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 1/22
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 I A Effect of Field Size on the CCDF of I A 2/22
Spectrum Sharing ◮ Radio spectrum: scarce resource but under-utilized. ◮ Spectrum sharing: a new spectrum management paradigm. ◮ Sharing schemes: overlay & underlay. 3/22
Harmful Interference ◮ Interference event vs. harmful interference. ◮ Different metrics to gauge harmful interference. ◮ These metrics ≡ f (system & channel parameters). 4/22
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? 5/22
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]. 6/22
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 or 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. 7/22
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. 8/22
System Model ◮ Field of secondary users sharing a spectrum with a primary user. ◮ Aggregate interference power: r − n I A = I i = W i � � i i ∈ N i ∈ N ◮ Analysis objective: Investigate effect of L on I A and spectrum sharing. 9/22
Interference Probability A harmful interference metric [Ghasemi08] and [Win09] ◮ Non-harmful interference: P ( I A ≥ I th ) ≤ β ⇒ spectrum sharing allowed ◮ Harmful interference: P ( I A ≥ I th ) > β ⇒ spectrum sharing NOT allowed 10/22
Mean of the Aggregate Interference Formulation i ∈ N r − n ◮ Mean of I A (i.e., � W i ): i 1 n − 2 D θ r 2 − n µ A = µ W o D : Density of active nodes n : Path loss exponent � n − 2 � � r o W i ’s are i.i.d. � µ W = E [ W i ] 1 − × r o + L ◮ For L << r o : µ A ≃ D θ r o 1 − n L µ W ◮ For L >> r o : 1 n − 2 D θ r 2 − n µ A ≃ µ W o 11/22
Mean of the Aggregate Interference Effect of Field Size −11 10 For L ≫ r o : An increase in L has no mean of the aggregate interference (Watt) significant effect on mean. −12 10 −13 10 For L ≪ r o : 10 dB increase in L leads to 10 dB increase in mean. −14 10 1 2 3 4 5 10 10 10 10 10 L (m) 12/22
Variance of the Aggregate Interference Formulation i ∈ N r − n ◮ Variance of I A (i.e., � W i ): i W ( 1 + σ 2 1 2 n − 2 D θ r 2 − 2 n W σ 2 µ 2 A = ) o µ 2 W D : Density of Active Nodes � 2 n − 2 � � r o n : Path loss exponent � W i ’s are i.id. 1 − × µ W = E [ W i ] r o + L σ 2 W = Var( W i ) ◮ For L << r o : W ( 1 + σ 2 A ≃ D θ r 1 − 2 n W L µ 2 σ 2 ) o µ 2 W ◮ For L >> r o : W ( 1 + σ 2 1 2 n − 2 D θ r 2 − 2 n W σ 2 µ 2 ) A ≃ o µ 2 W 13/22
Variance of the Aggregate Interference Effect of Field Size −27 10 Variance of the aggregate interference power For L ≫ r o : An increase in L has no significant effect on variance. −28 10 −29 10 For L ≪ r o : 10 dB increase in L leads to 10 dB increase in variance. −30 10 1 2 3 4 5 10 10 10 10 10 L (m) 14/22
Upper Bound on the Interference Probability Formulation ◮ Based on Chebyshev inequality, interference probability is bounded by: σ 2 A P ( I A ≥ I th ) ≤ ( I th − µ A ) 2 15/22
Effect of Field Expansion −70 β = 10 − 1 Zone 4: Non-Interfering Region; β = 10 − 2 Field is always in the non-interfering region β = 10 − 3 regardsless of its size ( L ). β = 10 − 4 −80 Zone 3: Non-Interfering Region; increasing L may move the field to the interfering region. I th (dBm) Zone 2: Interfering Region; −90 Decreasing the field size ( L ) may move the field to the non-interfering region. −100 Zone 1: Interfering Region; Field is always in the interfering region regardless of L . −110 1 2 3 4 5 10 10 10 10 10 L (m) 16/22
Effect of Exclusion Region −40 β = 10 − 1 β = 10 − 2 Non -Interfering Region −50 β = 10 − 3 β = 10 − 4 −60 −70 I th (dBm) −80 −90 −100 Interfering Region −110 1 2 3 4 5 10 10 10 10 10 r o (m) 17/22
Cumulants of I A i ∈ N r − n ◮ Cumulants of I A (i.e., � W i ): i 1 µ m ( W ) r 2 − mn κ m ( I A ) = nm − 2 D θ ˜ o D : Density of active nodes n : Path loss exponent � mn − 2 � � r o W i ’s are i.i.d. � µ m ( W ) = E [ W m ˜ i ] 1 − × r o + L ◮ For L << r o : κ m ( I A ) ≃ D θ r o 1 − mn L ˜ µ m ( W ) ◮ For L >> r o : 1 µ m ( W ) r 2 − mn κ m ( I A ) ≃ nm − 2 D θ ˜ o 18/22
Effect of Field Size on the CCDF of I A Simulation 1 L=10 meters 0.9 L=100 meters L=1000 meters 0.8 L=10000 meters 0.7 0.6 CCDF 0.5 0.4 0.3 0.2 0.1 0 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 I A 19/22
Effect of Field Size on Spectrum Sharing (2) 0 10 Interfering Region −1 10 Interference Probability Non−Interfering Region −2 10 I th = 0.004 −3 10 I th = 0.007 I th = 0.009 −4 10 1 2 3 4 10 10 10 10 L (meters) 20/22
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. 21/22
Thank you 22/22
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