Page 28 - Integrated Wireless Propagation Models

6 C h a p t e r O n e

2. Based on the bandwidth of the signal:
The fading of the received mobile signal can be reduced dependent on the
basis of the bandwidth of the signal. The COMA signal has less fading than
the narrow-band signal.
3. Based on the mobile speed and the impulse response rate:
Fast fading and slow fading.
4. Based on the mobile speed only:
Flat fading and time-selective fading caused by Doppler spread.

Before we describe the different types of fading, the attributes of the fading signal
should be discussed first.

1.6.3 Attributes of Signal Fading

1.6.3. 1 Local Mean
1
The signal strength r(t) or r(x), shown in Fig. . 6.3.1, is the actual received signal level in
1
dB. Based on what we know about the cause of signal fading/· 7 the received r(t) can be
artificially separated into two parts by its cause, long-term fading m(t) and short-term
fading r0(t) when measured in time as
r(t) = m(t) · r0(t) (1.6.3.1)
or when measured in distance as
r(x) = m(x) · r0(x) (1.6.3.2)
where m(t) or m(x) is the long-term fading.
We know the long-term fading is the average of the fading signal as the dotted curve
shown in Fig. . 6.3. . It is also called a local mean since, along the long-term fading, each
1
1
value corresponds to the mean average of the field strength at each local point. The esti­
mated local mean m (x1) at point x1 along x-axis can be expressed mathematically as
1
x,+L
x,+L
1
,
m(x1) = I r(x) dx = I m(x)r0(x) dx (1.6.3.3)
2L 2L
x1-L x1-L
Assume that m(x1) is the true local mean; then, if we choose the length properly at
point x1 in Fig. . 6.3.1, the estimated local and the true local mean should be equal:
1
1
( . 6.3.4)
Therefore, let m (x1) approach m(x1) in Eq. (1.6.3.3); then, the following relation must
hold:
1 x,+L
1
2L I r0(x) dx --7 1 ( . 6.3.5)
x1-L
The length L has been determined after fully understanding the statistical charac­
teristics of short-term fading r0(x). Lee was the first one to study the length of V8 in 1974
based on the signal received at 800 MHz. From the comparison of the standard devia­
tion a of sample mean m (x) with different length L, the length 2L = 40 "A is desirable
because the standard deviation a reduced to 1 dB at L = 40 "A. If the length 2L is shorter
than 40 "A, the average output would retain some portion of Rayleigh fading. The length