Transcript d - ProSense

Radiowave Channel
Modelling for Sensor
Networks
Costas Constantinou
Electronic, Electrical & Computer Engineering
The University of Birmingham, UK
http://www.eee.bham.ac.uk/ConstantinouCC/
[email protected]
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
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
Im
Two types of ‘arrow’


Vector
Phasor
exp  j   cos   j sin 

j 
1

Vector & Phasor addition illustrated
1

0
Re
3
Electromagnetic waves

Vector plane waves

Ex, y, z, t   E0eˆ x cos t  z c  ReE0eˆ x exp  j t  z c

 E0 ˆ

ˆ
Hx, y, z, t   H 0e y cos t  z c  Re 
e y exp  j t  z c
120



Frequency
f Hz  
Wavenumber
1
k (m ) 

 rad 
2

c
Wavelength
 m  
2
k



  f  c


4
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
r
i
E  Γ.E
   exp  j 
 TE    
cos  
cos  
 r  j
TM
||
  
 r  j
 r  j
 r  j
 0   sin 2 
 0   sin 2 
 0  cos  
 0  cos  
 r  j
 r  j
 0   sin 2 
 0   sin 
2
Plane of
incidence
5
Reflection of plane waves

Pseudo-Brewster angle
Typical reflection
coefficients for
ground as a function
of the grazing angle
(complement of the
angle of incidence).
In this instance,
 r  15,   102 Sm1
6
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
7
Electromagnetic waves

Spherical waves



 
1
 S  2 E H
Intensity (time-average) Wm 
Conservation of energy; the inverse square law
2
8
Electromagnetic waves

Conservation of energy; the inverse square law



 r2  A1 r12






P


r
A


r

A1
1
1
2  A2  PA2
2
 r1  A2 r2
  1

1
  r   2  Er  
r
r
 Ptransmitted in an angularsector of l steradians
 r  
lr2
 Ptransmitted
 r  
4 r 2
9
Radiation

Pictorial introduction to radiation from accelerated
charges
10
Radiation

Pictorial introduction to radiation from accelerated
charges
11
Radiation

Pictorial introduction to radiation from accelerated
charges
12
Radiation

Fields around a charge in non-uniform motion
13
Radiation

Fields around a charge in non-uniform motion
14
Radiation

Fields around a charge in non-uniform motion
15
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 L   & constant current I exp  jt )
1 
Eθ r,θ,   10 7   jIL exp  j t  r c     sin  
r 
j 60I exp  j t  r csin  L


r

in the far-field r  2L2 
16
Antennas

In general, the fields radiated by an arbitrary antenna in the farfield zone are of the form,

exp  j t  r c 
Er ,    60 Prad 
 eˆ g  ,    eˆ  g  ,  
r
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
17
Antennas

A general antenna pattern
18
Antennas

Radiation pattern: a polar
plot of power radiated per
unit solid angle (radiation
intensity)





Directional vs. omnidirectional antenna
Lobes: main lobe (boresight
direction), sidelobes,
backlobes
Half-power beamwidth
(HPBW); first null
beamwidth (FNBW)
Sidelobe levels (dB)
Front-to-back ratio (dB)
19
Antennas

Directivity
Radiation
D ,   

Radiation efficiency
intensity of antenna in direction  ,  
Average radiation intensity over all space
ant  Prad Pin


Gain (directive gain)
G ,    ant D ,  ,
GdBi  10 log 10 Gmax dBi 
Beamwidth and directivity (pencil beam antenna)
D

41,000
HPBW  HPBW
Bandwidth: impedance vs. pattern
20
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
Total available received power at antenna terminals
Ae 
Incident power density on antenna
tx
rx 4
Ae  aperture  Aphysical
G  Ae 2

Polarisation matching (dot product between incident
electric field vector and the unit vector of antenna
polarisation)


Co-polar pattern
Cross-polar pattern
21
Antennas

Antenna examples
Antenna
Gain
(dBi)
Bandwidth
Polarisation
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
22
Free space propagation
tx
rx
R



Transmitted power Ptx
EIPR (equivalent isotropically radiated power) Gtx Ptx
Power density at receiver S  Gtx Ptx
rx

G P
Received power Prx  tx tx2  Aerx ;
4 R

Friis power transmission formula
4 R 2
2
A  Grx
4
rx
e
  
Prx

 GtxGrx 
Ptx
 4 R 
2
23
Free space propagation

Taking logarithms gives
 4 R 
10 log 10 Prx  10 log 10 Ptx  10 log 10 Gtx  10 log 10 Grx  20 log 10 

  
Prx dBW   Ptx dBW   Gtx dBi   Grx dBi   L0 dB
where L0 is the free-space path loss, measured in decibels
 4 R 
L0  20 log 10 
 dB
  
L0 dB  32.4  20 log 10 f MHz  20 log 10 d km

Math reminder
 
log a b c  c  log a b,
log a b  
log c b
,
log c a
log a b  c   log a b  log a c
24
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
L0 dB  32.4  20 log 10 2400  20 log 10 0.1  80.0


Prx dBW   10 log 10 10 10 3  10 log 10 2  10 log 10 2  80.0  94.0


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 N  kBTB
where k B  1.38 1023 JK 1 is Boltzman’s constant, B is the
receiver bandwidth and T is the room temperature in Kelvin
25
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
N dBW   10 log 10 k BTB   10 log 10 F 


N dBW   10 log 10 1.38 10 23  300  200 103  10 log 10 10
N  140.8 dBW  110.8 dBm

Thus the signal to noise ratio (SNR) is given by
SNRdB  PdBW   N dBW    94.0  140.8
SNR  46.8 dB
26
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
27
Basic calculations
28
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
29
Propagation over a flat earth

The two ray model
z
Tx
r1
ht

Rx
r2

P
hr
air, 0, m0
x
ground, r, m0, 
d



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 dz  , f  30GHz)
Valid for short ranges where the earth’s curvature is negligible
(i.e. d  10–30 km, depending on atmospheric conditions)
30
Propagation over flat earth

The path difference between the direct and ground-reflected
paths is r  r2  r1 and this corresponds to a phase difference
  k r2  r1 

The total electric field at the receiver is given by



Er ,    E1 r ,    E 2 r ,  

exp  j t  r1 c 
Er ,    60 Prad 
 eˆ  gT  ,    eˆ  gT  ,  
r1
 60 Prad 

exp  j t  r2 c 
 eˆ  gT  ,    eˆ  gT  ,  . Γ
r2
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
31
Propagation over flat earth

This expression can be simplified considerably for vertical and
horizontal polarisations for large ranges d >> ht, hr, ,
2kht hr
2
2
  k r2  r1   k  d 2  ht  hr   d 2  ht  hr   


d
eˆ z Gtx   cos for vertic al polarisati on
eˆ  gT  ,    eˆ  gT  ,    
for horizontal polarisati on
eˆ y Gtx  
eˆ z TM  Gtx  cos for v. pol.
Γ.eˆ  gT  ,    eˆ  gT  ,    
for h. pol.
 eˆ y TE  Gtx  
TM  v   TE  h   1
Ev ,h  E0 1  v ,h exp  j 
32
Propagation over flat earth
Ev ,h  E0 1  v ,h exp  j 
Prx  Prx0 1  exp  j   4 Prx0 sin 2  2
2
 2ht hr 
Prx  4 Prx0 sin 2 

 d 

There are two sets of ranges to consider separated by a
breakpoint
 

2
2
 d
 

2
2
 d  db
4ht hr

 db
&
   
& sin 

 2  2
  
4sin 2 
 2
 2 
33
Propagation over flat earth

Thus there are two simple propagation path loss laws
LdB  L0  3.0  l for d  dc
where l is a rapidly varying (fading) term over distances of the
scale of a wavelength, and
LdB  L0  20 log 10   for d  d c
This simplifies to
 4ht hr 
 4d 
LdB  20 log 10 

  20 log 10 
  
 d 
 40 log 10 d  20 log 10 ht  20 log 10 hr

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
34
Propagation over flat earth
Typical
ground (earth)
with r = 15,
 = 0.005Sm-1,
ht = 20m and
hr = 2m
1/d4 power law regime (d > dc)
1/d2 power law regime (d < dc)
deep fade
35
Radio channels for Sensor Networks

Channels are:





Models can be:



Short-range (microcellular & picocellular)
Indoor or outdoor
UHF band (300MHz  f  3GHz, or 10cm    1m)
SHF band (3GHz  f  30GHz, or 1cm    10cm)
Deterministic, statistical, or empirical
Narrowband, broadband
Multipath propagation mechanisms of importance:




Reflection
Diffraction
Transmission
Scattering
36
Observed signal characteristics

Narrowband signal (continuous wave – CW) envelope
Area mean or path
loss (deterministic or
empirical)
Fast or multipath
fading (statistical)
Local mean, or shadowing, or slow
fading (deterministic or statistical)
37
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
38
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  102
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.
39
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)
40
Measurement system

HPIB
RF
R
XY Ctrl

A B
Laptop w . PCMCIA
Laser
100 m MM
Fibre
Receiver Front End
1m coax
LNA
1m coax
LNA
Photodetector
X-Y Positioner

PA (multistage)
Transmitter


VNA-based
Synthetic volume aperture Rx
antenna on a grid of 26x26x2
positions with a cell size of
3x3x40 cm3:
o
 Azimuth resolution 10
o
 Elevation resolution 30
(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 &
41
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
42
Measurement location
43
Measurement Antennas
44
Reflection measurement
45
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
46
Transmission measurement
47
Transmission measurement
48
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
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
? Multiple scat from Arts & Watson
? Scat from nearby tower block ?
49
Indoor measurements

Oxford indoor measurements at 5.5GHz (2ns resolution)
50
Indoor measurements

Oxford indoor measurements at 5.5GHz (2ns resolution)
51
Outdoor to Indoor measurements

Oxford outdoor to indoor measurements at 2.44Hz (27ns
resolution)
52
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
What matters to you

Interference can be controlled also in two ways



Dispersion can be mitigated through the use of



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)
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
54
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
55
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)
Zig-zag
Lateral
Staircase
Transverse
Tx
LOS
56
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 db  4ht hr  for LOS case
L  81.1  39.4 log 10 f GHz  0.1log 10 ht  15.8  5.7 log 10 ht log 10 d km
for d < db and where the distances are measured in km and the
frequency in GHz
L  48.4  47.5 log 10 f GHz  25.3 log 10 ht
 32.1  13.9 log 10 ht  log 10 d d b 
for d > db. Note that there is a 3dB discontinuity at d = db
57
Area mean models – outdoor

For the staircase and transverse NLOS cases in suburban
environments only
L  138.3  38.9 log 10 f GHz   13.7  4.6 log 10 f GHz sgn  y0  log 10 1  y0 
 40.1  4.4 sgn  y0  log 10 1  y0 log 10 d km
where y0  ht  H B ,  7.8m  y0  5.4m and HB is the mean building

height
For the lateral NLOS case in suburban environments only
L  127.4  31.6 log 10 f GHz   13.1  4.4 log 10 f GHz sgn  y0  log 10 1  y0 
 29.2  6.7 sgn  y0  log 10 1  y0 log 10 d km
58
Area mean models – outdoor

For the staircase and transverse NLOS cases in high-rise urban
environments only
L  143.2  29.7 log 10 f GHz  1.0 log 10 ht  47.2  3.7 log 10 ht log 10 d km

For the lateral NLOS case in high-rise urban environments only
L  135.4  12.5 log 10 f GHz  5.0 log 10 ht  46.8  2.3 log 10 ht log 10 d km

The standard deviation of the models from the actual data was
found to be approximately 6 – 12dB
59
Area mean models – outdoor

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
exp  d  a f  b f  if d  a f
pLOS d   
if d  a f
1


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
Ld   pLOS d LLOS d   1  pLOS d LNLOS d 
60
Area mean models – outdoor




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
Area mean models – indoor

COST231 (1999) models


Model 1: L  L1  10n log 10 d
Model 2:
2
L  L0  Lc   k wi Lwi  k
i 1
 k f 2 b 
 k f 1 
f
Lf
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: L  L0   d
62
Area mean models – indoor
L1 (dB)
 (dBm-1)
n
Lw1(dB)
Lw2(dB)
Lf(dB)
b
Dense
One floor
33.3
Two floors 21.9
Three floors 44.9
4.0
5.2
5.4
3.4
6.9
18.3
0.46 0.62
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
2.8
63
Area mean models – indoor



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
64
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
65
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)
66
Area mean models – on-body PANs & BANs

LOS links path loss (measured at 2450 MHz)
LLOS  5.33  20 log 10 dcm

with a standard deviation of 4.2 dB
NLOS links path loss (measured at 2450 MHz)
LNLOS  35  0.36d cm

with a standard deviation of 5.6 dB
Transition regions between LOS and NLOS have path
losses in-between these two equations
67
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 shortranges, but it is the best available that fits observations
68
Local mean model

Working in logarithmic units (decibels, dB), the total path loss is
given by
PLd   Ld   X 
where X is a random variable obeying a lognormal distribution
with standard deviation  (again measured in dB)
p X   

1
 dB 2

2
exp  X 2 2 dB

If x is measured in linear units (e.g. Volts)
p x  
 ln x  ln mx 
1
exp 

2
2 dB 
 dB x 2

where mx is the mean value of the signal given by the area mean
model
69
Local mean model

Cumulative probability density function
cdf PL  LThreshold  
LT  L  d 


1
 dB 2


2
exp  X 2 2 dB
dX
1
 L  Ld  
 1  erfc  T

2
2 



This can be used to calculate the probability that the signal-tonoise 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
70
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
 s d   exp  d dc 
where d is the distance between nearby points and dc ranges
between 20 m and 80 m with typical values for London being,
dc
LOS
NLOS
Urban
30 m
50 m
Suburban
25 m
55 m
71
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
Fast fading models

Constructive and destructive
interference



In spatial domain
In frequency domain
In time domain (scatterers, tx and rx in P
relative motion)




Im
Re
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 d
t
73
Fast fading models

The relation of the radio system channel bandwidth Bch to the
delay spread d is very important



Narrowband channel (flat fading, negligible inter-symbol interference
1
(ISI), diversity antennas useful) Bch  d
Wideband channel (frequency selective fading, need equalisation (RAKE
receiver) or spread spectrum techniques (W-CDMA, OFDM, etc.) to
avoid/limit ISI) Bch  d 1
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
74
Fast fading models

Working in logarithmic units (decibels, dB), the total path loss is
given by
PLd   Ld   X   20 log 10 Y
where Y is random variable which describes the fast fading and it
obeys the distribution
Y
 Y2 
 exp   2 , Y  0
pY     2
 2 
 0,
Y 0

for Rayleigh fading, where the mean value of Y is
Y    2  1    0.80
75
Fast fading models

For Rician fading
Y
 Y 2  ys2   Yy s 
 I 0  2 , Y  0
 2 exp  
2
pY    
2    

 0,
Y 0

where ys is the amplitude of the dominant (LOS) component with
power ys2 2. The ratio K Rice  ys2 2  2 is called the Rician K-factor.
The mean value of Y is
Y    21  K  I0 K 2  K I1 K 2exp  K 2
The Rician K-factor can vary considerably across small areas in
indoor environments
76
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
77
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
PLd   Ld   X   20 log 10 Y if appropriate
S  Ptx  Gtx  Grx  PLd 

Repeat the calculation above for all k interfering
transmitters I k  Ptxk  Gtxk  Grx  PLk d k 
78
How to use models in simulation

Calculate the noise at the receiver (B is the channel bandwidth)
N  10 log 10 k BTB   10 log 10 F 

Combine noise and interference powers linearly
k
 N 10

I rx
N  I  10 log 10 10
 10 10 
k



Calculate the signal-to-noise-plus-interference ratio
SNIR  S  ( N  I )

Look up what bit-error-rate this corresponds to for your system
pe  BER SNIR 
79
How to use models in simulation

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
Ppkt_loss   1  p0  p1  p2    pm
where pl is the probability of exactly l bits being received
erroneously in the packet, given by


 m
 m l 
pl    pel 1  pe 
l
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/)
80
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
81
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


We know practically nothing for ground-based sensors


Low antenna height models need refining
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)
82
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-toMobile UMTS Links,” IEEE 65th VTC, Spring-2007, pp. 529-533, 2009
83
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, AddisonWesley, 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]
84