1. 5.5 Types of Small-Scale Fading
Section 5.3 demonstrated that the type of fading experienced by a signal propagating
through a mobile radio channel depends on the nature of the transmitted signal with
respect to the characteristics of the channel. Depending on the relation between the
signal parameters (such as bandwidth, symbol period, etc.) and the channel parameters
(such as rms delay spread and Doppler spread), different transmitted signals will undergo
different types of fading. The time dispersion and frequency dispersion mechanisms in a
mobile radio channel lead to four possible distinct effects, which are manifested depending
on the nature of the transmitted signal, the channel, and the velocity. While multipath
delay spread leads to time dispersion and frequency selective fading, Doppler spread
leads to frequency dispersion and time selective fading. The two propagation mechanisms
are independent of one another. Figure 5.11 shows a tree of the four different types of fading.
2. 5.5.1 Fading Effects Due to Multipath Time Delay Spread
Time dispersion due to multipath causes the transmitted signal to undergo either flat or frequency
selective fading.
5.5.1.1 Flat fading
If the mobile radio channel has a constant gain and linear phase response over a bandwidth
which is greater than the bandwidth of the transmitted signal, then the received signal will
undergo flat fading. This type of fading is historically the most common type of fading described
in the technical literature. In flat fading, the multipath structure of the channel is such that the
spectral characteristics of the transmitted signal are preserved at the receiver. However the
strength of the received signal changes with time, due to fluctuations in the gain of the channel
caused by multipath. The characteristics of a flat fading channel are illustrated in Figure 5.12.
It can be seen from Figure 5.12 that if the channel gain changes over time, a change of
amplitude occurs in the received signal. Over time, the received signal r(t) varies in gain, but
the spectrum of the transmission is preserved. In a flat fading channel, the reciprocal bandwidth
Figure 5.11 Types of small-scale fading.
of the transmitted signal is much larger than the multipath time delay spread of the
channel, and can be approximated as having no excess delay (i.e., a single delta
function with
Flat fading channels are also known as amplitude varying channels and are sometimes referred to as
narrowband channels, since the bandwidth of the applied signal is narrow as compared to the channel
flat fading bandwidth. Typical flat fading channels cause deep fades, and thus may require 20 or 30 dB
more transmitter power to achieve low bit error rates during times of deep fades as compared to
systems operating over non-fading channels. The distribution of the instantaneous gain of flat fading
channels is important for designing radio links, and the most common amplitude distribution is the
Rayleigh distribution. The Rayleigh flat fading channel model assumes that the channel induces an
amplitude which varies in time according to the Rayleigh distribution.
To summarize, a signal undergoes flat fading if
and
where Ts is the reciprocal bandwidth (e.g., symbol period) and Bs is the bandwidth, respectively,
of the transmitted modulation, and
are the rms delay spread and coherence bandwidth, respectively, of the channel.
Figure 5.12 Flat fading channel characteristics.
5.5.1.2 Frequency Selective Fading
If the channel possesses a constant-gain and linear phase response over a bandwidth that is
smaller than the bandwidth of transmitted signal, then the channel creates frequency selective
fading on the received signal. Under such conditions, the channel impulse response has a multipath
delay spread which is greater than the reciprocal bandwidth of the transmitted message
waveform. When this occurs, the received signal includes multiple versions of the transmitted
waveform which are attenuated (faded) and delayed in time, and hence the received signal is distorted.
Frequency selective fading is due to time dispersion of the transmitted symbols within the
channel. Thus the channel induces intersymbol interference (ISI). Viewed in the frequency
domain, certain frequency components in the received signal spectrum have greater gains than
others.
Frequency selective fading channels are much more difficult to model than flat fading
channels since each multipath signal must be modeled and the channel must be considered to be a
linear filter. It is for this reason that wideband multipath measurements are made, and models are
developed from these measurements. When analyzing mobile communication systems, statistical
impulse response models such as the two-ray Rayleigh fading model (which considers the
impulse response to be made up of two delta functions which independently fade and have sufficient
time delay between them to induce frequency selective fading upon the applied signal), or
computer generated or measured impulse responses, are generally used for analyzing frequency
selective small-scale fading. Figure 5.13 illustrates the characteristics of a frequency selective
fading channel.
For frequency selective fading, the spectrum S (f) of the transmitted signal has a bandwidth
which is greater than the coherence bandwidth B c of the channel. Viewed in the frequency
domain, the channel becomes frequency selective, where the gain is different for
different frequency components. Frequency selective fading is caused by multipath delays which
Figure 5.13 Frequency selective fading channel characteristics.
approach or exceed the symbol period of the transmitted symbol. Frequency selective fading
channels are also known as wideband channels since the bandwidth of the signal
s(t) is wider than the bandwidth of the channel impulse response. As time varies, the channel varies in
gain and phase across the spectrum of s(t), resulting in time varying distortion in the received signal
r(t). To summarize, a signal undergoes frequency selective fading if
and
A common rule of thumb is that a channel is flat fading if
and a channel is frequency selective if
although this is dependent on the specific type of modulation used. Chapter 6 presents simulation
results which illustrate the impact of time delay spread on bit error rate (BER).
3. 5.5.2 Fading Effects Due to Doppler Spread
5.5.2.1 Fast Fading
Depending on how rapidly the transmitted baseband signal changes as compared to the rate of
change of the channel, a channel may be classified either as a fast fading or slow fading channel.
In a fast fading channel, the channel impulse response changes rapidly within the symbol duration.
That is, the coherence time of the channel is smaller than the symbol period of the transmitted
signal. This causes frequency dispersion (also called time selective fading) due to Doppler
spreading, which leads to signal distortion. Viewed in the frequency domain, signal distortion
due to fast fading increases with increasing Doppler spread relative to the bandwidth of the
transmitted signal. Therefore, a signal undergoes fast fading if
and
It should be noted that when a channel is specified as a fast or slow fading channel, it does
not specify whether the channel is flat fading or frequency selective in nature. Fast fading only
deals with the rate of change of the channel due to motion. In the case of the flat fading channel,
we can approximate the impulse response to be simply a delta function (no time delay). Hence, a
flat fading, fast fading channel is a channel in which the amplitude of the delta function varies
faster than the rate of change of the transmitted baseband signal. In the case of a frequency selective,
fast fading channel, the amplitudes, phases, and time delays of any one of the multipath
components vary faster than the rate of change of the transmitted signal. In practice, fast fading
only occurs for very low data rates.
5.5.2.2 Slow Fading
In a slow fading channel, the channel impulse response changes at a rate much slower than the
transmitted baseband signal s(t). In this case, the channel may be assumed to be static over one
or several reciprocal bandwidth intervals. In the frequency domain, this implies that the Doppler
spread of the channel is much less than the bandwidth of the baseband signal. Therefore, a signal
undergoes slow fading if
and
It should be clear that the velocity of the mobile (or velocity of objects in the channel) and the
baseband signaling determines whether a signal undergoes fast fading or slow fading.
The relation between the various multipath parameters and the type of fading experienced
by the signal are summarized in Figure 5.14. Over the years, some authors have confused the
terms fast and slow fading with the terms large-scale and small-scale fading. It should be emphasized
that fast and slow fading deal with the relationship between the time rate of change in the
channel and the transmitted signal, and not with propagation path loss models.
Figure 5.14 Matrix illustrating type of fading experienced by a signal as a function of: (a) symbol
period; and (b) baseband signal bandwidth.
4. Relevant NI products
Customers interested in this topic were also interested in the following NI products:
- RF and Communication Hardware and Software
- Other Modular Instruments (digital multimeters, digitizers, switching, etc...)
- LabVIEW Graphical Programming Environment
For the complete list of tutorials, return to the NI RF and Communications Fundamentals Main page.
5. Buy the Book
Publication Information | |
---|---|
Author: Theodore S. Rappaport | Book: Wireless Communications: Principles and Practice (2nd Edition) |
Copyright: 2002 | ISBN: 0130422320 |
Purchase Wireless Communications: Principles and Practice (2nd Edition) from Prentice Hall
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Excerpt from the book published by Prentice Hall Professional (http://www.phptr.com). Copyright Prentice Hall Inc. 2006. All rights reserved.