Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 283

1 and time-invariant parameters is
widely used in theoretical assessments of multipath performance due to its ease of
use. This time-invariant distortion produces a bias error in pseudorange. If the
multipath is specular, the MDR remains independent of range from receiver to
reflector, and hence independent of the multipath's excess delay. For a reflection to
be truly specular, the reflector must be very large, the reflecting surface must be
smooth (surface roughness less than a few centimeters for L-band signals), and have
consistent electrical properties. Observe that the one-path specular multipath model
provides the limiting case of zero Doppler spread (time-invariant impulse response)
and infinite delay spread.
On airplanes at altitude, multipath typically involves reflections from surfaces
such as the wings and tail, sometimes accompanied by creeping waves over the air-
craft skin. Aircraft multipath may be characterized as a discrete number of reflec-
tions all occurring with relative delays less than 20 ns and relative amplitudes less
than 0.3 for vehicles as large as a Boeing 747 [14]. The model (6.43) can be employed
for this situation; since the reflecting surfaces are close to the receive antenna and
share the same motion, the multipath parameters, including the phases ~

Despite its limited realism, (6.43) with N =

φ n ,may
remain constant over time periods exceeding the reciprocal of tracking loop
bandwidths, motivating use of time-invariant parameters over durations longer than
the reciprocal of the signal tracking loops. For this case, the delay spread is very short
(20 ns) and the Doppler spread is also small (perhaps thousandths of a hertz).
In terrestrial applications, there have been extensive efforts to measure, model,
and predict the diverse multipath environments that may be encountered. For some
applications, multipath can be characterized as a large number of reflections from
objects in the proximity of the user. A general model for this diffuse multipath is
presented in [15]. In this model, 500 small reflectors are randomly located within
100m of the user. Since the reflectors are small, each emanates a spherical wave, and
thus the received power from each reflector varies with the square of the distance
between the reflector and the user. Moreover, the large number of signal reflections,
spaced so closely in delay, make the multipath arrivals appear to result from passing
through a linear filter with continuous impulse response amplitude decreasing with
excess delay, rather than the discrete delays in (6.42) and (6.43). This diffuse scat-
terer model has been found to closely emulate measured multipath for an aviation
differential GPS reference station application with the receiver located in an open
environment. Here, the delay spread is hundreds of nanoseconds, and the Doppler
spread is tenths or hundredths of a hertz.
Among many attempts to measure and model real-world multipath environ-
ments, [16] stands out as offering a particularly comprehensive and useful represen-
tation of complex terrestrial multipath. As shown in Figure 6.9, the parametric
model is based on (6.42), with the arrivals grouped into three components: the
direct path, a discrete set of near echoes, and a discrete set of far echoes. Shadowing
of the direct path is represented by a Rice distribution of amplitude when LOS visi-
bility exists between the receiver and the transmitter, and a Rayleigh distribution
when LOS visibility does not exist. The mean received power of the near echoes falls
off exponentially with delay. The number of far echoes is typically much smaller
than the number of near echoes, and the mean value of the far echoes does not vary
over the range of delays. The numbers of near echoes and number of far echoes are