![Page 1: Competitive MAC under Adversarial SINR · Goal hence: Provable throughput in non-jammed rounds! Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant](https://reader030.vdocument.in/reader030/viewer/2022040821/5e6b398a1a10e9235347c960/html5/thumbnails/1.jpg)
Adrian Ogierman, Andrea Richa, Christian Scheideler, Stefan Schmid, Jin Zhang
Competitive MAC under Adversarial SINR
![Page 2: Competitive MAC under Adversarial SINR · Goal hence: Provable throughput in non-jammed rounds! Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant](https://reader030.vdocument.in/reader030/viewer/2022040821/5e6b398a1a10e9235347c960/html5/thumbnails/2.jpg)
Adrian Ogierman, Andrea Richa, Christian Scheideler, Stefan Schmid, Jin Zhang
Competitive MAC under Adversarial SINR
![Page 3: Competitive MAC under Adversarial SINR · Goal hence: Provable throughput in non-jammed rounds! Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant](https://reader030.vdocument.in/reader030/viewer/2022040821/5e6b398a1a10e9235347c960/html5/thumbnails/3.jpg)
Adrian Ogierman, Andrea Richa, Christian Scheideler, Stefan Schmid, Jin Zhang
Competitive MAC under Adversarial SINR
![Page 4: Competitive MAC under Adversarial SINR · Goal hence: Provable throughput in non-jammed rounds! Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant](https://reader030.vdocument.in/reader030/viewer/2022040821/5e6b398a1a10e9235347c960/html5/thumbnails/4.jpg)
Adrian Ogierman, Andrea Richa, Christian Scheideler, Stefan Schmid, Jin Zhang
Competitive MAC under Adversarial SINR
![Page 5: Competitive MAC under Adversarial SINR · Goal hence: Provable throughput in non-jammed rounds! Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant](https://reader030.vdocument.in/reader030/viewer/2022040821/5e6b398a1a10e9235347c960/html5/thumbnails/5.jpg)
MAC: A Distributed Coordination Problem
5
?!
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Models for Wireless
6
❏ The Radio Model ❏ All nodes within range
❏ The SINR Model ❏ Polynomial decay of signal
❏ Best explained with a rock concert
I can:
send xor receive
reach all nodes
Two or more collide
❏ The Unit Disk Graph Model ❏ Unit radius
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The SINR Model
7
❏ Roger Bild
© Roger Wattenhofer
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The SINR Model
8
❏ Roger Bild
© Roger Wattenhofer
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The SINR Model
9
❏ Roger Bild
© Roger Wattenhofer
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A Tough Model: External Interference
External interference due to:
❏ Co-existing networks
❏ Microwave Ovens
❏ Jammers
10
Noise
Time
Ideal world!
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A Tough Model: External Interference
External interference due to:
❏ Co-existing networks
❏ Microwave Ovens
❏ Jammers
11
Noise
Time
Ideal world!
MAC: exponential backoff, ALOHA, etc. will do the job:
constant cumulative probability «per disk»
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Adding External Interference
External interference due to:
❏ Co-existing networks
❏ Microwave Ovens
❏ Jammers
12
Noise
Time
Reality!
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Adding External Interference
External interference due to:
❏ Co-existing networks
❏ Microwave Ovens
❏ Jammers
13
Noise
Time
How to model?!
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Adding External Interference
External interference due to:
❏ Co-existing networks
❏ Microwave Ovens
❏ Jammers
14
Noise
Time
How to model?!
Adversary:
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The Adversary Model
15
Classic SINR
Adversarial SINR
worst-case (e.g., jammer)
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The (B,T)-Adversary Model
16
❏ So far: time bounded adversaries
❏ SINR requires new model!
❏ Energy-bounded adversary: the (B,T)-adversary ❏ In time period of duration T, the adversary can spend a budget of B*T to jam
each node arbitrarily («bursty», non-uniform)
❏ Theoretically can jam each round «a little bit»
❏ Adversary is adaptive: knows history and state!
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The Model
17
❏ Single channel, backlogged, synchronized
❏ Protocol is randomized
❏ Adversary is adaptive (but not reactive)
❏ Nodes cannot distinguish busy from «jammed»
❏ Nodes cannot distinguish idle from busy!
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The Holy Grail: Constant Competitive Throughput
18
❏ Obviously, cannot achieve a throughput if constantly jammed
❏ Goal hence: Provable throughput in non-jammed rounds!
❏ Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant number of messages are successfully transmitted and received
Success! Success!
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The Holy Grail: Constant Competitive Throughput
19
❏ Obviously, cannot achieve a throughput if constantly jammed
❏ Goal hence: Provable throughput in non-jammed rounds!
❏ Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant number of messages are successfully transmitted and received
Success! Success!
Non-jammed round: Node within transmission radius, i.e., P/rα > βν could still successfully send to that node (given no other transmissions).
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The Holy Grail: Constant Competitive Throughput
20
❏ Obviously, cannot achieve a throughput if constantly jammed
❏ Goal hence: Provable throughput in non-jammed rounds!
❏ Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant number of messages are successfully transmitted and received
Success! Success!
Let N(v) be the number of time steps in which v is non-jammed, and count the number S(v) of successful message receptions!
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The Holy Grail: Constant Competitive Throughput
21
❏ Obviously, cannot achieve a throughput if constantly jammed
❏ Goal hence: Provable throughput in non-jammed rounds!
❏ Constant competitive troughput: in non-jammed rounds, whenever they occur, a constant number of messages are successfully transmitted and received
Success! Success!
Constant: Sum of all S(v) is at least a constant fraction of N(v):
Σ S(v) ≥ const * Σ N(v)
Let N(v) be the number of time steps in which v is non-jammed, and count the number S(v) of successful message receptions!
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The Result: The Sade Protocol
22
Theorem 1
Sade has a 2−𝑂 1/𝜀 2/(𝛼−2)
-competitive throughput
if the jammer is uniform or the node density is high!
With ε constant, we obtain a constant throughput.
No MAC protocol can achieve any throughput against
a (𝐵, 𝑇)-bounded adversary with 𝐵 > 𝜗.
Theorem 2
SINR is fundamentally different from UDG: A second lower bound
shows that a constant cumulative probability per disk cannot yield a throughput polynomial in 𝜀 (for UDG it can).
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The MAC Protocol
23
First idea: “Exponential backoff with state” (goal: constant cumulative probability)
Problem 1: “Idle” is subjective.
Problem 2: Not robust to jamming: May miss “good” cumulative probability.
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The MAC Protocol SADE
24
Estimate adversary window: decrease more slowly!
(Tv, cv, pv) = (1,1,p), fixed noise threshold ν With probability pv, send a message Else: if successful reception, pv = pv /(1+γ) if sense idle channel, pv = pv * (1+γ), Tv – cv ++ if cv > Tv: if no idle among last rounds, pv = pv /(1+γ), Tv = Tv + 2
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The Analysis
25
Zone 1: (transmission range: constant)
- 𝑅1 ≔ 𝑃/(𝛽𝜗)𝛼
- If there is at least one sender, v will not sense
idle
- v successfully receives a message from
another node within R1 provided 𝐴𝐷𝑉(𝑣) ≤ 𝜗
and no collision occurs
Zone 2: (critical interference range: constant)
- 𝑅2 ≔ 𝑂 1/𝜀 1/(𝛼−1)𝑅1
- buffer: interference from Zone 3 is at most 𝜀𝜗
Zone 3: (noncritical interference range)
- every node outside Zone 1 and Zone 2
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Analysis
26
❏ Cumulative sending probabilities in Zone 1 and Zone 2 at most constant
❏ Power of Zone 3 grows in n, but at v received power is constant in expectation too
❏ Analysis over thresholds of cumulative probability:
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Simulations
27
❏ Throughput better than what expected from worst-case analysis
❏ Fast convergence
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Conclusion
28
❏ SADE: A very robust MAC protocol with provable throughput guarantees in a harsh and realistic environment
❏ A new adversary model: energy-constrained
❏ Future work: ❏ Polynomial throughput? Only possible with sub-constant cumulative
probability
❏ Adaptive power
2−𝑂 1/𝜀 2/(𝛼−2)
-competitive
poly(1/ 𝜀)-competitive?
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Thank you.