Upload
trong-nd
View
232
Download
0
Embed Size (px)
Citation preview
8/19/2019 WCCH2015 1 PathLoss and Shadowing
1/42
Ho Chi Minh City University of Technology
Faculty of Electrical and Electronics Engineering
Department of Telecommunications
Lectured by Ha Hoang Kha, Ph.D.
Ho Chi Minh City University of Technology
Email: [email protected]
Chapter 1
Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
2/42
References
A. Goldsmith, Wireless Commun icat ions , CambridgeUniversity Press, 2005.
T.S. Rappaport ,Wireless Commun icat ions , Prentice Hall
PTR, 1996.
J. G. Proakis , M. Salehi , G. Bauch Contemporary
Communication Systems Using MATLAB , Cengage
Learning, 2012.
Slides here are adapted from several sources on the
Internet.
2Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
3/42
Outline
Signal Propagation Overview
Path Loss Models• Free-space Path Loss• Ray Tracing Models
• Simplified Path Loss Model• Empirical Models
3Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
4/42
8/19/2019 WCCH2015 1 PathLoss and Shadowing
5/42
Pathloss is caused by dissipation of the power radiated bythe transmitter as well as effects of the propagation.
Shadowding: is caused by obstacles between the transmitterand receiver that absorb power.
Occuring over very large distances (100-100 meters)
Occuring over distances proportional to the length of theobstructing object (10-100 meters)
Pathloss and Shadowing are referred to as large-scalepropagation or local mean attenuation.
Path Loss and Shadowing 5
8/19/2019 WCCH2015 1 PathLoss and Shadowing
6/42
Path Loss Modeling
Maxwell’s equations
• Complex and impractical
Free space path loss model• Too simple
Ray tracing models
• Requires site-specific information
Empirical Models• Don’t always generalize to other environments
Simplified power falloff models
• Main characteristics: good for high-level analysis
6Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
7/42
2. Transmit and receive signal model
Signals in wireless communications is the UHF and SHF
(Ultra and super high frequency) bands, from 0.3-3 GHzand 3-30 GHz.
f c is the carrier frequency (B
8/19/2019 WCCH2015 1 PathLoss and Shadowing
8/42
Transmit and receive signal model
The received signal will have
If s(t) is transmitted through a time-invariant channel
v(t)=u(t)*c(t), where c(t) is the equivalent lowpass channelimpulse response for the channel.
Path loss:
Ptis transmitted power of s(t)
Pr is received power of r(t)
Path Loss and Shadowing
Remark: P(dB)=10log 10(P(W)), P(dBm)=10log 10(P(mW))
8
8/19/2019 WCCH2015 1 PathLoss and Shadowing
9/42
3. Free Space Propagation Model
Free space power received by a receiver antenna
which is separated from a radiating transmittingantenna by a distance d (Friis free space equation):
P t : the transmitted power
P r (d): the received power
Gt , GR : the transmitter and receiver antenna gain
d : the T-R separation distance in metersL: the system loss factor not related to propagation (L≥1)
λ: the wavelength in meters
2
2 2
. . .( )
(4 ) . .
t t r
r
P G G P d
d L
9Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
10/42
Free-space path loss
Assume there is no obstructions between the transmitter
and receiver, i.e., a line-of-sight (LOS) channel. Received signal:
Path Loss and Shadowing 10
=c/f c: wavelength d: distance of the wave travels : the product of the transmit and receive antenna field
radiation patterns in the LOS direction.
Ratio of received to transmitted power is computed by
8/19/2019 WCCH2015 1 PathLoss and Shadowing
11/42
Free Space Propagation Model
The path loss for the free space model when
antenna gain are included is given by
When antenna gains are excluded, the antennasare assumed to have unity gain and path loss is
given by
2
210log 10log
4
t t r
L
r
P G G P dB
P d
2
2
10 log 10 log4
t
L
r
P P dB
P d
11Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
12/42
Free Space Propagation Model
The free space propagation model is used to predict
received signal strength when the transmitter andreceiver have a clear, unobstructed line-of-sight path
between them.
The free space model predicts that received power
decays as function of the transmitter-receiver (T-R)
separation distance raised to some power .
The carrier frequency increases, the received power
decreases. However, the antenna gain of highlydirectional antennas can increase with frequency.
12Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
13/42
Example
Consider an indoor wireless LAN with f c=900 MHz, cell
radius 10m, and nondirectional antennas. Under thefree-space path loss model, what transmit power is
required at the access point such that all terminals
within the cell receive a minimum power of 10uW. How
does this change if the frequency is 5 GHz.
Path Loss and Shadowing 13
8/19/2019 WCCH2015 1 PathLoss and Shadowing
14/42
4. Ray Tracing Model
Models all signal components
• Reflections
• Scattering
• Diffraction
Requires detailed geometry and dielectric propertiesof site• Similar to Maxwell, but easier math.
Computer packages often used
14Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
15/42
Two-Ray Model
Used when a single ground reflection dominated the
multipath effect. Suitable for isolated areas with few reflectors, such as
rural roads or highways. Not a good model for indoor environments
15Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
16/42
Two-Ray Model
Received signal:
:the time delay of the ground reflection relative to
the LOS ray.’
: the product of transmit and receive antenna fieldradiation in the LOS direction.
: the product of transmit and receive antenna field
radiation patterns corresponding to the refection rays.
R: the ground refection coefficient
If the transmitted signal is narrowband relative to the
delay spread then
-
Path Loss and Shadowing 16
8/19/2019 WCCH2015 1 PathLoss and Shadowing
17/42
Ray Tracing Approximation
Represent wavefronts as simple particles Geometry determines received signal from each
signal component
Typically includes reflected rays, can also include
scattered and defracted rays. Requires site parameters
• Geometry
• Dielectric properties
17Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
18/42
Two-Ray Model
The received power of the two-ray model for
narrowband transmission
: the phase difference between the two signal
components.
When d>> ht+hr , we have
and θ≈0, and R=-1.
-
18Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
19/42
Two-Ray Model
For asymptotically large d,
and R=-1, the received power is approximately
or, in dB
The critical distance dc is the distance after that the signal
power falls off proportionally to d-4.
Cell radius are typically smaller than dc.
19Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
20/42
Received Power versus Distance
20Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
21/42
Two Path Model
Path loss for one LOS path and 1 ground (orreflected) bounce
Ground bounce approximately cancels LOSpath above critical distance
Power falls off
• Proportional to d2 (small d)• Proportional to d4 (d>dc)
• Independent of (f)
21Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
22/42
Example
Determine the critical distance for the two-way model
in an urban microcell (ht=10m, hr =3m) and indoormicrocell (ht=3m and hr =2m) at f c=2GHz.
Solution:
Urban microcell: dc=800 m
Urban microcells are on the order of 100 m to maintain
large capacity.
Indoor system: dc=160 m
Typically indoor system has a smaller cell radius, on the
order of 10-20 m.
22Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
23/42
Dielectric Canyon Ten-Ray Model)
A model for urban area transmission
Other empirical studies have obtained power falloff
with distance proportional to d- where lies anywhere
between to and six.
23Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
24/42
In the simplified model, path loss as a function of
distance is commonly used for system design. Most important parameter is the path loss exponent, determined empirically.
• d0 is a reference distance for the antenna far-field.(d0=1-10m for indoor and 10-100m for outdoorenvironments.
• K is the free space path loss at distance d0:
• The path loss exponent can be obtained via aminimum mean square error (MMSE) fit to empiricalmeasurements.
5. Simplified Path Loss Model
24Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
25/42
Macrocell radius: 1Km-30 Km
Microcell radius: 200-2000 m
Picocell radius: 4m-200 m
Typical Path Loss Exponents
25Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
26/42
Example
Given a transmitter produces 50 W of power. If this power is
applied to a unity gain antenna with 900 MHz carrierfrequency, find the received power at a free space distance
of 100 m from the antenna. What is P r (10 km). Assume
unity gain for the receiver antenna
Ans: Pr (100m)=-24.5 dBm; Pr(10Km)=-64.5 dBm
Path Loss and Shadowing 26
8/19/2019 WCCH2015 1 PathLoss and Shadowing
27/42
Consider the set of empirical measurements of Pr /Pt givenin the table below for an indoor systems at 2 GHz. Findthe path loss exponent that minimizes the MSE betweenthe simplified model and the empirical dB powermeasurements, assuming that d0=10m.
Example
27Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
28/42
6. Empirical Models
Okumura model
• Empirically based (site/freq specific)• Awkward (uses graphs)
Hata model
• Analytical approximation to Okumura model
Cost 136 Model:• Extends Hata model to higher frequency (2 GHz)
Walfish/Bertoni:• Cost 136 extension to include diffraction from rooftops
Common ly used in cellu lar system simulat ions
28Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
29/42
Indoor Propagation Models
Indoor environments differ widely in
• The materials used for walls and floors• The layout of rooms, hallways, windows, and open
areas,
• The location and material in obstructing objects
• The size of each room and the number of the floors. At higher frequency the attenuation loss per floor is
typically larger.
29Path Loss and Shadowing
Table is the
partition lossesmeasured at 900-1300 MHz
8/19/2019 WCCH2015 1 PathLoss and Shadowing
30/42
Indoor Propagation Models
The simple path loss for indoor environment:
• is obtained from the path loss for a same floormeasurement.
• FAFi represents the floor attenuation factor (FAF) forthe ith floor traversed by the signal.
• PAFi represents the partition attenuation factor (PAF)associated with the ith partition traversed by the
signals.• Nf and Np are the number of floors and partitions
traversed by the signal:
30Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
31/42
Example
Suppose, in an office building, a 2.4 GHz
transmitter located at a workstation is separatedfrom the network access node (receiver) by adistance of 35 m. The transmission must passthrough 5 m of an office, through a plasterboard
wall, and then through a large open area. Thepropagation is modeled as free space for the first 5m and with a loss exponent of 3.1 for the remainderof the distance. The plasterboard wall causes 6 dBattenuation of the signal. The isotropic transmitter
radiated 20 dBm. Can the link be closed if thereceiver has a sensitivity of -75 dBm?
31Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
32/42
Main Points
Path loss models simplify Maxwell’s equations Models vary in complexity and accuracy
Power falloff with distance is proportional to d2 in
free space, d4 in two path model
General ray tracing computationally complex
Empirical models used in 2G simulations
Main characteristics of path loss captured in
simple model Pr =PtK[d0/d]
32Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
33/42
In addition to path loss, a signal will typical
experience random variation due to blockage fromthe signal path
• Changes in the reflection surfaces and scattering
objects
is the path loss caused by shadowing which is a
random variable. Empirically, is a log-normaldistribution given by
7. Shadowing
33Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
34/42
In previous example, we found the exponent for the
simplified path loss model that best fit themeasurements was =3.17. Assuming the simplified
path loss model with this exponent and the same
K=-31.54 dB, find , the variance of log-normal
shadowing about the mean path loss based onthese empirical measurements.
Ans:
Example
34Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
35/42
Models for path loss and shadowing are typically
superimposed to capture power falloff versusdistance along with the random attenuation about
this path loss from shadowing.
8. Combined Path Loss and Shadowing
35Path Loss and Shadowing
Pr /Pt
(dB)
log d
Very slow
Slow10log
-10
is a Gauss-distributedrandom variable with mean zeroand variance
8/19/2019 WCCH2015 1 PathLoss and Shadowing
36/42
In wireless systems, there is typically a target
minimum received power level Pmin below whichperformance become unacceptable.
Outage probability is the probability that
the received power at a given distance d, , falls
below Pmin , i.e.
where
9. Outage Probability under Path Loss and
Shadowing
36Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
37/42
Normal or Gaussian Distribution
37Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
38/42
Q- function
38Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
39/42
Q- function
39Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
40/42
Example
40Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
41/42
Outage Probability
and Cell Coverage Area
Path loss: circular cells
Path loss+shadowing: amoeba cells
• Tradeoff between coverage and interference
Outage probability
• Probability received power below given minimum Cell coverage area
• % of cell locations at desired power
• Increases as shadowing variance decreases
• Large % indicates interference to other cells
r P
41Path Loss and Shadowing
8/19/2019 WCCH2015 1 PathLoss and Shadowing
42/42
Homeworks
Problems: 1, 2, 13, 18, 21 in Chapter 2 of [Goldsmith
2005]