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3/3/2013
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Lecture 02
Wireless channels - macro modeling
Instructor: Dr. Phan Van Ca
Simplified View of a Digital Radio Link
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Frequencies for communication
VLF = Very Low Frequency UHF = Ultra High Frequency
LF = Low Frequency SHF = Super High Frequency
MF = Medium Frequency EHF = Extra High Frequency
HF = High Frequency UV = Ultraviolet Light
VHF = Very High Frequency
Frequency and wave length: λ = c/f
wave length λ, speed of light c ≅ 3x108m/s, frequency f
Frequencies for communication
r VHF-/UHF-ranges for mobile radiom simple, small antenna for cars
m deterministic propagation characteristics, reliable connections
r SHF and higher for directed radio links, satellite communication
m small antenna, beam forming
m large bandwidth available
r Wireless LANs use frequencies in UHF to SHF rangem some systems planned up to EHF
m limitations due to absorption by water and oxygen molecules (resonance frequencies)• weather dependent fading, signal loss caused by heavy rainfall etc.
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Frequencies for communication
r VHF-/UHF-ranges for mobile radio� simple, small antenna for cars� deterministic propagation characteristics, reliable connections
r SHF and higher for directed radio links, satellite communication� small antenna, focusing� large bandwidth available
r Wireless LANs use frequencies in UHF to SHF spectrum� some systems planned up to EHF� limitations due to absorption by water and oxygen molecules
� (resonance frequencies)
Frequencies and regulations
r ITU-R holds auctions for new frequencies, manages frequency bands worldwide (WRC, World Radio Conferences)
Examples Europe USA Japan
Cellular
phones
GSM 880-915, 925-
960, 1710-1785,
1805-1880
UMTS 1920-1980,
2110-2170
AMPS, TDMA,
CDMA, GSM 824-
849, 869-894
TDMA, CDMA, GSM,
UMTS 1850-1910,
1930-1990
PDC, FOMA 810-888,
893-958
PDC 1429-1453, 1477-
1501
FOMA 1920-1980, 2110-
2170
Cordless
phones
CT1+ 885-887, 930-
932
CT2 864-868
DECT 1880-1900
PACS 1850-1910,
1930-1990
PACS-UB 1910-1930
PHS 1895-1918
JCT 245-380
Wireless
LANs
802.11b/g 2412-
2472
802.11b/g 2412-
2462
802.11b 2412-2484
802.11g 2412-2472
Other RF
systems
27, 128, 418, 433,
868
315, 915 426, 868
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Antennas: isotropic radiator
r Radiation and reception of electromagnetic waves, coupling of wires to space for radio transmission
r Isotropic radiator: equal radiation in all directions (three dimensional) - only a theoretical reference antenna
r Real antennas always have directive effects (vertically and/or horizontally)
r Radiation pattern: measurement of radiation around an antenna
Antennas: directed and sectorized
r Often used for microwave connections or base stations for mobile phones (e.g., radio coverage of a valley)
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Antenna: gain
Isotropic Dipole High gain directional
isotropic
ldirectiona
P
PG =
0 dBi2.2 dBi 14 dBi
Antennas: diversity
r Grouping of 2 or more antennasm multi-element antenna arrays
r Antenna diversitym switched diversity, selection diversity
• receiver chooses antenna with largest output
m diversity combining• combine output power to produce gain
• cophasing needed to avoid cancellation
+
λ/4λ/2λ/4
ground plane
λ/2
λ/2
+
λ/2
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Signals I
r physical representation of data
r function of time and location
r signal parameters: parameters representing the value of data
r classificationm continuous time/discrete time
m continuous values/discrete values
m analog signal = continuous time and continuous values
m digital signal = discrete time and discrete values
r signal parameters of periodic signals: period T, frequency f=1/T, amplitude A, phase shift ϕ
m sine wave as special periodic signal for a carrier:
s(t) = At sin(2 π ft t + ϕt)
Fourier representation of periodic signals
)2cos()2sin(2
1)(
11
nftbnftactgn
n
n
n ππ ∑∑∞
=
∞
=
++=
1
0
1
0
t t
ideal periodic signal real composition
(based on harmonics)
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Signals II
r Different representations of signals m amplitude (amplitude domain)m frequency spectrum (frequency domain)m phase state diagram (amplitude M and phase ϕ in polar coordinates)
r Composed signals transferred into frequency domain using Fourier transformation
r Digital signals needm infinite frequencies for perfect transmission m modulation with a carrier frequency for transmission (analog signal!)
f [Hz]
A [V]
ϕ
I= M cos ϕ
Q = M sin ϕ
ϕ
A [V]
t[s]
Signal propagation ranges
r Transmission range� communication possible
� low error rate
r Detection range� detection of the signal possible
� no communication possible
r Interference range� signal may not be detected
� signal adds to the background noise
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Signal propagationr Propagation in free space always like light (straight line)
r Receiving power proportional to 1/d²(d = distance between sender and receiver)
r Receiving power additionally influenced by� fading (frequency dependent)
� shadowing
� reflection at large obstacles
� refraction depending on the density of a medium
� scattering at small obstacles
� diffraction at edges
Effects of mobility
r Channel characteristics change over time and location
� signal paths change
� different delay variations of different signal parts
� different phases of signal parts
� quick changes in the power received (short term fading)
r Additional changes in
� distance to sender
� obstacles further away
� slow changes in the average power received (long term fading)
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Propagation Characteristics
r Path Loss (includes average shadowing)
r Shadowing (due to obstructions)
r Multipath Fading
Pr/Pt
d=vt
Pr
Pt
d=vt
v Very slow
Slow
Fast
���� Limit the Bit Rate and/or Coverage
Signal Propagation Effects
r Large scale Path lossm Large distances (w.r.t. to wavelength of the wave) between transmitter and receiver
r Small scale Fadingm Fluctuation in received signal strengths due to variations over short distances (w.r.t. to wavelength of the wave)
r Consider the wavelength of radio signals for 802.11m 802.11 a: Frequency = 5.2 GHz Wavelength = 5.8 cm
m 802.11 b/g: Frequency = 2.4 GHz Wavelength = 12.5 cm
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Large scale Path lossr General Observation:
m As distance increases, the signal strength at receiver decreases
r Maxwell’s equations
m Complex and impractical
r Free space path loss model
m Too simple
r Ray tracing models
m Requires site-specific information
r Empirical Models
m Don’t always generalize to other environments
r Simplified power falloff models
m Main characteristics: good for high-level analysis
Large scale Path loss
r Different, often complicated, models are used for different environments.
r A simple model used when path loss dominated by reflections:
r Most important parameter is the path loss exponent n, determined empirically.
82,0 ≤≤
= n
d
dKPP
n
tr
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Typical large-scale path loss
Free Space (LOS) Model
r Path loss for unobstructed LOS path
r Power falls off :m Proportional to 1/d2
m Proportional to λ2 (inversely proportional to f2)
d=vt
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Free Space Model
PT
PR
d
2/
24mW
d
PP T
Diπ
= Isotropic power
density
24 d
GPP TT
Dπ
=Power density along the
direction of maximum
radiation
effTT
R Ad
GPP
24π=
π
λ
4
2
=G
Aeff
2
4=
dGGPP RTTR
π
λ
Power received by
AntennaeffDR APP =
Predict received signal strength when the transmitter and receiver have a clear line-of-sight path between them
Also known as Friis
free space formula
Pt
PR 2
4=
dGG
P
PRT
T
R
π
λ
)log20log205.32()()( 1010 fdGGP
PdBRdBT
dBT
R ++−+=
2
3
)(
10*57.0
dfGG
P
PRT
T
R
−
=f is in MHz
d is in Km
Path Loss represents signal attenuation
(measured on dB) between the effective
transmitted power and the receive power
(excluding antenna gains)
Free Space Model
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Free Space model (Example)
Pt
PR
50 W
= 47 dBm
Assume that antennas are isotropic.
Calculate receive power (in dBm) at free space distance
of 100m from the antenna. What is PR at 10Km?
dBP
P
dBT
R 5.71−=
)log20log205.32()()( 1010 fdGGP
PdBRdBT
dBT
R ++−+=
dBP
P
dBT
R 5.111−=
)900log201.0log205.32(00 1010 ++−+=
dBT
R
P
P
-20 (for d = 0.1)
59
20 (for d = 10)
dBmP dBmR 5.245.7147)( −=−= dBmP dBmR 5.645.11147)( −=−=
Shadowing
r Models attenuation from obstructions
r Random due to random # and type of obstructions
r Typically follows a log-normal distributionm dB value of power is normally distributed
m µ=0 (mean captured in path loss), 4<σ<12 (empirical)
m LLN used to explain this model
m Decorrelated over decorrelation distance Xc
Xc
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Pr (dB) = Pr (dB) + Gs
where Gs ~ N(0, σσσσs ), 4 ≤≤≤≤ σσσσs ≤≤≤≤ 10 dB.2
R P = Pr0
� The received signal is shadowed by obstructions such as hills and buildings.
� This results in variations in the local mean received signal power.
Implications• non-uniform coverage• increases the required transmit power
Shadowing
Multipath propagation
r Signal can take many different paths between sender and receiver due to:m Reflection: From objects very large (wrt to wavelength of the wave).
m Diffraction: From objects that have sharp irregularities.
m Scattering• From objects that are small (when compared to the wavelength)
• E.g.: Rough surfaces
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Multipath propagation
r Time dispersion: signal is dispersed over time� interference with “neighbor” symbols, Inter Symbol Interference (ISI)
r The signal reaches a receiver directly and phase shifted� distorted signal depending on the phases of the different parts
Multipath propagation
dB With Respect
to RMS Value
0 0.5
0.5λλλλ
1.5
-30
-20
-10
10
0
1
t, in seconds
0 10 3020
x, in wavelength
Constructive and Destructive Interference of Arriving Rays
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Ray Tracing Approximationr Represent wavefronts as simple particlesr Geometry determines received signal from each signal component
r Typically includes reflected rays, can also include scattered and defracted rays.
r Requires site parametersm Geometry
m Dielectric properties
Two-ray tracing (Ground Reflection)
r Path loss for one LOS path and 1 ground (or reflected) bounce
r Ground bounce approximately cancels LOS path above critical distance
r Power falls off m Proportional to d2 (small d)
m Proportional to d4 (d>dc)
m Independent of λ (f)
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r Two-ray (Ground reflection) modelm Considers LoS path + Ground reflected wave path
θi θo
ELOS
Ei
Eg
ETOT = ELOS + Eg
Transmitter
Receiver
Two-ray tracing (Ground Reflection)
General Ray Tracingr Models all signal components: Reflections, Scattering, Diffraction
r Requires detailed geometry and dielectric properties of sitem Similar to Maxwell, but easier math.
r Computer packages often used
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Empirical models
r Above models are very simplistic in realistic settings
E.g: Points 4 and 5 in the above figure
r Alternative Approach:m Use empirical data to construct propagation models
m But, can measurements at few places generalize to all scenarios?• Different environments?
• Different frequencies?
m Recognize "patterns" in the empirical data and use statistical techniques for approximating.
Empirical Models
r Log-distance Path loss modelm Uses the idea that both theoretical and empirical evidence suggests that average received signal strength decreases logarithmically with distance
m Measure received signal strength near to transmitter and approximate to different distances based on above “reference” observation
r Log-normal shadowingm Observes that the environment can be vastly different at two points with the same distance of separation.• Empirical data suggests that the power observed at a location is random and distributed log-normally about the “mean” power
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Small scale fading
r Rapid fluctuations of the signal over short period of time
r Invalidates Large-scale path loss
r Occurs due to multi-path wavesm Two or more waves (e.g: reflected/diffracted/scattered waves)
m Such waves differ in amplitude and phase
m Can combine constructively or destructively resulting in rapid signal strength fluctuation over small distances
Example of Multipath
Phase difference between
original and reflected wave
Link measurement observations
r Is propagation disk shaped? m Directionality due to environment?
r Does it observe Free-space Propagation model?
Figure 2: Contour of probability
of packet reception wrt distanceFigure 1: SNR values v/s distance
� Distance v/s observed signal strength
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Link measurement observations
r Shows packet reception rates of 4 different links
r Temporal variations over a long time period (96 hours) is significantm Note: This is not the signal strength, but packet reception rate (broadcast
packet)
� Temporal variations
Impact of protocol design
r MAC protocolm Constant retransmissions needed
m Neighborhood discovery
m More problems when we consider asymmetry of links• Source can talk to receiver but not vice-versa
– ACKs?
r Routing protocolm Multi-hop reliability is low after 4 to 5 hops
• Consider 5 links each with packet-throughput 95%. Overall throughput (assuming no ACK) is 95%. Overall throughput (assuming no ACK) is ~77%.
r Transport protocolm Effect of unpredictable packet losses on TCP?
r And other effects like packet delivery success based on relative motion between transmitter and receiver
m Multipath effects?
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Main Points
r Path loss models simplify Maxwell’s equations
r Models vary in complexity and accuracy
r Power falloff with distance is proportional to d2 in free space, d4 in two path model
r Empirical models used in 2G simulations
r Main characteristics of path loss captured in simple model Pr=PtK[d0/d]n
r Random attenuation due to shadowing modeled as log-normal (empirical parameters)
