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

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 .


Site Percolation


• 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


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


• 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

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