WCCH2015 1 PathLoss and Shadowing

8/19/2019 WCCH2015 1 PathLoss and Shadowing

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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


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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


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Outline

Signal Propagation Overview

Path Loss Models• Free-space Path Loss• Ray Tracing Models

• Simplified Path Loss Model• Empirical Models



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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


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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



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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


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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


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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



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Free-space path loss

Assume there is no obstructions between the transmitter

and receiver, i.e., a line-of-sight (LOS) channel. Received signal:


=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


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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



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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.



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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.



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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



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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



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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

-



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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



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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.

-



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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.



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Received Power versus Distance



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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)



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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.



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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.



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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



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Macrocell radius: 1Km-30 Km

Microcell radius: 200-2000 m

Picocell radius: 4m-200 m

Typical Path Loss Exponents



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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



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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



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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



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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.


Table is the

partition lossesmeasured at 900-1300 MHz


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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:



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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?



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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]



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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



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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



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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


Pr /Pt

(dB)

log d

Very slow

Slow10log

-10

is a Gauss-distributedrandom variable with mean zeroand variance


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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



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Normal or Gaussian Distribution



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Q- function



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Q- function



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Example



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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



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Homeworks

Problems: 1, 2, 13, 18, 21 in Chapter 2 of [Goldsmith

2005]

WCCH2015 1 PathLoss and Shadowing

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