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

Radiowave Channel Modelling for Radio Networks

Costas ConstantinouElectronic, Electrical & Computer Engineering

The University of Birmingham, UK

http://www.eee.bham.ac.uk/ConstantinouCC/

[email protected]

2Mobihoc '03 Radio Channel Modelling Tutorial

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



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


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

2

00

200||TM

sincos

sincos

jj

jj

rr

rr

ir EΓE

.

jexp

Plane of incidence


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 r

Pseudo-Brewster angle


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



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

HES

212Wm



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


Radiation

Pictorial introduction to radiation from accelerated charges


Radiation



Radiation



Radiation

Fields around a charge in non-uniform motion


Radiation



Radiation



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


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 used as a

reference antenna!

,ˆ,êxp

60, rad ggr

crtjPr eeE


Antennas

A general antenna pattern


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)


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


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


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


Antennas

Antenna arrays Multiple elements Voltages at their elements are phasors Voltage phase-shifted then added to produce maximum

reception sensitivity to radiation from a particular direction (beam-forming)

Radiation pattern (and gain) is the product of the element pattern and the array factor– watch for electromagnetic coupling!

Phases may be shifted in real-time to have adaptive antenna

MIMO antennas (more later on this one)


Antenna arrays

Two point sources of equal amplitude and phase Phase difference of two fields at the

observation point

Total field at the observation point

cos

22

kd

2/exp2/exp 00 jEjEE zzz

2

2/exp2/exp2 0

jjEE zz

cos

2cos22/cos2 00

kdEEE zzz


Antenna arrays

Field pattern ( )

cos

2cos,

kdg

2/d


Antenna arrays

Point sources Same phase = 0, spaced /2

Phase quadrature = 90º, /2

Phase quadrature = 90º, /4


Antenna arrays

Principle of pattern multiplicationAntenna array field pattern = element pattern array pattern


Antenna arrays

Broadside array: main lobe perpendicular to array End-fire array: main lobe along array 2D, 3D arrays Side-lobe tapering via amplitude distribution

functions Grating lobes


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


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


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


Basic calculations

The noise power output by a receiver with a Noise Figure F = 10dB, 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


Basic calculations

The performance of the communication system (outside the scope of this tutorial) 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


Basic calculations


Basic calculations

In a multi-user environment we have to incorporate the 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


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 (i.e. r.m.s. roughness z, typically 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


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



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



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



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



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)


Radio channels for MANETS

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


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)


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.


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 (O2) Lloyd Lukama (BBC R&D) Junaid Mughal (Birmingham) Yuri Nechayev (Birmingham)


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


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


Measurement location


Measurement Antennas


Reflection measurement


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


Transmission measurement





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 ?


Indoor measurements

Oxford indoor measurements at 5.5GHz (2ns resolution)


Indoor measurements

Oxford indoor measurements at 5.5GHz (2ns resolution)


Outdoor to Indoor measurements

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


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


What matters to you

Interference can be controlled also in two ways Changing the 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


Area mean models

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 MANET 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

Short-range propagation in built-up areas is often done using deterministic techniques such as ray-tracing (more on this later)


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



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



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



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

km101010GHz10 loglog7.32.47log0.1log7.292.143 dhhfL tt

km101010GHz10 loglog3.28.46log0.5log5.124.135 dhhfL tt


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/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



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

Dense

One floor

Two floors

Three floors

33.3

21.9

44.9

4.0

5.2

5.4

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



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


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) 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.1411-1: 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.1238-2: 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


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


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


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


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

The variation of the log-normal fading with distance is not contained in the statistical model. We know from measurements that slow or shadow fades extend over distances of 5–300m, with the lower ranges being more appropriate to short ranges and indoor environments

In MANET simulations, the slow fading needs to be computer every 5–20m with intermediate values interpolated smoothly to ensure that simulations are meaningful


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


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 50dB in magnitude) typically in an analogue narrowband channel Dominant LOS component Rician fading NLOS components of similar magnitude Rayleigh fading

1chB

1chB


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


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

12exp2I2I12 10 KKKKKY


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

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


Delay spread models

To determine whether simple propagation models are suitable for predicting the performance of digital communications systems, we need to have a simple channel dispersion model

The simplest possible model for the PDP is that of an exponential decay function

where S is (approximately) the r.m.s. delay spread For an indoor channel measurements at 1.9 and 5.2GHz

have established that

where S is measured in ns, Fs is the floor space measured in m2 (assuming omnidirectional antennas are used)

0,exp0 SPP

0.11log3.2log10 1010 sFS


Delay spread models

For outdoor microcellular and picocellular channels from 2.5 to 15.75GHz and ranges 50-400m, the r.m.s. delay spread follows a normal distribution whose mean and standard deviation are range-dependent

nsadCa aS ns

dCS

Measurement conditions aS S

Area f(GHz) ht (m) hr (m) Ca a C

Urban

2.5 6.0 3.0 55 0.27 12 0.32

3.35-15.754.0

2.7 23 0.26 5.5 0.35

1.610 0.51 6.1 0.39

2.25-8.45 0.5

Residential3.35

4.02.7 2.1 0.53 0.54 0.77

3.35-15.75 1.6 5.9 0.32 2.0 0.48


Angular spread models

In open areas (rural environments), the angular spread S of the received signal is fairly narrow (S ~ 10° or less)

In urban areas in LOS situations, S30° (±11°) In urban areas in NLOS situations, S41° (±18°) In indoor environments angular spreads tend to vary

significantly, with observations reported in the literature varying from S15° to in excess of 180°

All the above results are based on measurements in the band 5-8GHz

22

dP

dPS


Diversity

Combining signals from more than one receiving channel can result in an overall improvement to the signal to noise ratio, provided these signals are appropriately combined.

This is expressed as a diversity gain To have significant diversity gain, the branches (channels)

of the diversity system must have a low statistical correlation and similar mean received powers Space diversity (more than one antenna location) – spatial fade

statistics needed to determine minimum antenna separation Polarisation diversity (detecting more than one polarisation) Frequency diversity (transmitting on more than one frequency

simultaneously) – coherence bandwidth needed to determine minimum frequency spacing

Time diversity (transmitting the same message more than once) RAKE reception (exploiting temporal resolution)


MIMO channels

Diversity antennas at both transmitter (M antennas/ports) and receiver (N antennas/ports), but their spacing is smaller than traditional diversity antennas

Can exploit any degree of de-correlation between transmitting-receiving antenna permutations due to the statistical independence of many scattering processes in the environment

Use coding techniques together with singular value decomposition (SVD) to find the subspace of the MxN channels which correspond to statistically independent channels which can be exploited simultaneously


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



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



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 MANET simulation

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

mppppP 2101pkt_loss

lme

lel pp

l

mp

1


Deterministic models

For more detailed simulations (which include specific instances of PDP, angles of arrival, etc.), you need to use a deterministic radio propagation prediction technique, together with an input environment database

Important in trying to assess the operation and benefits of directional and/or adaptive antennas, as radiation patterns can be incorporated in the simulation explicitly

Technique of choice for short-range propagation in the UHF/SHF bands (300MHz – 30GHz) is ray tracing


Ray tracing

This is a high-frequency technique based on geometrical optics

Site specific UHF and SHF propagation prediction Requires a building database Models reflected, diffracted and transmitted fields

along all possible ray paths connecting the transmitter and receiver

3D predictions Coherent field coverage vs. r.m.s. power coverage. Angle of arrival, power delay profile, polarisation

prediction and phase information capabilities


Ray tracing (cont.)

Ray tracing – geometrical calculation Image method Point and shoot method

Visibility (connectivity) matrix to accelerate computation Image method slowest, but guaranteed to trace all rays

(mixed reflected-diffracted paths the slowest) Point and shoot method fastest, but can miss rays

(reception sphere; secondary sources) Truncation of number of interactions per ray


Ray tracing (cont.)


Ray tracing (cont.)

Field calculation Specular reflection – GO (reflection coefficients in [7]) Diffuse scatter – non-GO process (difficult to model) Diffraction – GTD/UTD (diffraction coefficients in [7]) Transmission – GO, but interior structure of buildings

unknown (transmission coefficients in [7]) Research challenges

Efficient ray-tracing engines to deal with large enough problems

Better physical models for propagation mechanisms


Ray tracing (cont.)


Impact on protocol stack

MAC protocols can in principle have knowledge of the physical link states in their transmission contention zone

Power control ‘games’ need path loss table information (spatially resolved version more desirable) – can potentially simultaneously optimise power consumption and interference problems

Medium access control ‘games’ should be based on predictions of power control ‘games’ (i.e. base MAC protocols on predictions of physical channel state)



Transmission contention zone: Power control: determines size

Don’t make this bigger than you need to Increases frequency reuse ratio Increases SNIR, decreases BER and probability of

packet loss Improves battery life Can make adaptive modulation possible Impact on PHY and MAC layers (e.g. directional MAC

protocol – DMAC) Usually requires a channel to be reserved as a control

channel



Transmission contention zone: Adaptive antennas: determine shape

Impact on MAC and Network (routing) layers Introduces complexity Improve EIRP for same transmission power Improve effective receiving aperture area Improve SNIR – can steer nulls towards interferers

and main radiation pattern lobe towards wanted node (not always).

Antenna size is an issue But … eavesdropping is best done omni-directionally



Directional antennas, power control, equalisation (e.g. rake reception) and adaptive modulation are closely coupled systems and their individual optimal configurations are not the same as their total optimal configuration – complex interactions; not always well understood

The Physical, Data Link (including MAC) and Network layers all need to take into account and control the combined operation of all the above Protocols need path loss, angle of arrival and channel dispersion

information to exercise control (determine transmission powers and modulation schemes)

There is a need for standardised interface between hardware and protocol stack. Layer separation does not make sense in a highly adaptive MANETs.


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] D.A. McNamara, C.W.I. Pistorius and J.A.G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction, Artech House, 1990

[8] W.C. Jakes (Ed.), Microwave Mobile Communications, IEEE Press, 1974

[9] T.S. Rappaport, Wireless Communications: Principles & Practice, Prentice Hall, 1996

[10] S.R. Saunders, Antennas and Propagation for Wireless Communication Systems, Wiley, 1999

[11] L.W. Barclay (Ed.), Propagation of Radiowaves, 2nd Ed., IEE Press, 2003


Illustration credits

Figures on pp.3,7 © Scientific American Library [J.R. Pierce and A.M. Noll, Signals: The Science of Telecommunications, Scientific American Library, 1990]

Figures on pp.9-14 © Scientific American Library [J.A. Wheeler, A Journey into Gravity and Spacetime, Scientific American Library, 1990]

Figure on p.4, © Addison-Wesley [E. Hecht and A. Zajac, Optics, Addison-Wesley, 1974] Figures on p.5, © McGraw-Hill [R.E. Collin, Antennas and Radiowave Propagation,

McGraw-Hill, 1985] Figures on p.15,17,18,23-26 © McGraw-Hill [J.D. Kraus and R.J. Marhefka, Antennas For

All Applications, 3rd Edition, McGraw-Hill, 2003] Figures on p.33,40 © IEE [R. Vaughan and J Bach Andersen, Channels, Propagation and

Antennas for Mobile Communications, The Institution of Electrical Engineers, 2003] Figures on pp.88, 90 © Winprop [Winprop tool documentation, http://www.ihf.uni-

stuttgart.de/Winprop/winprop_e.html]

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