Introduction to
Wireless Networks
Davide Bilò
e-mail: [email protected]
Wired vs Wireless

Wired Networks: data is transmitted via a finite
set of communication links (physical cables)

Wireless Networks: data is transmitted via etere
using electromagnetic waves (radio and/or
infrared signals)
Wireless Devices
Advantages:


portability
mobility
Disadvantage:

limited energy supply
Types of Wireless Connections

Wireless Personal Area Networks

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Wireless Local Area Networks

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Bluetooth
ZigBee
Wi-Fi
Fixed Wireless Data
Wireless Metropolitan Area Networks

WiMax

Wireless Wide Area Networks

Mobile Device Networks

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Global System for Mobile Communications
Personal Communication Service
Digital Advanced Mobile Phone Service
Models of Wireless Networks
Cellular Networks
wireless communication is based on the single-hop model
Radio Networks

no fixed infrastructures are needed

collection of homogenous devices

radio transceivers equipped with



processor
some memory
omnidirectional antennas

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useful for broadcast communications
limited energy supply

device can set their transmission power level

all devices usually transmit at the same frequency

communication is based on the multi-hop model


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to save energy
to decrease interference
to increase network lifetime
Models of Radio Networks

Mobile

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high mobility of devices
Static

devices are stationary

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static ad-hoc radio networks
static sensor networks
main applications:

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emergency and disaster reliefs
battlefield
monitoring remote geographical regions
traffic control
…
Static Ad-Hoc Radio
Networks
wireless communication is based on the multi-hop model
Sensor Networks
wireless communication is based on the multi-hop model
static
dynamic
Signal Propagation in
(Static) Radio Networks
Signal Attenuation
The signal is a wave propagating in the open air.
The signal intensity depends on:
 the transmission power level of the source
 environmental conditions:



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background noise
interference from other signals
presence of obstacles
climatic conditions
…
the traveled distance
Transmission Power and
Transmission Quality

Transmission power: it is the amount of energy spent by
a device to send a signal at some intensity.
(thus energy consumption is proportional to signal intensity)

Transmission quality: it is a threshold >0 below which
the signal intensity does not have to drop so that the
msg it carries can be decoded correctly by any receiver
The Euclidean Model for
(Static) Radio Networks

Wireless devices are points on the Euclidean plane
v2=(x2,y2)
|y2-y1|
v1=(x1,y1)
|x2-x1|
Given two points v1=(x1,y1),v2=(x2,y2) 2, the distance
d(v1,v2) between v1 and v2 is d (v1 , v2 )  ( x2  x1 )2  ( y2  y1 )2
The Euclidean Model for
(Static) Radio Networks
v2
v1
If v1 sends a msg M with power p(v1), then the signal intensity perceived
by v2 is p(v1)/d(v1,v2), where 1 is the distance-power gradient.
The Euclidean Model for
(Static) Radio Networks
v2 signal intensity is <
v1
signal intensity is 
If v1 sends a msg M with power p(v1), then the signal intensity perceived
by v2 is p(v1)/d(v1,v2), where 1 is the distance-power gradient.
v2 can decode msg M if p(v1)/d(v1,v2) (>0 is the transmission-quality parameter)
The Euclidean Model for
(Static) Radio Networks
signal intensity is <
v1
signal intensity is 
If v1 sends a msg M with power p(v1), then every station in the
transmission range of v1 will receive the msg M
p (v1 )

The transmission range of v1 is the disk centered at v1 of radius

The Euclidean Model for
(Static) Radio Networks
M
v1
M
When v1 sends a msg M with power p(v1), M is sent over all
the transmission range of v1 (broadcast transmission) in one round
The transmission range of v1 is the disk centered at v1 of radius

p (v1 )

Static Radio Networks are
Synchronous Systems
All devices share the same global clock
So
Devices act in rounds
Message transmissions are completed within one round
The Euclidean Model for
(Static) Radio Networks
Each device v transmits at power p(v)0 (p(v) may not be equal to p(u))
The transmission range of all the devices uniquely determine a directed
communication graph G=(V,E)

V is the set of devices
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E={(v,u): u is in the transmission range of v}
Broadcast
Over
Static Radio Networks
(when all devices transmit at the same frequency)
Message Collisions
u
M
M
M
M
M
v
M
v
If v sends a msg M at round r, then all in-neighbors u of v receive M
unless
some other in-neighbors v of u sends a msg M at (the same) round r
(in this case u gets nothing)
Collision Free Messages
M
M
M
M
M
M
a node u receives a msg during round r
iff
exactly one of all its in-neighbors v sends a msg during round r
Broadcast Over
Static Radio Networks

Model:


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strongly connected directed graph G=(V,E)
nodes know n=|V|
(non-uniform)
nodes have distinct identifiers in [n]
(non-anonymous)
(id(v) is the identifier of node v)
(Observe that nodes do not know G as well as their neighborhood)

Task: a source node sV wants to inform all the
other nodes of a msg M
Completion and Termination of
the Broadcast Protocol

Completion


A protocol completes broadcast from s over G if
there is a round r s.t. every node is informed
about the source msg M
Termination

A protocol terminates if there is a round r s.t.
any node stops any action within round r
A First Attempt

Protocol Flooding
(description for node v at round r)
if node v is informed of M then
v sends M
else
v does nothing
Flooding does not work!!!
s
How can we avoid
msg collisions?
Protocol Round Robin

Protocol Round Robin
(description for node v at round r of phase i)
(a phase consists of n consecutive rounds)
if node v is informed of M and id(v)=r then
v sends M
else
v does nothing
Analysis of
Protocol Round Robin
Let Li={vV: the hop-distance from s to v is i}

Lemma: At the end of phase i, all nodes in Li will be informed of the
source msg M.
Proof: By induction on i.
Fact: At the beginning, only L0={s} is informed of the source msg M
Base case i=1: no msg collision occurs at round id(s) of phase 1 where
only s sends M.
Inductive case i>1: Consider any vLi. Let u Li-1 s.t. (u,v)E.
Hypothesis: At the end of phase i-1, u is informed of M.
No msg collision occurs at round id(u) of phase i where only u sends M.
Thus, v will be informed of M at the end of phase i.
s
uLi-1
vLi
Analysis of
Protocol Round Robin
Let Li={vV: the hop-distance from s to v is i}


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Lemma: At the end of phase i, all nodes in Li will be
informed of the source msg M.
Corollary: Let  be the (unkown) source eccentricity, i.e.,
the minimum over all the integers i s.t. Li=V. Then  phases
suffice to inform all the nodes of the source msg M.
Lemma: Protocol Round Robin completes broadcast in
O(n) rounds.
Analysis of
Protocol Round Robin
Let Li={vV: the hop-distance from s to v is i}


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Lemma: At the end of phase i, all nodes in Li will be informed of the
source msg M.
Corollary: Let  be the (unkown) source eccentricity, i.e., the minimum
integer i such that Li=V. Then  phases suffice to inform all the nodes of
the source msg M.
Lemma: Protocol Round Robin completes broadcast in O(n) rounds.
What about termination?
(n-1 as G is strongly connected)
(Thus nodes can decide to stop after n-1 phases)
Analysis of
Protocol Round Robin
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Theorem: Protocol Round Robin

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completes broadcast in O(n) rounds
terminates broadcast in O(n2) rounds
Can We Do Better Than
Protocol Round Robin?
Yes if the in-degree  of nodes is “not too large”
completion in O(log n)
termination in O(nlog n)
(most of “good” networks have small value of )

Observation: protocol Round Robin does not exploit
parallelism at all

Goal: Select parallel transmissions
=max{v:vV} where v=|{uV:(u,v)E}|
A Way of Selecting
Parallel Transmissions


Definition: Let n and k be two integers with kn. A family F of
subsets of [n] is (n,k)-selective if, for every non empty
subset X of [n] with |X|k, there exists a set FF s.t. |FX|=1.
A trivial example…
F={{1},{2},…,{n}} is (n,k)-selective for any kn
How can selective families be used for broadcast?
(Assumption: nodes know )
Protocol Select

Protocol Select
 Set-up: all nodes know the same (n,)-selective family F={F1,…,Ft}
 (description for node v at round r of phase i)
(a phase consists of t consecutive rounds)
if node v is informed of M and id(v)Fr then
v sends M
else
v does nothing
Analysis of Protocol Select:
A First (Wrong) Attempt
Let Li={vV: the hop-distance from s to v is i}

Lemma: At the end of phase i, all nodes in Li will be informed of the
source msg M.
Proof: By induction on i.
Fact: At the beginning, only L0={s} is informed of the source msg M
Base case i=1: no msg collision occurs at the first round r of phase 1
s.t. id(s)Fr where only s sends M.
Inductive case i>1: consider any vLi. Let Nv={id(u):(u,v)E and uLi-1}.
Hypothesis: At the end of phase i-1, Nv is informed of M.
Since Nv[n] and |Nv|, there exists r s.t. NvFr={id(u)}.
No msg collision occurs at v during round r of phase i where u sends M.
Therefore, v will be informed of M at the end of phase i.
What’s wrong?
Inductive case i>1: consider any vLi. Let Nv={id(u):(u,v)E and uLi-1}.
Hypothesis: At the end of phase i-1, Nv is informed of M.
Since Nv[n] and |Nv|, there exists r s.t. NvFr={id(u)}.
No msg collision occurs at v during round r of phase i where u sends M.
we are not considering the impact
of nodes id(w)Li\ Li-1 s.t. (w,v)E and id(w)Fr
1.
if w is informed at beginning of round r of phase i,
then it creates msg collision at v
(Is this a solution? we may add id(w) to Nv)
What’s wrong?
Inductive case i>1: consider any vLi. Let Nv={id(u):(u,v)E and uLi-1}.
Hypothesis: At the end of phase i-1, Nv is informed of M.
Since Nv[n] and |Nv|, there exists r s.t. NvFr={id(u)}.
No msg collision occurs at v during round r of phase i where u sends M.
we are not considering the impact
of nodes wLi\ Li-1 s.t. (w,v)E and id(w)Fr
1.
if w is informed at beginning of round r of phase i,
then it creates msg collision at v
(Is this a solution? we may add id(w) to Nv) NO
2.
if w is not informed at beginning of round r of phase i,
then no msg is sent to v
How to Adapt
Protocol Select

IDEA: Only nodes that have been informed of M at the
end of phase i-1 will be active during phase i

Proof of Lemma now works if
Nv={id(u):(u,v)E and u is informed at the end of phase i-1}

completion time is O(|F|)
(to minimize completion time, we need minimum-size selective family)

Theorem: For sufficiently large n and kn, there exists an
(n,k)-selective family of size O(klog n).
(and this is optimal!!!)
 for protocol Select, |F|=O(log n)
Analysis of
Protocol Select
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Theorem: Protocol Select

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completes broadcast in O(log n) rounds
terminates broadcast in O(nlog n) rounds
If you want to know more…

Algorithmic problems for radio networks
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S. Schmid and R. Wattenhofer, Algorithmic models for sensor
networks
T. Locker, P. von Rickenbach, and R. Wattenhofer, Sensor
networks continue to puzzle: selected open problems
Both papers can be downloaded from
http://www.dcg.ethz.ch/members/roger.html

Broadcast over radio networks

A.E.F. Clementi, A. Monti, and R. Silvestri, Distributed broadcast in
radio networks of unknown topology
www.informatica.uniroma2.it/upload/2010/ADRC/CMS%20TCS%2001.pdf