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Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users
Yingzhe Li, Xinbing Wang, Xiaohua TianDepartment of Electronic EngineeringShanghai Jiao Tong University, China
Xue LiuSchool of Computer Science
McGill University, CA
1
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 22
OutlineOutline IntroductionIntroduction
BackgroundBackground MotivationMotivation ObjectivesObjectives
System Model System Model
Routing and Scheduling SchemeRouting and Scheduling Scheme
Capacity and Delay Scaling PerformanceCapacity and Delay Scaling Performance
ConclusionConclusion
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 33
BackgroundBackground
Cognitive Radio Network (CRN)Cognitive Radio Network (CRN) The underutilization of limited spectral resource motivates
the study of cognitive radio network.
Cognitive Radio Network consists of primary users (PUs) licensed to the spectrum, and secondary users (SUs) which access the spectrum opportunistically.
Due to the characteristics of cognitive radio network, the study of throughput and delay scaling laws in cognitive radio network is challenging.
4
BackgroundBackground The throughput scaling of cognitive radio network is investigated The throughput scaling of cognitive radio network is investigated
in [S. Jeon, 2009] and [C. Yin, 2010].in [S. Jeon, 2009] and [C. Yin, 2010]. Study overlapping static primary and secondary network,
where secondary network has higher node density. Both networks can achieve the same throughput scaling as
the stand-alone network.
[L. Gao, 2011] proves that [L. Gao, 2011] proves that cooperation cooperation among PUs and SUs among PUs and SUs can improve the throughput and delay scaling in CRN.can improve the throughput and delay scaling in CRN. Secondary users are willing to relay the primary packets. When SUs are mobile (i.i.d. mobility model), primary network
can achieve near constant throughput and delay scaling.
[S. Jeon, 2009]: S. Jeon, N. Devroye, M. Vu, S. Chung, and V. Tarokh, “Cognitive networks achieve throughput scaling of a homogeneous network, ” IEEE Trans. Info. Theory, to appear.
[C. Yin, 2010]: C. Yin, L. Gao, and S. Cui, “Scaling laws for overlaid wireless networks: A cognitive radio network vs. a primary network,” IEEE Trans. Networking, vol. 18, no. 4, Aug. 2010.[L. Gao, 2011]: L. Gao, R. Zhang, C. Yin, and S. Cui, “Throughput and Delay Scaling in Supportive Two-tier Networks ” to appear in JSAC 2011.
BackgroundBackground
[X. Wang, 2011] studies a static primary network and a multi-[X. Wang, 2011] studies a static primary network and a multi-layer mobile secondary network coexist in the network.layer mobile secondary network coexist in the network. The secondary network follows a special-designed
hierarchical i.i.d. mobility model, where SUs of different layer have different moving areas.
Near constant capacity and delay
scaling laws for primary network
can be achieved, i.e.
and .
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 5
)log
1()(
nnp
)(log)( 2 nnDp
[X. Wang, 2011]: X. Wang, L. Fu, Y. Li, Z. Cao and X. Gan, “Mobility Reduces the Number of Secondary Users in Cognitive Radio Network” in Proc. of IEEE GLOBECOM, 2011.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 66
Motivation & ObjectivesMotivation & Objectives
Motivated by the fact that:Motivated by the fact that: Cooperation and Mobility could significantly improve the
scaling laws in Cognitive Radio Network. Different mobile secondary nodes could have different
moving areas in Cognitive Radio Network (Mobility Heterogeneity).
We study: We study: A more general and representative mobility model which
reflects the mobility heterogeneity. The routing and scheduling schemes which utilize the mobility
heterogeneity of secondary users. The impact of mobility heterogeneity on the scaling laws of
Cognitive Radio Network
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 77
OutlineOutline IntroductionIntroduction
System Model System Model
Hierarchical Relay AlgorithmHierarchical Relay Algorithm
Performance Of The Hierarchical Relay Performance Of The Hierarchical Relay
AlgorithmAlgorithm
ConclusionConclusion
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 88
System model – I/VISystem model – I/VI
Network ModelNetwork Model:: n static primary users are randomly and evenly distributed in
the unit square area. mobile secondary users, where Source and destination are randomly grouped one by one in
each network. The unit square is divided into non-overlapping small square
cells, with side length , where .
1)1( nhm 0),(log nOh
N
Nr
log2 1nN
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 99
System model – II/VISystem model – II/VI Channel ModelChannel Model::
We apply the Gaussian Channel Model to regulate the transmission rate.
• The data rate from primary transmitter to primary receiver :
• : interference from other primary transmitters• : interference from all the secondary transmitters
• The data rate from secondary transmitter to secondary receiver is defined similarly.
)||)(||
1log(),(0
)()(
spp
iDipiDi IIN
PPgPPPR
iP)(iDP
pI
spI
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 10
System model – III/VISystem model – III/VI
Mobility Model for Secondary Users: SUs are uniformly and randomly
distributed at the beginning.
Each secondary user moves
within a circular region centered
at its initial position according to
i.i.d. mobility model.
10
System model – IV/VISystem model – IV/VI
Mobility Model for Secondary Users: Among all the secondary users, the moving
area of each mobile SU is , where follows the discrete uniform distribution:
• with equal probability .
• h=O(log n) and are random positive values, h and would determine the mobility heterogeneity together.
We call the SUs with the i-th type secondary user,
and each type consists of mobile secondary users.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 11
n
000 ,...,
2,,0
hh
1
1
hp
0 0
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i 0
1)1( nhm
1nN
System model – V/VISystem model – V/VI Mobility Model for Secondary Users:
• Denote the k-th secondary user of type i as , and its initial position as , where , .
• Under the proposed mobility model: , where
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 12
kiS ,
kiX , hi 0 11 nNk
ikiki RXS |||| ,,
)( 2/0 hii nR
System model – VI/VISystem model – VI/VI Definition of Throughput:
The throughput per S-D pair is defined as the average data rate (in bits/time-slot) that each source node can transmit to its chosen destination.
Definition of Delay: The delay of a packet is defined as the average number of
time-slots passed before the packet reaches its destination, after it leaves the source node.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 13
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 1414
OutlineOutline IntroductionIntroduction
System ModelSystem Model
Routing and Scheduling SchemeRouting and Scheduling Schemes Primary Network Routing Scheme Secondary Network Routing Scheme Scheduling Scheme
Capacity and Delay Scaling PerformanceCapacity and Delay Scaling Performance
ConclusionConclusion
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 1515
Primary Network Routing SchemePrimary Network Routing Scheme
Secondary users are willing to act as the relay nodes for primary packets.
Primary routing scheme utilizes the mobility heterogeneity of SUs to make the packet relayed by a chain of different type SUs.
We define the maximum type of SU that can be exploited to relay the primary packets. Definition 1: (Critical Relay Type) The critical relay type
is defined as: , where
*h}22|max{* rRih i hi ,...2,1,0
Primary Network Routing SchemePrimary Network Routing Scheme
The primary relay algorithm would utilize the SU relay nodes from type 0 to type h*:
In the first step, the primary source
node would transmit the packet to a
0-type SU. In the intermediate relay steps, the
(i-1)-th type SU which holds
the packet would relay it to an
i-th type SU , whose moving
area contains the primary
destination node. ( ) In the final step, the h*-type SU
which holds the packet would relay
the packet to the primary receiver.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 16
1,1 iuiS
iuiS ,
*1 hi
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 17
Secondary Network Routing SchemeSecondary Network Routing Scheme
For i-th type secondary source node and j-th type destination node , the secondary relay algorithm utilizes SU relay nodes from type 0 to type h’=min{ j,h* } : In the first step, the i-th type secondary source node would
transmit its packet to a 0-type SU. In the intermediate relay steps, the (i-1)-th type SU
which holds the packet would relay it to an i-th type SU ,whose moving area contains the initial position of destination node. ( )
In the final step, the h’-the type SU which holds the packet would relay it to the j-th type destination node, when they are encountered in the same cell.
ikiS ,
jkjS ,
1'0 hi
1,1 iuiS
iuiS ,
Scheduling SchemeScheduling Scheme
25-TDMA scheme is adopted. We define preservation region to
limit interference from SUs to PUs: Preservation region is a square that
contains 9 cells, with the active
primary transmitter in the center cell. Only SUs outside the current
preservation region could transmit
or relay packets. The scheduling scheme consists of 2h*+3 phases, the first
h*+1 phases would transmit the primary packets, the next h*+2 phases would transmit secondary packets.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 18
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 1919
OutlineOutline IntroductionIntroduction
System Model System Model
Routing and Scheduling SchemeRouting and Scheduling Scheme
Capacity and Delay Scaling PerformanceCapacity and Delay Scaling Performance Scaling Laws of Primary Network Scaling Laws of Secondary Network Optimal Performance of Primary Network Optimal Performance of Secondary Network Comparison with Previous Works
ConclusionConclusion
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 20
Scaling Laws of Primary NetworkScaling Laws of Primary Network
Lemma 5&6: In any cell, there are at most PUs and SUs of each type with high probability.
Lemma 7: During the routing process of primary packets, the primary transmitters and secondary relay nodes can support constant data rate in each cell.
Theorem 1: Under the proposed relay algorithm, the
primary network can achieve the following average per-
node throughput with high probability:
Theorem 2: Under the proposed primary relay algorithm,
the primary network can achieve the following average
delay with high probability:
)1
(hp
)1( )(log n
)log( 22)1( 00*
nnhhnD hhh
p
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 21
Scaling Laws of Secondary NetworkScaling Laws of Secondary Network
Lemma 9: During the routing process of secondary packets, the secondary transmitters and relay nodes can support a constant data rate in each cell.
Theorem 3: Under the proposed secondary relay algorithm, the secondary network can achieve the following per-node throughput with high probability:
Theorem 4: Under the proposed secondary relay algorithm, the secondary network can achieve the following average delay with high probability:
where j is the type of destination node.
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1(
2 nhs
),logloglog()1(
2222,
0'
0
nnhnnhnhOD h
h
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Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 22
The effect of mobility heterogeneity (i.e., h and ) on the capacity and delay scaling laws of primary network:
If , denote , the primary network could achieve the following average delay:
with the per-node throughput
Despite the throughput performance is optimal, but the delay performance is still suboptimal, since
Optimal Performance of Primary NetworkOptimal Performance of Primary Network
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log/loglog21
th
thh
p
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Optimal Performance of Primary NetworkOptimal Performance of Primary Network
If , denote , the
primary network can achieve the following average delay:
with the per-node throughput .
In this case, the delay performance can be improved when
increase from 0 to , until near-optimal delay performance is achieved.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 23
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nnth /11
log/loglog31'
'0
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),log(
),(log0
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Optimal Performance of Primary NetworkOptimal Performance of Primary Network
Curve for the relation between Delay/Capacity tradeoff and mobility heterogeneity:
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 24
Optimal Performance of Secondary NetworkOptimal Performance of Secondary Network
Similar to primary network, the secondary network can also achieve the optimal performance when
and : The secondary network can achieve the following average
delay:
with per-node throughput of
The secondary network can achieve the near-optimal delay-capacity tradeoff when the type of destination SUs satisfies:
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 25
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1
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),log(
),(log0
hjifnn
hjifnD
h
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3 ns
*hj
Comparison with Previous WorksComparison with Previous Works
Under optimal condition, this paper achieves near-constant capacity and delay scaling for primary and secondary network.
Compared with [13], this paper achieves better delay scaling for secondary network and requires less secondary users.
Compared with [14], this paper achieves better capacity and delay scaling for secondary network and adopts a more general and flexible mobility model.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 26
[13]: L. Gao, R. Zhang, C. Yin, and S. Cui, “Throughput and Delay Scaling in Supportive Two-tier Networks ” to appear in JSAC 2011. [14]: X. Wang, L. Fu, Y. Li, Z. Cao and X. Gan, “Mobility Reduces the Number of Secondary Users in Cognitive Radio Network” in Proc. of IEEE GLOBECOM, 2011.
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 2727
OutlineOutline IntroductionIntroduction
System Model System Model
Routing and Scheduling SchemeRouting and Scheduling Scheme
Capacity and Delay Scaling PerformanceCapacity and Delay Scaling Performance
ConclusionConclusion
Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users 28
Conclusion Conclusion We propose a more general mobility model which
reflects the mobility heterogeneity of secondary users in CRN.
We show the increase of mobility heterogeneity could improve the delay-capacity tradeoff for both primary network and secondary network.
Under optimal condition, the proposed algorithm can achieve near-constant capacity and delay scaling for primary network and part of secondary network
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