Towards a Widely Applicable SINR Model for Wireless
Access Sharing
Towards a Widely Applicable SINR Model for Wireless
Access Sharing
Christian ScheidelerUniversity of Paderborn
Joint work with Andrea Richa and Stefan Schmid
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Motivation
SINR model: considered good compromise between realistic modelling of interference and algorithm design and analysis
Basic form: node v correctly receives message from node u if and only if
P(u)/d(u,v)a
N + Swu,v P(w)/d(w,v)a
● P(u): transmission power of u● d(u,v): distance between u and v● N: background noise
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b
Motivation
Background noise hard to model:●Temporary Obstacles● Background noise● Physical Interference● Co-existing networks ● Jammer
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Motivation
Ideal world:
Classical approach used in theory.
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Background noise
: noise level
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Motivation
Ideal world:
OR
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Background noise
: noise level
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Motivation
Ideal world:
OR Gaussian / predictable
Classical approach used in systems.
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Background noise
: noise level
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Motivation
Real world:
How to model this???
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backgroundnoise
: noise level
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Our Approach: Adversarial Noise
Background noise (microwave, radio signal, ...)
Intentional jammerTemporary obstacles (cars ...)
Co-existing networks …
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Our Approach: Adversarial Noise
● Idea: model unpredictable behavior via adversary (i.e., adversarial noise)!
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Our Approach: Adversarial Noise
● (B,T)-bounded adversary: has an overall noise budget of BT for each time interval of length T and each node v that it can distribute among the time steps as it likes
● Node v correctly receives a message from u if and only if
P(u)/d(u,v)a
ADV(v) + Swu,v P(w)/d(w,v)a
● ADV(v): adversarial noise at node v
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Our Approach: Adversarial Noise
● Node v correctly receives a message from u if and only if
P(u)/d(u,v)a
ADV(v) + Swu,v P(w)/d(w,v)a
● ADV(v): adversarial noise at node v
Other benefit beyond general model for noise:● softens strict “if and only if” condition of original SINR
(adversary controls correct receipt within range)
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Simple ADV-SINR Model● single frequency (e.g., sensor nodes) ● at each time step, a node can transmit a packet, and
the transmissions are synchronized● a node may transmit or sense the channel at any time
step (half-duplex)● when sensing the channel with threshold S, a node v
may– sense an idle channel whenever
ADV(v) + Suv P(u)/d(u,v)a < S
– sense a busy channel otherwise
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Simple ADV-SINR Model● single frequency (e.g., sensor nodes) ● at each time step, a node can transmit a packet, and
the transmissions are synchronized● a node may transmit or sense the channel at any time
step (half-duplex)● in addition to sensing an idle or busy channel, a node
v receives a message from u whenever the adversarial SINR formula holds
Is it possible to design algorithms for this model?
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Single-hop wireless network● [Awerbuch, Richa, S. PODC’08]● n reliable honest nodes and a jammer (adversary); all
nodes within transmission range of each other and of the jammer
jammer
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Simple (yet powerful) idea● each node v sends a message at current time step with
probability pv ≤ pmax, for constant 0 < pmax << 1. p = ∑ pv (aggregate probability) qidle = probability the channel is idleqsucc = probability that only one node is transmitting (successful transmission)
● Claim. qidle . p ≤ qsucc ≤ (qidle . p)/ (1- pmax)
if (number of times the channel is idle) = (number of successful transmissions) p = θ(1) qsucc = θ(1) ! (what we want!)
~
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Basic approach
● a node v adapts pv based only on steps when an idle channel or a successful message transmission are observed, ignoring all other steps (including all the blocked steps when the adversary transmits!)
steps jammed by adversary
idle steps
successful transmissions
steps where collision occurred but no jamming
time
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Basic approach
● a node v adapts pv based only on steps when an idle channel or a successful message transmission are observed, ignoring all other steps (including all the blocked steps when the adversary transmits!)
steps jammed by adversary
idle steps
successful transmissions
steps where collision occurred but no jamming
time
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Naïve protocol
Each time step:
● Node v sends a message with probability pv . If v does not send a message then– if the wireless channel is idle then pv = (1+ γ) pv
– if v received a message then pv = pv /(1+ γ)
(where γ = O(1/(log T + loglog n)) )
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Problems
● Basic problem: Aggregate probability p could be too large. – all time steps blocked due to message collisions w.h.p.
steps jammed by adversary
idle steps
successful transmissions
steps where collision occurred but no jamming
time
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Problems
● Basic problem: Aggregate probability p could be too large. – all time steps blocked due to message collisions w.h.p.
steps jammed by adversary
idle steps
successful transmissions
steps where collision occurred but no jamming
time
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Problems
● Basic problem: Aggregate probability p could be too large. – all time steps blocked due to message collisions w.h.p.
● Idea: If more than T consecutive time steps without successful transmissions (or idle time steps), then reduce probabilities, which results in fast recovery of p.
● Problem: Nodes do not know T. How to learn a good time window threshold? – It turns out that additive-increase additive-decrease is
the right strategy!
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MAC Protocol for Single Hop● each node v maintains
– probability value pv ,
– time window threshold Tv , and
– counter cv
● Initially, Tv = cv = 1 and pv = pmax (< 1/24).
● synchronized time steps (for ease of explanation)
● Intuition: wait for an entire time window (according to current estimate Tv) until you can increase Tv
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MAC Protocol for Single Hop
In each step:
● node v sends a message with probability pv . If v decides not to send a message then– if v senses an idle channel, then pv = min{(1+ γ)pv , pmax}
– if v successfully receives a message, then pv = pv /(1+ γ) and Tv = max{Tv - 1, 1}
● cv = cv + 1. If cv > Tv then
– cv = 1
– if v did not receive a message successfully in the last Tv
steps then pv = pv /(1+ γ) and Tv = Tv +1
MAC Protocol for ADV-SINR
MAC goal: successfully transmit messages
Performance metric adopted from [Richa, S., Schmid, Zhang, DISC’10]:
● potentially busy step: ADV(v) (1-e)S
Goal: achieve constant throughput
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for v steps busy timey potentiall #
by v received msgs successful#
v
v
Throughput =
MAC Protocol for ADV-SINR
Important prerequisites: ● For (B,T)-bounded adversary: B<(1-e)S
(otherwise, all steps can be (potentially) busy)● Area around each v suff.
dense, i.e., there must be nodes within a transmission range of r where
P/ra bS
● a>2
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r
MAC Protocol for ADV-SINR
Initially, each node v sets Tv:=1, cv:=1, pv:=pmax, and g=O(1/(log T + loglog n)).
In each round, every node v decides to transmit a message with probability pv.
● If v does not decide to send a message:– v receives a message: pv:=(1+g)-1 pv
– channel idle: pv:=min{(1+g)pv , pmax}, Tv:=max{1,Tv-1}
● cv:=cv+1
● If cv>Tv then cv:=1, and if there was no idle step within Tv steps then pv:=(1+g)-1 pv, Tv:=Tv+2
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Main Result
● Let N = max{T,n}
● Theorem. MAC protocol is 1/2Q((1/e)2/(a-2))-competitive under any ((1-ε)S,T)-bounded adversary if the protocol is executed for Ω((T log N)/ε + (log4 N)/(ε γ2)) steps w.h.p., for any constant 0<ε<1 and any T.
Main Result
Proof idea: 3 zones
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transmission zone
interference zone
outer zone
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Main Result
● Let N = max{T,n}
● Theorem. MAC protocol is 1/2Q((1/e)2/(a-2))-competitive under any ((1-ε)S,T)-bounded adversary if the protocol is executed for Ω((T log N)/ε + (log4 N)/(ε γ2)) steps w.h.p., for any constant 0<ε<1 and any T.
In unit-disk model, Q(1)-competitive possible!
Main Result
● ((1-e)S,T)-bounded adversary, e0
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transmission zone
interference zone
r=W((1/e)1/(a-2))
Main Result
● ideally, p=Q(e2/(a-2)) in each transmission zone
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transmission zone
interference zone
r=W((1/e)1/(a-2))
Main Result
● better: power control?
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transmission zone
interference zone
r=W((1/e)1/(a-2))
Other adversarial modeling in wireless networks
● Adversary: used to model external world● More benign:
– Control packet injection rates– Control mobility
● Intentionally disruptive:– jammers
● More disruptive: malicious adversaries– Undermine security– Control Byzantine nodes (introduce fake messages)
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Other adversarial modeling in wireless networks
● Adversarial packet injection/queueing:– [Chlebus, Kowalski, Rokicki, PODC’06],
[Andrews, Jung, Stolyar, STOC’07],[Anantharamu, Chlebus, Rokicki, OPODIS’09],[Chlebus, Kowalski, Rokicki, Distributed Computing’09],[Lim, Jung, Andrews, INFOCOM’12]
● Multi-channel access with adversarial jamming:– [Dolev, Gilbert, Guerraoui, Newport, DISC’07],
[Anantharamu, Chlebus, Kowalski, Rokicki, SIROCCO’11],[Dolev,Gilbert, Khabbazian, Newport, DISC’11], [Daum, Gilbert, Kuhn, Newport, PODC’12], [Ghaffari, Gilbert, Newport, Tan, OPODIS’12]
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Other adversarial modeling in wireless networks
● Broadcasting\Gossiping with adversarial jamming:– [Dolev, Gilbert, Guerraoui, Newport, DISC’07],
[Dolev,Gilbert, Khabbazian, Newport, DISC’11], [Daum, Gilbert, Kuhn, Newport, PODC’12], [Ghaffari, Gilbert, Newport, Tan, OPODIS’12]
● Capacity Maximization with adversarial jamming: [Dams, Hoefer, Kesselheim, unpublished]
● Malicious adversary:– [Dolev, Gilbert, Guerraoui, Newport, DISC’07],
[Gilbert, Young, PODC’12]
● Infection spreading with adversarial mobility: [Wang,Krishnamachari, ]
● Etc.WRAWN'13, Christian Scheideler 35
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Future Work: Adversarial Jamming
● Jamming-resistant protocols with power control:– Increasing power increases chance that signal will
overcome jamming activity, however…– Increasing power also generates more interference…– Also adapt noise threshold level?
● How about reactive jammers under SINR?● Can the protocols be modified so that no rough bounds
on n and T are required in g?
● Stochastic/oblivious jammers: Simpler to handle? E.g., a constant g seems to work fine here.
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Power Control
Problem: many parameters (pv, Tv, Pv, Sv)
● VERY tricky to find setup that avoids any scenarios where protocol can get stuck
● Even much more tricky to prove that a correct protocol works
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Thank you! Questions?