WC-Chapter 1-Path Loss and Shadowing.pdf

8/12/2019 WC-Chapter 1-Path Loss and Shadowing.pdf

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1

Chapter 1

a oss an a ow ngHa Hoang Kha, Ph.D

Ho Chi Minh City University of Technology

Email: [email protected]

Outline

Signal Propagation Overview

a oss o e s Free-space Path Loss Ray Tracing Models Simplified Path Loss Model Empirical Models

2 H. H. Kha, Ph.DPath Loss and Shadowing

1. Propagation Characteristics

Path Loss (includes average shadowing)

Shadowing (due to obstructions)

Multipath Fading

Pr/PtPr

Ptv Very slow

Slow

Fast

d=vt

d=vt


Pathloss is caused by dissipation of the power radiated by

the transmitter as well as effects of the propagation.

Shadowding: is caused by obstacles between the transmitterand receiver that absorb power.

ccur ng over very arge stances - meters

Occuring over distances proportional to the length of theobstructin ob ect 10-100 meters

Pathloss and Shadowing are referred to as large-scalepropagation or local mean attenuation.

Path Loss and Shadowing 4 H. H. Kha, Ph.D


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2

Path Loss Modeling

Maxwells equations Complex and impractical

Free s ace ath loss model Too simple

Ray tracing models Requires site-specific information

Empirical Models Dont always generalize to other environments

Simplified power falloff models

Main characteristics: good for high-level analysis


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.

where is a complex baseband signal with in-

We model the transmitted signal as

fc is the carrier frequency (B


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Free-space path loss

Assume there is no obstructions between the transmitterand receiver, i.e., a line-of-sight (LOS) channel.

Received si nal:

=c/fc: wavelength d: distance of the wave travels : the product of the transmit and receive antenna field


.

Ratio of received to transmitted power is computed by

Free Space Propagation Model

The path loss for the free space model when antennagain are included is given by

When antenna gains are excluded, the antennas are

assumed to have unity gain and path loss is given by

( )( )

210log 10log

4

t t r

L

r

P dBP d

= =

2P

( )2og og 4

L

rP d= =


Free Space Propagation Model

The free space propagation model is used to predict

received signal strength when the transmitter and

receiver have a clear unobstructed line-of-si ht ath

,between them.

The free space model predicts that received powerdecays as function of the transmitter-receiver (T-R)separation distance raised to some power.

,

decreases. However, the antenna gain of highlydirectional antennas can increase with frequency.


Example

Consider an indoor wireless LAN with fc=900 MHz,

cell radius 10m, and nondirectional antennas. Under the

free-s ace ath loss model what transmit ower 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 properties ofsite

m ar o axwe , u eas er ma .Computer packages often used


Two-Ray Model

Used when a single ground reflection dominated themultipath effect.

,

rural roads or highways.Not a good model for indoor environments


Two-Ray Model

Received signal:

-

:the time delay of the ground reflection relative to the

LOS ray. : the product of transmit and receive antenna field

radiation in the LOS direction.

: the product of transmit and receive antenna fieldradiation patterns corresponding to the refection rays.

R: the ground refection coefficient

If the transmitted signal is narrowband relative to the

delay spread then


Ray Tracing Approximation

Represent wavefronts as simple particles

Geometry determines received signal from eachsignal component

Typically includes reflected rays, can also includescattered and defracted rays.

Requires site parameters

Geometry

Dielectric properties



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Two-Ray Model

The received power of the two-ray model fornarrowband transmission

-

: the phase difference between the two signalcomponents.

When d>> ht+hr, we have

and 0, and R=-1.


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.


Received Power versus Distance


Two Path Model

Path loss for one LOS path and 1 ground (or

reflected) bounceGround bounce approximately cancels LOS path

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 modelin an urban microcell (ht=10m, hr=3m) and indoor

microcell h =3m and h =2m at f =2GHz. r c .

Solution:

Urban microcell: dc=800 m

Urban microcells are on the order of 100 m to maintainlarge capacity.

n oor system: c= mTypically indoor system has a smaller cell radius, on the

order of 10-20 m.


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 anywherebetween to and six.


In the simplified model, path loss as a function ofdistance is commonly used for system design.

Most important parameter is thepath loss exponent ,

5. Simplified Path Loss Model

eterm ne emp r ca y.

or, in dB d0 is a reference distance for the antenna far-field. (d0=1-10m

- .

K is the free space path loss at distance d0:

The path loss exponent can be obtained via a minimummean square error (MMSE) fit to empirical measurements.


Typical Path Loss Exponents

Macrocell radius: 1Km-30 Km

Microcell radius: 200-2000 m

Picocell radius: 4m-200 m



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Example

Given a transmitter produces 50 W of power. If this power isapplied to a unity gain antenna with 900 MHz carrier frequency,find the received power at a free space distance of 100 m fromthe antenna. What is Pr(10 km). Assume unity gain for thereceiver antenna

Ans: Pr(100m)=-24.5 dBm; Pr(10Km)=-64.5 dBm


Consider the set of empirical measurements of Pr/Pt given in thetable below for an indoor systems at 2 GHz. Find the path lossex onent that minimizes the MSE between the sim lified model

Example

and the empirical dB power measurements, assuming that d0=1mand K is determined from the free space path loss formula at thisd0.


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

Commonly used in cellular system simulations


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 istypically 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) for the ithfloor traversed by the signal.

PAFi represents the partition attenuation factor (PAF).

Nfand Np are the number of floors and partitions traversedby the signal:


Example

Suppose, in an office building, a 2.4 GHz transmitterlocated at a workstation is separated from the networkaccess node (receiver) by a distance of 35 m. Thetransmission must pass through 5 m of an office,through a plasterboard wall, and then through a largeopen area. The propagation is modeled as free space forthe first 5 m and with a loss exponentof 3.1 for theremainder of the distance. The plasterboard wall causes6 dB attenuation of the signal. The isotropic transmitter

radiated 20 dBm. Can the link be closed if the receiverhas a sensitivity of -75 dBm?


Main Points

Path loss models simplify Maxwells equations

Power falloff with distance is proportional to d2 in freespace, d4 in two path model

General ray tracing computationally complex

Main characteristics of path loss captured in simple

model Pr=PtK[d0/d]


In addition to path loss, a signal will typical experience

random variation due to blockage from the signal path

Changes in the reflection surfaces and scattering objects

7. Shadowing

is the path loss caused by shadowing which is a randomvariable. Empirically, is a log-normal distribution given by



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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

Example

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 on theseempirical measurements.

Ans:


Models for path loss and shadowing are typically

superimposed to capture power falloff versus distancealong with the random attenuation about this path loss

8. Combined Path Loss and Shadowing

from shadowing.

Slow10log is a Gauss-distributedrandom variable with mean zero


r t

(dB)

log d

Very sl ow-10

In wireless systems, there is typically a target minimumreceived power level Pmin below which performancebecome unacceptable.

9. Outage Probability under Path Loss and

Shadowing

Outage probability is the probability that thereceived power at a given distance d, , falls below Pmin , i.e.

where


Normal or Gaussian Distribution



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Q- function


Q- function


Example


Outage Probabilityand Cell Coverage Area

Path loss: circular cells

Path loss+shadowing: amoeba cellsr

P

Tradeoff between coverage and interference

Outage probability

Probability received power below given minimum

Cell coverage area

Increases as shadowing variance decreases

Large % indicates interference to other cells



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References

[1]A. Goldsmith, Wireless Communications, Cambridge UniversityPress, 2005.

. , , ,http://www.stanford.edu/class/ee359/archived_material/2010/lectures.html


Homeworks

Problems: 1, 2, 13, 18, 21 in Chapter 2 of [Goldsmith 2005]


WC-Chapter 1-Path Loss and Shadowing.pdf

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