**4.1 Description of observables, theoretical basis and retrieval technique**

For remote sensing purposes, the reflected and direct GNSS signals coming from the same satellite are collected on bistatic radar geometry; at least two antennas are required: the first RHCP (Right Hand Circularly Polarized) and zenith looking in charge of receiving the direct signal, the second LHCP (Left Hand Circularly Polarized) and nadir looking used to track the reflections.

In order to be more precise, the overall system could be considered as a multistatic observing system, since up to 6/7 GNSS transmitters are contemporary visible by the receiver antenna.

Each reflection is geo-referenced knowing the geometry of acquisition, looking at the point where the GNSS signal is reflected under specular condition; for doing this, the observer coordinates are necessary. Therefore the direct signal is used not only as a reference but also for computing the position of the receiver.

Three acquisition scenarios are possible:


meteorological events happened during the observing period. Anyway, an increase of wet refractivity (water vapour concentration) can be evidenced between the 100th (4 am, 16th October) and the 120th (midnight, 16th October) hours, with a peak around the 110th hour (2 pm, 16th October). The increase is well reproduced in terms of integrated wet refractivity along zenith (see ZWD evolution in Fig. 8(top)). Moreover, meteorological data (not shown

Other than for atmosphere monitoring, GNSS signals may be used to characterize the Earth surface. In this section this kind of remote sensing technique is described, considering two

The exploitation of GNSS signals reflected off the oceans allows to obtain altimetry measurements (sea surface heights), surface roughness from which wind intensity and direction is determined, sea-ice topography and its stratification. Additionally, land observations are used to determine the soil moisture content and to monitor the surface

The most of performed experiments are based on code measurements, since signal phase coherence after reflections is not many times maintained, because smooth surfaces are rarely

For remote sensing purposes, the reflected and direct GNSS signals coming from the same satellite are collected on bistatic radar geometry; at least two antennas are required: the first RHCP (Right Hand Circularly Polarized) and zenith looking in charge of receiving the direct signal, the second LHCP (Left Hand Circularly Polarized) and nadir looking used to track

In order to be more precise, the overall system could be considered as a multistatic observing system, since up to 6/7 GNSS transmitters are contemporary visible by the

Each reflection is geo-referenced knowing the geometry of acquisition, looking at the point where the GNSS signal is reflected under specular condition; for doing this, the observer coordinates are necessary. Therefore the direct signal is used not only as a reference but also

• Ground based: in this static configuration, the receiver is placed over mountains, towers and bridges and the collected measurements are used for testing the instrument functionalities and for monitoring small areas (i.e. coastal altimetry, local soil moisture

• On aircraft: the sensor is placed on aircrafts or rarely on balloons to demonstrate its performances and to monitor small regions with higher spatial resolution than spacebased measurements. This dynamic configuration requires an evaluation of the Doppler shift due to the non-zero velocity of the aircraft; furthermore, this Doppler

**4.1 Description of observables, theoretical basis and retrieval technique** 

here) confirmed an increase of cloud covering during that time interval.

**4. GNSS reflectometry** 

snow cover.

found in reality.

the reflections.

receiver antenna.

scenarios of observation: ocean and land.

for computing the position of the receiver. Three acquisition scenarios are possible:

content determination);

shift improves the resolution on the surface by means of iso-Doppler lines computation.

• Space based: the sensor is placed on board a LEO satellite (400-800 km) with the aim of monitoring the entire Earth surface assuring a global coverage of the acquired reflections, which may be detected also very far from coastal zones (i.e. in the middle of the ocean); the Doppler shift experienced by the signal is the largest achievable among the three described scenarios.

The shape and extension of the footprint of the reflections depends on: the surface roughness, the sensor height above the Earth surface, the elevation of the reflected ray, the direction of the incidence plane respect to the receiver velocity.

The footprint must be considered lying on a plane tangent to the Earth surface in the specular reflection point. The distance of the specular reflection point from the receiver nadir increases when the elevation of the GNSS satellite decreases.

Inside the area interested by the reflection, the smallest resolution achievable from a geometrical point of view is determined by the cells generated by the intersections of the iso-delay and iso-Doppler lines.

Iso-delay lines are determined considering the points on the surface by which the reflected signal arrives at the receiver with the same delay. Generally speaking, these points are ellipses and are determined considering a single chip of the GNSS code as relative delay associated to each ellipse respect to the adjacent one (Martin-Neira, 1993).

Iso-Doppler lines are determined considering the hyperbolas on the surface where reflected signals come to the receiver with the same Doppler shift. The zero Doppler line is computed as the line passing through the receiver and orthogonal to its velocity direction (Martin-Neira, 1993).

Clearly, we cannot forget the antenna footprint, which acts as a filter in delay and Doppler on the surface looks. When the surface is smooth, the total power received is almost coming from the first Fresnel zone defined around the specular scattering point (Beckmann & Spizzichino, 1987). In this case, the computation of the cross-correlation between the reflected signal and the local GPS code replica gives a waveform simply delayed respect to the cross-correlation of the direct signal, but with the same triangle shape and a noise floor around.

When the surface is rough non-coherent reflections are expected and the use of the Fresnel zone to model the received power is ineffective. In this case, the glistening zone represents the source of scattered power (Beckmann & Spizzichino, 1987).

N scattering elements contained in the glistening zone are considered in determining the cross-correlation function

$$R\_p(\Delta t\_m) = \sum\_{n=1}^{\infty} A\_n \cdot e^{i(\phi\_n - \phi\_n)} A(\Delta t\_m - \Delta t\_n) \tag{13}$$

where *Λ* is the triangle cross-correlation function and the m index indicates the quantities referred to the modelled signal generated with the local GPS code replica. Through this formulation Rp becomes a summation of triangle functions weighted with the amplitude of the nth element scattered field and delayed accordingly to the phase shift associated to each nth scattering element. The final correlation function shape in this case is shown in Fig. 9.

GNSS Signals: A Powerful Source for Atmosphere and Earth's Surface Monitoring 191

Winds retrieval and altimetry are the more consolidated applications, while soil moisture

Many instruments were developed up to now (Nogues-Correig et al.,2007) and the techniques of retrieval have been tested through many experimental activities. The early experiments deal basically with altimetry; measurements were collected either from a static position (Martin-Neira et al, 2001), from balloon (Cardellach et al., 2003) or from aircraft (Lowe et al, 2002). Other set of experiments were developed to retrieve the ocean surface state (Garrison et al., 2000), such as wind or sea roughness. Last but not least, the technique

From our point of view, during the SMAT-F1 project we developed a prototype based on a Software Defined Radio solution, using a navigation software receiver (Tsui, 2005). This is the NGene SW receiver, developed by NAVSAS group of Politecnico di Torino (Fantino et al., 2009). The instrument is highly reconfigurable, since collects raw I and Q IF samples of the incoming signals (direct and reflected). A sampling frequency of 8.1838 MHz is used,

Moreover, the small hardware architecture is made up of cheap COTS (Commercial Of The Shelf) components, with very low overall weight and power consumptions. These features make the system suitable to be easily placed on board aircrafts, also small U.A.V.s

Using the described receiving system, we carried out two experiments. The first data collection has been made on a static position looking at the sea surface from a high cliff. The second was performed placing the receiver on an aircraft and acquiring GNSS signals

The first data collection was carried out on December 2010, from Sardinia Eastern coast at 157 m above the sea surface, near Cala Gonone. This region is characterized by high cliffs

**RX** 

**H= 157** 

Fig. 10. The Sardinia Eastern Coast near Cala Gonone (©Google Maps)

was demonstrated on board a small satellite, the UK-DMC (Gleason et al., 2005).

Nevertheless, nowadays no operative missions exist in this field.

**4.2 State of the art** 

**4.3 Results** 

reflected from rice fields.

like those shown in Fig. 10.

**4.3.1 Sea surface data collection** 

and ice monitoring are under-development.

giving about 8 samples per C/A code chip.

(Unmanned Aerial Vehicle) (Cucca et al., 2010).

Fig. 9. Shape of the correlation function for non-coherent reflections (black); each triangle refers to the signals received by an isorange, 8 samples equal to 1 C/A chip

The basic observables are the delay of the reflected signal respect to the direct one, and the received power after reflection. Both observables are retrieved looking at the correlation function of the reflected signal and eventually comparing or normalizing it with the correspondent correlation of the direct signal.

The delay is used to determine the surface height, so is considered in case of GNSS signals reflected off water surfaces (Martin-Neira et al., 2001; Hajj & Zuffada, 2003). The height of the surface respect to the observer is retrieved in eq. 14 through the relative delay Δτ, the speed of light *c* and the elevation angle of the reflection γ.

$$\csc \Delta \mathbf{t} = \mathbf{2} \mathbf{h} \sin \chi \tag{14}$$

On the other hand, the reflected power is used to determine the surface reflectivity and the scattering cross section (Masters et al., 2004).

The surface reflectivity belongs to the coherent part of the scattered power that is measurable from the specular part of the received echo; it is used to determine the reflection coefficient that is related to the incident angle and dielectric constant. The dielectric constant is related to the soil composition and to its moisture content following empirical models or carefully calibrating the data (Masters et al., 2004).

The surface can be characterized looking at its roughness from the scattering cross section, since it contains the non-specular part of the reflected power. In this case we consider reflected power part calculated from the amplitude and the gradient of the correlation function on the right side of its maximum.

In order to retrieve surface winds over the sea, the shape of the non-specular echo is compared with a simulated one obtained using a sea surface model (Zavorotny & Voronovich, 2000; Elfouhaily et al., 2002).
