Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users Yingzhe Li,...

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


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 .


)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.


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




Hierarchical Relay AlgorithmHierarchical Relay Algorithm

Performance Of The Hierarchical Relay Performance Of The Hierarchical Relay

AlgorithmAlgorithm



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


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


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.


n

000 ,...,

2,,0

hh

1

1

hp

0 0

h

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


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.




System ModelSystem Model

Routing and Scheduling SchemeRouting and Scheduling Schemes Primary Network Routing Scheme Secondary Network Routing Scheme Scheduling Scheme




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.


1,1 iuiS

iuiS ,

*1 hi


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.






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



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 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.

)log

1(

2 nhs

),logloglog()1(

2222,

0'

0

nnhnnhnhOD h

h

hjs


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

)1(hh

nnth /11

log/loglog21

th

thh

p

ifn

ifnnD

01

02

),(

),log(0

0

)1(p

)log( npolyDp

0


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.


)(log nh h

nnth /11

log/loglog31'

'0

1

'04

),log(

),(log0

th

thp

ifnn

ifnD

)log

1(

np

0 'th


Curve for the relation between Delay/Capacity tradeoff and mobility heterogeneity:


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:


)(log nh 10

*3

1

*4

),log(

),(log0

hjifnn

hjifnD

h

jp

)log

1(

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.


[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.


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


Thank you !Thank you !

Scaling Laws for Cognitive Radio Network with Heterogeneous Mobile Secondary Users Yingzhe Li,...

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