Theory of GNSS Reflectometry - GNSS Remote Sensing: Theory, Methods and Applications - page 183

of the peak of such function corresponds to the time traveled by the specular ray
path: time distance between the transmitter and the specular image (equivalent to
the transmitter-specular point-receiver link).
When the reflection is not purely specular the waveform has contributions from
the rest of the glistening zone. The scattered signal then spreads in both delay and
frequency Doppler, as explained below.

8.4 Delay and Doppler

Under diffuse scattering the waveform has contributions from a broad area, the
glistening zone. The radio-links between the transmitter, off-specular surface points,
and the receiver, are longer than the path traveled through the specular point. The
delay relative to the specular radio-link can be defined: .x; y/ D .x;y/ spec ,
being .x;y/ the traveling time along the radio-link that reaches the receiver after
reflecting at surface coordinates (x,y), and spec after reflecting at the specular point
(x D y D 0 in our convention). Then, the locus of surface points .x; y/ such that all
have the same relative delay, now expressed in units of length D c describe
an ellipse on the XY-plane, under flat surface approximation:

y 2
a 2

x 2
b 2

1 D C (8.3)

where the scattering plane has been assumed along the Y-Z plane; the center of
coordinates is the specular point; and

p 2H
.sin e/ 3=2

a D (8.4)

p 2H
.sin e/ 1=2

b D (8.5)

being e the elevation angle of observation (complementary to incidence angle ),
and H the receiver's altitude (Fig. 8.8 ).
Any contribution from areas away from the specular add power at the trailing
edge of the waveform, that is, power accumulates at delays greater than the specular.
The waveform thus distorts, its power scatters, the peak gets rounder and shifts
towards positive delays. The distortion with respect to the code-autocorrelation
function gives information about the roughness of the surface and its geophysical
source (for example, wind blowing on the sea surface). Figure 8.9 shows the
difference between waveforms obtained under specular and diffuse scattering
conditions, because of the delay spreading.