2. Basic theory of GNSS-R

#### 2.1. Geometry

GNSS-R works as a bi-static radar in which the transmitter and the receiver are separated in the spatial distribution. It is noted that when GNSS-R receivers allow to track the scattered signal from different GNSS satellites, the system is called as multi-static radar as shown in Figure 1, in which for each GNSS satellite, bi-static observation occurs at different azimuth angle, and creates a glistening zone. To simplify observation geometry of GNSS-R, a bi-static geometry could be developed as Figure 2, in which (1) the coordinate origin is at Earth's core; (2) the YOZ plane is in the incident plane of GNSS signal; (3) Z axis has the same direction with the normal of the tangent plane of the specular point; and (4) it is assumed that Earth, the orbits of GNSS and Low Earth Orbit (LEO) satellite are circular. In Figure 2, hr and ht are the heights of LEO and GNSS satellite; Re is the Earth radius; θ is the incident angle of GNSS signal. In the coordinate system, the positioning of GNSS and LEO satellite are given as

$$\mathbf{T} = \begin{pmatrix} 0 \ D \sin \theta \ R\_{\epsilon} + D \cos \theta \end{pmatrix} \tag{1}$$

where D and d are the distance from GNSS and LEO satellite to the specular point, and are

q

q

where δ<sup>x</sup> and δ<sup>y</sup> are the included angles between the projection of the connection line of Sx, <sup>y</sup> and the coordinate origin at the XOZ and YOZ plane. From the above discussion, when the height of GNSS and LEO satellite, and the incident angle of GNSS signal are known, the

When Right-Hand Circular Polarization (RHCP) GNSS signal occurs reflection phenomenon, the polarization is changed. The Fresnel coefficients of RHCP and LHCP (Left-Hand Circular Polarization) are expressed as the combination of the vertical and horizontal polarization as

2

2

<sup>R</sup>RR <sup>¼</sup> <sup>R</sup>RR <sup>¼</sup> <sup>1</sup>

<sup>R</sup>RL <sup>¼</sup> <sup>R</sup>LR <sup>¼</sup> <sup>1</sup>

The Fresnel coefficients of vertical and horizontal polarization are computed as

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ ht <sup>þ</sup> Re <sup>2</sup> � <sup>R</sup><sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð Þ hr <sup>þ</sup> Re <sup>2</sup> � <sup>R</sup><sup>2</sup>

<sup>e</sup> sin<sup>2</sup>θ

GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149

<sup>e</sup> sin<sup>2</sup>θ

<sup>r</sup> <sup>¼</sup> <sup>δ</sup><sup>x</sup> <sup>δ</sup><sup>y</sup> <sup>1</sup> � � � Re (5)

ð Þ RVV þ RHH (6)

ð Þ RVV � RHH (7)

(3)

93

(4)

D ¼ �Recosθ þ

d ¼ �Recosθ þ

The coordinate of scattering unit r could be represented as

Figure 2. Scattering scenario and local coordinate system of GNSS-R.

geometry of GNSS-R could be determined.

2.2. Polarization of reflected GNSS signal

expressed as

$$\mathbf{R} = \begin{pmatrix} 0 & -d\sin\theta & R\_t + D\cos\theta \end{pmatrix} \tag{2}$$

Figure 1. Illustration of multi-static GNSS-R.

Figure 2. Scattering scenario and local coordinate system of GNSS-R.

geometry, the polarization, and the model of reflected GNSS signal. Section 3 will present some typical spaceborne GNSS-R receivers and processing methods of reflected GNSS signal. The explicit retrieval algorithms based on the regression will be developed in Section 4. Finally, the

GNSS-R works as a bi-static radar in which the transmitter and the receiver are separated in the spatial distribution. It is noted that when GNSS-R receivers allow to track the scattered signal from different GNSS satellites, the system is called as multi-static radar as shown in Figure 1, in which for each GNSS satellite, bi-static observation occurs at different azimuth angle, and creates a glistening zone. To simplify observation geometry of GNSS-R, a bi-static geometry could be developed as Figure 2, in which (1) the coordinate origin is at Earth's core; (2) the YOZ plane is in the incident plane of GNSS signal; (3) Z axis has the same direction with the normal of the tangent plane of the specular point; and (4) it is assumed that Earth, the orbits of GNSS and Low Earth Orbit (LEO) satellite are circular. In Figure 2, hr and ht are the heights of LEO and GNSS satellite; Re is the Earth radius; θ is the incident angle of GNSS signal. In the coordinate system, the positioning of GNSS and LEO satellite

T ¼ ð Þ 0 Dsinθ Re þ Dcosθ (1)

R ¼ ð Þ 0 �dsinθ Re þ Dcosθ (2)

conclusion of this chapter will be addressed in Section 5.

2. Basic theory of GNSS-R

92 Multifunctional Operation and Application of GPS

Figure 1. Illustration of multi-static GNSS-R.

2.1. Geometry

are given as

where D and d are the distance from GNSS and LEO satellite to the specular point, and are expressed as

$$D = -R\_\epsilon \cos \theta + \sqrt{\left(h\_t + R\_\epsilon\right)^2 - R\_\epsilon^2 \sin^2 \theta} \tag{3}$$

$$d = -R\_\epsilon \cos \theta + \sqrt{\left(h\_r + R\_\epsilon\right)^2 - R\_\epsilon^2 \sin^2 \theta} \tag{4}$$

The coordinate of scattering unit r could be represented as

$$\mathbf{p} = \begin{pmatrix} \delta\_x & \delta\_y & 1 \end{pmatrix} \cdot \mathbf{R}\_e \tag{5}$$

where δ<sup>x</sup> and δ<sup>y</sup> are the included angles between the projection of the connection line of Sx, <sup>y</sup> and the coordinate origin at the XOZ and YOZ plane. From the above discussion, when the height of GNSS and LEO satellite, and the incident angle of GNSS signal are known, the geometry of GNSS-R could be determined.

#### 2.2. Polarization of reflected GNSS signal

When Right-Hand Circular Polarization (RHCP) GNSS signal occurs reflection phenomenon, the polarization is changed. The Fresnel coefficients of RHCP and LHCP (Left-Hand Circular Polarization) are expressed as the combination of the vertical and horizontal polarization as

$$\mathfrak{R}\_{RR} = \mathfrak{R}\_{RR} = \frac{1}{2} (\mathfrak{R}\_{VV} + \mathfrak{R}\_{HH}) \tag{6}$$

$$\Re \mathcal{R}\_{RL} = \Re\_{LR} = \frac{1}{2} (\Re\_{VV} - \Re\_{HH}) \tag{7}$$

The Fresnel coefficients of vertical and horizontal polarization are computed as

$$\Re\_{VV} = \frac{\varepsilon \cos \theta - \sqrt{\varepsilon - \sin^2 \theta}}{\varepsilon \cos \theta + \sqrt{\varepsilon - \sin^2 \theta}} \tag{8}$$

gð Þ¼� R; t

R

GNSS and LEO satellite to scattering unit r; q is the scattering vector defined as

� �¼<sup>k</sup> <sup>d</sup>ð Þ <sup>r</sup>

q¼ q<sup>⊥</sup> q<sup>z</sup>

correlating with local replicas over a range of delay and Doppler as

ð<sup>t</sup>þTI t

j j <sup>Y</sup>ð Þ <sup>τ</sup>; <sup>f</sup> <sup>2</sup> D E <sup>¼</sup> <sup>1</sup>

RT<sup>2</sup> I ðð G<sup>2</sup>

Yð Þ¼ τ; f ; t

and speckle noise, the successive snapshots are averaged as

j j <sup>Y</sup>ð Þ <sup>τ</sup>; <sup>f</sup> <sup>2</sup> D E <sup>¼</sup> <sup>A</sup><sup>2</sup>

normalized bi-static cross section and it is as follows:

expression (14) as [19]

<sup>4</sup>πjDð Þ <sup>r</sup> <sup>d</sup>ð Þ <sup>r</sup> exp½ � jk Dð Þ ð Þþ <sup>r</sup> <sup>d</sup>ð Þ <sup>r</sup> <sup>q</sup><sup>2</sup>ð Þ <sup>r</sup>

where R is the Fresnel coefficient discussed in Section 2.2; Dð Þ r and dð Þ r are the distance from

where k is the wavenumber of GNSS signal; Dð Þ r and dð Þ r are the vectors from scattering unit r to GNSS and LEO satellite. The receiver processes reflected GNSS signal by cross-

where TI is the coherent integration time. The output of spaceborne GNSS-R receiver is the power level as a function of delay offset and Doppler shift. To reduce the influence of thermal

> Tincoh <sup>ð</sup>Tincoh 0

where Tincoh is the incohernt integration time. Zavorotny and Voronovivh first derived the

where τð Þ r and fð Þ r are the delay and Doppler frequency of scattering unit r; σ<sup>0</sup> is the

z q4 ⊥

where Ppdfð Þ� is the probability density function of mean square slopes of the sea surface, and could be usually assumed as a 2-D Gaussian distribution. Figure 4 shows the normalized DDM distribution for the wind speed of 5 m/s and 15 m/s, in which both DDMs show clear horseshoe shapes; moreover, with the increase in wind speed, DDM spreads to larger delay and Doppler. Different scattering units have different delay and Doppler frequency; hence, DDM not only represents the distribution in delay-Doppler domain, but also indicates the distribution in sea surface as illustrated in Figure 5. In practice, the one cell in delay-Doppler domain associates to two spatial solutions, i.e., the mapping between the space and the delay-Doppler domain exists with ambiguity. To reduce this mapping ambiguity, the one approach is to tilt the downward antenna beam away from the specular reflection point.

4πDð Þ r 2 dð Þ r

<sup>P</sup>pdf � <sup>q</sup><sup>⊥</sup> qz

ð Þ <sup>r</sup> <sup>Λ</sup><sup>2</sup>

<sup>σ</sup><sup>0</sup> <sup>¼</sup> <sup>π</sup>j j <sup>R</sup> <sup>2</sup> <sup>q</sup><sup>4</sup>

j j <sup>Y</sup>ð Þ <sup>τ</sup>; <sup>f</sup> ; <sup>t</sup> <sup>2</sup>

ð Þ� <sup>τ</sup> � <sup>τ</sup>ð Þ <sup>r</sup> sinc<sup>2</sup>ð Þ <sup>f</sup> � <sup>f</sup>ð Þ <sup>r</sup>

<sup>2</sup> <sup>σ</sup><sup>2</sup>

dð Þ r þ Dð Þ r Dð Þ r q2 <sup>⊥</sup>ð Þ r

GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149

� � (12)

urð Þ <sup>R</sup>; <sup>t</sup> p tð Þ � <sup>τ</sup> exp 2πj f <sup>0</sup> <sup>þ</sup> <sup>f</sup> � �<sup>t</sup> � �dt (13)

dt (14)

0d2

� � (16)

r (15)

(11)

95

$$\Re \Re\_{HH} = \frac{\cos \theta - \sqrt{\varepsilon - \sin^2 \theta}}{\cos \theta + \sqrt{\varepsilon - \sin^2 \theta}} \tag{9}$$

Figure 3 gives the simulated Fresnel coefficients of RHCP and LHCP for GPS L1 signal, when sea surface temperature is 25� and sea surface salinity is 35 psu. From the figure, it could be seen that as the incident angle increases, the Fresnel coefficients of RHCP and LHCP show decreasing and increasing trends, respectively. This illustrates that at nadir and small incident angle, the LHCP signal dominates GNSS signal reflected off the sea surface. Therefore, the combination of LHCP and RHCP antenna or only LHCP antenna is used to receive reflected GNSS signal from the sea surface.

#### 2.3. Model of reflected GNSS signal

The signal reflected from the sea surface is described as [21]

$$u\_r(\mathbf{R}, t) = A\_R \exp\left(-2\pi j f\_0 t\right) \iint G(\mathbf{p}) a\left(t - \frac{D + d}{c}\right) g(\mathbf{R}, t) d^2 \mathbf{p} \tag{10}$$

where f <sup>0</sup> is the carrier frequency; AR is the amplitude of reflected signal; G is the pattern of receiving antenna; a tð Þ is the baseband spreading signal; c is the speed of light; gð Þ R; t is the function as

Figure 3. Relationship between the amplitude of RHCP and LHCP Fresnel coefficient and incident angle.

GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149 95

$$\log(\mathbf{R}, t) = -\frac{\mathfrak{R}}{4\pi j D(\mathfrak{p} \mid d(\mathfrak{p} \mid))} \exp[jk(D(\mathfrak{p} \mid) + d(\mathfrak{p} \mid))] \frac{\mathbf{q}^2(\mathfrak{p} \mid)}{\mathbf{q}\_\perp^2(\mathfrak{p} \mid)} \tag{11}$$

where R is the Fresnel coefficient discussed in Section 2.2; Dð Þ r and dð Þ r are the distance from GNSS and LEO satellite to scattering unit r; q is the scattering vector defined as

<sup>R</sup>VV <sup>¼</sup> <sup>ε</sup>cos<sup>θ</sup> � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>R</sup>HH <sup>¼</sup> cos<sup>θ</sup> � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Figure 3 gives the simulated Fresnel coefficients of RHCP and LHCP for GPS L1 signal, when sea surface temperature is 25� and sea surface salinity is 35 psu. From the figure, it could be seen that as the incident angle increases, the Fresnel coefficients of RHCP and LHCP show decreasing and increasing trends, respectively. This illustrates that at nadir and small incident angle, the LHCP signal dominates GNSS signal reflected off the sea surface. Therefore, the combination of LHCP and RHCP antenna or only LHCP antenna is used to receive reflected

where f <sup>0</sup> is the carrier frequency; AR is the amplitude of reflected signal; G is the pattern of receiving antenna; a tð Þ is the baseband spreading signal; c is the speed of light; gð Þ R; t is the

Figure 3. Relationship between the amplitude of RHCP and LHCP Fresnel coefficient and incident angle.

GNSS signal from the sea surface.

94 Multifunctional Operation and Application of GPS

function as

2.3. Model of reflected GNSS signal

The signal reflected from the sea surface is described as [21]

urð Þ¼ <sup>R</sup>; <sup>t</sup> ARexp �2πjf <sup>0</sup><sup>t</sup> � � ðð

<sup>ε</sup>cos<sup>θ</sup> <sup>þ</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>ε</sup> � sin<sup>2</sup>

cos<sup>θ</sup> <sup>þ</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>ε</sup> � sin<sup>2</sup>

<sup>ε</sup> � sin<sup>2</sup> <sup>θ</sup> <sup>p</sup>

<sup>ε</sup> � sin<sup>2</sup> <sup>θ</sup> <sup>p</sup>

<sup>G</sup>ð Þ <sup>r</sup> a t � <sup>D</sup> <sup>þ</sup> <sup>d</sup>

c � �

<sup>g</sup>ð Þ <sup>R</sup>; <sup>t</sup> <sup>d</sup><sup>2</sup>

r (10)

<sup>θ</sup> <sup>p</sup> (8)

<sup>θ</sup> <sup>p</sup> (9)

$$\mathbf{q} = \begin{pmatrix} \mathbf{q}\_{\perp} & \boldsymbol{q}\_{z} \end{pmatrix} = k \begin{pmatrix} \mathbf{d}(\boldsymbol{\mathfrak{p}} \,) + \mathbf{D}(\boldsymbol{\mathfrak{p}} \,) \\ d(\boldsymbol{\mathfrak{p}} \,) + \frac{\mathbf{D}(\boldsymbol{\mathfrak{p}} \,)}{D(\boldsymbol{\mathfrak{p}} \,)} \end{pmatrix} \tag{12}$$

where k is the wavenumber of GNSS signal; Dð Þ r and dð Þ r are the vectors from scattering unit r to GNSS and LEO satellite. The receiver processes reflected GNSS signal by crosscorrelating with local replicas over a range of delay and Doppler as

$$Y(\tau, f, t) = \int\_{t}^{t + T\_l} u\_r(\mathbf{R}, t) p(t - \tau) \exp\left[2\pi j (f\_0 + f)t\right] dt\tag{13}$$

where TI is the coherent integration time. The output of spaceborne GNSS-R receiver is the power level as a function of delay offset and Doppler shift. To reduce the influence of thermal and speckle noise, the successive snapshots are averaged as

$$\left\langle \left| Y(\tau, f) \right|^2 \right\rangle = \frac{1}{\mathbf{T}\_{\rm inch}} \int\_0^{\mathbf{T}\_{\rm inch}} \left| Y(\tau, f, t) \right|^2 dt \tag{14}$$

where Tincoh is the incohernt integration time. Zavorotny and Voronovivh first derived the expression (14) as [19]

$$\left\langle \left| Y(\tau, f) \right|^2 \right\rangle = A\_R^2 T\_I^2 \left[ \left| \frac{G^2(\mathfrak{p} \mid \boldsymbol{\Lambda}^2(\mathfrak{r} - \tau(\mathfrak{p} \mid)) \cdot \mathrm{sinc}^2(f - f(\mathfrak{p} \mid))}{4\pi D(\mathfrak{p} \mid)^2 d(\mathfrak{p} \mid)^2} \sigma\_0^2 d^2 \mathfrak{p} \right. \tag{15} \right]$$

where τð Þ r and fð Þ r are the delay and Doppler frequency of scattering unit r; σ<sup>0</sup> is the normalized bi-static cross section and it is as follows:

$$
\sigma\_0 = \pi |\mathfrak{R}|^2 \frac{q\_z^4}{\mathbf{q}\_\perp^4} P\_{\mathrm{pdf}} \left( -\frac{\mathbf{q}\_\perp}{q\_z} \right) \tag{16}
$$

where Ppdfð Þ� is the probability density function of mean square slopes of the sea surface, and could be usually assumed as a 2-D Gaussian distribution. Figure 4 shows the normalized DDM distribution for the wind speed of 5 m/s and 15 m/s, in which both DDMs show clear horseshoe shapes; moreover, with the increase in wind speed, DDM spreads to larger delay and Doppler. Different scattering units have different delay and Doppler frequency; hence, DDM not only represents the distribution in delay-Doppler domain, but also indicates the distribution in sea surface as illustrated in Figure 5. In practice, the one cell in delay-Doppler domain associates to two spatial solutions, i.e., the mapping between the space and the delay-Doppler domain exists with ambiguity. To reduce this mapping ambiguity, the one approach is to tilt the downward antenna beam away from the specular reflection point.

processing reflected GNSS signal in real-time, but also with low-mass, -power and -cost. At present, some research groups have developed spaceborne GNSS receivers to meet their

GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149 97

To promote the development of spaceborne GNSS-R and explore its prospect of commercial application, Surrey Satellite Technology Ltd. (SSTL) designed and developed spaceborne GPS-R receiver which would be carried on UK-DMC. This receiver which was implemented based on spaceborne GPS receiver of SSTL consisted of a zenith antenna to receive direct GPS signal, a LCHP antenna with the gain of 11.8 dBi to downward point to receive reflected GPS signal, a real-time processor unit to perform delay-Doppler mapping of reflected GPS signal as well as log and download raw sampled IF data to the ground for more intensive postprocessing together with a solid state data recorder (SSDR) and high rate downlink (HRD) [14]. Moreover, the processor unit supported to track the direct signal provides the positioning, velocity and timing (PVT). When the receiver was configured as the collection mode, 20 s raw sampled data of the direct and reflected GPS signal could be

Following the success of the UK-DMC, SSTL embarked on the new generation spaceborne GNSS-R receiver Space Receiver Remote Sensing Instrument (SGR-ReSI) which had been equipped with UK-TechDemoSat-1 satellite launched in July, 2014 [25]. Compared to the receiver carried on UK-DMC, SGR-ReSI supported to process in real-time and save sampled IF data of multi-frequency GNSS signal. The core component of the receiver is a 24-channel navigation receiver of GPS L1 signal and reprogrammable to a co-processor unit based on Actel ProASIC3 FPGA. The reprogrammable capacity of SGR-ReSI also enables more scientific and remote sensing application. Two types of RF front-ends including Max2769 optimized for GPS L1 signal and Max2112 which is reconfigured to other GNSS bands have been adopted in the receiver. In operation, the receiver could be configured as fixed gain mode (FGM) and unmonitored automatic gain control (uAGC). To allow the storage of both sampled and processed data, a bank of DDR2 memory with a capacity of 1 GB was used. From September 2014 on, the GNSS-R basic observable DDM data formatted as TIFF were downloaded from

The main objectives of GEROS mission are to measure the sea surface height and mean square slope, and the secondary ones are to further explore the potential of monitoring vertical profiles of atmospheric using GNSS-RO and to assess the feasibility of GNSS-R for land application [17]. The receiving antenna has 4π steradian field of view capability to receive GNSS signal arriving from any direction and is distinguished into four distinct parts (FoV-1, FoV-2, FoV-3, FoV-4), in which FoV-1 is for altimetry and scatterometry, FoV-2 is for altimetry,

spaceborne missions.

3.1. Existing receivers

saved in SSDR to download to the ground.

UK-TechDemoSat-1 to the ground.

3.1.1. UK-DMC

3.1.2. SGR-ReSI

3.1.3. GEROS

Figure 4. Normalized DDM for the wind speed of (a) 5 m/s and (b) 15 m/s, when the height of LEO satellite is 657 km and the incident angle of GNSS signal is 60.

Figure 5. Mapping from space to the delay-Doppler domain.

The other approach is using two separate antennas from two different viewing angles to observe an ocean surface region.

#### 3. Processing of GNSS reflected signal

The GNSS-R receiver is a processing unit to cross-correlate reflected GNSS signal with locally generated replicas. Spaceborne GNSS-R receiver not only requires the capacity of processing reflected GNSS signal in real-time, but also with low-mass, -power and -cost. At present, some research groups have developed spaceborne GNSS receivers to meet their spaceborne missions.

#### 3.1. Existing receivers

## 3.1.1. UK-DMC

To promote the development of spaceborne GNSS-R and explore its prospect of commercial application, Surrey Satellite Technology Ltd. (SSTL) designed and developed spaceborne GPS-R receiver which would be carried on UK-DMC. This receiver which was implemented based on spaceborne GPS receiver of SSTL consisted of a zenith antenna to receive direct GPS signal, a LCHP antenna with the gain of 11.8 dBi to downward point to receive reflected GPS signal, a real-time processor unit to perform delay-Doppler mapping of reflected GPS signal as well as log and download raw sampled IF data to the ground for more intensive postprocessing together with a solid state data recorder (SSDR) and high rate downlink (HRD) [14]. Moreover, the processor unit supported to track the direct signal provides the positioning, velocity and timing (PVT). When the receiver was configured as the collection mode, 20 s raw sampled data of the direct and reflected GPS signal could be saved in SSDR to download to the ground.

#### 3.1.2. SGR-ReSI

Following the success of the UK-DMC, SSTL embarked on the new generation spaceborne GNSS-R receiver Space Receiver Remote Sensing Instrument (SGR-ReSI) which had been equipped with UK-TechDemoSat-1 satellite launched in July, 2014 [25]. Compared to the receiver carried on UK-DMC, SGR-ReSI supported to process in real-time and save sampled IF data of multi-frequency GNSS signal. The core component of the receiver is a 24-channel navigation receiver of GPS L1 signal and reprogrammable to a co-processor unit based on Actel ProASIC3 FPGA. The reprogrammable capacity of SGR-ReSI also enables more scientific and remote sensing application. Two types of RF front-ends including Max2769 optimized for GPS L1 signal and Max2112 which is reconfigured to other GNSS bands have been adopted in the receiver. In operation, the receiver could be configured as fixed gain mode (FGM) and unmonitored automatic gain control (uAGC). To allow the storage of both sampled and processed data, a bank of DDR2 memory with a capacity of 1 GB was used. From September 2014 on, the GNSS-R basic observable DDM data formatted as TIFF were downloaded from UK-TechDemoSat-1 to the ground.

#### 3.1.3. GEROS

The other approach is using two separate antennas from two different viewing angles to observe

Figure 4. Normalized DDM for the wind speed of (a) 5 m/s and (b) 15 m/s, when the height of LEO satellite is 657 km and

The GNSS-R receiver is a processing unit to cross-correlate reflected GNSS signal with locally generated replicas. Spaceborne GNSS-R receiver not only requires the capacity of

an ocean surface region.

the incident angle of GNSS signal is 60.

96 Multifunctional Operation and Application of GPS

3. Processing of GNSS reflected signal

Figure 5. Mapping from space to the delay-Doppler domain.

The main objectives of GEROS mission are to measure the sea surface height and mean square slope, and the secondary ones are to further explore the potential of monitoring vertical profiles of atmospheric using GNSS-RO and to assess the feasibility of GNSS-R for land application [17]. The receiving antenna has 4π steradian field of view capability to receive GNSS signal arriving from any direction and is distinguished into four distinct parts (FoV-1, FoV-2, FoV-3, FoV-4), in which FoV-1 is for altimetry and scatterometry, FoV-2 is for altimetry, and FoV-3 is for atmosphere/ionosphere sounding. The bandwidth of the GEROS payload is 47 MHz at L1 and 64 MHz at L2 frequency band so that GEROS can perform GNSS-R and GNSS-RO using the signal from different GNSS systems, such as GPS, Galileo, GLONASS, and BeiDou. GEROS can in parallel track three direct and corresponding reflected signals in both RHCP and LHCP at L1 band, only LHCP at L5 band using three antenna beams. The fourth dual-frequency beam could be used to perform either GNSS-R or GNSS-RO. The main Level 1 data of the first three beams are 1 Hz DDM for which the delay and Doppler domain is 1500 m 8 KHz and the delay resolution could be configured as 3.75 m and 11.25 m. The fourth beam outputs different Level 1 data depending on the application. GEROS payload has a total mass of 376 kg, a power of 395 W, a 2 GB memory, a 1.2 Mbps output data rate, and the overall dimension of 1.55 m 1.17 m 0.86 m.

3.2. General architecture of receiver

Figure 6. Architecture of Spaceborne GNSS-R receiver.

According to the description on the spaceborne GNSS-R receivers above, the general architecture of the receiver could be given as Figure 6, which consists of the antennas, the RF front-end, the processor of baseband signal, the computer on-board, and some external components. The antennas include zenith- and nadir-pointing antennas to receive direct and reflected GNSS signal. Usually, the zenith-pointing antenna is an omnidirectional RHCP GNSS antenna, and nadir-pointing antenna is a narrow-beam and high-gain LHCP antenna. However, it is able to be design the different combination of the zenith- and nadirpointing antennas to perform special spaceborne mission and application. For example, the zenith- and nadir-pointing antennas of PARIS are both the narrow-beam and high-gain antennas to make the incoming signal from the single satellite be received; to significantly measure the soil moisture of the land, the nadir-pointing antenna of GEROS is the combination of the LHCP and RHCP antenna. RF front-ends convert the analog RF signal to the sampled IF one, consisting of Low Noise Amplifier (LNA), bandpass filter, mixer, gain control, and A/D converter. According to the requirement of the mission, the gain control could have different configuration. For altimetry, the Automatic Gain Control (AGC) mode is utilized to dynamically adjust the power level of incoming signal to the most effective input range of A/D converter; however, the scatterometry of GNSS-R generally selects the fixed gain or monitoring AGC to correctly receiving gain to obtain accuracy power level of reflected signal. To improve the generality of the receiver, the gain control could be designed as reconfigurable mode, such as SGR-ReSI of which the gain control supports the fixed gain and unmonitoring AGC mode. The core of the receiver is a baseband processor which consists of controller and processor unit. The controller unit controls the acquirement

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#### 3.1.4. PAU/GNSS-R

Passive Advanced Unit (PAU) is a new instrument concept which aims to monitor ocean parameters. It consists of the PAU/RAD which is an L-band radiometer to measure the brightness temperature of the sea surface, the RAU/GNSS-R which is a reflectometer to measure the roughness of the sea surface and the PAU/IR which is two infrared radiometers used to observe the temperature of the sea surface. PAU/GNSS-R was designed based on FPGA to synchronously process the reflected GPS signal from different satellites in real-time and output corresponding to 2-D DDM [35]. To reduce the hardware resources of the payload, hardware reuse technique was adopted based on two RAM-like registers that change their respective input and output connections to allow the DDM generator to be implemented at a higher clock rate. A software running on MicroBlaze soft processor mainly performs functions including sending and receiving data from the GPS receiver, selecting the available satellites, and computing the DDM parameters transferred to the DDM generator. The computed DDM are transferred to a terminal computer using an USB and an external master based on FPGA.

#### 3.1.5. PYCARO

According to the research and demonstration mission planned by the Remote Sensing Lab and the NanoSat Lab at the Universitat Politècnica de Catalunya-Barcelona Tech, PYCARO will be carried on a 3 2 unit Cube satellite to perform the observation of Earth surface and atmosphere. Compared to the receivers above, the difference of PYCARO is a P(Y) and C/A ReflectOmeter, which adds the processing of encrypted L1 and L2 P(Y) signals by using semicodeless technique [36, 37]. The zenith antenna of PYCARO is a single microstrip patch, and the nadir-looking antenna is a 3 2 array of microstrip patches with 13 dB gain. A dual-channel Software Defined Radio (SDR) is used to sample and collect the signals from the up- and down-looking antennas, and a Gumstix Overo IronStorm OBC manages the payload, configures the SDR, and computes the DDM. PYCARO supports two reconfigurable operation modes including the nadir-pointing mode to perform the Earth surface observation of GNSS-R and the limb-pointing to implement the atmosphere observation GNSS-RO.

#### 3.2. General architecture of receiver

and FoV-3 is for atmosphere/ionosphere sounding. The bandwidth of the GEROS payload is 47 MHz at L1 and 64 MHz at L2 frequency band so that GEROS can perform GNSS-R and GNSS-RO using the signal from different GNSS systems, such as GPS, Galileo, GLONASS, and BeiDou. GEROS can in parallel track three direct and corresponding reflected signals in both RHCP and LHCP at L1 band, only LHCP at L5 band using three antenna beams. The fourth dual-frequency beam could be used to perform either GNSS-R or GNSS-RO. The main Level 1 data of the first three beams are 1 Hz DDM for which the delay and Doppler domain is 1500 m 8 KHz and the delay resolution could be configured as 3.75 m and 11.25 m. The fourth beam outputs different Level 1 data depending on the application. GEROS payload has a total mass of 376 kg, a power of 395 W, a 2 GB memory, a 1.2 Mbps output data rate, and the overall

Passive Advanced Unit (PAU) is a new instrument concept which aims to monitor ocean parameters. It consists of the PAU/RAD which is an L-band radiometer to measure the brightness temperature of the sea surface, the RAU/GNSS-R which is a reflectometer to measure the roughness of the sea surface and the PAU/IR which is two infrared radiometers used to observe the temperature of the sea surface. PAU/GNSS-R was designed based on FPGA to synchronously process the reflected GPS signal from different satellites in real-time and output corresponding to 2-D DDM [35]. To reduce the hardware resources of the payload, hardware reuse technique was adopted based on two RAM-like registers that change their respective input and output connections to allow the DDM generator to be implemented at a higher clock rate. A software running on MicroBlaze soft processor mainly performs functions including sending and receiving data from the GPS receiver, selecting the available satellites, and computing the DDM parameters transferred to the DDM generator. The computed DDM are transferred to a terminal computer using an USB and an external

According to the research and demonstration mission planned by the Remote Sensing Lab and the NanoSat Lab at the Universitat Politècnica de Catalunya-Barcelona Tech, PYCARO will be carried on a 3 2 unit Cube satellite to perform the observation of Earth surface and atmosphere. Compared to the receivers above, the difference of PYCARO is a P(Y) and C/A ReflectOmeter, which adds the processing of encrypted L1 and L2 P(Y) signals by using semicodeless technique [36, 37]. The zenith antenna of PYCARO is a single microstrip patch, and the nadir-looking antenna is a 3 2 array of microstrip patches with 13 dB gain. A dual-channel Software Defined Radio (SDR) is used to sample and collect the signals from the up- and down-looking antennas, and a Gumstix Overo IronStorm OBC manages the payload, configures the SDR, and computes the DDM. PYCARO supports two reconfigurable operation modes including the nadir-pointing mode to perform the Earth surface observation of GNSS-R and the limb-pointing to implement the atmosphere obser-

dimension of 1.55 m 1.17 m 0.86 m.

98 Multifunctional Operation and Application of GPS

3.1.4. PAU/GNSS-R

master based on FPGA.

3.1.5. PYCARO

vation GNSS-RO.

According to the description on the spaceborne GNSS-R receivers above, the general architecture of the receiver could be given as Figure 6, which consists of the antennas, the RF front-end, the processor of baseband signal, the computer on-board, and some external components. The antennas include zenith- and nadir-pointing antennas to receive direct and reflected GNSS signal. Usually, the zenith-pointing antenna is an omnidirectional RHCP GNSS antenna, and nadir-pointing antenna is a narrow-beam and high-gain LHCP antenna. However, it is able to be design the different combination of the zenith- and nadirpointing antennas to perform special spaceborne mission and application. For example, the zenith- and nadir-pointing antennas of PARIS are both the narrow-beam and high-gain antennas to make the incoming signal from the single satellite be received; to significantly measure the soil moisture of the land, the nadir-pointing antenna of GEROS is the combination of the LHCP and RHCP antenna. RF front-ends convert the analog RF signal to the sampled IF one, consisting of Low Noise Amplifier (LNA), bandpass filter, mixer, gain control, and A/D converter. According to the requirement of the mission, the gain control could have different configuration. For altimetry, the Automatic Gain Control (AGC) mode is utilized to dynamically adjust the power level of incoming signal to the most effective input range of A/D converter; however, the scatterometry of GNSS-R generally selects the fixed gain or monitoring AGC to correctly receiving gain to obtain accuracy power level of reflected signal. To improve the generality of the receiver, the gain control could be designed as reconfigurable mode, such as SGR-ReSI of which the gain control supports the fixed gain and unmonitoring AGC mode. The core of the receiver is a baseband processor which consists of controller and processor unit. The controller unit controls the acquirement

Figure 6. Architecture of Spaceborne GNSS-R receiver.

and tracking of direct signal, estimates the difference of delay and Doppler frequency between direct and reflected signal, and configures the DDM parameters, such as delay and Doppler frequency window range and resolution and others. The estimations of the differences of delay and Doppler frequency between direct and reflected signal are given as

$$
\Delta \tau = \frac{|\mathbf{T} - \mathbf{S}| + |\mathbf{R} - \mathbf{S}| - |\mathbf{T} - \mathbf{R}|}{c} \tag{17}
$$

reference for the assessments of parallel method. The assessment metric is defined as normalized

� � �

�

<sup>2</sup> � � � �

YS τi; f <sup>j</sup> � � � �

<sup>2</sup> �� � �

� YP τi; f <sup>j</sup> � � � �

> � � �

� � � �

<sup>2</sup> � � are the mean correlation power computed by serial

� � �

� �<sup>t</sup>

n o � � � � f g FFTf g p tð Þ <sup>∗</sup> n o (21)

n o (20)

� � � � 2

<sup>2</sup> (19)

GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149

; N<sup>τ</sup>

101

�

urð Þt p tð Þ � τ exp �2πj f <sup>0</sup> þ f <sup>j</sup>

YS τi; f <sup>j</sup> � � � �

j¼1

� �

and parallel method when the delay and Doppler frequency of local replica are τ<sup>i</sup> and f <sup>j</sup>

where NS is the sampling number in a GNSS-code period. The block diagram of the serial processing is shown in Figure 7, in which the channel is N<sup>τ</sup> � Nf . Each channel requires multiplier 3NS and adder 2NS. The total numbers of the multipler and the adder are 3NSNτNf

Parallel correlation in delay domain parallelly performs correlation operation for all code delay

where FFTf g<sup>∙</sup> and IFFTf g<sup>∙</sup> respresent the FFT and IFFT operator; and f g<sup>∙</sup> <sup>∗</sup> is the conjugate operator. Figure 8 is the block diagram of the parallel correlation in delay domain. The number of the processing channel is Nf . As it is known, FFT operation with NS sampled ponits requires multipler and adder 2NSlog2NS and 3NSlog2NS. From Figure 8, it is seen that each channel performs 2 FFT and 1 IFFT with NS sampled ponits. The total numbers of the required

Parallel correlation in Doppler domain performs spectrum estimation for the signal removed

<sup>2</sup> � �

�

P N<sup>τ</sup> i¼1 P Nf

> � � �

mean squared error (MSE) between serial and parallel correlation as

j¼1

� �

� � � �

NS X NS

i¼1

� � <sup>¼</sup> IFFT FFT urð Þ<sup>t</sup> exp �2πj f <sup>0</sup> <sup>þ</sup> <sup>f</sup> <sup>j</sup>

multipler and adder are 6Nf NSlog2NS and 9Nf NSlog2NS, respectively.

P N<sup>τ</sup> i¼1 P Nf

�

<sup>σ</sup><sup>2</sup> <sup>¼</sup>

and Nf are the number of delay and Doppler bin.

Serial correlation in time domain is expressed as

YS τi; f <sup>j</sup> � � <sup>¼</sup> <sup>1</sup>

based on Fourier transform in each Doppler channel as

where YS τi; f <sup>j</sup>

�

3.3.1. Serial correlation

and 2NSNτNf , respectively.

3.3.2. Parallel correlation in delay domain

YP :; f <sup>j</sup>

3.3.3. Parallel correlation in Doppler domain

the modulation of the code at each delay channel as

� � � �

� � � <sup>2</sup> � � and YP <sup>τ</sup>i; <sup>f</sup> <sup>j</sup>

$$
\Delta f = \frac{\mathbf{v}\_r \cdot \mathbf{u}\_{r\text{s}} - \mathbf{v}\_t \cdot \mathbf{u}\_{\text{ts}} - (\mathbf{v}\_t \cdot - \mathbf{v}\_r) \cdot \mathbf{u}\_{tr}}{\lambda} \tag{18}
$$

where T and v<sup>t</sup> are the positioning and velocity of GNSS satellite; R and v<sup>r</sup> are the positioning and velocity of LEO satellite; S is the positioning of the specular point; urs and uts are the unit vectors from LEO and GNSS satellite to the specular point; utr is the unit vector from the LEO to GNSS satellite; c is the speed of light; and λ is the wavelength of GNSS signal. To make the DDM in the window of delay and Doppler frequency, it is necessary to provide high-accuracy positioning and velocity of GNSS, LEO satellite and specular point to meet the estimated accuracy of expression (17) and (18). The processor unit performs the auto/cross-correlation operation, in which the autocorrelation mode correlates the reflected signal with locally generated replicas at the different delay and Doppler frequency, and the cross-correlation mode correlates the reflected signal with the direct signal after proper delay and Doppler adjustment. Compared to the auto-correlation mode, the cross-correlation mode overcomes the bandwidth limitation to improve the range resolution and decreases the computational complexity. However, the main shortcoming of the cross-correlation is that the large-size and narrowbeam antennas are required for both direct and reflected signal to separate signal from different satellites. To overcome the bandwidth limitation and decrease the antenna size, a new approach is to use semicodeless technique to locally reconstruct encrypted P(Y) code and then cross-correlate them with reflected signal. The computer on-board performs the control and management of satellite mission to receive and route ground commands for the configuration of the DDM parameters and the operation modes, assemble and packet useful data for downloading to the ground. External components include power supply unit, frequency synthesis unit and space link to provide the required power supplies, working clocks for the units of the whole system, and the spatial interface linking the satellite and ground station.

#### 3.3. Processing method

At present, the processing methods of reflected GNSS signal have serial and parallel correlation. The serial correlation correlates the reflected GNSS signal with the locally generated replicas at the different delay and Doppler frequency one by one in time domain. The parallel correlation first transforms the reflected and local signal to the frequency domain using fast Fourier transform (FFT) and performs a multiplication operation, then transforms multiple results to time domain using Inverse FFT (IFFT). The serial processing is lossless and can be considered as the reference for the assessments of parallel method. The assessment metric is defined as normalized mean squared error (MSE) between serial and parallel correlation as

$$\sigma^2 = \frac{\sum\_{i=1}^{N\_\tau} \sum\_{j=1}^{N\_f} \left| \left< \left| Y\_S \left( \tau\_i, f\_j \right) \right|^2 \right> - \left< \left| Y\_P \left( \tau\_i, f\_j \right) \right|^2 \right> \right|^2}{\sum\_{i=1}^{N\_\tau} \sum\_{j=1}^{N\_f} \left| \left< \left| Y\_S \left( \tau\_i, f\_j \right) \right|^2 \right> \right|^2} \tag{19}$$

where YS τi; f <sup>j</sup> � � � � � � � � <sup>2</sup> � � and YP <sup>τ</sup>i; <sup>f</sup> <sup>j</sup> � � � � � � � � <sup>2</sup> � � are the mean correlation power computed by serial and parallel method when the delay and Doppler frequency of local replica are τ<sup>i</sup> and f <sup>j</sup> ; N<sup>τ</sup> and Nf are the number of delay and Doppler bin.

#### 3.3.1. Serial correlation

and tracking of direct signal, estimates the difference of delay and Doppler frequency between direct and reflected signal, and configures the DDM parameters, such as delay and Doppler frequency window range and resolution and others. The estimations of the differences of delay and Doppler frequency between direct and reflected signal are

<sup>Δ</sup><sup>τ</sup> <sup>¼</sup> j j <sup>T</sup> � <sup>S</sup> <sup>þ</sup> j j <sup>R</sup> � <sup>S</sup> � j j <sup>T</sup> � <sup>R</sup>

<sup>Δ</sup><sup>f</sup> <sup>¼</sup> <sup>v</sup>r∙urs � <sup>v</sup>t∙uts � <sup>v</sup><sup>t</sup> ð Þ <sup>∙</sup> � <sup>v</sup><sup>r</sup> <sup>∙</sup>utr

where T and v<sup>t</sup> are the positioning and velocity of GNSS satellite; R and v<sup>r</sup> are the positioning and velocity of LEO satellite; S is the positioning of the specular point; urs and uts are the unit vectors from LEO and GNSS satellite to the specular point; utr is the unit vector from the LEO to GNSS satellite; c is the speed of light; and λ is the wavelength of GNSS signal. To make the DDM in the window of delay and Doppler frequency, it is necessary to provide high-accuracy positioning and velocity of GNSS, LEO satellite and specular point to meet the estimated accuracy of expression (17) and (18). The processor unit performs the auto/cross-correlation operation, in which the autocorrelation mode correlates the reflected signal with locally generated replicas at the different delay and Doppler frequency, and the cross-correlation mode correlates the reflected signal with the direct signal after proper delay and Doppler adjustment. Compared to the auto-correlation mode, the cross-correlation mode overcomes the bandwidth limitation to improve the range resolution and decreases the computational complexity. However, the main shortcoming of the cross-correlation is that the large-size and narrowbeam antennas are required for both direct and reflected signal to separate signal from different satellites. To overcome the bandwidth limitation and decrease the antenna size, a new approach is to use semicodeless technique to locally reconstruct encrypted P(Y) code and then cross-correlate them with reflected signal. The computer on-board performs the control and management of satellite mission to receive and route ground commands for the configuration of the DDM parameters and the operation modes, assemble and packet useful data for downloading to the ground. External components include power supply unit, frequency synthesis unit and space link to provide the required power supplies, working clocks for the units of the whole system, and the

At present, the processing methods of reflected GNSS signal have serial and parallel correlation. The serial correlation correlates the reflected GNSS signal with the locally generated replicas at the different delay and Doppler frequency one by one in time domain. The parallel correlation first transforms the reflected and local signal to the frequency domain using fast Fourier transform (FFT) and performs a multiplication operation, then transforms multiple results to time domain using Inverse FFT (IFFT). The serial processing is lossless and can be considered as the

spatial interface linking the satellite and ground station.

3.3. Processing method

<sup>c</sup> (17)

<sup>λ</sup> (18)

given as

100 Multifunctional Operation and Application of GPS

Serial correlation in time domain is expressed as

$$Y\_S\left(\tau\_i, f\_j\right) = \frac{1}{Ns} \sum\_{i=1}^{N\_S} u\_r(t)p(t-\tau) \exp\left\{-2\pi j \left(f\_0 + f\_j\right)t\right\} \tag{20}$$

where NS is the sampling number in a GNSS-code period. The block diagram of the serial processing is shown in Figure 7, in which the channel is N<sup>τ</sup> � Nf . Each channel requires multiplier 3NS and adder 2NS. The total numbers of the multipler and the adder are 3NSNτNf and 2NSNτNf , respectively.

#### 3.3.2. Parallel correlation in delay domain

Parallel correlation in delay domain parallelly performs correlation operation for all code delay based on Fourier transform in each Doppler channel as

$$Y\_P(\cdot; f\_j) = \text{IFFT}\left\{\text{FFT}\left\{u\_r(t)\exp\left(-2\pi j \left(f\_0 + f\_j\right)\right)\right\} \left\{\text{FFT}\{p(t)\}\right\}^\*\right\}\tag{21}$$

where FFTf g<sup>∙</sup> and IFFTf g<sup>∙</sup> respresent the FFT and IFFT operator; and f g<sup>∙</sup> <sup>∗</sup> is the conjugate operator. Figure 8 is the block diagram of the parallel correlation in delay domain. The number of the processing channel is Nf . As it is known, FFT operation with NS sampled ponits requires multipler and adder 2NSlog2NS and 3NSlog2NS. From Figure 8, it is seen that each channel performs 2 FFT and 1 IFFT with NS sampled ponits. The total numbers of the required multipler and adder are 6Nf NSlog2NS and 9Nf NSlog2NS, respectively.

#### 3.3.3. Parallel correlation in Doppler domain

Parallel correlation in Doppler domain performs spectrum estimation for the signal removed the modulation of the code at each delay channel as

$$Y\_P(\tau\_i, \cdot) = \text{FFT}\{\mu\_r(t)p(t-\tau)\exp\{-2\pi jf\_0 t\}\}\tag{22}$$

The block diagram is illustrated as in Figure 9, in which the number of processing channel is Nτ. In each channel, correlation operation is divided into two steps: decimation and spectrum estimation. To prevent the overlapping of the spectrum, it is necessary to add an anti-aliasing filter before resampling. In engineering, one of the most efficient anti-aliasing filters is Cascaded Integrator Comb (CIC) filter which requires adder about 2NS. The spectrum of decimated signal is estimated using FFT, which needs multipler and adder

about 2Nf log2Nf and 3Nf log2Nf . The total numbers of the multipler and adder are

Parallel correlation in delay-Doppler domain [38], as given in Figure 10, is a block processing

A1 A2 ⋮ ANb 9 >>>>=

GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149 103

>>>>;

Ai <sup>¼</sup> IFFTr FFTr Ui f g ½ � ; Uiþ<sup>1</sup> <sup>∙</sup> IFFTr Pi f g ½ � ; <sup>0</sup> <sup>∗</sup> f g (24)

(23)

8 >>>><

>>>>:

where Ui and Pi are the ith blocks of the reflected signal and local replica; 0 is the zero vector; FFTrf g∙ and IFFTrf g∙ respresent FFT and IFFT operation for the row of the matrix; and FFTcf g∙ is FFT operation for the column of the matrix. Expression (23) is the parallel correlation in delay domain for the block, and expression (24) could be considered as the spectrum estimation. To simplify the analysis of the computational complexity, it is assumed that Nb ¼ Nf =2

YPð Þ¼ :; : FFTc

2NτNf log2Nf and N<sup>τ</sup> 3Nf log2Nf þ 2NS

3.3.4. Parallel correlation in delay-Doppler domain

Figure 8. Block diagram of parallel correlation in delay domain.

� �.

technique called as double-block zero-padding (DBZP) expressed as

Figure 7. Block diagram of serial correlation method.

Figure 8. Block diagram of parallel correlation in delay domain.

YP <sup>τ</sup><sup>i</sup> ð Þ¼ ; : FFT urð Þ<sup>t</sup> p tð Þ � <sup>τ</sup> exp �2πjf <sup>0</sup><sup>t</sup> (22)

The block diagram is illustrated as in Figure 9, in which the number of processing channel is Nτ. In each channel, correlation operation is divided into two steps: decimation and spectrum estimation. To prevent the overlapping of the spectrum, it is necessary to add an anti-aliasing filter before resampling. In engineering, one of the most efficient anti-aliasing filters is Cascaded Integrator Comb (CIC) filter which requires adder about 2NS. The spectrum of decimated signal is estimated using FFT, which needs multipler and adder

Figure 7. Block diagram of serial correlation method.

102 Multifunctional Operation and Application of GPS

about 2Nf log2Nf and 3Nf log2Nf . The total numbers of the multipler and adder are 2NτNf log2Nf and N<sup>τ</sup> 3Nf log2Nf þ 2NS � �.

#### 3.3.4. Parallel correlation in delay-Doppler domain

Parallel correlation in delay-Doppler domain [38], as given in Figure 10, is a block processing technique called as double-block zero-padding (DBZP) expressed as

$$Y\_P(:,:) = \text{FFT}\_{\mathfrak{c}} \left\{ \begin{array}{c} A\_1 \\ A\_2 \\ \vdots \\ A\_{N\_b} \end{array} \right\} \tag{23}$$

$$A\_i = \text{IFFT}\_{\mathbf{r}}\{\text{FFT}\_{\mathbf{r}}\{[Ll\_i, \mathbf{U}\_{i+1}]\} \cdot \{\text{IFFT}\_{\mathbf{r}}[P\_i, \mathbf{0}]\}^\*\}\tag{24}$$

where Ui and Pi are the ith blocks of the reflected signal and local replica; 0 is the zero vector; FFTrf g∙ and IFFTrf g∙ respresent FFT and IFFT operation for the row of the matrix; and FFTcf g∙ is FFT operation for the column of the matrix. Expression (23) is the parallel correlation in delay domain for the block, and expression (24) could be considered as the spectrum estimation. To simplify the analysis of the computational complexity, it is assumed that Nb ¼ Nf =2

and the element number of the block N is 2Ns=Nf

3.3.5. Comparison of computational complexity

has to be considered to choose optimal DDM parameters.

Figure 11. Simulated number of multiplier and adder required correlation processing.

3.4. Processing of UK-TDS/UK-TDS-1 data

18NbNlog22N þ 3Nf log2Nf .

(½ �<sup>∙</sup> is rounding operator). The numbers of

GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149 105

the multipler and adder for each block is 12Nlog22N and 18Nlog22N. The numbers of multiplier and adder required by the spectrum estimation are 4Nblog22Nb and 6Nblog22Nb. The total numbers of multipler and adder for DBZP are 12NbNlog22N þ 2Nf log2Nf and

Although the computational complexities of the correlation processing have been analyzed above, here, the simulated comparison is conducted. It is assumed that the range and the resolution of Doppler frequency are [�8, 8] KHz and 500 Hz, respectively, and the numbers of delay bin and the DBZP block are same. Figure 11 gives the simulated computational complexities when the numbers of the sampling are 2048, 4096, 8192, and 16,384, from which it is seen that (1) serial correlation needs most multiplier and adder and consumes most hardware resources so that it is unsuitable for spaceborne receiver; (2) parallel correlation methods significantly reduce the number of required multiplier and adder, especially parallel correlation in Doppler domain. It should be noted FFT and IFFT on hardware is a 2-based operation which needs to padding zero to make the number of operating point to be the power of 2. Large number of padding zero causes the increasing of computational complexity; therefore, it

The raw IF data from UK-DMC and UK-TechDemoSat-1 satellite are used to demonstrate the correlation approaches above. UK-DMC satellite which first carried an experimental GNSS reflectometry aimed to monitor the disaster using optical imaging. In 2003, UK-DMC satellite was launched into the sun-synchronous orbit with 680 km altitude. Some

Figure 9. Block diagram of parallel in Doppler domain.

Figure 10. Block diagram of parallel correlation in delay-Doppler domain.

and the element number of the block N is 2Ns=Nf (½ �<sup>∙</sup> is rounding operator). The numbers of the multipler and adder for each block is 12Nlog22N and 18Nlog22N. The numbers of multiplier and adder required by the spectrum estimation are 4Nblog22Nb and 6Nblog22Nb. The total numbers of multipler and adder for DBZP are 12NbNlog22N þ 2Nf log2Nf and 18NbNlog22N þ 3Nf log2Nf .

#### 3.3.5. Comparison of computational complexity

Although the computational complexities of the correlation processing have been analyzed above, here, the simulated comparison is conducted. It is assumed that the range and the resolution of Doppler frequency are [�8, 8] KHz and 500 Hz, respectively, and the numbers of delay bin and the DBZP block are same. Figure 11 gives the simulated computational complexities when the numbers of the sampling are 2048, 4096, 8192, and 16,384, from which it is seen that (1) serial correlation needs most multiplier and adder and consumes most hardware resources so that it is unsuitable for spaceborne receiver; (2) parallel correlation methods significantly reduce the number of required multiplier and adder, especially parallel correlation in Doppler domain. It should be noted FFT and IFFT on hardware is a 2-based operation which needs to padding zero to make the number of operating point to be the power of 2. Large number of padding zero causes the increasing of computational complexity; therefore, it has to be considered to choose optimal DDM parameters.

#### 3.4. Processing of UK-TDS/UK-TDS-1 data

Figure 9. Block diagram of parallel in Doppler domain.

104 Multifunctional Operation and Application of GPS

Figure 10. Block diagram of parallel correlation in delay-Doppler domain.

The raw IF data from UK-DMC and UK-TechDemoSat-1 satellite are used to demonstrate the correlation approaches above. UK-DMC satellite which first carried an experimental GNSS reflectometry aimed to monitor the disaster using optical imaging. In 2003, UK-DMC satellite was launched into the sun-synchronous orbit with 680 km altitude. Some

Figure 11. Simulated number of multiplier and adder required correlation processing.

researchers have used GNSS-R data from UK-DMC satellite to demonstrate the feasibility of remotely sensing sea wind speed, sea ice, and others. Following the end of UK-DMC's operational life in 2011, SSTL launched UK-TDS-1 satellite equipped with new generation spaceborne GNSS-R receiver SGR-ReSI in 2014. The orbit of UK-TDS-1 satellite is also sunsynchronous orbit with the altitude and the inclination of 635 km and 98.4, respectively. UK-TDS-1 satellite is controlled and operated with a 8-day duty circle shared between 8 payloads. SGR-ReSI can be operated for only 2 days in every 8-day period. Both UK-DMC and UK-TDS-1 satellite support the collection of raw IF data, however, because of the limitation of the storage capacity, only a few raw IF data are available. Here, the data collected by UK-DMC on November 11, 2004 and UK-TDS-1 on January 27, 2015 are used. The corresponding ground track of GNSS, UK-DMC, and UK-TDS-1 satellite, and the positioning of the specular pointing are shown in Figure 12, in which both specular pointings lie to the ocean surface, i.e., the signals collected by UK-DMC and UK-TDS-1 satellite are both reflected from the ocean surface. Figure 13 shows the DDM distribution of reflected GNSS signal collected by UK-DMC and UK-TDS-1 satellite, in which from left to right, the DDMs are computed using serial correlation, parallel correlation in delay domain, parallel correlation in Doppler domain, and parallel correlation in delay-Doppler domain. From Figure 13, it could be seen that (1) the DDMs from UK-DMC and UK-TDS-1 satellites both show the distribution of the horseshoe shape as simulated in Figure 4 of Section 2.3; (2) the DDMs computed by four correlation methods have similar distribution in delay-Doppler domain. The assessment metrics defined by expression (19) are computed for the DDMs in Figure 13. The results are given in Table 1, which indicate that compared to the serial correlation, parallel correlations have negligible MSEs, and in addition, one-dimensional parallel methods have lower MSEs than two-dimensional ones. The results above illustrate that parallel correlations, especially the parallel correlation in Doppler domain, are better chosen to compute the DDM than serial one for spaceborne GNSS-R receiver.

4. Retrieving of wind speed

Figure 13. DDM of (a)–(e) UK-DMC and (f)–(j) UK-TDS-1 data.

UK-DMC 0 5.81 2.62 6.94 UK-TDS-1 0 0.09 0.32 1.17

Satellite Serial Parallel (<sup>10</sup>3)

speed are discussed.

Retrieving wind speed is an inversion problem of remote sensing, of which the key is to find and extract the sensitivity parameters to wind speed from the basic observables of the remote sensing sensors. In fact, L-band signals are less optimal frequency for the measurement of wind speed compared to scatterometers, however, are not significantly attenuated by rainfall so that they are available to observe wind speed in tropical cyclones. As mentioned in Section 1, at present, three types of retrieving approaches for spaceborne GNSS-R have been proposed. Here, the approaches based on the direct mapping from DDM metrics to wind

Table 1. Comparison of normalized MSE between correlation powers obtained by serial and parallel processing.

Delay domain Doppler domain Delay-Doppler domain

GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149 107

Figure 12. Ground track of satellites and the positioning of the specular pointing when (a) UK-DMC and (b) UK-TDS-1 data were collected.

#### GNSS Application in Retrieving Sea Wind Speed http://dx.doi.org/10.5772/intechopen.74149 107

Figure 13. DDM of (a)–(e) UK-DMC and (f)–(j) UK-TDS-1 data.

researchers have used GNSS-R data from UK-DMC satellite to demonstrate the feasibility of remotely sensing sea wind speed, sea ice, and others. Following the end of UK-DMC's operational life in 2011, SSTL launched UK-TDS-1 satellite equipped with new generation spaceborne GNSS-R receiver SGR-ReSI in 2014. The orbit of UK-TDS-1 satellite is also sunsynchronous orbit with the altitude and the inclination of 635 km and 98.4, respectively. UK-TDS-1 satellite is controlled and operated with a 8-day duty circle shared between 8 payloads. SGR-ReSI can be operated for only 2 days in every 8-day period. Both UK-DMC and UK-TDS-1 satellite support the collection of raw IF data, however, because of the limitation of the storage capacity, only a few raw IF data are available. Here, the data collected by UK-DMC on November 11, 2004 and UK-TDS-1 on January 27, 2015 are used. The corresponding ground track of GNSS, UK-DMC, and UK-TDS-1 satellite, and the positioning of the specular pointing are shown in Figure 12, in which both specular pointings lie to the ocean surface, i.e., the signals collected by UK-DMC and UK-TDS-1 satellite are both reflected from the ocean surface. Figure 13 shows the DDM distribution of reflected GNSS signal collected by UK-DMC and UK-TDS-1 satellite, in which from left to right, the DDMs are computed using serial correlation, parallel correlation in delay domain, parallel correlation in Doppler domain, and parallel correlation in delay-Doppler domain. From Figure 13, it could be seen that (1) the DDMs from UK-DMC and UK-TDS-1 satellites both show the distribution of the horseshoe shape as simulated in Figure 4 of Section 2.3; (2) the DDMs computed by four correlation methods have similar distribution in delay-Doppler domain. The assessment metrics defined by expression (19) are computed for the DDMs in Figure 13. The results are given in Table 1, which indicate that compared to the serial correlation, parallel correlations have negligible MSEs, and in addition, one-dimensional parallel methods have lower MSEs than two-dimensional ones. The results above illustrate that parallel correlations, especially the parallel correlation in Doppler domain, are better chosen to compute the DDM than serial one for spaceborne

Figure 12. Ground track of satellites and the positioning of the specular pointing when (a) UK-DMC and (b) UK-TDS-1

GNSS-R receiver.

106 Multifunctional Operation and Application of GPS

data were collected.


Table 1. Comparison of normalized MSE between correlation powers obtained by serial and parallel processing.
