Interference Models: Beyond the Unit-disk and Packet-Radio Models

1
Interference Models Beyond the Unit-disk and
Packet-Radio Models
Andrea W. Richa Arizona State University
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

3
Modeling Wireless Networks

• Wireless communication very difficult to model
  accurately
• Shape of transmission range
• Interference
• Mobility
• Physical carrier sensing

4
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

5
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

u
R
u'
v
6
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

7
Packet Radio Network (PRN)

• Can handle arbitrary transmission shapes
• Nodes u, v can communicate directly iff they are
  connected.
• Interference Model
• (interference range) (transmission range)
• too simplistic!

8
PRN What is the problem?
rt
v
s
rt
rt
t
ri
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

9
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
rt
u'
v
w
does not cause interference at u (even if all
nodes outside transmit at the same time)
may cause interference at u
10
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

11
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

12
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)
• d gt 0, depends on the environment
• c(u,v) Î d(u,v)/(1d), (1d) d(u,v)
• c may not be a metric

b
u
a
v
w
14
Transmission and Interference Ranges
u
ri(P)
v
c(v,w) rt(P) c(v,v') ri(P)
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.

15
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)
c(w,v) rst(T, P) c(w, v') rsi(T, P) c(w,
v'') ³ rsi(T, P)
w
v'
rst(T,P)
v
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)
c(w,v) rst(T) c(w, v') rsi(T) c(w, v'') ³
rsi(T)
w
v'
rst(T)
v
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.

18
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

19
SITWhat 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
Density 3

• 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)
• Transmission graph Gt(V,Et) edge (u,v) Î 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 resultsLocally 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).
• 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.

r-active
inactive
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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

r-active
inactive
changes from inactive to r-active in Step 1
25
Step 2 Leader Election

• Step 2
• Each r-active node transmits a LEADER signal with
  probability p (for some constant plt1).

r-active
inactive
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Step 2 Leader Election

• Step 2
• Each r-active node transmits LEADER signal with
  probability p (for some constant plt1).
• An r-active node not sending but either sensing
  or receiving a LEADER signal becomes inactive.

r-active
inactive
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

no active node transmitting here in round r whp
u
ri
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

v
u
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)

32
SIT What is the problem?

• 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 model

u
ri
rt
could still interfere at u
33
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

34
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)?
35
SINR Model

• Signal-Interference-Noise-Ratio (SINR)
  conditionA 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?
gt ?
N ?w in S P/w v?
36
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?
  gtT

37
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
38
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 causeinterference
v
interference range
may cause interference
39
SINR X Bounded Interference

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

transmission range
does not causeinterference
v
interference range
may cause interference
40
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
  pvmin(1?)pv, pmaxChannel busy
  pvmax(1-?)pv, pmin(?gt0 is a small constant)
• Multiplicative increase, multiplicative decrease
  scheme.

42
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.

43
SINR What is the problem?

• Is the model sufficiently realistic??
• Our interference model conservative
• signal cancellation
• different signal strengths
• bit recovery

44
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

45
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)

46
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?
48
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.

49
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 ?

50
Topological Spanner Protocol

• Three phase protocol
• Phase I Dominating set
• Phase II Refined Distributed Coloring
• Phase III Gateway Discovery

Phase III
Phase II
Phase II
Phase III
Ph. I
Ph. I
One round
Time

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

51
Quasi-Unit Disk Graphs (q-UDG)

• Kuhn et al03 Given parameter 0ltdlt1, modify UDG
  as follows
• d(u,v) d successful transmission
• d(u,v)gt1 v outside us transmission
  range
• d ltd(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
d
1
?
?
52

• 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

53
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