2. Contents
• Multipath characterstics of radio waves
• Fading
• LCR fading statistics
• Doppler spread
• Diversity techniques
3. Radio Propagation
• What is Radio?
• Radio Xmitter induces E&M fields
– Electrostatic field components ∝ 1/d3
– Induction field components ∝ 1/d2
– Radiation field components ∝ 1/d
• Radiation field has E and B component
– Field strength at distance d = E×B ∝ 1/d2
– Surface area of sphere centered at transmitter
4. General Intuition
• Two main factors affecting signal at receiver
– Distance (or delay) ⇒ Path attenuation
– Multipath ⇒ Phase differences
Green signal travels 1/2λ farther than
Yellow to reach receiver, who sees blue.
For 2.4 GHz, λ (wavelength) =12.5cm.
5. Objective
• Invent models to predict what the field
looks like at the receiver.
– Attenuation, absorption, reflection, diffraction...
– Motion of receiver and environment…
– Natural and man-made radio interference...
– What does the field look like at the receiver?
6. Models are Specialized
• Different scales
– Large scale (averaged over meters)
– Small scale (order of wavelength)
• Different environmental characteristics
– Outdoor, indoor, land, sea, space, etc.
• Different application areas
– macrocell (2km), microcell(500m), picocell
8. Fading
• Fading refers to the distortion that a carrier-
modulated telecommunication signal
experiences over certain propagation media.
• A fading channel is a communication
channel that experiences fading. In wireless
systems, fading is due to multipath
propagation and is sometimes referred to as
multipath induced fading.
9. • In wireless communications, the presence of reflectors in the environment
surrounding a transmitter and receiver create multiple paths that a
transmitted signal can traverse. As a result, the receiver sees the
superposition of multiple copies of the transmitted signal, each traversing a
different path.
• Each signal copy will experienced differences in attenuation, delay and
phase shift while travelling from the source to the receiver. This can result
in either constructive or destructive interference, amplifying or
attenuating the signal power seen at the receiver.
• Strong destructive interference is frequently referred to as a deep fade and
may result in temporary failure of communication due to a severe drop in
the channel signal-to-noise ratio
10. • Fading channel models are often used to model the
effects of electromagnetic transmission of
information over the air in cellular networks and
broadcast communication.
• Fading channel models are also used in underwater
acoustic communications to model the distortion
caused by the water.
• Mathematically, fading is usually modeled as a time-
varying random change in the amplitude and phase of
the transmitted signal.
11. Types of Fading
• Slow Fading
• Fast Fading
• The terms slow and fast fading refer to the rate at
which the magnitude and phase change imposed by
the channel on the signal changes.
• The coherence time is a measure of the minimum
time required for the magnitude change of the
channel to become decorrelated from its previous
value.
12. Slow fading
• Slow fading arises when the coherence time of the channel is
large relative to the delay constraint of the channel. In this
regime, the amplitude and phase change imposed by the
channel can be considered roughly constant over the period of
use.
• Slow fading can be caused by events such as shadowing,
where a large obstruction such as a hill or large building
obscures the main signal path between the transmitter and the
receiver.
• The amplitude change caused by shadowing is often modeled
using a log-normal distribution with a standard deviation
according to the Log Distance Path Loss Model
13. Fast Fading
• Fast Fading occurs when the coherence time
of the channel is small relative to the delay
constraint of the channel.
• In this regime, the amplitude and phase change
imposed by the channel varies considerably
over the period of use.
14. • In a fast-fading channel, the transmitter may take advantage of
the variations in the channel conditions using time diversity to
help increase robustness of the communication to a temporary
deep fade.
• Although a deep fade may temporarily erase some of the
information transmitted, use of an error-correcting code
coupled with successfully transmitted bits during other time
instances can allow for the erased bits to be recovered.
• In a slow-fading channel, it is not possible to use time
diversity because the transmitter sees only a single realization
of the channel within its delay constraint.
• A deep fade therefore lasts the entire duration of transmission
and cannot be mitigated using coding.
15. Flat vs. Frequency-selective
Fading
• In flat fading, the coherence bandwidth of the
channel is larger than the bandwidth of the signal.
Therefore, all frequency components of the signal
will experience the same magnitude of fading.
• In frequency-selective fading, the coherence
bandwidth of the channel is smaller than the
bandwidth of the signal. Different frequency
components of the signal therefore experience
decorrelated fading.
16. • In a frequency-selective fading channel, since
different frequency components of the signal are
affected independently, it is highly unlikely that all
parts of the signal will be simultaneously affected by
a deep fade.
• Certain modulation schemes such as OFDM and
CDMA are well-suited to employing frequency
diversity to provide robustness to fading.
• Frequency-selective fading channels are also
dispersive, in that the signal energy associated with
each symbol is spread out in time.
17. Mitigation
• Fundamentally, fading causes poor performance in
traditional communication systems because the
quality of the communications link depends on a
single path or channel, and due to fading there is a
significant probability that the channel will
experience a deep fade.
• The probability of experiencing a fade (and
associated bit errors as the signal-to-noise ratio drops)
on the channel becomes the limiting factor in the
link's performance.
18. • The effects of fading can be combated by using
diversity to transmit the signal over multiple channels
that experience independent fading and coherently
combining them at the receiver.
• The probability of experiencing a fade in this
composite channel is then proportional to the
probability that all the component channels
simultaneously experience a fade, a much more
unlikely event.
19. How to overcome fading?
• Common techniques used to overcome signal
fading include:
• Diversity reception and transmission
• OFDM
• Rake receivers
• Space–time codes
• MIMO
21. • In telecommunications, a diversity scheme refers to a method for
improving the reliability of a message signal by utilizing two or more
communication channels with different characteristics.
• Diversity plays an important role in combating fading and co-channel
interference and avoiding error bursts.
• It is based on the fact that individual channels experience different levels
of fading and interference.
• Multiple versions of the same signal may be transmitted and/or received
and combined in the receiver. Alternatively, a redundant forward error
correction code may be added and different parts of the message
transmitted over different channels.
• Diversity techniques may exploit the multipath propagation, resulting in a
diversity gain, often measured in decibels.
22. Classes of Diversity Schemes
• Time diversity: Multiple versions of the same signal are
transmitted at different time instants. Alternatively, a
redundant forward error correction code is added and the
message is spread in time by means of bit-interleaving before
it is transmitted. Thus, error bursts are avoided, which
simplifies the error correction.
• Frequency diversity: The signal is transferred using several
frequency channels or spread over a wide spectrum that is
affected by frequency-selective fading. Examples are:
– OFDM modulation in combination with subcarrier interleaving and
forward error correction
– Spread spectrum, for example frequency hopping or DS-CDMA.
23. • Space diversity: The signal is transferred over several different
propagation paths. In the case of wired transmission, this can be achieved
by transmitting via multiple wires. In the case of wireless transmission, it
can be achieved by antenna diversity using multiple transmitter antennas
(transmit diversity) and/or multiple receiving antennas (diversity
reception). In the latter case, a diversity combining technique is applied
before further signal processing takes place. If the antennas are at far
distance, for example at different cellular base station sites or WLAN
access points, this is called macrodiversity). If the antennas are at a
distance in the order of one wavelength, this is called microdiversity. A
special case is phased antenna arrays, which also can be utilized for
beamforming, MIMO channels and Space–time coding (STC).
• Polarisation diversity: Multiple versions of a signal are transmitted and
received via antennas with different polarization. A diversity combining
technique is applied on the receiver side.
24. • Multiuser diversity: Multiuser diversity is obtained by
opportunistic user scheduling at either the transmitter or the
receiver. Opportunistic user scheduling is as follows that the
transmit selects the best user among candidate receivers
according to qualities of each channel between the transmit
and each receiver. In FDD systems, a receiver must feed back
the channel quality information to the transmitter with the
limited level of resolution.
• Antenna diversity: transmitted along different propagation
paths.
• Cooperative diversity: enables to achieve the Antenna
diversity gain by the use of the cooperation of distributed
antennas belonging to each node.
25. LCR fading Statistics:
• Rayleigh fading is a statistical model for the effect of a propagation
environment on a radio signal, such as that used by wireless devices.
• It assumes that the magnitude of a signal that has passed through such a
transmission medium (also called a communications channel) will vary
randomly, or fade, according to a Rayleigh distribution — the radial
component of the sum of two uncorrelated Gaussian random variables.
• It is a reasonable model for tropospheric and ionospheric signal
propagation as well as the effect of heavily built-up urban environments on
radio signals.
• Rayleigh fading is most applicable when there is no dominant propagation
along a line of sight between the transmitter and receiver.
• If there is a dominant line of sight, Rician fading may be more applicable.
26. The model
• Rayleigh fading is a reasonable model when there are many objects in the
environment that scatter the radio signal before it arrives at the receiver.
The central limit theorem holds that, if there is sufficiently much scatter,
the channel impulse response will be well-modelled as a Gaussian process
irrespective of the distribution of the individual components.
• If there is no dominant component to the scatter, then such a process will
have zero mean and phase evenly distributed between 0 and 2π radians.
• The envelope of the channel response will therefore be Rayleigh
distributed. Calling this random variable R, it will have a probability
density function where Ω = E(R2).
• Often, the gain and phase elements of a channel's distortion are
conveniently represented as a complex number. In this case, Rayleigh
fading is exhibited by the assumption that the real and imaginary parts of
the response are modelled by independent and identically distributed zero-
mean Gaussian processes so that the amplitude of the response is the sum
of two such processes.
28. • One second of Rayleigh fading with a maximum Doppler shift
of 10Hz.
• The requirement that there be many scatterers present means
that Rayleigh fading can be a useful model in heavily built-up
city centres where there is no line of sight between the
transmitter and receiver and many buildings and other objects
attenuate, reflect, refract and diffract the signal.
• Rayleigh fading is a small-scale effect. There will be bulk
properties of the environment such as path loss and shadowing
upon which the fading is superimposed.
29. Doppler power spectral density
• The normalized Doppler power spectrum of Rayleigh fading with a
maximum Doppler shift of 10Hz.
• The Doppler power spectral density of a fading channel describes how
much spectral broadening it causes. This shows how a pure frequency e.g.
a pure sinusoid, which is an impulse in the frequency domain is spread out
across frequency when it passes through the channel. It is the Fourier
transform of the time-autocorrelation function. For Rayleigh fading with a
vertical receive antenna with equal sensitivity in all directions, this has
been shown to be where is the frequency shift relative to the carrier
frequency. This equation is only valid for values of between ; the spectrum
is zero outside this range.
• This spectrum is shown in the figure for a maximum Doppler shift of 10
Hz. The 'bowl shape' or 'bathtub shape' is the classic form of this doppler
spectrum.
30. Fading Models
• Nakagami fading
• Rayleigh fading
• Rician fading
• Dispersive fading models, with several echoes, each exposed
to different delay, gain and phase shift, often constant.This
results in frequency selective fading and inter-symbol
interference. The gains may be Rayleigh or Rician
distributed.The echoes may also be exposed to doppler-shift,
resulting in a time varying channel model.
• Log-normal shadow fading
