A Group-theoretic Framework for Rendezvous in Heterogeneous Cognitive Radio Networks

1. A Group-theoretic Framework for Rendezvousin Heterogeneous Cognitive Radio Networks Lin Chen∗, KaiguiBian∗, Lin Chen†Cong Liu#, Jung-Min Jerry Park♠, and Xiaoming Li∗ ∗ Peking University, Beijing, China † University Paris-Sud, Orsay, France # Sun Yat-Sen University, Guangzhou, China ♠ Virginia Tech, Blacksburg, VA, USA ACM MobiHoc 2014

2. What is the Rendezvous problem • Rendezvous dilemma, rendezvous search game

3. Rendezvous is a problem about “dating”… • Two young people want to date (meet or rendezvous)in a large park, where N places are suitable for dating.[Steve Alpern, 1976] • They need a strategy to visit these N places for early rendezvous. A C B

4. It is NOT a challenging problem today… • They can call each other directly by cell phone Let’s meet at “C” At 10AM! A C B

5. It is challenging as a mathproblem • No hidden assumptions here • E.g., no cell phones! • That means, no pre-shared knowledge • Places can be unavailable (due to congestion) • Clocks can be asynchronous • No pre-assigned roles (i.e., the strategy should be the same for two people)

6. Rendezvous channel = control channel Link establishment and control message exchange, etc. Subject to congestion, attack, primary user traffic, etc So, it is needed to rendezvous on multiple channels Rendezvous problem in multi-channel wireless networks Ch 2 Ch 1 Rdvch Data Data Rdv Rdv

7. Two interesting questions • Q1: How fast can they achieve rendezvous? • Is there a minimum, bounded latency? • Q2: What is the max # of rendezvous channels? • What if a given rendezvous channel is unavailable?

8. Existing research Channel hopping (CH) can create rendezvous

9. Random, common channel hopping • Random hopping：unbounded TTR • Common hopping: clock sync. required A B C

10. Sequence based channel hopping • Interleaving, [Dyspan08] • Modular clock, [MobiCom04, Infocom11, MobiHoc13] • Single rendezvous channel

11. Channel hopping over heterogeneous channel sets • Different sensing channel sets [MobiHoc13] • No common channel index, no integer channel indices Node j Node i a b c x y

12. A lower bound for rendezvous latency Q1: how fast to rendezvous?

13. A lower bound of rdv latency (TTR) • Nodes i has a number of Ni channels, in chan set Ci • Nodes jhas a number of Njchannels, in chan set Cj • Theorem 1: to rdv on every channel in Ci∩Cj • Two nodes need at leastNiNjtime slots • Intuition: Elements in group ZNi⊕ZNjenumerate all possible pairs of rendezvous channels in Ci∩Cj

14. Max # of rendezvous channels = |Ci ∩ Cj| Q2: what is the max # of rdv channels?

15. 3 steps of creating channel hopping sequences • Three channels: • Everyone has two short sequences: fast and slow • Choice bit sequence: 0/1 sequence • Interleavefast and slow sequence • If 0, pick fast; if 1, pick slow. 1 2 2 0 1 0 1 0 0 0 1 2 0 1 2 0 1 2 0 1 2 Fastseq 0 0 0 1 1 1 0 0 0 1 1 1 Slowseq Choice bit seq 0 Final seq used for rdv

16. Step 1: Rdv between fast and slow sequences • Fast hopping: hop across Ni channels by Ni slots • Slow hopping: stay on channel h for Ni slots • However, two nodes use different strategies! Fast seq. Slow seq.

17. Step 2: Creating choice bit sequences • Nodehas its ID as , then create its choice seq. • Any and are at least one bit different after any cyclic rotation • Symmetrization map: a unique ID  a unique bit-string • Example: • Assign 01010 to node and 10101 to node 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 1 1

18. Step 3: Interleaving fast and slow seqs for rdv Fast 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 Slow 0 0 0 1 1 2 2 2 1 0 0 0 1 1 2 2 2 1 Node i 3 chans Choice 1 0 1 … 0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 Finalseq 0 Final seq 2 2 2 2 2 0 0 0 0 0 … Node j 2 chans Choice 1 1 … Slow 0 0 0 0 0 0 2 2 0 0 2 2 2 2 2 2 Fast 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0

19. Simulation results

20. Legend of our protocol is “Advrdv” by light blue curve Small TTR (left) + Max robustness (right)

21. Conclusion

22. Conclusion • We formulate the rendezvous problem in heterogeneous cognitive radio networks. • We derive the lower bound of rdv latency in the heterogeneous environment. • By symmetrization and interleaving fast/slow seqs, we devise a near-optimal rdv protocol. • Max # of rdvchannels is |Ci ∩ Cj| • Achieve max rdv with a bounded latency ~ O(NiNj)

23. anyquestions? • Thanks& 感谢观看

24. Assignment of Choice Sequence Symmetrization

25. Assignment of choice seq. Finished!

26. Two distributed assignment algorithms • symmetrization map • symmetrization map

27. symmetrization • Suppose the length of ID is . Just append to it. • Length of choice seq.: 11000101 1000000000001 Node ’s 8-bit ID