Spectrum Underlay Cognitive Radio Networks / John George Sobhy Tadrous

Supervisor: Ahmed Sultan

Thesis (M.A.)—Nile University, Egypt, 2010 .

"Includes bibliographical references"

Contents:
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Dynamic Spectrum Access and Cognitive Radios . . . . . . . . . . 1
1.2 Spectrum Underlay Model . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Admission and Power Control . . . . . . . . . . . . . . . . . 4
1.2.2 Achievable Rates . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Main Contributions and Thesis Outlines . . . . . . . . . . . . . . . 10
2. Admission and Power Control . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1 System Model and Problem Formulation . . . . . . . . . . . . . . . 14
2.1.1 Primary Network Model . . . . . . . . . . . . . . . . . . . . 15
2.1.2 Secondary Network Model . . . . . . . . . . . . . . . . . . . 16
2.2 Maximizing the Number of Admitted Links . . . . . . . . . . . . . 19
2.2.1 DCPC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Distributed Online Algorithm . . . . . . . . . . . . . . . . . 22
x
2.2.3 Handling Events 2 or 3 . . . . . . . . . . . . . . . . . . . . . 25
2.2.4 Implementation Issues . . . . . . . . . . . . . . . . . . . . . 28
2.2.5 Algorithm Summary . . . . . . . . . . . . . . . . . . . . . . 29
2.3 Maximization of the Sum Throughput . . . . . . . . . . . . . . . . 30
2.3.1 Geometric Programming (GP) . . . . . . . . . . . . . . . . 32
2.3.2 Iterative Solutions . . . . . . . . . . . . . . . . . . . . . . . 33
2.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Admission Control Algorithm . . . . . . . . . . . . . . . . . 38
2.4.2 Throughput Performance . . . . . . . . . . . . . . . . . . . 40
3. Joint Power Allcoation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1 System Model and Problem Formulation . . . . . . . . . . . . . . . 49
3.2 Proposed Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.1 Distributed Ternary Power Allocation . . . . . . . . . . . . 51
3.2.2 Centralized Enhancement . . . . . . . . . . . . . . . . . . . 55
3.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3.1 Comparison with Greedy Algorithm . . . . . . . . . . . . . 59
3.3.2 Successive GP . . . . . . . . . . . . . . . . . . . . . . . . . 60
4. Achievable Rates: No Interference Cancellation at the Secondary . . . . 63
4.1 Basic Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.1.1 Treating Interference as Noise . . . . . . . . . . . . . . . . . 66
4.1.2 Interference Cancellation at the BS . . . . . . . . . . . . . . 68
4.2 Rate-Splitting Channel . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.3 Achievable Rate Region for CRS . . . . . . . . . . . . . . . . . . . . 76
4.4 Performance of Rate-Splitting in the Gaussian Channel . . . . . . . 82
5. Effect of Interference Cancellation by the Secondary . . . . . . . . . . . . 88
5.1 Rate-Splitting Channel with Decodable Primary Signal at the Secondary
Receiver Cp
RS . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.2 Achievable Rate Region for Cp
RS . . . . . . . . . . . . . . . . . . . . 90
5.3 Achievable Rate Region for the Channel CB . . . . . . . . . . . . . 96
5.4 Gaussian Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.4.1 Performance of Rate-Splitting . . . . . . . . . . . . . . . . . 98
5.4.2 On Decoding One Primary Signal . . . . . . . . . . . . . . . 100
6. Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . 103
Appendices:
xi
A. Rate Achievability Proof for Rate-Splitting Channel CRS . . . . . . . . . 108
A.1 Random Code Generation . . . . . . . . . . . . . . . . . . . . . . . 108
A.2 Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
A.3 Decoding: Jointly-Typical Decoding . . . . . . . . . . . . . . . . . 109
A.4 Probability of Error Analysis . . . . . . . . . . . . . . . . . . . . . 109
A.4.1 For the Primary Receiver . . . . . . . . . . . . . . . . . . . 109
A.4.2 For the Secondary Receiver . . . . . . . . . . . . . . . . . . 110
B. Rate-Splitting in Gaussian Channel without Interference Cancellation at
the Secondary Receiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
B.1 Sufficiency Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
B.2 Necessity Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
C. Proof of Primary Decodability Condition (PDC) . . . . . . . . . . . . . . 114
C.1 Sufficiency Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
C.1.1 Proof of RAo
p = RAr
p . . . . . . . . . . . . . . . . . . . . . . 114
C.1.2 Proof of RBo
s ≤ RBr
s . . . . . . . . . . . . . . . . . . . . . . 115
C.1.3 Proof of RFr
s ≥ RDo
s . . . . . . . . . . . . . . . . . . . . . . 117
C.1.4 Proof of the intersection point between the two lines 2Rs +
Rp = ρr
2p and Rs +Rp = ρo sp occurs at a point (R∗
s,R∗
p) where
R∗
s ≥ RDo
s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
C.2 Necessity Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
D. Proof of Theorem 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
D.1 For Ro(Z) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
D.2 For R′r
1 (Z) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
E. Performance of Rate-Splitting and Interference Cancellation by the Secondary
in Gaussian Channel . . . . . . . . . . . . . . . . . . . . . . . . . 125
E.1 Sufficiency part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
E.1.1 At Point A . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
E.2 At Point F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
E.3 Rr
s + Rrp
= ρr
sp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
E.4 Rr
s + 2Rrp
= ρr
s2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
E.5 2Rr
s + Rrp
= ρr
2p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
E.6 Necessity Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
E.6.1 At Point A . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
E.6.2 At Point F . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Bibliography . . . . . . . . . . . . . .

Abstract:
This thesis discusses the spectrum underlay paradigm in cognitive radio networks.
In this paradigm cognitive radios, or secondary users, are allowed to transmit concurrently
with the licensed users, or primary users, over the same channel. The main aim
of this scheme is to enhance the utilization of the licensed bands. However, the secondary
users may create excessive interference on the primary links, and this in turn
would reduce the quality of service (QoS) of such links. For this reason, secondary
users may transmit concurrently with the primary users under some interference constraint
that guarantees a certain degree of QoS for the primary network.
In this thesis, resource allocation for cognitive radios in spectrum underlay paradigm
is considered in terms of admission and power control. Moreover, an information theoretic
approach to characterize the achievable rates of such an underlay cognitive
network is developed. In the resource allocation framework, an optimization problem
that aims at maximizing the sum throughput of the secondary links under interference
constraint on the primary receivers and minimum QoS requirements for each
secondary link is considered. The problem is divided into two main subproblems.
The first one deals with the feasibility of the network, in which an admission control
algorithm that maximizes the number of admitted links into the network is proposed.
Whereas, the second is the throughput maximization problem for the admitted links
under the aforementioned constraints, where a solution based on sequential geometric
iv
programming (GP) is developed. The sum throughput maximization problem is then
extended to consider power allocation of maximizing the overall some throughput of
the primary and secondary networks.
Afterwards, the potential achievable rates for a simple model of underlay cognitive
networks (consists of a single secondary link and two primary links) have been characterized
from an information theoretic perspective. The main approach is to establish
an achievable rate region that depicts the sum rate of the primary network versus the
throughput of the secondary link. The secondary link is assumed to perform ratesplitting
so that the primary network can decode and cancel part of the interference
created from the secondary link. Moreover, the secondary receiver is assumed to be
able decode the signal of one primary transmitter and cancels its interference such
that the sum primary rate is not affected. A necessary and sufficient condition on
the satisfaction of the above constraint is introduced. Furthermore, the performance
of rate-splitting by the secondary link is investigated in a Gaussian setup.

Text in English, abstracts in English.