Large-Scale Path Loss

EE 424 Dr. Abdel Fattah Sheta KSU 1

Large scale Path Loss

EEEE424 424 Communication Communication SystemsSystems

Abdel Fattah Abdel Fattah ShetaShetaPart Part 55

Mobile Radio Propagation:Large-Scale Path Loss

Introduction to Radio Wave Propagation

The mobile radio channel places fundamental limitations on the performance of wireless communication systems

Mobile radio path is severely obstructed by buildings, mountains, and foliage

Radio channels are extremely random and do not offer easy analysis

The speed of motion impacts how rapidly the signal level fades as a mobile terminals moves in the space

Modeling radio channel is one of the most difficult part and typically done in a statistical manner based on measurements



Introduction. Cont.

Mechanisms affect radio wave propagation are:

Reflection

Diffraction

Scattering

In urban areas, there is no direct line-of-sight path between the transmitter and the receiver, and where the presence of high- rise buildings causes severe diffraction loss.

Multiple reflections cause multi-path fading

Introduction. Cont.

Small-Scale models (fading models)

Propagation models that characterize rapid fluctuations of the received signal strength over very short travel distances (few wavelengths) or short time duration (on the order of seconds)

Large Scale Propagation Models

Propagation models are usually required to predict the average received signal strength at a given distance from the transmitter and estimating the coverage area (averaged over meters)



Small Scale and Large-Scale fading for an indoor radio

Most radio propagation models are derived using a combination of analytical (from a set of measured data) and empirical methods. (based on fitting curves)

All propagation factors through actual field measurements are included.

Some classical propagation models are now used to predict large scale coverage for mobile communication systems design.

Propagation models



Free Space Propagation Model

Far-field is assumed d > 2D2/ , where

D is the largest linear dimension of antennais the carrier wavelengthNo interference, no obstructions

Pt Transmitted power,Pr(d) Received powerGt Transmitter antenna gain,Gr Receiver antenna gain,d T-R separation distanceL System loss factor not related to propagation

Free Space Propagation Model

Examples 3.1



Examples 3.2

(b)

Relating power to Electric Field



Relating power to Electric Field Cont..

Model for voltage applied to the input of a receiver

Power flux density at distance d from a point source

(open circuit)To matched

receiver

RantVant V

Example 3.3

(a)

(b)

(c)



Radio Propagation Mechanisms

ReflectionConductors & Dielectric materialsPropagation wave impinges on an object which is large as compared to wavelength

- e.g., the surface of the Earth, buildings, walls, etc.Diffraction

Radio path between transmitter and receiver obstructed by surface with sharp irregular edgesWaves bend around the obstacle, even when LOS (line of sight) does not exist

ScatteringThe through which the wave travels consists of objects with dimensions smaller than the wavelength and where the number of obstacles per unit volume is large rough surfaces, small objects, foliage, street signs, lamp posts.

Reflection from smooth surface

Geometry for calculating the reflection coefficients between two dielectrics

E-Field in the plane of incidence E-Field normal to the plane of incidence

The plane of incidence: The plane containing the incidence, reflected, and transmitted rays



If a dielectric material is lossy = o r j ( = /2pif)

Good conductor f < (/or): and are generally insensitive to frequencyLossy dielectric: o and r are generally constant with frequency ( may

be sensitive to operating frequency)

E-Field in the plane of incidence

E-Field normal to the plane of incidence

is the intrinsic impedance of a medium = /

Velocity = 1/

Using boundary conditions:



Brewster Angle

The angle at which no reflection occurs in the medium of origin.It occurs only for parallel polarization.



Reflection from perfect conductors

Total reflection with i = rEi = Er for E-Field in the plane of incidence

|| = 1

Ei = -Er for E-Field normal to the plane of incidence = -1

Ground Reflection (2-ray) ModelAccurate for predicting the large-scale signal strength over distances of several kilometers for mobile radio systems that use tall towers (heights ~ 50 m) as well as LOS microcell channels in urban environment.

If Eo is the free space E-field at a reference distance do from the transmitter, then for d > do, the free space propagating E-field is given by

Two propagating waves:Direct: Travel distance dreflected: Travel distance d



Direct

Reflected

At the ground surface Eg = Ei & Et = (1 + ) EiAssuming perfect ground reflection = -1, the resultant total E-field

|ETOT| = |ELOS + Eg|

2-Ray Model

Using the method of images

= d - d =

If d is very large, using Taylor series,

The phase difference between the two filed will be

= 2pi / = c /c

2-Ray Model



As d becomes large, the difference between the paths becomes very small and |ELOS| |Eg|

the difference only in phasei.e

At t = d/c

2-Ray Model

Using the phasor diagram

2-Ray Model



i.e For

Then

and

If /2 < 0.3 Radian sin (/2) /2

For d > hthr , the received power decreases as 40 dB/decade

2-Ray Model

Example 3.6



Diffraction

Allows radio signals to propagate around the curved surface of the earth, beyond the horizon, and propagate behind obstructions.

Can be explained using Huygens principal

All points on a wavefront can be considered as point sources for the production of secondary wavelets, and that these wavelets combine to produce a new wavefront in the direction of propagation

Diffraction



Fresnel Zone Geometry

Assuming h > , the difference between direct path and diffracted path, called the excess path length ()

The corresponding phase difference is

Fresnel Diffraction parameter () = +

= tan + tan

It can be shown that

The phase difference between the direct and reflected path is function of d1, d2, h, ht and hr

Fresnel Zone Geometry



Diffraction loss as a function of the path difference around an obstruction is explained by Fresnel Zones

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

The concentric circles on the plane represent the loci of the origins of the secondary wavelets which propagate to the receiver such that the total path length increases by /2 for successive circles.

Fresnel Zones

The radius of the nth Fresnel zone is given by

This approximation is valid for d1, d2, >> rn

Fresnel Zones

The maximum radii occurs if the plane is midway between the transmitter and receiver

The radii become smaller when the plane is moved towards either the transmitter or the receiver.



Fresnel Zones

For design of line-of-sight microwave links55% of the first Fresnel zone is kept clear

Prediction: (Theoretical approximation modified by necessary empirical corrections)

Knife edge case gives good insight into the order of magnitude of diffraction loss.

Knife-edge Diffraction Model

Knife edge approximation is good when shadowing is caused by a single object such as hill or mountain

It is impossible to make very precise estimates of the diffraction losses



Can be estimated using the classical Fresnel solutions for the field behind a knife edge. The field strngth at point R is a vector sum of the field due to all the scondary Huygens sources in the plane above the knife edge.

The electric field strength Ed of a knife edge diffracted wave is given by

Eo is the free space value with no obstacles or ground

F(), is the complex Fresnel integral

The diffraction gain due to the presence of knife edge as compared to the free space field

Gd(dB) = 20 log |||| F()||||


Graphical representation of Gd(dB) as a function of




Approximate solution by Lee

Example 3.7



Example 3.8



Multiple Kinfe-Edge Diffraction



Scattering

The diffusion, or the reflection in multiple different directions of a signal.

The medium which the wave travels consists of objects with dimensions smaller than the wavelength and where the number of obstacles per unit volume is large rough surfaces, small objects, foliage, street signs, lamp posts.

In mobile communication, the actual received signal is often stronger than that is predicted by reflection and diffraction models.

Scattering

Rough surfaces

hc Rayleigh Critical height

Angle of incidence of i

Smooth surface: Min to max protuberance (h < hc)ref can be used

If h > hc correction should be consider rough = s smooth

Scattering loss factor (s) is modeled with Gaussian distribution



Nearby metal objects (street signs, etc.)Usually modeled statistically

Large distant objectsAnalytical model: Radar Cross Section (RCS)Bistatic radar equation

Scattering

Ideal smooth surfaceGaussian rough surfaceMeasured dataGaussian rough surface



Ideal smooth surfaceGaussian rough surfaceMeasured dataGaussian rough surface

Practical Link Budget Design Using Path Models

Combination of analytical and emperical methods

The emperical approach is based on fitting curves and analytical expressions that recreate a set of measured data



The average large-scale propagation path loss

(PL) (d/do)n

d is the T-R (Transmitter-Receiver) separation,do is the free space reference distance which is closer to the

transmitter (should always be in the far field).n is the path loss exponent (it indicates the rate of path loss)

It depends on the propagation environment.

Log Distance Path Loss Model

Theoretical propagation models and measurement:(Average received signal strength decreases logarithmically with distance).

This relationship are valid for in-door and outdoor radio wave propagations.

In dB format:(PL)dB = PL(do) + 10nlog(d/do)

The PL includes all possible average path losses.

Bars denote the ensemble average of all possible path loss values for a given d

On a log-log scale plot, the modeled path loss is a straight line with a slope equal to 10n dB per decade.

In large coverage cellular system , 1 km reference distances are commonly used and in microcell systems much smaller distances (100 m to 1 m) are used





Path loss exponents for different environments

The reference path loss is calculated from free pace path loss or through measurements at do.

Log-normal shadowing

The environmental conditions are different and not considered in the above PL equation.

A simple statistical model can account for unpredictable shadowing

The measurement shows that all PL(d) are random at a distance d and distributed log-normally (normal in dB) about the mean distance-dependent value.

Thus, [PL(d)]dB = PL(do) + 10nlog(d/do) + X

where X is a zero mean Gaussian distributed random variable (in dB) with standard deviation (dB).



log-normal shadowing.

Simply implies that measured signal levels

at a specific T-R separation have a Gaussian (normal) distribution about the distance-dependent mean of (3.68),

d0, n, (the standard deviation),statistically describe the path loss model for an arbitrary location having a specific T-R separation

This model may be used in computer simulation toprovide received power levels for random locations incommunication system design and analysis.

The log-normal distribution describes the random shadowing effects which covers a large number of measurement locations which have the same TR separation but have different levels of clutter on propagation path. This phenomenon is referred to as log-normal shadowing.

In practice, the values of n and are computed frommeasured data, using linear regression such that thedifference between the measured and estimated pathlosses is minimized in a mean square error senseover a wide range of measurement locations and T-Rseparations.

Large-Scale Path Loss

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