Page 35 - Integrated Wireless Propagation Models

I n t r o d u c t i o n t o M o d e l i n g M o b i l e S i g n a l s i n W i r e l e s s C o m m u n i c a t i o n s 13

and
(1.6.5.2)
For a conservative guideline, we may set T5 < 0.1 11, to be the condition of having a
frequency-selective fading. In some types of modulation, T 5 of the signal can be larger
than 0.1 11, before causing the frequency-selective fading.

1.6.6 Fading Signal Caused by Doppler Spread
Based on Doppler spread, fading can be divided into two categories: fast fading and
slow fading. Fast fading and slow fading are classified based on how rapidly the trans­
mitted baseband signal changes compared to the rate of the channel impulse response
changes. If the former is at a rate much slower than the latter, the channel may be
assumed to be a fast-fading channel. Otherwise, it is assumed to be a slow-fading
channel. Therefore, the velocity of the mobile unit causes a baseband signal through the
channel at the terminal faded. The velocity determines whether a signal undergoes fast
fading or slow fading.

1.6.6. 1 Fast Fading
When the coherence time (Tc) of the channel is smaller than the symbol interval (T5) of
the transmitted signal, a fast fading channel is formed. In a fast-fading channel, the
frequency is dispersed due to Doppler spreading. Therefore, the fast-fading channel is
also called the time-selective fading channel. A transmitted signal suffers fast fading
if
(1.6.6.1.1)
and

(1.6.6.1.2)
where R5 is the data rate of the signal. When Eq. (1.6.6.1.2) is met, the random FM noise
2
occurs, and the signal is distorted. 3 As we can see from Eq. (1.6.6.1.2), it is rare to use a
very low data rate that is less than the Doppler frequency. Therefore, the fast-fading
case is not of interest here.

1.6.6.2 Slow Fading
In a slow-fading channel, the coherence time is much longer than the symbol interval of
the signal s(t), and the data rate of the signal is much faster than the Doppler spread
frequency, as shown below. Therefore, the condition of slow fading is
(1.6.6.2.1)
and
(1.6.6.2.2)
1
In this case, no random FM noise can distort the signal/ and the channel is consid­
ered static over the time of transmission. The velocity of the mobile unit, the carrier
frequency, and the signal symbol rates are the three factors that determine whether a
signal suffers fast fading. In general, we are always dealing with the slow-fading case.
Therefore, in general, flat fading and frequency-selective fading are the slow fading
also in the category of the short-term fading signal. The short-term fading signal is not
used to predict the propagation path loss models, as will be mentioned in the next section.