Page 166 - Fundamentals of Radar Signal Processing

The range-averaged reflectivity of Eq. (2.118) and the angle-averaged

reflectivity of Eq. (2.122) are examples of projections. In each case,
the three-dimensional reflectivity is reduced in dimension by integrating over
one or more dimensions. The range-averaged reflectivity was reduced to a two-
dimensional function by integrating over range, while the angle-averaged
reflectivity was reduced to a one-dimensional function by integrating over both
angle coordinates.

The idea of projections, particularly the angle-averaged projection
, will be important in deriving the polar format spotlight SAR
algorithm in Chap. 8. The projections that will be needed are integrals over
straight lines or planar surfaces. The averaging in Eq. (2.122) is over the
surface of a sphere. However, for small beamwidths only a region of θ radians
3
in azimuth and ϕ radians in elevation contributes significantly to the integral,
3
and at long ranges this limited region is nearly planar.

2.7.6 Multipath
The convolutional model of the measured range profile is based on the
assumption of superposition of backscattered fields and a one-to-one mapping
of echo arrival time to range, t → R = ct/2. The superposition of electric fields
is a valid assumption, but the mapping of time to range may not be. To illustrate,
consider Fig. 2.29, which diagrams two phenomena that violate this assumption.

Figure 2.29a illustrates the problem of multipath, in which echoes from the
same target arrive at the radar receiver via two different paths. The first is the
direct path of total length 2R . The second is the “multipath” or “ground bounce”
0
path with length R + R + R > 2R . Though not shown, it is also possible for a
2
0
1
0
portion of the transmitted wave to arrive at the target via the ground bounce and
be scattered back along both paths, meaning that there may also be an echo with
a time delay corresponding to a two-way path length of 2(R + R + R ).
0
1
2
Consequently, one scatterer may produce echoes at three different apparent
ranges if multipath is present. Whether these appear as distinct echoes depends
on the relationship between the path length difference and the pulse length. The
ground bounce echoes are often, but not always, significantly attenuated with
respect to the direct path echo. The degree of attenuation depends on the bistatic
scattering characteristics of the surface, the antenna pattern characteristics

(because the multipath bounce is not on the peak of the mainlobe) and the
problem geometry. As the range between target and radar varies, the path length
difference also varies, so that the direct and multipath bounces may alternately
add in and out of phase, provided the path length difference is such that the two
received echoes overlap. Multipath is generally most significant for targets
located at low altitude over a good reflecting surface such as a relatively
smooth terrain or calm ocean and at long range, so that the grazing angles

involved are small.