introductory radiowave propagation

7/27/2019 Introductory Radiowave Propagation

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Introduction to Radiowave

PropagationDr Costas Constantinou

School of Electronic, Electrical & Computer Engineering

University of BirminghamW: www.eee.bham.ac.uk/ConstantinouCC/

E: [email protected]


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Introduction

For an overview, see Chapters 1 4 of L.W. Barclay

(Ed.), Propagation of Radiowaves, 2nd Ed., London:

The IEE, 2003

The main textbook supporting these lectures is: R.E.Collin, Antennas and Radiowave Propagation, New

York: McGraw-Hill, 1985


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Introduction (cont.)

Simple free-space propagation occurs only rarely

For most radio links we need to study the influence

of the presence of the earth, buildings, vegetation,

the atmosphere, hydrometeors and the ionosphere In this lectures we will concentrate on simple

terrestrial propagation models only


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Radio Spectrum

Symbol Frequency range Wavelength, CommentsELF < 300 Hz > 1000 km Earth-ionosphere waveguide

propagationULF 300 Hz 3 kHz 1000 100 km

VLF 3 kHz 30 kHz 100 10 km

LF 30 300 kHz 10 1 km Ground wave propagation

MF 300 kHz 3 MHz 1 km 100 m

HF 3 30 MHz 100 10 m Ionospheric sky-wave propagation

VHF 30 300 MHz 10 1 m Space waves, scattering by objects

similarly sized to, or bigger than, a free-

space wavelength, increasingly affected

by tropospheric phenomena

UHF 300 MHz 3 GHz 1 m 100 mmSHF 3 30 GHz 100 10 mm

EHF 30 300 GHz 10 1 mm

8 1; 3 10 msc f c


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Electromagnetic waves

Spherical waves

Intensity (time-average)

Conservation of energy; the inverse square law

HES

212Wm


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Electromagnetic waves

Conservation of energy; the inverse square law

Energy cannot flow perpendicularly to, but flows along

light rays

2

dtransmitte

2

steradiansofsectorangularanindtransmitte

2

22112

2

2

1

2

1

1

2

4

11

21

r

P

rl

P

rr

PAAPrr

AA

l

AA

r

r

rEr

rrr

r


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Free-space propagation

Transmitted power

EIPR (equivalent isotropically radiated power)

Power density at receiver

Received power

Friis power transmission formula

txP

txtxPG

2

txtxrx

4 RPG

S

4;

4

2

rx

rxrx

2

txtxrx GAA

R

PGP ee

2

rxtx

tx

rx

4

RGG

P

P

Tx Rx

R


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Free-space propagation (cont.)

Taking logarithms gives

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

Maths reminder

RGGPP

4log20log10log10log10log10 10rx10tx10tx10rx10

cbcb aaa logloglog ,loglog bcba

c

a

dBdBidBidBWdBW 0rxtxtxrx LGGPP

0L

dB4

log20 100

RL

kmdfL 10MHz100 log20log204.32dB

,log

loglog

a

bb

c

c

a


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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 atthe receiver. In most instances antenna noise is dominated by

electronic equipment thermal noise, given by

where is Boltzmans constant, B is the

receiver bandwidth and T is the room temperature in Kelvin

0.801.0log202400log204.32dB 10100 L

0.940.802log102log1010log10dBW 10102

10rx P

TBkN B123 JK1038.1 Bk


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Basic calculations (cont.)

The noise power output by a receiver with a Noise FigureF=

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 10

323

10 N

dBm8.110dBW8.140 N

8.1400.94dBWdBWdB NPSNR

dB8.46SNR


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Basic calculations (cont.)


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Propagation over a flat earth

The two ray model (homogeneous ground)

Valid in the VHF, band and above (i.e. f 30MHz whereground/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 earths curvature is negligible (i.e. d 0 path obstraction)(u0 < 0 path clearance)

u

a

Site shielding


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Site sheilding

The Kirchhoff integral describing the summing of secondary

wavefronts in the Huygens-Fresnel principle yields the field at

the receiver

where k1 describes the transmitter power, polarisation and

radiation pattern,f(r) describes the amplitude spreading

factor for the secondary waves (2D cylindrical wavef(r) = r1/2,

3D spherical wavef(r) = r) and u1 is a large positive value ofu

to describe a distant upper bound on the wavefront

1

0

1

expu

u

jkrE R k du

f r


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Site shielding

Stationary phase arguments (since the exponent is oscillatory,

especially for high frequencies) show that only the fields in

the vicinity of the point O contribute significantly to the field

at R

If point O is obstructed by the knife-edge, then only the fields

in the vicinity of the tip of the knife-edge contribute

significantly to the field at R

Using the cosine rule on the triangle TPR, gives

2 2 22

2 2 2

2 1 2 1 1 2 1

1

2 cos

2 cos

r PR TP TR TP TR

ud d d d d d d

d

a


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Site shielding

If we assume that d1, d2 >> , u (stationary phase and far-field

approximations), then u/d1, a


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Site shielding

Since , we make the substitution

which simplifies the integral to the form,

where we have used the stationary phase argument to makethe upper limit

Using the definition of the complex Fresnel integral,

21 21 2

d dk u ud d

21 22

1 2 2

2&

2

d d du k u k du

d d k

0

1 2 2

2 2

expexp 2

k jkd E R j d

k f d

20

exp 2

x

F x j d


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Site shielding

To determine k3 we let and useF()=F() and

the fact that in this case we have free-space propagation (i.e.

E(R) =E0(R)) , to get,

1 2

3

2 2

3 0

3 0

exp

12

k jkd k

k f d

E R k F F

jE R k F

0 3

0 0

3

1

11 2

E R k j

E R E Rk j

j


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Site shielding

Therefore,

where,

The path-gain factor,F, is given by,

Useful engineering approximations:

0

0 21 exp 22

E RE R j j d

1 2

0 0

1 2

2 d du

d d

0

2

0

1exp 2

2

E RF j d

E R

10 10 0 0

2

10 0 0 0

2

10 0 0 0

20log 13 20log 2.4

20log 6.02 9.11 1.27 0 2.4

20log 6.02 9.0 1.65 0.8 0

F

F v

F v


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Site shielding


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Multipath propagation

Mobile radio channels are predominantly in the VHF

and UHF bands

VHF band (30 MHz f 300 MHz, or 1 m 10 m)

UHF band (300 MHz f 3 GHz, or 10 cm 1 m) In an outdoor environment electromagnetic signals

can travel from the transmitter to the receiver along

many paths

Reflection

Diffraction

Transmission

Scattering


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Multipath propagation

Narrowband signal

(continuous wave

CW) envelope

Area mean or path

loss (deterministic or

empirical)

Local mean, or shadowing, or slowfading (deterministic or statistical)

Fast or multipathfading (statistical)


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Multipath propagation The total signal consists of

many components

Each componentcorresponds to a signalwhich has a variableamplitude and phase

The power received variesrapidly as the componentphasors add with rapidlychanging phases

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

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

The signals at the receiver can be expressed interms of delay, and depend on polarisation, angle

of arrival, Doppler shift, etc.


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Area mean models

We will only cover the Hata-Okumura model, which

derives from extensive measurements made by

Okumura in 1968 in and around Tokyo between 200

MHz and 2 GHz The measurements were approximated in a set of

simple median path loss formulae by Hata

The model has been standardised by the ITU as

recommendation ITU-R P.529-2


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Area mean models

The model applies to three clutter and terrain

categories

Urban area: built-up city or large town with large buildings

and houses with two or more storeys, or larger villages

with closely built houses and tall, thickly grown trees

Suburban area: village or highway scattered with trees and

houses, some obstacles being near the mobile, but not

very congested

Open area: open space, no tall trees or buildings in path,

plot of land cleared for 300 400 m ahead, e.g. farmland,

rice fields, open fields


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Area mean models

where

citiessmalltomediumfor8.0log56.17.0log1.1

MHz300cities,largefor1.154.1log29.8

MHz300cities,largefor97.475.11log2.394.40log33.18log78.4

4.528log2

log55.69.44

log82.13log16.2655.69

2

2

2

2

cmc

cm

cm

cc

c

b

bc

fhfE

fhE

fhEffD

fC

hB

hfA

DRBAL

CRBALERBAL

logdB:areasopen

logdB:areassuburbanlogdB:areasurban


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Area mean models

The Hata-Okumura model is only valid for:

Carrier frequencies: 150 MHz fc 1500 MHz

Base station/transmitter heights: 30 m hb 200 m

Mobile station/receiver heights: 1 m hm 10 m Communication range:R > 1 km

A large city is defined as having an average building height

in excess of15 m


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Local mean model

The departure of the local mean power from the area meanprediction, or equivalently the deviation of the area meanmodel 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 manyrandom processes obeys a normal distribution, the product ofa large number of random processes obeys a log-normaldistribution

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


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Local mean model

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

whereX is a random variable obeying a lognormal

distribution with standard deviation (again measured in dB)

Ifx is measured in linear units (e.g. Volts)

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

XdLdPL

2dB2dB

2exp2

1

XXp

2

dBdB2

lnlnexp2

1

xmxx

xp


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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 threshold value.

This is called an outage calculation Typical values ofdB = 10 dB are encountered in urban

outdoor environments, with a de-correlation distance

between 2080 m with a median value of40 m

2erfc

211

2exp2

1cdf 2dB

2

dB

Threshold

dLL

dXXLPL

T

dLLT


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Fast fading models Constructive and destructive

interference

In spatial domain

In frequency domain

In time domain (scatterers, tx and rx inrelative motion)

Azimuth dependent Doppler shifts

Each multipath component travelscorresponds to a different path length.

Plot of power carried by eachcomponent against delay is called the

power delay profile (PDP )of thechannel.

2nd central moment of PDP is called thedelay spread

P

Im

Re


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Fast fading models

The relation of the radio system channel bandwidthBch 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 of50 dB in magnitude) typically in an analogue

narrowband channel

Dominant LOS component Rician fading

NLOS components of similar magnitude Rayleigh fading

1 chB

1 chB


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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 ofYis

YXdLdPL 10log20

80.012 Y

0,0

0,2

exp2

2

2

Y

YYY

Yp


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Fast fading models

For Rician fading

whereys is the amplitude of the dominant (LOS) componentwith power . The ratio is called the RicianK-factor. The mean value ofYis

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

0,0

0,I2

exp202

22

2

Y

YYyyYY

Ypss

22

sy22

Rice 2syK

2exp2I2I12 10 KKKKKY


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Fading models

Similar but much more complicated outage calculations

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

distribution

The spatial distribution of fades is such that the length of a

fade depends on the number of dB below the local meansignal we are concerned with

Fade depth (dB) Average fade length ()

0 0.479

-10 0.108

-20 0.033

-30 0.010


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Tropospheric propagation

Over long-distances, more than a few tens of km,

and heights of up to 10 km above the earths surface,

clear air effects in the troposphere become non-

negligible The dielectric constant of the air at the earths

surface of (approx.) 1.0003 falls to 1.0000 at great

heights where the density of the air tends to zero

A consequence of Snells law of refraction is that

radiowaves follow curved, rather than straight-line

trajectories


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The variation of the ray

curvature with refractive index is

derived:

AA: wavefront at time t

BB: wavefront at time t + dtAB and AB: rays normal to the

wavefronts

: radius of curvature ofAB

A

A

BB

O

d

d dh

n + dn

n

c dt

A B d v dt n

c dtAB d d v dv dt

n dn

d c c

dt n n dn d


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Retaining only terms which are correct to first order in small

quantities,

But this is the curvature, C, of the ray AB, by definition.

Furthermore,

For rays propagating along the earths surface is very small

and we may take cos= 1. Moreover, n1 1.

n n nd dn dnd

1 1

dn nd

dn

n d

cosdh d

1 1cos

dnC

n dh


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Ifn = constant, dn/dh = 0 C= 0 and the ray has zero

curvature, i.e. the ray path is a straight line

A ray propagating horizontally above the earth must have a

curvature C= (earths radius)1 = a1 in order to remain

parallel with the earths surface. But its actual curvature is

given by Cand not C.

The difference between the two curvatures gives the

curvature of an equivalent earth for which dn/dh = 0 andwhich has an effective radius ae,

dnCdh

1 1 1

e

dn

a a dh ka


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kis known as the k-factor for the earth

Typically, dn/dh0.039106 m1 1/(25,600 km)

Therefore,

The k-factor of the earth is k= 4/3

The effective radius of the earth is ae = 4a/3

These values are used in the standard earth model which

explains why the radio horizon is bigger than the radio horizon

1 1 1 1

6,400 km 25,600 km 6,400 kme

a k


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Problem: Find the radio horizon of an elevated antenna at a

height htabove the earth

Answer: 2 e tR a h

introductory radiowave propagation

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