn′
)
=(1− αη)
M∑r=1
dmax∑d=r+1
dΨd
(M∑i=r
ζ irhiqi−r
)Id−r ,r (αη)
+M∑r−1rΨr
M∑s=r
(M∑i=s
ζ ishiqi−s
)+ Kn′ln (1− αη)
, (2–10)
where n′ is number of batches required for decoding, dmax ≜ maxd
d : Ψd > 0 is the
maximal degree with non-zero probability, Ia,b (x) ≜a+b−1∑j=a
(a+b−1j
)x j(1− x)a+b−1−j is the
regularized incomplete beta function, and ζ ir is defined as follows
ζ ir ≜
(1− q−i
) (1− q−i+1
)· · ·
(1− q−i+r−1
), r > 0,
1, r = 0.
According to (Yang and Yeung, 2014, Thm-1), to successfully recover the original
file with high probability, the following condition is sufficient and necessary:
f (n′,α, η,K ,h,Ψ) > 0, ∀α ∈ [0, 1] . (2–11)
Then, n∗ can be calculated from Ψ∗,
n∗ = minn′∈N
n′ : f (n′,α, η,K ,h,Ψ∗) > 0, ∀α ∈ [0, 1] , (2–12)
By plugging (2–12) into (2–9), the achievable throughput can be obtained.
28
2.3.3 Rank Distribution
It can be concluded from (2–8) and (2–12) that the theoretical throughput for MF is
determined by the rank distribution h. Since a higher rank will lead to higher throughput,
it is desired to investigate the rank of the transfer matrix of MF.
2.3.3.1 Transfer matrix of MF
At the destination (Node L + 1), denote by Yi the i -th received batch of the flow, we
have
Yi ≜ Yi ,l+1 = [YRi ,l+1,YHi ,l+1] (2–13)
= [Yi ,lHRi ,lE
ti ,l ,Zi ,lH
Hi ,lE
di ,l ] (2–14)
= [Yi ,lHRi ,lE
ti ,l ,Yi ,l−1H
Ri ,l−1E
ui ,l−1H
Hi ,lE
di ,l ] (2–15)
= ... (2–16)
≜ XiHi , (2–17)
where Hi is the transfer matrix for the i -th batch. The specific rank for Hi is given as
hi = rank(Hi), (2–18)
which satisfies
hi ∼ h. (2–19)
Eqa. (2–15) shows the status of the received batch of MF is a second order Markov
chain: Yi ,l+1 is actually dependent on both Yi ,l and Yi ,l−1. Going backward along this
chain, (2–17) can be derived. However, it is unrealistic to have explicit formula for h
in (2–19). In section 2.5, we will conduct the numerical experiment to get the rank
distribution of MF.
29
2.3.3.2 Derivative formula for two-Hop network
In this section, we formulate the rank distribution of the receiver in a typical two hop
network. We define Sk = hk , r ′k , r ′′k , where hk is the rank received by Hk , and r ′k and r ′′k
is the rank received by Rk from Rk−1 and Hk−1 respectively.
To begin with, we consider only the helper and relay where S1 = h1, r ′1.
Now we focus on the distributions of the state variables. For one hop link with loss
rate ϵ11, the distribution of r1 (or r ′1) can be denoted as
hR1(r) =
(M
r
)(1− ϵ11)
r ϵM−r11 (2–20)
And accordingly, we compute distribution for h1 as follows:
hH1(r) =
(M
r
)(1− ϵ21)
r ϵM−r21 (2–21)
Since h1 and r1 are independent with each other, With (2–20) and (2–21) , we have
P(S1) = hH1(h1) ∗ hR1(r1) (2–22)
Then, we extend one more step and also consider R2, which is the destination in a
two-step scheme. With S2 = r2′, r2′′, we can factorize the probabilistic distribution as
P(S2/S1) = hR1→R2(r ′2/S1) ∗ hH1→R2(r ′′2 /S1). (2–23)
Then we can look into these items individually.
According to MF, the H1 may transmit the packets that are missing in R1. Notice
that, for any rank, the probability that the rank is in H1 but does not reside in R1 is
p1 = P(H1,R1/S1) =M − r1M
h1M
(2–24)
Then, we can regard the real rank distribution of H1 as the following:
gH1(m/S1) =
(M − r1m
)(p1)
m(1− p1)M−r1−m (2–25)
30
Now we can formulate hH1→R2 in (2–23) as follows:
hH1→R2(r/π1) =
h1∑m=r
gH1(m/π1) ∗(m
r
)(1− ϵ′21)
r ϵ′m−r21 (2–26)
Meanwhile, in this scenario, the R1 will recode to the same number of packets, so
we can have:
hR1→R2(r/S1) =
(r1r
)(1− ϵ12)
rϵr1−r (2–27)
With (2–22) and (2–23), we have
P(S1,S2) = P(S1) ∗ P(S2/S1) (2–28)
At last, we derive the rank distribution at the destination node, i.e. R2.
hR2(r/S1) =r∑x=0
hH1→R2(x/S1) ∗ hR1→R2(r − x/S1) (2–29)
hR2(r) =∑S1
hR2(r/S1) ∗ P(S1) (2–30)
2.3.3.3 Comparison with BATS
Using a two-hop network as an example, we give insights on why MF outperforms
BATS codes by comparing the rank of their transfer matrices. For notation simplicity, we
only focus on one batch thus sub-index i is left out. The transfer matrix of MF, as well as
BATS codes Yang and Yeung (2014) are given as follows: HMF = [Et1HR2Et2,E
u1HH2Ed2],
HBATS = [E1H2E2],(2–31)
where E1 and E2 are the loss matrices for BATS codes, and H2 ∈ FM×Mq . Denote by m
the number of packets the relay send, we have HR2 ∈ FM×mq , HH2 ∈ FM×(M−m)
q ,
Now it is unclear why the rank of HMF is higher than that of HBATS. For convenience
of comparison, we rewrite HBATS in the same form as HMF. Specifically, we split H2 into
31
H12 and H22, which have the same dimension as HR2 and HH2 respectively. Clearly, H12 and
H22 are still random matrices, and (2–31) can be rewritten as follows: HMF = [Et1HR2 ,E
u1HH2 ]E
′2,
HBATS = [E1H12,E1H
22]E2,
(2–32)
where E′2 =
Et2 0
0 Ed2
.
The form of two matrix multiple in (2–32) illustrates that the effects of the transfer
matrix can be divided into two parts. The first part are the matrices [Et1HR2 ,Eu1HH2 ]
and [E1H12,E1H22] on the left side. They summarize the overall impacts that a batch of
packets are subject to during the first hop including loss from channel and recoding from
the relay. The second part is the erasure matrices on the right side, which represent the
effect of channel loss only since the second hop does not involve recoding.
Viewing (2–32) from a different angle, for both schemes, the transfer matrix is
actually a random matrix, [HR2 ,HR2 ] or [H12,H22], multiplied by some different erasure
matrices from both the left and the right side. Thus to compare the rank of HMF and
HBATS, we start with these two random matrices, and look into how different erasure
matrices bring different rank losses to them. Shown in the first column of Fig 2-3 are
these two basic random matrices, where the gray color denotes random variables in the
finite field. Next, we will explain and visualize the rank-losing process caused by erasure
matrices.
To begin with, we address the rank loss caused by the first hop and look into the
difference between [Et1HR2 ,Eu1HH2 ] and [E1H12,E1H22]. Since the helper node is in the
vicinity of the relay, we can assume that all channels have almost the same condition in
the following analysis. Without loss of generality, we assume there are two packets lost
in a batch so that there are two zeros in the diagonal of the matrices E1, Et1, and Eu1. We
draw the pictures of them in the middle column in Fig 2-3, where the white part stands
32
𝐻𝑀𝐹
Packet loss caused by 𝐸2′
𝐸1𝑡𝐻2
𝑅 𝐸1𝑢𝐻2
𝐻Packet loss caused by 𝐸1
𝑡
(Relay)
𝐻2𝑅 𝐻2
𝐻
Packet loss caused by 𝐸1
𝑢
(Helper)
Packet loss caused by 𝐸1
𝑡
(Relay)
Packet loss caused by 𝐸1
𝑢
(Helper)
A Transfer matrix of MF
𝐻𝐵𝐴𝑇𝑆𝐸1𝐻21 𝐸1𝐻2
2Packet loss Caused by 𝐸1
𝐻21 𝐻2
2 Packet loss Caused by 𝐸1
Packet loss Caused by 𝐸2
B Transfer matrix of BATS
Figure 2-3. Comparison of transfer matrices: due to the diversity brought by the helper,the rank loss for MF is less that of BATS codes. Thus the overall rank ofMF’s end-to-end transfer matrix is higher, which leads to a higherthroughput.
for zero entries. In the second matrix in Fig 2-3B, the left part and the right part of the
matrix are corresponding to E1H12 and E1H22 respectively. Since they share the same
erasure matrix E1, the zero entries reside in the same row. As a result, the rank loss is
two. Since this rank loss is caused by zero entries in a row, we call it the horizontal rank
loss. However, with the diversity caused by two different paths, Et1 and Eu1 are different
and thus the zero entries lie in different rows in HR2 and HH2 as shown in the middle
matrix in Fig 2-3A. Since there is no all-zero row in the matrix, the horizontal rank loss
does not happen.
Then, we compare the effects brought by E′2 and E2. Here, we assume one packet
is lost for both cases. As a result, one column in both [Et1HR2 ,Eu1HH2 ] and [E1H12,E1H22]
will be replaced with zero entries as shown in the last column in Fig 2-3. Accordingly, we
call it the vertical rank loss. Clearly, this loss is one for both schemes.
The final rank loss should consider both horizontal and vertical losses in HMF and
HBATS. Specifically, it should be the larger one between the two. Under the case in
33
Fig 2-3, the final rank loss for BATS codes is two, while that for MF is one. Clearly, the
gain of MF over BATS codes all comes from the first hop where diversity exists.
One may argue that if during the second hop, two or more packets are lost, MF will
have same rank loss as BATS codes since the vertical rank loss is dominant. It is true
for this specific situation. However, since the packet loss is a purely random process,
as long as MF wins part of the games, the average performance will be better. More
importantly, when there are r(r > 2) hops instead of two, the gain can propagate with
snowball effect since diversity exists in r − 1 hops out of r .
Eqa. (2–32) also reveals the fact that under the scenario where helper nodes exist,
MF will downgrade into BATS codes if the channel loss Eu1 and Et1 are identical. Although
there is still a chance for this to happen, this probability is extremely low. Averagely, our
MF scheme achieves a higher rank distribution by exploiting the diversity.
2.4 Practical Design
In this section, we discuss some fundamental issues for the system design.
2.4.1 Packet Structure of MF
We design our packet header based on the practical intra-session network coding
header structure in Ref. Huang et al. (2014). With cooperative recoding, some more
information should also be contained in the header.
The header structure for MF is given in Fig 2-4. Apart from the basic fields used for
coding, there are two special field NC Switch and Sent Num. The NC switch consists
Packet Size Next Hop IP Address
Global Encoding Vector
Batch ID
0Source IP Address Destination IP Address
0
8
16
32
31 63
NC Switch Batch Size Packet ID Sent Num
Figure 2-4. The header structure of a MF packet
of two bits and indicates one of the following four schemes is used: 1) MF, 2) BATS, 3)
RLNC, 4) Fountain code. In other words, if the NC switch equals 00, MF is enabled. The
34
Sent Num is an 8-bit integer which plays a role only when MF is enabled and a helper is
pre-assigned. We have covered the function of it in section 2.2.
2.4.2 Helper Selection
The selection of helpers along the route of an end-to-end flow should be deter-
mined before the data flow starts. This selection of helper may relate to the many factors
such as instant link quality, nodes availability, etc. To make it simple, the helper selection
is mainly based on path loss in this paper, and the ones based on other criteria are left
for future works.
We use the following metric to measure one’s suitability to serve as Helper i :
Hi = minHi∈Cmax(PL(HiA),PL(HiC)), (2–33)
where PL(HiA) and PL(HiC) are the path loss from Relay A and Relay C to Hi respec-
tively, and C is the candidates set. Based on the selecting metric described above, we
designed a three-step handshake protocol.
2.4.2.1 Relay beaconing
To begin with, the relays along the routed path broadcast beacons sequentially so
that the candidates nearby can estimate the path loss in DB. The beacons should also
contain the sequence information i which notifies the candidates it is i th relay in the
path.
2.4.2.2 Candidates responding
When one candidate nearby hears beacons from relays, it will first check which
relay it should help. By our metric, it will
Ri = minRi∈Rmax(PL(Ri−1),PL(Ri+1)), (2–34)
where PL(Ri−1) is the pathloss from Ri−1 to itself. And then, it will send a responding
message to Ri , contains the value r = max(PL(Ri−1),PL(Ri+1)).
35
2.4.2.3 Relay confirming
After receiving multiple responses from candidates, Relay Ri will simply choose the
helper with minimum r , and send back a confirmation to the helper.
Note that MF doesn’t require every relay has its helper. If no one responds to some
relay, this relay will recode in the same way as BATS codes.
2.4.3 Rank Distribution Estimation
As we have concluded, there is no explicit formula to compute the rank distribution
for Miss-and-Forward. Even we can collect enough information of loss ratio for every
single hop with some beaconing overhead, it’s still impossible to generate a right
distribution for MF within a reasonable time. Therefore, we resort to an end-to-end rank
estimation of transfer matrix which requires a very small amount of feedback.
In the beginning, we assume that there is no knowledge at the source node about
what kind of degree distribution should be used. In this case, the source node may
transmit a certain number of full-rank batches as “pilot batches”. The pilot batches
can be generated from arbitrary degree distribution as long as they satisfy the full-rank
property. As those pilot batches reach the destination node, the actual rank K will be
known at the destination by the decoding process. After receiving sufficient batches, the
destination node can generate a histogram from the rank of them, which approximates
the actual rank distribution of the end-to-end transfer matrix. The estimated rank
distribution is then returned to the source node using a single M-sized feedback. To
ensure a reliable delivery of this important information, the end-to-end acknowledgment
(e.g., in TCP) may be used.
The benefit of this rank estimation method is three-fold. First, we do not need to
know the actual path each packet went through and the packet loss ratio of every hop.
Second, the feedback amount Θ(M) is negligible compared to the file size Θ(K). Last
but not least, different from the pilot signal in wireless communications that is considered
36
as pure overhead, the pilot batches here provides information about the source file, so
the efficiency can be guaranteed.
2.4.4 Overhead Discussion
The process of Miss and Forward can be divided into two phases: the transmission
phase and the helper selection phase. The overhead of MF compared to the non-
cooperative scheme (BATS code) is discussed here. During the transmission phase, the
helper node knows the information from the relay by overhearing. Thus no extra slot is
needed for communication between these two. However, for the helper selection phase,
some overhead lies in the fact that extra beacons are required to test the packet loss
ratios.
2.5 Performance Evaluation
In this section, we evaluate the performance of the proposed paradigm Miss-and-
Forward and compare it with other existing information spreading schemes. First of
all, we use the numerical experiment to demonstrate the effectiveness of MF from a
theoretical perspective; Then, we conduct simulations in a serials TDMA network to
show 1) the priority of MF over others from a practical sense and 2) the effect of the
number of helpers exploited in MF.
2.5.1 Numerical Result
First, we quantitatively analyze the rank distribution and throughput of MF based
on Sec 2.3 and compare them with that of the BATS codes Yang and Yeung (2014).
With no explicit formula for h in (2–19), we resort to numerical approaches to obtain the
practical rank distributions. For a L hops ad-hoc network with per-hop loss rate ϵ, we
generate 5000 full-rank batches of packets at the source node, each batching containing
M packets (we set M = 16 for all the experiment if otherwise stated). At the destination
node, the number of times that a k-th (0 ≤ k ≤ M) rank batch appears will be recorded.
And accordingly, the rank distribution is the discrete probability distribution estimated out
of this.
37
0 2 4 6 8 10 12 14 160
0.05
0.1
0.15
0.2
0.25
0.3
0.35
rank
prob
abili
ty d
ensi
ty
BATsMF
Figure 2-5. The rank distribution of 9 hops under loss rate 0.2
Once we have the rank distribution h, we can optimize the degree distributions
according to (2–8) and calculate the achievable throughputs from (2–12).
2.5.1.1 Rank distribution
An exemplary rank distribution of both BATS and MF are shown in Fig 2-5, which
is under the scenario of 9 hops path with 0.2 loss ratio. We can observe that compared
with BATS codes, the rank distribution of the proposed MF has a relatively higher
density on the higher ranks. Specifically, MF can achieve 2-3 fewer rank losses than
BATS codes averagely. The reason for the difference is MF takes advantage of diversity
so that missed rank can be captured by the helpers.
2.5.1.2 Achievable throughput
After collecting information for rank distribution, we refer the equation (2–9) to
compute the theoretical throughput for both BATS and MF. The results are plotted in
Fig 2-6. For convenience, all throughputs are normalized to the capacity of a single hop
network without any packet loss. From the results, we can observe that generally, MF
can achieve higher throughput than BATS, under different loss rate and the number
of hops. As the number of hops increases, the throughput of both MF and BATS
decreases, but MF has lower slop compared with BATS. This is because more number
of hops will lead to more use of diversity. Besides, the throughput gain is higher under
38
the worse channel. MF is more resistant to the higher loss rate compared with BATS
codes. When the channel loss is 0.3, the throughput gain is around 30%.
2 3 4 5 6 7 8 9 100.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
Number of hops
Nor
mal
ized
thro
ughp
ut
BATS: ε=0.1
MF: ε=0.1
BATS: ε=0.2
MF: ε=0.2
BATS: ε=0.3
MF: ε=0.3
Figure 2-6. Achievable throughput of MF and BATS under different loss rate
2.5.2 Experimental Results: Two-hop Network
We implement our scheme in C++ and transmit the real files. We examine the per-
formance of MF in a TDMA two-hop network2 . The time slots assigned to neighboring
nodes are non-overlapping so that inter-user interference is negligible. The transmit
buffer has enough capacity for the relay node. In this scenario, packet losses are mainly
caused by channel error and blocking effect. The service rate of each node can be
controlled by the number of time slots assigned to it.
The throughput performances of MF are compared with BATS codes, fountain
codes and RLNC. For RLNC, we divide the original file into many subsets, which
contains 64 packets, and send the next subset after receiving ACK of the previous one
from the destination node. While for BATS codes and proposed MF, the original file will
constantly generate batches of packets.
2 We use TDMA because retransmission can be naturally turned off, and there areless out-of-control factors from the MAC layer.
39
BSMobile Terminal
Macro BS
R
HS
D
Figure 2-7. Two hop settings in cellar network
We use UDP for transportation layer protocol and static routing In the network
layer. In all experiments, two end nodes simultaneously start to transmit a 16 Mbyte
file (16000 native packets) to each other. Some specific parameters are in Table 2-1.
The file throughput (in Gbps) is calculated by dividing the file size by the transmission
time. The transmission time is measured from the start of file transmission until all native
packets are correctly recovered. Since inter-session network coding is not addressed in
this work, our performance metric is one-way throughput. In each scenario, we transmit
twenty files and record the average value.
Since we choose the data rate Rs to be 1G bits/s, in our experiment, we divide the
actually tested throughput by Rs and use the normalized one as our metric.
Table 2-1. Some parametersScheme MF
packet number 16000packet size 1024 bytesdata rate 1G bit/s
2.5.2.1 Under different channel condition
We change the SNR value from low value to the high value and evaluate the
normalized throughput of MF and BATS codes under AWGN channel as well as fading
channel. BPSK is used as the modulation scheme. The result in shown in Fig 2-8. We
have the following observations:
40
7.5 8 8.5 9 9.5 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR(db)
Nor
mliz
ed th
roug
hput
MFBATSfountainRLNC
A Throughput under AWGN channel
10 12 14 16 18 200.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
SNR(db)
Nor
mliz
ed th
roug
hput
MFBATSfountainRLNC
B Throughput under fading channel
Figure 2-8. Throughputs for different coding scheme
• In both AWGN and fading channel, MF can achieve better performance thanBATS codes. Averagely, MF can have 0.05 more absolute normalized throughput.Depending on the SNR, the relative gain can be larger as the SNR goes down. Butif SNR is too small, the performance of two scheme will be equal.
• Compared with AWGN channel, fading channel should have larger SNR value toachieve the same throughput under both BATS codes and MF.
2.5.2.2 Under unexpected loss
The real channel condition may change with time, and it is hard to predict the
channel condition with 100% accuracy. For BATS codes, if the channel loss rate
increases for some reason, the throughput will degrade a lot. An intuitive solution for this
problem is that we can over estimation the channel loss rate. With this safety margin,
we believe the performance will degrade less. In Fig 2-9, we plot the result of three
schemes: 1) MF scheme with the same distribution with BATS codes, 2) BATS codes
41
with 30% over estimation of channel loss rate, and 3) the original BATS codes. The
estimated loss rate is 0.1 in this experiment.
0.1 0.12 0.14 0.16 0.18 0.20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Acutrall loss propbability
Nor
mliz
ed th
roug
hput
MFBATS(safety margin)BATS
Figure 2-9. The throughput under unexpected loss ratio
From the result, we have the following conclusions:
• Even with only a little increase on loss probability, the performance of BATS codes,no matter with or without safety margin, will degrade dramatically, while MF hasmuch better performance, which shows the stability of MF.
• Although safety margin leads to some performance gain, it will lower the through-put of the normal case, where the actual loss rate equals 0.1. However, MF canachieve the best performance on a normal case while gaining the benefit ofstability.
2.5.2.3 Under blockage channel
We change the blockage rate under different channel loss rate and measure
different throughput. The results are plotted in Fig 2-10, from which we have the
following observations:
• MF is the best among all schemes in terms of throughput. The gain grows withthe 1) blockage rate and 2) the loss rate of channel. The reason for this can beexplained as follows. First, as the blockage rate increases, the direct traffic willnot work effectively but MF can exploit the second path. Besides, regarding thediversity within one hop, when the channel’s loss rate is higher, the helper tends tocapture more missed information and thus gives more help. These results verifythe effectiveness of our proposed design.
42
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Blockage rate
Nor
mliz
ed th
roug
hput
MFBATSfountainRLNC
A Throughput under loss rate 0.1
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Blockage rate
Nor
mliz
ed th
roug
hput
MFBATSfountainRLNC
B Throughput under loss rate 0.3
Figure 2-10. Throughputs for different coding scheme
Table 2-2. Slope comparison under 0.1 loss channelDifferent methods BATS MF fountain RLNC
Average slop 0.01077 0.00188 0.0640 0.07681
2.5.3 Experimental Results: Multi-hop TDMA Network
We extend our experiment to multihop now. The set up of the experiment is as
before.
43
2 3 4 5 6 7 8 9 100.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of hops
Nor
mliz
ed th
roug
hput
MFBATSfountainRLNC
A Throughput under loss rate 0.1
2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Number of hops
Nor
mliz
ed th
roug
hput
MFBATSfountainRLNC
B Throughput under loss rate 0.3
Figure 2-11. Throughputs for different coding scheme
2.5.3.1 Under different hops and loss rate
We change the number of hops under different channel loss rate and measure
different throughput. The results are plotted in Fig 2-11, from which we have the
following observations:
• MF is the best among all schemes in terms of throughput. There are 5%-30%throughput gain over BATS codes, and the gain is even more significant whencompared with RLNC and fountain codes. The gain grows with the 1) numberof hops and 2) the loss rate of channel. The reason for this can be explainedas follows. First, as the number of hops increases, diversity can be exploitedmore times and the gain can be accumulated. Besides, regarding the diversitywithin one hop, when the channel’s loss rate is higher, the helper tends to capturemore missed information and thus gives more help. These results verify theeffectiveness of our proposed design.
44
Table 2-3. Throughput under different number of helpers exploitedloss rate(%) number of helpers throughput
0 0.7292 0.758
0.1 4 0.7836 0.8098 0.8230 0.4672 0.502
0.3 4 0.5336 0.5578 0.579
• MF has an obvious advantage when it comes to the throughput degradation perhop. As shown in Table 2-2, the slope of MF is only one-fifth of that of BATS codes,which makes MF especially favorable under massive relays.
• The experimental throughput result of MF is only 5% lower than the analyticalthroughput calculated under perfect rank estimation (see Fig. 2-6, Fig. 2-11). Thismeans our analysis and design have successfully bridged the gap between theoryand practice.
2.5.3.2 With different number of helpers
As we have mentioned, it is not required that every relay in the path should find a
helper. Under a 9 hop network, we fix the number of helpers that can be exploited, and
measure the throughput of MF scheme. Clearly, the maximum number of helpers is 8,
and if no helper exists, the scheme is actually BATS codes. The results are in Table 2-3.
It can be concluded from the results that as the number of helpers goes larger,
the throughput is better, which is perfectly logical and reasonable. When more helpers
are involved in the transmission, more diversity can be exploited. This trade-off can be
further considered in real systems.
2.6 Conclusion
In this chapter we propose Miss-and-Forward (MF) for the emerging ultra dense
network scenario. By designing a new cooperative recoding scheme, the assigned
helper nodes in vicinity can “forward” the “missed” information. Theoretically, we show
45
that the reason for the better performance of MF lies in a more desirable rank distri-
bution. Besides, some important design issues like helper selection, rank distribution
estimation are covered. Experiment results show that our method achieves higher
throughput than fountain codes and existing network coding schemes.
46
CHAPTER 3REGRET BENEFIT RATIO LINK SCHEDULER FOR WIRELESS BACKHAUL WITH
DIRECTIONAL ANTENNAS
3.1 Introduction
In Chapter 1, we have mentioned that an effective and efficient backhaul scheduling
schemes need to be designed with the characteristics of mmWave communications
taken into account.
The connectivity between the small cells and the aggregation point could be based
on point-to-point, point- to-multipoint, or mesh topologies cis (2013). In Fig. 3-1, we
present a typical scenario of densely deployed small cells underlying the macrocell
cellular network. In the small cells, mobile users are associated with the base stations
(BSs), and the BSs are connected via backhaul links with the mesh topology. There
are one or more BSs connected to the backbone network via the macrocell site, which
are called gateways. In this targeted small cells system, the backhaul network is in the
E-band, which provides high data rates. For the scheduling problem of the backhaul
network for small cells densely deployed, there are two aspects of challenges. In the
first aspect, concurrent transmissions need to be fully exploited to maximize the spatial
reuse gain. In the second aspect, the scheduling scheme should provide the quality
of service (QoS), which is either guranteed or desired throughput, for each link in the
Small Cells
Gateway
E-band Backhaul
Macrocell
Figure 3-1. The mesh backhaul network in the small cells densely deployed scenario.
47
backhaul network. However, the two objective can not be satisfied at the same time,
which further complicates this problem.
In this chapter, we propose Regret Benefit Ratio Scheduler (RBRS) for two different
MAC layers. The contributions of this paper are summarized as follows.
• We formulate the of optimal scheduling to maximize the number of links with theirQoS requirements satisfied in the slot based mmWave network as a nonlinearinteger programming problem. And a heuristic scheduling algorithm is proposedto solve this with low complexity. Specifically, for the first time, the two primaryobjective, maximizing the QoS and minimizing contention under directionalantenna, are combined into single objective function, which is summerzised asRegret Benefit Ratio (RBR). By utilizing this concept, a suitable concurrent groupof links can be scheduled at single time slot and the total network throughput canbe greatly improved.
• In order to make RBRS practical for wider usage scenarios, we also propose anextended implementation of it, the Distributed Regret Benefit Ratio Scheduler(D-RBRS), that can be deployed on CSMA/CS based network systems withoutmuch effort. We redefine the Regret and Benefit under the distributed setting, anda Coarse-to-Fine window mapping algorithm is exploited to bridge the RBR withbackoff window. Same as centralized version, the D-RBRS optimizes both QoSand contention.
• We evaluate our protocols for slot based and CSMA/CS based network respec-tively under the 73 GHz band. We propose different evaluation metrics for themand the simulation results demonstrate up to 60% performance gain for slot basedsettings and 30% gain for CSMA scenario respectively compared with otherexisting schemes.
The structure of this chapter is as follows. Section 3.2 describes the related work.
Section 3.3 gives an overview of the system model. Section 3.4 presents the RBRS for
the slot based mmWave backhaul network. And Section 3.5 introduces its distributed
version. Extensive experiments are conducted and evaluated in Section 3.6 and Section
3.7. Section 3.8 concludes this paper.
3.2 Related Work
Time division multiple access (TDMA) has been a widely used solution for mmWave
backhaul Taori and Sridharan (2015); Qiao et al. (2015). Taori et al. Taori and Sridharan
(2015) proposed a time-division multiplexing (TDM) based scheduling scheme to
48
support point-to-multipoint, non-line-of-sight, mmWave backhaul. Islam et al. Islam et al.
(2014) performed the joint cost optimal aggregator node placement, power allocation,
channel scheduling and routing to optimize the wireless backhaul network in mmWave
bands. In Niu et al. (2015), the scheduling for the radio access and backhaul networks
were jointedly designed. To the best of our knowledge, none of the previous works
are devoted to address the balance between the QoS requirement and the contention
between links in the mmWave network. On the other hand, similar problems have also
been investigated in WPANs Cai et al. (2010); Qiao et al. (2011, 2012). One influential
work is the Exclusive Region (ER) based scheduling which is introduced and derived
in Cai et al. (2010). It ensures that concurrent transmissions always outperform the
serial TDMA by co-scheduling links in the exclusive region. Qiao et al. Qiao et al.
(2012) proposed a concurrent transmission scheduling with the QoS requirements of
links considered. In Ref. Qiao et al. (2012) , the set of concurrent links are chosen in a
greedy manner to maximize the overall system throughput, through which the number
of links successfully scheduled is maximized. However, the global information of the
contentions residing in the network has not fully utilized under existing works. Besides,
there is a lack of QoS-favorable strategy. Most importantly, most works avoid addressing
the implicit connection and trade-off between minimizing contention and maximizing
QoS . In this paper, for the first time we introduce the concept of Regret Benefit Ratio to
the scheduling problem under mmWave bands. And this new indicator considers both
the global contention information as well as QoS benefit, and perfectly combines them.
With these advantages, the RBR Scheduler can find better concurrent transmission links
than existing solutions.
The slot-based nature of all the works above poses a big disadvantage that they
all heavily rely on centralized backhaul network controller to coordinate scheduling
process. In recent years, there are a few emerging works that propose applying CSMA
contention based scheduling on 60Ghz mmWave band. Gong et al. Gong et al. (2010b)
49
propose a directional CSMA/CA protocol designed specifically for 60GHz WPANs. It
adopts virtual carrier sensing and relies on a central coordinator to distribute network
allocation vector (NAV) information. The authors also extended the work to support
spatial reuse in Gong et al. (2010a). Similar works can also be found in Lee et al.
(2011). Another notable work by Zheng et al. Zheng et al. (2009) propose an optimal
scheduling algorithm for contention based network although it does not specifically
target on mmWave band. However, all these approaches only target on channel access
control and are generally lack of QoS support. Thus they cannot be applied to QoS-
aware backhaul networks. To the best of our knowledge, our proposed D-RBRS is the
first CSMA contention based scheduling protocol that prioritizes the MAC contention
window to better facilitate both concurrent transmission and QoS support.
3.3 System Model and Assumption
3.3.1 MAC Layer Structure
In our centralized scheme, we consider the scenario where small cells are densely
deployed, and assume there is a backhaul network controller (BNC) residing on one of
the gateways. Each BS in the network is equipped with an electronically steerable direc-
tional antenna, and can direct its beam towards other BSs for directional transmission.
In our investigated system, time is partitioned into superframes, and each superframe
consists of M time slots called channel time allocation (CTA). We further assume the
transmission requests and signaling information for mmWave backhauling are collected
by the 4G BS by its reliable transmission Qiao et al. (2015). Thus the BNC is able to ob-
tain the transmission requests and the location information of other BSs. In our scheme,
with directional transmission, multiple links can be scheduled concurrently in the same
time slot, which is also referred to as the spatial-time division multiple access (STDMA)
Qiao et al. (2012).
In our CSMA-based version, the proposed scheme operates in a completely dis-
tributed fashion and does not need centralized controller to coordinate link scheduling.
50
Before data transmission from source to destination within a link, the pair of directional
antennas should face to each other. This is coordinated by extra beacons, which use
different channels. Due to this reason, omni-directional antenna is also equipped for
beacon transmissions.
3.3.2 Physical Model
Since non-line-of-sight (NLOS) transmissions suffer from higher attenuation
than line-of-sight (LOS) transmissions Geng et al. (2009), we assume the directional
LOS transmission between BSs can be achieved with the locations of BSs adjusted
appropriately (e.g., on the roof). We assume there are N links requesting transmission
slots in the superframe, and each link represents one backhaul link. We denote the
distance between the transmitter si of link i and the receiver rj of link j by dij . We also
denote the antenna gain of si in the direction of from si to rj by Gt(i , j), and the antenna
gain of ri in the direction of from sj to ri by Gr(j , i). Then considering the path loss and
signal dispersion over distance, the received power at the receiver ri from si can be
calculated as
Pr(i , i) = k0Gt(i , i)Gr(i , i)d−nii Pt , (3–1)
where k0 is a constant coefficient and proportional to ( λ4π)2 (λ denotes the wavelength),
n denotes the path loss exponent, and Pt denotes the transmission power Qiao et al.
(2012). Due to the half-duplex assumption, adjacent links cannot be scheduled for
concurrent transmissions. If link i and link j are not adjacent, we denote it by i ∝ j . Then
under concurrent transmissions, the received interference at ri from sj can be calculated
as
Pr(j , i) = ρk0Gt(j , i)Gr(j , i)d−nji Pt . (3–2)
where ρ is the multi-user interference (MUI) factor related to the cross correlation of
signals from different links.
51
In this paper, we use the realistic antenna model Toyoda and Iiguse (2006) as
follows:
G(θ) =
G0 − 3.01(2θ
θ−3db), 0 ≤ θ ≤ θml ,
Gsl , otherwise;(3–3)
Gml = 2.6 ∗ θ−3db, (3–4)
G0 = 10 ∗ log(1.6162
sin(θ−3db/2))2, (3–5)
Gsl = −0.4111 ∗ lnθ−3db − 10.579, (3–6)
where θml is the main lobe width in unit of degree; and G0 and Gsl are maximum antenna
gain and side lobe gain respectively.
According to the Shannon’s channel capacity, the achievable data rate of link i can
be estimated as
Ri = ηW log2(1 +Pr(i , i)
N0W +∑j∝iPr(j , i)
), (3–7)
whereW is the bandwidth, and N0 is the onesided power spectra density of white
Gaussian noise Qiao et al. (2012). η ∈ (0, 1) describes the efficiency of the transceiver
design.
3.4 RBRS under Slot based MAC
3.4.1 Problem Formulation And Analysis
In this section, we formulate the optimal scheduling problem into a nonlinear integer
programming problem.
We assume there is a minimum throughput requirement for each link i , and denote
it by qi . We denote a schedule as S, and assume it has K stages. In each stage,
multiple links are scheduled for concurrent transmissions. For each link i , we define a
52
binary variable aki to indicate whether link i is scheduled in the k th stage. If so, aki = 1;
otherwise, aki = 0. We denote the number of time slots of the k th stage by δk .
Since there are different links in different stages, we denote the transmission rate of
link i in the k th stage by Rki . Then we can obtain Rki as
Rki = ηW log2(1 +aki k0Gt(i , i)Gr(i , i)d
−nii Pt
N0W + ρ∑j
akj k0Gt(j , i)Gr(j , i)d−nji Pt
). (3–8)
Then we can obtain the throughput of link i based on S as
Ti =
K∑k=1
δk · Rki · tslot
t0 +M · tslot, (3–9)
where t0 is the time duration of collecting transmission requests and signaling informa-
tion, and tslot is the time duration of each time slot in the CTA period (CTAP). Then we
define a binary variable Qi to indicate whether the QoS requirement of link i is satisfied
in S. If so, Qi = 1; otherwise, Qi = 0. Given the throughput requirements of links, with
the limited number of time slots in the CTAP, the optimal schedule should accommo-
date as many links as possible. Therefore, the optimal scheduling problem P1 can be
formulated as follows.
(P1) max
N∑i=1
Qi (3–10)
s.t.
Qi =
1, if Ti ≥ qi ,0, otherwise;∀ i (3–11)
K∑k=1
δk ≤ M; (3–12)
aki + akj ≤ 1, if flow i and j are adjacent; ∀ i , j (3–13)
53
This is a nonlinear integer programming problem, and is NP-hard. Constraint
(3–11) indicates if the throughput of link i in the schedule is larger than or equal to its
throughput requirement, Qi = 1; otherwise, Qi = 0. Constraint (3–12) indicates there
are at most M time slots in the CTAP. Constraint (3–13) indicates due to the half-duplex
operation of BSs, adjacent links cannot be scheduled for concurrent transmissions since
there is at most one connection for each node.
Since it is difficult to solve the problem of P1 in polynomial time, we propose an
efficient and practical scheduling algorithm instead in the next section.
3.4.2 Heuristic Algorithm Design
In this section, we propose the Regret Benefit Ratio Scheduler for problem P1. The
key issue for scheduling is to find a combination of links that are suitable for concurrent
transmission. It requires those links have minimal internal interference and are beneficial
for QoS achievement. In our algorithm, links in a concurrent set at one time slot are
selected based on our new metric regret benefit ratio. To present the overall scheduling
algorithm, we first introduce the contention graph under directional antennas, which
captures the global knowledge of interference; Then, we define priority for each link out
of the consideration of QoS requirement; After that, we give definition for regret benefit
ratio, which combines contention and QoS into single indicator. With this new indicator,
we present the algorithm for finding concurrent set. For the sake of convenience, we
summarize some mathematical notations in Table 4-1.
3.4.2.1 Contention graph
The RBRS summarizes the global interference information in the contention graph,
in which a node represents a real link and an edge between a pair of nodes marks the
contention. We judge the existence of contention between every pair of links based
on two principles: 1) the half duplex nature where a single BS can not receive and
transmit packets at the same time. In other words, if two links share the same source or
destination, there will be a contention edge between them; 2) the impact that one link
54
Table 3-1. Mathematical notationsMath symbol Meaning
G contention graphv vertex in the graphpv priority of vertexV (G) vertex setE(G) edge setW (G) sum of the weights of all verticesN(G) the number of vertices in the graphNG(v) the neighbors set of vertex vN+G (v) v and its neighbors setd(v ,G) degree of vertex v
has on another. For every link pair, we define the relative-interference (RI) as follows:
RIj ,i =Pr(j , i)
Pr(i , i)(3–14)
where Pr(j , i) and Pr(i , i) is defined by (3–2) and (3–1) respectively. We insert an edge
between link i and link j if max(RIi ,j ,RIj ,i) > σ, where σ is a threshold.
3.4.2.2 QoS-aware priority
We assign a priority value to each link out of QoS considerations. Links that can
achieve requested throughput more quickly are preferred in our scheduling because
they can soon stop transmission and leave time slots for others to use. To give more
weight to those links, we define the priority as the inverse of the number of slots that a
link needs in CTAP to achieve its QoS requirement. Based on previous definitions, the
priority value of link v can be expressed as follows:
pv =Rvqv
(3–15)
where
Rv = ηW log2(1 +Pr(i , i)
N0W). (3–16)
This definition is the ratio of actual achievable throughput and required one. In other
words, if one link has much higher chance to achieve the what is required, it has more
priority value.
55
3.4.2.3 Regret Benefit Ratio for each link
We need a metric to incorporate both the contention graph and the QoS priorities
of the links. Note that once a node is picked, the neighbors of it will not be picked again
due to contention between them. In other words, to maximize the QoS priority of the
scheduling, one should always pick the node that has the large priority value while that
of its neighbors are small. To achieve that, we combine the two objective function into a
single one, which maximize the beneift while minimize the regret of its neighbors at the
same time. We mathematically formulate this metric as follows:
rv =
∑i∈NG(v) pi
pv, (3–17)
where rv is the regret benefit ratio, and NG(v) is the neighbor set of node v .
3.4.2.4 Find concurrent set
With regret benefit ratio defined above, we can now formulate the algorithm to find a
suitable concurrent set at every signle time slot. In the RBRS, the set of links scheduled
at any slot should be a QoS-aware independent set. Obviously when some links achieve
QoS requirement and are removed from current scheduling, this condition may no
longer be satisfied. When this happens, we will select links from contention graph G to
add to the current scheduling set to generate a new concurrent set.
To begin with, the “unqualified” links which we will not select from should be
removed from G. A link is “unqualified” if it satisfies one of the following conditions: 1) It
has already achieved QoS requirement so there is no need to consider it; 2) It has been
scheduled and thus ongoing now; 3) It is a neighbor of one of the ongoing links. The
third condition comes from the fact that neighbors in G should never appear together in
the independent set.
Then, we iteratively select the node (or link) with smallest RB ratio from the remain-
ing graph and add it to the scheduling set. In this way, we maximize the the total priority
56
values within the scheduled set in a greedy manner. This step is summarized in Eqa. 3–
18. Once the node is picked, we remove the chosen node as well as its neighbors in G
and begin to select the next one as long as the remaining contention graph is not empty.
The detailed algorithm is summarized in Algorithm 3.1. We use s to denote the
scheduling set. In this algorithm, we use the existing scheduling set as the input and
generate a new one.
Algorithm 3.1. FindConcurrentSet
Input:
1: existing schedule set s
2:
Output:
3: new scheduling set , s;
4: remove unqualified links from G
5: while G = ∅ do
6:
v = minv∈Grv (3–18)
7: s := s ∪ v
8: G := G[V (G)− N+G (v)]
9: end while
return s
3.4.2.5 Admission control
Before the scheduling among links, admission control is exploited to get rid of links
that are never able to achieve its QoS requirement. In computing priority in Eqa.(3–15),
we seek the number of slots that are needed to transmit all bits. When the number is
larger than all the number of slots within a superframe, this link can be rejected and will
not be considered in scheduling.
57
3.4.2.6 Overall scheduler design
Now we summarize the overall scheduling algorithm for the backhaul network.
After the BNC receives QoS requests from BSs, it will construct the contention graph
G and make scheduling decisions. According to (3–8) (3–9), the slots can be divided
into a number of stages during which the same scheduling is kept. In RBRS, the end of
one stage is the slot in which some scheduling links have achieved QoS requirement.
We call those links “finished”. In other words, we should check at every slot if there
are some newly finished links, and if so, a new concurrent set should be found using
Algorithm 3.1.
For N links and M slots in CTAP, we use a N ∗M binary matrix B to denote the final
scheduling S, where B(i , j) = 1 means the link i at slot j is scheduled. The detailed
process is shown in Algorithm 3.2. The initialization steps are among line 1-5. In line
6-12, we will call Algorithm 3.1 to generate the new scheduling array whenever needed.
In line 10, we will denote the scheduling set s as a vector and then assign it to B.
Algorithm 3.2. Regret Benefit Ratio Scheduler
1: BNC receives transmission request ri(i = 1, 2, ...N) requiring minimum throughput
R imin
2: construct contention graph G
3: compute p for links
4: do admission control
5: initialize empty set s
6: for slot k(1 ≤ k ≤ M) do
7: if k = 1 or some links newly finished then
8:
s = FindConcurrentSet(G, s,p)
9: end if
10: B(:, k) = s
58
11: B(:, k) = B(:, k − 1)
12: end for
return B
3.4.3 Performance Analysis
In algorithm 3.1, we use RBR to iteratively find the propoer node into concurrent
set. Note that with priority assigned with each link, it is desired that the concurrent set
should contain larger total priority values. To ensure the performance of RBRS, we seek
to show that the total priority values within the concurrent transmission set is at least as
much as some lower bound.
Proposition 3.1. Assume xi > 0, yi > 0, ∀1 ≤ i ≤ n. We have
∑i
y 2ixi
≥ (∑i yi)
2∑i xi
(3–19)
Proof. By using Cauchy-Schwarz inequality,
(∑i a2i )(
∑i b2i ) ≥ (
∑i aibi)
2
and assigning ai =√xi , bi =
yixi
, we can get the result.
To analyze the total priority value a concurrent set can produce, first we define the
total priority value the graph G contains as P. And the priority degree is defined as the
regret benefit ratio in Eqa. 3–17.
pd(v ,G) = rv . (3–20)
In accordance, we define the average priority degree as the following:
pd(G) =
∑v∈G pvpd(v ,G)
P. (3–21)
Let Gi be the subgraph induced by the remaining vertices at the beginning of the
i -th iteration. And p(G) means the total priority values within the graph G. And we define
59
the total priority values within a concurrent set to be γG , which can be expressed as the
following:
γG =∑i
pvi , (3–22)
where one node is picked at i th step.
We have the following theorem.
Theorem 3.1.
γG ≥ P
pd(G) + 1(3–23)
Proof. By definition, we have :
pd(G) ∗ P =∑v∈G
pvpd(v ,G)
≥∑i
∑v∈N+Gi (v)
pv ∗ pd(v ,Gi)
≥∑i
∑v∈N+Gi (v)
pv ∗ pd(vi ,Gi)
=∑i
p(N+Gi (v)) ∗ pd(vi ,Gi)
(3–24)
Since P =∑i p(N
+Gi(v)), we can deduce the following:
(pd(G) + 1) ∗ P ≥∑i
p(N+Gi (v))2
pvi. (3–25)
Finally, we apply Proposition 1 with xi = pvi , yi = p(N+Gi(v)). The inequality
(pd(G) + 1) ∗ P ≥ P2
γG(3–26)
holds, which implies the theorem.
60
3.5 D-RBRS under CSMA/CA based MAC
In the CSMA/CA settings, the QoS is no longer a restricted requirement, but
a desirable objective. And we also want to let the number of links that achieve its
QoS to be large. We can imagine that if one link, who has low desirable throughput,
continues to take up the channel, it will kill other transmissions and drag down the total
performance. On the other hand, if one has high demand but low chance to transmit,
it will kill itself. Thus, a proper situation should be that every link intelligently behave
according to their demand and its actual situation in the contented graph, so that they all
achieve their objective.
In this section, we propose a practical Distributed Regret Benefit Ratio Scheduler
(D-RBRS) to solve the scheduling problem under CSMA/CA framework. The key
idea is that we adjust the back of window with new Regret Benefit Ratio. Without the
global knowledge introduced by the central scheme, D-RBRS collects the contention
information with neighbor detection algorithm. After that, it implement the regret benefit
ratio with the back-off window mechanism.
3.5.1 Contention Window and Regret Benefit Ratio
In the distributed network, centralized control is not allowed. For every base station
that sends traffic, the probability for channel acquisition is dependent on the size of
contention window it utilizes on the MAC layer, which we denote as CW . And intuitively,
we want CW to be smaller if its traffic has a higher priority to acquire the channel.
Since the QoS awareness and the contention are still the key aspects for the
distributed scenario, we reuse the concept of regret benefit ratio to determine the priority
of the traffic. To summarize, we have the following equation:
CW ∝ RBR = regretbenefit
. (3–27)
However, If we directly reuse the definition of RBR in the centralized scheme in
eqa. (3–17), it is required to acquire others’ priority information. This may require
61
extra header for overhearing , which incurs overhead. To make our solution simple to
implement and consistent with existing CSMA/CA MAC scheme, we redefine the two
component, benefit and regret, respectively. For the benefit value, we define it positively
relative to the desired QoS. Intuitively, if this value is large, we should assign more
chance for such link. And the regret value is defined as number of contented neighbors,
which is easy to obtain with our neighbor detection algorithm which we will discuss next.
In stead of directly computing RBR, we seperate the benefit and regret component and
then use two window mapping process to map different RBR to CW .
3.5.2 Neighborhood Detection
In order to effectively calculate the regret value, each station needs to keep track
of how many other stations that can potentially cause interference to the station. One
straight-forward way to conduct neighborhood detection could be that every node
periodically broadcasts beacon signal to its neighbors. If the other node is able to
receive such beacon signal, then it knows it has one neighbor that could possibly
in the interference range. However, since interference only occurs when nodes are
transmitting, such active signaling mechanism can cause unnecessary overhead over
time. The increased overhead will not only impact the performance of the network, but it
also increases the energy consumption. We can eliminate such overhead by setting up
an overhearing mechanism at each base station.
The neighborhood detection algorithm works as follows. At time slot t, each base
station bi counts the number of distinct sources for links not destined to bi by letting the
NIC operate in promiscuous mode. Therefore, when a nearby base station bj(j = i)
sends a packet, base station bi is able to detect the signal and effectively count bj as its
neighbor. The detailed procedure is described in Algorithm 3.3.
Algorithm 3.3. Neighborhood Detection
Each base station does the following:
Output: the number of interfering neighbors detected.
62
1: Enable promiscuous mode;
2: Define and initialize a neighbor set N;
3: while received a packet p do
4: src = source address of p;
5: dest = destination address of p;
6: if dest is not a broadcast address then
7: Define bsrc as the base station that sent packet p;
8: Add bsrc to neighbor set N;
9: end if
10: end while
return size of N;
While signal in mmWave band is more concentrated and less likely that it will
cause interference in large range, yet it is still not uncommon that interference does
happen when several base stations are located in densely deployed small cells and,
in the meantime, the directional antennas’ orientation is also set within the interfering
sidelobe or mainlobe area. Thus, for a base station bi , there could be simultaneously
several neighbor base stations contending for the same channel. This will cause the
degradation of network throughput if we don’t take measures to mitigate the problem.
Our proposed D-RBRS is right designed for this task. D-RBRS is able to schedule links
according to a base station’s contention level, which is positively proportional to its
number of neighbors.
3.5.3 Window Prioritization
In the following two section, we will discuss the window mechanism that we ex-
ploited. We define eight priority levels indexed from 0 to 7. The larger index number
represents higher priority level and vice-versa. Each priority level has parameters of
minimum contention window size (CWmin) and maximum contention window size
(CWmax). The configuration of these parameters are shown in Table 3-2.
63
Table 3-2. Contention Window Prioritization
Priority 0 1 2 3 4 5 6 7
CWmin 512 256 128 64 32 16 8 3
CWmax 1023 511 255 127 63 31 15 7
For a specific priority, the CWmin and CWmax regulate the back-off behavior
of current contending base station. When contention occurs, similar to CSMA/CA
mechanism, the scheduler will initialize a random back-off window of size within CWmin
and CWmax. If contention still occurs after back-off, the scheduler will double the size
of current back-off window until it reaches CWmax and will keep it at CWmax until
reset. The back-off procedure continues. Generally, the average size of back-off window
determines how contentious current base station is. The larger the size of back-off
window, the longer the base station will wait to try to initiate next transmission, thus
exhibiting less contentious behavior, and vice-versa.
Therefore, we utilize this fact to configure the CWmin and CWmax parameters
with respect to their associated priority levels. For contention resolving purposes, we
want the base stations operating in lower priority level to be less contentious. Thus we
assign them with relatively larger CWmin and CWmax values. Vice-versa, the base
stations with higher priority levels will be assigned with smaller CWmin and CWmax
values. Furthermore, we also try to adjust CWmin and CWmax to make each priority
level more distinct and disparate from one another; such that, for a given priority level i ,
the probability that the randomized back-off window size will overlap with that of priority
level j(j = i) will be reduced to minimum. Table 3-2 shows the exact configuration of
these parameters, where we completely eliminate the possible back-off window size
overlapping between different priority levels.
3.5.4 Coarse-to-Fine Window Mapping Algorithm
Based upon prioritized contention window configuration in Table 3-2, we propose
a Coarse-to-Fine Window Mapping (CFWM) algorithm. Namely, CFWM is a two-phase
64
process. In the coarse-phase, the algorithm addresses the regret, while in the fine-
phase, benefit is accommodated.
3.5.4.1 Coarse phase
Let’s first define contention degree d ic , as the number of neighboring base stations a
base station bi detects. The value of d ic will be calculated by Algorithm 3.3 described in
Section 3.5.2. CFWM works by assigning priority level to current schedule according to
its base station bi ’s contention degree d ic . We call this coarse phase of CFWM, which is
illustrated in Algorithm 3.4.
Algorithm 3.4. Priority Level Computation (Coarse)
Input: contention degree d ic for base station bi .
Output: the corresponding priority level.
1: Define Pi as the priority level to be assigned for base station bi ;
2: if d ic > 7 then
3: Pi = 0;
4: else
5: Pi = 7− d ic ;
6: end if
return Pi ;
The intuition behind Algorithm 3.4 is that the scheduler always tries to assign higher
priority level to base station bi that has smaller value of contention degree d ic . In such
case, since the base station has less number of neighbors contending with it (smaller
value of contention degree), it is more likely that this base station is able to fulfill the
QoS requirement and increase the overall network throughput of the system. Thus,
CFWM will assign it with a higher priority level. On the other hand, if base station bi
has a larger value of contention degree, the CFWM will assign it with a lower priority
level which tends to curb the sending rate of base station bi . In practice, the number of
contention neighbors a base station potentially has usually would not exceed 7, thus
65
we believe the linear mapping between contention degree and priority level (line 2–5
in Algorithm 3.4) is reasonable. For cases where contention degree does exceed 7,
CFWM just assigns priority level 0, the lowest, to the corresponding base stations.
In essence, each priority level determines the contention window adjustment
strategy. Since the lower the priority level is, the larger CWmin/CWmax will be set, which
leads to a less contentious base station. It is also true vise-versa. Our rationale behind
this mechanism is that we always want the least contending base station to transmit
first, because the less contending a base station is, the higher throughput the base
station can potentially create. As will be seen in Section 3.7, our experimental results
also support this rationale.
3.5.4.2 Fine phase
So far, the priority level assignment procedure described in Algorithm 3.4 only con-
siders the contention between base stations, which is the regret. The more neighbors a
base station bi has, the more contending bi becomes, the lower priority level bi will be
assigned. Another important issue that we need to address is QoS-awareness (benefit)
of the D-RBRS. On top of the scheduling scheme in Algorithm 3.4, we equip D-RBRS
with QoS scheduling capability which is described in Algorithm 3.5. We call this fine
phase of CFWM.
Algorithm 3.5. Contention Window Adjustment (Fine)
Input:
1: Pi – current priority level at base station bi ;
2: qf – desired throughput of link f ;
3: α – scaling parameter;
4: β – window size.
Output:
5: CWmin – the adjusted CWmin value.
6: CWmax – the adjusted CWmax value.
66
7: Retrieve CWmin and CWmax values with respect to Pi ;
8: Let f (t) = 21+e−αt − 1;
9: CWmax = CWmin + f (qf )· (CWmax − CWmin);
10: CWmin = max (CWmax − β,CWmin);
return CWmin and CWmax .
In Algorithm 3.5, CFWM tries to make a finer contention window parameter ad-
justment based on QoS, which is the benefit. According to our QoS-aware schedule
policy, the higher QoS a link has, the sooner it needs to be scheduled in order to achieve
optimal throughput over the network. CFWM achieves this purpose by adjusting the
CWmin and CWmax value according to the QoS inside current priority level Pi . Recall in
Section 3.5.3, we described that CWmin and CWmax determine the range within which
the size of contention window could be. Although not guaranteed, statistically, when
CWmin or CWmax increases, the back-off time for current DCF will become longer since
the probability to randomize a larger back-off slot number becomes higher. Therefore,
when a link with higher QoS priority needs to be scheduled, Algorithm 3.5 will return a
decreased CWmax and CWmin value (line 3 and line 4 of Algorithm 3.5) which essen-
tially leads to a shorter back-off time. This will make the link be able to have much larger
probability to be scheduled earlier than its contending counterparts if there are any.
Algorithm 3.4 and Algorithm 3.5 altogether constitute the cornerstone of our
proposed CFWM algorithm. They work cooperatively to schedule links according to both
their contention degree and QoS, i.e. regret and benefit. When a base station bi has a
link to send, CFWM will first retrieve appropriate priority level by referring to Algorithm
3.4 with contention degree information. Afterwards, CFWM will continue to run Algorithm
3.5 to set proper CWmin and CWmax values for scheduler’s back-off window inside
current priority level. Results returned from Algorithm 3.4 only indicates which priority
level current link should be associated with, while Algorithm 3.5 further deals with the
exact values of CWmin and CWmax inside that priority level. Thus Alogrithm 3.4 is
67
called coarse phase while Algorithm 3.5 is called fine phase. That is how CFWM deals
with both contention issue and QoS-awareness in a unified framework.
3.5.5 Inner Competition
The window mapping mechanism can not deal with the competition between links
that share the same source node. For example, when we have two links starting from A,
which denoted as LAB and LAC respectively, the packets that head for B will be contained
in a different queue from packets heading for C. And, we need some mechanism to
decide which packets go first. In our implementation, the source node would rank the
links according to their RBR directly computed by (3–27) , and then do a simple query
starting from the best candidate. The query itself is achieved by beacons (see Section
3.3.1).
3.5.6 Admission Control
In our centralized scheme, admission control is desired since the QoS is a hard
requirement. In the distributed design, although QoS is best-effort oriented, if the actual
achievable throughput is much lower than the desired one, the terminal is allowed to
terminate the transmission.
3.6 Numerical Results
In this section, we evaluate the performance of RBRS in the mmWave band. First,
we introduce the setup of our experiments and then we delve into detailed performance
evaluations for it.
3.6.1 Experiment Setup
We consider a backhaul network with 10 base stations which have at most 90 links.
Since the scheduling performance is dependent on the location of stations, we randomly
generate a position for each BS within a 1000 square meters area. Meanwhile, for every
link, we randomly choose its source and destination. And the requested throughput
for this link is uniformly distributed between 1 Gbps and 3 Gpbs. For the path loss, we
use the channel model in Ref Akdeniz et al. (2014). Besides, we adopt the widely used
68
realistic directional antenna model in Ref Toyoda and Iiguse (2006). All the BSs in the
system use the same transmission power level. Some other parameters are shown in
Table 3-3. We conduct our experiments on MATLAB.
Table 3-3. Simulation parametersmeaning parameter value
system bandwidth W 1.2 GHztransmission power Pt 30 dbmbackground noise N0 -134 dmb/MHz
slot time tslot 18 µsbeacon period tBP 50 µs
random access period tCAP 800 usnumber of slots in transmission period M 2000
We implemented the serial TDMA, and the state-of-the-art protocol STDMA Qiao
et al. (2012) for comparison. To evaluate our proposed protocol, the following metrics
are considered:
• Number of successful links: the number of links that achieve the required QoS.Note that if a link has been scheduled but can not satisfy the QoS, it will not becounted as successful a link.
• System throughput: the achieved total throughput of the backhaul network. Inother words, this metric is the average of sum of the throughputs of all links.
3.6.2 Performance Evaluation for RBRS under slotted MAC
In this subsection, we design experiments to study the scheduling algorithm
performance under different situation. To reduce random error for each experiment, we
repeat the same experiment for 50 times and the average results are calculated and
taken.
3.6.2.1 Effects of number of links
In this case, we choose the number of slots in CTAP as 2000, and set σ = 10−4.
We vary the number of links in the backhaul network from 10 to 90. With the increasing
number of demanding links, we evaluate the two metrics and plot the results in Fig 3-2.
From the results, we can observe the trend of the performance of the RBRS under
the increasing number of demanding links. The more demanding links there are, the
69
Number of Demanding Links10 20 30 40 50 60 70 80 90
Num
ber
of S
ucce
ssfu
l Lin
ks
4
6
8
10
12
14
16
18
RBRSSTDMATDMA
A Number of successful links
Number of Demanding Links10 20 30 40 50 60 70 80 90
Sys
tem
Thr
ough
put(
Gbp
s)
10
15
20
25
30
35
RBRSSTDMATDMA
B System throughput
Figure 3-2. Performance under different number of links
more chances for the spatial reuse, and thus both the number of successful links and
the system throughput keep increasing. Due to the system capacity constraint, they
gradually become flat and reaches the capacity.
Compared with TDMA and STDMA, the RBRS has obvious advantages. TDMA
has no spatial reuse at all so it can only schedule limited links. When only a few links
are to be scheduled, the difference between STDMA and RBRS is trivial because
both scheme can almost accommodate all the demanding links. But as the number of
demanding links increases, the RBRS can achieve better performance in two aspects.
First of all, when the number of demanding links is around 10 to 20, the performance of
STDMA has already entered the flattened phase where more number of links will not
bring obvious better performance; However, the proposed scheme keeps increasing
dramatically until the number of demanding links reaches 80. Moreover, when the traffic
demand is large, the RBRS can achieve around 60% more number of successful links
and about 40% more system throughput than STDMA.
The better performance of RBRS comes from two facts. First, it uses global
contention knowledge to make scheduling. For STDMA, a new link will be added to
scheduling set as long as it can increase the total throughput. This method may get
stuck to bad local optimal, where highly contented links are co-scheduled. While in
70
Number of Slots in CTAP500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Num
ber
of S
ucce
ssfu
l Lin
ks
4
6
8
10
12
14
16
18
RBRSSTDMATDMA
A Number of successful links
Number of Slots in CTAP500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Sys
tem
Thr
ough
put(
Gbp
s)
5
10
15
20
25
30
35
RBRSSTDMATDMA
B System throughput
Figure 3-3. Performance under different number of slots
RBRS, we always schedule the links that are relatively independent with each other, and
thus more close to the global optimal. Secondly, the QoS of a link is considered as an
priority in RBRS, and contributes to the overall performance.
3.6.2.2 Effects of number of slots
In this case, we aim to compare the performance of different protocols under
different number of slots in CTAP. The number of demanding links is kept to be 90. We
change the number of slots in CTAP from 500 to 5000, and evaluate the two metrics as
before. The results are shown in Fig 3-3. As we can observe, the number of successful
links and system throughput only slightly increase as the number of slots in CTAP
changes. With enough time slots, the RBRS can achieve 17 successful links while
STDMA can only schedule around 11 links. Besides, the system throughput of the
RBRS is 10 Gbps higher then that of STDMA.
3.6.2.3 Effect of beam width of the antenna
In this case, we aim to compare the performance of different protocols under
different beam width of the antenna. Specifically, we change the degree of half power
beam width from 15 to 90 degree. The number of demanding links is kept to be 90. And
the number of time slots is fixed to be 200. We evaluate the two metrics as before. The
results are shown in Fig 3-4. As we can see, the number of successful links and system
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Degree of half power beam width10 20 30 40 50 60 70 80 90
Num
ber
of S
ucce
ssfu
l Lin
ks
0
5
10
15
20
25
RBRSSTDMATDMA
A Number of successful links
Degree of half power beam width10 20 30 40 50 60 70 80 90
Sys
tem
Thr
ough
put(
Gbp
s)
5
10
15
20
25
30
35
40
45
RBRSSTDMATDMA
B System throughput
Figure 3-4. Performance under different beam width
throughput decrease as the half power beam width gets wider. This is because the
narrower the beam width, the less contention it will produce. Our proposed RBRS can
achieve best performance with difference beam width.
3.6.2.4 Theoretical bound evaluation
In section 3.4.3, we have proved the existence of the lower bound of the produced
total priority within one concurrent transmission set. In this part, we test the correctness
of this bound. We fixed the link number to be 50 and randomly placed the nodes.
Then, in every single slot, we calculate the real-time total priority within the current
transmitting links. Meanwhile, based on the current contention graph, we also calculated
the theoretical lower bound of this value. The result is plotted in figure 3-5. We can have
the following observations:
• The 2000 slots can be divided as many phases, and each of them is correspond-ing to one concurrent transmission set.
• The theoretical bound is decreasing as time goes. This is because when some ofthe link achieves the QoS, they are removed from the contention graph, and thusthe right side of Eqa. 3–23 is changing.
• The theoretical bound is always lower than the actual produced value of the totalpriority, which proved the correctness of the theory.
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Time slots0 200 400 600 800 1000 1200 1400 1600 1800 2000
Tot
al p
riorit
y
10
15
20
25
30
35
40
45
50
55
Real time valueTheoretical bound
Figure 3-5. The lower bound of total priority
3.7 Simulation Results
In this section, we evaluate the performance of D-RBRS in the mmWave band.
First, we introduce the setup of our simulators and then we delve into detailed perfor-
mance evaluations for D-RBRS.
3.7.1 Development of Simulators
For performance evaluation of D-RBRS, we still consider a backhaul network
consisted of 10 base stations (nodes) randomly distributed over a 1000 square meters
area . Each base station is equipped with directional antennas as well as quasi omni-
directional antennas. And for each node, we still implemented the widely adopted
directional antenna model as described in Toyoda and Iiguse (2006). The beamwidth of
the directional antennas is set to 30 degrees and the channel is set to work on 73GHz
band. On top of directional antenna model, our proposed D-RBRS is implemented.
The simulation system is developed under NS-3 ns3 (2007). To be consistent with the
centralized version, we set the range of the demanding throughput of links the same
as before. For parameters such as system bandwidth, power, and noise, we reuse the
configuration as Table 3-3.
For performance comparison, we also implemented the optimal D-RBRS scheme
proposed in Zheng et al. (2009) and a default 802.11 random access scheme as a
73
baseline. To evaluate our proposed scheme, we still consider the two following metrics
as the centralized control:
• Number of successful links: Although the throughput requirement is elastic, westill want more links to achieve their objective.
• System throughput: Needless to say, system throughput is a key performancemetric we primarily concern about. By throughput, we mean the overall point-to-point throughput on the whole backhaul network.
3.7.2 Performance Evaluation for D-RBRS under CSMA/CA
In this subsection, we design experiments to study the scheduling algorithm
performance under different scenarios. To reduce random error for each experiment,
we repeat the same experiment for 10 times and the average results are calculated and
taken.
3.7.2.1 Effects of number of links
The number of links is varied in range of 10 to 90. And each link is a data steam
that contains 100 packets. Once the number of links is determined, these links are
generated and added randomly among the base stations. For each base station,
one packet is scheduled to be generated and sent from transport layer in every 30
milliseconds, i.e., the sending interval. We recorded the elapsed time between moment
when first packet of the whole network was sent at transport layer and moment when
last packet of the whole network was successfully received at one base station. Then
we calculated the overall system throughput for each scheme. We recorded number of
successful links and throughput performance of each scheme for different number of
links. Finally, we plotted the comparison results shown in Figure 3-6.
We have the following observations:
• With RBR exploited, D-RBRS achieves higher number of successful links. FromFigure 3-6, we observe that 30% more links can achieve their desired throughputthan DOS under full demanding links. Thanks to the coarse-to-fine hierarchicalstructure of D-RBRS, the scheduler is able to make best use of the availablecontention window values and assigns them to links according to both theircontention and QoS priorities.
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Number of Demanding Links10 20 30 40 50 60 70 80 90
Num
ber
of S
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ks
3
4
5
6
7
8
9
10
11
12
D-RBRSDOSCSMA/CA
A Number of successful links
Number of Demanding Links10 20 30 40 50 60 70 80 90
Sys
tem
Thr
ough
put (
Gbp
s)
12
13
14
15
16
17
18
19
20
21D-RBRSDOSCSMA/CA
B System throughput
Figure 3-6. Performance under different number of links
• Our proposed D-RBRS achieves the best performance in terms of system through-put among all of the three schemes. It achieves an average of 20% throughputgain over DOS and 40% over 802.11. This is because the contention betweendifferent links with different priorities can be reduced to minimum.
• Our proposed D-RBRS is better suited for practical environment. From Figure 3-6,we see that DOS does not achieve the best performance although it is theoreticallyproved to be optimal. This is due to the fact that DOS relies on highly accuratepast channel estimation to determine current scheduling scheme. However, inpractical environment, it is difficult to achieve such an accurate channel estimationin real time. This makes D-RBRS perform much better than DOS.
3.7.2.2 Effects of number of packets in each link
In this experiment, we randomly add 90 links in the system. Then, we vary the
number of packets for each link from 100 to 1000. Other setups remain the same as
described in Section 3.7.2.1. For the throughput calculation, as previously, we recorded
the elapsed time between moment when first packet of the whole network was sent at
transport layer and moment when last packet of the whole network was successfully
received at one base station. The performance comparison is shown in Figure 3-7.
It clearly shows that:
• With more number of packets in each link, the successful links and systemthroughput increase slowly for all the three schemes. However our proposed D-RBRS can achieve 3 more successful links than DOS and double the performanceof pure CSMA/CA. In terms of throughput gain, we can achieve 20% gain over
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Number of Packets in Each Link100 200 300 400 500 600 700 800 900 1000
Num
ber
of S
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ssfu
l Lin
ks
5
6
7
8
9
10
11
12
D-RBRSDOSCSMA/CA
A Number of successful links
Number of Packets in Each Link100 200 300 400 500 600 700 800 900
Sys
tem
Thr
ough
put (
Gbp
s)
14
15
16
17
18
19
20
21
22
D-RBRSDOSCSMA/CA
B System throughput
Figure 3-7. Performance under different number of links
DOS and 40% gain over 802.11 as the number of packets increases. Judging fromthe result, it is consistent with Fig 4.
• The general trend is that when the number of packets in each link increases,the overall system throughput also increases. This is because more transmitteddata will decrease the percentage of overhead such as link setup time. And it willconverge.
3.7.2.3 Effects of beam width of the antenna
In this experiment, we randomly add 90 links in the system as before. Then, we fix
the number of packets for each link to be 500. And other setups remain the same as
described in Section 3.7.2.1. For the throughput calculation, as previously, we recorded
the elapsed time between moment when first packet of the whole network was sent at
transport layer and moment when last packet of the whole network was successfully
received at one base station. The performance comparison is shown in Figure 3-8.
It clearly shows that:
• When the beam width get larger, the successful links and system throughputdecrease slowly for all the three schemes. This is because as the half powerbandwidth increases, the contention in the network increases. Besides, this isconsistent with our findings in the centralized scheme.
• As the beam width changes, our proposed D-RBRS can always achieve moresuccessful links and system throughput than DOS and double the performance ofpure CSMA/CA.
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Degree of Half Power Beam Width10 20 30 40 50 60 70 80 90
Num
ber
of S
ucce
ssfu
l Lin
ks
2
4
6
8
10
12
14
16
18
D-RBRSDOSCSMA/CA
A Number of successful links
Degree of Half Power Beam Width10 20 30 40 50 60 70 80 90
Num
ber
of S
ucce
ssfu
l Lin
ks
5
10
15
20
25
30
D-RBRSDOSCSMA/CA
B System throughput
Figure 3-8. Performance under different beam width
Discussion: Comparing with the performance of RBRS, the D-RBRS has some
performance degradation. This makes sense since the distributed control lacks the
knowledge of global information and CSMA/CA will definitely incur unwanted back off by
its nature. Both RBRS and D-RBRS can achieve best performance in their own settings.
3.8 Conclusion
In this chapter, we consider the problem of optimal scheduling to maximize the
number of links with their QoS requirements satisfied in the mmWave backhaul network.
The key concept we proposed is Regret Benefit Ratio (RBR), which can be utilized to
schedule the best concurrent links in both centralized and distributed network scnario.
And RBRS and D-RBRS are designed and implemented respectively. Extensive
experiments show that compared to existing works, both RBRS and D-RBRS are able to
achieve more successfully scheduled links as well as higher network throughput.
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CHAPTER 4GAME THEORETIC APPROACH FOR NETWORK ACCESS CONTROL IN
HETEROGENEOUS NETWORKS
4.1 Introduction
As we have mentioned in Chapter 1, the selection of path under multiple TCP
is a difficult issue under the heterogeneous network. In Fig 4-1, we present a typical
wireless heterogeneous network with three different types of network: cellular, WiFi,
and airborne. And there is only one access point(AP) for each of these networks.
We assume multipath TCP is exploited where users in one heterogeneous network
establish the connections with all three access points during the transmission phase.
After reaching the backbone, data will be routed to the destination, which could either
be an Ethernet or another wireless network. This scenario imposes three challenges.
First of all, congestion should be properly addressed. Since the terminal might time-
varyingly switch the path or APs between different networks, the traffic load in each
network may also change with time. With higher traffic load, the network would have
a high probability of going through congestion status, which would affect the quality
of service for terminals selecting this network. That is to say, the benefit of using the
network resources would be determined by the decision of all other users as well as
his own. Secondly, fairness among users should be guaranteed. Since everybody tries
to maximize his own benefit, some users may seldom or never access the network
resources during the data transmission. It is desired that some central manager can
give suggestions to individual terminals to avoid this. Last but not the least, robustness
against random link/node failures and intentional attacks should be considered in the
system design. To this end, the key technology to enable the described multipath TCP is
the network selection: to find out how terminals should choose the right path, or network
access point, in different time slots under random events, so that the overall network
utility can be maximized, while the fairness among the users can be achieved.
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User Terminals
Cellular AP WiFi AP Airborne AP Airborne APCellular AP WiFi AP
Ethernet
Network 1 Network 2
Figure 4-1. The typical heterogeneous network and backbone communication
To optimize the systematic scheduling by intelligently utilizing the available network
resources from heterogeneous networks, in this chapter, we propose a Lyapunov
optimization algorithm for the heterogeneous network selection problem. To our best
knowledge, the forehead described problem has not been addressed by any works
of literature yet, and it is the first time the Lyapunov theory is applied to such network
selection problem. The contributions of this chapter are as follows.
• We model dynamics of the problem as a repeated stochastic game, in which par-ticipating players are capable of accessing the common resource of randomnessfrom which they can optimally correlate their decisions.
• We propose a Lyapunov optimization based on-line algorithm to achieve maximumproportional fairness utility while achieving equilibrium between players.
• We did experiments with different scenarios, and results shows that our proposedalgorithm achieves the best utility while retains good fairness compared with otherrelated schemes.
The rest of this chapter is organized as follows. Related works are reviewed in
Section 4.2. We introduce our system model in Section 4.3. Section 4.4 presents the
formulation of repeated stochastic game model for the network selection problem in a
dynamic heterogeneous network. The drift-plus-penalty algorithm based network se-
lection algorithm for the Lyapunov optimization problem is implemented in Section 4.5.
Section 4.6 presents the performance evaluation results and discussion. Section 4.7
concludes this chapter.
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4.2 Related Works
In the heterogeneous network, terminals should be able to rank the access net-
works and always select the best at any time anywhereWang and Kuo (2013). The key
issue involved, the selection of the best network has been discussed in a large number
of research works in recent years. The most common approach is the utility based ones.
Utilities such as RSS Stevens-Navarro and Wong (2006); Shen and Zeng (2008); Wu
et al. (2008), bandwidth Guo et al. (2005); Nguyen-Vuong et al. (2008); Stevens-Navarro
et al. (2008), battery Stevens-Navarro and Wong (2006); Zhang (2004), price Stevens-
Navarro and Wong (2006); Niyato and Hossain (2009), etc. are considered to make
decisions. Some other literature makes the selection decisions based on alternatives
that are characterized by multiple conflicting attributes Bari and Leung (2007a,b, 2009).
Different from the forehead-mentioned approaches, game theoretical approach
Osborne (2004) focuses on the relative position of the decision makers, who consciously
know that their actions can affect other players, under one setting. Game theory
provides a straightforward tool to study the network resource management problem in
both wired and wireless networks. Existing works on this track can be further divided
into different categories according to the type of game.
Congestion game Rosenthal (1973); Bhawalkar et al. (2010) models the negative
congestion effects when users compete for limited resources. These games has been
exploited in wireless spectrum sharingTekin et al. (2012), wireless access point selection
Ibrahim et al. (2010); Malanchini et al. (2013), etc. In Malanchini et al. (2013), the
non-cooperative game is modeled that users selfishly minimize their predefined cost
and mathematical programming is used to achieve the Nash equilibrium. A two-stage
game is proposed, and it turns out to improve both throughput and fairness. However,
it only considers the performance of one-time point. Our approach aims to optimize the
performance over a series of time slots.
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An evolutionary game approach was used in Niyato and Hossain (2009) where
users in different service areas form different populations. In such game, players make
their decision based on the current state of population and user in one population may
choose strategies against players in another one. Both centralized and distributed
schemes have been proposed in Niyato and Hossain (2009). But it does not consider
fairness. Our problem considers the fairness in the objective function.
In Vassaki et al. (2009), a cooperative bargaining game is exploited to solve
the bandwidth allocation problem. Users are free to bargain to achieve the mutual
understanding, and the Nash bargaining solution is found. However, this work focuses
on the allocation of one single base station, and our problem extends this problem to
multiple access points.
For more different kinds of games such as Bayesian game Zhu et al. (2010),
auction game, etc. between users, a comprehensive survey can be found in Trestian
et al. (2012). However, none of the existing works has applied the repeated stochastic
games into the field of network selection. Our approach focuses on the time varying
game and maximizes the utilities while maintaining the fairness among users.
4.3 System Model
As shown in Fig. 4-1, the overall system can be divided into two parts. The hetero-
geneous wireless network where users try to connect to the best access points, and the
wired backbone network where data streams are routed to the destinations.
At the user side, we assume that the device which wants to transfer some data
(files, audio or video, etc.), is equipped with multiple NICs for all available networks in
such specific area. There are several types of independent networks available in this
area, which includes the cellular network, WiFi network, and airborne network, etc.
We denote the set of N users (devices) by N = 1, 2, ...,N and the set of M types
of available independent networks by M = 1, 2, ...,M. For each of these networks,
we assume it has a capacity limit. And mathematically we denote the capacity as
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C(t) = c1(t), c2(t), ..., cM(t), where ci(t) is the capacity of the i th network. Each user
connects to only one type of network at some specific time slot t. Thus devices can
dynamically perform automated network selection between different time slots, based
on network conditions. If multiple users choose the same one network, congestion could
happen. We model the congestion probability as the follows:
pi(t) =
∑j sji (t)
ci (t),
∑j sji(t) ≤ ci(t),
1, otherwise;(4–1)
where sji is the actual data rate that user j choose network i . When the congestion
happens, no packet can be delivered to that specific network access point.
At the backbone side, we assume there is a routing protocol in place. The capacity
of the wired links are denoted as C ′ = c ′1, c ′2, c ′3..., where c ′i is the capacity of the i th
link of the backbone network. Obviously, the data rate should not exceed the capacity of
the wired link. Thus we have:
qk =
∑i∈N
∑j∈D rijk fij ,
∑i∈N
∑j∈D rijk fij ≤ c ′k ,
c ′k , otherwise;(4–2)
where qk is the data rate go through link k at the backbone. fij is defined as the date rate
of the stream from terminal i to the destination j . D is the set of the destination nodes.
rijk is the coefficient that denotes the percentage of the flow fij that would go through the
backbone link k . Note that these coefficients are decided by the routing protocol being
used. If the actual data rate is larger than the capacity, then the data rate would not
exceed the capacity.
Please refer to Table 4-1 for some key notations used in this chapter.
4.4 Repeated Stochastic Game and Problem Formulation
4.4.1 Repeated Stochastic Game – An Overview
A repeated stochastic game is played in a sequence of stages, where each player,
given the whole history (including the current state), chooses an action ai(t) in his
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Table 4-1. Mathematical notationsmath symbol meaning
N the number of usersM the number of networksN the set of users nodesM the set of networksD the set of destination nodesC the set of capacity of wireless networksC ′ the set of capacity of wired linksci(t) the capacity of the i th network on time tsji the actual data rate that user j choose network ic ′i the capacity of the i th link of the backbone networkqk the data rate go through link kfij the date rate of the stream from terminal i to the destination jrijk percentage of the flow fij going through the backbone link k .a(t) action vector on time tω(t) event vector on time tA strategy setβ alternative strategiesC ij (t) congestion conditions of user i on network j on time tS(t) suggestion message on time txi(t) throughput of user i on time t
action space. The action combination a(t) = (a1(t), ..., aN(t)) that was chosen by all
players, together with the current state, determines the stage payoff ui(a(t)) that each
player receives and the probability distribution according to which the random state of
the new stage is chosen. In a stochastic game, the players have two goals: high future
opportunities and stage payoff. There is a clear balance between two goals when the
game is discounted.
Players would choose strategies or randomize over strategies independently
in one Nash equilibrium. And it is desired to have randomizations between Nash
equilibrium by communication before the start of the game in the game with multiple
Nash equilibrium. But the concept of CE is that for every slot t, a game manager can
provide separate recommendations to different players. From the point view of play i ,
posterior beliefs about the recommendations given to the other players can be formed
from conditional probability with such a recommendation from the manager. A correlated
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equilibrium, which mathematically can be defined as a distribution ϕ with probability
mass function Pr [a], means a game in which if other players play according to their
recommendations, one can never expect to unilaterally gain by deviating from his own
recommendationNeyman (1997).
Consider changing a single entry ai into βi from ai . This new vector is represented
by the notation (βi , a−i ). Define A−i as the set of all vectors a−i , we have
Definition 4.1. A probability mass function Pr [a] is a correlated equilibrium if∑a−i ∈A
−iPr [ai , a
−i ](u(ai , a
−i ) − ui(βi , a
−i )) ≥ 0 for all players i , and all strategies
ai ∈ Ai , and all alternative strategies βi ∈ Ai with βi = ai .
Thus, The number of correlated equilibrium constraints is∑Ni=1 |Ai |(|Ai | − 1).
By definition, the correlated equilibrium requires the non-participating players to
receive recommendations from the manager. But if those players do not receive any
recommendations, a coarse correlated equilibrium Moulin and Vial (1978) would be
formed.
Definition 4.2. A probability mass function Pr [a] is a coarse correlated equilibrium if∑a∈A Pr [a](ui(a− ui(βi , a
−i )) ≥ 0, for all players i and all alternative strategies βi ∈ Ai .
The number of coarse correlated equilibrium constraints is∑Ni=1 |Ai |, which helps
reduce the computational complexity compared with correlated equilibrium constraints.
4.4.2 Game Formulation of the Network Selection Problem
We model the dynamic network selection problem by using repeated stochastic
games. We assume there are M networks, N ground users, and one game manager.
In this game, N users are players, while the available bandwidth of M networks for
each user is a part of event ω of each player. Over an infinite time slot t ∈ 0, 1, 2, ...,
each player i ∈ 1, 2, ...,N experiences a random event ωi(t) at each time slot t.
Generally, ωi(t) is defined to be a 1×M vector [C i1(t),C i2(t), ...,C iM(t)], which represents
congestion conditions of each type of networks for player i . For example, C ij (t) provides
the information of network availability for user i at time t.
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After observing the full event vector ω(t) = (ω1(t),ω(t), ...,ωN(t)) at one time
slot, a suggested action message Si(t) will be sent to each participating player i by
the manager of the game. Assume Si(t) ∈ Ai , where Ai is the action set which
contains available actions to player i . Then, Each player chooses a control action
ai(t) ∈ Ai based on the suggested message. Under the protocol that each player i
would only select one network at each time slot t as its serving network, the available
action set Ai including all types of available network. For simplifying demonstration,
we assigned each type of networks with an identification number. For example, We
define 0 for no network access, 1 for the cellular network, 2 for Wi-Fi network, and 3 for
UAV network, etc. Thus, the action set Ai is equal to 0, 1, 2, ...,M. Meanwhile, the
network id j ∈ 1, 2, ...,M. Each player is free to choose whether follow or not follow the
suggested message. The follower always choose ai(t) = Si(t), while the non-follower
choose ai(t) using knowledge of only ωi(t) and of events that occurred before time t.
We define the utility of the player i who access network j is defined as ui(a(t),ω(t))
at time t, where
ui(t) = xi(t)− gi(t)with probability 1− pj(t)
0− gi(t)with probability pj(t)(4–3)
where gi(t) is the signaling cost function, which is defined as
gi(t) = Kjt ,jt−1, jt = jt−1
0, jt = jt−1
(4–4)
where Kjt ,jt−1 is the switching cost from the previous network jt−1 to the new network jt .
At each time slot t, the available strategy set for each player i ∈ 1, ...,N is
determined by the random event ω. And the utility ui(t) of player i on slot t should be a
real-valued function of a(t) and ω(t):
ui(t) = ui(a(t),ω(t)) (4–5)
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Here we define the utility function ui(a(t),ω(t)) as below:
• if ai(t) = j AND j = 0, then ui(t) = 0;
• if ai(t) = j AND j = 0 AND j /∈ ωi(t), then ui(t) = 0;
• if ai(t) = j AND j = 0 AND j ∈ ωi(t), then ui(t) = xi(t)− gi(t);
Specifically, let Pr [a|ω] be a conditional probability mass function defined over
ω ∈ Ω, a ∈ A. It is assumed that:
Pr [a|ω] ≥ 0 ∀a ∈ A,ω ∈ Ω (4–6)
∑a∈A
Pr [a|ω] = 1, ∀ω ∈ Ω (4–7)
If actions a(t) are independently selected in each time slot according to the same
conditional probability mass function Pr [a|ω] and i.i.d event ω(t), with the law of large
numbers, the time average utility of each player i ∈ 1, ...,N can be formulated as:
ui =∑ω∈Ω
∑a∈A
π[ω]Pr [a|ω]ui(a,ω), ∀i ∈ 1, ...,N (4–8)
In this situation, every player tries to maximize the time average of its own utility, while
the game manager is devoted to providing suggestions which lead to a fair allocation
of time average utilities among players. The fairness function is supposed to be an
increasing and concave function. Thus we define the proportional fairness function as
the follows:
ϕ(u1, ..., uN) =N∑i=1
log(ui) (4–9)
4.4.3 Optimization objective
From the perspective of the game manager, it should choose control action mes-
sages M(t) = a(t) according to a conditional probability mass function Pr [a(t)|ω(t)]
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which can solve the following optimization problem:
Maximizea
ϕ(u1, ..., uN) (4–10a)
Subject to: ui =∑ω∈Ω
∑a∈A
π[ω]Pr [a|ω]ui(a,ω), (4–10b)
∑ω∈Ω
∑a∈A
π[ω]Pr [a|ω]ui(a,ω) ≥ (4–10c)
∑ω∈Ω
∑a∈A
π[ω]Pr [a|ω]ui((b(s)i (ωi)),ω) (4–10d)
∀i ∈ 1, 2, ...,N, ∀s ∈ Si (4–10e)
Pr [a|ω] ≥ 0, ∀a ∈ A,ω ∈ Ω (4–10f)∑a∈A
Pr [a|ω] = 1, ∀ω ∈ Ω (4–10g)
∑i
∑j∈D
rijk fij ≤ c ′k , ∀k ∈ 1, 2, ... (4–10h)
where π[ω] ≜ Pr [ω(t) = ω], ∀ω ∈ Ω is probability mass function of vector process ω(t)
over time slots, Si is the pure strategy for player i , b(s)i (ωi) is the pure strategy function
for player i and s ∈ Si . And |Si | = |Ai ||Ωi | = 2M . Equations (4–10c) -(4–10g) are the
coarse correlated equilibrium constraints. The last equation (4–10h) implies that the
sum of the data rate should be less than the capacity.
4.5 Implementation of the Network Selection Algorithms
To solve the problem (4–10) requires the knowledge of the graph and routing
information at the backbone side.And the network manager usually only has the
information of the wireless network. Considering the capacity of the wired links is
typically much larger than the wireless counterpart, we assume that congestion only
happens at the wireless segments. In this way, we exploited the Lyapunov optimization
approach Neely (2013) to address our problem.
87
In the problem (4–10), the utility u(t) can be seen as a real-valued stochastic
process over time slots t ∈ 0, 1, 2, ..... We define:
u(t) =1
t
t−1∑τ=0
E[u(τ)] (4–11)
We define ui(t) = ui(a(t),ω(t)). Furthermore, we define u(s)i (t) = u(s)i (a(t),ω(t)),
where u(s)i (a(t),ω(t)) is the corresponding transmission rate when user i choose
another available strategy b(s)i (ωi). Thus,
u(s)i (a(t),ω(t)) = u
(s)i ((b
(s)i (ωi(t)), a
−i (t)),ω(t)) (4–12)
Every time slot, the game manager observes network congestion status ω(t) and
then chooses an action vector a(t) ∈ A as recommendation message. The action vector
a(t) solves the following modification of the problem (4–10):
Maximizea
limt→∞inf ϕ(u1(t), ..., uN(t))
Subject to: limt→∞inf[ui(t)− u(s)i (t)] ≥ 0 ∀i ∈ 1, ...,N,
∀s ∈ Si , a(t) ∈ A, ∀t ∈ 0, 1, 2, ...
(4–13)
Obviously, a simple randomized algorithm could solve the optimization problem: in
every time slot, it just independently selects a(t) after observing ω(t), with the same
conditional probability mass function Pr [a|ω]. By comparing problem (4–10) and (4–13),
it can be found that if one probability mass function Pr [a|ω] can solve problem (4–10),
it must be able to solve problem (4–13); Besides, the time average expectations of the
solution to problem (4–13) and conditional probability mass functions Pr [a|ω] that solve
problem (4–10) should be arbitrarily close to each otherNeely (2013).
By using the auxiliary variable techniqueNeely (2010), the original problem, which
tries to maximize a nonlinear function of a time average, can be turned into a new one
88
that maximizes the time average of a nonlinear function. Then we define
g(t) = ϕ(β1(t), ..., βN(t)) (4–14)
With Jensen’s inequality, we have
g(t) ≤ ϕ(β1(t), ..., βN(t)), ∀t ∈ 0, 1, 2, ... (4–15)
In every time slot t, the game manager chooses the a(t) ∈ A and an auxiliary
vector β(t), where 0 ≤ β(t) ≤ umaxi for all t and all i . Then it utilizes these vectors to
solve the problem (4–16).
Maximize limt→∞inf g(t)
Subject to: limt→∞
|βi(t)− ui(t)| = 0, ∀i ∈ 1, ...,N
limt→∞inf[ui(t)− u(s)i (t)] ≥ 0, ∀i ∈ 1, ...,N,
∀s ∈ Si , a(t) ∈ A, ∀t ∈ 0, 1, 2, ...
0 ≤ βi(t) ≤ umaxi , ∀t, ∀i ∈ 1, ...,N
(4–16)
Suppose all limits exist in problem (4–16), then we have βi = ui . Considering this
with Jensen’s inequality (4–15), the optimal solution of the problem (4–16) is less than or
equal to that of the problem (4–13). Thus, the problem (4–13) and (4–16) are equivalent.
The problem (4–16) could be solved via the drift-plus-penalty algorithm Neely
(2010). Define a virtual queue Q(s)i (t) and Z (s)i (t) Neely (2013) where
Q(s)i (t + 1) = max[Q
(s)i (t) + u
(s)i (t)− ui(t), 0] (4–17)
Zi(t + 1) = Zi(t) + βi(t)− ui(t) (4–18)
When the control algorithm is designed that makes the queues mean rate stable,
limt→∞
E[Q(s)i (t)]t
= 0 (4–19)
89
and
limt→∞
E[Z (s)i (t)]t
= 0 (4–20)
then constraints in problem (4–16) are satisfied.
We define the Lyapunov function L(t) as a sum of squares of all virtual queues at
time t in our problem:
L(t) =1
2
N∑i=1
∑s∈Si
Q(s)i (t)
2 +1
2
N∑i=1
Zi(t)2. (4–21)
Then the Lyapunov drift is defined as ∆(t) = L(t + 1 − L(t). To maximizing the time
average of the objective function in problem (4–16) while maintaining virtual queues
stable, the drift-plus-penalty algorithmNeely (2013) is implemented. This algorithm
observes the current state of the queue and then takes control actions to minimize a
bound on ∆(t) − Vg(t), which is called the “drift-plus-penalty expression”. −g(t) is
the “penalty” term and the non-negative constant V represents a trade-off between
convergence time and proximity to the optimal solution. For all time slots t we have:
∆(t)− Vg(t) ≤ B − Vg(t)
+
N∑i=1
∑s∈Si
Q(s)i (t)[u
(s)i (t)− ui(t)]
+
N∑i=1
Zi(t)[βi(t)− ui(t)]
(4–22)
where B = 12
∑Ni=1
∑s∈Si (u
maxi )
2 + 12
∑Ni=1(u
maxi )
2. The (4–22) can be proved by the fact
that max[x , 0]2 ≤ x2.
We implement the following algorithm to greedily minimize the right-hand-side of
(4–22) in every time slot.
• (1) At time slot t = 0, the game manager initializes both Q(s)i (0) = 0 andZ(s)i (0) = 0;
90
• (2) Choose auxiliary variable βi(t) ∈ [0, umaxi ] for all i ∈ 1, ...,N to maximize:
Vϕ(β1(t), ..., βN(t))−N∑i=1
Zi(t)βi(t) (4–23)
• (3) Choose a to minimize:
−N∑i=1
Zi(t)ui(a(t),ω(t))
+
N∑i=1
∑s∈Si
Q(s)i (t)[u
(s)i (a(t),ω(t))− ui(a(t),ω(t))]
(4–24)
Then the game manager send suggested actions ai(t) to each player i ∈1, ...,N.
• (4) The game manager update virtual queue equation (4–17) and (4–18).
• (5) Go back to step 2 for next time slot t + 1.
4.6 Experiment Evaluation
4.6.1 Experiment Settings
We use the scenario of Fig 4-1 where there is 3 different types of the network for
users in one area: the cellular network, Wi-Fi network, and airborne network. And there
is only one access point(AP) for each type of network. We further assume the capacities
of the wired paths between backbone routes are unlimited. In other words, with routing
protocol in place, the data stream that reaches the APs will be routed to destinations in
the backbone network without any congestions.
For the wireless part, many user terminals are trying to connect to the networks.
With multiple NICs, it can connect to the 3 networks at will, with different achievable data
rate towards different APs. For convenience, We randomly generate the user data rate
from 1 Gbps to 2 Gbps. We run each experiment 100 times and take the mean value of
them.
Besides our proposed algorithm, We implemented another three schemes.
91
Total network capacity10 15 20 25 30 35 40
Util
ity
0
2
4
6
8
10
12
14
16
18
20
GreedyRandomCAGT
A Total utility in network
Total network capacity10 15 20 25 30 35 40
Fai
rnes
s
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-2. From a wireless terminal to a wired terminal: the impact of total capacity
• Greedy scheme: each user chooses an AP which has the highest available(unused) data-rate.
• Random scheme: in a time slot, each user randomly selects an AP with a probabil-ity proportional to the capacity of the AP, regardless of the congestion status of theprevious time slot.
• Congestion Avoidance (CA) scheme: if there is no congestion, each user uses theGreedy scheme. Otherwise, it will use the Random method to avoid/mitigate thecongestion.
All the described approach is applied to the network selection of the heterogeneous
network.
To evaluate the performance of different schemes, we use two metrics.
• Utility. The overall achievable throughput in the network is measured.
• Fairness. We use the Jain’s fairness Jain et al. (1999) as our indicator. It is a valuebetween 0 and 1. When it equals 1, every user has the equal chance to take theresources.
4.6.2 Experiment Results
In this section, we did simulations on different settings to see how our proposed
approach performed compared with other schemes. For each setting, we will consider
two different cases based on Fig 4-1. The first one considers only one wireless hetero-
geneous network and the destination is the Ethernet. And the second case is where
92
Total network capacity10 15 20 25 30 35 40
Util
ity
0
2
4
6
8
10
12
14
16
18
GreedyRandomCAGT
A Total utility in network
Total network capacity10 15 20 25 30 35 40
Fai
rnes
s
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-3. From a wireless terminal to a wireless terminal: the impact of total capacity
user terminals try to connect to terminals in another far-away wireless network. In this
case, the flows go through two wireless hops between terminals and access points.
We assume the two wireless networks has the same settings; Furthermore, users in
two wireless network would apply network selection algorithm independently. The final
achievable data rate of one flow is minimal of the two date rate from the two wireless
hops.
4.6.2.1 With different network capacity
In the first experiment, we examine the performance of different algorithms under
different network capacity. We change the network condition from high congested to
low congested. Specifically, we choose the capacities of the three different networks as
an arithmetic sequence but control the total capacity as our independent variable. The
results are plotted in Fig. 4-2 and Fig. 4-3.
We have the following conclusions:
• As the capacity of the total network increases, we see that both the utility andfairness increases with different approaches. This is because a larger capacity willbenefit the individual flows with less contention.
• When we have enough network capacity where congestion never happens, thegreedy based approaches win the random approach since they try to optimize theindividuals while luckily no contention happens among users. And our proposedapproach can achieve the as good utility as the greedy based approaches.
93
Number of users2 4 6 8 10 12 14 16
Util
ity
0
1
2
3
4
5
6
7
8
9
10
GreedyRandomCAGT
A Total utility in network
Number of users2 4 6 8 10 12 14 16
Fai
rnes
s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-4. From a wireless terminal to a wired terminal: the impact of the number ofusers
Number of users2 4 6 8 10 12 14 16
Util
ity
0
1
2
3
4
5
6
7
8
GreedyRandomCAGT
A Total utility in network
Number of users2 4 6 8 10 12 14 16
Fai
rnes
s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-5. From a wireless terminal to a wireless terminal: the impact of the number ofusers
This means our game manager is able to learn the network condition is greatand smartly suggest every flow maximize its own individuals. When it comes tofairness, the large network capacity almost ensures that every flow gets its chance,and thus all the scheme can achieve great fairness as the figure shows.
• Things are different when the network resource is limited. In this case, the ran-domized based approaches can do a better job regarding both utility and fairness,especially for the fairness. It makes sense since the greedy approach can notadjust to the congested environment while the random approach can achievethis by its nature. The proposed approach has an obvious advantage when thenetwork resource is limited. Firstly, it can achieve many times larger utility. Andthe more limited the capacity is, the more performance gain we can achieve. Wecan do it better than the random approach because the network manager is able
94
to minimize the congestion in networks more efficiently than the random approach.Secondly, when the total capacity is not too small, the proposed approach canachieve nearly the same fairness as the random approach, which by nature canachieve the best fairness. Note that with the huge gain in the utility, some trade-offshould be made. And clearly, it still outperforms the other two schemes.
• We almost got the same conclusion for the two cases. The only difference be-tween the two cases is that the utility performance is a little bit lower from wirelessto wireless network. This is because the achievable throughput is minimal of thetwo data rate residing in the two wireless network.
4.6.2.2 With different number of users
In this setting, we fix the network capacity and change the number of user terminals
in the wireless network. In a real heterogeneous network, the number of users present
is an unpredicted issue and should be well addressed. We make all the three network to
be 4 Gigabytes, and thus 12 GB in total. And we change the number of users from 2 to
16. The results are plotted in Fig. 4-4 and Fig. 4-5. Compared with Fig. 4-2 and Fig. 4-3,
we have the following new observations:
• All the schemes follow the same trend: first go up, then go down. This is becausewhen user number reaches 6, the network is saturated; After that, the networkbecomes congested, and the utility value thus decrease.
• The proposed method has highest utility value among all the schemes. Moreover,when the user number keeps increasing, the utility value will not decrease tremen-dously as other schemes. The network game manager can adjust its strategieswhen the number of users changes, and thus greatly counteract the congestioncaused by incoming users.
• After the network become highly congested where user number is larger than 6,the fairness of the proposed scheme will decrease. As we have mentioned, thistrade-off also happens in Fig. 4-4 and Fig. 4-5. But it is still much better than thegreedy method, and will not degrade too much. Note that in this experiment, wechoose the setting where the network capacity is small, which will cause the dropof fairness according to the previous experiment. With more total network capacity,the fairness can be much better.
95
Disturbance factor0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Util
ity
8
10
12
14
16
18
20
GreedyRandomCAGT
A Total utility in network
Disturbance factor0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fai
rnes
s
0.4
0.5
0.6
0.7
0.8
0.9
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-6. From a wireless terminal to a wired terminal: one access point underrandom failures/attacks
Disturbance factor0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Util
ity
0
2
4
6
8
10
12
14
16
18
GreedyRandomCAGT
A Total utility in network
Disturbance factor0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fai
rnes
s
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-7. From a wireless terminal to a wired terminal: two access points underrandom failures/attacks
4.6.2.3 With network turbulence
In this experiment, we test the heterogeneous network where some network’s
capacity is greatly impaired due to the unexpected accident from outside. We call it
turbulence. In this way, the new random events are introduced to our setting.
We assume that in perfect condition, all the three network have V Gigabytes
capacity. However, at some time during the transmission range, the capacity of some
of the networks will decrease to Vl , which is the capacity under failures or attack. And
96
Disturbance factor0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Util
ity
0
2
4
6
8
10
12
14
16
18
GreedyRandomCAGT
A Total utility in network
Disturbance factor0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fai
rnes
s
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-8. From a wireless terminal to a wired terminal: three access points underrandom failures/attacks
Disturbance factor0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Util
ity
0
2
4
6
8
10
12
14
16
18
GreedyRandomCAGT
A Total utility in network
Disturbance factor0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Fai
rnes
s
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-9. From a wireless terminal to a wireless terminal: three access points underrandom failures/attacks
we control the turbulence time divides the overall transmission time as the turbulence
factor(TF).
Specifically, we create five situations as follows:
• Case 1: Data flows are from the wireless network to Ethernet. Besides, only oneaccess point is under the impact of the turbulence. We fix the Vl = 2, and changethe turbulence factor increases from 0 to 1. We tested the utility and fairness valueand plotted the result in Fig 4-6.
• Case 2: Same as case 1, but two access points are influenced. The result isshown in Fig 4-7.
97
Impacted Capacity2 3 4 5 6 7 8
Util
ity
4
6
8
10
12
14
16
18
GreedyRandomCAGT
A Total utility in network
Impacted Capacity2 3 4 5 6 7 8
Fai
rnes
s
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
GreedyRandomCAGT
B Fairness of the system
Figure 4-10. From a wireless terminal to a wired terminal: impact of capacity underfailure or attack
• Case 3: Same as case 1, but all three access points are influenced. The result isshown in Fig 4-8.
• Case 4: Data flows are from the wireless network to wireless network. All threeaccess points are influenced. Again we fix the Vl = 2 and change the turbulencefactor increases from 0 to 1. The result is shown in Fig 4-9.
• Case 5: Data flows are from the wireless network to Ethernet. All three accesspoints are influenced. We fix V = 8, TF = 60%, but change the Vl from 2 to V .The result is shown in Fig 4-10.
From the results of experiment (1) to (5) (Fig 4-6, 4-7, 4-8 , 4-9, and Fig 4-10
respectively), we can have the following observations:
• Generally, for all the schemes, the utility value decreases as the disturbance factorgoes up. But the proposed approach has the highest utility among all. The samestory applies to the fairness as well. The fairness value has the trend to decreasefor all the schemes. The proposed one can achieve as good performance as therandom approach when the disturbance factor is small and stand between randomand greedy approach when DF goes up.
• By comparing vertically, it can be seen that the more access points impacted bythe turbulence, the lower performance all the scheme would achieve. However,we can notice that when only one access point is impacted, our scheme hasonly slight performance degradation for both utility and fairness. And when moreaccess points are impacted, the congestion is greatly introduced to the system.But the performance gain of the proposed approach still exists.
98
• As the capacity under failures or attack goes up, the overall performance of allschemes gets better. This is because the overall capacity under the circumstanceof turbulence goes up. And more capacity will result in better performance. Ourscheme can achieve the best utility among all schemes with different capacityunder turbulence. Averagely it has 5 Gbits higher throughput. Besides, ourscheme can achieve as good performance as randomized approaches regardingfairness when the tabulated capacity reaches some value.
• The reasons behind all the above observations is that our game theoreticalapproach is modeled based on the stochastic repeated game. And the randomevent is by nature considered in this problem. With the different situation withdisturbance, the game manager of the proposed approach can give suggestion toeveryone dynamically.
In conclusion, the proposed stochastic game approach ensures high performance
regarding total utility and proportional fairness utility due to the suggestion from the
game manager, no matter there is unexpected turbulence or not.
4.7 Conclusion
In this work, we proposed a game theoretical approach for network selection in the
heterogeneous networks’ environment. The objective was to maximize network resource
utilizing efficiency (total utility of users) while maintaining fairness between users. We
formulated the problem as a repeated stochastic game and exploited the concept of
Lyapunov optimization method to guide the users to choose the best network. Our
approach outperforms the other schemes in terms of total utility and fairness between
users.
4.8 Future Work
In this work, we assume there is a game manager who has the global view of the
network condition. This is not practical in the real world. In the future, we will investigate
into learning equilibrium with partial information in decentralized wireless networks.
99
CHAPTER 5CONCLUSIONS
This dissertation devotes to addressing the new challenges with the next generation
of wireless network: Ultra-dense Heterogeneous Small Cell Networks (HetSNets).
In chapter 2, we have address the opportunity from massive relays under HetSNets.
Different from traditional cooperative diversity techniques, a new network coding based
approach is invented. We propose Miss-and-Forward (MF), a intra-session network
coding, in which a special relay called “helper” is assigned to exploit the rich diversity.
In accordance, a network coding based scheme is designed which has the ability to
restore the “missed” information and in the meanwhile retains the benefit of state-of-
the-art batched sparse coding. Mathematically, we show that the source of throughput
gain is the higher ranked end-to-end transfer matrix. Besides, we provide a systematical
design to address some practical issues such as helper selection and rank distribution
estimation.
In chapter 3, we introduced the Regret Benefit Ratio Scheduler. With huge band-
width available in the mmWave band, wireless backhaul at mmWave frequencies can
be a promising backhaul solution for small cells densely deployed underlying the ho-
mogeneous macrocells. With multiple links under such mmWave wireless network, the
proposed RBRS is a scheduling mechanism that can effectively improve the capacity
of network with Quality of Service (QoS) considered. Our proposed indicator, which is
called Regret Benefit Ratio (RBR), allows us to simultaneously maximize the QoS ben-
efit and minimize contention among links under directional antennas. We design RBRS
for a time slot based centralized control mmWave network in which we utilize RBR to
find a suitable concurrent transmission links for every single time slot. Furthermore,
we also propose a distributed scheme under CSMA/CA, which implements the RBR by
prioritizing MAC contention window to provide better concurrent transmission support
while achieving QoS-aware capability.
100
Chapter 4 presents our game theoretical approach for network selection scheme.,
which is a mechanism of an access network selection at each given time to provide 1)
best user experience and 2) improve network fairness. We formulated the problem as
a repeated stochastic game to maximize total utility and achieve maximum proportional
fairness among all users in the service area, The Lyapunov optimization algorithm
is used to compute the optimized suggested actions for each user from the game
manager.
101
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BIOGRAPHICAL SKETCH
Yun Zhu received B.E. degree in University of Science and Technology of China,
China, in 2013. He obtained his Ph.D. degree at University of Florida, USA. His re-
search interest includes networking, communication, etc.
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