collaborative transmission in wireless sensor networks - introduction to wireless ... · 2010. 5....

Collaborative transmission in wireless sensornetworks

Introduction to wireless communications

Stephan Sigg

Institute of Distributed and Ubiquitous SystemsTechnische Universität Braunschweig

May 17, 2010

Stephan Sigg Collaborative transmission in wireless sensor networks 1/51

Overview and Structure

Introduction to context aware computing

Wireless sensor networks

Wireless communications

Basics of probability theory

Randomised search approaches

Cooperative transmission schemes

Distributed adaptive beamforming

Feedback based approachesAsymptotic bounds on the synchronisation timeAlternative algorithmic approachesAlternative Optimisation environments


OutlineWireless communications

1 Introduction

2 Aspects of the mobile radio channel

3 MIMO

4 Centralised beamforming


IntroductionWireless communications

Wireless communication

Utilisation of shared mediumElectromagnetic waveform transmitted betweencommunication partnersInformation modulated on top of a signal wave


IntroductionWireless communications



1 Introduction


3 MIMO



Aspects of the mobile radio channelWireless communications

RF transmission

Electromagnetic signals

Transmitted in wave-Form

Omnidirectionaltransmission

Speed of light

c = 3 · 108 ms



RF signal

Transmission power:

PTX [W ]

Frequency:

f [ 1sec ]

Phase offset:

γ[π]

Wavelength:

λ = cf [m]



RF signal

Real part of rotating vector

ζ = <(e j(ft+γ)

)Instantaneous signal stength:

cos(ζ)

Rotation Speed: Frequency f



Noise

In every realistic setting, noise can be observed on thewireless channel

Tpyical noise power:a

PN = −103dBm

Value observed by measurements

a3GPP: 3rd generation partnership project; technical specification group radio access networks; 3g home

nodeb study item technical report (release 8). Technical Report 3GPP TR 25.820 V8.0.0 (2008-03) (March)



Noise

Thermal noise can also be estimated analytically as

PN = κ · T · B

κ = 1.3807 · 10−23 JK : Boltzmann constantT : Temperature in Kalvin

B: Bandwidth of the signal.



Example

GSM system with 200kHz bands

Average temperature: 300K

Estimated noise power:

PN = κ · T · B

= 1.3807 · 10−23 JK· 300K · 200kHz

PN = −120.82dBm



Path-loss

Signal strength decreases while propagating over a wirelesschannel

Order of decay varies in different environments

Impact higher for higher frequencies

Can be reduced by antenna gain (e.g. directed)



Path-loss

For analytic consideration:Path-loss approximated

Friis free-space equation:

PTX ·(

λ

2πd

)2·GTX ·GRX



Path-loss

PRX = PTX ·(

λ

2πd

)2· GTX · GRX

Utilised in outdoor scenarios

Direct line of sightNo multipath propagation

d impacts the RSS quadratically

Other values for the path-loss exponent α possible.

Path-loss:

PLFS(ζi ) =PTX (ζi )

PRX (ζi )



Path-loss (Log-distance model)

Path-loss model suited in buildings or densely populated areas:

PLLD(ζi ) =PTX (ζi )

PRX (ζi )= 10

L010 · dα · 10

xg10

in dB:

PLLD(ζi ) = PTX (ζi )− PRX (ζi )

= L0 + 10 · α · log10(

d

d0

)+ Xg [dB]

L0: Path-loss at reference distance d0

Xg : Attenuation due to fading (random with zero mean)



Superimposition of RFsignals

Broadcast channel

Multipath transmission

ReflectionDiffractionDifferent path lengthsSignal componentsarrive at different times

Interference



Superimposition of RF signals

At a receiver, all incoming signals add up to onesuperimposed sum signal

Constructive and destructive interference

Normally: Heavily distorted sum singal



Fading

Signal quality fluctuating with location and time

Slow fading

Fast fading



Slow fading

Result of environmental changes

Temporary blocking of signal paths

Changing reflection angles

Movement in the environment

TreesCarsOpening/closing doors

Amplitude changes can be modelled by log-normal distribution



Fast fading

Signal components of multiple paths

Cancelation of signal components

Fading incursions expected in the distance of λ2Channel quality changes drastically over short distances

Example: Low radio reception of a car standing in front of aheadlight is corrected by small movement

Stochastic models are utilised to model the probability offading incursions

RiceRayleigh



Fast fading

Fast fading weakened when direct signal component observed

Modelled by Rice distribution:

f (A) =A

σ2e−

A2+s2

2σ2 I0

(As

σ2

)s: Dominant component of received signal

σ: Standard deviation

Modified Bessel function with order 0:

I0(x) =1

2π

∫ 2π0

ex cos(Ψ)dΨ



Ricean factor:

K =s2

2σ2

Impacts probability density function of Rice distributionMost probable outcome impacted



For K = 0, Rice distribution migrates to Rayleigh distribution:

limK→0

f (A) = limK→0

A

σ2e−

A2

2σ2−K I0

(A√

2K

σ

)

= limK→0

A

σ2e−

A2

2σ2−K 1

2π

∫ 2π0

eA√

2Kσ

cos(Ψ)dΨ

=A

σ2e−

A2

2σ2−0 1

2π

∫ 2π0

eA√

2·0σ

cos(Ψ)dΨ

=A

σ2e−

A2

2σ2



Rayleigh distribution

Probability density function of received sum singal for n� 1Assumption:

No direct signal component existsReceived signal components of approximately equal strength

Example: Urban scenarios with dense house blocks



With large K , Rice distribution evolves to Gauss distr.:

I0(x) →x�1→ex√2π

⇒ f (A) →x�1→A

σ2e−

A2

2σ2−K e

A√

2Kσ√

2πA√

2Kσ

f (A) =A

σ2√

2πσ

√A√

2Ke−

A2

2σ2− s

2

2σ2 eA√

2Kσ

=A

σ2√

2πσ

√A√

2Ke−

A2+s2−2As2σ2

=

√A

s

1

σ2πe−

12 (

A−sσ )

2



The term √A

s

1

σ2πe−

12 (

A−sσ )

2

differs from the Gauss distribution in√

As :

fGauss(x) =1

σ√

2πe−

12 (

A−sσ )

2

With√

As ≈ 1, Rice distribution can be approximated by

Gauss distribution



Interference

Signal components arrive from more than one transmitter

Neighbouring nodes generate interference:

ζsum =ι∑

i=1

<(e j(fi t+γi )

)



Interference

A radio system typically requires a specific minimum signalpower over interference and noise level:

SINR =Psignal

Pnoise + Pinterference

Concepts to reduce interference:

Clustering (cellular networks)Spread spectrum techniques (Code divisioning)



Clustering

Cells with identicalfrequencies separatedInterference in onefrequency band reduced



Clustering

Further reduction ofinterference bysectioning antennasTypically notimplemented in WSNs

Relative locationsof sensors unknownOrganisation ofcluster structureproblematic



Spread spectrum system

Utilise a very wide bandwidth for transmission

Interference in a small frequency band has reduced impact onthe overall transmission



Spread spectrum system – Frequency hopping

E.g. Bluetooth

79 sub-frequency bandsHop 1600 times per secondPseudo random hop sequenceMaster node controls hopping sequence



Spread spectrum system – Frequency hopping

Not well suited for WSNsProcessing required for frequency hopping would surchargeprocessing capabilities of sensor nodes



Spread spectrum system – Code divisioning

Spread transmit signal over whole frequency band

Add redundancy to the signal

Combination of the transmit symbols with pseudo-randomcode sequence

Interference in limited frequency band with low effect

Transmitters simultaneously utilise identical frequency




Transmitters share the same frequency

Unique, orthogonal pseudo noise sequences

Decoding possible: Pseudo noise sequence linked totransmitter

Transmission below noise level possible

Creation of pseudo noise sequences: E.g. OVSF



Orthogonal VariableSpreading Factor (OVSF)

Root spreading code:

ci ,j ∈ {0, 1}i ; i , j ∈ N

Create

c2i ,2j−1 = (ci ,jci ,j)

c2i ,2j = (ci ,jci ,j)




Utilised also in WSNsE.g. CDMANumber of code seqeunces of a given length restricted



α

Movement direction

Receive node

Transmit node

sign

al p

ropa

gatio

n

rela

tive

spee

d be

twee

n tran

smitt

er a

nd re

ceiv

er (v

)

Doppler ShiftFrequency of a received signal may differ to the frequency ofthe transmitted signalDependent on relative speed between transmitter and receiverfd =

vλ · cos(α)



1 Introduction


3 MIMO



MIMOWireless communications

Wireless communicationTypically one transmitter and one receiver

SISO

Capacity increased by diversity schemes as

Time diversityFrequency diversityCode divisioning



Spatial diversity

ClusteringMultiple transmit or receive antennas for a singlecommunication link

SIMOMISOMIMO

Spatially separated antennas

Independent communication channelsFading characteristics for these channels differentProbability of inferior reception on all channels simultaneouslylow



Vector-Matrix of a MIMO-System:

−−→ζRX =

ζRX1ζRX2

...ζRXM

=

h11 h12 · · · h1Lh21

. . . h2L...

. . ....

hM1 hM2 · · · hML

ζTX1ζTX2

...ζTXL

+ζnoise1ζnoise2

...

ζnoiseM



−−→ζRX =

ζRX1ζRX2

...ζRXM

=

h11 h12 · · · h1Lh21

. . . h2L...

. . ....

hM1 hM2 · · · hML

ζTX1ζTX2

...ζTXL

+ζnoise1ζnoise2

...

ζnoiseM

Vector of received signal components:

−−→ζRX = (ζRX1 , ζ

RX2 , . . . , ζ

RXM )

T

Vector of noise signals:

−−−→ζnoise = (ζnoise1 , ζ

noise2 , . . . , ζ

noiseM )

T

Channel Matrix H describes connection of inputs and outputs.Stephan Sigg Collaborative transmission in wireless sensor networks 46/51


Potential gain of a MIMO systemImprove communication speed

Parallel transmission over all channels

Improve robustness of communication

Transmit redundant information over all channels



MIMO for WSNs?Not probable since antennas have to be sufficiently separated

Typical estimation: λ2

With 2.4GHz:3 · 108 m

sec

2.4 ∗ 109 1sec

= 12.5cm

Typical sensor nodes smaller in size



1 Introduction


3 MIMO



Centralised beamformingWireless communications

Centralised beamforming

Create an antenna beam of synchronised transmissions that isfocused on a restricted area

Signal components form transmit antennas coherently overlaid

Constructive interference at the receiver

Outside the restricted area, signal components vanish in thenoise signal

Reduced interference to neighbouring receivers


Centralised beamformingWireless communications

Centralised beamforming

Fixed antenna Array

Exact relative location of all antennas knownAll antenna elements tightly synchronisedSignals from each antenna element suitably weighted

Focus and control transmission beam

Received sum signal:

n∑i=1

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