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