Types of Small-Scale Fading

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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.

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

 

[+] Enlarge Image

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 T_s is the reciprocal bandwidth (e.g., symbol period) and B_s 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).

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.

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