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

1WRAWN'13, Christian Scheideler

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

WRAWN'13, Christian Scheideler 2

b

Motivation

Background noise hard to model:●Temporary Obstacles● Background noise● Physical Interference● Co-existing networks ● Jammer


Motivation

Ideal world:

Classical approach used in theory.

0 time

Background noise

: noise level


Motivation

Ideal world:

OR

0 time

Background noise

: noise level


Motivation

Ideal world:

OR Gaussian / predictable

Classical approach used in systems.

0 time

Background noise

: noise level


Motivation

Real world:

How to model this???

0 time

backgroundnoise

: noise level


Our Approach: Adversarial Noise

Background noise (microwave, radio signal, ...)

Intentional jammerTemporary obstacles (cars ...)

Co-existing networks …

XX

X

X

X



● Idea: model unpredictable behavior via adversary (i.e., adversarial noise)!

XX

X

X

X



● (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


b


● 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)


b


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


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?


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


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!)

~


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


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!)


idle steps



time


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)) )


Problems

● Basic problem: Aggregate probability p could be too large. – all time steps blocked due to message collisions w.h.p.


idle steps



time


Problems



idle steps



time


Problems


● 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!


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


MAC Protocol for Single HopIn 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


for v steps busy timey potentiall #

by v received msgs successful#

v

v

Throughput =


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>2WRAWN'13, Christian Scheideler 25

r


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



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


transmission zone

interference zone outer zone


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


transmission zone

interference zone

r=W((1/e)1/(a-2))

Main Result

● ideally, p=Q(e2/(a-2)) in each transmission zone


transmission zone

interference zone

r=W((1/e)1/(a-2))

Main Result

● better: power control?


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)



● 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]



● 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.


36

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.

WRAWN'13, Christian Scheideler

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



Thank you! Questions?

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Towards a Widely Applicable SINR Model for Wireless Access Sharing