Post on 30-Dec-2015
description
transcript
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
SERIAL ETHERNET
Ch 2
Ch 1
Rdv ch Rdv Data
SERIAL ETHERNET
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
C1 C2C0 C1 C2C0 C1 C2C0
C1 C2C0 C1 C2C0 C1 C2C0
Random, common channel hopping
Random hopping: unbounded TTR
Common hopping: clock sync. required
C1 C2C0
C1 C2 C0
C1 C2 C0
C1C2 C0
…...
…...
A
B C
School of EECS, Peking University
10
Sequence based channel hopping
Interleaving, [Dyspan08]
Modular clock, [MobiCom04, Infocom11, MobiHoc13]
Single rendezvous channel
C1 C2C0 C1 C2C0 C1 C2C0C0 C1 C2
C1 C2C0 C1 C2C0 C1 C2C0C0 C1 C2
C1 C2C0 C1 C2C0 C0 C0 C0
C1 C2C0 C1 C2C0 C0 C0 C0
School of EECS, Peking University
11
Different sensing channel sets [MobiHoc13] No common channel index, no integer channel indices
Node i Node j
x y a b c
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 Ni channels, in chan set Ci Nodes j has a number of Nj channels, in chan set Cj
Theorem 1: to rdv on every channel in Ci ∩ Cj
Two nodes need at least Ni Nj time slots
Intuition: Elements in group ZNi⊕ZNj enumerate all
possible pairs of rendezvous channels in Ci ∩ Cj
A lower bound of rdv latency (TTR)
School of EECS, Peking University
14
Max # of rendezvous channels = |Ci ∩ Cj|
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.
10 2 10 2
10 10 10
10 1 00 0
1 0
10 1 10
12
0
0 2Fast seq
Slow seq
Choice bit seq
Final seqused for rdv
0 1 22
School of EECS, Peking University
16
Fast hopping: hop across Ni channels by Ni slots Slow hopping: stay on channel h for Ni slots
However, two nodes use different strategies!
C1 C1 C1 C0C0C0C2 C2C2
C1 C1 C1 C0C0C0C2 C2C2
Step 1: Rdv between fast and slow sequences
C1 C2 C1 C1C0 C0 C0C2 C2 C1 C2 C1 C1C0 C0 C0C2 C2Fast seq.
Slow seq.
School of EECS, Peking University
17
Step 2: Creating choice bit sequences
Node has 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
𝜔 (𝑖 )
𝜔 ( 𝑗 )
10 1 00
1 1 00 1
10 1 00
1 1 00 1
School of EECS, Peking University
18
Step 3: Interleaving fast and slow seqs for rdv
10 2 10 2 10 2
10 210 210 2
1 1 00
10 1 00 10 1 00 …
1 0 0 2
10 21 10
12
0
0 2 1
2 2Node i3 chans
Node j2 chans
Fast
SlowChoice
Final seq
1
2 0
0 20 2
0
0 2
2
0 2
Fast
Slow
Choice
0 2
1 1 00 1 …
Final seq
2 002 2 002 2 002
0 20 20 20 2
0 0 0 0 22 22 …
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 |Ci ∩ Cj| Achieve max rdv with a bounded latency ~ O(Ni Nj )
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
symmetrization map
School of EECS, Peking University
27
Suppose the length of ID is . Just append to it.
Length of choice seq.:
symmetrization
11000101Node ’s 8-bit ID 1000000000001