Handbook of Propagation Effects for Vehicular and ... - Courses

Theoretical Modeling Considerations 11-5
the estimation of fade distributions. The physics associated with the empirical models
exist to the extent that the models are based on the categorized measureables, such as
frequency, elevation angles, heading, and percentage of shadowing due to trees.
The common disadvantage associated with these models is that difficulties may
exist in extrapolating these models to cases not considered; such as other "road-types' or
frequencies outside the interval of scaling.
11.3.1 Large-scale - Small-scale (LS-SS) Coverage Model
The first propagation experiments targeted towards land mobile satellite communications
were conducted by observing 860 MHz and 1550 MHz transmissions emanating from
NASA's ATS-6 spacecraft [Hess, 1980]. Using the database from measurements taken
over about 1200 km in or near nine cities of the Western and Midwestern United States,
an empirical model was derived relating the probabilities of exceeding fades for largescale
(LS) and small-scale (SS) "coverages." Coverage in broadcasting is defined either
in terms of percentage of locations within an area or percentage of time at a particular
location that there exists satisfactory service. For LMSS scenarios, signal level variations
as a function of time are produced by vehicular motion. The model under discussion
(denoted by LS-SS) describes statistics from measured data for small and large spatial
scales. Small-scale coverage (as defined by Hess) represents a driving interval of 100 m.
For a vehicle speed of 25 m/s ( ≈ 55 mph), this converts to a time interval of 4 seconds or
the time interval of a short conversational sentence. For each 100 m interval, Hess
derived a cumulative fade distribution given by
P Si ( A,
Aq
) = PSi[
A < Aq
] , (11-7)
where the right hand side of (11-7) is read as "the probability that the attenuation A is
smaller than a designated attenuation level Aq, for the i th small-scale distribution." The
"large-scale" distribution function PL may be derived as follows. We first construct a
large family of small-scale distributions of the type depicted by (11-7) on a graph. We
next intersect each of these distributions by a fixed percentage (e.g., PS = 90%) and arrive
at a family of fade levels Aq from which a new cumulative fade distribution may be
derived. We call this new cumulative distribution the "large-scale" case and represent it
by
P L ( A)
= PL
[ A < Aq
PS
] . (11-8)
The right hand side may be read as "the probability that the attenuation A exceeds a
designated threshold level Aq, given the condition that the small-scale probability PS
assumes a particular value (PS = 90% for the given example). The physical significance
that may be attributed to (11-8) is that it predicts the probability that the fade will be less
than a particular fade level over many kilometers of driving, assuming a given PS which
denotes likelihood of successful reception over a 100 m driving distance.
Families of distributions of the type given by (11-7) and (11-8) were derived from
data collected for different vehicle environments and path geometries. A normal