A General Model of Wireless Interference

LL.. Qiu, Y Qiu, Y.. Zhang, F Zhang, F.. Wang, M. Wang, M. Han, RHan, R.. Mahajan Mahajan

Mobicom 2007Mobicom 2007

A Model for ?

• Misleading title– Nothing new about wireless interference

• Indeed, a model for predicting the throughput/goodput of wireless networks

• Motivation– Helpful in evaluating design/protocols (e.g.

channel assignment)– Direct measurements alone is insufficient

• Lacks predictive power and scalability

Problem Statement

• Given characteristics of– RSS between each pair

(RSSm,n)– Background noise (Bn)– Traffic demand between pairs

(dm,n)

• What is the pairwise throughput/goodput?

• My dumb solution– Calculate SINR at every node– Throughput = B*log2(1+SINR)

RSSm,n

Bn

• Problems– Non-constant RSS– Ignoring Underlying MAC

Contributions

• State of the Art: only handle restricted traffic – Only two senders or two flows – Only broadcast traffic– Only saturated demands

• Contributions– Interference among an arbitrary number of senders – Both broadcast and unicast traffic– Both saturated and unsaturated demand

Reality

Dumb solution

This paperState of the Art

Limit of analytical methods

Its limit

Overview of the Model

• How it works– Measure pairwise RSS via broadcast probes

• One node broadcast at a time, others measure RSS O(n) probes

– Saturated broadcast sender/receiver models• Markov-chain model

– Extend to unsaturated broadcast– Extend to saturated/unsaturated unicast

given network

RF profile measurement

traffic demand

sender model

receiver model

throughput

goodput

pairwise RSS

Broadcast Sender: Overview• Estimate how much a sender can send

– MAC: 802.11 DCF

• Markov chain (simplification #1)– State i: a set of active nodes Si

– Stationary probabilities: i (fraction of time that the system is in state i)– Throughput of node m: tm = ∑i|mSi i

00 01

1011

0…0

0…1

0..10

1…1

.

...

Broadcast Sender: Overview Broadcast Sender: Overview (Cont.)(Cont.)

• State transition probability– Staying idle: P00(n|Si)– Idle to active: P01(n|Si)– Active to idle: P10(n|Si)– Staying active: P11(n|Si)– Assume node independence (simplification #2)

• Compute stationary probabilities i by solving LP– Highly efficient for sparse M

Broadcast Sender: Transition ProbabilitiesBroadcast Sender: Transition Probabilities

)|(1)|(

)()|(

)|(1)|(P

demands saturatedunder 1)( where

)()()(

1)S|C(m

0]counter &clear is medium |data has Pr[m

clear] is medium|0Pr[counter

clear] is Pr[medium

data] has m & 0counter &clear is mediumPr[

)|(

1010

10

0100

_____________________i

01

ii

sloti

ii

i

SmPSmP

mT

TSmP

SmPSm

mQ

mQmOHmCW

SmP

2/minCW

tT slotDIFS /

Under the assumption that both transmissionand idle times are exponential (simplification #4)

Simplification #3

Broadcast Sender: Clear Broadcast Sender: Clear ProbabilityProbability

•

• How to estimate Im|Si?

– Im|Si=Wm+Bm+∑sSi\{m} Rsm

– Assume each term is lognormal variable (simplification #5)

– Approximate the sum using a lognormal variable by matching mean and variance

]Pr[)|( | mSmi iISmC

Broadcast Sender: Broadcast Sender: Handle Similar Packet SizesHandle Similar Packet Sizes

• Synchronization occurs when packet sizes used by different nodes are similar– When several nearby nodes transmit together, they will end

transmission together– Independence assumption fails

• Handle synchronization– Construct synchronization graph Gsyn

• Two nodes are connected iff C(m|{n}) 0.1 and C(n|{m}) 0.1– Find all synchronization groups

• Each connected component in Gsyn is a synchronization group (simplification #6)

– If m and n in the same synchronization group• mSj and n Sj’ M(i,j) = 0• P10(mn|Si) = Tslot/T(m) instead of (Tslot/T(m))|G|

Broadcast Sender: Broadcast Sender: Handle Unsaturated DemandsHandle Unsaturated Demands

• Estimate Q(m): probability m has data to send when its backoff counter is 0 and channel is clear at m

• Under saturated demands, Q(m) = 1 • Under unsaturated demands, compute Q(m) iteratively to

ensure that demands are not exceeded

Initialize Q(m) = 1

Solve the Markov chain

Update Q(m)

Brief overview of other parts

• Broadcast Receiver– Estimate packet loss rate

• Extending to unicast: challenges– Binary backoff

• Sending rate depends on loss rates

– DATA losses due to collisions with ACKs• Model ACK sending rate, which in turn depends on

DATA sending rate and loss rates

– Traffic demand• Account for retransmissions

Simulation Evaluation: Simulation Evaluation: Saturated BroadcastSaturated Broadcast

2 saturated broadcast

More accurate than UW 2-node model

(a) throughput (b) goodput

0

0.2

0.4

0.6

0.8

1

1.2

0 100 200 300 400 500G

oodp

ut

Sender-Receiver Pair ID

Ours (RMSE=0.0050)UW (RMSE=0.1664)Actual

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

0 2 4 6 8 10 12 14 16 18 20

Thro

ughp

ut

Sender ID

Ours (RMSE=0.0028)UW (RMSE=0.1450)Actual

Simulation Evaluation: Simulation Evaluation: Saturated BroadcastSaturated Broadcast

10 saturated broadcast

Accurate for 10 saturated broadcast

(a) throughput (b) goodput

0

0.1

0.2

0.3

0.4

0.5

0.6

0 500 1000 1500 2000 2500G

oodp

ut

Sender-Receiver Pair ID

Ours (RMSE=0.0189)Actual

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 10 20 30 40 50 60 70 80 90 100

Thro

ughp

ut

Sender ID

Ours (RMSE=0.0460)Actual

Testbed EvaluationTestbed EvaluationUW traces: 2 senders, 30 mW, broadcast, saturated

(a) throughput (b) goodput

More accurate than UW-model for 2-sender

Summary

• A model for predicting the throughput of wireless networks

• Validated by simulation and testbed evaluation

Reality

Dumb solution

This paperState of the Art

Limit of analytical methods

Its limit

Less simplifications

RTS/CTS, different MAC

Traffic modelling, human behavior