1. Lin Chen∗, Kaigui Bian∗, Lin Chen† Wei Yan∗, and Xiaoming Li∗
ACM CRAB 2013
On the Cascading Spectrum Contention Problem in Self-coexistence of Cognitive Radio Networks
Lin Chen∗, Kaigui Bian∗, Lin Chen† Wei Yan∗, and Xiaoming Li∗
Add page number to each slide in upper-right corner.
∗ Peking University, Beijing, China
† University Paris-Sud, Orsay, France

2. Outline Cascading spectrum contention problem Problem formulation
Formulated as a site percolation 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 : 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
Contention msg exchange between BSs
BS (SRC)
BS (DST)
Win or not

5. Winner = the one that has the largest SCN
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
W is contention window size.
Other BSs that fail to win will vacate the channel.

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
In this figure, local contention  neighbors lose channels  it starts new contention against its neighbors
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?
Let me introduce a few terms first. Most of you might be familiar w/ these.

10. Bond Percolation Each bond is open with an independent probability .

11. Site Percolation Open cluster
Each site is open with an independent probability .
Open cluster
Mean open cluster size
Open cluster

12. Phase Transition: 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

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 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

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

22. Theorem 3: Criteria 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 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.
Three parts:
Contention source
Contention destination
Spectrum contention resolution

26. Theorem 6 li = length of contention path
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
We intentionally put no restrict on the lattice size

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. any questions?
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