Transcript EEM619_lecture2x

WIRELESS COMMUNICATIONS
Assist.Prof.Dr. Nuray At
The Three Basic Propagation Mechanisms
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Diffraction
Occurs when the radio path between the T-R is obstructed by a surface that has
sharp irregularities (edges).
 Diffraction allows radio signals to propagate around the curved surface of the
earth, beyond the horizon, and to propagate behind obstructions.
 Diffraction field has often sufficient strength to produce a useful signal.
Fresnel Zone Geometry
Obstructing screen is placed between T-R at
a distance d1 from the transmitter and
d2 from the receiver
h: effective height
The Three Basic Propagation Mechanisms
Knife-edge diffraction geometry
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Equivalent knife-edge geometry
Assume that
and
The excess path length, the difference between the direct path and the diffracted
path:
The corresponding phase difference is
The Three Basic Propagation Mechanisms
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The Fresnel-Kirchoff diffraction parameter v is given by
𝜙 then can be expressed as
 Generally, it is impossible to make very precise estimates of the diffraction
losses.
 When shadowing is caused by a single object such as a hill or mountain, the
attenuation caused by diffraction can be estimated by treating the obstruction
as a diffracting knife edge.
The Three Basic Propagation Mechanisms
The electric field strength, Ed, of a knife edge diffracted wave
The diffraction gain:
An approximate solution provided by Lee is
Hwk: Plot both the diffraction gain and its approximate solution by Lee.
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The Three Basic Propagation Mechanisms
Knife-edge diffraction gain
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The Three Basic Propagation Mechanisms
Example: Given the following geometry, determine
a. The loss due to knife-edge diffraction
b. The height of the obstacle required to induce 6dB diffraction loss.
Assume f = 900 MHz.
Knife edge
T
100m
50m
R
25m
10km
2km
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The Three Basic Propagation Mechanisms
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Scattering
Occurs when the medium through which the wave travels consists of objects with
dimensions that are small compared to the wavelength, and where the number of
obstacles per unit volume is large.
 When a radio wave impinges on a rough surface, the reflected energy is spraed
out (diffused) in all directions due to scattering.
 Surface roughness is tested using the Rayleigh criterion, which defines a critical
height (hc) of surface protuberances for a given angle of incidence 𝜃𝑖
A surface is considered smooth if its minimum to maximum protuberance
h < hc, and is considered rough if the protuberance h > hc
The Three Basic Propagation Mechanisms
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For rough surfaces, the flat surface reflection coefficient needs to be multiplied by
a scattering loss factor, 𝜌𝑠 .
Ament found 𝜌𝑠 to be given by
where 𝜎ℎ is the standard deviation of the surface height about the mean surface
height.
 Modified scattering loss factor by Boithias:
Link Budget Design Using Path Loss Models
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Most radio propagation models are derived using a combination of analytical and
emprical methods.
Log-distance Path Loss Model
Both theoretical and measurement-based propagation models indicate that
average received signal power decreases logarithmically with distance, whether in
outdoor or indoor radio channels.
 The average large-scale path loss for an arbitrary T-R separation
or
where n is the path loss exponent, d0 is the close-in reference distance.
Link Budget Design Using Path Loss Models
 The value of a path loss exponent n depends on the specific propagation
environment . Typical path loss exponents
Environment
Path Loss Exponent, n
Free space
2
Urban area cellular radio
2.7 to 3.5
Shadowed urban cellular radio
3 to 5
In building line-of-sight
1.6 to 1.8
Obstructed in building
4 to 6
Obstructed in factories
2 to 3
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Link Budget Design Using Path Loss Models
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Log-normal Shadowing
The previous model (log-distance path loss model) does not consider the fact that
the surrounding environmental clutter may be vastly different at two different
locations having the same T-R separation.
 Measurements have shown that at any value of d, the path loss PL(d) at a
particular location is random and distributed log-normally (normal in dB)
about the mean distance-dependent value.
𝑋𝜎 is a zero-mean Gaussian distributed random variable (in dB) with standart
deviation 𝜎 (also in dB)
Link Budget Design Using Path Loss Models
Log-normal shadowing implies that measured signal levels at a specific T-R
separation have a Gaussian distribution about the distance dependent mean.
 In practice, the values of n and 𝜎 are computed from measured data.
Since PL(d) is a random variable with a normal distribution in dB about the
distance dependent mean, so is Pr(d)
 Thus, the probability that the received signal level (in dB power units) will
exceed a particular level 𝛾 can be given by
where the Q-function is defined as
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Link Budget Design Using Path Loss Models
Determination of Percentage of Coverage Area
 Due to random effects of shadowing, some locations within a coverage area
will be below a particular desired received signal threshold.
 For a circular coverage area having radius R from a base station, let there be
some desired received signal threshold 𝛾.
 Let U(𝛾) be the percentage of useful service area, the percentage of area with
a received signal that is equal or greater than 𝛾, given a known likelihood of
coverage at the cell boundary.
Letting d = r represent the radial distance from the transmitter. Then,
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Link Budget Design Using Path Loss Models
By choosing the signal level such that
where
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Link Budget Design Using Path Loss Models
Example: Four received power measurements were taken at distances of 100m,
200m, 1km, and 3km from a transmitter. Let d0 = 100m. Assuming the log-normal
shadowing path loss model,
a. Find the minimum mean square error (MMSE) estimate for the path loss
exponent, n.
b. Calculate the standard deviation about the mean value.
c. Estimate the received power at d = 2km using the resulting model.
Distance from Transmitter
Received Power
100m
0 dBm
200m
-20 dBm
1000m
-35 dBm
3000m
-70 dBm
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Small-Scale Multipath Propagation
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 In built-up urban areas, fading occurs because the height of the mobile
antennas are well below the height of surrounding structures.
 The incoming radio waves arrive from different directions with different
propagation delays.
 The signal received by the mobile at any point in space may consist of a large
number of plane waves having randomly distributed amplitudes, phases and
angles of arrival.
 These multipath components combine vectorially at the receiver antenna, and
can cause the signal received by the mobile to distort or fade.
 Even when a mobile receiver is stationary, the received signal may fade due to
movement of surrounding objects in the radio channel.
Small-Scale Multipath Propagation
The three most important small-scale fading effects:
 Rapid changes in signal strength over a small travel distance or time interval
 Random frequency modulation due to varying Doppler shifts on different
multipath signals
 Time dispersion (echoes) caused by multipath propagation delays.
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Small-Scale Multipath Propagation
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The Doppler Shift
 Due to the relative motion between the mobile and the base station, each
multipath wave experiences an apparent shift in frequency. The shift in
received signal frequency due to motion is called the Doppler shift.
Consider a mobile moving at a constant velocity v, along a path segment having
length d between points X and Y, while it receives signals from a remote source S.
The difference in path lengths
Small-Scale Multipath Propagation
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The phase change in the received signal due to the difference in path lengths
The apparent change in frequency, or Doppler shift fd:
 If the mobile is moving toward the direction of arrival of the wave, the Doppler
shift is positive (i.e., the apparent received frequency is increased)
 If the mobile is moving away from the direction of arrival of the wave, the
Doppler shift is negative (i.e., the apparent received frequency is decreased)