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

1. ACM CRAB 2013 On the Cascading Spectrum Contention Problem in Self-coexistence of Cognitive Radio Networks Lin Chen∗, KaiguiBian∗, Lin Chen†Wei Yan∗, and Xiaoming Li∗ ∗ Peking University, Beijing, China †UniversityParis-Sud, Orsay, France

2. Outline • Cascading spectrum contention problem • Problem formulation • Formulated as a sitepercolation problem • Main results • Conclusion and future work

3. Why cascading spectrum contention? • Root causes and feasibility

4. 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. Request BS (SRC) BS (DST) Win or not

5. 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 largestSCN

6. 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

7. Feasibility of cascading spectrum contentions • 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 http://www.ams.org/featurecolumn/images/august2008/triangular.shaded.jpg Cascades of contentions

8. Percolation and problem formulation A site percolation problem

9. 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

10. 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

11. Site Percolation • Each site is open with an independent probability . • Open cluster • Mean open cluster size Open cluster http://www.ams.org/featurecolumn/images/august2008/triangular.shaded.jpg

12. 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.

13. Applications of Percolation Theory • Connectivity of a network Let the probability that two neighboring nodes can communicate greater than • Disease of trees Keep 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

14. The percolation process describes The diffusion in a networked structure

15. 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., .

16. 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.

17. 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, squareand honeycomblattices. BSs placed on a lattice

18. Site percolation over a lattice • Each BS is affected (open) with . • Open cluster contains affected BSs • Mean open cluster size Open cluster of BSs http://www.ams.org/featurecolumn/images/august2008/triangular.shaded.jpg Diffusion of starvation in a lattice To describe the magnitude of the starvation

19. Analytical and numerical results • Starving probability, cluster size, etc

20. Lower bound of starving probability • Lower bound of starving probability • : the minimum probability that a 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

21. Theorem 2: Mean open cluster size M. Aizenman and C. M. Newman Tree Graph Inequalities and Critical Behavior in Percolation Models. Journal of Statistical Physics, 36(1/2):107–143, 1984 is a lattice, then for , ; and for , . Theorem 2: Mean open cluster size

22. Theorem 3: Criteria • is a lattice, • If , the spectrum contention protocol induces a global cascade of spectrum contentions with probability 1. • If • where is the modified critical probability, then the mean open cluster size . Theorem 3: Criteria

23. Theorem 4: Applicable 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 • e.g. suppose IEEE 802.22 contention resolution protocol is used, and let . If • ( ) • ( ) • ( ) a global cascade occurs.

24. Solution: cooperative or non-cooperative? • Biased contention resolution

25. Biased spectrum contention Protocol • Contention path • Reduce winning prob. for long contention paths • The longer path, the smaller winning prob. for a SRC.

26. 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

27. Numerical results

28. Numerical results (cont.)

29. 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.

30. anyquestions? • Thanks& 感谢观看

31. 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.

32. 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.

33. 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.

34. 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.

35. 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