IEEE Geoscience and Remote Sensing Magazine - December 2014 - 28

lag, and that, unfortunately, is smaller where the waveform
is larger, where it is carrying the information. Fig. 20c shows
the variation of N i /N i, eff vs. the lag position for this data set.

Waveform Std. (a.u.)

2

0
0

40

80 120 160 200 240 280
Correlation Lags (1 Lag = 12.5 ns)

320

SNR (lin)

(a)

12
10
8
6
4
2
0
100
80

60
N 40
i

300
250
200
150
5 ns)
2
100
=1 .
g
a
L
50
s (1
n Lag
relatio

20
0

0
Cor

(b)
7
6

Ni /Ni,eff

5
4
3
2
1
0

50
100
150
200
250
Correlation Lags (1 Lag = 12.5 ns)

300

(c)
FIgUrE 20. (a) Standard deviation of each waveform lag as a
function of the number of incoherent averages, (b) evolution of the
SNR with the number of incoherent averages as a function of the
correlation lag, and (c) ratio of the number of incoherent averages
and the "effective number" of incoherent averages [132].

28

x cor = 2m$ v

h
,
2 $ c $ x c $ sin ^c h

(27)

and the coherent integration time (Ti), which determines
roughly the number of consecutive correlated waveforms. In
this experiment m = 0, 19 m, v = 237 km/h, h = 3.000 m,
x c = 97, 7 ns (P-chips), c+70c-77c, and Ti = 1 ms, so
x cor = 10, 6 ms, and x cor /Ti = 10, 6.
Fortunately, for a spaceborne instrument t cor = 1-2 ms,
and N i /N i, eff is much closer to 1, so noise reduction by incoherent averaging becomes more effective.

1

0

This value is actually related to the ratio of the correlation
time of the sea surface xcor:

VII. APPLICATIONS AND TECHNIQUES
This section compiles a set of remote sensing applications
of the GNSS-R technique, some of their retrieval algorithms and performance. Most of these applications have
been developed in the last ten years, the ocean altimetric
(sea-surface height) and the scatterometric (sea winds and
surface roughness) being the first suggested and attempted, more than 15 years ago ([6] and [10], respectively).
One can find accounts of various GNSS-R applications in
[50], [75], [133], [134].
The section is first organized in five sub-sections,
each one devoted to a particular scientific application.
For GNSS-R altimetry and ocean scatterometry, several
GNSS-R techniques are explained and their performances
discussed. Only the basic measurement principles are given for the rest of applications.
Table 3 compiles a summary of the remote sensing applications, and the scenarios from which it is possible to
obtain their products. The applications are not fully proven, or those with immature algorithms will not be further
detailed, but bibliographical references are provided.
A. Altimetry
The first application foreseen for GNSS-R was ocean altimetry, that is, determination of the sea-surface height. However, the altimetric measurement principles are quite general and also valid for altimetry over any other surface that
can reflect enough power to enable precise observables. For
GNSS-R, this is typically ocean and ice.
The product of interest in altimetric applications is the
vertical height of the reflecting surface, either in absolute
terms (e.g., with respect to the center of the Earth) or in
relative terms (e.g., with respect to a given reference surface
such as the ellipsoid, geoid, or a well-established spatiotemporal average of the elevation surface). Given that a
GNSS-R observation is representative of a certain area over
the surface (see Section IV), the GNSS-R measured surface
height will be an averaged value across this area.
The way to estimate the vertical component of the surface
location is done by measuring it with respect to the receiving
system, the position of which must be properly known. The
strong point of GNSS-R altimetry is its multi-static capability
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Table of Contents for the Digital Edition of IEEE Geoscience and Remote Sensing Magazine - December 2014
