Theory of GNSS Reflectometry - GNSS Remote Sensing: Theory, Methods and Applications - page 182

zone is then defined as the area from where well-oriented facets might exist above
a probability threshold. The glistening zone corresponds to the deterioration of the
specular image described above. Note that (1) points on the surface away from the
nominal specular require higher slopes of the facet to forward the signal towards the
receiver; and (2) the rougher the surface the higher the probability of largely tilted
facets, meaning higher probability of well-oriented facets at coordinates far away
from the nominal specular point. Therefore, the rougher the surface the largest the
resulting glistening zone.
The wave-optics picture of the diffuse scattering results of the coherent sum of
the spherical waves re-emitted by every point on the surface. We define then a re-
radiation pattern or simply scattering beam, as the curve that relates each direction
with the power forwarded towards it by the rough surface (panel d in Fig. 8.7 ).
Note that the field received after diffuse scattering can be seen as the coherent
sum of many individual radio-link contributions, each introducing a phase-offset.
Because in diffuse scattering the roughness scales are comparable or higher than the
electromagnetic wavelength, the phase-offsets of each contribution, i , can be any
number within a cycle ΠWC /:
X

k i

E i exp f ! 0 t r i C i g (8.2)

i

As it will be shown in Sect. 8.7 , moving receivers (air-borne and space-based) or
dynamic surfaces (e.g. sea), make the individual contribution in Eq. 8.2 change,
producing random-like time series of the total received phase (fading/speckle).
Signal coherence thus requires strong specular components, or both platforms and
surface static conditions.
As explained in Chap. 1, the detection of GNSS signals is done at the receiver
by cross-correlating them against replicas or models. The result of this correlation
will be called waveform hereafter. These replicas include modulations to identify
the transmitters, working as nearly orthogonal codes: either the Binary Offset
Carrier (BOC) modulation, or the Binary Phase Shift Keying (BPSK) in the Pseudo-
Random Noise (PRN). Each code or part of a code is assigned to a different GNSS
transmitter, so that a sufficiently long cross-correlation process yields power above
the noise level if both signal and replica contain the same code modulation, or
it yields just noise if they are not coincident. The shape of the matching cross-
correlation response (waveform) is determined by the code itself. GPS C/A and P
codes are series of phase-shifts, they can be seen as a train of rectangular chips. Its
autocorrelation forms a triangle centered at the reception delay, and length ˙ chip
(being chip the length of the modulation chip). The new BOC modulations in GPS
L5 and GALILEO are more complex, and they result in narrower waveforms, but
with secondary peaks (see Chap. 1). Then, a purely specular reflection of GNSS
signals produces a waveform shaped like the autocorrelation of its modulation code.
That is, it produces the same waveform as the direct signal, but at a longer delay,
corresponding to a reception at the specular image. For GPS C/A and P codes, it is
the triangle function in amplitude, and squared triangle in power units. The delay