Radiowave Channel Modelling for Sensor Networks Costas Constantinou Electronic, Electrical &...

Radiowave Channel Modelling for Sensor Networks

Costas ConstantinouElectronic, Electrical & Computer Engineering

The University of Birmingham, UKhttp://www.eee.bham.ac.uk/ConstantinouCC/

[email protected]

2

Motivation

Sensor networks are inevitably wireless The notion of a link between two nodes is neither

simple nor something that can be abstracted trivially Protocol design is fundamentally dependent on

behaviour of wireless “links” MAC – which nodes interfere with each other Routing – selection of next hop Security – identification/estimation of which nodes can

overhear a transmission This talk will focus on wireless propagation

fundamentals (physics layer) – essentially it is a tutorial

2

33

Electromagnetic waves

Electric & Magnetic fields Basic notions

Fields are mechanisms of transfer of force and energy Distributed in space and time Have direction as well as magnitude

Two types of ‘arrow’ Vector Phasor

Vector & Phasor addition illustrated

1sincosexp jjj

Im

Re0

1

44


Vector plane waves

Frequency

Wavenumber

Wavelength

cztjE

cztHtzyx

cztjEcztEtzyx

yy

xx

expˆ120

Recosˆ,,,

expˆRecosˆ,,,

00

00

eeH

eeE

2

radHz f

cmk

)( 1

k

m 2

cf

55

Reflection of plane waves

Reflection coefficient is a tensor

The reflection coefficient can be resolved into two canonical polarisations, TE and TM and has both a magnitude and phase

2

0

20TE

sincos

sincos

j

j

r

r

ir EΓE

.

jexp

Plane of incidence

2

00

200||TM

sincos

sincos

jj

jj

rr

rr

66

Reflection of plane waves

Typical reflection coefficients for ground as a function of the grazing angle (complement of the angle of incidence). In this instance,

12 Sm10,15 rPseudo-Brewster angle

77

Common electrical constants

Electrical properties of typical construction materials in UHF band (300MHz – 3GHz)Material r (Sm-1)

Ground 7-30; typical 15 0.001-0.02; typical 0.005

Fresh water 81 0.01

Sea water 81 4

Brick 4 0.02

Concrete (dry) 7 0.15

Concrete (aerated) 2 0.08

Gypsum (plaster) board 2.25 0.02

Glass 3.8-8 0.001

Wood 1.5-2.1 0.01

88


Spherical waves Intensity (time-average) Conservation of energy; the inverse square law

HES

212Wm

99


Conservation of energy; the inverse square law

2

dtransmitte

2

steradians ofsector angular an in dtransmitte

2

221122

21

2

1

1

2

4

11

21

r

P

rl

Prr

PAAPr

r

A

A

l

AA

r

r

rEr

rrr

r

1010

Radiation

Pictorial introduction to radiation from accelerated charges

1111

Radiation


1212

Radiation


1313

Radiation

Fields around a charge in non-uniform motion

1414

Radiation


1515

Radiation


1616

Radiation

Radiated fields proportional to charge acceleration (current proportional to charge velocity) and number of charges

Radiated wave is spherical provided the observation point is far enough away from the source

Radiated wave is transverse electromagnetic The field magnitude is proportional to the sine of the angle from

the axis of charge acceleration Small antenna (Length & constant current )

in the far-field 22Lr

L tjI exp

L

r

crtjIj

rcrtjILjr, θ,Eθ

sinexp60

sin1

exp10 7

1717

Antennas

In general, the fields radiated by an arbitrary antenna in the far-field zone are of the form,

where the last term is the antenna radiation pattern (including its polarisation characteristics) Radiation pattern: a polar plot of power radiated per unit solid angle

(radiation intensity) Isotropic antenna does not exist in 3D, but is still being used as a

reference antenna

,ˆ,êxp

60, rad ggr

crtjPr eeE

1818

Antennas

A general antenna pattern

1919

Antennas

Radiation pattern: a polar plot of power radiated per unit solid angle (radiation intensity) Directional vs. omni-

directional antenna Lobes: main lobe (boresight

direction), sidelobes, backlobes

Half-power beamwidth (HPBW); first null beamwidth (FNBW)

Sidelobe levels (dB) Front-to-back ratio (dB)

2020

Antennas

Directivity

Radiation efficiency

Gain (directive gain)

Beamwidth and directivity (pencil beam antenna)

Bandwidth: impedance vs. pattern

space allover intensity radiation Average

,direction in antenna ofintensity Radiation ,

D

,,, ant DG

inradant PP

HPBWHPBWD

000,41

dBilog10 max10dBi GG

2121

Antennas

Reciprocity and receiving effective aperture area The gain of an antenna in transmission mode is proportional to its

effective aperture area in reception mode and the constant of proportionality is universal for all antennas

Polarisation matching (dot product between incident electric field vector and the unit vector of antenna polarisation) Co-polar pattern Cross-polar pattern

antennaon density power Incident

terminalsantennaat power received available TotaleA

2

4

rx

etx AG physicalaperture AAe

2222

Antennas Antenna examplesAntenna Gain

(dBi)Band-width

Pola-risation

Half-power beamwidth ()

Half-power beamwidth ()

Small dipole or loop (L<< )

1.76 N/A Linear 90° Omni-directional

Half-wavelength (/2) dipole

2.16 15% Linear 78° Omni-directional

Yagi-Uda array of /2 dipoles

12 5% Linear 65° 45°

Patch antenna (typical)

6 5% Linear 80° 80°

Helical antenna: axial mode – typ.

13 2:1 Circular 20° 20°

Helical antenna: normal mode – typ.

2.16 15% Linear 78° Omni-directional

2323

Free space propagation

Transmitted power EIPR (equivalent isotropically radiated power) Power density at receiver

Received power

Friis power transmission formula

txP

txtx PG

2txtx

rx 4 R

PG

S

4;

4

2

rxrxrx

2txtx

rx GAAR

PGP ee

2

rxtxtx

rx

4

RGG

P

P

tx rx

R

2424

Free space propagation

Taking logarithms gives

where is the free-space path loss, measured in decibels

Math reminder

R

GGPP4

log20log10log10log10log10 10rx10tx10tx10rx10

cbcb aaa logloglog ,loglog bcb ac

a

dBdBidBidBWdBW 0rxtxtxrx LGGPP

0L

dB4

log20 100

R

L

kmdfL 10MHz100 log20log204.32dB

,log

loglog

a

bb

c

ca

2525

Basic calculations

Example: Two vertical dipoles, each with gain 2dBi, separated in free space by 100m, the transmitting one radiating a power of 10mW at 2.4GHz

This corresponds to 0.4nW (or an electric field strength of 0.12mVm-1)

The important quantity though is the signal to noise ratio at the receiver. In most instances antenna noise is dominated by electronic equipment thermal noise, given by where is Boltzman’s constant, B is the receiver bandwidth and T is the room temperature in Kelvin

0.801.0log202400log204.32dB 10100 L

0.940.802log102log101010log10dBW 10103

10rx P

TBkN B123 JK1038.1 Bk

2626

Basic calculations

The noise power output by a receiver with a Noise Figure F = 10, and bandwidth B = 200kHz at room temperature (T = 300K) is calculated as follows

Thus the signal to noise ratio (SNR) is given by

FTBkN B 1010 log10log10dBW

10log10102003001038.1log10dBW 10323

10 N

dBm 8.110dBW 8.140 N

8.1400.94dBWdBWdB NPSNR

dB 8.46SNR

2727

Basic calculations

The performance of the communication system depends on the SNR, modulation and coding (forward error correcting (FEC) coding) employed and is statistical in nature

We can look up graphs/tables to convert from SNR to bit error rate, BER for each modulation scheme (next slide)

Assuming that the probability of each bit being detected erroneously at the receiver is independent, we can find the probability for the number of erroneous bits exceeding the maximum number of errors the FEC code can cope with in any one packet and thus arrive at the probability (or frequency) of receiving erroneous packets

2828

Basic calculations

2929

Basic calculations

In a multi-user environment we have to incorporate the effects of the co-channel interference in these calculations

In practice we need to model interferer power probabilistically

These calculations are known as outage probability calculations

This is not a problem, as the desired link power often needs to be modelled probabilistically too

Let us turn our attention back to this problem now, by considering more realistic propagation models

3030

Propagation over a flat earth

The two ray model

Valid in the VHF, band and above (i.e. f 30MHz where ground/surface wave effects are negligible)

Valid for flat ground (r.m.s. roughness z, f 30GHz) Valid for short ranges where the earth’s curvature is negligible

(i.e. d 10–30 km, depending on atmospheric conditions)

z

ht

hr

d

r1

r2 air, 0, 0

ground, r, 0,

Tx

Rx

P

x

3131

Propagation over flat earth

The path difference between the direct and ground-reflected paths is and this corresponds to a phase difference

The total electric field at the receiver is given by

The angles and are the elevation and azimuth angles of the direct and ground reflected paths measured from the boresight of the transmitting antenna radiation pattern

12 rrr 12 rrk

Γ.ee

eeE

,ˆ,êxp

60

,ˆ,êxp

60,

2

2rad

1

1rad

TT

TT

ggr

crtjP

ggr

crtjPr

,,, 21 rrr EEE

3232


This expression can be simplified considerably for vertical and horizontal polarisations for large ranges d >> ht, hr, ,

jEE hvhv exp1 ,0,

d

hkhhhdhhdkrrk rt

rtrt

2222212

onpolarisati horizontalfor ˆ

onpolarisati alfor verticcosˆ,ˆ,ˆ

txy

txzTT G

Ggg

e

eee

pol. h.for ˆ

pol. for v.cosˆ,ˆ,ˆ

TE

TM

txy

txzTT G

Ggg

e

eee.Γ

1hTEvTM

3333


There are two sets of ranges to consider separated by a breakpoint

jEE hvhv exp1 ,0,

2sin4exp1 20

2

0 rxrxrx PjPP

d

hhPP rt

rxrx 2

sin4 20

22sin&

4

22

b

rt dhh

d

22

4sin&22

2

bdd

3434


Thus there are two simple propagation path loss laws

where l is a rapidly varying (fading) term over distances of the scale of a wavelength, and

This simplifies to

The total path loss (free space loss + excess path loss) is independent of frequency and shows that height increases the received signal power (antenna height gain) and that the received power falls as d-4 not d-2

cddlLL for0.3dB 0

cddLL forlog20dB 100

rt

rt

hhd

d

hhdL

101010

1010

log20log20log40

4log20

4log20dB

3535


Typical ground (earth) with r = 15, = 0.005Sm-1, ht = 20m and hr = 2m

deep fade1/d2 power law regime (d < dc)

1/d4 power law regime (d > dc)

3636

Radio channels for Sensor Networks

Channels are: Short-range (microcellular & picocellular) Indoor or outdoor UHF band (300MHz f 3GHz, or 10cm 1m) SHF band (3GHz f 30GHz, or 1cm 10cm)

Models can be: Deterministic, statistical, or empirical Narrowband, broadband

Multipath propagation mechanisms of importance: Reflection Diffraction Transmission Scattering

3737

Observed signal characteristics Narrowband signal (continuous wave – CW) envelope

Area mean or path loss (deterministic or

empirical)

Local mean, or shadowing, or slow fading (deterministic or statistical)

Fast or multipath fading (statistical)

38

Observed signal characteristics

Deterministic models – complex Statistical models – statistics are as is a lamp-post to a

drunken man: it is there more for support rather than illumination But statistical methods are useful when you understand the

principles behind them

3939

Observed signal characteristics

The total signal consists of many components Each component

corresponds to a signal which has a variable amplitude and phase

The power received varies rapidly as the component phasors add with rapidly changing phases

Averaging the phase angles results in the local mean signal over areas of the order of 102

Averaging the length (i.e. power) over many locations/obstructions results in the area mean

The signals at the receiver can be expressed in terms of delay or frequency variation, and depend on polarisation, angle of arrival, Doppler shift, etc.

40

Actual measurements

We shall look at some examples which I have taken together with: Prof. David Edwards (Oxford) Andy Street (now at Agilent) Alan Jenkins (now in Boston) Jon Moss (now O2) Lloyd Lukama (now at Sharp Research) Junaid Mughal (now at GIKI, Pakistan) Yuri Nechayev (Birmingham)

41

Measurement system

VNA-based Synthetic volume aperture Rx

antenna on a grid of 26x26x2 positions with a cell size of 3x3x40 cm3: Azimuth resolution 10o

Elevation resolution 30o (with grating lobes)

Reflection measurement:f0 = 2.440 MHz; B = 80 MHz

Transmission measurement:f0 = 2.500 MHz; B = 200 MHz

S21 response calibrated and checked for phase stability & repeatability

42

Measurement location

Four-storey brick building 25 cm thick exterior walls 12 cm thick interior walls Foyer near T-junction Corridor along length Offices & labs either side of

corridor Staircases at ends surrounded

by offices Exterior wall structure:

windows with ledges, small balcony

43

Measurement location

44

Measurement Antennas

45

Reflection measurement

46

Reflection measurement

LOS at 125ns and at expected path loss Specular reflection at 237ns (correct path length

geometrically) and a path loss corresponding to 5dB of reflection loss Experimental reflection coefficient || = 0.56 (= -5 dB) Theoretical Fresnel reflection coefficient for brick with 10%

moisture content (r = 8.5 + j0.9 & 31o angle of incidence) || = 0.54

Additional scattered energy at 249ns & nearby spatial AoA is comparable to specular reflection

Non-simple “reflection” (i.e. scattering) process

47

Transmission measurement

48


49


Delay Path loss

Path length

Map dist.

Possible propagation mechanism

175 ns 119 dB 52 m 50 m Ground floor tx through window

190 ns 120 dB 57 m 54 m Ground floor tx through window

249 ns 121 dB 75 m 69 m 1st floor tx through stairwell

279 ns 122 dB 84 m 84 m Tx through ground floor foyer

324 ns 122 dB 97 m 99 m Arts & Watson refl and Arts diffr

409 ns 125 dB 123 m ? Multiple scat from Arts & Watson

554 ns 128 dB 166 m 166 m Multiple scattering from Physics

589 ns 111 dB 177 m 175 m Arts 1 refl & Physics 2 refl

853 ns 119 dB 256 m ? Scat from nearby tower block ?

50

Indoor measurements

Oxford indoor measurements at 5.5GHz (2ns resolution)

51

Indoor measurements

Oxford indoor measurements at 5.5GHz (2ns resolution)

52

Outdoor to Indoor measurements

Oxford outdoor to indoor measurements at 2.44Hz (27ns resolution)

53

What matters to you

You need to be able to calculate the probability (or frequency) with which a packet will be received successfully on a wireless link

This will depend on Link signal power Interference levels Dispersion in the channel

Link power can be controlled in two ways Changing the transmitted power Changing antenna gains Adopting diversity reception techniques

53

5454

What matters to you

Interference can be controlled also in two ways Changing the effective transmitted power at more than one node Having an adaptive antenna radiation pattern to introduce a null in the

direction(s) of the dominant interferer(s) Dispersion can be mitigated through the use of

Equalisers and/or diversity schemes Adaptive antennas (filtering out multipath components)

BUT, beware of Unwanted complexity/expense in receiver technology Effects on battery power Exceeding maximum permissible EIRP Size of antenna system becoming unwieldy Difficulties in optimising more than one simultaneous link

5555

Area mean models – applicability to SANETs

Most published models of this form are linear regression models established through measurements in macro-cellular scenarios (Hata-Okumura and Walfisch-Bertoni models and their variants) and are not applicable to SANET research

The majority of models applicable to short-range propagation in open areas are based on the two-ray model (usually modified to take into account terrain undulations

Range dependence only is not sufficient for understanding the operation of SANETs

There is scant data available for low antenna heights typical of SANETs

5656

Area mean models – outdoor Range dependence for microcells is strongly influenced by street

geometry Line-of-sight paths (LOS) Non-line-of-sight paths (NLOS) (Lateral vs. transverse)

Tx LOS

Staircase

Zig-zag

Transverse

Lateral

5757

Area mean models – outdoor

Based on measurements by AirTouch Communication in San Francisco at 900MHz and 1900MHz for ht = 3.2, 8.7 and 13.4m and hr = 1.6m

Two slope models with a breakpoint distance as predicted by the two ray model for LOS case

for d < db and where the distances are measured in km and the frequency in GHz

for d > db. Note that there is a 3dB discontinuity at d = db

rtb hhd 4

km101010GHz10 loglog7.58.15log1.0log4.391.81 dhhfL tt

bt

t

ddh

hfL

1010

10GHz10

loglog9.131.32

log3.25log5.474.48

5858


For the staircase and transverse NLOS cases in suburban environments only

where and HB is the mean building height

For the lateral NLOS case in suburban environments only

km100100

0100GHz10GHz10

log1logsgn4.41.40

1logsgnlog6.47.13log9.383.138

dyy

yyffL

m4.5m8.7, 00 yHhy Bt

km100100

0100GHz10GHz10

log1logsgn7.62.29

1logsgnlog4.41.13log6.314.127

dyy

yyffL

5959


For the staircase and transverse NLOS cases in high-rise urban environments only

For the lateral NLOS case in high-rise urban environments only

The standard deviation of the models from the actual data was found to be approximately 6 – 12dB



60


Integrating LOS and NLOS models Most cities have a non-regular geometry and as the distance

from a transmitter increases there is a decreasing probability that a line of sight path will exist to the transmitter

Measurements in European built-up areas have shown that for urban areas, af = 5 m and bf = 35 m and for suburban areas, af = 6 m and bf = 40 m

The overall path loss model then becomes

60

f

fffLOS ad

adbaddp

if

if

1

exp

dLdpdLdpdL NLOSLOSLOSLOS 1

61


The area mean propagation models considered cannot be safely extrapolated to low antenna heights

Few measurements exist to confirm the validity of the path loss models for low antennas at heights below 1.8 m

Such measurements typically fail to distinguish the effects of the close proximity of a human body to the antenna with low antenna height effects

Among the few notable exceptions are: The work by Wang et al (2004), which considers mobile-to-mobile

propagation at 2.1 GHz and 5.2 GHz and antenna heights of 1.5 m The work by Konstantinou et al (2007), which considers mobile-to-mobile

UMTS propagation in 3G mobile telephony, which applies to frequencies around 2 GHz and antenna heights in the range 0.5 – 3.0 m

61

6262

Area mean models – indoor

COST231 (1999) models Model 1: Model 2:

L0 is the free-space loss, Lc is a constant, kwi is the number of penetrated walls of type i (type 1 is a light plasterboard or aerated concrete wall, type 2 is a heavy thick wall made of brick or concrete), Lwi is the associated transmission loss, kf is the number of penetrated adjacent floors and Lf is the associated floor transmission loss

Model 3:

dnLL 101 log10

f

b

fi

wiwic LkLkLLL fkfk

1

22

10

dLL 0

6363


L1 (dB) n Lw1(dB) Lw2(dB) Lf(dB) b (dBm-1)

DenseOne floorTwo floorsThree floors

33.321.944.9

4.05.25.4

3.4 6.9 18.3 0.46 0.62

2.8

Open 42.7 1.9 3.4 6.9 18.3 0.46 0.22

Large 37.5 2.0 3.4 6.9 18.3 0.46

Corridor 29.2 1.4 3.4 6.9 18.3 0.46

6464


The models were developed at 1800MHz, but subsequent measurements at 0.85, 1.9, 2.4, 4.0, 4.75, 5.8 and 11.5GHz have shown no significant frequency dependence

In corridors path loss exponents less than 2 (waveguiding effects) have been reported, but were only significant in very specific cases

The standard deviation of the models from the actual data was found to be approximately 10dB

6565

Area mean models

The ITU, headquartered in Geneva, Switzerland is an international organization within the United Nations System where governments and the private sector coordinate global telecom networks and services

ITU-R (International Telecommunications Union – Radiocommunication sector http://www.itu.int/ebookshop) recommendations are internationally agreed models you can use and are based on numerous measurements

You can download up to three recommendations for free from the Electronic Bookshop ITU-R P.1411-4: Propagation data and prediction methods for the planning of

short-range outdoor radiocommunication systems and radio local area networks in the frequency range 300 MHz to 100 GHz

ITU-R P.1238-5: Propagation data and prediction methods for the planning of indoor radiocommunication systems and radio local area networks in the frequency range 900 MHz to 100 GHz

66

Area mean models – on-body PANs & BANs

Very recent activity from antennas and propagation perspective

Birmingham University and Queen Mary College, University of London pioneering work and first book on subject

Antennas on body, polarisation perpendicular to body, 2.4 GHz band measurements

PANs and BANs Off-body (body to environment links) On-body (body to same body links) In-body (implants)

67

Area mean models – on-body PANs & BANs

LOS links path loss (measured at 2450 MHz)

with a standard deviation of 4.2 dB NLOS links path loss (measured at 2450 MHz)

with a standard deviation of 5.6 dB Transition regions between LOS and NLOS have path

losses in-between these two equations

cmLOS dL 10log2033.5

cmNLOS dL 36.035

6868

Local mean model

The departure of the local mean power from the area mean prediction, or equivalently the deviation of the area mean model is described by a log-normal distribution

In the same manner that the theorem of large numbers states that the probability density function of the sum of many random processes obeys a normal distribution, the product of a large number of random processes obeys a log-normal distribution

Here the product characterises the many cascaded interactions of electromagnetic waves in reaching the receiver

The theoretical basis for this model is questionable over short-ranges, but it is the best available that fits observations

6969

Local mean model

Working in logarithmic units (decibels, dB), the total path loss is given by

where X is a random variable obeying a lognormal distribution with standard deviation (again measured in dB)

If x is measured in linear units (e.g. Volts)

where mx is the mean value of the signal given by the area mean model

XdLdPL

2dB

2

dB

2exp2

1 XXp

2dBdB 2

lnlnexp

2

1

xmx

xxp

7070

Local mean model

Cumulative probability density function

This can be used to calculate the probability that the signal-to-noise ratio will never be lower than a desired value and thus the bit-error-rate and packet/frame error rate will be always smaller than a given value which can be easily calculated. This is called an outage calculation

Note that all this is range-dependent

2erfc

2

11

2exp2

1cdf 2

dB2

dB

Threshold

dLL

dXXLPL

T

dLLT

7171

Local mean model

In simulations, we need to generate random numbers X from the p.d.f. and then simulate the corruption of a radio packet probabilistically from the BER model of the given communication system

In outdoor microcellular urban environment measurements at 900 MHz – 2 GHz, the autocorrelation function s(d) of the shadow fading was found to be well-approximated by

where d is the distance between nearby points and dc ranges between 20 m and 80 m with typical values for London being,

cs ddd exp

dc LOS NLOS

Urban 30 m 50 m

Suburban 25 m 55 m

72

Local mean model

In SANET/MANET research, this simple correlated local mean fading model can be very easily incorporated into simulators by filtering a white Gaussian random process with a standard deviation of dB and the empirically found exponential correlation function (in this case a simple first-order filter with a pole at dc)

Otherwise, simulations/theory are only as meaningful as those carried out using the unit disc model

72

7373

Fast fading models

Constructive and destructive interference In spatial domain In frequency domain In time domain (scatterers, tx and rx in

relative motion) Azimuth dependent Doppler shifts

Each multipath component travels corresponds to a different path length.

Plot of power carried by each component against delay is called the power delay profile (PDP )of the channel.

2nd central moment of PDP is called the delay spread

P

Im

Re

7474

Fast fading models

The relation of the radio system channel bandwidth Bch to the delay spread is very important Narrowband channel (flat fading, negligible inter-symbol interference (ISI),

diversity antennas useful) Wideband channel (frequency selective fading, need equalisation (RAKE

receiver) or spread spectrum techniques (W-CDMA, OFDM, etc.) to avoid/limit ISI)

Fast fading refers to very rapid variations in signal strength (20 to in excess of 50 dB in magnitude) typically in an analogue narrowband channel Dominant LOS component Rician fading NLOS components of similar magnitude Rayleigh fading

1chB

1chB

7575

Fast fading models

Working in logarithmic units (decibels, dB), the total path loss is given by

where Y is random variable which describes the fast fading and it obeys the distribution

for Rayleigh fading, where the mean value of Y is

YXdLdPL 10log20

80.012 Y

0,0

0,2

exp2

2

2

Y

YYY

Yp

7676

Fast fading models

For Rician fading

where ys is the amplitude of the dominant (LOS) component with power . The ratio is called the Rician K-factor. The mean value of Y is

The Rician K-factor can vary considerably across small areas in indoor environments

0,0

0,I2

exp202

22

2

Y

YYyyYY

Ypss

22sy 22

Rice 2syK

2exp2I2I12 10 KKKKKY

7777

Fast fading models Similar but much more complicated outage calculations

E.g. Rayleigh and log-normal distributions combine to give a Suzuki distribution

Simulations with random number realisations for X and Y are run as before (Y decorrelates over distances < /2)

For many nodes the same methodology can be used to calculate interferer powers to compute the total S/(N+I) ratio

The spatial distribution of fades is such that the “length” of a fade depends on the number of dB below the local mean signal we are concerned with (see Parsons [5], pp.125-130)

Fade depth (dB) Average fade length ()

0 0.479

-10 0.108

-20 0.033

-30 0.010

7878

How to use models in simulation

To calculate the probability of packet loss Generate random numbers for the slow fading, X, and, if

appropriate for the communication system in question (depends on wideband/narrowband system for the channel and/or use of diversity reception techniques), for the fast fading, Y, from the appropriate distributions

Calculate the received signal in the radio link using the path loss model

Repeat the calculation above for all k interfering transmitters

eappropriat if10log20 YXdLdPL

dPLGGPS rxtxtx

kkrx

ktx

ktx

k dPLGGPI

7979


Calculate the noise at the receiver (B is the channel bandwidth)

Combine noise and interference powers linearly

Calculate the signal-to-noise-plus-interference ratio

Look up what bit-error-rate this corresponds to for your system

FTBkN B 1010 log10log10

k

IN krxIN 1010

10 1010log10

)( INSSNIR

SNIRBERpe

8080


If there are n bits in each frame/packet and a maximum of m errors can be corrected for by the FEC coding, the probability that the packet has been corrupted is

where pl is the probability of exactly l bits being received erroneously in the packet, given by

A random decision based on P(pkt_loss) can then be made in a SANET simulation

To perform more conventional outage calculations, it is simpler to use a simulator (e.g. SEAMCAT – freely available from http://www.ero.dk/)

mppppP 2101pkt_loss

lme

lel pp

l

mp

1

8181

Impact on protocols

Current practice Makes inappropriate use of path loss exponents Does not distinguish between LOS and NLOS Ignores fading correlations

And therefore makes Optimistic predictions for MAC layer operation Pessimistic predictions for network layer (routing/forwarding)

operation Unrealistic performance predictions for power/topology

control schemes Optimistic predictions for security/eavesdropping implications

8282

Way forward – help us to help you

We have just enough radiowave propagation channel knowledge to make a better start in theory and modelling of sensor networks

Testbeds/deployments of sensor networks chould collect propagation data to improve models Low antenna height models need refining

We know practically nothing for ground-based sensors Radio link quality is likely to be either extremely good or

extremely bad There is little information on the temporal variability of

links for low antenna heights (incl. temporal correlations)

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References

[1] J.R. Pierce and A.M. Noll, Signals: The Science of Telecommunications, Scientific American Library, 1990

[2] R.E. Collin, Antennas and Radiowave Propagation, McGraw-Hill, 1985 [3] J.D. Kraus and R.J. Marhefka, Antennas For All Applications, 3rd Edition, McGraw-Hill, 2003 [4] R. Vaughan and J Bach Andersen, Channels, Propagation and Antennas for Mobile

Communications, The Institution of Electrical Engineers, 2003 [5] H.L. Bertoni, Radio Propagation for Modern Wireless Systems, Prentice Hall, 2000 [6] J.D. Parsons, The Mobile Radio Propagation Channel, Pentech,1992 [7] W.C. Jakes (Ed.), Microwave Mobile Communications, IEEE Press, 1974 [8] T.S. Rappaport, Wireless Communications: Principles & Practice, Prentice Hall, 1996 [9] S.R. Saunders, Antennas and Propagation for Wireless Communication Systems, Wiley,

1999 [10] L.W. Barclay (Ed.), Propagation of Radiowaves, 2nd Ed., IEE Press, 2003 [11] Z. Wang, E.K. Tameh and A.R. Nix, “Statistical Peer-to-Peer Channel Models for Outdoor

Urban Environments at 2GHz and 5GHz,” IEEE 60th VTC, Fall-2004, pp. 5101-5105, 2005 [12] K. Konstantinou, S. Kang and C. Tzaras, “A Measurement-Based Model for Mobile-to-

Mobile UMTS Links,” IEEE 65th VTC, Spring-2007, pp. 529-533, 2009

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Illustration credits

Figures on pp.3,4,8 © Scientific American Library [J.R. Pierce and A.M. Noll, Signals: The Science of Telecommunications, Scientific American Library, 1990]

Figures on pp.10-15 © Scientific American Library [J.A. Wheeler, A Journey into Gravity and Spacetime, Scientific American Library, 1990]

Figure on p.5, © Addison-Wesley [E. Hecht and A. Zajac, Optics, Addison-Wesley, 1974]

Figures on p.6, © McGraw-Hill [R.E. Collin, Antennas and Radiowave Propagation, McGraw-Hill, 1985]

Figures on p.16,18,19 © McGraw-Hill [J.D. Kraus and R.J. Marhefka, Antennas For All Applications, 3rd Edition, McGraw-Hill, 2003]

Figures on p.28,37,35 © IEE [R. Vaughan and J Bach Andersen, Channels, Propagation and Antennas for Mobile Communications, The Institution of Electrical Engineers, 2003]

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