measuring and modeling the impact of wireless interference

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Measuring and Modeling the Impact of Wireless Interference

Lili QiuUT Austin

Rice UniversityNov. 21, 2005

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IntroductionWireless interference affects network capacity

1 Mbps 1 Mbps

Throughput = 2 Mbps

Throughput = 1 Mbps

A B DC

1 Mbps

1 Mbps 1 Mbps

A B DC

1 Mbps

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Capacity of Wireless Networks• Many research on computing capacity of

multi-hop wireless networks

• Most of it focuses on asymptotic performance bounds– Gupta and Kumar 2000:

• O(1/sqrt(N)) under optimal node placement• O(1/sqrt(NlogN)) under random node placement

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Community Networking Scenario

Asymptotic analysis is not useful in this case

4 houses talk to the central ITAP. What is the maximum possible throughput?

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Capacity of Wireless Networks

• A framework to compute network capacity of specific topologies with specific traffic patterns– Our Mobicom 03 paper, joint work with

Jain, Padhye, and Padmanabhan

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Assumptions• Fluid model of data transmission

• Data transmissions can be finely scheduled by an omniscient central entity– The derived network capacity is under optimal

scheduling and optimal routing– Applications

• Assess the efficiency of the existing network protocols

• Help network provision (e.g., what-if analysis)

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Interference Models• Protocol model

– Transmission is successful if d(i,j) R(i) and any node k with d(k,j) R’(k) is not tranmitting

– Binary interference model

• Physical model– Transmission is successful if SNR(i,j)

threshold– Non-binary interference model

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Overview of Our Framework1. Model the problem as a standard network

flow problem• Described as a linear program

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Step 1: Network Flow Model• Create a connectivity graph

– Each vertex represents a wireless node– Draw a directed edge from vertex A to vertex B

if B is within range of A

• Write a linear program that solves the basic MAXFLOW problem on this connectivity graph

• Several generalizations possible– Discussed later in the talk.

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Example: Network Flow Model

A (Sender) C (Receiver)B

Linear Program:

Maximize Flow out of A

Subject to:

1. Flow on any link can not exceed 1

2. At node B, Flow in == Flow out.

Answer: 1 (Link 1, Link 2)

A B C

Connectivity Graph

Link capacity = 1

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4 3

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2. Represent interference among wireless links using a conflict graph

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Step 2: Model Interference using Conflict Graph

• A conflict graph that shows which wireless links interfere with each other

• Represent each link in the connectivity graph by a vertex in the conflict graph

• Draw an edge between two vertices if the wireless links interfere with each other

• Several generalizations possible– Discussed later in the talk.

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Example: Conflict GraphConnectivity Graph

A B C

1

4

2

3

1 2

3 4

Conflict Graph

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3. Derive constraints on utilization of wireless links using cliques in the conflict graph• Augment the linear program to obtain upper

bound on optimal throughput

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Step 3: Clique Constraints• At most one of the vertices in a clique can

be active at any given instant– Total utilization of links belonging to a clique is

100%

• MAXFLOW LP can be augmented with these clique constraints to get a better upper bound

• Speed-up convergence: consider maximal cliques in the conflict graph– A maximal clique is a clique to which we can not

add any more vertices

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Example: Clique Constraints

Link capacity = 1

Linear Program:


Subject to:

1. Flow on any link can not exceed 1 * link utilization


3. Sum of utilizations of links 1, 2, 3 and 4 (a clique) can not exceed 100%

1 2

3 4

Clique = {1, 2, 3, 4}

A B C

1

4

2

3

Answer = 0.5 (Link1, Link 2)

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Properties of Clique Constraints

• Finding all cliques can take exponential time– Moreover, finding all cliques does not guarantee

optimal solution (due to odd holes and odd anti-holes)

• The upper bound is monotonically non-increasing as we find and add new cliques– As we add each clique, the link utilizations are

constrained further

• More computing time can provide better solution

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Overview of Our Framework1. Model the problem as a standard network flow

problem• Described as a linear program


3. Derive constraints on utilization of wireless links using cliques in the conflict graph• Augment the linear program to obtain upper bound on

optimal throughput

4. Derive constraints on utilization of wireless links using independent sets in the conflict graph • Augment the linear program to obtain lower bound on

optimal throughput

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Step 4: Independent Set Constraints

• All links belonging to an independent set can be active at the same time

• No two independent sets are active at the same time

• MAXFLOW LP can be augmented with constraints derived from independent sets to get a lower bound

• Speed up convergence: consider maximal independent sets in the conflict graph– An independent set to which we cannot add

any nodes

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Example: Independent Set Constraints

Link capacity = 1

Linear Program:


Subject to:

1. Flow on any link can not exceed 1 * link utilization


3. Sum of utilizations of all independent sets can not exceed 100%

4. Utilization of a link can not exceed the sum of utilization of independent sets it belongs to.

1 2

3 4

Independent sets: {1}, {2}, {3}, {4}

A B C

1

4

2

3

Answer = 0.5 (Link1, Link 2)

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Properties of Independent Set Constraints

• Lower bound is always feasible – LP also outputs a transmission schedule

• Finding all independent sets can take exponential time– If we do find all independent sets, the resulting lower bound is

guaranteed to be optimal

• Lower bound is monotonically non-decreasing as we find and add more independent sets– More computing time provides better answers

• If upper and lower bounds converge, optimality is guaranteed

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Putting It All Together1. Model the problem as a standard network flow

problem• Described as a linear program


3. Derive constraints on utilization of wireless links using cliques in the conflict graph• Augment the linear program to obtain upper bound on

optimal throughput

4. Derive constraints on utilization of wireless links using independent sets in the conflict graph • Augment the linear program to obtain lower bound on

optimal throughputIterate over steps 3 and 4 to find progressively tighten bounds on optimal throughput

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Putting It All Together (Cont.)

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0.5

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0.9

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0 20 40 60 80 100 120

IterationsN

orm

aliz

ed T

hrou

ghpu

t

Upper Bound

Lower Bound

Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

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What-if Analysis

Scenario Aggregate Throughput

Baseline 0.5

Double range 0.5

Two ITAPs 1

Two Radios 1

Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

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Physical Interference

• Represent wireless links as vertices in conflict graphs

• Directed conflict graph

• Weight on edge X->Y represents the fraction of the maximum permissible noise at the receiver of link Y when link X is active

• Schedulable sets instead of independent sets

• Non-schedulable sets instead of cliques

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Other Generalizations• Multiple senders and/or receivers

– Write LP to solve multi-commodity flow problem

• Non-greedy sender– Create a virtual sender– Include a “virtual link” of limited capacity from the virtual

sender to the real sender in the connectivity graph– This link does not conflict with any other links– LP maximizes flow out of virtual sender

• Single path routing– Integer linear programming

• Multiple radios on orthogonal channels– Represent with multiple, non-interfering links between

nodes

• Directional antennas– Include appropriate links in the connectivity graph– Conflict graph can accommodate any interference pattern

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Other Generalizations (Cont.)

• Multirate radios• Create multiple virtual links corresponding to a

physical link, one for each data rate• Only one of the virtual links corresponding to a

physical link can be active at a time• The edge weights (under physical interference

model) reflect the specific noise tolerance for each rate

• Other objectives• Any linear function (e.g., fairness or revenue)

can be used

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Limitations• Linear programs can take a long time to

solve– Especially when single path routing is used

• There is no guarantee that optimal solution will be found in less than exponential time

• Upper bound might not converge to optimal even if we find all cliques– Graphs with odd-holes and anti-holes

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Summary• A flexible framework for deriving capacity of

specific topologies with specific traffic patterns– Computes upper and lower bounds on optimal

throughput – Accommodate various models of network

connectivity and interference, routing constraints, traffic demands

• How to get a conflict graph for a given network?– IMC 05 paper, joint work with Padhye, Agarwal,

Padmanabhan, Rao, and Zill

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Estimate Wireless Interference• What is the metric to quantify wireless

interference?– Interference is not a binary relationship

• How to estimate wireless interference?– Using heuristics– Using empirical measurement

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Pairwise Interference Metric• Two links, A->B and C->D

– Throughputs U1 and U2 when operating individually

– Throughputs U1’U1’ and U2’U2’ when operating simultaneously

• Link Interference Ratio (LIR) = (U1U1/ / +U2U2/ / ) / (U1 + U2)– LIR = 1 implies no interference– LIR < 1 implies interference– Not just binary: full range of values between 0 and 1.

• Challenge: Estimate LIR for all link pairs without requiring O(n4) experiments

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Existing Heuristics• Heuristic 1

– All links in the multi-hop network interfere with each other

– Pessimistic Model• Heuristic 2

– Links which share an endpoint interfere with each other

– Optimistic Model• Heuristic 3

– Links AB and CD interfere if

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Evaluation of Heuristics• Experimental Setup

– A testbed of 22 nodes, 802.11 wireless cards,RTS/CTS disabled, 75 random links selected,1000 byte UDP packets for 30 seconds

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Proves 1st

heuristic wrong

Proves 2nd heuristic wrong

Median LIR of 75 links

Experimental results showed3rd to be pessimistic model

Existing heuristics are inaccurate. We need to look for methods to empirically measure wireless interference.

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Impact of Interference on Unicast Transmissions: #1

• Carrier sense– A and C can hear each other. – Only one transmits at a time.

A B

C D

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• Collision of data packets– Transmissions from A and C collide at B– Reception of data fails at B

A B

C D

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• Collision of data and ACK packets– ACK from D collides with data from A– Reception of data fails at B

A B

CD

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Impact of Interference on Unicast Transmissions: Other

Cases4. Data/ACK collision prevents reception of

ACK5. ACK/ACK collision

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Impact of Interference on Unicast Transmissions

1. Carrier sense2. Data/Data collision3. Data/ACK collision prevents reception of

data4. Data/ACK collision prevents reception of

ACK5. ACK/ACK collision

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Key Idea• Only consider carrier sense (#1) and data

packet collisions (#2)– Ignore ACKs

• Broadcast packets are sufficient for measurements– Consider only sender pairs, instead of link pairs– O(n2) experiments instead of O(n4)

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Methodology

Measure A’s receive rate @ B = M

Measure C’s receive rate @ D = N

Measure A’s receive rate @ B = M//

Measure C’s receive rate @ D = N//

Broadcast Interference Ratio (BIR) = (B1/ + B2/) / (B1 + B2)

A

C

D

B

= 1 no interference< 1 interference

Pairwise InterferenceIndividual Broadcasts

Hypothesis: BIR is a good approximation of LIR

BIR for all pairs can be calculated with O(n2) experiments

BIR Captures1. Carrier sense2. Data/Data collisions

BIR Ignores1. Data/ACK collisions2. ACK/ACK collsions3. AutoRate

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Evaluation: Baseline Scenario

Median LIR and BIR of 75 pairs CDF of |LIR-BIR|

802.11a, full power, 6Mbps, no RTS/CTS. 75 link pairs selected at random.

Average of 5 runs

Median error is zero!

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Evaluation: Other Scenarios

Three other scenarios 5 days apart

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Summary of results• BIR is a good approximation for LIR in

various scenarios – Low power– 802.11 a/b/g– Autorate

• BIR experiments need to be repeated regularly as link interference patterns change over time.

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Future work• More evaluation:

– On different testbeds

– Different power levels

• Interference among larger groups of links (not just pairs)

• Further reduce measurement overhead– Combine heuristics with measurements– Leverage passive measurement

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Thank you!

measuring and modeling the impact of wireless interference

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