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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
Andrea Richa 3
Modeling Wireless Networks
● Wireless communication very difficult to model accurately:– Shape of transmission range
– Interference
– Mobility
– Physical carrier sensing
Andrea Richa 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
Andrea Richa 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
uR
vu'
Andrea Richa 6
● 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
Andrea Richa 7
● 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)
Andrea Richa 8
●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
Andrea Richa 9
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
Andrea Richa 10
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
Andrea Richa 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
Andrea Richa 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
Andrea Richa 13
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
Andrea Richa 14
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)
Andrea Richa 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
Andrea Richa 16
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)
Andrea Richa 17
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.
Andrea Richa 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
Andrea Richa 19
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
Andrea Richa 20
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
Andrea Richa 21
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!
Andrea Richa 22
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…. ….
Andrea Richa 23
Step 1: “Waking up” nodes
Step 1: ● Each r-active node transmits an ACTIVE signal.
inactive r-active
Andrea Richa 24
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
Andrea Richa 25
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
Andrea Richa 26
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
Andrea Richa 27
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!
Andrea Richa 28
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
Andrea Richa 29
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] , …
Andrea Richa 30
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
Andrea Richa 31
Simulations
● 90% of work through physical carrier sensing● Performance comparable with other overlay network
protocols (which need more assumptions, use simpler communication models)
Andrea Richa 32
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
Andrea Richa 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
Andrea Richa 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)
Andrea Richa 35
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||>
Andrea Richa 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|| >T
Andrea Richa 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
PHY
MACExtended SINR model
Bounded interference model
Andrea Richa 38
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
Andrea Richa 39
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
Andrea Richa 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
Andrea Richa 41
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.
Andrea Richa 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.
Andrea Richa 43
SINR: What is the problem?
Is the model sufficiently realistic??
● Our interference model conservative:– signal cancellation
– different signal strengths
– bit recovery
Andrea Richa 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
Andrea Richa 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)
Andrea Richa 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
Andrea Richa 47
Questions?
Andrea Richa 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.
Andrea Richa 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
Andrea Richa 50
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
Andrea Richa 51
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
?
?
?
?
?
Andrea Richa 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
Andrea Richa 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…
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