Institute of Network Computing and Information Systems On the Cascading Spectrum Contention Problem...

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Institute of Network Computing and Information Systems On the Cascading Spectrum Contention Problem in Self- coexistence of Cognitive Radio Networks Lin Chen , Kaigui Bian , Lin Chen Wei Yan , and Xiaoming Li Peking University, Beijing, China University Paris-Sud, Orsay, France ACM CRAB 2013

Transcript of Institute of Network Computing and Information Systems On the Cascading Spectrum Contention Problem...

Institute of Network Computing and Information Systems

On the Cascading Spectrum Contention Problem in Self-coexistence of Cognitive Radio Networks

Lin Chen∗, Kaigui Bian∗, Lin Chen†

Wei Yan∗, and Xiaoming Li∗

∗ Peking University, Beijing, China † University Paris-Sud, Orsay, France

ACM CRAB 2013

Outline

• Cascading spectrum contention problem• Problem formulation

– Formulated as a site percolation problem• Main results• Conclusion and future work

Why cascading spectrum contention?

Root causes and feasibility

Inter-BS spectrum contention in cognitive radio (CR) networks

• IEEE 802.22: the first worldwide wireless standard based on CR technology

• A starving Base Station (BS) in need of spectrum can initiate an inter-BS spectrum contention process to acquire more channels from neighboring BSs to satisfy the QoS of its workload.

BS (SRC) BS (DST)

Request

Win or not

Who is the winner?

• The Unbiased Contention Resolution Rule• Every BS (either SRC or DST) is required to select

a Spectrum Contention Number (SCN) that is uniformly distributed in the range and exchange the SCN values.

• Winner = the one that has the largest SCN

Causes for a starving BS

• There are three causes that make a BS starving– Channels reclaimed by the primary

user;– The increase of spectrum demand due to

increased intra-cell workload;

– Losing channels due to spectrum contentions.

Non-contention cause

Contention cause

Feasibility of cascading spectrum contentions

http://www.ams.org/featurecolumn/images/august2008/triangular.shaded.jpg

• Every DST BS is willing to accept the contention requests.

• It is possible that – A DST loses channels– It starts new contentions

• Cascade: a series of events

Cascades of contentions

Percolation and problem formulation

A site percolation problem

Percolation

• In this paper, we use the percolation theory.• What is the percolation theory?• What is the application of the percolation theory

in the network theory?

http://pages.physics.cornell.edu/~myers/teaching/ComputationalMethods/ComputerExercises/Fig/BondPercolation_10_0.4_1.gif

http://audiobrad.com/wp-content/uploads/2012/02/Water-Cycle-Percolation.jpg

Bond Percolation

• Each bond is open with an independent probability .

http://pages.physics.cornell.edu/~myers/teaching/ComputationalMethods/ComputerExercises/Fig/BondPercolation_10_0.4_1.gif

Site Percolation

http://www.ams.org/featurecolumn/images/august2008/triangular.shaded.jpg

• Each site is open with an independent probability .

• Open cluster• Mean open cluster

size

Open cluster

Phase Transition: Percolation Threshold• Percolation threshold:• If , there exists

no infinite open cluster with probability 1.

• If , there exists an infinite open cluster with probability 1.

Applications of Percolation Theory

• Connectivity of a networkLet the probability that two neighboring nodes can communicate greater than

• Disease of treesKeep the distance of two neighboring trees so that the probability that a diseased tree communicates the disease to its neighbor is less than

http://pages.physics.cornell.edu/~myers/teaching/ComputationalMethods/ComputerExercises/Fig/BondPercolation_10_0.4_1.gif

The percolation process describes

The diffusion in a networked structure

Spectrum/service requirement

• Every BS requires channels to satisfy the QoS of its admitted workload.

• : service requirement of BS , depending on the intra-cell traffic demand raised by the secondary users, or SUs (i.e., CPEs).

• : the set of channels that are occupied by BS . • Neighboring BSs and occupy disjoint sets of

channels, i.e., .

Network state

• Starving BS:• Satisfied BS:• Every BS tries to claim as many unoccupied

channels as possible until or there is no unoccupied channels that can be claimed.

• Starving BS = a contention will be initiated.

BS placement on a lattice

• In an 802.22 system, the rural area is divided into regular shaped cells, which can be hexagonal, square, or some other irregular shapes.

• We generalize them to the notion of lattice.• Three common types of lattices are triangular,

square and honeycomb lattices.

BSs placed on a lattice

Site percolation over a lattice

http://www.ams.org/featurecolumn/images/august2008/triangular.shaded.jpg

• Each BS is affected (open) with .

• Open cluster contains affected BSs

• Mean open cluster size

Open cluster of BSs

Diffusion of starvation in a lattice

To describe the magnitude of the starvation

Analytical and numerical results

Starving probability, cluster size, etc

Lower bound of starving probability

• Lower bound of starving probability

• : the minimum probability thata BS becomes starving due to non-contention reasons.• : the degree of each vertex• : the winning probability of the contention

source in a pairwise contention• : the number of pairwise contentions initiated

by a SRC in each spectrum contention process

is a lattice, then for , ; and for , .

Theorem 2: Mean open cluster size

Theorem 2: Mean open cluster size

M. Aizenman and C. M. NewmanTree Graph Inequalities and Critical Behavior in Percolation Models. Journal of Statistical Physics, 36(1/2):107–143, 1984

is a lattice, 1. If , the spectrum contention protocol induces a

global cascade of spectrum contentions with probability 1.2. If

where is the modified critical probability, then the mean open cluster size .

Theorem 3: Criteria

Theorem 3: Criteria

is a lattice with vertex degree . A spectrum contention protocol induces the mean open cluster size if

where and are constants for the given .

Theorem 4: Applicable Criteria

Theorem 4: Applicable criteria

• e.g. suppose IEEE 802.22 contention resolution protocol is used, and let . If – ( ) – ( )– ( )

a global cascade occurs.

Solution: cooperative or non-cooperative?

Biased contention resolution

Biased spectrum contention Protocol

• Contention path

• Reduce winning prob. for long contention paths

• The longer path, the smaller winning prob. for a SRC.

Theorem 6

There is no infinite contention path if the biased contention resolution rule is used for contention resolution in the case of .

Theorem 6: Finite Cluster Size

li = length of contention path

Numerical results

Numerical results (cont.)

Conclusions and further work

• Formulation of cascading spectrum contentions using percolation

• Biased spectrum contention resolution rule

• The (lower bound) estimation of can be replaced by scaling relations.

• The state of each BS can be more precisely characterized by a stochastic process, e.g. Markov chain.

any questions?

Thanks & 感谢观看

Contention Source

• Every contention source BS includes the target channel number , its SCN chosen from , and the current length of the contention path measured by BS .

• If the BS does not belong to any contention path, it sets , which implies that it is the starting vertex of a new contention path.

Contention Destination

• Every contention destination BS checks the values of and SCN in the contention request from the contention source BS .

• Let denote the set of contention sources that send contention requests to BS during a self-coexistence window.

Contention Destination (Cont.)

• If , BS is being reached by more than one contention paths.

• The contention destination BS measures its as , and generates its own SCN from a modified contention window .

• The measured value of will be used by BS in future contention requests if it becomes a contention source.

Spectrum Contention Resolution

• If the contention destination BS has the greatest SCN value, it wins the contention.

• Otherwise, the contention source who has the greatest SCN value wins, and the contention destination BS releases the target channel.

Theorem 1 (cont.)

• Properties of lower bound function– – A strictly increasing function with respect to , and .– A strictly decreasing function with respect to .– With fixed, a strictly increasing function with respect

to . – – , , and