Introduction to Wireless Networks

Introduction to Wireless Networks

Davide Bilòe-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 Bluetooth ZigBee

Wireless Local Area Networks Wi-Fi Fixed Wireless Data

Wireless Metropolitan Area Networks WiMax

Wireless Wide Area Networks

Mobile Device Networks 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

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

to save energy to decrease interference to increase network lifetime

Models of Radio Networks Mobile

high mobility of devices Static

devices are stationary static ad-hoc radio networks static sensor networks

main applications: 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:

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

Given two points v1=(x1,y1),v2=(x2,y2) 2, the distance

d(v1,v2) between v1 and v2 is2 2

1 2 2 1 2 1( , ) ( ) ( )d v v x x y y

v1=(x1,y1)

v2=(x2,y2)

|x2-x1|

|y2-y1|

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.


v1

v2

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)


v1

v2 signal intensity is <

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

The transmission range of v1 is the disk centered at v1 of radius


v1

1( )p v

signal intensity is <

signal intensity is

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


v1

1( )p v

M

M

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

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 directedcommunication graph G=(V,E) V is the set of devices E={(v,u): u is in the transmission range of v}


Broadcast

Over

Static Radio Networks(when all devices transmit at the same frequency)

uv

v

Message Collisions

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

MM

M

(in this case u gets nothing)

M M

M

Collision Free Messages

a node u receives a msg during round r

iff

exactly one of all its in-neighbors v sends a msg during round r

M

M

MM

MM

Broadcast Over Static Radio Networks

Model: 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 sV 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

s

Flooding does not work!!!

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={vV: 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 vLi. 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.

suLi-1 vLi




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.




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)


Theorem: Protocol Round Robin 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(nlog 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:vV} where v=|{uV:(u,v)E}|

A Way of Selecting Parallel Transmissions

Definition: Let n and k be two integers with kn. 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 FF s.t. |FX|=1.

A trivial example…

F={{1},{2},…,{n}} is (n,k)-selective for any kn

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



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 vLi. Let Nv={id(u):(u,v)E and uLi-1}. Hypothesis: At the end of phase i-1, Nv is informed of M. Since Nv[n] and |Nv|, there exists r s.t. NvFr={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 vLi. Let Nv={id(u):(u,v)E and uLi-1}. Hypothesis: At the end of phase i-1, Nv is informed of M. Since Nv[n] and |Nv|, there exists r s.t. NvFr={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 vLi. Let Nv={id(u):(u,v)E and uLi-1}. Hypothesis: At the end of phase i-1, Nv is informed of M. Since Nv[n] and |Nv|, there exists r s.t. NvFr={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 wLi\ 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 kn, 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

Theorem: Protocol Select completes broadcast in O(log n) rounds terminates broadcast in O(nlog n) rounds

If you want to know more… Algorithmic problems for radio networks

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 fromhttp://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 topologywww.informatica.uniroma2.it/upload/2010/ADRC/CMS%20TCS%2001.pdf

Documents

Introduction to Wireless Networks