Relative Permittivity Measurement of Sea and Land by Ground-Based Dual Circularly Polarized GNSS-Reflectometry

The reflection characteristics of electromagnetic (EM) waves can be used to estimate certain environmental properties of the Earth surfaces. In this study, a low-cost and low-complexity dual circularly polarized reception (DCPR) system is used to measure the relative permittivity of land and seawater. This system consists of a custom, phase stable, dual circularly polarized antenna (DCPA) and off-the-shelf receivers for simultaneous reception of direct and reflected global navigation satellite system (GNSS) signals. DCPR offers two distinct improvements in comparison to the dual linear polarization reception. First, the DCPR system enables two low-correlation data streams due to the utilization of GNSS polarization and its orthogonal counterpart. Second, it enables easy observation of the surface scattering characteristics through the behavior of the reflected cross-polarized carrier-to-noise density ratio (C/N0). The right-hand (RHCP) and left-hand circularly polarized (LHCP) reflection coefficients were extracted from the received C/N0 streams using the GNSS-interference pattern technique (GNSS-IPT). The extracted signal peaks were fit with low-order curve functions for a better approximation of the Brewster angles. The measured RHCP and LHCP reflection coefficients enabled the determination of the Brewster angle position, leading to the relative permittivity estimate for the reflecting surfaces. The measured mean relative permittivity for the sea was 84.5 and for the land 13.57. The corresponding standard deviations (stds) were 10.48 and 8.05, and the standard error of mean was 0.23 and 0.17, respectively. The main factors for the uncertainties were the topography of sea and land surfaces, randomly distributed vegetation growth on land, and the receiver quantization process.


I. INTRODUCTION
T HE utilization of global navigation satellite system (GNSS) signals that are reflected or scattered by various objects or surfaces is known as GNSS-reflectometry (GNSS-R).GNSS-R has evolved over the years and is being used increasingly in several remote sensing applications, for example, monitoring of different parameters such as sea level, significant wave height [1], [2], [3], wind speed [4], [5], snow depth, ice thickness [6], [7], [8], [9], [10], storm/hurricane detection [11], soil moisture, vegetation monitoring, forests, and other geophysical properties of the Earth's surface, [12], [13], [14], [15], [16].Several GNSS-R analysis methods have been developed for different data types, including raw radio frequency (RF) data, Doppler, signal-to-noise ratio (SNR), carrier-to-noise density ratio (C/N 0 ), carrier phase, and pseudorange.The data type, size, power, and cost of the GNSS-R system may depend on the required accuracy and criticality of the particular environment parameter.
In recent years, low-cost and lightweight GNSS-R platforms have been under rapid development.Development of cheap GNSS receivers and utilization of low-level parameters such as received signal strength, SNR, or C/N 0 instead of raw RF signal, carrier phase, or delay-Doppler signals (which requires more costly receivers) have given the opportunity for research and development of new technologies in the field of geoscience and remote sensing.One of the low-cost GNSS-R systems is the dual circularly polarized reception (DCPR) system that has proven to be capable of estimating multiple environmental parameters such as ice thickness [9], [17], wind speed over the sea, and monitoring sea level, and for identification of different surfaces using reflected GNSS signals [5], [18].
The complex relative permittivity of a medium is typically the measure of several underlying properties of the medium under investigation.For example, the permittivity of soil can be used to extract the soil moisture [13], characterize the type of soil, or define the penetration depth of the RF used for sensing the soil properties.Similar deductions can be performed for other natural surfaces such as water, snow, ice, and vegetation.Several studies have shown the possibility of estimating the relative permittivity of natural Earth surfaces such as soil, ice, and snow using the GNSS-R technique [19], [20].GNSS-R polarimetric studies have been performed in [16], [20], and [21].In [20], a fully polarimetric forward model for terrestrial GNSS-R is proposed to investigate various aspects of near-surface reflections.The effects on the received interferometric GNSS signals due to surface properties, types of antennas, the role of the radiation pattern, and different orientations of the antenna are discussed for various GNSS observables such as SNR, carrier phase, and pseudorange.
In [22], a single right-hand circularly polarized (RHCP) antenna was used to study the GPS multipath signal characteristics due to reflection from different dielectric surfaces such as grass, asphalt, and lake.The best-fitting value of relative permittivity was chosen to compare the theoretical simulations with the measured results.The horizontally polarized (Hpol) and vertically polarized (V-pol) reflection coefficient magnitude and phase were estimated based on the best-fit value of the permittivity.In [23], a single RHCP antenna was used to characterize the thickness of various layered dielectric media such as polystyrene, styrofoam, and snow.Here, low antenna height was used to receive GPS multipath signal which resulted in a single dominant null in the RHCP interference pattern (IP) signal.The position and magnitude of the null were analyzed and compared with the theoretical dielectric layered model to characterize the thickness of the dielectric medium.
In [12], [14], and [24], the GNSS IP technique (GNSS-IPT) was used to estimate soil moisture content and different land geophysical parameters using a single or dual linearly polarized antenna.The authors argued that better performance for soil moisture estimation could be achieved using two linearly polarized antennas (V-pol and H-pol) instead of using only left-hand circularly polarized (LHCP) antenna.The LHCP signal alone is not able to give an estimation of the Brewster angle that could be used to retrieve the permittivity of the reflecting surface.The Brewster angle is the angle of elevation at which the reflection of V-pol signals is minimum or zero (for lossless media).In the case of circular polarization, both the RH and LH signals are required to find the Brewster angle.The advantage of observing the Brewster angle indicated by the notch in the received V-pol signal justifies the author's arguments.However, the formation of the notch in the V-pol signal does not point at one angle but spreads through a few degrees in elevation.
In this article, we propose the DCPR system capable of simultaneous reception of direct and reflected GNSS signals using one dual circularly polarized (RHCP and LHCP) antenna.The study demonstrates the potential of the DCPR system for more accurate determination of Brewster angle from the DCP reflection coefficients.The DCP reflection coefficients are extracted and studied for the first time using the GNSS-IPT, enabling the estimation of relative permittivity of the land and sea surfaces through the inversion of the measured Brewster angles.Section II discusses the fundamentals of the reflection of electromagnetic (EM) waves at the interface between two semi-infinite media.The fundamentals of GNSS-R and GNSS-IPT for the DCPR scenario are discussed in Section III.The detailed description of the dual circular polarized antenna (DCPA) and the measurement setup are presented in Section IV.Measurement observations for sea and land surface are discussed in Section V.The estimation of the reflection coefficient, Brewster angle, and the corresponding relative permittivity is shown in Section VI along with the fitting error statistics.The conclusion is presented in Section VII.

II. REFLECTION OF EM WAVES
The EM waves undergo fundamental propagation phenomena such as reflection, refraction, absorption, diffraction, and scattering upon interaction with objects or surfaces in nature.This section focuses on the reflection of EM waves from the Earth's surface and the characteristics of the reflected signal at GPS L1 C/A center frequency of 1.575 GHz.A specular reflection from a smooth surface can be described by the Fresnel reflection coefficient (FRC).For H-pol and V-pol waves traveling from medium i and incident on medium i + 1, the FRC is given by [25] h = Here, ϵ i and ϵ i+1 are the complex relative permittivity of the media i and i + 1, respectively, and θ el is the satellite elevation angle considering a horizontally flat reflecting surface.FRC for circular polarization can be derived from linear FRC as [25] where r c and lc correspond to the co-polarization (co-pol) and cross-polarization complex FRCs, respectively, with respect to the incident RHCP signal.
Many natural Earth surfaces are not smooth at GPS wavelengths, and the reflection of waves in specular directions could be affected by the roughness of the surface.Therefore, roughness has to be taken into account as defined by the Rayleigh criterion for rough surface scattering [26] Here, φ roughness is the phase change due to excess surface roughness defined by the standard deviation (std) of surface height variation h for a normally distributed surface.The condition defined by the Rayleigh criteria for a surface to be considered smooth is [26] h < λ The scattering coefficient describes the attenuation of the reflection coefficient in a specular direction due to rough surface scattering.Hence, the FRC for the rough surface can be written as [26] sca−x = ρ sca x .
Here, x stands for FRC for the chosen polarization of the EM wave.The FRC for linear and circular polarization for reflection from land (ϵ land = 11 [28]) and seawater (ϵ sea = 86 [27]), respectively, is simulated and plotted in Fig. 1(a) and 1(b) for elevation angles 2  surface roughness defined by h in Fig. 1(c) and (d).Note that the curves for surface roughness, h = 0 in Fig. 1(c) and (d), correspond to the blue (solid and dotted) curves of Fig. 1(b), respectively, [25], [26].

A. Brewster Angle
In the case of oblique incidence, the elevation angle for which the reflection coefficient of the V-pol wave becomes zero for dielectrics (or attains minimum value for lossy medium) is called the Brewster angle.Circularly polarized waves are the combination of H-pol and V-pol components of the wave as given by (3) and (4).At the Brewster angle, v undergoes 180 • phase reversal, which reverses the circular polarization handedness.The phase reversal of v at the Brewster angle reverses the direction of rotation of the electric field components for circular polarization.At the Brewster angle, sca−r c becomes equal to sca−lc , and the circularly polarized signal becomes linearly polarized.The Brewster angles are shown in Fig. 1(a) and (b), by the arrows for the linear and circular polarization cases, respectively, [25], [26].
The Brewster angle has a direct relationship to the dielectric properties of the reflecting surface.The position of the Brewster angle is used to determine the relative permittivity of the surface using the following relationship [25]: where θ b is the Brewster angle and ϵ r is the relative permittivity of the reflecting surface.Relative permittivity of the reflecting surfaces is calculated by rearranging (9) as

A. Dual Circular Polarized Reception
The GNSS satellites transmit RHCP signals at the carrier frequencies defined by their respective constellations.For the GNSS-IR scenario, the direct and reflected/scattered signals combine at the receiver to create an IP.The direct and reflected signals add up constructively and destructively at the same and opposite phases, respectively, due to the phase difference introduced by the excess path length traveled by the reflected signal.A continuously changing phase difference is introduced between the direct and reflected signals as the satellite moves in the elevation plane that creates the IP.In the case of an RHCP receiving antenna, a strong IP is observed for elevation angles less than the Brewster angles for which the reflected signal is still dominantly RHCP.For elevation angles greater than the Brewster angle, the reflected signal is predominantly LHCP, and the magnitude of the reflected RHCP signal is significantly weaker, resulting in a damped IP pattern behavior as a function of the elevation angle.The received RHCP signal in the absence of a reflected component is mostly the direct RHCP signal.
The frequency of IP is related to the geometry of the signal reception and is the function of the distance of the antenna from the reflecting surface (h), satellite elevation angle (θ el ), polarization, and carrier wavelength (λ), and EM properties of the reflecting surface.The received signal characteristics also depend on the antenna-specific radiation pattern and orientation [20].Here, we define the antenna gain pattern as F(±θ x y ), where ±θ are the positive or negative angles of the radiation pattern, and x and y parameters in the subscripts of antenna gain patterns signify the polarization states of the antenna and received signal, respectively.In the case of a horizontally tilted antenna (boresight-facing horizon), the direct signal is assumed to enter the antenna through positive angles of the radiation pattern, whereas the reflected signals enter through the negative angles.Note that the gains for a horizontally tilted hemispherical antenna pattern are approximately equal at equal positive and negative angles.Therefore, ± sign in the gain pattern will be ignored, henceforth.
The direct GNSS signal can be assumed to be purely RHCP [13]; however, the nature of reflected signals depends on the properties of the reflecting surface and angle of incidence.The reflected signals are neither purely RHCP nor LHCP but the mixture of both the polarization states [20], [29].Therefore, the reflected signals can be characterized by combining the reflection coefficients of both the polarizations in different proportions.The reflection coefficients will be treated as mixed or coupled reflection coefficients, to model signals received by the RHCP and LHCP port of the DCPA as [20], [29] Here, X r is the coupled FRC, where the dominant reflected component is RHCP, whereas LHCP is the dominant reflected polarization for X l .The second term in (11) and ( 12) accounts for the coupled cross-polarized (cross-pol) reflection coefficient entering through the cross-pol radiation pattern of the antenna.
Using coupled reflection coefficients from ( 11) and ( 12), the excess path length (epl) for a horizontal reflector, epl = 2hsinθ el [29], and the phase variation due to the excess path length difference between the direct and reflected signals, φ epl = (2π/λ)epl [30], the received signals by the RHCP and LHCP ports of the DCPA can be written as [20] R rh = P d F(θ rr ) + ρ sca X r e j(φ epl +φ arb ) 2 ( 13) Here, P d is the direct signal power, ρ sca is the scattering coefficient given in (7), φ epl represents the geometric phase lag between direct and reflected signals, and φ arb is the arbitrary phase difference introduced due to unknown factors.The modeled RHCP (13) and LHCP signals (14) are plotted in Fig. 2 along with their respective coupled power reflection coefficients and the measured co-pol antenna gains of the DCPA, for the incident signal strength (power available at the antenna), P d = 1, and antenna height, h = 1.5 m, above the smooth reflecting sea water and land surfaces ( h = 0) at GPS L1 frequency of 1.575 GHz (λ = 0.1905 m).Note that the co-pol pattern F(θ ll ) in Fig. 2(b) is scaled to half-power for clarity.
The RHCP interferometric signal is captured by the co-pol radiation pattern of the right-hand (RH) port of the antenna, whose gain is denoted by F(θ rr ).The signal received by the left-hand (LH) port of the antenna is the reflected LHCP and direct plus reflected RHCP signal.In the case of the LHCP signal, the co-pol radiation pattern (F(θ ll )) of the LH port of the antenna captures the reflected LHCP signal, whereas direct and reflected RHCP are received through the cross-pol pattern of the antenna.From ( 14) and Fig. 2(b), it should be noted that due to the presence of cross-pol direct RHCP signal for all the observation angles, a notable IP can be observed in the received LHCP time-series created by the phase lag due to the excess path length between the cross-pol RHCP and co-pol LHCP signals.
The RHCP IP frequency for sea and land is the function of the antenna height and their respective FRC.Since the simulations are performed considering only the real part of the complex relative permittivity of sea and land and the same antenna heights, the frequency and phase of the IP are the same for both the signals.Therefore, the main parameter distinguishing the two RHCP signals is their peak-to-peak magnitude.It is clearly seen that the peak-to-peak range is greater in the case of land when compared with the sea.This is due to the characteristics of their respective coupled FRC as the function of satellite elevation angle [shown in Figs. 1 and 2(a)].In the case of the simulated LHCP signal, a clear difference in magnitude is observed for the two different surfaces.Sea water being a more reflective medium shows a higher magnitude level compared with that of land.Peak maxima observed between 15 • and 20 • elevation angle for the LHCP signal is due to the shape of the co-pol antenna pattern.The oscillating behavior observed in the received LHCP signals is attributed to imperfections in the polarization states and the antenna.This allows the RHCP signal to infiltrate through the cross-pol pattern (F(θ lr )) and interfere with the reflected LHCP signal of the same polarization.The similar trend of the simulated LHCP signals and coupled FRC shows the possibility of interpreting the reflection characteristics of the surface from the observed LHCP received signal.

B. IP Technique
The studies in [12] and [14] used the IPT to identify the position of the notch created at the Brewster angle in the time-series data for the V-pol signal.Since the Brewster angle is the function of the relative permittivity of the medium, a change in the moisture content changes its permittivity, and hence, the position of the notch.The position of the notch and its deviation were used to estimate different soil moisture conditions on the land surface.In [24], IPT was used to extract the envelope of the received IP of the linearly polarized H-pol and V-pol signals using a dual linearly polarized antenna.The envelope of the IP as the function of the reflection coefficient of the reflecting surface was derived for the case of linear polarization.
In this study, the IPT is studied in the case of circularly polarized signals.The circularly polarized signal is the combination of linearly polarized vertical and horizontal components of the signal as described by ( 3) and ( 4).In the case of circular polarization, notable IP can be observed for RHCP and LHCP signals [20]; however, the IP oscillation received using LHCP antenna is modulated to the trend of the LHCP-dominated coupled reflection coefficient [refer to Fig. 2(b)].Using the IPT, the peak maxima and minima of the IP are extracted to estimate the reflection coefficients from the RHCP and LHCP signals.The maxima and minima in the IP signal occur when the phase term in ( 13) is even and odd multiple of π, respectively, as φ epl +φ X r +φ arb = 2nπ and φ epl +φ X r +φ arb = (2n + 1)π [14].Thus Here, R max and R min are the maxima and minima peaks of the RHCP IP.Similarly, the peaks of the modeled LHCP signal ( 14) are given by The peak envelopes of the IP are the function of the coupled reflection coefficient, surface roughness, and antenna radiation pattern.In the case of the LHCP signal, the peak envelopes are the function of cross-pol RHCP direct plus reflected signal and the dominant LHCP reflection coefficient.Using the peak envelopes of the IP, ( 15) and ( 16), the RHCP reflection coefficient can be calculated as [14], [26] Here, |R ipt | is the approximation of ρ sca |X r |.Whereas we equate (17) and (18) to calculate LHCP reflection coefficient as where   Next, we investigate XPI and surface roughness effects on the FRC.The absolute difference between the RHCP and LHCP FRC ( = |X r − X l |) and the IPT-derived coefficients are plotted as the function of XPI with fixed surface roughness ( h = λ/16) and h with fixed XPI = 5 in Fig. 4(a) and (b), respectively.For this simulation, XPI is considered only on the LHCP FRC due to the presence of a strong LOS cross-pol RHCP signal for all the elevation angles.Here, the Brewster angle is indicated by the elevation angle, where = 0. From the simulations, we can observe the change in the position of the Brewster angle with the change in the XPI level.Whereas no change in the Brewster angle is observed for rough surface scattering, that only takes into account the coherent reflections in the specular direction.A change in the Brewster angle was reported through measurements in [31] due to rough surface scattering, which was not predicted by the theory.The reason for the change was reported to be unresolved.
In Fig. 5, θ b is plotted as the difference in the Brewster angle value due to different proportions of XPI on the  proportion of XPI in the RHCP (XPI RH≫LH ) and LHCP signals (XPI LH≫RH ), respectively.We can observe that the effect of XPI is greater on the Brewster angle of land when compared with sea.Due to the presence of a strong direct RHCP signal for all the elevation angles, the level of XPI in the RHCP signal has less effect on the Brewster angle when compared with the XPI in the LHCP signal.In addition, note the direction of shifting of the Brewster angle, for XPI RH≫LH , the Brewster angle shifts toward higher elevation angles, whereas it is opposite in case of XPI LH≫RH and XPI RH=LH .
Note that using only the IPT-extracted peaks for calculation of FRC leads to a mismatch between extracted samples and corresponding elevation angle and could lead to a false estimation of the Brewster angle due to missing sample at the correct position.Therefore, continuous peak envelopes can be constructed by fitting the IPT-extracted peaks with suitable fitting functions.Hence, peak-to-peak synchronization in the elevation domain and smooth behavior of the reflection coefficients is performed by the following.
1) Fitting the maximum and minimum RHCP peaks with low-order exponential ( , respectively.2) Fitting low-order polynomial to maximum and minimum LHCP peaks (a 3 θ 2 el + b 3 θ el + c 3 ).The analysis presented in Section III-A and III-B shows the characteristics of the received dual circularly polarized signals and discusses the impact of XPI and surface roughness on the FRC and its retrieval using the IPT.The change in the Brewster angle position was observed due to XPI and no effect was seen due to surface roughness.This method shows good agreement with the classical FRC equations and it is used to study GNSS signal behavior for reflecting media and thus their relative dielectric permittivities.

A. Measurement System
The proposed DCPR system to perform GNSS-R analysis over sea and land consisted of a dual circularly polarized antenna (DCPA) [32], two low-cost and lightweight USB GNSS receivers [33] (each for receiving RH and LH signals, separately), a single board Raspberry Pi computer for storing GNSS data, and an LTE USB dongle for remote control and transfer of GNSS data over the 4G LTE network.The hardware was assembled inside a 10-L plastic bucket that acted as a radome providing protection from harsh environmental conditions, mostly wind, storm, rain, hail, and snow.The DCPR setup assembled inside the bucket radome and the block diagram of the setup are shown in Fig. 6

B. Dual Circularly Polarized Antenna
The performance requirements of the GNSS-R antennas include rotationally symmetrical radiation pattern, good polarization purity, and stable phase properties [34], [35].Cross-polarization discrimination (XPD) of an antenna quantifies the leakage of one polarization onto its orthogonal counterpart or signifies the depolarization of the corresponding polarization states.A good XPD of a dual-polarized antenna is important in recognizing depolarized signals.Another important, but not widely discussed parameter is the antenna phase center variation (PCV) [35].Especially, PCVs of two orthogonal polarizations have not been discussed earlier in the case of dual-antenna reflectometry [14], although being a potential source for phase errors.In addition, a large deviation of the phase centers of a dual-polarized antenna or the use of two separate antennas leads to different specular reflection points due to the change in propagation geometry.In this article, a DCPA with accurate phase center locations and stable phase patterns [32] is used to enable the simultaneous reception of two independent data streams for the extraction of surface parameters.The measured radiation patterns for the antenna with and without the bucket are shown in Fig. 7(a) and (b).The bucket was used as a low-cost and inexpensive radome solution.Based on the measurement, the bucket radome has negligible effects on the radiation pattern of the antenna.The measured co-pol maximum gain at each port of the DCPA is approx.6.6 dBi.The XPD of the antenna is indicated by the difference between the co-pol and crosspol gains at each port and is greater than 25 dB for all the satellite angles under consideration.The XPD signifies the antenna's ability to suppress the incoming orthogonal polarized signal.Therefore, the level of XPI or depolarization could be recognized with the known XPD of the antenna and the observed signal characteristics.Note that the radiation pattern is plotted with respect to the orientation of the antenna, where the boresight is directed toward the horizon.The side view (or side cut) of the pattern represents the gain in the elevation plane, while the top view (or uppercut) shows the gains in the azimuth plane.The top view of the pattern is shown considering the azimuth direction relative to the sea and land measurement sites.
The measured phase patterns for the RHCP and LHCP antenna ports are shown in Fig. 7(c) and (d) at 1575 MHz.It is observed that rotationally symmetrical antenna structure generates a very flat phase response where the maximum deviation stays below 9 • .Once known, the phase response of the antenna can be either taken into account for the GNSS-R analysis or can be ignored if the maximum phase deviation has negligible effect on the phase of the incoming signal.From the geodetic or reflectometry application point of view, an interesting figure of merit is the PCV (φ, θ) of the antenna, since it has an effect on the positioning inaccuracy [36] and it is typically taken into account in the measurement data analysis.The measured PCVs for LHCP and RHCP, as shown in Fig. 7(e), indicate small phase variations over the azimuth and elevation planes of interest.Since the maximum PCV for the elevation angles of interest between 0 • and 40 • is less than 1 mm, the antenna error on GNSS-R is minimum.

C. Test Sites
The GNSS-R setups for sea and land measurements were located in Oulu, Finland.The measurement locations and the installations are shown in Fig. 8.The coastal sea measurements were performed at the Vihreäsaari Harbor, Port of Oulu, from Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.February 2021 to June 2022.The DCPR system was horizontally mounted on a wooden pole at a height of approx.3 m from the ground and 6 m from the sea surface, facing the Baltic Sea.The antenna boresight direction (θ ant = 0 • ) was pointing approx.335 • in the azimuth direction.
The inland GNSS-R setup was installed on an agricultural field in Kiiminki, Oulu, during the spring season in May 2022.Usually, during April, the melting of snow starts in Finland and continues until the end of April and in May as well.During this period, inland areas could be flooded due to rapid melting of snow and slow discharge of water on land.A manual investigation of the land surface at the time of installation of measurement revealed wet and damp conditions due to recently melted snow.Dried vegetation was found on the top of the land surface, which was buried under the snow throughout the winter.During long days in the spring and summer seasons, the ground situation changes rapidly in Finland.Within a month of the measurement, new vegetation over the land was observed with different vegetation heights ranging from 10 to 60 cm.FFZs are plotted to illustrate the approximate area of the specular reflections toward the receiving antenna that account for most of the total received power [26].The FFZ is the function of the satellite elevation angle, the vertical height of the GNSS antenna above the reflecting surface, and the carrier wavelength.The FFZ for both the coastal and inland setup for antenna heights 6 and 2.5 m, elevation angle range of (2 • -17 • ) and ( 5• -40 • ), respectively, and azimuth mask of ±30 • from antenna boresight direction is shown in Fig. 8 [37].

D. Data Processing
Satellites were chosen according to their best position in azimuth and elevation planes relative to the position of the measurement system.An azimuth mask was defined for both the locations, according to their respective antenna boresight direction.The azimuth mask of 335 • ± 30 • was set for sea surface analysis and 225 • ±30 • for land analysis.The receivers generated GNSS parameters at a resolution of 1 dB•Hz for C/N 0 and 1 • for satellite elevation and azimuth angles.The elevation and azimuth angles were converted into linearly increasing/decreasing quantities, taking into account the angular velocities of satellites in elevation and azimuth planes.The angular velocities of satellites are the rate of change in satellites' position in the elevation and azimuth planes per second as Here, v i and v j are the angular velocities of satellites in the elevation and azimuth planes, respectively.θ i el and φ i az are the elevation angle and azimuth angles, respectively, given by the receiver.The sign of angular velocities, v i and v j , signifies the trajectory of the satellites, i.e., whether the satellite is rising or setting, relative to the local horizon.If the angular velocity is positive, the satellite is rising in the respective plane and vice versa.MATLAB is used for the signal processing and analysis, throughout this study.

E. Coordinate System Transformation and Detrending
The radiation pattern of the antenna was measured for the zenith-facing antenna boresight direction.Since the effect of the antenna co-pol radiation pattern was removed from the GNSS-R measurements, the horizontally mounted antenna (boresight direction toward the local horizon) required coordinate transformation to access the correct gain of the antenna.The zenith oriented patterns θ ant and φ ant were transformed to respective horizontal tilted coordinate system θ el and φ az by the relationships [38] θ ant = θ el , and tan φ ant = tan θ el / sin θ az . ( Using ( 22), the radiation pattern was extracted for the satellite trajectory that contributes to the trend of the incident signal.
The following equation was used to perform the detrending of the signal: Here, δ R rh is the detrended RHCP signal, and τ R rh is the mean of the RHCP received signal after removing the trend of the radiation pattern gain, F(θ rr ).The LH signal is normalized using the relationship where δ R lh is the normalized LH signal, and R lh and F(θ ll ) are the LH received signal and LHCP is the radiation pattern gain.Note that the calculations in ( 23) and ( 24) are in dB scale.

V. MEASUREMENT OBSERVATIONS AND ANALYSIS
The measured RHCP and LHCP signals in Fig. 9 are chosen to illustrate the characteristics of measured data from the DCPR system for open sea and land.The RHCP and LHCP signals are plotted for approx. 2 • -15 • elevation angle for sea and approx.8 • -40 • for land, in Fig. 9(a) and (b), respectively.For land observations, elevation angles < 8 • showed large fluctuations in the measured data that could be the result of the scattering area extending beyond the FFZ with variations in surface topography and trees from the surrounding area.The rapid fluctuations in the received signals at higher elevation angles can be attributed to the inhomogeneity of the surface and probable contributions from the higher order Fresnel zones [39], [40].
The measured RHCP signals are detrended using the co-pol radiation pattern of the antenna and converted to linear scale.
A 30-sample moving average window is applied to the RHCP signal to remove the 1-dB•Hz step of the original recorded C/N 0 data.The LHCP measured signals were normalized using (24).The LHCP signals were observed to be more sensitive to noise and multipath, as can be seen in Fig. 9. Therefore, a low-pass filter was used to filter out the high-frequency noise from the LHCP signal.With the XPD ≤ 25 dB, the effect of the cross-pol RHCP component on the trend of the LHCP signal was considered negligible.However, the cross-pol RHCP can be observed modulated to the trend of the LHCP signal.The peak maxima and minima and the fit curves show the envelope of the RHCP and LHCP signals in Fig. 9.

A. Observations: Open Sea
The measured RHCP signals show good and consistent quality of the IP for the observed satellite elevation angles.However, in Fig. 9(a), the measured signal peaks are not as smooth as shown by the simulated signal in Section III-B.The observed difference is due to the assumed theoretical model that only accounts for the coherent reflections coming from the FFZ.In practice, coherent and incoherent contributions from larger areas than the FFZ or higher order Fresnel zones can also cause fluctuations in the received signal, especially at higher elevation angles [39], [40], [41].Furthermore, continuous movement of the sea surface, sea surface roughness, and GNSS receivers' internal processes, such as quantization effect and noise, affects the envelope of the signal which could result in the fluctuation of the peaks from their true magnitude.As observed, the RHCP envelopes of the GPS 22 signal show more consistent behavior with the simulated curves that assume reflection from a smooth surface when compared with the peak envelopes of GPS 29 which shows a flat envelope curve.
As in simulations (Section III-B), it is observed that the measured LHCP signals are modulated with the cross-pol RHCP IP.However, the LHCP signal quality varies for different satellites.The interference fringes are more clearly observed in the case of GPS 22 when compared with GPS 29, which could be the effect of the sea state at the time of measurement.Observations suggest the XPI in the measured data is greater than expected considering the laboratory-measured XPD of the antenna.This could be due to the unaccounted depolarization of the GNSS signals propagating through different layers of the atmosphere and scattering from the surface.The noise in some measured LHCP data restricted the formation of observable interference fringes, making it significantly challenging to locate the LHCP IP peaks.As seen in the figure, the LHCP IP peak maxima and minima are very close to each other, leading to errors in the recognition of correct peak locations.For elevation angles close to 15 • for GPS 22, the peak maxima and minima are inseparable, which leads the fit envelopes to converge.The characteristics of the LHCP received signal suggested that the signal follows the trend of the LHCP reflection coefficient, and therefore, the measured and fit peak envelopes will be used to estimate the reflection coefficient using the IPT.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

B. Observations: Land
The measured RHCP and LHCP signals for land surface are shown in Fig. 9(b).The permittivity of the land surface depends on the type of soil, soil moisture, and type, and height and density of vegetation on top of the soil surface [27], [28].The specular reflection of the EM wave can change due to the varying topology of the land surface.However, this does not affect the dielectric properties of the reflecting surface.Typically, the permittivity of different soil surfaces' L-band frequencies ranges from 3 to 30, depending on the soil moisture [28].The characteristics of DCPR signals are similar for sea surface and open land surface as seen in Fig. 9(a) and (b), respectively.However, clear observations can be made by comparing the quality of the data between land and sea.Weaker reflectivity characteristics of the land surface and the presence of vegetation degrade the RHCP IP and the quality of LHCP signals significantly.Despite the decrease in the quality of the signals, the interference fringes for RHCP signals can be clearly identified in Fig. 9(b).Some important characteristics were observed for the measured signal for the land site.The quality of IP improved only after satellite elevation greater than approx.8 • .This could be due to the larger area covered by the footprint (Fresnel ellipse) for lower elevation angles, the topology of the land, and the uneven distribution of different types of vegetation.According to the Rayleigh rough surface scattering criterion, the smoothness of the surface is determined by the std of the surface roughness height compared with the carrier wavelength [26].Rough surface scattering leads to attenuation of the reflected signal in the specular direction.It is also observed that the peak-to-peak difference of some RHCP interference fringes is smaller which could be due to the loss of coherency between direct and specular reflected signals due to rough surface scattering [2].
The measured RHCP and LHCP data for GPS 6 and the corresponding envelopes do not resemble the trend of the simulated curves.Here, LHCP data at ≈ 30 • show a strong amplification in the signal.An increase in peak-to-peak magnitude is witnessed, at the same location in the RHCP signal.The measured data for GPS 6 coincide with the period when the presence of the vegetation in the measurement site was significant, which suggests constructive interference between multilayer reflected signals [12], [17], [24], [42].The study presented in [12] analyzed V-pol IP with multiple notches that were created due to multilayer reflections from vegetation and soil layers.The number of notches was found to be directly proportional to the vegetation heights above the soil, where the presence of the vegetation layer also affected the location of the Brewster angle.Analysis of multilayer propagation is out of the scope of this study and will not be discussed further.Here, the soil and vegetation are considered as a single semi-infinite medium and are referred to together as land.In the figure, GPS 11 shows the data after the vegetation had been mowed from the measurement site and significantly better quality for both RHCP and LHCP is observed when compared with GPS 6.Note that the peak samples that appear above signal strength 0.6 (for peak maxima) and 0.4 (for peak minima) are excluded from the fitting process.

VI. RESULTS AND ANALYSIS: REFLECTION COEFFICIENT, BREWSTER ANGLE, RELATIVE PERMITTIVITY
The peaks and their respective fit curves in Fig. 9 are used to extract reflection coefficients from the measured RHCP and LHCP signals using IPT.The measured signal peaks are interpolated to synchronize with the samples at the same elevation angles and to get a better approximation of the Brewster angle.The maximum and minimum peak values were extracted from the LHCP signal relative to the positions of the RHCP peak samples in the elevation domain, which were used to estimate the LHCP reflection coefficients using (20).Similarly, the reflection coefficients were estimated from the fit envelopes using the IPT.The measured and fit absolute differences between RHCP and LHCP reflection coefficients for the entire duration of measurements are shown in Fig. 10 The 2-D histogram in Fig. 10 shows the distribution of meas and fit with the elevation angle.Here, the Brewster angle is observed where the sample concentration is the highest in the elevation angle.From the figure, a clear distinction can be made between the reflection characteristics of the two different surfaces (sea and land).The distribution of the Brewster angle for sea shows much less deviation in comparison to land.In the case of land, many variables on the surface such as vegetation, topography, and surrounding trees significantly degrade the signal reflection in specular direction and impact the reflection coefficient behavior.
The fit shows good agreement of the measured data and gives a better approximation of the Brewster angle and reflection characteristics for sea and land.The Brewster angle is inverted to the respective permittivity using (10).The theoretical curves are also plotted in Fig. 10(b) and (d) using the mean value Brewster angle.The measured samples and the curve fit underestimate the magnitude of the reflection coefficient at lower elevation angles when compared with the theoretical curve (XPI = 0).This could be due to two reasons, first, the GNSS receiver limits the maximum allowable signal strength (C/N 0 ) to be recorded.According to the specifications of the used GNSS receivers [33], the maximum signal strength that can be recorded was 56 dB•Hz which could limit the peak-to-peak magnitude of RHCP IP at lower elevation angles where the antenna gain is maximum.This could lead to an underestimation of the reflection coefficient at lower elevation angles.The second is the unknown level of XPI, as shown by the theoretical curve with XPI = 10, which matches the behavior of the fit curve at the lower elevation angles.For land, Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE I STATISTICAL DISTRIBUTION OF THE RETRIEVED BREWSTER ANGLES AND THE CORRESPONDING RELATIVE PERMITTIVITY
Fig. 11.Process of permittivity estimation using the DCPR system. the measured and fit curves overestimate the theoretical fit curve, as can be seen in Fig. 10(d).As mentioned previously, the quality of the received signals improved for elevation angles exceeding 8 • , which could be due to scattering and diffraction effects at elevation angles less than 8 • .In the case of diffraction, it can result in an approximate increase of 6 dB in signal strength when the specular point aligns with the receiver's line-of-sight from the shadow region, according to the theory of knife-edge diffraction [43].The fit curves also clearly show the effect of surface roughness.The theoretical curves plotted with h = λ/6 and h = λ/4 agree well with the surface roughness behavior observed in the fit distribution.The steps involved in the estimation of permittivity of the reflecting surface using the DCPR system are shown in the flowchart in Fig. 11.
The relative permittivity of most of the natural Earth surfaces ranges from 1.5 to 30, and that of water bodies ranges from 66 to 110 [28], [44], [45], [46].The Brewster angle and the corresponding relative permittivity values from all the suitable satellites for sea and land measurements are estimated using the GNSS-R IPT analysis.The measured data were analyzed for the period from June to October 2021 for the sea and from May to August 2022 for the land.Due to unavailability of the ground-truth measurement data, the relative permittivity values presented in [46] are used as a valid range of retrieved value of permittivity between 66 and 110 for sea water and 3-30 for land with vegetation based on the EM properties of various types of soil and vegetation [27], [44].Five days moving average and daily cumulative average of the Brewster angles and the corresponding relative permittivity values for sea and land are shown in Fig. 12.The mean value of retrieved seawater permittivity was 84.5, corresponding to the mean Brewster angle of 6.24 • .Similarly, the mean permittivity of the land surface was approx.13.57, corresponding to the mean Brewster angle of 17.18 • .The estimated values show good agreement with the permittivity values found in the literature for both land and sea [27], [28], [44], [45], [46].The statistical distribution [mean, std, and standard error of the mean (SEM)] of retrieved parameters for sea and land surfaces for the measured and fit data is presented in Table I.The estimated values presented here cannot be verified with the actual ground-truth situation but they represent the opportunity and feasibility to characterize properties of various Earth surfaces using the DCP GNSS-R.

A. Fitting Statistics
Errors can be contributions from individual factors or accumulation from a long chain of data flow through measurement instruments or algorithms.This study is based on commercial off-the-shelf (COTS) devices to record and process data.Hence, GNSS instrumentation errors cannot be taken into account due to limited information provided by the manufacturers on the performance of the devices.In addition, due to the unavailability of ground-truth data, the estimated values could not be verified against the exact ground conditions.Here, we present the statistics of the goodness-of-fit (GOF) parameter R 2 (coefficient of determination), to get the measure of reliability of the fitting functions used to fit the IPT peak envelopes of the RHCP and LHCP signals.
R 2 distribution for fitting the RHCP and LHCP signal peaks for sea and land is shown in Fig. 13(a) and (b), respectively.R 2 values for RHCP show similar behavior for sea and land in Fig. 13 (top panels), with the minima peaks showing more stable behavior when compared with the peak maxima.Therefore, R 2 values for peak minima are more concentrated closer toward one which suggests the function fit well with the peak minima samples.Whereas peak maxima show more variation as also observed in the measured data, and therefore, R 2 is uniformly distributed with more concentration toward zero.The LHCP signal peaks for sea show significantly better  fit when compared with the case of land.The degraded signal quality for land measurements resulting in poor fitting statistics was due to restricted propagation environment, vegetation, and topography affecting bistatic reflection geometry.

VII. CONCLUSION
This study presents a low-cost and low-complexity DCPR system for measuring the relative permittivity of land and sea using the GNSS-IPT.The DCPR system enables the simultaneous reception of GNSS direct and reflected signals through the RHCP and LHCP ports of the DCPA.The use of a horizontally tilted DCPA enhances the quality of the received signals allowing the RHCP and LHCP signals to be captured with similar antenna gains.The antenna effects were considered negligible due to accurate PCV and stable phase response.Further investigation is necessary to determine the level of depolarization or XPI due to scattering of GNSS signals from Earth surfaces, as the observed level of XPI exceeded the laboratory-measured XPD of the antenna.The reflection coefficients are extracted from the measured RHCP and LHCP signals using the GNSS-IPT.The position of the Brewster angle is determined by finding the minimum absolute difference between RHCP and LHCP coefficients, which is then inverted to obtain the corresponding relative permittivity.The effects of dynamic sea, land topography, vegetation on top of the land and receiver internal processes demonstrate clear effects on the received C/N0 and the measured reflection coefficients, potentially affecting the position of the Brewster angle.Low-order curve functions were fit to the IPT-extracted signal peaks to improve the accuracy and smoothness of the reflection coefficients.The measured and estimated values of relative permittivity show a clear distinction between sea and land and agree well with known reported values.The combined use of both circularly polarized signals gave better and clearer information about the reflectivity and the roughness of the surface.Overall, the observations highlight the effectiveness of the DCPR system as a technology for permittivity measurements of different Earth surfaces.
possible to install the GNSS-R test station at the harbor area.They also like to thank the University of Oulu Innovation Centre for providing the Proof-of-Concept funding, which helped in setting up our inland GNSS-R test station.

Fig. 2 .
Fig. 2. Simulated (a) RHCP and (b) LHCP signals using incident signal strength, Pd = 1, considering the gain of the horizontally oriented DCP receiving antenna at a height of 1.5 m above sea water and land at GPS L1 frequency of 1.575 GHz.
ipt | is the approximation of ρ sca |X l |.The RHCP and LHCP signals and their corresponding coupled power FRC are plotted in Fig.3(a) and (b), respectively, along with the signal peaks extracted using (15)-(18).The maximum and minimum peaks in the figure represent the upper and lower envelopes of the IP.The RHCP and LHCP signals are simulated for different levels of cross-pol interference (XPI), with incident power P d = 1 and considering a smooth sea surface ( h = 0).Here, XPI is the additional interference caused by the cross-pol signal entering through the cross-pol pattern of the DCPA.XPI level can vary due to several factors such as depolarization of the signal or due to a strong incoming orthogonally polarized signal.Here, the values of XPI signify the multiplication factor applied to the cross-pol antenna pattern to indicate the level of interference.Increasing the amount of XPI resulted in an increase in signal level and an increase in the FRC magnitude.The most notable effect is observed for the LHCP signal, where the interference is caused by the direct plus reflected RHCP signals.The magnitude of the peak-to-peak envelope of the LHCP received signal is dictated by the proportion of the XPI by the direct and scattered RHCP signal.

Fig. 3 .
Fig. 3. IP magnitudes with the upper and lower envelopes (left column) and comparison between FRC and IPT-derived reflection coefficients (right column) for (a) RHCP and (b) LHCP.

Fig. 4 .
Fig. 4. Absolute difference between RHCP and LHCP coupled reflection coefficients of the sea (solid lines) and land (dashed lines) as a function of XPI (a) and as a function of std of surface roughness height h (b).The IPT retrieved samples of are shown by "square" and "diamond" markers for sea and land, respectively.
(a) and (b), respectively.The design and properties of DCPA enable the separation of two orthogonal circularly polarized (direct and scattered RHCP and scattered LHCP) signals with high cross-pol discrimination and will be discussed further in detail.The two u-blox M8T GNSS receivers continuously recorded GNSS data in National Marine Electronics Association (NMEA) format at the rate of one sample per second.C/N 0 , elevation and azimuth angles, UTC, and GPS time are the GNSS parameters used in the analysis.The RHCP and LHCP data are time-synchronized according to the GPS time provided by the receivers.The computing steps are performed in a postprocessing computer using MATLAB software.

Fig. 7 .
Fig. 7. Measured radiation patterns (in dBi) of a horizontally tilted DCPA with and without bucket radome (a) side view of RHCP and LHCP radiation patterns and (b) top view showing the azimuth plane and boresight direction at sea and land measurement locations for DCPA antenna with the bucket radome.Measured antenna phase patterns for (c) RHCP port and (d) LHCP port.(e) PCV as a function of azimuth (φ) and elevation (θ ) angles (in degrees) at 1575 MHz.

Fig. 9 .
Fig. 9. Examples of measured RHCP and LHCP signals using the DCPR system for (a) seawater and (b) land surface.The signal peaks and their respective fit curves are also shown in the figure.
(a) and (b) for sea and Fig. 10(c) and (d) for land, respectively.Here, the Brewster angle is indicated by the elevation angle where their absolute difference becomes zero, i.e., when | r c − lc | ≈ 0 θ b = min| |.

Fig. 12 .
Fig. 12.Estimated Brewster angle and relative permittivity of sea and land as (a) 5 days moving average and (b) daily cumulative average.