School of EECS, Peking University 1 A Group-theoretic Framework for Rendezvous in Heterogeneous Cognitive Radio Networks Lin Chen ∗, Kaigui Bian ∗, 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

School of EECS, Peking University 2 What is the Rendezvous problem Rendezvous dilemma, rendezvous search game

School of EECS, Peking University 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 B C

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

School of EECS, Peking University 5 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) It is challenging as a math problem

School of EECS, Peking University 6 Rendezvous problem in multi-channel wireless networks 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 Ch 2 Ch 1 Rdv ch Rdv Data Rdv Data

School of EECS, Peking University 7 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? Two interesting questions

School of EECS, Peking University 8 Existing research Channel hopping (CH) can create rendezvous

School of EECS, Peking University 9 Random, common channel hopping Random hopping ： unbounded TTR Common hopping: clock sync. required A BC

School of EECS, Peking University 10 Sequence based channel hopping Interleaving, [Dyspan08] Modular clock, [MobiCom04, Infocom11, MobiHoc13] Single rendezvous channel

School of EECS, Peking University 11 Different sensing channel sets [MobiHoc13] No common channel index, no integer channel indices Node i Node j xy a bc Channel hopping over heterogeneous channel sets

School of EECS, Peking University 12 A lower bound for rendezvous latency Q1: how fast to rendezvous?

School of EECS, Peking University 13 Nodes i has a number of N i channels, in chan set C i Nodes j has a number of N j channels, in chan set C j Theorem 1: to rdv on every channel in C i ∩ C j  Two nodes need at least N i N j time slots Intuition: Elements in group Z Ni ⊕ Z Nj enumerate all possible pairs of rendezvous channels in C i ∩ C j A lower bound of rdv latency (TTR)

School of EECS, Peking University 14 Max # of rendezvous channels = || Max # of rendezvous channels = |C i ∩ C j | Q2: what is the max # of rdv channels?

School of EECS, Peking University 15 3 steps of creating channel hopping sequences Three channels:  Everyone has two short sequences: fast and slow  Choice bit sequence: 0/1 sequence  Interleave fast and slow sequence  If 0, pick fast; if 1, pick slow Fast seq Slow seq Choice bit seq Final seq used for rdv

School of EECS, Peking University 16 Fast hopping: hop across N i channels by N i slots Slow hopping: stay on channel h for N i slots However, two nodes use different strategies! Step 1: Rdv between fast and slow sequences Fast seq. Slow seq.

School of EECS, Peking University 17 Step 2: Creating choice bit sequences

School of EECS, Peking University 18 Step 3: Interleaving fast and slow seqs for rdv … Node i 3 chans Node j 2 chans Fast Slow Choice Final seq Fast Slow Choice … Final seq … 0

School of EECS, Peking University 19 Simulation results

School of EECS, Peking University 20 Legend of our protocol is “Adv rdv” by light blue curve Small TTR (left) + Max robustness (right)

School of EECS, Peking University 21 Conclusion

School of EECS, Peking University 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 rdv channels is |C i ∩ C j |  Achieve max rdv with a bounded latency ~ O(N i N j )

School of EECS, Peking University 23 any questions? Thanks & 感谢观看

School of EECS, Peking University 24 Assignment of Choice Sequence Symmetrization

School of EECS, Peking University 25 Finished! Assignment of choice seq.

School of EECS, Peking University 26 Two distributed assignment algorithms symmetrization map

School of EECS, Peking University 27 Suppose the length of ID is. Just append to it. Length of choice seq.: symmetrization