Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
Cognitive Radio Ad Hoc Networks:
A Local Control Approach
by
Peng Hu
A thesis submitted to the
Department of Electrical and Computer Engineering
in conformity with the requirements for
the degree of Doctor of Philosophy
Queen’s University
Kingston, Ontario, Canada
February 2013
Copyright c© Peng Hu, 2013
Abstract
Cognitive radio is an important technology which aims to improve the spectrum
resource utilization and allows a cognitive radio transceiver to detect and sense spec-
trum holes without causing interference to the primary users (PUs). As a result of
the development of cognitive radio technology, the concept of cognitive radio ad hoc
networks (CRAHNs) has recently been proposed in the literature, which aims to ap-
ply the cognitive radio to traditional ad hoc networks. However, this new network
paradigm creates more research challenges than those in classical cognitive radio net-
works (CRNs). These research challenges in CRAHNs are due to the variable radio
environments caused by spectrum-dependent communication links, hop-by-hop trans-
mission, and changing topology. This study will focus on important research topics in
spectrum management in scalable CRAHNs driven by local control, such as spectrum
sharing, allocation, and mobility. To conduct this study, a local control approach is
proposed to enable system-level analysis and protocol-level design with distributed
protocols for spectrum sharing. In the local control approach, we can evaluate the
system dynamics caused by either protocol-specific parameters or application-specific
parameters in CRAHNs, which is hard to explore using existing methods. Moreover,
combining the previous evaluations and scaling law analysis based on local control
i
concept, we can design new distributed protocols based on the features of the medi-
um access control (MAC) layer and the physical layer. In this study, the proposed
research themes and related research issues surrounding spectrum sharing are dis-
cussed. Moreover, justification of the research has been made by experimental and
analytical results.
ii
Acknowledgments
I would like to express my sincere gratitude in the support and help to Dr. Mohamed
Ibnkahla. He encouraged me greatly to work in this topic. His willingness to motivate
us contributed tremendously to my research. He offered invaluable assistance, support
and guidance.
I am indebted to my colleagues for providing a stimulating environment in which
to learn and grow, especially grateful to our group members and friends: Vivien
Kan, Amr El Mougy, Basel Nabulsi, Zouheir El-Jabi, Gayathri Vijay, Parisa Abedi
Khoozani, Abdallah Alma’Aitah, Ala Abu Alkheir, Ayman Sabbah, and Yang Li,
just to name a few.
I wish to thank my entire extended family for providing a loving environment for
me. And most importantly, I wish to thank my parents. To them I dedicate this
thesis.
iii
Contents
Abstract i
Acknowledgments iii
Contents iv
List of Tables vii
List of Figures viii
Chapter 1: Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 Distributed Local Control Schemes & Dynamics . . . . . . . . 61.4.2 Emergent Behavior of CRAHNs . . . . . . . . . . . . . . . . . 71.4.3 Local Control Driven MAC Protocol Design . . . . . . . . . . 71.4.4 Scaling Law Based on Local Control . . . . . . . . . . . . . . 8
1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 2: Background & Related Work 102.1 Cognitive Radio Ad Hoc Networks . . . . . . . . . . . . . . . . . . . 102.2 Cognitive Radio Networks Vs. Cognitive Radio Ad Hoc Networks . . 122.3 Spectrum Sharing in CRAHNs . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Spectrum Allocation . . . . . . . . . . . . . . . . . . . . . . . 132.3.2 Spectrum Access Model . . . . . . . . . . . . . . . . . . . . . 152.3.3 Spectrum Sensing . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Cognitive MAC Protocols . . . . . . . . . . . . . . . . . . . . . . . . 162.5 Scaling Law of CRAHNs . . . . . . . . . . . . . . . . . . . . . . . . . 19
Chapter 3: System Model and Approach 22
iv
3.1 Spectrum Availability Map . . . . . . . . . . . . . . . . . . . . . . . . 223.1.1 Cell-Based Spectrum Availability Map . . . . . . . . . . . . . 233.1.2 Radio Environment Map . . . . . . . . . . . . . . . . . . . . . 24
3.2 Spectrum Availability Probability . . . . . . . . . . . . . . . . . . . . 253.3 Variable Size of Spectrum Bands . . . . . . . . . . . . . . . . . . . . 263.4 Multi-Channel Multi-Radio Support . . . . . . . . . . . . . . . . . . . 273.5 Resultant Channel Model . . . . . . . . . . . . . . . . . . . . . . . . 273.6 Local and Global Information . . . . . . . . . . . . . . . . . . . . . . 303.7 Local Control in Spectrum Management . . . . . . . . . . . . . . . . 313.8 Game Theoretic Approach . . . . . . . . . . . . . . . . . . . . . . . . 323.9 Graph Coloring Based Algorithms . . . . . . . . . . . . . . . . . . . . 353.10 Partial Observable Markov Decision Process . . . . . . . . . . . . . . 363.11 Bio-Inspired Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.12 Conclusive Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter 4: Local Control Schemes for Spectrum Sharing 394.1 Applicability of A Local Control Scheme to CRAHNs, CRSNs, And
Sensor Networks for CRAHNs . . . . . . . . . . . . . . . . . . . . . . 394.2 Revisit of Spectrum Sharing in the Perspective of Local Control Schemes 414.3 Framework of Local Control Schemes . . . . . . . . . . . . . . . . . . 424.4 Fairness in Spectrum Sharing . . . . . . . . . . . . . . . . . . . . . . 434.5 Protocol Design And Experimental Results . . . . . . . . . . . . . . . 49
4.5.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.5.2 Protocol Design . . . . . . . . . . . . . . . . . . . . . . . . . . 524.5.3 Computer Simulation Results . . . . . . . . . . . . . . . . . . 554.5.4 Convergence Performance And Feedback Quality . . . . . . . 564.5.5 Fairness Performance in Various Network Sizes . . . . . . . . . 60
4.6 Conclusive Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Chapter 5: Local Control Driven Medium Access Control Protocol 685.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 Primary Exclusive Regions . . . . . . . . . . . . . . . . . . . . . . . . 705.3 Proposed CM-MAC Protocol . . . . . . . . . . . . . . . . . . . . . . . 75
5.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.3.2 Channel Aggregation Technique . . . . . . . . . . . . . . . . . 775.3.3 Spectrum Access and Sharing . . . . . . . . . . . . . . . . . . 785.3.4 Mobility Support Algorithm . . . . . . . . . . . . . . . . . . . 79
5.4 Throughput Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.4.1 Average Time Spent on Mobility . . . . . . . . . . . . . . . . 835.4.2 Link Throughput Performance . . . . . . . . . . . . . . . . . 85
v
5.4.3 Upper Bound of Spectrum Utilization . . . . . . . . . . . . . 885.4.4 A Special Case of the Proposed CM-MAC Protocol . . . . . . 89
5.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.6 Conclusive Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Chapter 6: Scaling Law of CRAHNs Based on Local Control 1016.1 PU Interference Region . . . . . . . . . . . . . . . . . . . . . . . . . . 1016.2 Network Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.2.1 Virtual PU in the Resultant Spectrum Band . . . . . . . . . . 1056.2.2 Medium Access Probability . . . . . . . . . . . . . . . . . . . 107
6.3 Network Divisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096.4 Multi-Hop Data Transmission Scenario . . . . . . . . . . . . . . . . . 111
6.4.1 Probability of A Transmission over Multiple Hops . . . . . . 1136.4.2 Packet Reception Probability . . . . . . . . . . . . . . . . . . 114
6.5 Scaling Law of CRAHNs . . . . . . . . . . . . . . . . . . . . . . . . . 1146.6 Discussion on IEEE 802.22 Based CRAHNs & IEEE 802.11 Based
CRAHNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.7 Conclusive Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Chapter 7: Conclusion 1217.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . 1217.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
vi
List of Tables
3.1 Local information associated with cost values . . . . . . . . . . . . . 30
5.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.1 Common parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
vii
List of Figures
1.1 An example of a CRAHN . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Spectrum management framework . . . . . . . . . . . . . . . . . . . . 3
2.1 An example of (a) a CRAHN and (b) a CRSN . . . . . . . . . . . . . 11
3.1 An example of C-SAM in a CRAHN with 3 spectrum band indexes for
each CR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 The architecture of a CRAHN with REM servers . . . . . . . . . . . 25
3.3 Throughput performance in a CRAHN with multi-channel multi-radio
support in different settings. The network has 10 CRs and the com-
munication range per node is 250m in 2GHz band. . . . . . . . . . . . 28
3.4 Example of the resultant channel model . . . . . . . . . . . . . . . . 29
4.1 A CRAHN deployed in a radio environment . . . . . . . . . . . . . . 41
4.2 Framework of a local control scheme . . . . . . . . . . . . . . . . . . 42
4.3 Analytical results for stability when using the consensus-based feed-
back. Nyquist plots with different time delays τ and with maximum
degree of three in the CRAHN . . . . . . . . . . . . . . . . . . . . . . 48
4.4 Results of the proposed open-loop local control scheme for spectrum
allocation in a CRAHN . . . . . . . . . . . . . . . . . . . . . . . . . . 51
viii
4.5 Pseudo code of consensus-based spectrum allocation protocol . . . . . 53
4.6 A randomly distributed CRAHN with 350 CRs and initially allocated
spectrum bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.7 Convergence performance of the proposed consensus-based protocol,
Rule-A, and Rule-A (P) . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.8 Convergence performance of the consensus-based protocol and Rule-A
in multiple iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.9 An example of the ZigZag network. In (a), there is only one shaded
region of PU activity L, while in (b), there are two shaded regions of
PU activities, denoted by L(1) and L(2), respectively. We will show
that the feedback adopted in Rule-A is overestimated in both cases. . 59
4.10 The value of L versus the maximum number of spectrum bands with
the different number of CR nodes M . . . . . . . . . . . . . . . . . . 61
4.11 Fairness performance versus different network sizes when (a) M=100,
(b) M=150, (c) M=200, and (d) M=350 . . . . . . . . . . . . . . . . 62
4.12 Intermediate spectrum sharing results in CRAHN when (a) FG=1, (b)
FG=2, and (c) FG=3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.13 Convergence performance with different number of FGs . . . . . . . . 64
4.14 Fairness performance in a network when (a) FG=2 (b) FG=3 . . . . 65
5.1 A CRAHN with a PER and multiple CRs . . . . . . . . . . . . . . . 69
5.2 An example of the necessity of a CRAHN MAC protocol in a CRAHN.
The available spectrum bands for the nodes covered by a PU are shown
in brackets. The links are broken (shown in dashed arrows) when the
data transmission from S to D is operated on channel 3. . . . . . . . 71
ix
5.3 The normalized throughput of a PU and CRs versus PCR and R/R0,
when (a) v = 0.3 and (b) v = 0.7 . . . . . . . . . . . . . . . . . . . . 74
5.4 Frame structures of (a) the traditional CSMA/CA-based MAC proto-
col and (b) the proposed CM-MAC protocol . . . . . . . . . . . . . . 75
5.5 An example of channel aggregation in the view of (a) the MAC frame
and (b) the sequence diagram . . . . . . . . . . . . . . . . . . . . . . 77
5.6 An example of intermediate results of the spectrum sharing procedure
after (a) a RTS transmission, (b) a CTS transmission, and (c) an ACTS
transmission. The dotted lines are transmission ranges of CR node 1
and CR node 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.7 Description of the mobility support algorithm (MSA) . . . . . . . . . 81
5.8 An example of a CRAHN with PUs and CRs . . . . . . . . . . . . . . 82
5.9 Description of a successful data transmission . . . . . . . . . . . . . . 86
5.10 Description of a successful data transmission . . . . . . . . . . . . . . 92
5.11 CR link throughput versus N and λ′ . . . . . . . . . . . . . . . . . . 94
5.12 CR link throughput versus N and λ . . . . . . . . . . . . . . . . . . . 95
5.13 CR link throughput performance with different values of Kp in the (a)
saturated mode, and (b)-(c) non-saturated mode . . . . . . . . . . . . 97
5.14 CR link throughput performance versus P0, where CR traffic is in the
(a) saturated mode and (b)-(c) non-saturated mode with PU traffic . 98
5.15 Simulation results. (a) Response time and (b) throughout performance 99
6.1 Network layout of a CRAHN . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Toff and Ton based on resultant channel model . . . . . . . . . . . . . 107
6.3 MAP results based on the resultant channel model . . . . . . . . . . 110
x
6.4 Multi-hop data transmission from CR 1 to CR n. . . . . . . . . . . . 111
6.5 Throughput results of a single-hop scenario. (a) The whole network
within an area S is considered; (b) the throughput performance in a
subarea of S is considered. . . . . . . . . . . . . . . . . . . . . . . . . 116
6.6 Normalized throughput results when hop counts are 2, 3, and 4 in a
bounded circular area. . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.7 Normalized throughput results of a multi-hop scenario with different
hop counts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
xi
1
Chapter 1
Introduction
Radio spectrum is a precious resource for wireless communications. However, for
decades, this resource has been underutilized. From the Federal Communications
Commission (FCC) report in 2003 [1], the variation of spectrum utilization ranges
from 15% to 85%, which means that a large portion of the radio spectrum is not effi-
ciently used most of the time. A recent long-term study for a wideband (30 MHz to
3 GHz) spectrum observatory system [2] in downtown Chicago indicates the spectral
capacity is underutilized over the entire range. In order to use the radio spectrum
more efficiently, the concept of cognitive radio (CR) [3, 4] has been introduced. D-
ifferent from the traditional radio frequency (RF) system, cognitive radio enables
real-time interaction and adaptation to the surrounding radio environment in order
to determine the communication parameters, such as data rate, modulation scheme,
and transmission power. The ultimate objective of cognitive radio is to obtain the
best available spectrum resource through cognitive capability and reconfigurability
[5]. To achieve this objective, cognitive radio needs to have certain capabilities, such
as spectrum sensing, spectrum analysis, and spectrum decision [6].
As a result of the development of CR technology, the concept of cognitive radio
1.1. MOTIVATION 2
ad hoc networks (CRAHNs) has been proposed in 2009 [5]. A CRAHN is an ad hoc
network composed by CR nodes (a.k.a. secondary users or CRs) and primary users
(PUs) applying the cognitive radio technology on CR transceivers. As such, the CRs
in CRAHNs do not favor central coordination when performing spectrum sharing
processes. Instead, CRs have to perform local observation most of the time. An
example of a CRAHN that can work in different spectrum bands can be seen in Fig.
1.1. Similar to CRAHNs, the concept of cognitive radio sensor networks (CRSNs) [7]
was coined in 2009, where each sensor node in a CRSN can be considered as a CR
with limited hardware and capability to obtain surrounding information.
1.1 Motivation
Due to the lack of central network entities in CRAHNs [8], each CR node necessi-
tates that all the spectrum-related CR capabilities and distributed operations must be
mostly based on local observations. As such, the new features introduced by CRAHNs
mean that spectrum management in CRAHN opens a range of new research topics
that differ from traditional cognitive radio or cognitive radio networks (CRNs). Based
on the cognitive cycle proposed in [6], Akyildiz et al. [8] defined the spectrum man-
agement problems in CRAHNs, where the authors specified several essential topics
of spectrum management, including spectrum sensing, spectrum sharing, spectrum
mobility, and spectrum decision.
As an important research topic in cognitive radio and CRAHNs, spectrum man-
agement in CR has been an intensive research area but the spectrum management for
CRAHNs is open to be answered. Spectrum management in CR research is mainly
1.1. MOTIVATION 3
CR
PU
CR
PU
PU
CRCR
CR
CR
CR
PU
PU
PU
CR
Figure 1.1: An example of a CRAHN
Link Layer Protocol
Spectrum Sharing
PHY Layer
NWK Layer ProtocolSpectrumMobility
Spectrum Sensing
Cooperation
Upper Layers
SpectrumDecision
Figure 1.2: Spectrum management framework
focused on physical layer (PHY) issues. Haykin in [6] defined the objective of the spec-
trum management algorithm for CR mostly in the PHY layer, which is to “build on
the spectrum holes detected by the radio-scene analyzer and the output of transmit-
power controller, select a modulation strategy that adapts to the time-varying con-
ditions of the radio environment, all the time assuring reliable communication across
the channel”. However, spectrum management in CRAHNs has to deal with issues
not only in the PHY layer but also in the medium access control (MAC) layer and
the network (NWK) layer. As such, spectrum management in CRAHNs should solve
1.2. PROBLEM 4
spectrum management issues by taking advantage of functions across layers. Further-
more, spectrum management in CRAHNs can address the application-specific quality
of service (QoS) requirements [5]. As the spectrum availability fluctuates over time
and location [9], a CR should be intelligent enough to make a spectrum decision.
Spectrum sharing shown in Fig. 1.2 [8] plays a key role in the whole spectrum man-
agement module, where it requires cross-layer support from the PHY layer to the
NWK layer. This cross-layer nature of a spectrum sharing function requires us to
propose a new approach to distributed operations for the local information driven
CRAHNs.
1.2 Problem
CRAHNs have recently attracted intensive research interest, but some key theoretical
questions have yet to be answered. The previously proposed algorithms and tech-
niques for solving spectrum management problems are not suited to CRAHNs. For
the CRs relying on the local control with local observation and limited local informa-
tion, we need to design the local control schemes for the spectrum sharing function.
Moreover, with the features brought by CRAHNs, MAC protocols for traditional
CRNs or ad hoc networks need to be re-designed because they need to address the
spectrum availability, interference, as well as mobility issues. For example, mobility
issues that can cause spectrum mobility will result in the negative effects to the data
transmissions in CRAHNs, such as interference to PU communications and spectrum
variations. More importantly, when we consider a CRAHN as a complex system, a
change of a parameter value in initial conditions may cause unexpected results to the
CRAHN. In this sense, we propose to study the system stability condition in order to
1.3. OBJECTIVE 5
explore system-level properties and behaviors for spectrum management problems in
CRAHNs. Because the system-level properties are related to the protocols or algo-
rithms used in a certain layer of the CRAHN, we must study protocols or algorithms
used for spectrum management problems. Subsequently, the scaling law should be
considered because a change in system-level parameters or protocol-level parameters
may result in a new scaling law for PUs and CRs data transmissions in CRAHNs. In
addition, because the protocols/algorithms in CRAHNs are mostly based on the local
sensing, an important problem is to determine how the local information acquired by
local sensing can be used in the protocols/algorithms and how the local information
can affect the performance of these protocols/algorithms.
Furthermore, the throughput performance in a CRAHN based on the local control
approach together with the MAC and PHY features needs to be addressed. For
example, an accurate channel profile can be considered when analyzing the scaling
law. Furthermore, after a successful dynamic spectrum access, CRs must be able to
relay packets to the destination node with the available CRs in the CRAHN. In this
sense, how the cognitive environment can affect the performance degradation for CRs
is a challenge. The analysis in multi-hop data transmission scenarios can provide
some insights to this issue.
1.3 Objective
Fundamental problems of spectrum sharing in CRAHNs need to be investigated.
A light-wight and effective scheme for spectrum sharing of CRAHN needs to be
investigated, not only because it utilizes the cross-layer information but also because
it can take advantage of the main features introduced by scalable CRAHNs. These
1.4. CONTRIBUTIONS 6
features can provide opportunities for solving spectrum sharing problems in local
control approach with radio environment information, including global information
and local information. In this way, we are required to propose a local control approach
to address the spectrum sharing related problems. This study defines and develops
the local control approach concept. In the local control approach, we need to consider
the distributed operations for CRs, where a CR or a PU can perform a local control
scheme with sensing inputs and decision outputs. We also need to address the mobility
and interference issues in the MAC layer and perform the system-level analysis for the
local control driven CRAHNs. By studying some fundamental problems regarding
spectrum sharing in local control approach, we can model, analyze, and evaluate
essential system and protocol-specific performance for CRAHNs.
1.4 Contributions
1.4.1 Distributed Local Control Schemes & Dynamics
We propose a local control framework for the distributed protocols for spectrum
sharing. We address the time delay in the transmission delay for the proposed local
control scheme. For example, the delay may be significant if an energy-detection-
based spectrum sensing scheme [10] is used. Therefore, the issue of how the delay
variation can affect the spectrum decision and sensing control should be explored.
To address this issue, together with the system-level analytic results of local control
schemes, we propose a cross-layer local control scheme.
Considering the scalable deployment of a CRAHN, we should exploit the system
dynamics of local control schemes. As such, we aim to prove the applicability and
conditions of using consensus-based protocols in local control schemes in spectrum
1.4. CONTRIBUTIONS 7
sharing problems in CRAHNs. The main goals of our research based on consensus
protocols are the following:
• We analyze and evaluate the algorithmic performance in a scalable CRAHN;
• We investigate how the collective intelligence will occur and how it helps to
solve spectrum sharing problems;
• We explore the system dynamics by employing a consensus protocol in local con-
trol schemes. For example, the analytic results from system dynamics analysis
can tell us the equilibrium condition when using a local control scheme.
1.4.2 Emergent Behavior of CRAHNs
Because of the existence of “emergent behavior” in a large-scale CRAHN, a cognitive
protocol or algorithm that works well in an individual cognitive radio may behave
differently in a large scale. On the one hand, this phenomenon can be examined before
the protocol design. On the other hand, it is not clear what emergent behaviors might
arise when the CR interacts with legacy radios or with other heterogeneous systems,
and whether these behaviors can inadvertently lead to communication failures in
critical applications. Without investigating the CRAHN at the system level, it is
not possible to justify the effectiveness and robustness of spectrum policy changes
for spectrum management. We have addressed this topic in the local control scheme
design.
1.4.3 Local Control Driven MAC Protocol Design
The protocols in the MAC sub layer has the scope of only exchanging the informa-
tion with neighbouring CRs. Therefore, it is an ideal place for applying the local
1.5. ORGANIZATION OF THESIS 8
control approach for CRAHNs. With local control concept, a MAC protocol needs to
solve the issues including mobility and PU interference with cognitive radio capability
without inducing significant communication efforts. In this research theme, in order
to address these issues, we propose a cognitive MAC protocol called CM-MAC. The
main contributions are listed as follows:
• We propose a CM-MAC protocol that addresses CR mobility and PER issues;
• We analyze the throughput and spectrum utilization of CM-MAC protocol as-
suming that the PU traffic follows a Poisson process;
• We show that the throughput and spectrum utilization are improved by CM-
MAC compared to classical MAC protocols.
1.4.4 Scaling Law Based on Local Control
As a main goal of CRAHNs, throughput performance needs to be investigated and
analyzed in single-hop and multi-hop scenarios. The state-of-the-art research in the
literature has addressed throughput analysis in CRNs, but several key factors in
CRAHNs have not been comprehensively addressed. As a result, we develop a model
for throughput analysis because in this way some key factors such as the route selec-
tion, local observation & control, spectrum sharing, and multi-hop data transmission
scenarios can be addressed.
1.5 Organization of Thesis
We proceed by introducing the CRAHN and spectrum sharing functions and dis-
cussing related work in Chapter 2. The related system models and approaches are
1.5. ORGANIZATION OF THESIS 9
presented in Chapter 3. We discuss the local control framework for the spectrum
sharing fairness problem with experimental results in Chapter 4. Chapter 5 discusses
the mobility supported MAC which further shows the local control concept. The s-
caling law analysis is discussed in Chapter 6. Chapter 7 concludes and outlines future
work.
10
Chapter 2
Background & Related Work
In this chapter, we briefly introduce the background knowledge about CRAHNs and
discuss the related work regarding the thesis research topics.
2.1 Cognitive Radio Ad Hoc Networks
A CRANH is a network composed by CRs nodes and PUs in an ad hoc manner in
a changing radio environment induced by the time and location and PU activities.
In order to ensure the successful data transmissions, accessing the spectrum resource
needs to be coordinated to prevent collisions. As such, with a spectrum sharing
module, a CR is able to share spectrum resources among CRs [5]. As an example of
a CRAHN shown in Fig. 2.1(a), the CRs are co-located with PUs, where PUs and
CRs are able to move. In order to make CRs aware of the available spectrum bands,
the spectrum sharing module in each CR is required to ensure changing spectrum
resources in a region can be fairly shared with CRs. Similarly, the CRSN needs the
spectrum sharing module to ensure spectrum resources available to sensor nodes (SNs)
as shown in Fig. 2.1(b). Besides, if we consider a spectrum sharing scheme, we need
to choose a spectrum sharing model. There are two competing models of spectrum
2.1. COGNITIVE RADIO AD HOC NETWORKS 11
sharing [11]: (1) sharing among equals and (2) sharing between licensed primary
and secondary, where the former can be considered as the underlay technique and
the latter can be considered as the overlay technique (i.e., a CR does not use the
spectrum bands occupied by the PUs).
(a)
(b)
Figure 2.1: An example of (a) a CRAHN and (b) a CRSN
2.2. COGNITIVE RADIO NETWORKS VS. COGNITIVE RADIO ADHOC NETWORKS 12
2.2 Cognitive Radio Networks Vs. Cognitive Radio Ad Hoc Networks
The concept of cognitive radio networks is defined as the wireless networks that
consist of primary and secondary users [12]. The traditional CRNs are often modeled
as small networks in licensed bands with one PU and multiple SUs as seen in the
current IEEE 802.22 networks. However, the CRN paradigm can be extended to
the unlicensed industrial, scientific and medical (ISM) radio bands and therefore can
be used in the current ad hoc networks and wireless sensor networks. Some current
research topics of CRNs can be found in the recent survey papers [13, 14].
The CRAHN has different specific research foci compared with CRNs. Inherited
from the features in traditional ad hoc networks, nodes in a CRAHN can communicate
with each other without a fixed infrastructure [15]. The ad hoc topology and data
transmissions of ad hoc networks as well as the cognitive capabilities of CRNs bring
the new features and new challenges to CRAHNs. With the new features, the research
of CRAHN is expected to shed light on some current and future wireless networks.
2.3 Spectrum Sharing in CRAHNs
Spectrum sharing is a important function of spectrum management in CRAHNs. In
[5], spectrum sharing is defined to provide the capability of sharing the spectrum
resource opportunistically with multiple CRs while avoiding interference caused to
the primary network. Basically, spectrum sharing involves spectrum access, spectrum
allocation, and spectrum sensing with cross-layer information. In this sense, in the
protocol architecture point of view, it has to collaborate with PHY, MAC, and NWK
layers.
2.3. SPECTRUM SHARING IN CRAHNS 13
2.3.1 Spectrum Allocation
In order to ensure the data communications, CRs need to maximize their own share of
spectrum resources for data transmission sessions. Furthermore, CRs need to perform
channel selection and power allocation while choosing the best channel. Cooperation
among neighbors can help enhance the performance of spectrum sharing. However,
with the local observation to radio environment, CRs have limited radio information
from their neighbors by cooperation, and this constraint is expected to be able to affect
the performance of the network in terms of throughput and spectrum utilization.
Several distributed schemes or algorithms have been proposed in the literature
to solve the spectrum sharing problems. A single-channel asynchronous distributed
pricing scheme for spectrum selection and power control was proposed in [16], where
each CR determines the transmit power by maximizing the received utility minus the
total cost of the associated interference. A graph coloring based scheme was proposed
in [17], which is essentially a global optimization algorithm. This global optimiza-
tion algorithm is centralized in nature and is required to be recomputed whenever
there is a change in CRAHNs. Compared to a centralized scheme, a distributed
scheme is more suitable for the CRAHN due to its robustness in varying radio en-
vironments (e.g., topology and spectrum availability, etc.). A distributed spectrum
allocation scheme, referred as local bargaining, was proposed in [18], where CRs can
self-organize and form a local group to improve system utility. Results in [18] show
that the communication overhead using local bargaining can be significantly reduced
compared to a greedy coloring algorithm. A device-centric spectrum access approach
for spectrum allocation problem was introduced in [9], where five different rules are
applied to individual CRs. Although these rules have a slightly worse performance
2.3. SPECTRUM SHARING IN CRAHNS 14
than local bargaining [9], they have lower computational complexity and communica-
tion overhead. Furthermore, learning algorithms like reinforcement learning [19, 20]
can be involved in the spectrum sharing problems, but they may need much more in-
formation and collaboration efforts across the layers and hops, and a new architecture
is required.
Another type of algorithm, known as swarm intelligence algorithms, has been
proposed in the literature to solve spectrum sharing problems. In [21], the spectrum
sharing problem is solved by an insect colony based algorithm. In [22], an algorithm
based on the schooling mechanism of fish is studied to solve the spectrum sharing
problem. However, both papers do not give a formal proof for the convergence condi-
tion, which is important when applying the swarm intelligence algorithms to spectrum
management. Moreover, the swarm intelligence algorithms belong to a more general
type of protocols, called the consensus protocol, which is inspired by observing the
flocking or schooling phenomenon in nature. Moreover, we found that consensus pro-
tocols can be used to analyze some non-swarm-intelligence algorithms, such as local
bargaining and device-centric algorithms. The consensus protocols have been used for
the data fusion problems in sensor networks, robotic control, and multi-agent system-
s (MASs). Recently, Li et al. [23] have applied the consensus protocol to spectrum
sensing in order to control the fusion of sensing data. Yu et al. [24] have proposed a
distributed and scalable scheme for spectrum sensing based on consensus algorithms.
The above references have given hints of how to use consensus protocols in CRNs,
but they hardly address spectrum sharing fairness in CRAHNs and CRSNs. In this
study, we will formulate the convergence condition when applying a general consen-
sus protocol, which is necessary to theoretically show the applicability of consensus
2.3. SPECTRUM SHARING IN CRAHNS 15
protocols in spectrum sharing for CRAHNs and CRSNs. Moreover, we will discuss
how to use the consensus protocol for the spectrum sharing fairness.
2.3.2 Spectrum Access Model
Spectrum access techniques aim to make sure CRs can access the spectrum bands
without causing harmful interference to PUs, SUs need opportunistic or negotiation-
based spectrum access techniques [25]. There are three techniques (i.e., overlay, under-
lay or interweave) that aim to ensure the concurrent PU and SU data transmissions.
With the underlay technique, simultaneous PU and CR are allowed as in ultra-
wideband (UWB) systems. A CR spreads signal over a bandwidth large enough
to ensure that the amount of interference caused by the PUs is within a desired
threshold. With the overlay technique, PU messages sensed at the CR transmitter
are used to perform dirty paper coding in order to mitigate the interference seen by
the CR. With the interweave technique, CRs monitor the available channels absent
of PUs, and interweave the secondary signal through the gaps that arise in frequency
and time. The spectrum detection is critical in this interweave technique.
Spectrum overlay and spectrum underlay are considered as hierarchical access
models [26]. The overlay approach under the hierarchical access model is discussed in
[26] referred as opportunistic spectrum access, which includes spectrum opportunity
identification, spectrum opportunity exploitation, and regulatory policy.
In this thesis, we will consider the underlay and overlay techniques in the spectrum
sharing and the terms underlay spectrum sharing and overlay spectrum sharing will
be used correspondingly.
2.4. COGNITIVE MAC PROTOCOLS 16
2.3.3 Spectrum Sensing
The spectrum sensing function is closely related to the spectrum sharing as a under-
lying technology. There are two technologies to perform spectrum sensing: energy
detection and feature detection [27].
Time delay in sensing is an important factor to consider. The current sensing
technologies require us to consider the time delay caused to either PHY or upper-
layer schemes. For example, when cooperation is used for spectrum sensing, the
combination of the results from various users may have different sensitivities and
sensing times [28]. How to make the quickest detection is one of the current open
problems in spectrum sensing [27, 29, 30, 31], where it aims to detect the beginning
of a PUs transmission as quickly as possible after it happens. In fact, the well-known
sensing technology shows that sensing task takes up to several tens of milliseconds
per channel. Due to the out-of-band interference, a channel considered to be free
needs the additional sensing efforts from the adjacent channel. Moreover, a multi-
band detection technique was introduced in [32], and the sensing optimization with
MAC protocols were discussed in [33].
In the thesis, we will assume the existence of the spectrum sensing module and
consider the time delay in the spectrum sensing.
2.4 Cognitive MAC Protocols
The objectives of the CRAHN MAC protocol not only include the improvement of
channel utilization and throughput without degrading PU communications, but also
include the control of spectrum management modules such as spectrum access and
spectrum sharing functions to determine the timing for data transmissions [5].
2.4. COGNITIVE MAC PROTOCOLS 17
The use of multiple channels for throughput improvement has been addressed
in several MAC protocols. A feasible solution for throughput improvement is to
find a set of good-quality channels. A dual-channel MAC protocol (DUCHA) was
proposed in [34] which can improve the one-hop throughput up to 1.2 times and
multi-hop throughput up to five times compared to the IEEE 802.11 MAC protocol.
An opportunistic multi-radio MAC (OMMAC) was proposed in [35], where a multi-
channel-based packet scheduling algorithm was employed and packets were sent on a
channel having best spectral efficiency (i.e., the channel with the highest bit rate). A
CSMA/CA-based multichannel cognitive radio medium access control (MCR-MAC)
protocol was proposed in [36].
In a CRN, the spectrum utilization can be improved if we choose the appropriate
set of channels that meet the transmission rate requirement. A MAC protocol based
on statistical channel allocation (SCA) was proposed in [37] which uses a channel ag-
gregation approach to improve the throughput and dynamic operating range to reduce
the computational complexity. Results of [37] show that SCA-MAC can use spectrum
holes effectively to improve spectrum efficiency while keeping the performance of co-
existing PUs. In order to meet data rate requirement for data transmissions, a MAC
with a so-called multi-channel parallel transmission protocol was proposed in [38],
where the minimum number of channels were selected to meet a certain data rate.
The results of [38] show that the proposed MAC protocol has better spectrum uti-
lization and system throughput than the results shown in [39], which only selected
the channels by the best signal-to-interference-plus-noise ratio (SINR) value. In [40],
an opportunistic auto-rate MAC protocol is used to maximize the utilization on in-
dividual channels.
2.4. COGNITIVE MAC PROTOCOLS 18
Spectrum sharing and spectrum access functions are explicitly addressed in [41],
where spectrum access and spectrum allocation schemes are introduced into the pro-
posed cognitive radio MAC (COMAC) protocol. Specifically, the spectrum utilization
is improved by providing enough channels instead of assigning all the possible chan-
nels to a CR node, so that the other available channels could be reserved for other
CR transmissions. In [42], the authors employed a distance-dependent channel as-
signment scheme in a proposed distance-dependent MAC (DDMAC).
In fact, the aforementioned works do not comprehensively consider several impor-
tant factors. Firstly, although the spectrum sensing can be simultaneously performed
in one shot [43], the sensing time cannot be ignored, as it may be relatively large
and lead to end-to-end throughput degradation [44]. Secondly, with the existence of
the primary exclusive region (PER) where CR communications will interfere with PU
communications, the CR should keep silent when moving into this region if maintain-
ing PU communication is a priority.
As CRAHN MAC protocols favor distributed solutions, a distributed function
like distributed coordination function (DCF) is a good option for protocol design.
In fact, most of the aforementioned MAC protocols [35, 36, 38, 39, 40, 41, 42] are
DCF-based with request-to-send (RTS)/clear-to-send (CTS) handshaking procedures,
which intrinsically deal with the hidden terminal problem. Other non-CSMA/CA-
based MAC protocols like multi-channel MAC (MMAC) [45] and cognitive MAC
(C-MAC) [46] can also solve the hidden terminal problem, but they need a periodic
synchronization which can hardly be applied to large-scale CRAHNs.
2.5. SCALING LAW OF CRAHNS 19
Carrier sense multiple access/collision avoidance (CSMA/CA) based MAC pro-
tocols have the advantage of dealing with hidden terminal problems and having dis-
tributed operations (e.g., distributed coordination function in IEEE 802.11 MAC).
Thus, some state-of-the-art MAC protocols [36, 37, 38, 39, 40, 41, 42, 47] for CRNs
have been proposed. However, PER, PU activity and CR mobility have not been
comprehensively addressed in the literature.
2.5 Scaling Law of CRAHNs
The scaling law analysis for wireless networks can give hints to the theoretical bound-
s of throughput performance. Guptar and Kumar [48] firstly give the throughput
bounds for a general wireless network. They show that the throughput will decrease
with an increase of the number of nodes. However, the bounds given by Gupta and
Kumar [48] are loose for the CR network in CRAHNs, because, in CRAHNs, com-
munications between CR nodes can be affected by the PU activities. By utilizing
the multiple spectrum bands for data communications, system capacity, multi-path
diversity, and data rate can be improved [49]. However, how to comprehensively ad-
dress the design parameters across different layers in the randomly deployed CRAHN
is a challenge. Vu et al. [50] have analyzed the throughput for cognitive networks,
where the authors merely discussed the network model with one PU transmitter. This
analysis is suitable for some cognitive networks, such as the cognitive network with
one TV tower and multiple CRs. However, the analysis in [48, 50] is not suitable
for CRAHNs, as more than one PU transmitters can be present with CRs. More-
over, considering the possible flexible deployment of CRAHNs, we should analyze the
scaling law of throughput in different transmission scenarios.
2.5. SCALING LAW OF CRAHNS 20
Some research work has been done regarding the throughput scaling law for
CRAHNs. Shi et al. [51] have recently given lower and upper bounds for the through-
put in a randomly distributed CRAHN by using two auxiliary networks. The authors
show that the lower and upper bounds for the throughput are Ω(Cα/√n lnn) and
O(Cζ/√n lnn) respectively, where the number of CR nodes is n. However, PU activ-
ities and multi-hop transmission scenarios have not been considered in the discussion.
When the primary exclusive region (PER) was addressed in [52], where interference
and outage probability was derived for bipolar and nearest-neighbor network models.
When employing underlay transmissions with PUs, CRs will experience transmission
delay because of the reduced transmission range from increased interference. The op-
portunistic multi-channel MAC protocols for CRAHNs were analyzed in [53], where
a Markov model is used to estimate the number of sensed channels. The relation-
ship of delay, connectivity, and interference were analyzed in [54]. Besides, with new
features brought to CRAHNs, different spectrum management schemes can result in
new scaling laws in the CRAHN. Moreover, although some recently proposed physical
layer techniques, such as physical-layer network coding (PLNC) [55, 56] or interfer-
ence based network, may help to derive new scaling laws in CRAHNs, we need to
explore the essential factors that affect the CRAHN throughput performance. S-
tochastic geometry has been employed as an analytical tool for fundamental limits of
wireless networks [57] which is able to include many essential factors and transmission
scenarios [58] in the analysis.
In this thesis, we mainly explore the CRAHN with essential cognitive capabili-
ties instead of reiterating the use of new PHY technologies. We will start with our
throughput analysis by constructing the network model with the consideration of
2.5. SCALING LAW OF CRAHNS 21
PER, deployment of PUs and CRs, spectrum access scheme, and spectrum sharing
scheme.
22
Chapter 3
System Model and Approach
In this chapter, we discuss the essential modelling techniques and approaches re-
garding the thesis research. We compare the existing approaches and introduce the
research approach for our study.
3.1 Spectrum Availability Map
Spectrum availability varies from node to node and from link to link in CRAHNs. In
the same radio environment, node spectrum availability and link spectrum availability
can be converted to each other. It is known that spectrum availability in a CRN is
usually modelled as conflict graph [18, 59]. However, in this study, we model the
spectrum availability in the perspective of PUs. In this sense, we can start from the
introduction of spectrum availability map in a CRAHN with grid topology.
Spectrum availability map (SAM) is defined against time and it is the probability
of using some available spectrum bands for data transmissions in a time slot ∆t.
Although in a time slot, a CR can do the spectrum hopping from one spectrum band
to another, here we start with considering an example that, in a time slot ∆t, there
are only two available spectrum bands for data communication. It is worth noting
3.1. SPECTRUM AVAILABILITY MAP 23
that the correlation between two SAMs are based on the previous time slot ∆(t− 1)
and the immediate next time slot ∆t. The value of SAM for a data communication
using two spectrum bands in a time slot ∆t for the ith CR and jth CR with k available
spectrum bands on the two CRs is:(
2k
)(2
k−2
), k ≥ 2.
The knowledge of SAM known a priori can be considered as global information;
the knowledge of local SAM known a priori is considered as local information.
For a CR in a CRAHN, the local SAM is enough and this local SAM can be
constructed by: (1) sensing the available spectrum bands; and (2) capturing the
available spectrum bands from different PUs and store them into the internal memory.
3.1.1 Cell-Based Spectrum Availability Map
A cellular automaton (CA) is a discrete model that has been broadly studied in dif-
ferent disciplines including computer science [60]. A cellular automaton is composed
by a regular grid of cells with a finite number of states in each cell.
The spectrum availability of a CRAHN can be modeled as a map by the concept
of CA and we name it cell-based spectrum availability map (C-SAM). Suppose each
CR has different spectra at a time t, we can explore the dynamics of the available
spectrums in a large-scale CRAHN. With this model , the dynamics of the CRAHN’s
system behaviour can be evaluated by this 2-D CA model. In Fig. 3.1, assumptions
regarding the CA based model are:
1. Available spectrums at a time t are identical to all CRs;
2. Each CR can only communicate the immediate neighbors, which states decide
the availability of the spectrums of CR i;
3. Numbers in the following figure represent the different spectrum indexes.
3.1. SPECTRUM AVAILABILITY MAP 24
1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3
Figure 3.1: An example of C-SAM in a CRAHN with 3 spectrum band indexes foreach CR
3.1.2 Radio Environment Map
Instead of obtaining the radio environment parameters at CR nodes, the radio envi-
ronment map (REM) proposed in [61] can be used to store environmental and opera-
tional information. A REM can provide many kinds of radio environment information
over a CRN, such as geographical features, available services, spectral regulations, lo-
cation and radio activities, and experience. The REM can be classified as global
REM and local REM [62].These two classes of REMs can be used by cognitive ra-
dio regional area networks (e.g., IEEE 802.22 networks) or cognitive radio local area
networks (e.g., CRAHNs). According to the link-level and network-level analysis
in [63], using the REM can significantly improve the network performance in terms
of reduced adaptation time, average packet delay, and the mitigation of the hidden
terminal problem.
3.2. SPECTRUM AVAILABILITY PROBABILITY 25
Global REM Server
Local REM Server
CR
CR
CR
CH
CR
Local REM Server CR
CR
CR
CH
CR
Local REM Server
CR
CR
CR
CH
CR PU
PU
Figure 3.2: The architecture of a CRAHN with REM servers
The REM is a practical solution when reliable information (e.g., a certain amount
of local information and global information) regarding radio environment is needed in
CRAHNs. As an example of the REM-based architecture, in Fig. 3.2, the CH is the
cluster head which is responsible of exchanging information to the local REM server.
The local REM server contains the information collected from CRs in each cluster.
The data in local REMs will be sent to the global REM server.
3.2 Spectrum Availability Probability
For the spectrum sharing protocols, it is natural to see the relationship between the
spectrum availability map and the CRs. In fact, we propose that the two models
can be converted from one to another. With the proposed spectrum availability
probability (SAP), we can divide a CRAHN into different sub areas. In this sense,
the data transmission scenario can be converted to the probability of a CR transmitter
at the center of a sub area and the SAP of this transmitter at a location.
Definition 1. (Spectrum availability probability): SAP, %(∆t, k, s), is defined as the
3.3. VARIABLE SIZE OF SPECTRUM BANDS 26
probability of when a CR is able to access a spectrum band k in a time period ∆t in
an area s.
With a Poisson traffic flow of PUs deployed in an area S, we know that in an area
s ∈ S, SAP can be determined by three parameters ∆t, k, and S.
If we consider the flow of fairness, i.e., each data transmission flow needs differ-
ent bandwidths, we have to improve the aforementioned SAP and SAM. With an
application-specific QoS requirement, if the speed cannot be met by the available
spectrum band, the spectrum band is considered not available.
3.3 Variable Size of Spectrum Bands
From the results we discussed about SAP, we assume that the size of the spectrum
bands is identical in terms of same traffic model. The problem is more complicated
when we consider a more general case that the spectrum bands have variable sizes.
This means that a large chunk of spectrum can be split into two or more smaller
chunks of spectrum, or a smaller chunks of spectrum can be combined into a larger
chunk. We consider this variation occurs only when the current available spectrum
bands cannot meet the flow bandwidth requirement.
In fact, multiple available spectrum bands can be virtually combined as one when
we use the channel aggregation technique to boost the throughput, where, for exam-
ple, a large packet can be split into two and transmitted in the two channels in a
faster speed. With these assumptions, we can convert this case into a case similar to
SAP that spectrum bands have identical sizes. We are able to calculate the bound of
probability of the presence of variable spectrum bands.
3.4. MULTI-CHANNEL MULTI-RADIO SUPPORT 27
3.4 Multi-Channel Multi-Radio Support
The CRAHN can be considered a network paradigm with multi-channel multi-radio
support. The network throughput performance can be boosted by multi-channel
multi-radio capability in CRs. It is readily to see the NWK layer schemes can take
advantage of that capability in CRs, because the multiple routes brought by the CR
capability can increase the data transmitted per unit time. To see this, we plot Fig.
3.3 showing the throughput performance of a CRAHN based on different routing
protocols with K spectrum bands and R multiple radios. We can see from Fig.
3.3 that, when more channels and radios are available, the routing protocol metric,
i.e., weighted cumulative expected transmission time (WCETT) [64], which can take
advantage of multi-channel multi-radio capability, has better performance than the
network with the ad hoc on-demand distance vector (AODV) routing protocol. More
cognitive routing protocols have been discussed in [65, 66, 67, 68].
In the subsequent chapters, we will address the multi-channel multi-radio capa-
bility for the MAC protocol design.
3.5 Resultant Channel Model
With the proposed concept of SAM, we are able to visualize spectrum availability at
a time t. It will be more useful if we can map spectrum availability in different bands
into one spectrum band at a time t. This can be achieved by using the resultant
channel model [69].
The resultant channel model can be seen in Fig. 3.4, where for the ith PU the
time spent in “busy” and “idle” states are exponentially distributed with mean αi and
βi, respectively. In this model, the PU activity is determined by a ON-OFF model,
3.5. RESULTANT CHANNEL MODEL 28
0 50 100 150 200 250 300 350 400 4500
50
100
150
200
250
300
350
400
4501
2 3
45
6
7
8
9
10
X (m)
Y (
m)
(a)
0 5 10 15 20 25 30 35 40 45 500
2
4
6
8
10
12
14x 10
4
Time (s)
Ave
rag
e T
hro
ug
hp
ut (
B/s
)
WiFi Network (AODV, K=1, R=1)
ZigBee Network (AODV, K=1, R=1)
WiFi Network (AODV, K=2, R=2)
WiFi Network (WCETT, K=2, R=2)
(b)
Figure 3.3: Throughput performance in a CRAHN with multi-channel multi-radiosupport in different settings. The network has 10 CRs and the communi-cation range per node is 250m in 2GHz band.
3.5. RESULTANT CHANNEL MODEL 29
Channels 1 to Kwith PU activities
“OFF” state
“ON” state
E[Ton]
Ch 1
Ch 2
Ch K...
E[Toff] Resultant Channel
Figure 3.4: Example of the resultant channel model
where ON or ‘1’ means PU is busy and is occupying a channel; OFF or ‘0’ means
PU is not transmitting and is not occupying a channel. It is worth noting that by
using the resultant channel model, multiple PU transmitters can be modelled as one
virtual PU transmitter.
From [69], the expected number of idle and busy channels can be estimated as:
ω0,i =αi
αi + βiω1,i =
βiαi + βi
(3.1)
The expected length of the resultant idle period and busy period are:
E[Toff ] =
1−K∏i=1
ω1,i
K∏i=1
ω1,i
K∑i=1
βi−1
E[Ton] =1
K∑i=1
βi−1
(3.2)
The expected number of idle channels can be estimated as
L =K∑m=1
mπoffch (m) =πch(m)
1−K∏j=1
1− ω0,j
(3.3)
3.6. LOCAL AND GLOBAL INFORMATION 30
Local InformationChannelstate (i-dle/busy)
Numberof neigh-bors
Immediateneighborsspectrumusage
Spectrumutiliza-tion
OverheardMAC in-fo
Signalstrength
Cost C1 C2 C2 C3 0 0
Table 3.1: Local information associated with cost values
3.6 Local and Global Information
Local information is the information that can be acquired by local observation (e.g.,
local sensing) or communications with neighbors. We can refer to the categorization
for local information in IEEE 1900.4 standard [70], where information is categorized
into terminal class and network class. The former can be used for classifying the local
information and the latter can be used for classifying the global information. Terminal
class includes application information and device information. Application informa-
tion contains information about measurements supported by applications, such as
delay, packet loss, and bandwidth. Device information contains information about
the current active links and channels. Information about links includes block er-
ror rate, power, signal-to-interference-plus-noise ratio, etc., while information about
channels includes channel ID, frequency range, etc.
When obtaining local information, we should consider the communication cost
of obtaining the information. Due to the changing radio environments in CRAHNs,
some cost values may be dynamic, while others are not. Moreover, the cost values
can be considered in the metrics for distributed protocol design. As an example, we
show some pieces of local information with cost values in Table 3.1.
In Table 3.1, we can see the cost of obtaining the channel state and the cost
3.7. LOCAL CONTROL IN SPECTRUM MANAGEMENT 31
of obtaining channel utilization are C1 and C3, respectively. The cost of obtaining
the number of neighbors and the cost of obtaining the neighboring spectrum usage
are the same, i.e., C2. This is true when some information such as the number of
neighbors can be estimated from overheard incoming packets, which contain MAC
address fields and data fields with spectrum utilization of neighbors. Therefore, we
can assume MAC information needs no cost to obtain. For the signal strength that
can be easily estimated by most receivers, we assume the cost of obtaining it is zero.
If we initiate a particular communication process to obtain channel state and channel
utilization, the values of C1 or C3 would be larger than C2.
The global information refers to information over the network. For example, from
the IEEE 1900.4 standard [70], the network information includes channel information,
cell information, and base station information. Channel information is mainly about
the frequency channel, including frequency channel ID, frequency range, etc. Cell
information is the general information about a cell configuration, including cell ID,
location, coverage area, etc. Base station information contains the general information
about the current base station configuration, including transmission power, load, etc.
3.7 Local Control in Spectrum Management
The local control can be considered as a distributed control of individual CRs in
CRAHNs. Because of the lack of a central controller and changing radio conditions, a
centralized control is not suitable. Moreover, the cooperation between CRs can help
create and distribute radio environment information, which makes an individual node
have a macroscopic view of the network status. It has been proven that cooperation
between CRs can help improve the spectrum sharing process. However, cooperation
3.8. GAME THEORETIC APPROACH 32
can lead to increasing communication overhead and underlying interference. As such,
the approach of spectrum management based on global information would be costly.
Here we discuss the different between local control schemes and spectrum etiquette
[71]. The former may include a set of protocols, rules, or schemes, enabling system-
level and protocol-level modeling and analysis for spectrum management problems,
such as spectrum sharing, spectrum mobility, and spectrum decision. The latter may
be considered as a mere set of rules, which regulate access to spectrum and its usage
[71] (i.e., a set of rules dictating when, where and how may devices transmit [72]).
Therefore, the two concepts may overlap to some extent, but, in fact, they focus on
different problems.
3.8 Game Theoretic Approach
Due to the features of the CRAHN, a non-cooperative scheme is desirable for spectrum
sharing and allocation as it can reduce the communication overhead and underlying
interference. In game theoretic approach, Nash equilibrium is an important tool to
measure the outcome of a non-cooperative game [25, 73, 74, 75, 76] in the spectrum
management problems.
A game theoretic approach for spectrum allocation is proposed in [77], where the
CR nodes (i.e., players) make decision based on the utility function to select a channel
without causing interference to other nodes. In [78], a spectrum sharing solution based
on game theoretic approach for the primary-secondary model is proposed, where
an oligopoly market model is used to maximize the profit of all CRs based on the
equilibrium adopted by all CRs.
3.8. GAME THEORETIC APPROACH 33
The game theory is used for multi-player optimization to achieve individual opti-
mal solution. Mathematically, the game can be defined as Γ = N, Si(i∈N), Ui(i∈N)
, where N is the finite set of players, and Si is the set of strategies associated with
player i. For every player in game Γ, the utility function Ui is a function of si, (the
strategy selected by player i) and s−i (the current strategy profile of its opponents).
All the players make decisions independently and have to converge into equilibrium.
For Nash equilibrium, a strategy profile for players should meet
Ui(S) ≥ Ui(s′i, s−i), ∀i ∈ N, s′i ∈ Si (3.4)
In order to select a channel without interfering other CRs, the authors of [77]
define two utility functions. One utility function is a selfish scheme that a user values
a channel based on its own perception of interference on a particular channel. The
other is less selfish as a user will measure the interference perceived by its neighbor.
A selfish utility function is useful to some extent because it uses less information
than a less selfish utility function. In order to achieve convergence, both utility
functions have to be a potential function, P , which is defined as:
P : S → R, if ∀i and si, s′i ∈ Si
Ui(si, s−i)− Ui(s′i, s−i) = P (si, s−i)− P (s′i, s−i)
(3.5)
where S = ×Si is the strategy space.
However, to model a spectrum sharing problem in game theoretic approach, the
players have to make decisions sequentially, i.e., a coordinator to control the playing
order is required. To transform the game theoretic scheme into a distributed ver-
sion, a Bernoulli trial is used to make the sequential decision-making process happen
3.8. GAME THEORETIC APPROACH 34
at players by probability. In other words, at the beginning of every iteration, the
decision-making process is performed at players who win a Bernoulli trial.
From the above discussion, the game theoretic approach can model strategic inter-
actions among agents using formalized incentive structures [25]. The general method-
ology in game theoretic approach is to: (1) find a suitable game model for a problem,
(2) formulate a utilization function, and (3) prove the equilibrium condition. Due to
the autonomous and learning properties of CRs, the game theoretic approach maybe
a suitable way to solve problems in CRAHNs.
However, we should note that modeling a problem as a game cannot always get
an optimal solution. For example, the authors of [79] show that when the nodes have
complete information about the network, the steady-state topologies are suboptimal.
In order to make a game have a convergence property, the utility function also has to
meet some conditions.
In [6], Haykin indicated that Nash equilibrium assumes the players are rational,
meaning each player has a view of the world. Haykin also argues that the Nash equi-
librium has two practical limitations: (1) best-response strategy required to achieve
Nash equilibrium does not always hold. For example, in a two-player game, if on-
ly one player adopts a non-equilibrium strategy, the optimal response of the other
player is of a non-equilibrium kind too. (2) Description of a non-cooperative game is
essentially confined to an equilibrium condition, which is not enough to be used in
cognitive radio with underlying dynamics.
In the state-of-the-art research work, although the game theoretic approach is
popular for decision-making in spectrum allocation and spectrum sharing, the real-
ization in this approach is dependent on a certain centralized flow control protocol
3.9. GRAPH COLORING BASED ALGORITHMS 35
in the MAC or NWK layer. A zero-player game may be included in a local control
scheme to show the system-level characteristics. In this thesis, the further discussion
on game theoretic based local control schemes is out of the scope of this study.
3.9 Graph Coloring Based Algorithms
Graph coloring based algorithms can be directly used to solve the spectrum allocation
problem. As soon as the available spectrum bands for each CR are transformed to the
colors of a map, the objective of the graph coloring algorithm for spectrum allocation
is to minimize the use of colors.
Here we show the classical graph coloring algorithm proposed in [17]. In a undi-
rected graph G = (V,E), the number of users is N = |V |, and E = eij, where eij = 1
if there is an edge between vertices i and j and eij = 0 if i and j use the same spec-
trum bands. The availability of spectrum bands at vertices of G is represented by a
N ×K matrix L = lik, referred to as a coloring matrix. For example, lik=1 means a
color (spectrum band) k is available at vertex i.
A channel assignment policy is denoted by N×K matrix S = sik, where sik = 0, 1.
If sik=0, channel k is assigned to the node i and 0 otherwise. S is a feasible assign-
ment if the assignments satisfy the interference constraint and the color availability
constraint, which can be denoted by siksjkeij = 0,∀i, j = 1, . . . , N, k = 1, . . . , K.
The above constraint means that two connected nodes cannot be assigned to the same
colors (channels).
The objective of the resource allocation is to maximize the spectrum utilization.
3.10. PARTIAL OBSERVABLE MARKOV DECISION PROCESS 36
The formal representation of the spectrum allocation problem is
MaximizeN∑i=1
K∑k=1
sik
Subject to sik ≤ lik
siksjkeij = 0,
sik = 0, 1
∀i, j = 1, . . . , N, k = 1, . . . , K.
(3.6)
If a time slotted communication between the network nodes is considered, at each
time unit, the optimization problem in (3.6) needs to be recomputed.
We can see from (3.6) that, in the varying radio environment in CRAHNs, the
optimization problem has to be executed many times, which make the graph coloring
algorithm inefficient. Moreover, the graph coloring algorithm is an innate central-
ized algorithm, so it is not suitable for the CRAHN. However, it can be used as a
benchmark to compare with distributed algorithms.
3.10 Partial Observable Markov Decision Process
The partial observable Markov decision process (POMDP) is a generalization of a
Markov decision process (MDP). A POMDP models a decision process of a CR where
the system dynamics is determined by an MDP, but the CR cannot directly observe
the underlying state of a channel. Therefore, the POMDP is more practical than an
MDP model when solving spectrum access problems.
For example, if the channel is modeled as a Markov channel with two states“good”
and “bad”and four transition probabilities given by pij, i, j = 0, 1, a transmitter can
3.11. BIO-INSPIRED SCHEMES 37
select one of the channels to sense based on its prior observations, and the selected
channels obtain some fixed award if it is in the good state. This problem can be
described as a POMDP, as the states of the Markov chains are not fully observable.
In [80], the myopic policy (i.e., a policy that maximizes one-step reward) is examined
that, when p11 ≥ p01, it is optimal for any number of channels; when p11 < p01, it is
optimal when the number of channels n = 3.
As we can see that, a POMDP is suitable for modeling a channel access problem,
as the channel states are not fully observable to a CR. However, there are some
limitations of a POMDP. One limitation is that a POMDP is often computationally
intractable to be solved. Another problem is that a POMDP is suited to the single
player with multiple states. As an MDP is in fact a special case of stochastic game
[6], in spectrum management, a POMDP may be suitable for spectrum sensing in
individual CRs but not the spectrum sharing based on local observation.
3.11 Bio-Inspired Schemes
There are some swarm intelligence algorithms which have been proposed recently.
Atakan and Akan [21] propose a spectrum sharing algorithm called BIOSS (BIOlogically-
inspired Spectrum Sharing) based on the task allocation model of an insect colony.
This algorithm does not need any coordination among the CRs compared to non-bio-
inspired ones. Another swarm intelligence algorithm is proposed by Doerr et al. [22],
which is inspired by the emergent behavior of a school of fish. In [22], CRs’ behavior
can be analogous to a school of fish, where CRs can sense the radio environment by
local observation and react to the changing radio environment. Each CR has lim-
ited intelligence but in the entire network they have better overall intelligence than
3.12. CONCLUSIVE REMARKS 38
individual intelligence for a certain task.
The existing work in the literature prove the idea of applying swam intelligence
to spectrum management problems, where each CR embedded with this algorithm
can evolve to show a collective intelligence. However, there is still much work to do
in order to critically derive analytical results. Unless the advantages can still hold in
a scalable CRAHN, we can hardly apply the existing schemes directly. For example,
the authors of [81]indicate that the additional information is not always advantageous
by using a consensus protocol.
3.12 Conclusive Remarks
We discussed the essential models and approaches regarding CRAHNs in this chapter.
In the next chapter, we will discuss in more detail about the proposed local control
approach for spectrum sharing.
39
Chapter 4
Local Control Schemes for Spectrum Sharing
In this chapter, we first introduce the concept of local control schemes, by which a
CR can locally perform a spectrum sharing process with sensing inputs and decision
outputs. Then we define the spectrum sharing fairness issue and investigate the con-
vergence condition when applying a consensus-based protocol to spectrum sharing to
address the defined fairness issue. Based on the local observation and local control
scheme using spectrum-related information, an individual cognitive node can effec-
tively perform the spectrum sharing. Supported with computer simulation results,
we show the effectiveness of using the proposed consensus-based protocol to solve
spectrum sharing problems in CRAHNs.
4.1 Applicability of A Local Control Scheme to CRAHNs, CRSNs, And
Sensor Networks for CRAHNs
We discuss how to apply a local control scheme in these types of networks due to the
characteristics of the CRAHNs, CRSNs, and sensor networks for CRAHNs.
Compared to the classical ad hoc network, a CRAHN is able to deal with the
4.1. APPLICABILITY OF A LOCAL CONTROL SCHEME TOCRAHNS, CRSNS, AND SENSOR NETWORKS FOR CRAHNS 40
problems caused by changing radio environment and to protect licensed users trans-
missions. Compared to classical CRNs. CRAHNs inherit some important features
from ad hoc networks, such as node mobility, hop-by-hop spectrum availability, and
unidirectional links. Other features in CRAHNs include spectrum-dependent links,
topology control, multi-channel transmission, and spectrum mobility, implying more
challenges than those in either classical CRNs or ad hoc networks. Due to the lack of
central network entities in CRAHNs [8], each CR node necessitates that all spectrum-
related CR capabilities and distributed operations must be based mostly on local
observations.
In CRSNs, each cognitive sensor node has cognitive capability and the network is
usually intensively deployed with co-located PUs. Therefore, this type of networks
inherits the similar cognitive modules as those in CRAHNs. A CRSN can use similar
local control schemes in the spectrum sharing module. A CRSN, which has limited
coverage and power supply, can be considered as the extension of a CRAHN, so the
local control schemes can be applied to CRSNs.
Moreover, a local control scheme is suitable for another network paradigm called
sensor networks for CRAHNs, where sensor nodes are aided for cognitive actuation.
With local observation and local knowledge, sensor nodes perform the collective be-
havior for spectrum sharing, monitoring, and decision. The enabling technology for
this network, called sensor network-aided cognitive radio, is discussed in [82]. As the
local control scheme on sensor nodes in this network is very similar to the CRs in a
CRAHN, we will not give detailed discussion for this network in this study.
Based on the aforementioned discussion, we see that CRAHN is a more general
network prototype than the sensor network for CRAHNs or CRSN, and a local control
4.2. REVISIT OF SPECTRUM SHARING IN THE PERSPECTIVEOF LOCAL CONTROL SCHEMES 41
scheme for CRAHNs is also applicable to CRSNs. Therefore, we will focus on how
the local control scheme can be applied to CRAHNs.
4.2 Revisit of Spectrum Sharing in the Perspective of Local Control
Schemes
The radio environment in CRAHNs is subject to change from time to time, which is
the major problem for the spectrum sharing function. Typically, a change of radio
environment can be caused by:
1. PU activities;
2. Interference during communications;
3. Spatial-temporal characteristics of radio signals.
In this work, we only consider the first two factors.
CR
CRCR CR
CR
CR
CR
CR
CR
CR CR
CR
CR
CR
CR
CRCR
CRCR
CR
Radio Environment
PU
PU
PU
PU
PU
PU
Figure 4.1: A CRAHN deployed in a radio environment
As an example, Fig. 4.1 shows that CRs are deployed in an area with a changing
radio environment. Each CR senses and observes the local radio environment. When
4.3. FRAMEWORK OF LOCAL CONTROL SCHEMES 42
CRs request the spectrum bands occupied by PUs, they need to invoke local control
to share spectrum resources. A natural question one may raise is how the local control
for spectrum sharing can be performed by using local observation? In order to answer
the question, we introduce a block diagram to present a local control scheme, which
each CR will run for a spectrum sharing process.
4.3 Framework of Local Control Schemes
Process for spectrum
sharing
Feedback
[·]Sensing Input Output
Radio environment
Figure 4.2: Framework of a local control scheme
In Fig. 4.2, a local control scheme framework can be represented in a block dia-
gram. In this block diagram, when a CR receives a sensing input from sensors (e.g.,
a spectrum sensor or a global positioning system device, etc.), together with feed-
back information, a CRs will process the information and make a spectrum sharing
decision. At the sensing input, due to the different sensing capabilities, a CR may
have comprehensive, partial, or strictly limited sensing information. At the junction
of sensing input and feedback, we can adopt arbitrary types of combinations, where
we use the symbol “·” to represent any combination. In Fig. 4.2, the feedback block
is important for a decision-making process, which may contain a consensus feedback
(i.e., feedback from consensus process of nodes in a CRAHN), or a partial consensus
feedback (i.e., feedback partially from consensus), or no feedback. In the spectrum
sharing process block, a dynamic or a static process may be involved. A dynamic
process occurs at an individual CR when the position or spectrum availability of PUs
4.4. FAIRNESS IN SPECTRUM SHARING 43
and CRs in CRAHNs changes. A static process occurs when the position or spectrum
availability of PUs and CRs does not change. At the decision output, we can have
different kinds of solutions, such as optimal solution, sub-optimal solution, or inter-
mediate solution. If an optimal solution, such as Pareto optimum, is not achievable,
it is feasible to find a sub-optimal solution. The intermediate solution may neither be
optimal or sub-optimal; however, this solution can achieve the optimal or sub-optimal
solution by iterations.
To give an example for the aforementioned framework, we can consider a local con-
trol scheme in each CR in a CRAHN where each CR only takes the local information
as sensing inputs, such as the network-related information and spectrum information
from neighbors. After running a process for spectrum sharing functions in the local
control scheme, a CR will make a decision of what spectrum bands to use based on
the available spectrum resources.
4.4 Fairness in Spectrum Sharing
Definition 2. (fairness) The spectrum resource allocation is fair to each CR at time
t if the available spectrum resources at time t are evenly distributed among CRs.
We mainly consider the available spectrum bands as a spectrum resource requiring
fairness. The fairness of spectrum sharing is important as: (1) it can help ensure equal
communication opportunity for each CR; (2) it best responds to the changing radio
environment in terms of available spectrum bands.
In order to achieve fairness by local observation, each CR tries to achieve fairness
by considering the number of available spectrum bands of surrounding neighbors. In
order to achieve this goal, we propose to use a consensus feedback in the local control
4.4. FAIRNESS IN SPECTRUM SHARING 44
scheme, which can be mathematically formulated in the following.
Suppose the CRAHN can be represented by a graph G = (V (t), E(t)), where V (t)
is the set of vertices at time t and E(t) is the set of communication edges at time t.
We can analyze the system performance using a local control scheme executed by each
CR node. In an ideal condition (without any time delay), the consensus feedback is
defined in the form of variation as follows:
xi(t) =∑j∈Ni
aij(xj(t)− xi(t)) (4.1)
where the dot operator in xi(t) is used to show the variation of the values of x(t)
between CR i and neighboring nodes, xi(t) indicates the number of spectrum bands
available to a node i at time t, Ni(t) is the set of neighbors of node i at time t,
and aij is the 0 − 1 element in adjacency matrix of the network G. Equation (4.1)
shows that the spectrum allocation decision is made based on the feedback informa-
tion xi(t)calculated from neighbors spectrum information xj(t) and xi(t). With the
aforementioned notations, in order to measure fairness, we use the following expres-
sion:
σF =
√√√√√ M∑i=1
(xi(t)−m)2
M, (4.2)
where m is the fairness goal (e.g., m equals to the desired number of spectrum bands
of a CR) and M is the total number of CR nodes.
From (4.1), the fairness can be ensured if we can make sure that the number of
4.4. FAIRNESS IN SPECTRUM SHARING 45
spectrum bands are evenly distributed among CRs. However, since the CRAHN per-
forms hop-by-hop communication, a one-hop time delay t is inevitable when receiving
the information of spectrum availability from immediate neighbors. Then, (4.1) can
be transformed as
xi(t− τ) =∑j∈Ni
aij(xj(t− τ)− xi(t− τ)) (4.3)
Note that (4.1) and (4.3) are inherited from the Vicsek model [83].
In fact, the challenge of using the consensus protocol is to to make sure the domain
of xi(t) is applicable to the domain of spectrum bands. Therefore, we must prove that
the consensus feedback can be used in this spectrum sharing problem.
Proposition 1. Suppose ωi(t) is the number of available spectrum bands at the i-th n-
ode in a CRAHN at time t, where ωi(t) ∈ K and C is a constant, K= k < C|k ∈ Z+.
Given a discrete-time consensus feedback ωi(t) =∑
j∈Ni aij (ωj(t)− ωi(t)), ωj(t) ∈
R+, there exists a mapping γ : R+ → K, with which this consensus feedback can
ensure the fairness of spectrum sharing over the CRAHN.
Proof. The discrete consensus protocol can reach the average ωl = 1n
∑ωi when
ωi(t) ∈ R+. Therefore, when ω ∈ Z+, Z+ ⊂ R+, the discrete-time consensus
protocol holds. Now we have to prove that the consensus still holds in a mapping
function γ, which is:
f(γ) = dωi(t) mod |K|e (4.4)
where |K| is the length of K, i.e., the maximum number of spectrum bands available
to a CR.
From the mapping function f(γ), we can see that ωi(t) is essentially a periodic
4.4. FAIRNESS IN SPECTRUM SHARING 46
function with period |K| and we can see ωi(t) ∈ xi(t), where both xi(t) and t
are continuous. To see the stability of this transformed consensus protocol, first we
take the Laplace transformation of 4.3 by assuming x(t) is not a periodic function,
and thus we get
sXi(s)− xi(0−) =∑j∈Ni
aije−sτij (Xj(s)−Xi(s)) (4.5)
Then, considering the n periods n|K| in 4.5, we can get the Laplace transform of
xi(t) as+∞∑n=0
xi (t− n|K|) = Xi(s)+∞∑n=0
e−ns|K| =Xi(s)
1− e−s|K|(4.6)
Combining (4.5) and (4.6), we get the transfer function of 4.5 shown as follows
G(s) =[(In − e−s|K|L
) (sIn + e−sτL
)]−1(4.7)
where In is the identity matrix and L is the graph Laplacian defined by
lij =
∑n
k=1 aik, j = i
−aij, j 6= i(4.8)
Now we have to prove the stable conditions of (4.7). From Gershgorin’s theorem,
as L is strictly diagonally dominant and symmetric, the eigenvalues of L can be ranked
in a descending order as
0 = λ1 ≤ λ2 ≤ · · · ≤ λn ≤ 2 max d(i) (4.9)
where d(i) is the degree of node i. Suppose βm is the mth normalized eigenvector of
4.4. FAIRNESS IN SPECTRUM SHARING 47
L associated with the eigenvalues λm in an ascending order. Thus, when s = 0 in
the direction β1, G(s)−1 = Lβ1 = 0. When s 6= 0, then G(s)−1βm = (1− e−s|K|)(s +
e−τijsλm)βm = 0, (m > 1).
Since βm > β1 = 0 and 1 − e−s|K| ∈ (0, 1) when s > 0, s + e−τijsλm = 0. If we
suppose the one-hop time delay is identical to all the CRs, i.e., τij = τ , we get
s+ e−τsλm = 0 (4.10)
Note that the convergence condition of G(s) with a upper bound of τ has been
proven in [84], which is τ ∈ (0, τ ∗) with τ ∗ = π2λn
, λn = λmax(L). As such, we know
max(τ) = π4 max d(i)
.
For some cases that not all the CRs have the same need of spectrum resources,
i.e., different groups of nodes have different degrees of fairness, the degree of fairness
needs to be defined.
Definition 3. (degree of fairness) We refer the value of consensus feedback as a
degree of fairness for a node, which is defined as:
DF(i) = minE[Xi,j −Xi,j+1], j ∈ N
where Xij is the number of spectrum bands of the jth node in the ith group of nodes.
We denote by DFj(i) the degree of fairness for a node j in the ith group of nodes.
Definition 4. (fairness group) A set of CRs with the same degree of fairness is
called a fairness group (FG), i.e., group i and group j are in the same fairness group,
if DF(i) = DF(j) = p, where p is a constant. The notation FG can be used to denote
the number of fairness groups in CRAHNs.
4.4. FAIRNESS IN SPECTRUM SHARING 48
The concept of fairness group is useful when describing the heterogeneous nodes
that require different spectrum bands. Moreover, the concept can be used to virtually
divide a large-scale network into different groups with different degrees of fairness.
In order to show the stability shown in Proposition 1, we can see in Fig. 4.3, by
using Nyquist criterion, the two Nyquist plots on the top show the fairness solution
for spectrum sharing is stable, as we can see that the point (−1, j0) is not encircled.
However, the Nyquist plot at the bottom of Fig. 4.3 shows the spectrum fairness
solution for spectrum sharing is unstable. If the time delay of the links is beyond the
maximum value, the system is unstable. In other words, if the hop-by-hop time delay
in a CRAHN is over the maximum value, the fairness cannot be guaranteed.
-30 -20 -10 0 10 20 30 40
0
20
40
Ima
gin
ary
Nyquist Plot (max(di) = 3, t=0.0105, l=6)
Real
-30 -20 -10 0 10 20 30
0
20
40
Ima
gin
ary
Nyquist Plot (max(di) = 3, t=0.0524, l=6)
Real
-40 -20 0 20 40
0
20
40
60
Ima
gin
ary
Real
iNyquist Plot (max(d ) = 3, t=1.0472, l=6)
Figure 4.3: Analytical results for stability when using the consensus-based feedback.Nyquist plots with different time delays τ and with maximum degree ofthree in the CRAHN
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 49
4.5 Protocol Design And Experimental Results
4.5.1 System Model
In this section, we will mainly perform computer simulations to show the convergence
performance of the local control scheme without a consensus feedback and with a
consensus feedback for spectrum sharing in CRAHNs. The general system model
for computer simulations is based on Fig. 4.1 and 4.2, where each CR runs a local
control scheme in a CRAHN. CRs will use a common control channel to communicate
with each other for the information of spectrum availability. Moreover, we will focus
on the spectrum allocation performance and convergence performance of the local
control scheme.
In order to evaluate an open-loop local control scheme (i.e., the local control
scheme without a consensus feedback), we use a grid topology in the CRAHN with
the number of CR nodes, M , where each CR is denoted by the row number and
column number in a grid network, i.e., (i, j). We describe the proposed open-loop
local control scheme for evaluation in the following. The sensing input is the spectrum
bands chosen by the neighboring CRs. The initial spectrum bands are randomly
allocated to each CR. The local information used here is the spectrum bands selected
by a CRs immediate neighbors. The proposed process in this local control scheme is
to randomly select the available bands of neighboring CRs, i.e., the local information
is the available spectrum bands chosen by eight immediate neighboring nodes (where
in this case the average number of |Ni| equals to 8). To make the local control scheme
configurable, we set a control parameter λ in the process to represent the frequency
parameter with which a CR randomly selects a portion of spectrum bands from a
neighbor. This parameter can be considered as the feedback information shown in
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 50
Fig. 4.2.
Fig. 4.4 shows the results of the aforementioned open-loop local control scheme
(which can also be considered as a zero-player game) in different scenarios, where the
spectrum utilization results can reflect the convergence performance of the scheme
and the results are smoothed every 20 iterations. The spectrum utilization is defined
as the ratio of already allocated spectrum bands to a CR and the total available
spectrum bands to a CR. From Fig. 4.4, we can see that, although the spectrum
bands are randomly selected based on the neighbors spectrum availability and the
parameter λ, the spectrum utilization can show a certain pattern. By changing the
value of λ from 1.0 to 1+ε, where ε is a small positive number, a phase transition
occurs. When λ > 1.0, the spectrum utilizations are fluctuating among the available
spectrum bands; however, when λ = 1.0, the spectrum utilization over the network
is bifurcated into two groups—one is increasing and the other is declining. To show
whether the phase transition is applicable to the case with more spectrum bands
(i.e., |K| > 3), we plot the Fig. 4.4(d), where the phase transition still happens when
|K| = 8. We also found when |K| > 1 the results are similar. In fact, we found the
number of nodes and we find the phase transition is only dependent on the control
parameter λ.
From this example, we can conclude that the overall performance in terms of spec-
trum utilization is to some extent controllable by using the limited local information.
However, as the convergence cannot be achieved, this controllability may not be suf-
ficient to some applications as more variables should be considered. Furthermore, we
can see the possible structure of a local control scheme with local information, where
the local control scheme described above is an open-loop local control scheme without
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 51
0 100 200 300 400 500 600 700 800 900 10000.32
0.325
0.33
0.335
0.34
0.345
0.35
Iterations
Spe
ctru
m U
tiliz
atio
n
Spectrum band #1Spectrum band #2Spectrum band #3
(a)
0 100 200 300 400 500 600 700 800 900 10000.32
0.325
0.33
0.335
0.34
0.345
0.35
Iterations
Spe
ctru
m U
tiliz
atio
n
Spectrum band #1Spectrum band #2Spectrum band #3
(b)
0 100 200 300 400 500 600 700 800 900 10000.1
0.2
0.3
0.4
0.5
0.6
0.7
Iterations
Spe
ctru
m U
tiliz
atio
n
Spectrum band #1Spectrum band #2Spectrum band #3
(c)
0 100 200 300 400 500 600 700 800 900 10000
0.1
0.2
0.3
0.4
0.5
0.6
Iterations
Spe
ctru
m U
tiliz
atio
n
Spectrum band #1Spectrum band #2Spectrum band #3Spectrum band #4Spectrum band #5Spectrum band #6Spectrum band #7Spectrum band #8
(d)
Figure 4.4: Results of the proposed open-loop local control scheme for spectrum al-location in a CRAHN
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 52
any feedback. Therefore, the local information may be helpful to spectrum sharing if
we employ it in a closed-loop local control scheme with a feedback.
We will use the spectrum information to calculate the consensus feedback in the
closed-loop local control scheme in the following simulations.
4.5.2 Protocol Design
Before doing a further simulation using the consensus feedback, we propose a commu-
nication protocol based on the theory in Section IV. The protocol is expected to show
the applicability of using a consensus feedback to solve the fairness problem for spec-
trum sharing fairness. The protocol is briefly described in Fig. 4.5, where Step (1)
aims to process the proposed consensus-based feedback from neighboring nodes, while
Step (2) performs standard data communications in the RTS/CTS MAC protocol.
For example, after a CR receives the handshaking frames with spectrum information
from neighboring CRs, it will update its local cache with available spectrum band
indexes, and the fairness group it belongs to from the value p. Then, a CR can know
the available spectrum bands from the neighbors feedbacks and then inform the other
CRs in the similar way.
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 53
FOR EACH CR node i at time slot t
IF a spectrum change is detected
do spectrum sensing
do overhear incoming RTS/CTS frames from neighboring CRs
(1) IF the frame piggybacked spectrum information
do parse the information from frames, xi(t)= k, DFi(j) = p
do perform the local control scheme based on the consensus feedback of the
spectrum information in the same FG
ELSE
(2) do normal communication with other CRs
END IF
ELSE
do normal communication with other CRs
END IF
END FOR
Figure 4.5: Pseudo code of consensus-based spectrum allocation protocol
In addition, in order to determine which spectrum bands the neighboring CRs
are using, we assume that a CR node can acquire this information by overhearing
the neighboring CRs communications. A feasible and economic way of overhearing
that information is by encapsulating a data field containing that information and
piggybacking it in a frame sent by a neighboring CR. For example, the consensus
feedback is derived from the spectrum information piggybacked in protocol-specific
frames or packets, such as request-to-send (RTS) or clear-to-send (CTS) frames in an
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 54
IEEE 802.11-based MAC protocol. The slotted time characteristic in the 802.11-like
MAC protocol can also meet the requirements of the proposed protocol. Therefore,
the proposed protocol can be readily integrated in the IEEE 802.11 based CRAHN.
More importantly, the proposed consensus-based protocol will not result in extra
communication efforts or cause delays affecting throughput.
Now we analyze the complexity of the proposed protocol. We denote by M the
number of CRs, and denote by d the average degree of a CR. The spectrum sensing
takes s1 time units; Step (1) and Step (2) take s2 and s3 time units, respectively.
Step (1) will repeat at maximum dM times, so the average time spent on each CR
is dM(cs2 + (1 − c)s3) + s1, where c is a constant denoting the fraction of times
that the protocol will go to Step (1). As CRs in different FGs can individually
perform the protocol, and in each group we have approximately MFG
nodes, the total
number of times is therefore MFG
(dM(s2 + s3) + s1). Therefore, we can obtain the time
complexity as O((
MFG
)2)
, and we can see that more FGs result in less complexity.
Then we analyze the power consumption of the propose protocol based on RT-
S/CTS handshaking procedure. We take the typical value of the RTS frame length
and CTS frame length as 20 bytes and 14 bytes, respectively, and we consider
the power consumption model for 802.11 transmissions with 2Mbps speed in [85].
The power consumption of sending an RTS frame and receiving a CTS, EA, is
1.9 × 20 + 454 + 0.5 × 14 + 356 = 855µW ; similarly, the power consumption of
receiving an RTS and sending a CTS frame, EB, is 846.6µW ; the power consumption
of only receiving an RTS, EC , is 0.5 × 20 + 356 = 366µW ; and the power of only
receiving a CTS, ED, is 0.5×14+356 = 363µW . With this profile, if we have one fair-
ness group (FG=1), considering the 4-way RTS and CTS handshaking procedure, the
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 55
energy consumption of the protocol, E, has the form as E = M(EA+EB+d·EC+d·ED
2d·c
),
where 2d · c is the total number of the surrounding CRs of the two CRs who involve
in the RTS/CTS procedure, and c is the ratio parameter (≤ 1) because the two CRs
may share some neighbors.
4.5.3 Computer Simulation Results
In this section, we are going to show the results based on the proposed consensus-based
communication protocol, implemented by using the simulator NetLogo 4.1 (available
at http://ccl.northwestern.edu/netlogo). We will compare the proposed protocol with
a classical scheme on CRs, called device centric Rule-A [9], where a so-called prop-
erty line measure calculated from the available spectrum bands of neighboring CRs
is used for spectrum sharing. The reason we make comparison with Rule-A is that
Rule-A is the most similar scheme to our proposed protocol with basic local informa-
tion (i.e., connectivity and spectrum availability of neighboring CRs) without extra
communication efforts, while some other schemes like the local bargaining scheme or
graph coloring scheme are centralized and require extra information through extra
communication efforts. Moreover, the max-min fairness based schemes, which have
a different spectrum sharing objective from the proposed Definition 2, will not be
considered in the thesis.
Suppose the number of spectrum bands at a CR at the beginning is randomly
allocated. Each CR performs the proposed consensus-based protocol to ensure the
number of spectrum bands is decided by the consensus feedback from immediate
neighbors. The consensus-based communication protocol will be executed once in
an iteration; and therefore a successful run needs several iterations. Considering
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 56
PU activities, the spectrum band availability varies at the beginning of each run.
Moreover, we keep the total number of available spectrum bands in the network as
1900 for the following simulations.
Next, we describe the simulation settings for this computer simulation. In Fig.
4.6, we can see a dense CRAHN with 350 CR nodes (i.e., M = 350) and each link
has a negligible data transmission delay. The darkness of the node color indicates a
higher number of available spectrum bands. The darker the node color, the more the
number of available spectrums for CR nodes.
4.5.4 Convergence Performance And Feedback Quality
We compare the convergence performance using the metric of unallocated spectrum
bands after running the proposed consensus-based protocol and device centric Rule-A.
The results are shown in Fig. 4.7 and Fig. 4.8.
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 57
Figure 4.6: A randomly distributed CRAHN with 350 CRs and initially allocatedspectrum bands
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60
5
10
15
20
25
30
Una
lloca
ted
Spe
ctru
m B
ands
(%
)
Consensus-based protocolDevice centric Rule-ADevice centric Rule-A (P)
+ +
+ +
+ +
Figure 4.7: Convergence performance of the proposed consensus-based protocol,Rule-A, and Rule-A (P)
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 58
5 10 15 20 25 300
5
10
15
20
25
30
Iterations
Una
lloca
ted
spec
trum
ban
ds (
%)
Consensus-based protocolDevice centric Rule-A
Figure 4.8: Convergence performance of the consensus-based protocol and Rule-A inmultiple iterations
The convergence performance of Rule-A and the proposed consensus-based pro-
tocol is shown in Fig. 4.7, where we can see that the proposed consensus protocol
converges very quickly, whereas Rule-A and Rule-A (P) has stable convergence per-
formance in one iteration. Rule-A (P) in Fig. 4.7 is the improved version of Rule-A,
where we increase the accuracy of the poverty line as the feedback; it has better
performance than the original Rule-A. At the end of the iteration, all the CRs are
allocated with spectrum bands. The reason that the consensus protocol is better
is the consensus spectrum availability information is accurate during the spectrum
sharing process, while the device centric Rule-A and Rule-A (P) use the feedback
based on poverty line, which does not accurately estimate the spectrum availability
of CR nodes.
In Fig. 4.8 we can see how the consensus-based protocol converges over multiple
iterations, where at the end of each iteration (i.e., each run of the protocol) all the
nodes can be successfully assigned with desired spectrum bands. We use a randomly
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 59
i+1
i
i-1
i-2
1
L(1)
(a)
i+1
i
i-1
i-2
1
L(1)
L(2)
(b)
Figure 4.9: An example of the ZigZag network. In (a), there is only one shadedregion of PU activity L, while in (b), there are two shaded regions of PUactivities, denoted by L(1) and L(2), respectively. We will show that thefeedback adopted in Rule-A is overestimated in both cases.
generated topology for the CRAHN in each iteration epoch, during which the con-
sensus protocol will converge as expected, i.e., it can make all the spectrum bands
be shared among all the CRs. Moreover, the convergence time is quite stable even
if we change the network topology before each iteration. In addition, the spectrum
information mentioned in Step (1) of Fig. 4.5 in this simulation is the spectrum
bands.
The proposed scheme outperforms Rule-A because the inaccurate so-called poverty
line is used as a feedback in Rule-A. This inaccurate feedback is considered as a low-
quality feedback in the view of local control framework. We give an example to show
why the poverty line feedback is not sufficient to provide accurate feedback. In the
network shown in Fig. 4.9, where each CR node (except for the start node i+ 1 and
end node 1) has a degree of two.
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 60
Ω(i+ 1) = L(i+ 1)− Ω(i)
Ω(i) = L(i)− Ω(i+ 1)− Ω(i− 1)
Ω(i− 1) = L(i− 1)− Ω(i)− Ω(i− 2)
...
Ω(2) = L(2)− Ω(3)− Ω(1)
Ω(1) = L(1)− Ω(2) (4.11)
where Ω(i) is the number of spectrum bands chosen by a CR node i, and L(i) is the
number of available spectrum bands left by the PU activities.
We can further derive ((4.11)) as
L =3∑i+1
j=1 Ω(j)− Ω(1)− Ω(i+ 1)
i+ 1(4.12)
The value of L fluctuates with Ω if Ω(i + 1) = Ω(i), i ∈ Z+. From the results
shown in Fig. 4.10, we can see that the value of L overestimates the number of
maximum spectrum bands no matter what the value of M is. In other words, the
estimation using the poverty line is not accurate, and it gives low quality feedback
for the spectrum sharing problem.
4.5.5 Fairness Performance in Various Network Sizes
In order to see the fairness performance in different network sizes, we plot Fig. 4.11,
where the fairness measure is calculated by (2). From Fig. 4.11, we can see that the
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 61
0 20 40 60 80 1000
20
40
60
80
100
120
140
160
Max. number of spectrum bands
Val
ue
of
L
M=40
M=100M=1000
Figure 4.10: The value of L versus the maximum number of spectrum bands with thedifferent number of CR nodes M
fairness measure of Rule-A is larger than the fairness measure of proposed consensus-
based protocol when network size varies, which means the proposed consensus pro-
tocol has better fairness performance than Rule-A. Furthermore, we can see how the
spectrum sharing goal is achieved by these two algorithms, where we count the num-
ber of CRs with distributed spectrum bands in Fig. 4.11. Fig. 4.11(a)-(d) show
the proposed consensus-based protocol can fairly distribute and meet the spectrum
sharing goal better than Rule-A.
Now we are going to discuss the fairness group in the spectrum sharing process.
First, we show the intermediate results of using the consensus protocol for spectrum
allocation in Fig. 4.12, where the nodes pointed by arrows indicate different leading
nodes in FGs, and, in the initial stage, only the leading nodes have been allocated
with spectrum bands. From Fig. 4.12(a), we can see the CRs running the consensus
protocol can adjust the spectrum availability based on a leading node, which gives
response to the changing spectrum bands and thus causes the spectrum reallocation
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 62
0 2 4 6 8 10 12 14 16 18 200
20
40
60
80
100
Spectrum band index per CR
Dis
trib
utio
n of
the
num
ber
of C
Rs
(%)
Device centric Rule-A (F=6.33)
Consensus-based protocol (F=0.00)
(a)
1 2 3 4 5 6 7 8 9 10 11 12 130
20
40
60
80
100
Spectrum band index per CR
Dis
trib
utio
n of
the
num
ber
of C
Rs
(%)
Device centric Rule-A (F=4.05)
Consensus-based protocol (F=0.35)
(b)
1 2 3 4 5 6 7 8 9 100
20
40
60
80
100
Spectrum band index per CR
Dis
trib
utio
n of
the
num
ber
of C
Rs
(%)
Device centric Rule-A (F=3.27)
Consensus-based protocol (F=0.50)
(c)
1 2 3 4 5 60
20
40
60
80
100
Spectrum band index per CR
Dis
trib
utio
n of
the
num
ber
of C
Rs
(%)
Device centric Rule-A (F=1.44)
Consensus-based protocol (F=0.57)
(d)
Figure 4.11: Fairness performance versus different network sizes when (a) M=100,(b) M=150, (c) M=200, and (d) M=350
to neighboring CRs. The neighboring CRs will run the proposed consensus-based
protocol to spontaneously change their spectrum bands. In other words, the leading
node can share the spectrum bands to the rest of CRs in this case. Similarly, in
Fig. 4.12(b) and (c), the leading nodes can share the spectrum bands to the other
CRs. Therefore, we can see that the nodes following the spectrum information of the
leading node belong to the same FG. Furthermore, if the leading nodes are considered
as cluster heads reflecting the accurate changing radio environment, all the CRs in a
cluster can instantly be informed of the spectrum change accordingly. If we consider
the extreme case that the number of FGs equals to the number of CRs, we can actually
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 63
(a) (b)
(c)
Figure 4.12: Intermediate spectrum sharing results in CRAHN when (a) FG=1, (b)FG=2, and (c) FG=3
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 64
convert this case to the CRAHN similar to Fig. 4.6.
5 10 15 20 25 30 350
20
40
60
80
100
Iterations
Una
lloca
ted
spec
trum
ban
ds (
%)
FG=1FG=2FG=3
Figure 4.13: Convergence performance with different number of FGs
In order to see the convergence performance of the proposed consensus-based
protocol versus different FGs, we compare the convergence performance in three net-
works with one FG, two FGs, and three FGs, respectively. The experimental results
are shown in Fig. 4.13, where all the nodes can be shared with spectrum bands at
the end of each run. Moreover, we can see that the convergence time per iteration
when FG=1 is in general longer than the convergence time when FG=2 or FG=3.
This makes sense because the more FGs in a network, the fewer nodes in each FG,
and therefore the quicker decision can be made by a consensus protocol. This phe-
nomenon can also be explained by the aforementioned complexity expression. If we
experiment with a larger number of FGs, similar results can be obtained.
Additionally, as we have evaluate the fairness performance when FG=1 (as shown
in Fig. 4.11), here we evaluate the fairness performance when FG=2 and FG=3 in
Fig. 4.14. In Fig. 4.14(a), we evenly divide the network into two fairness group with
two separate spectrum sharing goals, where one group wants to get three spectrum
4.5. PROTOCOL DESIGN AND EXPERIMENTAL RESULTS 65
1 2 3 4 5 60
10
20
30
40
50
Spectrum band index per CR
Dis
trib
utio
n of
the
num
ber
of C
Rs
(%)
Device centric Rule-A (FG1
=0.46, FG2
=2.03)
Consensus-based protocol (FG1
=0, FG2
=0.07)
(a)
1 2 3 4 5 60
5
10
15
20
25
30
35
Spectrum band index per CR
Dis
trib
utio
n of
the
num
ber
of C
Rs
(%)
Device centric Rule-A (FG1
=0.34, FG2
=0.56, FG3
=1.57)
Consensus-based protocol (FG1
=0, FG2
=0, FG3
=0.16)
(b)
Figure 4.14: Fairness performance in a network when (a) FG=2 (b) FG=3
4.6. CONCLUSIVE REMARKS 66
bands (m=3) and the other group wants to get six spectrum bands (m=6). From
the results shown in Fig. 4.14(a), we can see that after running the two schemes,
the proposed consensus-based protocol can fairly distribute the spectrum bands and
meet the desired spectrum goal. Similarly, in Fig. 4.14(b), we evenly divide the
network into three fairness groups and the spectrum goals are m=2, m=4, and m=6,
respectively. From Fig. 4.14(b), the proposed consensus-based protocol can meet the
spectrum sharing goal while obtaining much better fairness performance than Rule-A.
In conclusion, the proposed consensus-based protocol can meet the spectrum sharing
goals in different FGs compared to Rule-A.
4.6 Conclusive Remarks
In this chapter, we have explored the effectiveness of using a consensus-based proto-
col to solve the fairness problem in spectrum sharing. Consensus-based protocols can
provide light-weight and efficient solutions for CRAHNs but the theoretical ground
needs to be investigated for spectrum sharing fairness. In order to analyze the con-
vergence condition using a consensus protocol, we introduce the local control scheme
as we can consider the consensus procedure as the consensus feedback in the system
block diagram of the local control scheme. In this way, the convergence condition is
identical to the system stability of the local control scheme. Furthermore, we have
proven and shown the applicability of using a proposed consensus-based protocol for
spectrum sharing problems in CRAHNs. We show the effectiveness of applying the
proposed consensus-based protocol to a randomly deployed network, by which the
desired convergence and fairness can be achieved. When we show the cases of apply-
ing the concept of FG in the spectrum sharing for CRAHNs, the CR nodes that lead
4.6. CONCLUSIVE REMARKS 67
to spectrum changes are subject to being affected by PU activities, which result in
spectrum availability. In addition, although in a small-scale network, a centralized
spectrum sharing scheme may be more efficient than the proposed consensus-based
protocol, the proposed consensus-based protocol is economic, robust, and efficient for
keeping spectrum sharing fairness in a large-scale network. Besides, the related work
presented in this chapter has been published in [86, 87, 88].
68
Chapter 5
Local Control Driven Medium Access Control
Protocol
In this chapter, we propose a cognitive MAC protocol called CM-MAC which address-
es CR mobility and PER issues in CRAHNs. We adopt the local control concept in
the MAC design considering the local information. Then, we analyze the throughput
and spectrum utilization of CM-MAC protocol assuming that the PU traffic follows
a Poisson process. In the end, we show that the throughput and spectrum utilization
are improved by CM-MAC compared to classical MAC protocols.
5.1 System Model
Before further discussion, we detail the system model used in this section. The
CRAHN is deployed in a plane containing Np PUs and NCR CR nodes. In a certain
time interval, a set of channels, denoted by Ki(t), is available to a CR node i and thus
the total number of channels available to CR node i is |Ki(t)|. The set of channels
on the transmission link between ith CR and (i + 1)th CR is Ki,i+1(t). There are
5.1. SYSTEM MODEL 69
K spectrum bands available in total to CRs and PUs, while the (K + 1)th out-
of-band common control channel (CCC) is used for control information exchange.
When the jth PU is active for transmission, its traffic flow takes one channel Ck, i.e.,
Kj(t) = Ck. For simplicity, we will use the following notation:Kj(t) = k. When
multiple PUs are active, Kj(t) = k|k > 1 and k ≤ K. In this chapter, the PU
traffic flow is assumed to follow a Poisson process with parameter λ [89]. Besides, a
PU that occupies multiple channels is equivalent to multiple PUs that occupy different
channels.
PU CR
ε
SPER
Figure 5.1: A CRAHN with a PER and multiple CRs
We consider a CRAHN with PER regions as shown in Fig. 5.1. A PER area
operating on channel k is denoted by SPER(k). SPER(k) (i.e., the shaded area shown in
Fig. 5.1) has a radius of R0, and the interference region (i.e., the area circled by dotted
line in Fig. 5.1) has a radius ofR, whereR0 < R. In the SPER(k), CR communications
will not only severely affect the PU, but also cause interference to CRs; while within
the interference region, a CR has less effect on the PU communications.
In [11], the combination of two models (a cooperation model and a coexistence
5.2. PRIMARY EXCLUSIVE REGIONS 70
model) with two types of spectrum-sharing arrangements (i.e., sharing among equal-
s and primary-secondary sharing) is introduced. In this chapter, we will use the
model with primary-secondary sharing arrangement and coexistence-based model for
CRAHNs. The coexistence-based model means that devices try to avoid interference
without explicit signaling [11]; and the primary-secondary sharing arrangement re-
sults in the primary system having exclusive rights to access the spectrum through
licensing.
5.2 Primary Exclusive Regions
A MAC protocol needs to decide the available spectrum bands for current and future
transmissions. These spectrum bands will facilitate the upper-layer protocol (e.g.,
routing protocol) to obtain an optimized path for packet transmissions. Moreover, in
order to keep a desirable throughput, a MAC protocol needs to perform local obser-
vation without inducing extra communication efforts. As such, the communication
procedures on top of CSMA/CA MAC protocol are not favored by CRAHNs.
Traditionally, the MAC sub-layer is at the link layer, where the link layer is in
charge of the communication between adjacent nodes. Therefore, if we follow the
layered perspective for the CRAHN protocol stack, the challenge becomes maintaining
the communications with adjacent nodes while keeping the spectrum resources shared
among nodes.
To see why a CRAHN MAC is important, we consider a typical packet transmis-
sion in CRAHNs shown in Fig. 5.2, where a source S tries to transmit data packets
to destination D through the path from CR node 1 to CR node 4. Suppose that
in the previous time slots the data transmission occurs on channel 3. However, PU
5.2. PRIMARY EXCLUSIVE REGIONS 71
Figure 5.2: An example of the necessity of a CRAHN MAC protocol in a CRAHN.The available spectrum bands for the nodes covered by a PU are shown inbrackets. The links are broken (shown in dashed arrows) when the datatransmission from S to D is operated on channel 3.
2 is now active and channel 3 is taken and the links from node 3 to node 4 and
node 4 to node D are broken. Therefore, the rest of nodes (i.e., S and node 1 to 3)
need to be informed of the spectrum change of nodes 4 and D. Besides, perform-
ing updates of spectrum change is efficient before each transmission, as a result of
the opportunistic and unpredictable PU activity, which can take a spectrum band.
Furthermore, the CRAHN MAC protocol needs to consider PER regions, which can
affect the throughput performance.
To see how PER region can affect CR and PU throughput, we consider the network
of Fig. 5.1, where CRs are distributed out of PER of a PU when CRs and PUs are
operating on the same channel k.
In the case of one PU transmitter and multiple CRs covered by the PU transmit
5.2. PRIMARY EXCLUSIVE REGIONS 72
range, Vu et al. [50] derive the worst-case interference power that the PU transmitter
experienced from all CR nodes (where a PU transmitter communicates with another
PU receiver at a distance R0) as:
E[I0]α=4 = θπP
[R2
(R2 −R20)
2 +(R + ε)2
ε2(2R0 + ε)2
](5.1)
where αis the path loss exponent, R0 is the radius of SPER(k) and R is the coverage
radius of the PU; θ is the density of the CR nodes; ε is the guard band radius, which
ensures the interference caused by CRs will not affect the PU communications.
As a CSMA/CA MAC protocol is based on time frames, we consider a time interval
[0, T ]. If the PU transmitter/receiver pair is active for v time units, while CR nodes
are active for the entire time span, CRs can interfere with PU communications in the
v time units. Based on the data rate equation in [50], and, in this case, the data rate
of PU, DPU , and data rate of CR, DCR, can be expressed as:
DPU ≤ν
Tlog
(1 +
PPUR2
0(N0 + E [I0])
)(5.2)
DCR ≤ν
Tlog
(1 +
PCR
(R0 + ε)2(N0 + PPU)
)+ (1− ν
T)log(1 +
PCR
(R0 + ε)2N0
) (5.3)
where N0 is the noise power spectral density, and PPU and PCR are the transmit
power of a PU and a CR, respectively.
In reality, PU activities may not be continuous and v is not a constant, but
a random variable. If we assume the PU activity follows a Poisson process with
5.2. PRIMARY EXCLUSIVE REGIONS 73
parameter λ, the mean of the probability of inter-arrival time is 1/λ. In this sense,
on average, CR nodes can be considered to have v = T (1− x/λ) time units without
interfering with PUs during [0, T ], where x is the number of PU flows. Additionally,
we can adjust the value of v to reflect the spectrum sharing technique in (5.2) and
(5.3). For example, if we let v be T in (5.3), then (5.2) and (5.3) can represent a
spectrum sharing model where PUs and CRs can access the spectrum resources at
the same time and avoid interference without explicit signaling.
Based on (5.2) and (5.3), Fig. 5.3 shows two cases in which adjusting the CR
transmit power PCR or the radius of PER can change the data rates for both CRs
and PUs, when CR nodes are distributed with a density θ. These two cases exemplify
the effect of PER region and throughput. Furthermore, we can see that in order to get
an optimal DPU we should choose a proper R/R0, which is 1.33 in the example shown
in Fig. 5.3(a). In Fig. 5.3(a), as PCR increases, DCR increases more quickly than the
declining DPU , which is the reason that throughput always rises when PCR increases.
In Fig. 5.3(b), DCR increases more slowly than the declining DPU . In fact, in order
to choose a proper value of PCR, we have to consider a feasible range of PCR. We
can select a reasonable value of PCR by considering the maximum transmit power for
PPU and PCR regulated in current wireless network standards, such as Global System
for Mobile Communications (GSM) (where PPU is about 1˜2W), IEEE 802.22 (where
PPU is less than 4W [90]), IEEE 802.11 (where PCR is less than 100mW), IEEE
802.15.4 (where PCR is less than 100mW).
With the aforementioned discussion, we can see that the PER region has significant
impact on the throughput of both PUs and CRs. Furthermore, given a certain data
rate C0 for a PU, and a certain CR output power, PCR, based on a standard regulation,
5.2. PRIMARY EXCLUSIVE REGIONS 74
(a)
(b)
Figure 5.3: The normalized throughput of a PU and CRs versus PCR and R/R0,when (a) v = 0.3 and (b) v = 0.7
5.3. PROPOSED CM-MAC PROTOCOL 75
we can choose an optimal value of R/R0.
5.3 Proposed CM-MAC Protocol
5.3.1 Overview
In order to meet the requirements of a CRAHN MAC protocol, we have to improve the
traditional CSMA/CA based MAC protocol shown in Fig. 5.4(a). In Fig. 5.4(b), we
use an out-of-band common control channel (CCC) in order to exchange the control
packets such as RTS packets, CTS packets, and acknowledgement (ACK) packets.
After the MAC protocol data unit (MPDU) transmission, a node will wait for a short
inter-frame space (SIFS) period and then transmit the ACK packet. Before sending
an RTS packet, the spectrum sensing process will be initiated by a CR to make sure
there is a data transmission link on a certain channel k.
ACKCW MPDU
RT
S
CT
S
SIF
S
SIF
S
SIF
S
(a)
CWCommon Control Channel
MPDU
MPDU
Channel 1
Channel 2
Channel k
… …
TS
S
MPDU
RS
S
RT
S
CT
S
SIF
S
SIF
S
ACK
ACK
ACK
SIF
S
AC
TS
SIF
S
(b)
CWCommon Control Channel
MPDU
MPDU
Channel 1
Channel 2
Channel k
… …
TS
S
MPDU
RS
S
RT
S
CT
S
SIF
S
SIF
S
ACK
ACK
ACK
SIF
S
AC
TS
SIF
S
RSS: Receiver Spectrum Sensing CW: Contention WindowTSS: Transmitter Spectrum Sensing RTS: Request to SendSIFS: Short Inter Frame Space CTS: Clear to SendMPDU: MAC Protocol Data Unit ACK: AcknowledgmentACTS: Acknowledgement CTS
Figure 5.4: Frame structures of (a) the traditional CSMA/CA-based MAC protocoland (b) the proposed CM-MAC protocol
There are two advantages of using a CCC in CRAHNs. First, possible collisions
5.3. PROPOSED CM-MAC PROTOCOL 76
of control packets and data packets can be avoided. Second, assigning a CCC can
alleviate the communication efforts required to consult other CRs in a new spectrum
band for exchanging control messages when spectrum availability changes.
The transmitter spectrum sensing (TSS)/receiver spectrum sensing (RSS) proce-
dure is employed, which is dedicated to ensuring spectrum availability of links for
upcoming packet transmissions. Checking the spectrum availability before transmis-
sion on links can avoid transmission failures. The TSS is done by a CR transmitter
and the transmitter will combine the spectrum information into the immediate RTS
packet field meanwhile RSS is completed by a receiver and the spectrum information
into the CTS packet. After the broadcasting stage of RTS/CTS packets with piggy-
backed spectrum information, the neighboring CRs of the transmitter and receiver
have the local knowledge of the one-hop spectrum availability. We should note that
as we integrate the spectrum information into the RTS/CTS routine, the update fre-
quency of spectrum information on neighboring CRs is dependent on the RTS/CTS
request frequency (i.e., the data transmission load). It is expected that in the satu-
rated mode of a CRAHN (i.e., a CR always has data payload to send), the spectrum
information can be frequently updated. For CRAHNs with less data load, the spec-
trum information may be updated less frequently, subject to the possible failures of
data transmissions caused by inaccurate spectrum information on the links.
Another solution to the problem of notifying CRs of the spectrum availability is
to use a periodic updating mechanism that maintains broadcast packets containing
the spectrum information. This solution may cause collisions with the routine con-
trol packets and may result in significant delays; therefore, we will not consider this
solution in the study.
5.3. PROPOSED CM-MAC PROTOCOL 77
5.3.2 Channel Aggregation Technique
The separation of CCC and data channel cannot significantly improve the through-
put. This is because the data transmission channel cannot be utilized at all before a
successful RTS/CTS process.
A feasible way to further improve the throughput is to decrease the transmission
time of a data packet. We will employ the channel aggregation, in a similar manner
to the method mentioned in [37, 40]. An example of channel aggregation is shown in
Fig. 5.5(a), where compared with Fig. 5.4, the transmission time for a data payload
in a MPDU is reduced as the MPDU is split into three segments and transmitted on
three channels simultaneously. In each segment, we will add a sequence number to
each split data payload.
We should note that the channels used for this technique are dependent on the
available channels assigned by the spectrum sharing scheme. In Fig. 5.5(b), we can
see that the actual channels for transmission are obtained after a negotiation stage,
which can be a RSS/TSS procedure or the SPEC CHANGE notification procedure
from MSA algorithm, which we will discuss later. Because the channel aggregation is
used, the sender is expected to receive three ACKs for the three split data payloads.
SIF
SMPDU#1-1
ACK
SIF
SMPDU#1-2
ACK
SIF
SMPDU#2-1
ACK
SIF
SMPDU#2-2
ACK
Channel k
Channel k+1
SIF
SMPDU#1-3
ACK S
IFSMPDU
#2-3
ACK Channel k+2
(a)
ith CR (i+1)th CR
ACK(1)
Transmission Stage:Transmit data on the
channels
Negotiation Stage: Get agreement on the
transmission channels
ACK(2)
ACK(3)
TSS/RSS
SPEC_CHANGE
(b)
Figure 5.5: An example of channel aggregation in the view of (a) the MAC frame and(b) the sequence diagram
5.3. PROPOSED CM-MAC PROTOCOL 78
5.3.3 Spectrum Access and Sharing
In the proposed CM-MAC, a simplified spectrum access scheme is considered where a
CR will access the minimum available channels that can meet a certain rate DCR on
the link between ith CR and (i+ 1)th CR. Therefore, the set of channels accessed by
the CR on this link is Ki,i+1(t) = Ki(t)∪Ki+1(t) and RCR =|Ki,i+1(t)|∑
k=1
r(k), where r(k)
is the rate supported on channel k. Besides, if we consider the case that a CR uses
all available channels to meet the rate DCR, the link will have |Ki,i+1(t)| available
channels for data transmissions.
For spectrum sharing, instead of using the central coordination in IEEE 802.22
standard [91], we will employ the distributed spectrum information exchange. An
important goal in the proposed CM-MAC is to ensure a successful next one-hop trans-
mission. Therefore, it is necessary to show the convergence of spectrum information
exchange of the TSS/RSS procedure.
1
2
4
5
3
67RTS
(a)
1
2
4
5
3
67CTS
(b)
1
2
4
5
3
67ACTS
(c)
Figure 5.6: An example of intermediate results of the spectrum sharing procedureafter (a) a RTS transmission, (b) a CTS transmission, and (c) an ACTStransmission. The dotted lines are transmission ranges of CR node 1 andCR node 6.
For example, Fig. 5.6 shows that after TSS procedure, CR nodes 2, 4, and 6 have
the updated spectrum information of CR node 1; after RSS procedure, CR nodes 1,
3, 5, 7 can get spectrum information updates from node 6. Although CR nodes 2
5.3. PROPOSED CM-MAC PROTOCOL 79
and 4 cannot get the updated spectrum information of CR node 6, we can see it is
not a problem as CR nodes 2 and 4 will not be on the next transmission link. The
candidate CR nodes for the next transmission are CR nodes 1, 3, 5, and 7. As such,
we can see that the TSS/RSS procedure integrated in RTS/CTS/ACTS handshaking
is sufficient enough and no significant communication overhead will occur. All neigh-
boring CRs can receive the spectrum information which assures the successful next
one-hop transmission.
The time for spectrum sensing is not negligible in the proposed CM-MAC protocol
because a spectrum sensing can take around 6ms [92] in a 100ms frame duration,
which is comparable to a typical short inter-frame space (SIFS) duration. Although
it is better to reduce the number of times running spectrum sensing when PUs are
inactive, the TSS/RSS procedure with RTS/CTS is the most general way as PU
activity may not be known in advance.
5.3.4 Mobility Support Algorithm
As CRs in a CRAHN are able to move and cause significant interference to PU traffic,
we have to consider the case that CRs may move in a PER. The negative effects when
a CR moves into a PER include: (1) PU communications will experience interference
and (2) CRs communications will experience interference. Both of these situations
result from the case that PUs are not aware of the spectrum band the CRs are using.
As such, we need an algorithm to deal with these problems.
A challenge here is how a CR can know its vicinity to the PER region with low
cost. We propose to use the radio signal strength indicator (RSSI) at the PHY layer
to solve this problem. As the radio signal strength (RSS) received by a ith CR,
5.3. PROPOSED CM-MAC PROTOCOL 80
RSS(i, j), is inversely proportional to the distance (d) between the ith CR and the
jth PU , the RSS value can readily indicate the vicinity to a PU if RSS(i, j) is close to a
constant threshold RSSthres. If we assume all the PUs have the same transmit power,
the RSSthres value is sufficient at the network level. If we assume the (i + 1)th CR
node is communicating with the ith CR node, we can describe the proposed mobility
support algorithm (MSA) as follows:
In Fig. 5.7, State(i) records the current CM-MAC state on a CR. If the ith CR
is in a PER region then State(i) = MAC PER; if the CR is out of a PER then
State(i) = MAC OPER; if the CR is in a CTS/ACTS procedure with a transmit-
ter, then State(i) = MAC CTS/ACTS; if a CR is transmitting data packets then
State(i) = MAC TRANSMIT ; State(i) = MAC IN TRANSMIT means some
packet segments have been transmitted through the channel aggregation technique.
func SS(j) is the spectrum sensing routine to sense which channel is occupied by the
jth PU. The STOP packet contains short control information on the current channel,
while the SPEC CHANGE packet contains the available channels for transmission.
When the (i+ 1)th CR receives SPEC CHANGE packet, it will then use the avail-
able channels to send the data packets. If a CR is in the process of sending CTS/ACTS
packets, then an updated CTS/ACTS will be resent to the transmitter/receiver with
the updated channel information in the packets.
From the MSA algorithm, we can see that once the CR is in the PER region, the
data transmission should immediately stop and may cause retransmissions of packets.
When the state is MAC IN TANSMIT , meaning the packets or packet segments
have been in the process of transmission, the CR in a PER region should notify the
transmitter immediately in order to resume the transmission of remaining packets or
5.3. PROPOSED CM-MAC PROTOCOL 81
Input: RSSI(i, j), State(i), Ki,i+1(t), Kj(t)FOR EACH CRIF RSSI(i, j) > RSSIthres AND State(i) == MAC OPERKj(t)← func SS(j)
IF Kj(t) ∈ Ki,i+1(t)IF State(i) == MAC TRANSMITIF |Ki,i+1(t)| == 1
send a STOP frame over CCC to the (i+ 1)th node on channelthe (i+ 1)th node will stop the data transmission
ELSE IF |Ki,i+1(t)| > 1Ki,i+1(t)← k|k ∈ Ki,i+1(t), k /∈ Kj(t)send the SPEC CHANGE frame with Ki,i+1(t) to the (i+ 1)th node
END IFEND IFIF State(i) == MAC IN TRANSMIT
send a STOP frame over CCC to the (i+ 1)th nodethe (i+ 1)th node will record the data frames/segments already transmittedthe (i+ 1)th node will reinitiate the transmission for the remaining frames
END IFIF State(i) == MAC CTS/ACTS
Ki,i+1(t)← k|k ∈ Ki,i+1(t), k /∈ Kj(t)send a CTS or ACTS frame piggybacking Ki,i+1(t) to the transmitter over
CCCEND IFIF RSSI(i, j) ≤ RSSIthres AND State(i) == MAC PER
State(i)←MAC OPEREND IFEND FOR
Figure 5.7: Description of the mobility support algorithm (MSA)
5.4. THROUGHPUT ANALYSIS 82
segments on the other CR.
5.4 Throughput Analysis
This section provides the throughput analysis of the proposed CM-MAC. The theo-
retical spectrum utilization for the two scenarios will also be discussed. First we will
discuss the scenario of one pair of transmitter and receiver CRs. Then we will analyze
the link throughput.
PU CR
Figure 5.8: An example of a CRAHN with PUs and CRs
As the PU topology can affect the performance in terms of throughput and spec-
trum utilization, we assume that the center of each PU network will be at a distance
of at least 2R. An example of this CRAHN is shown in Fig. 5.8.
5.4. THROUGHPUT ANALYSIS 83
5.4.1 Average Time Spent on Mobility
The mobility should be considered in the throughput analysis as it affects the time
spent on spectrum sensing and MSA algorithm. We let the coverage of a CR be SCR,
where ‖SPER‖ > ‖SCR‖, and we assume all the CRs have identical coverage disk in
the CRAHN. CR nodes are deployed in the disk area SPER (with radius R), following
a homogeneous Poisson process with density θ per unit area.
When a CR node moving into the PER, it will run the MSA algorithm. We are
interested in the number of moving nodes in an annulus area with radius [R0−r0, R0+
e+ r0] shown in Fig. 5.8. We can get the average degree [93] between the CRs inside
the PER and the CRs outside the PER at a distance r0, i.e.,
E[Deg] = 2πθ
∫ R0+ε+r0
R0−r0P (Λ(i, i+ 1)|s(i, i+ 1))sds (5.4)
where Λ(i, i+ 1) means the event that ith CR and (i+ 1)th CR has a radio link while
s(i, i+ 1) is the distance between them. From [93], if we assume s(i, i+ 1) = r0
P (Λ(i, i+ 1)|s(i, i+ 1)) =1
2− 1
2erf
(10α√
2ϑlog
r0
10βth
α10dB
)(5.5)
where βth is the threshold value of the received power to maintain the radio link; ϑ
is the shadow fading variance; a is the path loss exponent.
When there is mobility, there is still connectivity to a CR node outside the PER,
and we know that P (Deg > 0) = 1 − e−E[Deg]. By algebraically manipulating (5.4)
and (5.5), we can determine the value of r0.
Next, we assume all CRs are moving and we consider the case that at time t, a
CR in the area with radius [R0− r0, R0 + e+ r0] just moved in the PER, the average
5.4. THROUGHPUT ANALYSIS 84
time spent regarding MSA is
E[TMSA] = P0 (TSS + (P11T STOP + P12TS CHANGE)P1 + TSTOPP2 + TCTSP3) (5.6)
where P1 = P (state = MAC TRANSMIT ), P2 = P (state = MAC IN TRANSMIT ),
P3 = P (state = MAC CTS/ACTS). P11 is the probability of sending a STOP pack-
et
P12 is the probability of sending a S CHANGE packet. The average time spent
on one shot of spectrum sensing is TSS; TSTOP and TS CHAGE are the time spent on
transmitting the STOP and SPEC CHANGE packets, respectively. P0 is the prob-
ability that the ith CR just moves in a PER region, we can obtain P0 = P (state(t) =
MAC PER|state(t− 1) = MAC OPER). As it is difficult to give an exact value of
P1, P2, or P3 due to the fact that they are application-specific, we use an estimated
value for each of them. For P1, we can take TdataTdata+TCTS+ω
as its value, where ω is the
delay and empty slot time to consider.
For P3, we can take TCTSTdata+TCTS+ω
as its value. P2 is difficult to know because when
there is a bulk of data to send, P2 is large; when there is a small bulk of data to send,
P2 is small. However, we can know the maximum probability to P2, i.e., ωTdata+TCTS+ω
.
Furthermore, as P0 is usually dependent on the mobility pattern of the CRs, if we
assume the CRs are moving following 1-dimensional (i.e., 1-D) correlated random
walks with bounds [0, 2R] with equal probability moving in two opposite directions,
the steady-state probability at any location is 1/4R [94] if the speed is one-unit length
per time, which can be used as the estimate value for P0.
5.4. THROUGHPUT ANALYSIS 85
5.4.2 Link Throughput Performance
The link throughput performance for a CR is considered, and we use the normalized
throughput defined in [95] as:
η =E[Payload transmitted in a slot time]
E[length of a slot time](5.7)
If a CR has a successful transmission, it should be noted that the spectrum avail-
ability may change because of the PU activity. As such, we let the time spent on
during the TSS procedure and data transmission be Tct, and the time spent during
the RSS procedure and data transmission be Tcr. We can obtain:
Tct = TCTS+RTS + SIFS +D + SIFS + TRSS (5.8)
Tcr = TCTS + SIFS +D (5.9)
where D is the propagation delay.
Moreover, for the PU activity following a Poisson process (N(t), t ≥ 0 with
rate parameter λ) during the time interval [0, Ts]. Thus, we denote by Pre(k) the
probability that an available channel will be taken by a PU activity on data channel
k during Ts. If the number of PU flow in a time frame is larger than zero, the data
channel k will be taken by PUs and in this case we have
Pre(k) = P (N(t+ Ts)−N(t) > 0) = 1− e−λTs (5.10)
Apart from Pre(k), probabilities that affect the length of a time slot include: (a) the
5.4. THROUGHPUT ANALYSIS 86
probability of no CR transmitting 1 − Ptr where Ptr is the probability that there
is at least one transmission in the considered slot time; (b) the probability of a
packet successfully transmitted PtrPs, where Ps is the probability of a transmission
occurring on the channel is successful; (c) the probability of a packet not successfully
transmitted because of a collision Ptr(1−Ps). Based on the aforementioned discussion,
we can determine from (5.7) that
TS
S
RS
S
RT
S
CT
S
SIF
S
D D
Common Control Channel
SIF
S
MPDU Channel kACK
D
DIF
S
AC
TS
SIF
S
SIF
S
D
D: propagation delay
Figure 5.9: Description of a successful data transmission
η =PsPtrE[P ]
(1− P0)(
(1− Ptr)σ + PtrPsTs + Ptr(1− Ps)Tc + Pre(k)Ts1−Pre(k)
)+ P0TMSA
(5.11)
where Ts is the slot time length of a successful transmission; Tc is the time length that
a channel is busy because of a collision; s is the empty slot time; P0 is the probability
of CRs moving into PER regions (P0 < 1); TMSA is the average time length spent
on MSA algorithm when mobility occurs and the data transmission time after MSA
process; and P is the data packet length (i.e., the length of MPDU). Moreover, from
Fig. 5.9, although we have a CCC and the other channel for data transmission, we
5.4. THROUGHPUT ANALYSIS 87
can combine the factors on these two channels together so that
Ts = DIFS + TRTS+CTS+ACTS + 4D + 4SIFS + TRRS
+ TTRS + Tdata + TACK
(5.12)
where TRTS+CTS+ACTS = TRTS +TCTS +TACTS, while Tc is related to the RTS packet
collision on CCC as
Tc = SIFS +D +DIFS (5.13)
At this point, from the assumption that the packets have the same length (i.e.,
E[P ] = P ), and the expressions of functions Ptrand Ps of p, where p is the stationary
probability of a packet transmission by a CR, as well as equations (5.8)-(5.13), we
can get the average throughput result as
η =Pζ
(1− P0)(σ + (Tc − σ)ζ ′ + (Ts − Tc)ζ + CTs1−C ) + P0TMSA
(5.14)
where ζ = np(1− p)n−1, ζ ′ = (1− p)n, C = 1−e−λTse−λTs
, and n is the number of CRs for
transmission. If we suppose the payload in MPDU will be transmitted on the available
channels on the link between the ith CR and (i + 1)th CR, the time spent on each
available channel can be |Ki,i+1(t)| times less at most (when each available channel
has the same bandwidth). However, in order to assemble the split data packets on the
receiver side, we keep the same MPDU header for each available channel. Therefore,
the average time length on a data packet transmission is
T ′data = Tdata
(ϕ+ 1−ϕ
|Ki,i+1(t)|
)(5.15)
5.4. THROUGHPUT ANALYSIS 88
where ϕis the ratio of header length to payload length in MPDU, which is usually
less than 1.
The new throughput will be readily derived if we substitute the Tdatawith T ′data
in (5.12). We can express η as η (n, p, λ, |Ki,i+1(t)| , P0).
5.4.3 Upper Bound of Spectrum Utilization
First we discuss the spectrum utilization of CM-MAC. For the general case that the
spectrum band of the link from the ith CR to the (i + 1)th CR affected by the PU
traffic, we can derive the average spectrum utilization of a CR as
UCR =|Ki,i+1(t)|
K, (5.16)
where |Ki,i+1(t)| is the available channels for data transmissions on a link. Then
we consider the case when a PU operates on Kp channels (Kp < K) in a PER
region. In a time interval [0, T ], the inter-arrival time τ = (τ1, τ2, ..., τq) follows an
exponential distribution with mean 1λ. The inter-arrival time of PU traffic is therefore
P (τ < T ) = 1− e−λτ . If we consider the PU activity factor m = TONTOFF
, i.e., the ratio
of PU traffic activity and PU traffic inactivity, the channels not occupied by PUs are
Kp(1+m)K
. In this sense, we can further derive UCR as:
UCR =Kp
(1 +m)K+ S (5.17)
where 0 ≤ S ≤ K−Kp
K. S = K−Kp
Konly if the rest of channels are fully utilized. When
CR Poisson traffic is considered with parameter λ′, S = (1− e−λ′T )K−Kp
K. Note that
as limλ→∞
11+m
= 0, which means that when PU traffic is heavy a CR has no chance to
5.4. THROUGHPUT ANALYSIS 89
operate on the Kp channels occupied by PU. Moreover, if we want to obtain a more
accurate value of UCR over the entire CRAHN, we need to get the mean value of UCR.
By assuming that the rest of the channels that are not occupied by PUs can be fully
used by a CR, we can get an upper bound of the link throughput.
5.4.4 A Special Case of the Proposed CM-MAC Protocol
If CR’s traffic model also follows a Poisson process N ′(t), t ≥ 0 with parameter
λ′, we can conduct the similar analysis in order to estimate the CR link throughput
in this case. Compared to the aforementioned analysis in the saturated-mode case
(i.e., a CR always has a packet to send), the special case we are discussing now is
the non-saturated mode (i.e., a CR does not always have a packet to transmit). The
introduction of Poisson traffic model will impose two changes to the aforementioned
analytical model. One is the stationary transmission probability p of a packet; the
other is retransmission times of a packet.
We denote by p′ the new stationary transmission probability of a packet. From
[96], by assuming each CR has a packet buffer and the probability of a packet arrival
is q, the non-saturated mode of CRs will finally affect the value of transmission
probability. Moreover, for the Poisson traffic model, q = PN ′(t) = 1 = 1 − e−λ′T .
The value of p′ can be calculated by the collision probability pc and the total number
of stages ρ, as well as q.
We can obtain the retransmission probability on a channel k, P ′re(k), as follows
P ′re(k) = PN(t) > 0|N ′(t) > 0 = 1− e−λTs (5.18)
As such, we can derive the estimated link throughput results when we consider
5.5. NUMERICAL RESULTS 90
Poisson traffic model for both PUs and CRs.
However, if there is no MSA algorithm and TSS/RSS procedure, the retransmis-
sion probability,Pre(k), can be calculated by the channel availability and spectrum
hole sufficiency [37]. If we take the channel aggregation factor as one, we can obtain
[37]:
Pre(k) = 1−(
1− UCR · n(1− UCR+PU)r
)1
m+ 1(5.19)
where r is the dynamic operating range (i.e., the number of channels a PU is operating
on). Therefore, we can substitute the variable C in (5.14) with (5.19). In this sense,
we can compare the proposed CM-MAC protocol with SCA-MAC protocol.
5.5 Numerical Results
This section shows some numerical results based on the aforementioned analysis.
The parameters are shown in Table 5.1. Besides, all the switching intervals from
transmitting to receiving are set to zero. We assume that the number of CRs N , is
identical to n in (5.14), and these CRs are transmitters in a CRAHN and can interfere
with each other. Moreover, the channel aggregation is not considered in SCA-MAC
and CM-MAC. The essential parameters represented in Table 5.1, for example, are
ϕ = 0.03,P = 8584bits, TRTS+CTS+ACTS = 768µs, Tc = 141µs, and TACK = 240µs.
With the parameter values, we can get Ts = 1151.03 + 7938.48|Ki,i+1(t)| . Then, we can
derive (5.14) as
η =8584(
91ζ′
ζ+
257.6P0+50+(1151.03+7938.481
K−KP)C/(1−C)
ζ
)+ (1010.03 + 7938.48
K−KP)
(5.20)
5.5. NUMERICAL RESULTS 91
Table 5.1: Parameters
Parameter ValueMAC data payload 8184bitsMAC header 272bitsPHY header 128bitsRTS payload 160bits + PHY headerCTS payload 112bits + PHY headerACTS payload 112bits + PHY headerSIFS 20µsDIFS 120µsSlot Time 50µsChannel bit rate 1MbpsACK length 112 bits + PHY headerPropagation delay (D) 1µsNo. of spectrum bands (K) 6PHY max transmit power 100mWPHY sensitivity −100dBmRx spectrum sensing time (TRSS) 20µsTx spectrum sensing time (TTSS) 20µsEmpty slot time (σ) 50µsReceiving threshold power (βth) 50dBPath loss exponent (α) 4Dynamic operating range (r) 1000Stationary probability of a CR (p)(saturated mode) 0.02
where Kp = K−E [|Ki,i+1(t)|], i.e., the average number of available channels on a CR.
For the non-saturated mode throughput, note that the variable C and p will change.
Moreover, it is expected that the larger the value of λ, the more frequent the PU
traffic occupies the available spectrum bands. Note that the throughput η is defined
as the probability of successful transmitted frames per frame time. Furthermore, we
will compare CM-MAC protocol with the aforementioned special case of CM-MAC
protocol.
5.5. NUMERICAL RESULTS 92
0 10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Number of CRs
Thr
ough
put
CM-MACCSMA/CA RTS/CTS MACSCA-MAC
=0.001 =0.002 =0.003 =0.004(Kp=1; P0=0.5)
PU Poisson traffic (parameter λ)Saturated mode for CR traffic
(a)
0 20 40 60 80 1000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
=0.002, =0.0001
Number of CRs
Thr
ough
put
=0.002, =0.0015
CM-MACCSMA/CA RTS/CTS MACSCA-MAC
(pc = 0.3; ρ = 3; Kp=1; P0=0.5)
PU Poisson traffic (parameter λ)CR Poisson traffic (parameter λ)
(b)
Figure 5.10: Description of a successful data transmission
5.5. NUMERICAL RESULTS 93
Fig. 5.10(a) shows the throughput performance versus the number of CRs (as-
sumed to be in the saturated mode) when we take the value Kp = 1 for all links.
The CR throughput decreases when the value of λ increases. This is because the
PU traffic with increasing λ has a high possibility of affecting TSS/RSS procedures.
In this case, the PU becomes more active which reduces CR access. Moreover, as
shown in Fig. 5.10(a), with any given value of λ and N , the throughput performance
of CM-MAC outperforms that of SCA-MAC. The reason for this result is that the
delay caused by MSA algorithm and TSS/RSS procedures in CM-MAC is smaller
than that of SCA-MAC. Furthermore, when the PU traffic is heavy, CM-MAC can
successfully reduce the effect of the existence of PER regions. Besides, if we consider
the non-saturated mode for CR traffic (Fig. 5.10(b)), we can see that the CM-MAC
still outperforms CSMA/CA MAC and SCA-MAC protocols.
Fig. 5.11 shows how the CR throughput changes versus N and λ′. We can see
that, when the CR traffic intensity increases, the throughput curves rise, reach a
maximum, and then decline. Moreover, in Fig. 5.11(a) and (b), when N increases
from 10 to 20, the CR throughput increases as well. However, in Fig. 5.11(c), when
N = 50, the throughput sharply increases when λ′ is small and decreases faster than
the throughput curves shown in Fig. 5.11(a) and (b). The reason of this phenomenon
is that having more CRs will increase the traffic which increases the chances of more
packet transmission conflicts. This results in decreased CR throughput.
Fig. 5.12 shows how the CR throughput changes versus N and PU Poisson traffic
parameter, λ. It can be seen that the throughput curves decline with the increasing
intensity of PU traffic. Furthermore, in Fig. 5.12(a) and (b), when N increases
from 10 to 20, the CR throughput increases correspondingly; however, when N = 50,
5.5. NUMERICAL RESULTS 94
0 0.5 1 1.5
x 10-3
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Thr
ough
put
N=10λ=0.0015
(a)
0 0.5 1 1.5
x 10-3
0
0.05
0.1
0.15
0.2
0.25
0.3
Thr
ough
put
N=20λ=0.0015
(b)
0 0.5 1 1.5
x 10-3
0
0.05
0.1
0.15
0.2
0.25
0.3
Thr
ough
put
N=50λ=0.0015
(c)
Figure 5.11: CR link throughput versus N and λ′
5.5. NUMERICAL RESULTS 95
0 0.5 1 1.5
x 10-3
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
Thr
ough
put
N=10λ′=0.0015
(a)
0 0.5 1 1.5
x 10-3
0.05
0.1
0.15
0.2
0.25
0.3
Thr
ough
put
N=20λ′=0.0015
(b)
0 0.5 1 1.5
x 10-3
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
Thr
ough
put
N=50λ′=0.0015
(c)
Figure 5.12: CR link throughput versus N and λ
5.5. NUMERICAL RESULTS 96
the overall throughput is slightly less than the throughput when N = 20. This is
expected because the increasing number of CR nodes results in increasing conflicts in
the packet transmission, which affects the throughput performance.
Fig. 5.13 shows how the throughput performance can be affected by the different
values of Kp (i.e., the number of exclusive channels occupied by PUs). Fig. 5.13(a)
shows the analytical results when CR Poisson traffic is in saturated mode. The results
for Poisson CR traffic (i.e., non-saturated mode) are presented in Fig. 5.13(b) and (c).
We can see that when we consider different intensities of CR Poisson traffic (reflected
by λ′), the throughput performance will change accordingly. Furthermore, we can
see from Fig. 5.13(a)-(c) that when the number of available spectrum bands to CRs
increases (i.e., Kp decreases), the throughput performance improves correspondingly.
These results meet our expectations because with more channels available to CRs,
the overall throughput will increase.
Fig. 5.14 displays how the CR mobility factor, P0, affects the CM-MAC through-
put performance. Fig. 5.14(a) mainly shows the MSA algorithm when the CR traffic
is in the saturated mode; Fig. 5.14(b) and (c) show the throughput performance re-
sults for CR Poisson traffic. It is clear that P0 only slightly decreases the throughput
performance. Therefore, we can conclude the proposed CM-MAC is robust in the CR
mobility case.
The simulation results are shown in Fig. 5.15, where a CRAHN is randomly de-
ployed in a square area and the average speed of CR nodes is about 5m/s. The other
parameters are used as listed in Table 5.1. Fig. 5.15(a) shows that our proposed
protocol has a slightly longer average response time than the CSMA/CA RTS/CTS
5.5. NUMERICAL RESULTS 97
0 10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Number of CRs
Thr
ough
put
KP=0KP=1KP=2KP=3KP=4KP=5
PU Poisson traffic: λ=0.002Mobility probability: P0=0.5
(a)
0 20 40 60 80 1000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Number of CRs
Th
rou
ghpu
t KP=0
KP=1KP=2KP=3KP=4KP=5
PU Poisson traffic: λ=0.002CR Poisson traffic: λ'= 0.0001Mobility probability: P0=0.5
(b)
0 20 40 60 80 1000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Number of CRs
Thr
oug
hpu
t
KP=0KP=1KP=2KP=3KP=4KP=5
PU Poisson traffic: λ=0.002CR Poisson traffic: λ'= 0.0015Mobility probability: P0=0.5
(c)
Figure 5.13: CR link throughput performance with different values of Kp in the (a)saturated mode, and (b)-(c) non-saturated mode
5.5. NUMERICAL RESULTS 98
0 20 40 60 80 1000
0.05
0.1
0.15
0.2
0.25
0.3
Number of CRs
Thr
ough
put
P0= 0.0
P0= 0.1
P0= 0.3
P0= 0.5
P0= 0.7
PU Poisson traffic: λ=0.0015
(a)
0 20 40 60 80 1000
0.05
0.1
0.15
0.2
0.25
0.3
Number of CRs
Thr
ough
put
P0= 0.0
P0= 0.1
P0= 0.3
P0= 0.5
P0= 0.7
PU Poisson traffic: λ=0.0015CR Poisson traffic: λ'= 0.0001
(b)
0 20 40 60 80 1000
0.05
0.1
0.15
0.2
0.25
0.3
Number of CRs
Thr
ough
put
P0= 0.0
P0= 0.1
P0= 0.3
P0= 0.5
P0= 0.7
PU Poisson traffic: λ=0.0015CR Poisson traffic: λ'= 0.0015
(c)
Figure 5.14: CR link throughput performance versus P0, where CR traffic is in the(a) saturated mode and (b)-(c) non-saturated mode with PU traffic
5.5. NUMERICAL RESULTS 99
CM-MACCSMA/CA RTS/CTS MAC
0 10 20 30 40 50 600
0.02
0.04
0.06
0.08
0.1
0.12
Network size
Res
pons
e tim
e (s
)
(a)
0 10 20 30 40 50 600
10
20
30
40
50
60
Network size
Thro
ughp
ut (s
ucce
ss ra
te%
)
CM-MAC (Simulation)CM-MAC (Simulation w/ mobility)CM-MACCSMA/CA RTS/CTS MAC (Simulation)CSMA/CA RTS/CTS MAC (Simulation w/ mobility)CSMA/CA RTS/CTS MAC
(b)
Figure 5.15: Simulation results. (a) Response time and (b) throughout performance
MAC. This is because we employed the ACTS and some spectrum management fea-
tures in the protocol. In Fig. 5.15(b), as the essential features have been captured
by the analysis, the simulation throughput results have the same tendency as the
analytical results. Moreover, the mobility of the CR nodes in CM-MAC has slighter
effect than that of the CSMA/CA RTS/CTS MAC.
In the simulation, we used a speed that can address the P0 in the analysis. How-
ever, we have to make sure the nodes are moving within the deployed area in order
to model the case in the analytical discussion where CR nodes can switch a spectrum
band to maintain the data transmissions. Furthermore, If a different channel bit rate
5.6. CONCLUSIVE REMARKS 100
(e.g., 54Mb/s) is used, the simulation results are expected in the same tendency as
the link throughput is not mainly dependent on the channel bit rate. Besides, we can
expect the performance of other CSMA/CA based protocols like the IEEE 802.15.4
MAC protocol, which may have a better response time when RTS/CTS mechanism
is reduced.
5.6 Conclusive Remarks
In this chapter, we have introduced the CM-MAC protocol, a MAC protocol for
CRAHNs, by mainly considering CR mobility of CRs and PUs PER regions. We
included the spectrum sensing in the handshaking procedure, and thus the spectrum
information updates on CRs are highly dependent on the PU traffic and the CR
data traffic. Moreover, we demonstrated the effectiveness of CM-MAC by showing
the analytical link throughput, which is mainly related to the following parameters:
number of CRs, stationary probability of a packet transmission by a CR, probability of
CR mobility, PU and CR traffic (Poisson factors), and the set of available channels.
These parameters can be considered for a local control scheme and the feedback
information and the inaccurate or changing value of the parameters can result in
different throughput performance. The analytical results showed that the CM-MAC
protocol outperforms the IEEE 802.11 MAC and SCA-MAC protocols in terms of
throughput performance. The results also showed the proposed protocol is effective
and robust with respect to CR movements. The work related to this chapter has been
published in [97]. In the next chapter, we will discuss the system-level throughput of
CRAHNs.
101
Chapter 6
Scaling Law of CRAHNs Based on Local Control
This chapter discusses the theoretical throughput performance of a CRAHN based
on local control. We discuss the scaling law of throughput for CRAHNs using the
resultant channel model in multi-hop transmission scenarios. Our work extends the
current scaling law analysis in single-hop cognitive radio networks to CRAHNs. We
show the derived throughput results based on the stochastic geometry framework in
the system level.
6.1 PU Interference Region
Definition 5. (PU interference region) The region being interfered by PU transmis-
sions using a specific spectrum band is called a PU interference region (PUIR).
In a CRAHN, as PUs may use different spectrum bands, a PUIR has spatial-
temporal characteristics.
Proposition 2. If we denote by Si a PUIR having one or more PU interferers,
and the CRs are deployed following a Poisson point process Φ, the shot-noise [98]
6.2. NETWORK MODEL 102
experienced by a CR in Si is as follows
I0i =
∑Xj∈Φ,j 6=i
F ij/l(|Xj −Xi|)
where Xi and Xj are the locations of CRs and the PU, respectively, F ij is the fading
from the interfering PU j to a CR i, and l(·)is the omni-directional path-loss model.
If we denote by I0i the so-called shot-noise experienced by CRs in a j-th PUIR
Sj from PUs, we can get the SINR of a CR transmitter in (6.1). For the Rayleigh
fading, the shot-noise is∑
i f(|Xi −Xj|α′), where α′ is the path loss exponent.
SINR(i, j) =F ii /l(|Xi − yi|)W + I1
i + I0j
(6.1)
where W is the shot-noise of Gaussian noise, I0j is the shot-noise between CRs and
the interfering PU in PUIRs, while I1i is the shot-noise only between CRs.
Now we can get the throughput of the CRAHN. The average transmission rate of
a CR transmitter can be expressed as
τ(r, λS) = E [log(1 + SINR(0, j)|e0 = 1] (6.2)
where e0 is the retaining indicator and e0 = 1 means a transmission event occurs.
Because different PUIRs may cause different interferences to CRs, we need a
specific network model in order to derive the network-level throughput.
6.2. NETWORK MODEL 103
Figure 6.1: Network layout of a CRAHN
6.2 Network Model
We consider a basic CRAHN network, where a PU coexists with multiple CRs. In
general, this network in a broad area includes two types of networks, i.e., the PU
network and the CR network. However, in reality, as the TV stations are sparsely
deployed in different regions, we can consider the network as a basic cell with one
PU transmitter and multiple CR transmitters, as shown in Fig. 6.1. This model
can be extended to a network with multiple PU transmitters, where the multiple PU
activities can be modelled as the activities from one virtual PU transmitter.
In this basic network, the CR network is deployed following a Poisson point process
with the intensity parameter λS. There are K spectrum bands available per PU. The
nodes in the CR network are assumed to follow a bipolar model in single-hop data
transmission scenario, where nodes are exactly split into transmitter-receiver pairs.
6.2. NETWORK MODEL 104
The PU’s activity on a channel follows a Poisson traffic model. This Poisson traffic
model over K channels allows us to estimate the probability of the availability of m
channels during a time period T .
In summary, we can list the following assumptions made to this network model.
1. The PU transmitter-receiver pair is stationary with known locations.
2. CRs are deployed following a Poisson point process with the intensity parameter
λS;
3. Each CR pair has a transmission radius r;
4. PUs and CRs experience the Rayleigh fading.
For a large CRAHN composed by multiple basic networks as shown in Fig. 6.1,
we assume the communication among CRs will not suffer from interference in the
overlap region between basic networks. This assumption also implies that the PUs
cannot communicate with each other.
For the CR communication with Aloha protocol in the MAC layer, similar to the
Kendall-like notation used in [98], the model mentioned above is GIW+M/M+D/M
type,
where GI means in the nominator a general distribution for the virtual power F, M/M
means the shot-noise interference is generated by a Poisson pattern of interferers (M)
with a Rayleigh distribution (M) for the virtual powers, and the D/M means the
deterministic distribution of PU interferers with a Rayleigh distribution of virtual
powers.
We can obtain the results of the coverage of a CR node (or probability of a
6.2. NETWORK MODEL 105
successful transmission) in two areas S1 and S2 as [57]:
E0
[es(I
1+W )]
= LI1(s)LW (s)
E1
[es(I
1+I01+W )]
= LI1(s)LI01 (s)LW (s)
E2
[es(I
1+I02+W )]
= LI1(s)LI02 (s)LW (s) (6.3)
where L(·) is the Laplace transform and s = µρl(r), and ρ is the reception threshold
seen by CR receiver from CR transmitter and µ is the mean of the Rayleigh fading
random variables. Therefore, the total throughput of CRs in this case is
τtotal(r, λS, S) = λS |S| τ(r, λS) (6.4)
τ(r, λS) = p0E0 + p1E1 + p2E2 (6.5)
where pi is the probability of area Si.
Because the values of r1 and r2 are dependent on the CRs in areas S1 and S2, it is
useful to calculate the average length of r1 and r2. As the distribution of CRs follows
a Poisson point process, we know the number of CRs in S1 is λS|S1|.
Because r1 and r2 are highly related to pi, we can substitute pi with r1 and r2 in
(6.4).
6.2.1 Virtual PU in the Resultant Spectrum Band
With PUIR, we are able to consider multiple PUs into a single virtual PU. We are
able to consider a PU operating in multiple spectrum bands in a PUIR as a virtual PU
operating in a single resultant spectrum band by using the resultant channel model
6.2. NETWORK MODEL 106
[69] introduced in Chapter 3. With the resultant channel model, for the ith PU, the
time in “busy” state or “idle” state is exponentially distributed with mean αi and βi,
respectively.
We know that, with resultant channel model, the expected length of the resultant
busy and idle periods E[Ton] and E[Toff ] are
E[Ton] =1∑K
i=1 βi−1
(6.6)
E[Toff ] = E[Ton]1−
∏Ki=1 ω1,i∏K
i=1 ω1,i
(6.7)
In order to simplify our discussion, we represent E[Ton] by Ton and E[Toff ] by
Toff .
The steady state probability of idle and busy states on channel i are
ω0,i =αi
αi + βi, ω1,i =
βiαi + βi
(6.8)
The aforementioned model can be extended to a network with multiple PU trans-
mitters, where the multiple PU activities can be virtually modelled as the activities
from one virtual PU transmitter. In this way, the network model with one (virtual)
PU and multiple CRs shown in Fig. 6.1 is sufficient for our discussion.
Suppose there are K spectrum bands which can be used by PUs. We can plot
the results of Toff and Ton shown in Fig. 6.2, where we can see when K > 3, Toff
increases.
6.2. NETWORK MODEL 107
1 2 3 4 5 6 7 8 9 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Available spectrum bands (K)
Exp
ecte
d le
ngth
of t
he r
esul
tant
per
iod
α = 0.4, β=0.6
Ton
Toff
Figure 6.2: Toff and Ton based on resultant channel model
6.2.2 Medium Access Probability
The term medium access probability (MAP) [99, 100] is the probability of a node
trying to access the wireless medium. Thus, MAP determines the probability of data
transmission and the throughput performance of the PU and CR networks.
In order to simplify our discussion, we consider the time-slotted MAC protocol.
In [91], Stevenson et al. analyzed the throughput order of CRs with multiple PU
pairs and employed a 25-TDMA transmission pattern for PU activities. However, we
consider a general case that the PU pairs and CRs coexist, and PU activities are not
limited in specified TDMA slots. In order to simplify our analysis, we assume that
the PU activities are conceptually separated into time frames, each with a length T .
The time frame T can be considered as a time slotted MAC protocol.
Based on the resultant channel model, we can transform a K-channel case into
6.2. NETWORK MODEL 108
a single-channel case. Therefore, as we are interested in finding out the throughput
of the PU network and the CR network, we can focus on evaluating the number
of packets sent during the T = Toff + Ton period. Without loss of generality, we
can assume a PU does not transmit packets during [0, Toff ] but it transmits packets
during (Toff , T ] in the busy state at time ti following the so-called retaining indicator:
UPj = 1Toff<ti<T (6.9)
In (6.9), CR i can transmit packets at time ti with the following retaining indicator:
USi = 1ti<Toff + 1Toff<ti<T1FS−P0,i /|TSi,0−RP0 |α
′<ρ (6.10)
In fact, (6.10) depends on a spectrum sharing model. If we just allow a PU to
exclusively occupy a channel when it is in the busy state, then we can simplify (6.10)
to
USi = 1ti<Toff (6.11)
The retaining indicator in (6.10) can be referred as the underlay spectrum sharing,
where the CRs try to perform the data transmissions with or without PU activities.
The retaining indicator in (6.11) can be referred as the overlay spectrum sharing,
where CRs only transmit without PU activities.
Then the MAP or transmission probability of a CR is:
P (USi = 1) = P (ti ≤ Toff ) + P (Toff < t < T )P (F S−P
i,0 /|T Si,0 −RP0 | < ρ) (6.12)
6.3. NETWORK DIVISIONS 109
For the given parameters µ = 10, ρ = 15, α′ = 3, R0 = (0.2, 0.2) in a unit circular
area, we can plot the MAP results in Fig. 6.3.
Based on [101], given a CR transmitter at location y and a CR receiver at location
z in the CRAHN shown in Fig. 6.1, the coverage probability (COP) can then be
obtained as:
PCOPS = Py,z(SINR
Si > Pth)
= Py,zFS−S1,1 > Pthr
α′(W (z) + F P−S0,1 /|z|α′ + ΓS(z))
= Ey,z[e−µPthrα
′W (z)]Ey,z[e
−µPthrα′FP−S0,1 /|z|α′ ]Ey,z[e
−µPthrα′ΓS(z)]
= LW (µPthrα′)LFP−S0,1
(µPthr
α′
|z|α′)(1− E[US
i ] + E[USi ]
|T Si − z|α′
|T Si − z|α′ + Pthrα
′ )
(6.13)
where E[USi ] = P (US
i = 1).
Usually, in a CRAHN, the parameters α′, µ, Pth, z, and λS are known a priori. In
this way, although the multi-integral in 6.13 can hardly be derived into a simple form
but it can be solved by the Monte Carlo method. We can even make the CRAHN
more general if one or more parameters are not known.
Furthermore, if we assume that CR transmitters are in the saturated mode, each
CR transmitter will immediately transmit packets once a spectrum band is not oc-
cupied and a transmission back-off timer expires.
6.3 Network Divisions
It is not unusual that a network needs to be divided into different areas of CRs.
Suppose we divide the CRAHN with area S into two areas S1 and S2, we can obtain
the throughput of CRs as
6.3. NETWORK DIVISIONS 110
0 0.5 1 1.5 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mean of idle state holding time
Med
ium
acc
ess
prob
abili
ty
K=3
Underlay spectrum sharingOverlay spectrum sharing
(a)
0 0.5 1 1.5 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Mean of idle state holding time
Med
ium
acc
ess
prob
abili
ty
K=5
Underlay spectrum sharingOverlay spectrum sharing
(b)
Figure 6.3: MAP results based on the resultant channel model
6.4. MULTI-HOP DATA TRANSMISSION SCENARIO 111
CR 1 CR 2 CR n...
PUIR
Figure 6.4: Multi-hop data transmission from CR 1 to CR n.
P SCOP = λS
∫S1
P SCOP (y)(1− e−µρ|y−RP0 |α
′
)dy + λS
∫S2
P SCOP (y)(1− e−µρ|y−RP0 |α
′
)dy
(6.14)
If a PER region is considered in the CRAHN with the area SPER = S1 and
therefore S2 = S ∪ \S1, then the throughput can be readily derived accordingly by
(6.14).
6.4 Multi-Hop Data Transmission Scenario
An important feature in CRAHNs is the multi-hop data transmission. We are now
extending the aforementioned analysis from a single-hop data transmission scenario
to a multi-hop data transmission scenario. Fig. 6.4 is an example of the multi-hop
transmission scenario, where each CR tries to transmit the packets over multiple hops.
In Fig. 6.4, we can see that as all CRs are covered by the same PUIR, we can assume
the data transmission over each link is independent. In this way, if we have n CRs in
a data transmission scenario over n− 1 hops, the retaining indicator in this case is:
6.4. MULTI-HOP DATA TRANSMISSION SCENARIO 112
The retaining indicator in the multi-hop fashion can be represented as
U(n)S =n−1∏i=1
USi (6.15)
Because there are n− 1 CR transmitters in the unidirectional multi-hop scenario,
from (6.12), we can derive the multi-hop transmission probability and COP as
P (U(n)Si = 1) =n−1∏i=1
P (USi ) (6.16)
PCOPS (n)(U(n)Si = 1) =
n−1∏i=1
P (USi )PCOP
i,S (6.17)
Here we discuss how the local control and information can affect PCOPS (n). In
(6.17), PCOPi,S is the COP in a hop i. Due to the inaccurate feedback or local infor-
mation regarding radio environment, the parameters (e.g., α′, µ, etc.) are subject to
change from link to link and therefore PCOPi,S is different from link to link. Given a
local control scheme which can result in the identical value of PCOPi,S for all links, we
can simplify PCOPi,S to PCOP
Si. If we divide the CRAHN with c identical subareas, then
Si = S/c.
In the model shown in Fig. 6.4 we need to know the average number of hops
from the source CR to the destination CR directly from the average distance of CR
transmitter-receiver pairs. However, with our model, CR transmitters are distributed
following a Poisson point process, so we are able to estimate the probability for a
certain number of hops along a transmission path.
6.4. MULTI-HOP DATA TRANSMISSION SCENARIO 113
6.4.1 Probability of A Transmission over Multiple Hops
In a Poisson point process, the connectivity of a CRAHN can be expressed as a
function of distance distributions between nodes [102]. If the CRs in a Borel set S is
distributed in a Poisson process with parameter λS, the probability of having n CRs
along a path is
P (n, S) =(λSL(S))n
n!e−λSL(S). (6.18)
where L(S) = πr2 and r is the radius of the circular area S. In an area S, the
probability that it contains exactly n CRs (or n− 1 hops) is (6.18).
The probability of the origin to the nth nearest point in an area S can be expressed
as
P (n, S) =
∫S
2(πλS)n
(n− 1)!r2n−1e−πλSr
2
dr (6.19)
Eq. (6.18) can be used to calculate the probability of an exact number of hops,
but this probability is suited to the case that a circular area contains exactly n CR
nodes (or n−1 hops). The limitation of (6.18) is that a CRAHN needs to be carefully
divided into small circular areas without overlaps. For a network in a small circular
area and a low density of CRs, (6.18) is appropriate. For a network with a large
number of hops with CRs beyond the PU coverage, using (6.18) is not accurate.
Eq. (6.19) is suited to the case when we want to guarantee a data transmission
involves n− 1 hops in a given area S. Therefore, we should not use (6.19) to the case
of traditional networks with a constant link length per hop.
From the aforementioned two equations, we know the route selection is important
6.5. SCALING LAW OF CRAHNS 114
to determine the probability of having an exact number of CRs in the multi-hop fash-
ion. There are two generic route selection schemes corresponding to (6.18) and (6.19)
if we have specified the hop count: (1) the route selection for a CR link transmitter is
randomly chosen in a given area S; (2) the route selection for a CR link transmission
is determined by the subareas Si ⊂ S where each subarea Si should guarantee the
single-hop transmission.
6.4.2 Packet Reception Probability
There are several transmission scenarios when we consider the multi-hop transmission
on routers. We introduce the packet reception possibility, Prx, which indicates the
possibility when a router receives a packet from a node. With Prx, we are able to
discuss the different transmission cases on a router. For example, if a router uses
a flooding routing algorithm where the transmission progresses in the broadcasting
fashion, we can take Prx = 1. If a router employs an opportunistic routing algorithm
where the next hop is randomly chosen, we can take Prx = c, 0 < c < 1.
In the multi-hop transmission model we discussed above, if we take Prx into con-
sideration, we can derive the throughput over n− 1 hops as P n−1rw PCOP
S , where PCOPS
depends on (6.13) and the route selection schemes in (6.18) or (6.19).
6.5 Scaling Law of CRAHNs
We discuss the throughput results using the aforementioned analysis. The throughput
performance is measured based on the derived COP as in the Poisson point process
the probability of having CRs in an area is important. For the multi-hop data com-
munication we shown above, COP can be translated as the successfully transmitted
6.5. SCALING LAW OF CRAHNS 115
packets per second per unit area. We take the values of the key parameters as: K = 5,
α′ = 3, αi = 1.5, βi = 1, r = 0.3, R0 = (0.2, 0.2), µ = 10, ρ = 15, and Pth = 15.
First, the results of the single-hop data transmission are shown in Fig. 6.5. From
the aforementioned discussion, we employ the underlay spectrum sharing in the CR
network as it can reflect the interference induced by PUs. From Fig. 6.5, the curve
of the CR throughput linearly grows with the increasing value of λS, because, in the
single-hop scenario, growing CR density directly increases MAP and the concurrent
transmission sessions. However, because the PU suffers from the interference of the
increasing CR transmission, the curve of PU throughput declines with the increasing
value of λS. Compared to Fig. 6.5(a), Fig. 6.5(b) show the results when we consider
a subarea of a network in an area S. The throughput performance for CRs drops in
Fig. 6.5(b) mainly because the number of CR transmitters becomes less in this case.
In Fig. 6.6, we show the throughput result using the route selection scheme in
(6.18) and the throughput result using an opportunistic routing scheme (Prw = 0.98)
in the multi-hop data transmission scenario. When λS is less than 1.45, the 2-hop
transmission case has better throughput than the 3-hop and 4-hop transmission cases.
However, when λS is greater than 1.85, a throughput curve with a greater hop count
has better performance than a curve with a smaller hop count. The reason of this
phenomenon is that with more number of CRs per area, a greater number of hops
can help relay the data; a smaller number of hops can result in the longer average
link length and therefore reduce the probability of delivering a packet. We note
that all curves in Fig. 6.6 become zero as λS increases. This is because we adopt
the probability of an exact number of hops in (6.18), and it is readily to see that
when the density of CRs increases, the probability of having exact 2, 3 or 4 hops
6.5. SCALING LAW OF CRAHNS 116
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3
Thro
ughp
ut (P
acke
ts/s
/m2 )
PUCR
S
(a)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.2
0.4
0.6
0.8
1
1.2
1.4
Thro
ughp
ut (P
acke
ts/s
/m2 )
PUCR
S
(b)
Figure 6.5: Throughput results of a single-hop scenario. (a) The whole network with-in an area S is considered; (b) the throughput performance in a subareaof S is considered.
6.5. SCALING LAW OF CRAHNS 117
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
λS
Suc
cess
fully
tran
smitt
ed p
acke
ts
Hop count=2Hop count=3Hop count=4Hop count=2 (Opportunistic)Hop count=3 (Opportunistic)Hop count=4 (Opportunistic)
Figure 6.6: Normalized throughput results when hop counts are 2, 3, and 4 in abounded circular area.
in an area becomes less. Moreover, as the packet reception probability can affect
the probability of successfully transmitted packets, the throughput result with the
opportunistic routing scheme has a bit lower performance than the result without a
opportunistic routing scheme.
Keeping the same condition, we show the throughput results with the second route
selection scheme based on (6.19) and the the throughput results with an opportunistic
routing scheme (Prw = 0.98) in Fig. 6.7, where the throughput increases with the
increasing number of hops involved in the data transmissions. Fig. 6.7 also shows
that when λS < 2.45 a curve a the smaller hop count has greater throughput than
the one with a larger hop count, where this phenomenon is consistent with the results
shown in Fig. 6.6. When λS > 2.45, the curve with a smaller hop count has less
throughput than the one with a larger hop count. This tendency results from two
6.5. SCALING LAW OF CRAHNS 118
factors. First, as we make the guaranteed number of hops in a given area, which is
a part of the entire network, with the density of CRs increases, the probability of
ensuring the small number of hops (e.g. 2, 3, or 4) increases. Second, as the area for
a one-hop transmission is reduced, the throughput is actually decreased. Similarly,
the throughput results with opportunistic routing scheme have the same tendency
and theoretical ground as the results without the opportunistic routing scheme.
In summary, from the results in Fig. 6.6 and 6.7, we know that the route selection
is important when the density of CRs is increased.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
λS
Suc
cess
fully
tran
smitt
ed p
acke
ts
Hop count=2Hop count=3Hop count=4Hop count=2 (Opportunistic)Hop count=3 (Opportunistic)Hop count=4 (Opportunistic)
Figure 6.7: Normalized throughput results of a multi-hop scenario with different hopcounts.
The applications of the two generic route selection schemes can be applied in
several different areas. Specifically, the first route selection scheme is suitable for a
randomly deployed CRAHN where the hop distance between CRs is not known a
priori but the maximum number of hops is expected. For example, a CRAHN with
a bunch of cognitive sensor nodes by random deployment without an infrastructure
6.6. DISCUSSION ON IEEE 802.22 BASED CRAHNS & IEEE 802.11BASED CRAHNS 119
Table 6.1: Common parameters
Parametersµ Rayleigh fading parameter
SPER Area of primary exclusive regionλS Poisson point process parameter of CRsK Number of spectrum bands
can be seen as the first route selection scheme. The second route selection scheme
is for the CRAHN with a constant hop-distance. For example, a CRAHN used in
the micro grids of a Smart Grid where CRs in the micro grids are almost static with
known distance between each other can be considered in this case.
6.6 Discussion on IEEE 802.22 Based CRAHNs & IEEE 802.11 Based
CRAHNs
From the above discussion, we have derived the theoretical results based on a time-
slotted abstracted MAC model. However, it is possible to extend the analysis to the
real-world networks compatible with existing standards.
The aforementioned throughput performance can be applied to the IEEE 802.22
[103] based CRAHNs and the IEEE 802.11-based CRAHNs, because the network can
be formed in the similar way and the key parameters used in the proposed network
model can be used in these networks.
The key parameters of PHY and MAC layers shared in both IEEE 802.22 or IEEE
802.11 based CRAHNs are shown in Table 6.1. These parameters capture the global
radio environment in the two networks. With additional parameters given in the IEEE
802.22 or IEEE 802.11 based CRAHNs, we can extend the results in a fine granularity.
In IEEE 802.22 based networks, the TV stations can be statistically modelled by the
6.7. CONCLUSIVE REMARKS 120
Voronoi diagrams [104], which means that the network can be divided into cells with
one PU per cell. Furthermore, we know the minimum channel for data transmission
can be included in the throughput expression. In this way, the IEEE 802.11 based
CRAHN has similar throughput results to IEEE 802.22 based CRAHN, because the
support of multiple channels is a must in the IEEE 802.11 based CRAHN.
6.7 Conclusive Remarks
In this chapter, we have discussed the scaling law of the CR throughput in single-hop
and multi-hop transmission scenarios when CR transmitters can communicate with
each other in the network. The model proposed in this chapter can estimate the
throughput of PUs and CRs for the underlay spectrum sharing and overlay spectrum
sharing. In this sense, the key parameters of a cross-layer protocol of CRAHNs can
be analyzed. Moreover, although we studied the basic network topology of CRAHNs
which contains a PU and multiple CRs, we can derive more complicated topologies
based on this topology. Furthermore, the route selection scheme was considered as
a key factor for throughput performance because of the characteristics of a Poisson
point process. We showed the effectiveness of the proposed models by the presented
results. Moreover, for some real-world CRAHNs with fixed number of nodes in a
given area [105], the binomial point process can be employed as the CRs following
Poisson point process have no definite locations in a given area.
121
Chapter 7
Conclusion
7.1 Summary of Contributions
The increasing demand for wireless services and the spectrum sharing policies has led
to spectrum scarcity in wireless communications. As a precious resource, the under-
utilized spectrum is required to be put to use in CRAHNs with spectrum management.
Research on CRAHNs can provide solutions to this problem and to a broad spectrum
of wireless network paradigms.
In this preliminary study, we focused on the local control approach in order to
address the spectrum sharing fairness, cognitive MAC protocol design, and system-
level throughput performance in CRAHNs.
In Chapter 4, we proposed the framework of local control approach. This approach
allows us to model and analyze the stability of consensus-based protocols for spectrum
sharing. Then we discussed two local control schemes with feedback and without
feedback and compared their performance in terms of convergence and fairness. With
the local information brought by local observations from spectrum sensing and MAC-
layer functions, the proposed local control scheme can effectively achieve the goal of
7.2. FUTURE WORK 122
the spectrum sharing fairness.
In Chapter 5, we proposed the cognitive MAC protocol with mobility support,
which is called CM-MAC. In the design of CM-MAC we employed the local control
concept to devise the mobility support algorithm, which can take advantage of the
local information from the neighboring CRs and address the negative effects induced
by the existence of the PER area in a CRAHN.
In Chapter 6, we discussed the throughput in single-hop and multi-hop scenarios.
We discussed the local control concept in the analysis with the inaccurate local infor-
mation from observations. In this way, we can comprehensive investigate the scaling
law based on the network model with abstract PHY and MAC functions. Although
the network modelling is not in a fine granularity, the theoretical results give hints
on the scaling law and fundamental limits of a CRAHN.
7.2 Future Work
A few open topics and questions are discussed in the following.
Local Control Schemes
• A local control scheme in spectrum sharing was proposed in the thesis. More
schemes can be investigated for possible applications. We assumed each CR
has the same capability but the heterogeneity of CRAHNs is not unusual in
many applications. It is worthwhile to investigate local control schemes for the
heterogenous CRs. Moreover, it is worthwhile to explore a local control scheme
with a learning algorithm.
• The applicability of using local control approach to analyze other CR enabled
7.2. FUTURE WORK 123
networks worth being investigated. For example, if we consider a CRSN as
a CRAHN with new PHY features. A CRSN brings more topological and
hardware constrains compared to CRAHNs. However, with several essential
common characteristics between the two networks, the system-level analysis in
CRAHNs can be extended to and local control approach for protocol design can
be applied.
Models in the MAC Layer
• In this thesis, the 1-D mobility was addressed in the mobility analysis; how-
ever, more sophisticated mobility models in higher dimensions and in different
topologies need to be investigated in the future work. For example, the CR de-
vices can move following 2-D or 3-D random walks in a bounded area or space,
and the performance may vary because of the possible transmission handoffs
and unpredictable interference caused by primary exclusive regions.
• Different PU activity models need to be considered in different scenarios. Al-
though it is popular to model the PU activity as a Poisson process, it is possible
in some applications that a PU activity pattern can be modelled as a more com-
plex model. Moreover, real-world data for PU activities can be employed in the
evaluation in order to see the stability and applicability of the protocol.
System-Level Modelling and Analysis
• The PHY and MAC layers were abstracted in the system-level analysis. A
further detailed modelling for either PHY or MAC layers is expected to result
in new theoretical bounds.
7.2. FUTURE WORK 124
• The multi-hop data transmission can involve quite a few CRs, where the CRs
along the path can be formed in different ways. We assumed the path was
formed by two route selection schemes but other route selection schemes need
to be considered. Moreover, a path can be formed in many ways if we involve
different NWK features. Therefore, the formation of a path and throughput
performance needs to be investigated further because it may hinder data trans-
missions along the path. Besides, a closed-form approximated expression of the
throughput with the routing schemes with local control schemes needs to be
investigated.
BIBLIOGRAPHY 125
Bibliography
[1] FCC. Et docket no 03-222 notice of proposed rule making and order. Technical
report, December 30 2003.
[2] R.B. Bacchus, A.J. Fertner, C.S. Hood, and D.A. Roberson. Long-term, wide-
band spectral monitoring in support of dynamic spectrum access networks at
the iit spectrum observatory. In Proceedings of the 3rd IEEE Symposium on
New Frontiers in Dynamic Spectrum Access Networks (DySPAN), pages 1–10,
2008.
[3] J. Mitola. Cognitive Radio: An Integrated Agent Architecture for Software.
PhD thesis, Dept. of Teleinformatics, Royal Institute of Technology (KTH),
Stockholm Sweden, May 2000.
[4] J. Mitola. Cognitive Radio Architecture: The Engineering Foundations of Radio
XML, volume 1. Wiley-Interscience, 1 edition, Aug 2006.
[5] I.F. Akyildiz, W.Y. Lee, and K.R. Chowdhury. Crahns: Cognitive radio ad hoc
networks. Ad Hoc Networks, 7(5):810–836, 2009.
[6] S. Haykin. Cognitive radio: brain-empowered wireless communications. IEEE
Journal on Selected Areas in Communications, 23(2):201–220, 2005.
BIBLIOGRAPHY 126
[7] O. Akan, O. Karli, and O. Ergul. Cognitive radio sensor networks. IEEE
Network, 23:34–40, 2009.
[8] I.F. Akyildiz, W.Y. Lee, and K.R. Chowdhury. Spectrum management in cog-
nitive radio ad hoc networks. IEEE Network, 23(4):6–12, 2009.
[9] L. Cao and H. Zheng. Distributed rule-regulated spectrum sharing. IEEE
Journal on Selected Areas in Communications, 26(1):130–145, 2008.
[10] S.M. Mishra, A. Sahai, and R.W. Brodersen. Cooperative sensing among cog-
nitive radios. In Proceedings of the IEEE International Conference on Commu-
nications (ICC), pages 1658–1663, 2006.
[11] J.M. Peha. Sharing spectrum through spectrum policy reform and cognitive
radio. Proceedings of the IEEE, 97(4):708–719, 2009.
[12] N. Devroye, M. Vu, and V. Tarokh. Cognitive radio networks. IEEE Signal
Processing Magazine, 25(6):12 –23, november 2008.
[13] B. Wang and K.J.R. Liu. Advances in cognitive radio networks: A survey. IEEE
Journal of Selected Topics in Signal Processing, 5(1):5 –23, feb. 2011.
[14] P. Lassila and A. Penttinen. Survey on performance analysis of cognitive radio
networks. Technical report, Helsinki University of Technology, 2008.
[15] L. Zhou and Z.J. Haas. Securing ad hoc networks. IEEE Network, 13(6):24–30,
1999.
BIBLIOGRAPHY 127
[16] J. Huang, R.A. Berry, and M.L. Honig. Spectrum sharing with distributed in-
terference compensation. In Proceedings of the First IEEE International Sym-
posium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN),
pages 88 –93, nov. 2005.
[17] C. Peng, H. Zheng, and B. Zhao. Utilization and fairness in spectrum assign-
ment for opportunistic spectrum access. Mobile Networks and Applications,
11(4):555–576, 2006.
[18] L. Cao and H. Zheng. Distributed spectrum allocation via local bargaining. In
Proceedings of the 2nd Annual IEEE Communications Society Conference on
Sensor and Ad Hoc Communications and Networks, pages 475–486, 2005.
[19] C. Wu, K. Chowdhury, M. Di Felice, and W. Meleis. Spectrum management of
cognitive radio using multi-agent reinforcement learning. In Proceedings of the
9th International Conference on Autonomous Agents and Multiagent Systems:
Industry track, AAMAS ’10, pages 1705–1712, Richland, SC, 2010. International
Foundation for Autonomous Agents and Multiagent Systems.
[20] T. Jiang, D. Grace, and P.D. Mitchell. Efficient exploration in reinforce-
ment learning-based cognitive radio spectrum sharing. IET Communications,
5(10):1309 –1317, 1 2011.
[21] B. Atakan and O.B. Akan. Biologically-inspired spectrum sharing in cognitive
radio networks. In Proceedings of the IEEE Wireless Communications and
Networking Conference (WCNC), pages 43–48, 2007.
BIBLIOGRAPHY 128
[22] C. Doerr, D. Grunwald, and D. Sicker. Local control of cognitive radio networks.
Annals of Telecommunications, 64(7):503–534, 2009.
[23] Z. Li, F. Yu, and M Huang. A cooperative spectrum sensing consensus scheme
in cognitive radios. In Proceedings of the IEEE International Conference on
Computer Communications (INFOCOM), pages 2546–2550, 2009.
[24] F. Richard Yu, editor. Cognitive Radio Mobile Ad Hoc Networks. Springer,
2011.
[25] Z. Ji and K.J.R. Liu. Cognitive radios for dynamic spectrum access - dynamic
spectrum sharing: A game theoretical overview. IEEE Communications Mag-
azine, 45(5):88–94, may 2007.
[26] Q. Zhao and B.M. Sadler. A survey of dynamic spectrum access. IEEE Signal
Processing Magazine, 24(3):79 –89, may 2007.
[27] E. Axell, G. Leus, E.G. Larsson, and H.V. Poor. Spectrum sensing for cognitive
radio : State-of-the-art and recent advances. IEEE Signal Processing Magazine,
29(3):101 –116, May 2012.
[28] D. Cabric, S.M. Mishra, and R.W. Brodersen. Implementation issues in spec-
trum sensing for cognitive radios. In Proceedings of the 38th Asilomar Confer-
ence on Signals, Systems and Computers, volume 1, pages 772 – 776 Vol.1, nov.
2004.
[29] S. Zarrin. Spectrum Sensing in Cognitive Radio Networks. PhD thesis, Graduate
Department of Electrical and Computer Engineering, University of Toronto,
2011.
BIBLIOGRAPHY 129
[30] H.T. Cheng and W. Zhuang. Simple channel sensing order in cognitive radio
networks. IEEE Journal on Selected Areas in Communications, 29(4):676 –688,
april 2011.
[31] T. Yucek and H. Arslan. A survey of spectrum sensing algorithms for cognitive
radio applications. IEEE Communications Surveys Tutorials, 11(1):116 –130,
quarter 2009.
[32] Z. Quan, S. Cui, A.H. Sayed, and H.V. Poor. Optimal multiband joint detection
for spectrum sensing in cognitive radio networks. IEEE Transactions on Signal
Processing, 57(3):1128 –1140, march 2009.
[33] H. Kim and K.G. Shin. Efficient discovery of spectrum opportunities with
mac-layer sensing in cognitive radio networks. IEEE Transactions on Mobile
Computing, 7(5):533 –545, 2008.
[34] H. Zhai, J. Wang, and Y. Fang. Ducha: A new dual-channel mac protocol for
multihop ad hoc networks. IEEE Transactions on Wireless Communications,
5(11):3224–3233, 2006.
[35] F. Chen, H. Zhai, and Y. Fang. An opportunistic multiradio mac protocol in
multirate wireless ad hoc networks. IEEE Transactions on Wireless Communi-
cations, 8(5):2642–2651, 2009.
[36] R. Hasan and M. Murshed. A novel multichannel cognitive radio network with
throughput analysis at saturation load. In Proceedings of the 10th IEEE In-
ternational Symposium on Network Computing and Applications (NCA), pages
211 –218, Aug. 2011.
BIBLIOGRAPHY 130
[37] A. Chia-Chun Hsu, D. S. L. Weit, and C. C. J. Kuo. A cognitive mac protocol
using statistical channel allocation for wireless ad-hoc networks. In Proceedings
of the IEEE Wireless Communications and Networking Conference (WCNC),
pages 105–110, 2007.
[38] T. Shu, S. Cui, and M. Krunz. Medium access control for multi-channel parallel
transmission in cognitive radio networks. In Proceedings of the IEEE Global
Telecommunications Conference (GLOBECOM), pages 1–5, 2006.
[39] N. Jain, S.R. Das, and A. Nasipuri. A multichannel csma mac protocol with
receiver-based channel selection for multihop wireless networks. In Proceedings
of the International Conference on Computer Communication Networks, pages
432–439, 2001.
[40] B. Sadeghi, V. Kanodia, A. Sabharwal, and E. Knightly. Oar: an opportunistic
auto-rate media access protocol for ad hoc networks. Wireless Networks, 11(1-
2):39–53, 2005.
[41] H.B. Salameh, M. Krunz, and O. Younis. Mac protocol for opportunistic cogni-
tive radio networks with soft guarantees. IEEE Transactions on Mobile Com-
puting, 8(10):1339–1352, 2009.
[42] H.B. Salameh, M. Krunz, and O. Younis. Distance- and traffic-aware channel
assignment in cognitive radio networks. In Proceedings of the IEEE Interna-
tional conference on sensing, communicaiton, and networking (SECON), pages
10–18, 2008.
[43] D. Cabric and R. W. Brodersen. Physical layer design issues unique to cognitive
BIBLIOGRAPHY 131
radio systems. In Proceedings of the International Symposium on Personal,
Indoor and Mobile Radio Communications (PIMRC), volume 2, pages 759–763,
2005.
[44] K. R. Chowdhury, M. Di Felice, and I.F. Akyildiz. Tp-crahn: A transport
protocol for cognitive radio ad-hoc networks. In Proceedings of the IEEE Inter-
national Conference on Computer Communications (INFOCOM), volume 1-5
of IEEE Infocom, pages 2482–2490, 2009.
[45] J. So and N.H. Vaidya. Multi-channel mac for ad hoc networks: handling
multi-channel hidden terminals using a single transceiver, 2004.
[46] C. Cordeiro and K. Challapali. C-mac: A cognitive mac protocol for multi-
channel wireless networks. In Proceedings of the IEEE International Symposium
on New Frontiers in Dynamic Spectrum Access Networks (DySPAN), pages 147–
157, 2007.
[47] H. Su and X. Zhang. Cream-mac: An efficient cognitive radio-enabled multi-
channel mac protocol for wireless networks. In Proceedings of the 2008 Inter-
national Symposium on a World of Wireless, Mobile and Multimedia Networks
(WoWMoM), pages 1–8, 2008.
[48] P. Gupta and P.R. Kumar. The capacity of wireless networks. IEEE Transac-
tions on Information Theory, 46(2):388–404–, 2000.
[49] C. Cordeiro, K. Challapali, and M. Ghosh. Cognitive phy and mac layers
for dynamic spectrum access and sharing of tv bands. In Proceedings of the
BIBLIOGRAPHY 132
first international workshop on technology and policy for accessing spectrum,
TAPAS’06, New York, NY, USA, 2006. ACM.
[50] M. Vu, N. Devroye, and V. Tarokh. On the primary exclusive region of cognitive
networks. IEEE Transactions on Wireless Communications, 8(7):3380–3385,
2009.
[51] Y. Shi, C. Jiang, Y.T. Hou, and S. Kompella. On capacity scaling law of
cognitive radio ad hoc networks. In Proceedings of the IEEE International
Conference on Computer Communication Networks (ICCCN), 2011.
[52] C. Lee and M. Haenggi. Interference and outage in doubly poisson cognitive
networks. In Proceedings of 19th International Conference on Computer Com-
munications and Networks (ICCCN), pages 1 –6, Aug. 2010.
[53] H. Su and X. Zhang. Cross-layer based opportunistic mac protocols for qos
provisionings over cognitive radio wireless networks. IEEE Journal on Selected
Areas in Communications, 26(1):118 –129, 2008.
[54] W.C. Ao, S.M. Cheng, and K.C. Chen. Phase transition diagram for underlay
heterogeneous cognitive radio networks. In Proceedings of the IEEE Global
Telecommunications Conference (GLOBECOM), pages 1 –6, dec. 2010.
[55] C. Chen and X. Haige. The throughput order of ad hoc networks with physical-
layer network coding and analog network coding. In Proceedings of the 18th
IEEE International Conference on Communications (ICC), pages 2146–2152,
2008.
BIBLIOGRAPHY 133
[56] P. Hu and M. Ibnkahla. A survey of physical-layer network coding in wireless
networks. In Proceedings of the 25th Biennial Symposium on Communications
(QBSC), pages 311–314, May 2010.
[57] M. Haenggi, J.G. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti. S-
tochastic geometry and random graphs for the analysis and design of wireless
networks. IEEE Journal on Selected Areas in Communications, 27(7):1029 –
1046, Sept. 2009.
[58] P.H.J. Nardelli, M. Kaynia, and M. Latva-aho. Efficiency of the aloha protocol
in multi-hop networks. In Proceedings of the 2010 IEEE Eleventh Interna-
tional Workshop on Signal Processing Advances in Wireless Communications
(SPAWC), pages 1 –5, June 2010.
[59] M.C. Golumbic. Algorithmic Graph Theory and Perfect Graphs. Elsvier, 2nd
ed. edition, Feb 2004.
[60] Stephen Wolfram. A New Kind of Science. Wolfram Media, 2002.
[61] Y. Zhao, L. Morales, J. Gaeddert, K.K. Bae, Jung-Sun Um, and J.H. Reed.
Applying radio environment maps to cognitive wireless regional area networks.
In Proceedings of the 2nd IEEE International Symposium on New Frontiers in
Dynamic Spectrum Access Networks (DySPAN), pages 115 –118, april 2007.
[62] A.B. MacKenzie, J.H. Reed, P. Athanas, C.W. Bostian, R.M. Buehrer, L.A.
DaSilva, S.W. Ellingson, Y.T. Hou, M. Hsiao, Jung-Min Park, C. Patterson,
S. Raman, and C. da Silva. Cognitive radio and networking research at virginia
tech. Proceedings of the IEEE, 97(4):660 –688, april 2009.
BIBLIOGRAPHY 134
[63] Y. Zhao, J. Gaeddert, K.K. Bae, and J.H. Reed. Radio environment map
enabled situation-aware cognitive radio learning algorithms. In Proceedings of
the Software Defined Radio Forum (SDRF) technical conference, Orlando, FL,
2006.
[64] R. Draves, J. Padhye, and B. Zill. Routing in multi-radio, multi-hop wireless
mesh networks. In Proceedings of the 10th annual international conference on
mobile computing and networking, MobiCom ’04, pages 114–128, New York,
NY, USA, 2004. ACM.
[65] J. Li, Y. Zhou, and L. Lamont. Routing schemes for cognitive radio mobile
ad hoc networks. In F. Richard Yu, editor, Cognitive Radio Mobile Ad Hoc
Networks, pages 227–248. Springer New York, 2011.
[66] I. Pefkianakis, S.H.Y. Wong, and S. Lu. Samer: Spectrum aware mesh routing
in cognitive radio networks. In Proceedings of the 3rd IEEE International Sym-
posium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN),
pages 1 –5, oct. 2008.
[67] G. Cheng, W. Liu, Y. Li, and W. Cheng. Spectrum aware on-demand routing
in cognitive radio networks. In Proceedings of the 2nd IEEE International Sym-
posium on New Frontiers in Dynamic Spectrum Access Networks (DySPAN),
pages 571 –574, april 2007.
[68] M. Cesana, F. Cuomo, and E. Ekici. Routing in cognitive radio networks:
Challenges and solutions. Ad Hoc Networks, 9(3):228 – 248, 2011.
BIBLIOGRAPHY 135
[69] R. Hasan and M. Murshed. Provisioning delay sensitive services in cognitive ra-
dio networks with multiple radio interfaces. In Proceedings of the IEEE Wireless
Communications and Networking Conference (WCNC), pages 162 –167, march
2011.
[70] S. Filin, H. Harada, H. Murakami, K. Ishizu, and G. Miyamoto. Ieee 1900.4 wg
on architecture and enablers for optimized radio & spectrum resource usage. In
Proceedings of the International Conference on Ultra Modern Telecommunica-
tions & Workshops (ICUMT), pages 1–8, 2009.
[71] D.P. Satapathy and J.M. Peha. Etiquette modification for unlicensed spectrum:
approach and impact. In Proceedings of the 48th IEEE Vehicular Technology
Conference (VTC), volume 1, pages 272–276, 1998.
[72] D.P. Satapathy and J.M. Peha. Performance of unlicensed devices with a spec-
trum etiquette. In Proceedings of the IEEE Global Telecommunications Con-
ference (GLOBECOM), volume 1, pages 414–418, 1997.
[73] M.M. Halldorsson, J.Y. Halpern, L. Li, and V.S. Mirrokni. On spectrum sharing
games. In Proceedings of the 23rd annual ACM symposium on Principles of
distributed computing, PODC ’04, pages 107–114, New York, NY, USA, 2004.
ACM.
[74] R. Etkin, A. Parekh, and D. Tse. Spectrum sharing for unlicensed bands. IEEE
Journal on Selected Areas in Communications, 25(3):517 –528, april 2007.
[75] I. F. Akyildiz, Won-Yeol Lee, Mehmet C. Vuran, and Shantidev Mohanty. Next
BIBLIOGRAPHY 136
generation/dynamic spectrum access/cognitive radio wireless networks: a sur-
vey. Comput. Netw., 50(13):2127–2159, September 2006.
[76] C. Zou, T. Jin, C. Chigan, and Z. Tian. Qos-aware distributed spectrum sharing
for heterogeneous wireless cognitive networks. Computer Networks, 52(4):864–
878, March 2008.
[77] N. Nie and C. Comaniciu. Adaptive channel allocation spectrum etiquette for
cognitive radio networks. In Proceedings of the First IEEE International Sym-
posium onNew Frontiers in Dynamic Spectrum Access Networks (DySPAN),
pages 269–278, nov. 2005.
[78] D. Niyato and E. Hossain. A game-theoretic approach to competitive spectrum
sharing in cognitive radio networks. In Proceedings of the IEEE Wireless Com-
munications and Networking Conference (WCNC), pages 16–20, march 2007.
[79] R.S. Komali, A.B. MacKenzie, and R.P. Gilles. Effect of selfish node behavior on
efficient topology design. IEEE Transactions on Mobile Computing, 7(9):1057
–1070, Sept. 2008.
[80] S. Ahmad, Mingyan Liu, T. Javidi, Qing Zhao, and B. Krishnamachari. Opti-
mality of myopic sensing in multichannel opportunistic access. IEEE Transac-
tions on Information Theory, 55(9):4040–4050, sept. 2009.
[81] R. Olfati-Saber, J.A. Fax, and R.M. Murray. Consensus and cooperation in
networked multi-agent systems. Proceedings of the IEEE, 95(1):215 –233, jan.
2007.
BIBLIOGRAPHY 137
[82] B. Mercier, V. Fodor, R. Thobaben, M. Skoglund, V. Koivunen, S. Lind-
fors, J. Ryynanen, E.G. Larsson, C. Petrioli, G. Bongiovanni, O. Grondalen,
K. Kansanen, G. Oien, T. Ekman, A.M. Hayar, R. Knopp, and B. Beferull-
Lozano. Sensor Networks for Cognitive Radio: Theory and System Design.
Proceedings of the ICT Mobile and Wireless Communications Summit (ICT),
2008.
[83] T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Sochet. Novel type of
phase transition in a system of self-driven particles. Physical Review Letters,
75(6):1226, 1995.
[84] R. Olfati-Saber and R.M. Murray. Consensus problems in networks of agents
with switching topology and time-delays. IEEE Transactions on Automatic
Control, 49(9):1520–1533, 2004.
[85] L.M. Feeney. Investigating the energy consumption of a wireless network inter-
face in an ad hoc networking environment. In Proceedings of the 20th Annual
Joint Conference of the IEEE Computer and Communications Societies (IN-
FOCOM), pages 1548–1557, 2001.
[86] P. Hu and M. Ibnkahla. Consensus-based local control schemes for spectrum
sharing in cognitive radio sensor networks. In Proceedings of the 26th Biennial
Symposium on Communications (QBSC), pages 115–118, May 2012.
[87] P. Hu and M. Ibnkahla. A consensus-based protocol for spectrum sharing fair-
ness in cognitive radio ad hoc & sensor networks. In Proceedings of the 19th
IEEE International Conference on Communications (ICC), pages 93–97, June
2012.
BIBLIOGRAPHY 138
[88] P. Hu and M. Ibnkahla. A consensus-based protocol for spectrum sharing fair-
ness in cognitive radio ad hoc and sensor networks. International Journal of
Distributed Sensor Networks, 2012, 2012.
[89] V.S. Frost and B. Melamed. Traffic modeling for telecommunications networks.
IEEE Communications Magazine, 32(3):70–81, 1994.
[90] C. Corderio, K. Challapali, D. Birru, and S. Shankar. Ieee 802.22: an intro-
duction to the first wireless standard based on cognitive radios. Journal of
Communications, 1(1):38–47, 2006.
[91] C. Stevenson, G. Chouinard, Z. Lei, W. Hu, S. Shellhammer, and W. Caldwell.
Ieee 802.22: The first cognitive radio wireless regional area network standard.
IEEE Communications Magazine, 47(1):130–138, 2009.
[92] Y. Pei, Y. Liang, K. Teh, and K. Li. How much time is needed for wide-
band spectrum sensing? IEEE Transactions on Wireless Communications,
8(11):5466 –5471, november 2009.
[93] C. Bettstetter and C. Hartmann. Connectivity of wireless multihop networks
in a shadow fading environment. Wireless Networks, 11(5):571–579, 2005.
[94] S. Bandyopadhyay, E.J. Coyle, and T. Falck. Stochastic properties of mobility
models in mobile ad hoc networks. IEEE Transactions on Mobile Computing,
6(11):1218–1229, 2007.
[95] G. Bianchi. Performance analysis of the ieee 802.11 distributed coordination
function. IEEE Journal on Selected Areas in Communications, 18(3):535–547,
2000.
BIBLIOGRAPHY 139
[96] K. Duffy, D. Malone, and D.J. Leith. Modeling the 802.11 distributed coor-
dination function in non-saturated conditions. IEEE Communications Letters,
9(8):715–717, 2005.
[97] P. Hu and M. Ibnkahla. Cm-mac: A cognitive mac protocol with mobility
support in cognitive radio ad hoc networks. In Proceedings of the 19th IEEE
International Conference on Communications (ICC), pages 430–434, June 2012.
[98] F. Baccelli and B. Blaszczyszyn. Stochastic Geometry and Wireless Networks,
Part II: Applications. Now Publishers Inc, 2009.
[99] T.V. Nguyen and F. Baccelli. A probabilistic model of carrier sensing based
cognitive radio. In Proceedings of the 2010 IEEE Symposium on New Frontiers
in Dynamic Spectrum, pages 1 –12, 2010.
[100] Nguyen T.V. and F. Baccelli. Stochastic modeling of carrier sensing based
cognitive radio networks. In Proceedings of the 2010 Proceedings of the 8th
International Symposium on Modeling and Optimization in Mobile, Ad Hoc
and Wireless Networks (WiOpt), pages 472 –480, 312010-june4 2010.
[101] Tien Viet Nguyen and Franois Baccelli. A stochastic geometry model for cog-
nitive radio networks. The Computer Journal, 2011.
[102] D. Moltchanov. Distance distributions in random networks. Ad Hoc Networks,
10(6):1146 – 1166, 2012.
[103] M.J. Marcus. Unlicensed cognitive sharing of tv spectrum: the controversy
at the federal communications commission. IEEE Communications Magazine,
43(5):24 – 25, may 2005.
BIBLIOGRAPHY 140
[104] J. Riihijarvi and P. Mahonen. Exploiting spatial statistics of primary and sec-
ondary users towards improved cognitive radio networks. In Proceedings of the
3rd International Conference on Cognitive Radio Oriented Wireless Networks
and Communications (CrownCom), pages 1 –7, may 2008.
[105] S. Srinivasa and M. Haenggi. Distance distributions in finite uniformly random
networks: Theory and applications. IEEE Transactions on Vehicular Technol-
ogy, 59(2):940 –949, 2010.