
122
IEEE
TRANSACTIOKS
ON
VEHICULAR
TECHNOLOGY,
VOL. VT-34,
NO.
3,
AUGUST
1985
A
Statistical Model
for
a Land Mobile Satellite
Link
Abstract-A
statistical model for a land mobile satellite link is
described. The model assumes that the amplitude of the line-of-sight
component under foliage attenuation (shadowing) is lognormally distrib-
uted and the received multipatb interference has a Rayleigh distribution.
Expressions for the level crossing rate and average fade duration are
given. Comparison between results calculated from the model and from
measurements show reasonably good agreement. The model should be
useful for designing communications systems and for simulating propaga-
tion effects in the laboratory.
A
I.
INTRODUCTION
STATISTICAL model for received signal envelope
fading encountered on a land mobile satellite channel is
useful for predicting communications systems performance
with various modulation schemes. The model will also
facilitate the design of propagation simulator. There have been
many papers published on the modeling of mobile radio
channels in urban environments, a few of which are given in
[1]-[9].
The model which is of interest here is for a land
mobile satellite channel in a rural environment, where, for
most of the time, a line-of-sight signal component is available
at the receiver.
This paper describes a statistical model in terms of its
probability density function, level crossing rate (LCR) and
average fade duration (AFD). These characteristics were
obtained under the hypothesis that foliage not only attenuates
but also scatters radio waves at UHF and at L-band frequen-
cies. The model assumes that the line-of-sight component
under foliage attenuation (shadowing) is lognormally distrib-
uted and that the multipath effect is Rayleigh distributed.
Additionally, these two random processes are assumed to be
correlated. Although no attempt is made at physical justifica-
tion of the model, results derived from the model are
compared with those derived from measurements and are
found to be good engineering approximations.
The probability density function of the model facilitates the
calculation
of
fade margins in the designs of communication
systems. The results of LCR and AFD provide information
relevant to modem designs and error correction techniques.
Section
I1
of the paper describes the statistical model and
numerical results are given in Section 111. Conclusions are
presented in Section IV.
Manuscript received February
20,
1984, revised January 7, 1985.
The author is with the Department
of
Communications, Communications
Research Centre,
P.O.
Box
11490. Station
H,
Ottawa, Ontario, Canada
K2H
8S2. Telephone
(613)
998-2574.
LI.
STATISTICAL MODEL
The mathematical derivations required to describe the
model are given in this section.
A.
Probability Density
Function
Consider the sum of a lognormally distributed random
phasor and a Rayleigh phasor
[lo],
r
exp
(jO)=z
exp
WO)+
w
exp
(j4),
z,
w>O
(1)
where the phases
4o
and
4
are uniformly distributed between
0
and
2a,
z
is lognormally distributed, and
w
has a Rayleigh
distribution.
If
z
is temporarily kept constant, then the conditional
probability density function of
r
is simply that of a Rician
vector
[
101
:
where
bo
represents the average scattered power due to
multipath, and
Zo
(a)
is the modified Bessel function of zeroth
order. Applying the theorem of total probability, one obtains
From this,
p(r)
is given by
p(r)
=
r/bo
56
exp
[
-
(r2
+z2)/2bo]Zo(rz/b~)p(z) dz.
(4)
It has been assumed that
p(z)
is lognormal, given by
where &and
p
are the standard deviation and mean,
respectively.
Thus, substituting
(5)
into
(4),
one obtains
p(r)=r/(bo=)
jm
l/z
exp [-(ln
z
0
It has been shown
[lo]
that
r
is lognormal for large values
OO18-9545/85/0800-0122$01
.OO
0
1985
IEEE