interference in cognitive radio networks chia han lee

7/31/2019 Interference in Cognitive Radio Networks Chia Han Lee

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IntroductionApproximations

ExamplesConclusions

Interference in Cognitive Radio Networks

Chia-han LeeUniversity of Notre Dame

2nd Annual North American School of Information Theory,Evanston, IL, August 10-13, 2009

Chia-han Lee Interference to cognitive radio networks

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ExamplesConclusions

Outline

1 IntroductionModelMotivation

2 ApproximationsApproximating hole process using cluster processInterference to primary usersInterference to cognitive users

3 Examples

4 Conclusions


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ExamplesConclusions

ModelMotivation

Model

We consider a network which has two groups of users: primaryusers (PU) and cognitive users (CU).

The locations of the primary users and the cognitive usersfollow two independent Poisson point processes (PPP) Φp andΦc with density λp and λc , respectively.

Cognitive users are allowed to transmit only when there is no

primary user within a distance D . Cognitive users who aretransmitting: active cognitive users.


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ExamplesConclusions

ModelMotivation

Motivation

The interference in such network is hard to analyze becausethe process by the primary users (PPP) and the processformed by the active cognitive users (called“hole process ”

here) are not independent.

Approximations for hole process need to be performed!Cluster process seems to be a good candidate.

The overall process is approximated by two independent

processes. In this way, the Laplace transform of theinterference is simply the product of the Laplace transforms of these two independent processes.


I d i

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ExamplesConclusions

ModelMotivation

Example

−8 −6 −4 −2 0 2 4 6 8−8

−6

−4

−2

0

2

4

6

8

Figure: Example of hole process.


I t d ti

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ExamplesConclusions

Approximating hole process using cluster processInterference to primary usersInterference to cognitive users

Hole Process vs. Cluster Process

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.2

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0.6

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1

1.2

1.4

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r

L ( r )

L(r)

Hole on

Cluster (Matern)

Cluster (Thomas)

Ideal PPP

Figure: Modeling hole process using cluster process, D = 0.6, σ = 1.5D .

Metric: L-function (normalization of K -function).

λK (r ) = φ(B 0(r )P !0(d φ), L(r ) =

K (r )π

.

Thomas process is a better choice than Matern process.Chia-han Lee Interference to cognitive radio networks

Introduction

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ExamplesConclusions


Hole Process vs. Cluster Process

−8 −6 −4 −2 0 2 4 6 8−8

−6

−4

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8Hole process

−8 −6 −4 −2 0 2 4 6 8−10

−8

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10Thomas cluster process

(a) (b)

Figure: Examples: (a) Nodes formed by hole process. (b) Nodes formedby Thomas cluster process.


Introduction

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ExamplesConclusions


Interference to Primary Users

Interference from other primary users

Simply a PPP.

Interference from cognitive users

Form a cluster process with a parent point at the origin.Exclude nodes within range of D − Z p , where Z p is the

location of the desired primary receiver.


Introduction

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ExamplesConclusions


Interference to Cognitive Users

Interference from primary users

PPP, except that there should not be any users within therange of D .The same as CSMA-type MAC scheme.

Interference from other cognitive users

Use cluster process.


Introduction

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ExamplesConclusions

Simulation Setup

The desired primary transmitter is placed at the origin, andthe desired primary receiver is placed at (0, D /2).

We randomly pick one cognitive node as the receiver andother nodes as interfering transmitters.

Setup:

λp = 0.97, λc = 3.Transmission power of primary users = 1, and transmission

power of cognitive users = 0.01.Path loss factor α = 4, and path loss model g (x ) = x

−α.Mean amplitude of Rayleigh fading E {h} = 1.


Introduction

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ApproximationsExamples

Conclusions

Example 1

0 10 20 30 40 50 60 70 80 90 1000

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Interference

C C D

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Interference between CU

Actual CU

Matern as CU

Thomas as CU

0 10 20 30 40 50 60 70 80 90 1000

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Interference

C C D

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Actual interference to PU

Approximation (Matern) interference to PUApproximation (Thomas) interference to PU

Actual interference to CUApproximation (Matern) interference to CU

Approximation (Thomas) interference to CU

(a) (b)

Figure: (a) CCDF of the interference between cognitive users whenD = 0.3. (b) CCDF of the intereference to primary users and cognitiveusers when D = 0.3.


Introduction

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Conclusions

Example 2

0 10 20 30 40 50 60 70 80 90 1000

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Interference

C C D

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Interference between CU

Actual CU

Matern as CU

Thomas as CU

0 10 20 30 40 50 60 70 80 90 1000

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Interference

C C D

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Actual interference to PU

Approximation (Matern) interference to PUApproximation (Thomas) interference to PU

Actual interference to CUApproximation (Matern) interference to CU

Approximation (Thomas) interference to CU

(a) (b)

Figure: (a) CCDF of the interference between cognitive users whenD = 0.6. (b) CCDF of the intereference to primary users and cognitiveusers when D = 0.6.


Introduction

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Conclusions

Concluding Remarks and Future work

Concluding remarks:

The cluster process gives good approximations of the hole

process in the cognitive radio network. In particular, theThomas cluster process models better than the Matern clusterprocess.The overall interference can be well approximated by twoindependent processes.

Future work:Derive the bounds for this approximation.


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interference in cognitive radio networks chia han lee

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