Impact of Secondary Users Field Size on Spectrum Sharing - - PowerPoint PPT Presentation

Impact of Secondary Users’ Field Size on Spectrum Sharing Opportunities

Muhammad Aljuaid and Dr. Halim Yanikomeroglu

Department of Systems and Computer Engineering Carleton University

IEEE WCNC 2010

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Outline

Introduction Spectrum Sharing Harmful Interference Motivation System Model Characterization of the Aggregate Interference Mean of the Aggregate Interference Variance of the Aggregate Interference Upper Bound on the Interference Probability Spectrum Sharing Opportunities Effect of Field Expansion Effect of Exclusion Region Results Beyond WCNC10 Paper Cumulants of IA Effect of Field Size on the CCDF of IA

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Spectrum Sharing

◮ Radio spectrum: scarce resource but under-utilized. ◮ Spectrum sharing: a new spectrum management

paradigm.

◮ Sharing schemes: overlay & underlay.

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Harmful Interference

◮ Interference event vs. harmful interference. ◮ Different metrics to gauge harmful interference. ◮ These metrics ≡ f(system & channel parameters).

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Motivation

◮ Field size receives least attention. ◮ Usually infinite field size is assumed, e.g., in [Menon05],

[Menon06], [Ghassemi08] and [Win09].

◮ Impact of field size on spectrum sharing?

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Interference Characterization in Large Wireless Networks (1/2)

Literature Overview

◮ Many papers investigate interference in large wireless

networks using Poisson Point Process, e.g., [Sousa90], [Sousa92], [Ilow98], [Chan01], [Yang03], [Haenggi05], [Menon05], [Menon06], [Weber07], [Hasan07], [Ghasemi08], [Salbaroli09] and [Win09].

◮ Using a singular distance-dependent attenuation model

leads to having an alpha-stable distribution of the aggregate interference power. This distribution has a closed form expression for the characteristic function but not for the CDF/PDF except for one special case [Sousa90].

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Interference Characterization in Large Wireless Networks (2/2)

Literature Overview

◮ More realistic performance results are obtained by using

non-singular distance-dependent attenuation models [Inaltekin09].

◮ If an exclusion region is imposed around the victim receiver

• r a non-singular distance-dependent attenuation model is

used, the distribution of the aggregate interference power has a characteristic function in a closed form expression.

◮ However, no closed form expression is known for the

distribution function. A numerical inversion of the characteristic function is an option.

◮ Alternatively, approximating the distribution of the

aggregate interference using a finite set of moments (or cumulants) is a viable option.

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Our Approach and Contributions

◮ We consider a finite field with an exclusion region (an

infinite field is a special case of our results).

◮ First, we investigate the effect of field size on spectrum

sharing by deriving an upper bound on the interference probability using the first two cumulants, i.e., mean and variance.

◮ Then, we extend cumulants formulations provided in

[Menon06], and approximate the distribution of the aggregate interference based on a finite set of these cumulants.

◮ Finally, we repeat the investigation of the effect of the field

size on spectrum sharing opportunities utilizing the approximation of the distribution of the aggregate interference.

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System Model

◮ Field of secondary users sharing a

spectrum with a primary user.

◮ Aggregate interference power:

IA =

• i∈N

Ii =

• i∈N

r−n

i

Wi

◮ Analysis objective:

Investigate effect of L on IA and spectrum sharing.

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Interference Probability

A harmful interference metric [Ghasemi08] and [Win09]

◮ Non-harmful interference:

P(IA ≥ Ith) ≤ β ⇒ spectrum sharing allowed

◮ Harmful interference:

P(IA ≥ Ith) > β ⇒ spectrum sharing NOT allowed

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Mean of the Aggregate Interference

Formulation

◮ Mean of IA (i.e., i∈N r−n i

Wi): µA = 1 n − 2 Dθr2−n

• µW

×

• 1 −
• ro

ro + L n−2

◮ For L << ro:

µA ≃ Dθro1−nL µW

◮ For L >> ro:

µA ≃ 1 n − 2 Dθr2−n

• µW

11/22 D: Density of active nodes n: Path loss exponent Wi ’s are i.i.d. µW = E[Wi ]

Mean of the Aggregate Interference

Effect of Field Size

10

1

10

2

10

3

10

4

10

5

10

−14

10

−13

10

−12

10

−11

L (m) mean of the aggregate interference (Watt)

12/22 For L ≫ ro: An increase in L has no significant effect on mean. For L ≪ ro: 10 dB increase in L leads to 10 dB increase in mean.

Variance of the Aggregate Interference

Formulation

◮ Variance of IA (i.e., i∈N r−n i

Wi): σ2

A =

1 2n − 2 Dθr2−2n

• µ2

W(1 + σ2 W

µ2

W

) ×

• 1 −
• ro

ro + L 2n−2

◮ For L << ro:

σ2

A ≃ Dθr1−2n

• L µ2

W(1 + σ2 W

µ2

W

)

◮ For L >> ro:

σ2

A ≃

1 2n − 2 Dθr2−2n

• µ2

W(1 + σ2 W

µ2

W

)

13/22 D: Density of Active Nodes n: Path loss exponent Wi ’s are i.id. µW = E[Wi ] σ2

W =Var(Wi)

Variance of the Aggregate Interference

Effect of Field Size

10

1

10

2

10

3

10

4

10

5

10

−30

10

−29

10

−28

10

−27

L (m) Variance of the aggregate interference power

14/22 For L ≫ ro: An increase in L has no significant effect on variance. For L ≪ ro: 10 dB increase in L leads to 10 dB increase in variance.

Upper Bound on the Interference Probability

Formulation

◮ Based on Chebyshev inequality, interference probability is

bounded by: P(IA ≥ Ith) ≤ σ2

A

(Ith − µA)2

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Effect of Field Expansion

10

1

10

2

10

3

10

4

10

5

−110 −100 −90 −80 −70 L (m) Ith (dBm)

β = 10−1 β = 10−2 β = 10−3 β = 10−4 Zone 4: Non-Interfering Region; Field is always in the non-interfering region regardsless of its size (L). Zone 2: Interfering Region; Decreasing the field size (L) may move the field to the non-interfering region. Zone 1: Interfering Region; Field is always in the interfering region regardless of L. Zone 3: Non-Interfering Region; increasing L may move the field to the interfering region.

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Effect of Exclusion Region

10

1

10

2

10

3

10

4

10

5

−110 −100 −90 −80 −70 −60 −50 −40 ro (m) Ith (dBm)

β = 10−1 β = 10−2 β = 10−3 β = 10−4 17/22 Non-Interfering Region Interfering Region

Cumulants of IA

◮ Cumulants of IA (i.e., i∈N r−n i

Wi): κm(IA) = 1 nm − 2Dθ˜ µm(W)r2−mn

• ×
• 1 −
• ro

ro + L mn−2

◮ For L << ro:

κm(IA) ≃ Dθro1−mnL ˜ µm(W)

◮ For L >> ro:

κm(IA) ≃ 1 nm − 2Dθ˜ µm(W)r2−mn

• 18/22

D: Density of active nodes n: Path loss exponent Wi ’s are i.i.d. ˜ µm(W) = E[W m

i ]

Effect of Field Size on the CCDF of IA

Simulation

0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 IA CCDF L=10 meters L=100 meters L=1000 meters L=10000 meters

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Effect of Field Size on Spectrum Sharing (2)

10

1

10

2

10

3

10

4

10

−4

10

−3

10

−2

10

−1

10 L (meters) Interference Probability Ith= 0.004 Ith= 0.007 Ith= 0.009 Non−Interfering Region Interfering Region

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Summary

◮ Asymptotic results for infinite fields:

◮ Applicable for finite but relatively large fields. ◮ Too conservative otherwise.

◮ Spectrum sharing vs. field size:

◮ In some cases, small reduction in size may create spectrum

sharing opportunities.

◮ In some other cases, huge increase in size may not

eliminate spectrum sharing opportunities.

◮ In certain cases, concurrent and continuous spectrum

sharing is possible without the need for cognitive radio functionalities.

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Thank you

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