Andrea Richa 1

Interference Models: Beyond the Unit-disk and

Packet-Radio Models

Interference Models: Beyond the Unit-disk and

Packet-Radio ModelsAndrea W. Richa

Arizona State University

Andrea Richa 2

Ad hoc Networks ● Wireless stations communicating over a wireless

medium with no centralized infrastructure

● How to model ad hoc networks?– Need models that are close to reality, but which still

allow for the design and formal analysis of algorithms

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Modeling Wireless Networks

● Wireless communication very difficult to model accurately:– Shape of transmission range

– Interference

– Mobility

– Physical carrier sensing

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Outline Introduction

→Simple Models of Wireless networks

● Bounded Interference Models● SIT Model

– What have we done? Leader Election; Constant Density Spanner

● Extended SINR Model● Future Work and Conclusions

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Unit-Disk Graph

● Unit-Disk Graph (UDG)– Given a transmission radius

R, nodes u, v are connected iff d(u,v) ≤ R

– Too simple a model

uR

vu'

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● Transmission range could be of arbitrary shape

●Does not consider interference R u

UDG: What is the Problem?

● quasi-UDGs [Kuhn et al. 03]: - some uncertainty/non-uniformity

in transmission, but still does not consider interference

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● Can handle arbitrary transmission shapes● Nodes u, v can communicate directly iff they are

connected.● Interference Model:

– (interference range) = (transmission range)

– too simplistic!

u

v

w

v'

Packet Radio Network (PRN)

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●While in the PRN model, s can send a message to t in 2 steps, no uniform protocol can successfully send a message in expected o(n) number of steps: linear slowdown

PRN: What is the problem?

v

n-2 nodes

st ≤

rt

≤ rt

≤ ri

≥ rt

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Transmission and Interference Ranges:● Separate values.● Interference range constant times bigger

than transmission range.Preliminary work:

– most assume disk-shaped interference – [Adler and Scheideler '98]: too restrictive

model for transmission– …

Bounded Interference Models

u rt

vw

u'

ri

does not cause interference at u (even if all nodes outside transmit at the same time)

may cause interference at u

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OutlineIntroduction

Simple Models of Wireless Networks

Bounded Interference Models

→SIT Model

– What have we done: Leader Election; Constant Density Spanner

● Extended SINR Model

● Future Work and Conclusions

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SIT Model● SIT (Sensing - Interference - Transmission)

– Separate transmission and interference ranges via cost function

– arbitrary, non-disk communication shapes

– bounded interference

● Carrier sensing:–Physical carrier sensing: sense whether the

channel is busy or not–Virtual carrier sensing

● fully probabilistic model

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Why Physical Carrier Sensing?

● Using physical carrier sensing, we can extract information from the network without relying on successful message transmissions– quite often it is enough just to know if at least one node is

sending a message, rather than receiving the message– linear speedup

● It comes for “free”

v

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Cost Function

● Euclidean distance d(•,•)

● Cost function c:

– symmetric: c(u,v) = c(v,u)

− , depends on the environment

– c(u,v) [d(u,v)/(1+), (1+) d(u,v)]

– c may not be a metric

w

u

va

b

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Transmission and Interference Ranges

● Transmission power P

● Transmission range rt(P); Interference range ri(P)

– A node v can only cause interference at node v’ if c(v,v’) ≤ r

i(P), w.h.p.

– If c(v,w) ≤rt(P) then v successfully receives a message

from w provided no other node v' with c(v, v') ≤ ri(P) also

transmits at the same time, w.h.p.

w

rt(P)v'

ri(P)

u

vc(v,w) rt(P)

c(v,v') ri(P)

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Physical Carrier Sensing

● Clear Channel Assessment (CCA) circuit:– Monitors the medium as a function of Received Signal

Strength Indicator (RSSI)

– Energy Detection (ED) bit set to 1 if RSSI exceeds a certain threshold

– Has a register to set the threshold T in dB

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Physical Carrier Sensing

● Carrier sense transmission (CST) range, denoted rst(T, P)

● Carrier sense interference (CSI) range, denoted rsi(T, P)

● Both ranges grow monotonically in both T and P.

● We will assume that P is fixed, and omit this parameter in the remainder of this talk.

w

vr

st(T,P)v'

v''

rsi(T,P) c(w,v) rst(T, P)

c(w, v') rsi(T, P)

c(w, v'') rsi(T, P)

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Carrier Sensing Ranges

w

vr

st(T)v'

v''

rsi(T) c(w,v) rst(T)

c(w, v') rsi(T)

c(w, v'') rsi(T)

● If c(v,w) ≤ rst(T), then w senses a transmission by node v, w.h.p.

● If w senses a transmission then there is at least one node v' transmitting a message such that c(v',w) ≤ rsi(T), w.h.p.

● Nodes outside of rsi(T) cannot be sensed by node w, w.h.p.

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Outline Introduction

Simple Models of Wireless Networks

Bounded Interference Models

SIT Model

→What have we done? Leader Election; Constant Density Spanner

● Extended SINR Model

● Future Work and Conclusions

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SIT:What have we done?● Constant density dominating set and topological

spanner:– Local-control– Self-stabilizing [Dijkstra '74], even in the presence of

adversarial behavior– No knowledge (estimate) of the size or topology of the

network– Nodes do not need globally distinct labels– Constant size messages

● Broadcasting and information gathering: Use constant density spanner

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Dominating Sets

● Dominating set (DS): a subset U of nodes such that each node v is either in U or has a node w in U within its transmission range (i.e., c(v,w) ≤ r

t)

● Transmission graph Gt(V,Et): edge (u,v) Et iff c(u,v) ≤ rt

● Density of U: maximum number of neighbors that a node has in U.

● Seek for connected dominating set of constant density Dominator / Leader

Density = 3

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Constant Density Dominating Set● Our results:

Locally self-stabilizing randomized protocol that converges to a constant density dominating set of the transmission graph Gt in O(log4 n) steps w.h.p.

● Uncertainties in our model make it harder!● Without any estimate on the size of network, we

need to exploit physical carrier sensing!

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Dominating Set AlgorithmBasic principles:● Nodes are either inactive or active (the potential

leader nodes) and work in synchronous rounds ● Rounds organized into time frames of k rounds each

(k sufficiently large constant).

● i-active node: active node that selected round i of the k rounds in a frame for its activities (like k-coloring)

● Initially, all nodes are 1-active● Each round r of given frame consists of 2 steps:

Round 1 Round 2 Round k Round 1 Round 2…. ….

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Step 1: “Waking up” nodes

Step 1: ● Each r-active node transmits an ACTIVE signal.

inactive r-active

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Step 1: “Waking up” nodes

Step 1: ● Each r-active node transmits an ACTIVE signal.● Each inactive node performs physical carrier sensing.

No channel acitivity for last k rounds, including round r : inactive node becomes r-active

inactive changes from inactive to r-active in Step 1

r-active

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Step 2: Leader Election

Step 2: ● Each r-active node transmits a LEADER signal with

probability p (for some constant p<1).

inactive r-active

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Step 2: Leader Election

Step 2: ● Each r-active node transmits LEADER signal with

probability p (for some constant p<1). ● An r-active node not sending but either sensing or

receiving a LEADER signal becomes inactive.

inactive r-active

changes from r-active to inactive in Step 2

such conflicts will eventually be resolved

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Why k rounds (k-coloring)?

Fact: In Gt ,any Maximal Independent Set (MIS) is also a dominating set of constant density [Luby '85, Dubhashi et al., '03, Kuhn et al., '04, Gandhi and Parthasarathy '04]

● Given uncertainties in our model, we cannot guarantee that leader nodes will form an independent set without risking loss of coverage (i.e., having some inactive nodes not covered by any leader)

Solution: we use k independent sets (one for each color) to guarantee coverage!

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Different Sensing Ranges

● E.g., an inactive node v uses different sensing ranges for the round r when it attempts to become active, and for other rounds.

● Interference-free communication among r-active (leader) nodes

● Coverage for all nodes

u rtri

no active node transmitting here in round r whp

if an active node transmitted here in a round other than r, v would have sensed whp

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Topological Spanners

● Definition: Given a graph G(V,E), find a subgraph H(V,E') such that d

H(u,v) ≤ t dG(u,v)

– Distances measured in number of edges (number of hops)

– H is also called a t-spanner

● Previous Work (weaker models): [Alzoubi et. al., '03], [Dubhashi et. al., '03] , …

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Constant Density Topologial Spanner

● Our results: Our local self-stabilizing protocol achieves a constant density 5-spanner of the transmission graph Gt,, in O(log4 n + (D log D) log n) time w.h.p.– D: density of the original network

u

l

l'v

st

Active node

Inactive nodeGateway nodeGateway edgeOther edges

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Simulations

● 90% of work through physical carrier sensing● Performance comparable with other overlay network

protocols (which need more assumptions, use simpler communication models)

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SIT: What is the problem?

u rtri

Problem: Sharp threshold for transmission?– forward error correction

Problem: Does not consider signal-to-noise ratio?– conservative model

Problem: Does not consider unbounded (physical) interference!!– many transmitting nodes far away

from u could still interfere at node u

Solution: Extended SINR modelcould still interfere at u

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Outline Introduction

Simple Models of Wireless Networks

Bounded Interference Models

SIT Model

What have we done? Leader Election; Constant Density Spanner

→Extended SINR Model

● Future Work and Conclusions

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Log-normal Shadowing

● Well-approximated by our cost model (SIT model)– irregular coverage area– sharp transmission threshold (forward error correction)

● when node u transmits with power P, received power at node v is

: path loss coefficient

P

c(u,v)

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SINR Model

● Signal-Interference-Noise-Ratio (SINR) condition:A message sent by node u is received at node v iff

- N: Gaussian variable for background noise- S: set of transmitting nodes- : constant that depends on transmission scheme

● “Unbounded interference“

P/||u v||

N + w in S P/||w v||>

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Extended SINR Model

● Extend SINR model to incorporate physical carrier sensing

● ED-bit set to 1 at v iff N + w in S P/||w v|| >T

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Extended SINR Model

Problem: Difficult to rigorously analyze routing protocols in this model!

Solution: Reduce (extended) SINR model to bounded interference model with proper MAC scheme

PHY

MACExtended SINR model

Bounded interference model

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SINR X Bounded Interference

Fact: If node distribution in ad hoc network is of constant density, then SINR simplifies to bounded interference.

v

transmission range

interference range

may cause interference

does not causeinterference

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SINR X Bounded Interference

So how do we get from arbitrary distribution to constant density distribution of nodes???

v

transmission range

interference range

may cause interference

does not causeinterference

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Getting Down to Constant Density

● Each node is initially inactive.

● Each node v maintains a probability of transmission pv.

Goal: For each transmission range Rv of node v,

w in Rv pw = (1)

bounded interference

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Getting Down to Constant Density

Density Estimation:● Each node v chooses one of two time steps uniformly

at random, say step s (the other step is s):– Step s: v transmits PING signal with probability pv

– Step s: v senses channelChannel free: pv:=min{(1+)pv, pmax}Channel busy: pv:=max{(1-)pv, pmin}(>0 is a small constant)

Multiplicative increase, multiplicative decrease scheme.

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Algorithms for SINR Model

● W.h.p., in O(log n) time steps, our locally self-stabilizing algorithm converges to the right density estimates for all nodes.– the subset of nodes actively transmitting at any time

step is of constant density, w.h.p.

● Current Work: Dominating set algorithm for extended SINR model is locally self-stabilizing and needs O(log n) time steps, w.h.p., to arrive at a stable constant density dominating set.

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SINR: What is the problem?

Is the model sufficiently realistic??

● Our interference model conservative:– signal cancellation

– different signal strengths

– bit recovery

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Self-Stabilization

● wireless communication too complex: no model will be able to accurately take into account all that can happen

Problem: What happens if things deviate from proposed model?

Solution: Protocols need to be self-stabilizing, i.e., they need to go back to a valid configuration for the model

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Collaborators● Wireless Models:

– Christian Scheideler (Technical U. of Munich),– Paolo Santi (U. of Pisa), – Kishore Kothapalli (IIIT), – Melih Onus (ASU)

● Simulations: – Martin Reisslein (ASU), – Luke Ritchie (ASU)

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More Future Work

● throughput

● power control

● future devices: MIMO (send/receive at same time), cognitive radio (continuous scan of available frequencies)

● alternatives to pure multihop ad-hoc networks?

– wireless mesh networks: basestations form a mesh, everybody else ad-hoc

● energy-efficiency

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Questions?

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Publications● K. Kothapalli, C. Scheideler, M. Onus, A.W. Richa. Constant density

spanners for wireless ad-hoc networks. In Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), pages 116-125, 2005.

● K. Kothapalli, M. Onus, A.W. Richa and C. Scheideler. Efficient Broadcasting and Gathering in Wireless Ad Hoc Networks. In Proceedings of the IEEE International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN), pages 346-351, 2005.

● L. Ritchie, S. Deval, M. Onus, A. Richa, and M. Reisslein. Evaluation of Physical Carrier Sense Based Spanner Construction and Maintenance as well as Broadcast and Convergecast in Ad Hoc Networks. Submitted to IEEE Transactions on Mobile Computing.

● A.W. Richa, C. Scheideler, P. Santi. Leader Election Under the Physical Interference Model in Wireless Multi-Hop Networks. Manuscript.

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Log-Normal Shadowing

● Received power at a distance of d relative to received power at reference distance d0 in dB is

-10 log(d/d0) + X

- : path loss coefficient- X: Gaussian variable with standard deviation

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Topological Spanner Protocol

● Each round has time slots reserved for each phase of the protocol

Three phase protocol:1. Phase I: Dominating set2. Phase II: Refined Distributed Coloring3. Phase III: Gateway Discovery

One round

Ph. I Phase II Phase III Ph. I Phase II Phase III

Time

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Quasi-Unit Disk Graphs (q-UDG)[Kuhn et al’03] Given parameter

0< modify UDG as follows:● d(u,v)≤ successful transmission● d(u,v)>1: v outside u’s transmission

range● <d(u,v) ≤ 1: transmission may or

may not be successful

What is the problem?– model for transmission too conservative– does not model interference– green zone as “interference zone”?

• no interference within transm. range• disk shaped interference

u δ1

?

?

?

?

?

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– senses an ACTIVE signal with CSI range of rt; if it did

not sense any signal for the last k-1 rounds it senses with CST range of ri and if channel is clear, it

becomes r-active

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Maximal Independent Sets

Fact: In Gt ,any Maximal Independent Set (MIS) is also a dominating set of constant density – [Luby '85], [Dubhashi et. al., '03], [Kuhn et. al., '04],

[Gandhi and Parthasarathy '04]

● Ideally, we would like to be able to show that the set of leader nodes form a MIS. However…