where (.) is the gamma function, and m
l
is the Nakagami-m fading parameter which ranges from 1/2
to
. In this case the SNR per symbol,
l
, of the lth channel is distributed according to a gamma
distribution given by
p
l
(
l
;
l
, m
l
) =
m
m
l
l
m
l
-1
l
m
l
l
(m
l
)
exp
-
m
l
l
l
;
l
0.
(7.23)
The Nakagami-m distribution spans via the m parameter the widest range of fading among all the
multipath distributions we consider. For instance, it includes the one-sided Gaussian distribution (m
l
=
1/2) and the Rayleigh distribution (m
l
= 1) as special cases. In the limit as m
l
- +, the Nakagami-m
fading channel converges to a nonfading AWGN channel.
Log-normal Shadowing
In log-normal shadowing the lth path SNR per
symbol
l
has a PDF given by the standard log-normal expression
p
l
(
l
; µ
l
,
l
) =
10
ln 10
2
l
l
exp
-
(10 log
10
l
- µ
l
)
2
2
2
l
,
(7.24)
where µ
l
(dB) and
l
(dB) are the mean and the standard deviation of 10 log
10
l
, respectively. Next we
consider composite multipath/shadowing channels.
Composite Multipath/Shadowing
A composite multipath/shadowed fading environment consists
of multipath fading superimposed on log-normal shadowing. In this environment the receiver does not
average out the envelope fading due to multipath but rather reacts to the instantaneous composite
multipath/shadowed signal [8, Sect. 2.4.2]. This is typically the scenario in congested downtown areas
with slow moving pedestrians and vehicles [9, 10, 11]. This type of composite fading is also observed in
land-mobile satellite systems subject to vegetative and/or urban shadowing [12, 13, 14, 15, 16]. There
are two approaches and various combinations suggested in the literature for obtaining the composite
distribution. Here, as an example, we present the composite gamma/log-normal PDF introduced by Ho
and St¨
uber [11]. This PDF arises in Nakagami-m shadowed environments and is obtained by averaging
the gamma distributed signal power (or equivalently the SNR per symbol) (7.23) over the conditional
density of the log-normally distributed mean signal power (or equivalently the average SNR per symbol)
(7.24), giving the following PDF for the lth channel:
p
l
(
l
; µ
l
, m
l
,
l
) =
0
m
m
l
l
m
l
-1
l
w
m
l
(m
l
)
exp
-
m
l
l
w
10
ln 10
2
l
w
exp
-
(10 log
10
w
- µ
l
)
2
2
2
l
dw.
(7.25)
For the special case where the multipath is Rayleigh distributed (m
l
= 1), (7.25) reduces to a composite
exponential/log-normal PDF which was initially proposed by Hansen and Meno [10].
Combined (Time-Shared) Shadowed/Unshadowed
From their land-mobile satellite channel char-
acterization experiments, Lutz et al. [15] and Barts and Stutzman [17] found that the overall fading process
for land-mobile satellite systems is a convex combination of unshadowed multipath fading and a compos-
ite multipath/shadowed fading. Here, as an example, we present in more detail the Lutz et al. model [15].
When no shadowing is present, the fading follows a Rice (Nakagami-n) PDF. On the other hand when
shadowing is present, it is assumed that no direct LOS path exists and the received signal power (or
equivalently SNR per bit) is assumed to follow an exponential/log-normal (Hansen-Meno) PDF [10]. The
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