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Large-Scale Path Loss
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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
EE 424 Dr. Abdel Fattah Sheta KSU 2
Large scale Path Loss
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)
EE 424 Dr. Abdel Fattah Sheta KSU 3
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 4
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 5
Large scale Path Loss
Examples 3.2
(b)
Relating power to Electric Field
EE 424 Dr. Abdel Fattah Sheta KSU 6
Large scale Path Loss
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)
EE 424 Dr. Abdel Fattah Sheta KSU 7
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 8
Large scale Path Loss
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:
EE 424 Dr. Abdel Fattah Sheta KSU 9
Large scale Path Loss
Brewster Angle
The angle at which no reflection occurs in the medium of origin.It occurs only for parallel polarization.
EE 424 Dr. Abdel Fattah Sheta KSU 10
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 11
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 12
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 13
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 14
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 15
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 16
Large scale Path Loss
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.
EE 424 Dr. Abdel Fattah Sheta KSU 17
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 18
Large scale Path Loss
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()||||
Knife-edge Diffraction Model
Graphical representation of Gd(dB) as a function of
Knife-edge Diffraction Model
EE 424 Dr. Abdel Fattah Sheta KSU 19
Large scale Path Loss
Approximate solution by Lee
Example 3.7
EE 424 Dr. Abdel Fattah Sheta KSU 20
Large scale Path Loss
Example 3.8
EE 424 Dr. Abdel Fattah Sheta KSU 21
Large scale Path Loss
Multiple Kinfe-Edge Diffraction
EE 424 Dr. Abdel Fattah Sheta KSU 22
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 23
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 24
Large scale Path Loss
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
EE 424 Dr. Abdel Fattah Sheta KSU 25
Large scale Path Loss
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
Log Distance Path Loss Model
EE 424 Dr. Abdel Fattah Sheta KSU 26
Large scale Path Loss
Log Distance Path Loss Model
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).
EE 424 Dr. Abdel Fattah Sheta KSU 27
Large scale Path Loss
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.
EE 424 Dr. Abdel Fattah Sheta KSU 28
Large scale Path Loss