Radiowave Channel Modelling for Sensor Networks
Costas ConstantinouElectronic, Electrical & Computer Engineering
The University of Birmingham, UKhttp://www.eee.bham.ac.uk/ConstantinouCC/
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
Electromagnetic waves
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
Electromagnetic waves
Spherical waves Intensity (time-average) Conservation of energy; the inverse square law
HES
212Wm
99
Electromagnetic waves
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
Pictorial introduction to radiation from accelerated charges
1212
Radiation
Pictorial introduction to radiation from accelerated charges
1313
Radiation
Fields around a charge in non-uniform motion
1414
Radiation
Fields around a charge in non-uniform motion
1515
Radiation
Fields around a charge in non-uniform motion
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,ˆexp
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,ˆexp
60
,ˆ,ˆexp
60,
2
2rad
1
1rad
TT
TT
ggr
crtjP
ggr
crtjPr
,,, 21 rrr EEE
3232
Propagation over flat earth
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
Propagation over flat earth
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
Propagation over flat earth
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
Propagation over flat earth
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
Transmission measurement
49
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 ?
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
Area mean models – outdoor
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
Area mean models – outdoor
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
60
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
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
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
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
Area mean models – indoor
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
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
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
How to use models in simulation
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
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
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)
8383
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
8484
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]