M. Junaid Mughal 2006 Wireless Communications Principles and Practice 2 nd Edition T.S. Rappaport Chapter 4: Mobile Radio Propagation: Large-Scale Path.

M. Junaid Mughal 2006

Wireless CommunicationsPrinciples and Practice

2nd EditionT.S. Rappaport

Chapter 4: Mobile Radio Propagation: Large-Scale Path Loss

UMAIR HASHMI Spring 2011


Reflection from Conductors

A perfect conductor reflects back all the incident wave back.

Ei = Er

Өi = Өr ( E in plane of incidence)

Ei = - ErӨi = Өr ( E normal to plane of incidence)



Ground Reflection (Two-Ray) Model


• Propagation Model that considers both the direct (LOS) path and a ground reflected path between transmitter and the receiver.

• Reasonably accurate model for predicting large scale signal strength over distance of several kilometres.

• The E-field due to Line-Of-Sight is given by ELOS

• The E-field for the ground reflected wave is given by Eg

• The Total E-field is a sum of LOS and Reflected components,













• The path difference between the LOS path and the ground reflected path is represented by lambda




• The phase difference and the time arrival delay between the two E-components is given by:

• When d becomes large, difference between d’ and d’’ becomes negligible and ELOS and Eg could be considered equal in magnitude







• Now sin(Ө) is approximately equal to Ө when Ө < 0.3 radians.




• The received power Pr and Path Loss PL will be given by:




101

102

103

104

-140

-120

-100

-80

-60

-40

-20

0

20

40

Distance (m)

20lo

g(|E

|)

d = 20 ht h

r/

1/d4

1/d2




ExampleA mobile is located 5 km away from a BS and uses vertical

lambda/4 monopole antenna with gain of 2.55 dB to receive cellular signals. The E-field at 1 km from the transmitter is measured to be 10-3 V/m. The carrier frequency is 900 MHz.

a) Find length and gain of receiving antenna

b) Find receiver power at the mobile using 2-ray ground reflection model assuming height of transmitting antenna is 50m and receiving antenna is 1.5 m.


Diffraction


• Diffraction is a process that allows radio signals to propagate around curved surfaces and objects and to propagate behind obstructions.

Visible Region

Shadow Region

Obstruction


Diffraction geometry



Diffraction geometry


Visible Region

Shadow Region

Obstruction


Contribution of Huygen’s Secondary Sources at the Receiver


Obstruction

TxRx


Fresnel Zone Geometry


• A transmitter and receiver separated in free space.

• An obstructing screen of height h is placed at a distance d1 from the transmitter and d2 from the receiver.

• The difference between the direct path and the diffracted path is called the excess path length Δ. Assuming h << d1,d2 and h>>λ







• Now tan x is approximately equal to x for x < 0.5 radians

• Fresnel – Kirchoff Diffraction Parameter v is given by




• The phase difference between LOS and diffracted path is a function of

i) Height and Position of the obstructionii) Transmitter and Receiver Location

FRESNEL ZONES

• Fresnel Zones represent successive regions where secondary waves have a path length from the transmitter to the receiver which are nλ/2 greater than the total path length of a LOS path

The successive concentric circles on the plane have path length increment by λ/2. The successive circles are called Fresnel Zones and successive Fresnel Zones have the effect of producing constructive and destructive interference.




• The radius of the nth Fresnel Zone is given by


Knife-Edge Diffraction Model





• The receiver is at point R which is located in the shadowed region (called Diffraction Zone). The field strength at R is a vector sum of the fields due to all of the secondary Huygen;s sources in the plane.

• The Electric Field of a knife edge diffracted wave is

• The Diffraction Gain due to the presence of a knife edge is given by







• The Diffraction Gain for different values of v is:


Knife-edge diffraction loss(Summing Secondary Sources)


-3 -2 -1 0 1 2 3 4 5-30

-25

-20

-15

-10

-5

0

Fresnel Diffraction Parameter v

Kni

fe E

dge

Diff

ract

ion

Gai

n (d

B)




EXAMPLECompute the diffraction loss for the three cases in fig. when

λ=1/3m, d1=1km, d2=1km and (a) h=25m, (b) h=0 (c) h= -25m. Compare the answers with the values obtained from the graph.




EXAMPLEDetermine (a) Loss due to knife-edge diffraction and (b) the height

of the obstacle required to induce 6 dB diffraction loss. Assume f = 900MHz


Scattering


• When a wave impinges on a rough surface, the reflected wave is spread out (diffused) in all directions due to scattering.

• The dimensions of the objects inducing Scattering are comparable to λ

• To judge if a surface is smooth or rough (if we will have reflection or scattering) when a wave impinges upon that surface, the Critical Height hc is given by

hc = λ / ( 8 sin Өi)

• If maximum protuberance hmax < hc : Smooth Surface hmax > hc : Rough Surface

• The reflected E-Fields for h > hc is given by :


Radar Cross Section Model (RCS Model)


• The Radar Cross Section (RCS) of a scattering object is defined as the ratio of the power density of the signal scattered in the direction of the receiver to the power density of the radio wave incident upon the scattering object.

• The bistatic radar equation is used to compute the propagation of a wave travelling in free space that impinges on a distant scattering object and then reradiated in the direction of the receiver. The objects are assumed to be in the Far-Field region (Fraunhofer region)

PR (dBm) = PT (dBm) + GT (dBi) + 20 log λ + RCS [dB m2 ] – 30 log (4 pi) – 20 log dT – 20 log dR


Radar Cross Section Model (RCS Model)



SUMMARY


• What is Large Scale Path Loss?• Free space Propagation Model

• Friis Free space propagation model• Relating power to Electric field

• The three Basic Propagation mechanisms• Reflection

•Reflection coefficients•Polarization rotation•Brewster angle•Reflection from perfect conductors• Ground Reflection (Two Ray Model)


SUMMARY


• Diffraction • Fresnel Zone Geometry• Knife Edge Diffraction• Multiple Knife edge Diffraction

• Scattering• Rough Surface Scattering• Radar Cross section

Now we know all the propagation mechanisms and can use

them to predict path loss in any environment


Log-Distance Path Loss Model


• Radio Propagation Models • Log-distance Path Loss Model

• Received Power decreases logarithmically with distance, whether in outdoor or indoor radio channels

• Reference distance should be in the far field region of the antenna


Log-Distance Path Loss Model



Log-Normal Shadowing


• Surrounding environment clutter not considered in previous model.

• Received power can vary at quite a significant value at 2 points having same T-R separation distances.

• Path Loss (PL) is random and distributed log-normally about the mean distance-dependent value.




• Log-Normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same T-R separation distance.

• This phenomenon is called the log-normal shadowing. Implies that measured signal levels at specific T-R separation have a Gaussian (normal) distribution about the distance-dependent mean.








Determination of Percentage of Coverage Area


• The percentage of useful service area i.e. the percentage of area with a received signal level that is greater or equal to a threshold value.




















Outdoor Propagation ModelsLongley Rice Model


• Point to point communication

• 40 MHz to100 GHz

• Different kinds of terrain

• Median Tx loss predicted by path geometry of terrain profile & Refractivity of troposphere

• Diffraction losses predicted by?

• Geometric losses by?


Outdoor Propagation ModelsLongley Rice Model


• Operates in 2 modes

• Point-to-point mode

• Area mode prediction

• Modification

• Clutter near receiver

• Doesn’t determine corrections due to environmental factors


Outdoor Propagation ModelsDurkin’s Model


• Computer simulator described for field strength contours of irregular terrain

• Split into 2 parts, first reconstructs radial path profile & second calculates path loss

• Rx can move iteratively to establish contour• Topographical database can be thought of as 2-

dimensional array• Each array element corresponds to a point on map &

elevation• Radial path may not correspond to discrete data points

thus interpolation


2-D Propagation Raster Model



Representing Propagation


M. Junaid Mughal 2006UMAIR HASHMI Spring 2011

• Height reconstructed by diagonal, vertical & horizontal interpolation methods

• Reduced to 1 D

• Now determine whether LOS – difference btw heights and line joining Tx & Rx

• Positive height difference


Algorithm for LOS


M. Junaid Mughal 2006UMAIR HASHMI Spring 2011

• Then checks first Fresnel Zone clearance

• If terrain profile fails first Fresnel Zone Clearance

• a) non LOS

• b) LOS but inadequate Fresnel Zone Clearance


Non-LOS Cases


• a) Single Diffraction Edge

• b) Two Diffraction Edges

• a) Three Diffraction Edges

• a) More than three Diffraction Edges

• Method sequentially tests for each

• Angles btw pine joining Tx & Rx and each point on reconstructed profile. Max angle (di,hi)

• Angles between line joining Tx & Rx and Tx Antenna to every point on reconstructed profile

• For single diffraction di=dj


Multiple Diffraction Computation



Okumura’s and Hata’s Model



Hata’s Model


• Empirical formulation of graphical path loss data• Valid from 150 MHz to 1500 MHz.• Urban Area Propagation loss as a standard and supplied

correction equations for application to other situations• hte=30 m to 200m, hre=1m to 10m

•Compares very closely with Okumura model as long as d doesn’t exceed 1km•Well suited for large cell communications but not PCS


PCS Extension to Hata Model


• Hata’s model to 2GHz


ASSIGNMENT


Review the Outdoor Propagation Models presented in the slides showing their salient features and how they differentiate from each other.

M. Junaid Mughal 2006 Wireless Communications Principles and Practice 2 nd Edition T.S. Rappaport Chapter 4: Mobile Radio Propagation: Large-Scale Path.

Documents

junaid mughal

ray model umair hashmi

receiver umair hashmi

ray ground reflection

h slide

lambda slide

magnitude slide

ground reflected path