Transcript Interference Models: Beyond the Unit-disk and Packet-Radio Models Andrea W. Richa Arizona State University Andrea Richa.

Interference Models:
Beyond the Unit-disk and
Packet-Radio Models
Andrea W. Richa
Arizona State University
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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
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u
u'
R
v
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UDG: What is the Problem?
● Transmission range could be of
arbitrary shape
● Does not consider interference
R
u
● quasi-UDGs [Kuhn et al. 03]:
- some uncertainty/non-uniformity
in transmission, but still does not
consider interference
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Packet Radio Network (PRN)
u
v'
v
w
● Can handle arbitrary transmission shapes
● Nodes u, v can communicate directly iff they are
connected.
● Interference Model:
– (interference range) = (transmission range)
– too simplistic!
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PRN: What is the problem?
s
≤ rt
≥ rt
v ≤ rt
≤ ri
t
n-2 nodes
● 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
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Bounded Interference Models
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
–…
u
ri
u'
rt
v
w
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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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 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
v
● It comes for “free”
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Cost Function
● Euclidean distance d(•,•)
● Cost function c:
– symmetric: c(u,v) = c(v,u)
− d > 0, depends on the
environment
u
b
a
v
w
– c(u,v)  [d(u,v)/(1+d), (1+d) d(u,v)]
– c may not be a metric
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Transmission and Interference
Ranges
u
c(v,w)  rt(P)
c(v,v')  ri(P)
ri(P)
v'
v
rt(P)
w
● 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’) ≤
ri(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.
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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
rsi(T,P)
v'
c(w,v)  rst(T, P)
w
rst(T,P)
v
c(w, v')  rsi(T, P)
c(w, v'')  rsi(T, P)
v''
●
●
●
●
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.
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Carrier Sensing Ranges
rsi(T)
v'
c(w,v)  rst(T)
w
rst(T)
c(w, v')  rsi(T)
v
c(w, v'')  rsi(T)
v''
● 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) ≤ rt)
Density = 3
● 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
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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 Algorithm
Basic 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).
Round 1 Round 2
….
Round k Round 1 Round 2
….
● 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:
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Step 1: “Waking up” nodes
r-active
inactive
Step 1:
● Each r-active node transmits an ACTIVE signal.
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Step 1: “Waking up” nodes
r-active
inactive
changes from inactive
to r-active in Step 1
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
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Step 2: Leader Election
r-active
inactive
Step 2:
● Each r-active node transmits a LEADER signal with
probability p (for some constant p<1).
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Step 2: Leader Election
r-active
inactive
changes from r-active
to inactive in Step 2
such conflicts will eventually be resolved
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.
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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
no active node transmitting here
in round r whp
ri
u
rt
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 dH(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
v
Active node
Inactive node
Gateway node
Gateway edge
Other edges
l'
l
s
t
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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?
Problem: Sharp threshold for
transmission?
– forward error correction
Problem: Does not consider signal-tonoise ratio?
ri
u
rt
– 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 model
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could 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
P
c(u,v)
- : path loss coefficient
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SINR Model
● Signal-Interference-Noise-Ratio (SINR) condition:
A message sent by node u is received at node v iff
P/||u v||
N + w in S P/||w v||
>
- N: Gaussian variable for background noise
- S: set of transmitting nodes
- : constant that depends on transmission scheme
● “Unbounded interference“
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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
Bounded interference model
MAC
Extended SINR model
PHY
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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.
transmission range
does not cause
interference
v
interference range
may cause interference
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SINR X Bounded Interference
So how do we get from arbitrary distribution to constant
density distribution of nodes???
transmission range
does not cause
interference
v
interference range
may cause interference
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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 channel
Channel 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 selfstabilizing 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
Three phase protocol:
1. Phase I: Dominating set
2. Phase II: Refined Distributed Coloring
3. Phase III: Gateway Discovery
Ph. I
Phase II Phase III Ph. I
Phase II Phase III
One round
Time
● Each round has time slots reserved for each phase
of the protocol
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Quasi-Unit Disk Graphs (q-UDG)
[Kuhn et al’03] Given parameter 0<d<1,
modify UDG as follows:
● d(u,v)≤ d: successful transmission
● d(u,v)>1: v outside u’s transmission
range
● d <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
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?
?
?
u δ
1
?
?
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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…
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